http://soft-matter.seas.harvard.edu/api.php?action=feedcontributions&user=Xingyu&feedformat=atomSoft-Matter - User contributions [en]2022-12-01T21:04:14ZUser contributionsMediaWiki 1.24.2http://soft-matter.seas.harvard.edu/index.php?title=Modeling_Surfactant_Adsorption_on_Hydrophobic_Surfaces&diff=26323Modeling Surfactant Adsorption on Hydrophobic Surfaces2012-11-27T22:14:26Z<p>Xingyu: </p>
<hr />
<div>== General Information ==<br />
'''Authors:''' S. O. Nielsen, G. Srinivas, C. F. Lopez, and M. L. Klein<br />
<br />
'''Publication:''' Physical Review Letters<br />
<br />
'''Keywords:''' [[Surfactant]], [[micelle]], [[adsorption]]<br />
<br />
== Summary ==<br />
As the authors mentioned, the self-assembly behavior of surfactants is useful in many contexts, including manipulating single wall carbon nanotubes or solubilization of hydrophobic quantum dots.<br />
However, such processes are not well understood because their dimensional and temporal scales are ill-suited for experiments or atomistic simulations.<br />
This study presents a coarse grain method used to simulate surfactant (aqueous n-alkyl poly(ethylene oxide)) adsorption on an hydrophobic surface (graphite).<br />
This is done by modeling the surface with an implicit potential, coarse graining for interactions using respective center of masses, then returning to the explicit model for the surface.<br />
The simulation results agree with experimental measurements using atomic force microscopy and demonstrate interesting behavior for adsorption.<br />
<br />
==Theory==<br />
[[Image:msa1.jpeg|thumb|300px|right| Fig. 1: a) the probability distribution for the c.m. of two bonded particles interacting with the surface, b) the probability distribution for z = 3.38Å, denoted by the filled circle in a), c) the potential energy for one particle, c.m. of 2 unbonded and bonded particles, d) the potential for -O-<math>CH_2</math>- in poly(ethylene oxide) due to a graphite surface From [1].]]<br />
For the implicit model, the authors used a semi-infinite geometry with the surface as a continuum for z ≤ 0 and atoms in the liquid phase in z > 0.<br />
They then used a Lennard-Jones potential, U(z), for the potential energy of the atom at a height z.<br />
For the coarse graining, groups of atoms are reparameterized by their center of masses (c.m.) for the interactions with the solid surface.<br />
Probability distributions are used for the interactions rather than potential energies since they are more tractable for larger numbers of particles.<br />
For example, the joint probability that particle 1 is at a height <math>z_1</math> and particle 2 at height <math>z_2 </math> is given by:<br />
<br />
<math>P(z_1,z_2) = e^{-\beta U(z_1)} e^{-\beta U(z_2)}</math><br />
<br />
where <math>\beta</math> denotes the inverse of Boltzmann's constant times the temperature. <br />
So, the probability that the c.m. for a pair of non-interacting particles is at height z is given by the marginal distribution:<br />
<br />
<math>P(z)=(2z)^{-1} \int_{0}^{2z} e^{-\beta U(z_1)} e^{-\beta U(2z-z_1)} dz_1 </math><br />
<br />
and similarly, for particles with some interaction <math>P_I(z_1,z_2)</math> independent of the surface, the probability that the center of mass is at height z is then<br />
<br />
<math>P(z)=\frac{\int_{0}^{2z} e^{-\beta U(z_1)}e^{-\beta U(2z-z_1)}P_I(2z_1-2z) dz_1 }{\int_0^{2z}P_I(2z_1-2z) dz_1} </math><br />
<br />
which are appropriately normalized and have features shown in Fig. 1.<br />
<br />
==Simulation==<br />
Applying these probability distributions for large numbers of particles is more tricky.<br />
One issue is that pair interactions are often non-radial (e.g. conformational details for poly(ethylene oxide) mentioned in the paper).<br />
Another challenge is the large number of particles that must be incorporated in the simulation.<br />
To alleviate this, common coarse graining methods combine several (>2) heavy atoms and H atoms associated with them to a single position.<br />
The authors explained that a judicious choice for the implementation of coarse grain is required with a -O-<math>CH_2</math>- piece of poly(ethylene oxide).<br />
One method is to coarse grain <math>CH_2</math> then combine it with O.<br />
Another method is to coarse grain CHO, then combine it with H.<br />
The third method is to coarse grain HH and CO separately, then combine the pairs.<br />
Only first and third are reasonable since the first combines heavy atoms (and their associated H atoms in groups) and the third retains symmetry by first coarse graining light and heavy atoms together then combining them.<br />
The discrepancy for the second method is shown in Fig. 1d where the potential energy is different than those from the other methods.<br />
These principles are applied for a coarse grain simulation of aqueous n-alkyl poly(ethylene oxide), specifically C12E5, adsorbing on a graphite surface.<br />
The nonionic surfactant CnEm were coarse grained with 3 <math>CH_2</math> groups at each hydrophobic site and one ethylene monomer at each hydrophilic site in order to observe the overall shape of the surfactant.<br />
Specific parameters used to model details of the interactions were previously measured experimentally with bulk density, surface tension, and interfacial surface tension.<br />
The diffusion coefficients were reported to have been calculated from mean square displacement curves for binary mixtures of C12E5 at different concentrations and water and confirmed by experiment.<br />
<br />
==Results and discussion==<br />
[[Image:msa2.jpeg|thumb|300px|right| Fig. 2: Simulation results for C12E5 adsorption onto a graphite surface at t = 0, 0.64, 3.3, 3.75, 4.3, and 6 ns (a-f) with solid-liquid interfaces at the top and bottom separated by 12 nm and 3D periodic boundary conditions. From [1].]]<br />
As the authors mentioned, the self-assembly of nonionic surfactants at graphite-liquid interfaces have been characterized using methods such as atomic force microscopy.<br />
C12E5 was found to form cylindrical micelles in solution and hemicylinders at the graphite-liquid interface.<br />
The results from the simulation (Fig. 2) what that initially, the surfactants coat the graphite surface or begin to self-assemble into spherical micelles (but never fuse completely since they are saturated) far away from the surface (Fig. 2b).<br />
However, when a micelle approaches the partly coated surface, the head groups in the micelle interact with those adsorbed to the surface.<br />
The authors describe what occurs next as "feeding," where two sets of head groups open so that the hydrophobic tails of the micelles touch those of the monolayer on the graphite surface (Fig. 2c,d)<br />
The tails then quickly disperse onto the surface and the head groups rearrange so that the entire micelle is adsorbed onto the surface (Fig. 2e).<br />
Reorganization then occurs and hemicylinders of surfactants form on the graphite surface with spacing ~5 nm which agrees with experimental data (Fig. 2f).<br />
Simulations with C9E3 gave similar feeding phenomena but the final state is that of a monolayer with the surfactants perpendicular to the surface, as predicted by the geometry of C9E3 and agrees with experiment.<br />
An explicit representation of the surface was also recovered so that more general and detailed surface geometries can be modeled.<br />
As explained in [1], this method is computationally more efficient and holds promise for nanoscale studies of hydrophobic surfaces interacting with aqueous surfactant solutions, including examining how different surfactants solubilize carbon nanotubes and or how to deposit quantum dots on a substrate.<br />
<br />
==References==<br />
[1] Nielsen, S. O., Srinivas, G., Lopez, C. F., & Klein, M. L. (2005). Modeling surfactant adsorption on hydrophobic surfaces. Physical review letters, 94(22), 228301.<br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Modeling_Surfactant_Adsorption_on_Hydrophobic_Surfaces&diff=26322Modeling Surfactant Adsorption on Hydrophobic Surfaces2012-11-27T22:13:46Z<p>Xingyu: </p>
<hr />
<div>== General Information ==<br />
'''Authors:''' S. O. Nielsen, G. Srinivas, C. F. Lopez, and M. L. Klein<br />
<br />
'''Publication:''' Physical Review Letters<br />
<br />
'''Keywords:''' [[Surfactant]], [[micelle]], [[adsorption]]<br />
<br />
== Summary ==<br />
As the authors mentioned, the self-assembly behavior of surfactants is useful in many contexts, including manipulating single wall carbon nanotubes or solubilization of hydrophobic quantum dots.<br />
However, such processes are not well understood because their dimensional and temporal scales are ill-suited for experiments or atomistic simulations.<br />
This study presents a coarse grain method used to simulate surfactant (aqueous n-alkyl poly(ethylene oxide)) adsorption on an hydrophobic surface (graphite).<br />
This is done by modeling the surface with an implicit potential, coarse graining for interactions using respective center of masses, then returning to the explicit model for the surface.<br />
The simulation results agree with experimental measurements using atomic force microscopy and demonstrate interesting behavior for adsorption.<br />
<br />
==Theory==<br />
[[Image:msa1.jpeg|thumb|300px|left| Fig. 1: a) the probability distribution for the c.m. of two bonded particles interacting with the surface, b) the probability distribution for z = 3.38Å, denoted by the filled circle in a), c) the potential energy for one particle, c.m. of 2 unbonded and bonded particles, d) the potential for -O-<math>CH_2</math>- in poly(ethylene oxide) due to a graphite surface From [1].]]<br />
For the implicit model, the authors used a semi-infinite geometry with the surface as a continuum for z ≤ 0 and atoms in the liquid phase in z > 0.<br />
They then used a Lennard-Jones potential, U(z), for the potential energy of the atom at a height z.<br />
For the coarse graining, groups of atoms are reparameterized by their center of masses (c.m.) for the interactions with the solid surface.<br />
Probability distributions are used for the interactions rather than potential energies since they are more tractable for larger numbers of particles.<br />
For example, the joint probability that particle 1 is at a height <math>z_1</math> and particle 2 at height <math>z_2 </math> is given by:<br />
<br />
<math>P(z_1,z_2) = e^{-\beta U(z_1)} e^{-\beta U(z_2)}</math><br />
<br />
where <math>\beta</math> denotes the inverse of Boltzmann's constant times the temperature. <br />
So, the probability that the c.m. for a pair of non-interacting particles is at height z is given by the marginal distribution:<br />
<br />
<math>P(z)=(2z)^{-1} \int_{0}^{2z} e^{-\beta U(z_1)} e^{-\beta U(2z-z_1)} dz_1 </math><br />
<br />
and similarly, for particles with some interaction <math>P_I(z_1,z_2)</math> independent of the surface, the probability that the center of mass is at height z is then<br />
<br />
<math>P(z)=\frac{\int_{0}^{2z} e^{-\beta U(z_1)}e^{-\beta U(2z-z_1)}P_I(2z_1-2z) dz_1 }{\int_0^{2z}P_I(2z_1-2z) dz_1} </math><br />
<br />
which are appropriately normalized and have features shown in Fig. 1.<br />
<br />
==Simulation==<br />
Applying these probability distributions for large numbers of particles is more tricky.<br />
One issue is that pair interactions are often non-radial (e.g. conformational details for poly(ethylene oxide) mentioned in the paper).<br />
Another challenge is the large number of particles that must be incorporated in the simulation.<br />
To alleviate this, common coarse graining methods combine several (>2) heavy atoms and H atoms associated with them to a single position.<br />
The authors explained that a judicious choice for the implementation of coarse grain is required with a -O-<math>CH_2</math>- piece of poly(ethylene oxide).<br />
One method is to coarse grain <math>CH_2</math> then combine it with O.<br />
Another method is to coarse grain CHO, then combine it with H.<br />
The third method is to coarse grain HH and CO separately, then combine the pairs.<br />
Only first and third are reasonable since the first combines heavy atoms (and their associated H atoms in groups) and the third retains symmetry by first coarse graining light and heavy atoms together then combining them.<br />
The discrepancy for the second method is shown in Fig. 1d where the potential energy is different than those from the other methods.<br />
These principles are applied for a coarse grain simulation of aqueous n-alkyl poly(ethylene oxide), specifically C12E5, adsorbing on a graphite surface.<br />
The nonionic surfactant CnEm were coarse grained with 3 <math>CH_2</math> groups at each hydrophobic site and one ethylene monomer at each hydrophilic site in order to observe the overall shape of the surfactant.<br />
Specific parameters used to model details of the interactions were previously measured experimentally with bulk density, surface tension, and interfacial surface tension.<br />
The diffusion coefficients were reported to have been calculated from mean square displacement curves for binary mixtures of C12E5 at different concentrations and water and confirmed by experiment.<br />
<br />
==Results and discussion==<br />
[[Image:msa2.jpeg|thumb|300px|right| Fig. 2: Simulation results for C12E5 adsorption onto a graphite surface at t = 0, 0.64, 3.3, 3.75, 4.3, and 6 ns (a-f) with solid-liquid interfaces at the top and bottom separated by 12 nm and 3D periodic boundary conditions. From [1].]]<br />
As the authors mentioned, the self-assembly of nonionic surfactants at graphite-liquid interfaces have been characterized using methods such as atomic force microscopy.<br />
C12E5 was found to form cylindrical micelles in solution and hemicylinders at the graphite-liquid interface.<br />
The results from the simulation (Fig. 2) what that initially, the surfactants coat the graphite surface or begin to self-assemble into spherical micelles (but never fuse completely since they are saturated) far away from the surface (Fig. 2b).<br />
However, when a micelle approaches the partly coated surface, the head groups in the micelle interact with those adsorbed to the surface.<br />
The authors describe what occurs next as "feeding," where two sets of head groups open so that the hydrophobic tails of the micelles touch those of the monolayer on the graphite surface (Fig. 2c,d)<br />
The tails then quickly disperse onto the surface and the head groups rearrange so that the entire micelle is adsorbed onto the surface (Fig. 2e).<br />
Reorganization then occurs and hemicylinders of surfactants form on the graphite surface with spacing ~5 nm which agrees with experimental data (Fig. 2f).<br />
Simulations with C9E3 gave similar feeding phenomena but the final state is that of a monolayer with the surfactants perpendicular to the surface, as predicted by the geometry of C9E3 and agrees with experiment.<br />
An explicit representation of the surface was also recovered so that more general and detailed surface geometries can be modeled.<br />
As explained in [1], this method is computationally more efficient and holds promise for nanoscale studies of hydrophobic surfaces interacting with aqueous surfactant solutions, including examining how different surfactants solubilize carbon nanotubes and or how to deposit quantum dots on a substrate.<br />
<br />
==References==<br />
[1] Nielsen, S. O., Srinivas, G., Lopez, C. F., & Klein, M. L. (2005). Modeling surfactant adsorption on hydrophobic surfaces. Physical review letters, 94(22), 228301.<br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Modeling_Surfactant_Adsorption_on_Hydrophobic_Surfaces&diff=26321Modeling Surfactant Adsorption on Hydrophobic Surfaces2012-11-27T22:13:06Z<p>Xingyu: </p>
<hr />
<div>== General Information ==<br />
'''Authors:''' S. O. Nielsen, G. Srinivas, C. F. Lopez, and M. L. Klein<br />
<br />
'''Publication:''' Physical Review Letters<br />
<br />
'''Keywords:''' [[Surfactant]], [[micelle]], [[adsorption]]<br />
<br />
== Summary ==<br />
As the authors mentioned, the self-assembly behavior of surfactants is useful in many contexts, including manipulating single wall carbon nanotubes or solubilization of hydrophobic quantum dots.<br />
However, such processes are not well understood because their dimensional and temporal scales are ill-suited for experiments or atomistic simulations.<br />
This study presents a coarse grain method used to simulate surfactant (aqueous n-alkyl poly(ethylene oxide)) adsorption on an hydrophobic surface (graphite).<br />
This is done by modeling the surface with an implicit potential, coarse graining for interactions using respective center of masses, then returning to the explicit model for the surface.<br />
The simulation results agree with experimental measurements using atomic force microscopy and demonstrate interesting behavior for adsorption.<br />
<br />
==Theory==<br />
[[Image:msa1.jpeg|thumb|300px|right| Fig. 1: a) the probability distribution for the c.m. of two bonded particles interacting with the surface, b) the probability distribution for z = 3.38Å, denoted by the filled circle in a), c) the potential energy for one particle, c.m. of 2 unbonded and bonded particles, d) the potential for -O-<math>CH_2</math>- in poly(ethylene oxide) due to a graphite surface From [1].]]<br />
For the implicit model, the authors used a semi-infinite geometry with the surface as a continuum for z ≤ 0 and atoms in the liquid phase in z > 0.<br />
They then used a Lennard-Jones potential, U(z), for the potential energy of the atom at a height z.<br />
For the coarse graining, groups of atoms are reparameterized by their center of masses (c.m.) for the interactions with the solid surface.<br />
Probability distributions are used for the interactions rather than potential energies since they are more tractable for larger numbers of particles.<br />
For example, the joint probability that particle 1 is at a height <math>z_1</math> and particle 2 at height <math>z_2 </math> is given by:<br />
<br />
<math>P(z_1,z_2) = e^{-\beta U(z_1)} e^{-\beta U(z_2)}</math><br />
<br />
where <math>\beta</math> denotes the inverse of Boltzmann's constant times the temperature. <br />
So, the probability that the c.m. for a pair of non-interacting particles is at height z is given by the marginal distribution:<br />
<br />
<math>P(z)=(2z)^{-1} \int_{0}^{2z} e^{-\beta U(z_1)} e^{-\beta U(2z-z_1)} dz_1 </math><br />
<br />
and similarly, for particles with some interaction <math>P_I(z_1,z_2)</math> independent of the surface, the probability that the center of mass is at height z is then<br />
<br />
<math>P(z)=\frac{\int_{0}^{2z} e^{-\beta U(z_1)}e^{-\beta U(2z-z_1)}P_I(2z_1-2z) dz_1 }{\int_0^{2z}P_I(2z_1-2z) dz_1} </math><br />
<br />
which are appropriately normalized and have features shown in Fig. 1.<br />
<br />
==Simulation==<br />
Applying these probability distributions for large numbers of particles is more tricky.<br />
One issue is that pair interactions are often non-radial (e.g. conformational details for poly(ethylene oxide) mentioned in the paper).<br />
Another challenge is the large number of particles that must be incorporated in the simulation.<br />
To alleviate this, common coarse graining methods combine several (>2) heavy atoms and H atoms associated with them to a single position.<br />
The authors explained that a judicious choice for the implementation of coarse grain is required with a -O-<math>CH_2</math>- piece of poly(ethylene oxide).<br />
One method is to coarse grain <math>CH_2</math> then combine it with O.<br />
Another method is to coarse grain CHO, then combine it with H.<br />
The third method is to coarse grain HH and CO separately, then combine the pairs.<br />
Only first and third are reasonable since the first combines heavy atoms (and their associated H atoms in groups) and the third retains symmetry by first coarse graining light and heavy atoms together then combining them.<br />
The discrepancy for the second method is shown in Fig. 1d where the potential energy is different than those from the other methods.<br />
These principles are applied for a coarse grain simulation of aqueous n-alkyl poly(ethylene oxide), specifically C12E5, adsorbing on a graphite surface.<br />
The nonionic surfactant CnEm were coarse grained with 3 <math>CH_2</math> groups at each hydrophobic site and one ethylene monomer at each hydrophilic site in order to observe the overall shape of the surfactant.<br />
Specific parameters used to model details of the interactions were previously measured experimentally with bulk density, surface tension, and interfacial surface tension.<br />
The diffusion coefficients were reported to have been calculated from mean square displacement curves for binary mixtures of C12E5 at different concentrations and water and confirmed by experiment.<br />
<br />
==Results and discussion==<br />
[[Image:msa2.jpeg|thumb|300px|left| Fig. 2: Simulation results for C12E5 adsorption onto a graphite surface at t = 0, 0.64, 3.3, 3.75, 4.3, and 6 ns (a-f) with solid-liquid interfaces at the top and bottom separated by 12 nm and 3D periodic boundary conditions. From [1].]]<br />
As the authors mentioned, the self-assembly of nonionic surfactants at graphite-liquid interfaces have been characterized using methods such as atomic force microscopy.<br />
C12E5 was found to form cylindrical micelles in solution and hemicylinders at the graphite-liquid interface.<br />
The results from the simulation (Fig. 2) what that initially, the surfactants coat the graphite surface or begin to self-assemble into spherical micelles (but never fuse completely since they are saturated) far away from the surface (Fig. 2b).<br />
However, when a micelle approaches the partly coated surface, the head groups in the micelle interact with those adsorbed to the surface.<br />
The authors describe what occurs next as "feeding," where two sets of head groups open so that the hydrophobic tails of the micelles touch those of the monolayer on the graphite surface (Fig. 2c,d)<br />
The tails then quickly disperse onto the surface and the head groups rearrange so that the entire micelle is adsorbed onto the surface (Fig. 2e).<br />
Reorganization then occurs and hemicylinders of surfactants form on the graphite surface with spacing ~5 nm which agrees with experimental data (Fig. 2f).<br />
Simulations with C9E3 gave similar feeding phenomena but the final state is that of a monolayer with the surfactants perpendicular to the surface, as predicted by the geometry of C9E3 and agrees with experiment.<br />
An explicit representation of the surface was also recovered so that more general and detailed surface geometries can be modeled.<br />
As explained in [1], this method is computationally more efficient and holds promise for nanoscale studies of hydrophobic surfaces interacting with aqueous surfactant solutions, including examining how different surfactants solubilize carbon nanotubes and or how to deposit quantum dots on a substrate.<br />
<br />
==References==<br />
[1] Nielsen, S. O., Srinivas, G., Lopez, C. F., & Klein, M. L. (2005). Modeling surfactant adsorption on hydrophobic surfaces. Physical review letters, 94(22), 228301.<br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Modeling_Surfactant_Adsorption_on_Hydrophobic_Surfaces&diff=26320Modeling Surfactant Adsorption on Hydrophobic Surfaces2012-11-27T22:01:16Z<p>Xingyu: </p>
<hr />
<div>== General Information ==<br />
'''Authors:''' S. O. Nielsen, G. Srinivas, C. F. Lopez, and M. L. Klein.<br />
<br />
'''Publication:''' Physical Review Letters<br />
<br />
'''Keywords:''' [[Surfactant]], [[micelle]], [[adsorption]]<br />
<br />
== Summary ==<br />
As the authors mentioned, the self-assembly behavior of surfactants is useful in many contexts, including manipulation of single wall carbon nanotubes or solubilization of hydrophobic quantum dots.<br />
However, such processes are not well understood because their dimensional and temporal scales are ill-suited for experiments or atomistic simulations.<br />
This study presents a coarse grain method used to simulate surfactant (aqueous n-alkyl poly(ethylene oxide) adsorption on an hydrophobic surface (graphite).<br />
This is done by modeling the surface with an implicit potential, coarse graining for interactions using respective center of masses, then returning to the explicit model for the surface.<br />
The simulation results agree with experimental measurements using atomic force microscopy and demonstrate interesting behavior for adsorption.<br />
<br />
==Theory==<br />
[[Image:msa1.jpeg|thumb|300px|right| Fig. 1: a) the probability distribution for the c.m. of two bonded particles interacting with the surface, b) the probability distribution for for z = 3.38Å, denoted by the filled circle in a), c) the potential energy for one particle, c.m. of 2 unbonded and bonded particles, d) the potential for -O-<math>CH_2</math>- in poly(ethylene oxide) due to a graphite surface From [1].]]<br />
For the implicit model, the authors used a semi-infinite geometry with the surface as a continuum for z ≤ 0 and atoms in the liquid phase in z > 0.<br />
They then used a Lennard-Jones potential, U(z), for the potential energy of the atom at a height z.<br />
For the coarse graining, groups of atoms are reparameterized by their center of masses (c.m.) for the interactions with the solid surface.<br />
Probability distributions are used for the interactions rather than potential energies to aid the coarse graining.<br />
For example, the joint probability that particle 1 is at a height <math>z_1</math> and particle 2 at height <math>z_2 </math> is given by:<br />
<math>P(z_1,z_2) = e^{-\beta U(z_1)} e^{-\beta U(z_2)}</math><br />
where <math>\beta</math> denotes the inverse of Boltzmann's constant times the temperature. <br />
So, the probability that c.m. for a pair of non-interacting particles is at height z is given by the marginal distribution:<br />
<math>P(z)=(2z)^{-1} \int_{0}^{2z} e^{-\beta U(z_1)} e^{-\beta U(2z-z_1)} dz_1 </math><br />
and similarly, for particles with some interaction <math>P_I(z_1,z_2)</math> independent of the surface, the probability that the center of mass is at height z is then<br />
<math>P(z)=\frac{\int_{0}^{2z} e^{-\beta U(z_1)}e^{-\beta U(2z-z_1)}P_I(2z_1-z) dz_1 }{\int_0^{2z}P_I(2z_1-2z) dz_1} </math><br />
which are appropriately normalized and have features visualized in Fig. 1<br />
<br />
==Simulation==<br />
Applying these probability distributions for large numbers of particles is more tricky.<br />
One issue is that pair interactions are often non-radial (e.g. conformational details for poly(ethylene oxide) mentioned in the paper).<br />
Another challenge is the large number of particles that must be incorporated in the simulation.<br />
To alleviate this, common coarse graining methods combine several (>2) heavy atoms and H atoms associated with them to a single position.<br />
The authors explained that a judicious choice for the implementation of coarse grain is required with a -O-<math>CH_2</math>- piece of poly(ethylene oxide).<br />
One method is to coarse grain <math>CH_2</math> then combine it with O.<br />
Another method is to coarse grain CHO, then combine it with H.<br />
The third method is to coarse grain HH and CO separately, then combine the pairs.<br />
Only first and third are reasonable since the first combines heavy atoms (and their associated H atoms in groups) and the third retains symmetry by first coarse graining light and heavy atoms together then combining them.<br />
The discrepancy for the second method is shown in Fig. 1d where the potential energy is different than those from the other methods.<br />
These principles are applied for a coarse grain simulation of aqueous n-alkyl poly(ethylene oxide), specifically C12E5, adsorbing on a graphite surface.<br />
The nonionic surfactant CnEm were coarse grained with 3 <math>CH_2</math> group at each hydrophobic site and one ethylene monomer at each hydrophilic site in order to observe the overall shape of the surfactant.<br />
Specific parameters such used to model details of the interactions were previously measured experimentally with bulk density, surface tension, and inter-facial surface tension.<br />
The diffusion coefficients were reported to have been calculated from mean square displacement curves for binary mixtures of C12E5 at different concentrations and water and confirmed by experiment.<br />
<br />
==Results and discussion==<br />
[[Image:msa2.jpeg|thumb|300px|left| Fig. 2: Simulation results for C12E5 adsorption onto a graphite surface at t = 0, 0.64, 3.3, 3.75, 4.3, and 6 ns (a-f) with solid-liquid interfaces at the top and bottom separated by 12 nm and 3D periodic boundary conditions. From [1].]]<br />
As the authors mentioned, the self-assembly of nonionic surfactants at graphite-liquid interfaces have been characterized using methods such as atomic force microscopy.<br />
C12E5 was found to form cylindrical micelles in solution and hemicylinders at the graphite-liquid interface.<br />
The results from the simulation (Fig. 2) what that initially, the surfactants coat the graphite surface or begin to self-assemble into spherical micelles (but never fuse completely since they are saturated) far away from the surface (Fig. 2b).<br />
However, when a micelle approaches the partly coated surface, the head groups in the micelle interact with those adsorbed to the surface.<br />
The authors describe what occurs next as "feeding," where two sets of head groups open so that the hydrophobic tails of the micelles touch those of the monolayer on the graphite surface (Fig. 2c,d)<br />
The tails then quickly disperse onto the surface and the head groups rearrange so that the entire micelle is adsorbed onto the surface (Fig. 2e).<br />
Reorganization then occurs and hemicylinders of surfactants form on the graphite surface with spacing ~5 nm which agrees with experimental data (Fig. 2f).<br />
Simulations with C9E3 gave similar feeding phenomena but the final state is that of a monolayer with the surfactants perpendicular to the surface, as predicted by the geometry of C9E3 and agrees with experiment.<br />
An explicit representation of the surface was also recovered so that more general and detailed surface geometries can be modeled.<br />
The computational techniques are also four orders of magnitude more efficient than atomistic simulations.<br />
As the authors mentioned, this holds promise for nanoscale studies of hydrophobic surfaces interacting with aqueous surfactant solutions.<br />
This includes examining how different surfactants solubilize carbon nanotubes and depositing quantum dots on a substrate.<br />
<br />
==References==<br />
[1] Nielsen, S. O., Srinivas, G., Lopez, C. F., & Klein, M. L. (2005). Modeling surfactant adsorption on hydrophobic surfaces. Physical review letters, 94(22), 228301.<br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Surfactant&diff=26296Surfactant2012-11-27T06:02:04Z<p>Xingyu: /* Keyword in references: */</p>
<hr />
<div>Entry by Haifei Zhang, AP 225, Fall 2009<br />
<br />
== What is surfactant ==<br />
[[Image:Surfactant.png|right|thumb|A micelle—the lipophilic tails of the surfactant molecules remain on the inside of the micelle due to unfavourable interactions. ]]<br />
<br />
Surfactant is a combination of three words: Surface Active Agents. Surfactants are wetting agents that lower the surface tension of a liquid, allowing easier spreading, and lower the interfacial tension between two liquids. Surfactants are usually organic compounds that are amphiphilic, meaning they contain both hydrophobic groups (their "tails") and hydrophilic groups (their "heads"). Therefore, they are soluble in both organic solvents and water. <br />
<br />
As shown in the figure on right, the polar "heads" of the micelle, due to favourable interactions with water, form a hydrophilic outer layer that in effect protects the hydrophobic core of the micelle. The compounds that make up a micelle are typically amphiphilic in nature, meaning that not only are micelles soluble in protic solvents such as water but also in aprotic solvents as a reverse micelle<br />
<br />
== Properties ==<br />
Surfactants reduce the surface tension of water by adsorbing at the liquid-gas interface. They also reduce the interfacial tension between oil and water by adsorbing at the liquid-liquid interface. Many surfactants can also assemble in the bulk solution into aggregates. Examples of such aggregates are vesicles and micelles. The concentration at which surfactants begin to form micelles is known as the critical micelle concentration or CMC. When micelles form in water, their tails form a core that can encapsulate an oil droplet, and their (ionic/polar) heads form an outer shell that maintains favorable contact with water. When surfactants assemble in oil, the aggregate is referred to as a reverse micelle. In a reverse micelle, the heads are in the core and the tails maintain favorable contact with oil. Surfactants are also often classified into four primary groups; anionic, cationic, non-ionic, and zwitterionic (dual charge).<br />
Thermodynamics of the surfactant systems are of great importance, theoretically and practically. This is because surfactant systems represent systems between ordered and disordered states of matter. Surfactant solutions may contain an ordered phase (micelles) and a disordered phase (free surfactant molecules and/or ions in the solution).<br />
Ordinary washing up (dishwashing) detergent, for example, will promote water penetration in soil, but the effect would only last a few days (many standard laundry detergent powders contain levels of chemicals such as sodium and boron, which can be damaging to plants and should not be applied to soils). Commercial soil wetting agents will continue to work for a considerable period, but they will eventually be degraded by soil micro-organisms. Some can, however, interfere with the life-cycles of some aquatic organisms, so care should be taken to prevent run-off of these products into streams, and excess product should not be washed down.<br />
<br />
== Applications ==<br />
=== Many applications ===<br />
Surfactants play an important role in many practical applications and products, including: <br />
* Detergents<br />
* Fabric softener<br />
* Emulsifiers and Emulsions<br />
* Paints<br />
* Adhesives<br />
* Inks<br />
* Anti-fogging<br />
* Soil remediation<br />
* Dispersants<br />
* Wetting<br />
* Ski wax, snowboard wax<br />
* Deinking of recycled paper, both in flotation, washing and enzymatic processes<br />
* Foaming agents<br />
* Defoamers<br />
* Laxatives<br />
* Agrochemical formulations<br />
** Herbicides some<br />
** Insecticides<br />
* Quantum dot coating<br />
* Biocides (sanitizers)<br />
* Shampoo<br />
* Hair conditioners (after shampoo)<br />
* Spermicide (nonoxynol-9)<br />
* Firefighting<br />
* Pipeline, Liquid drag reducing agent<br />
* Alkali Surfactant Polymers (used to mobilize oil in oil wells)<br />
* Ferrofluids<br />
* Leak Detectors<br />
<br />
=== Detergent ===<br />
<br />
[[Image:Sur1.gif|thumb|300px|left|Schematic Sketch of Surfactant Molecule]]<br />
[[Image:Sur2.gif|thumb|300px|right|Schematic Sketch of Surfactant Molecules in Water]]<br />
<br />
A particular type of molecular structure performs as a surfactant. This molecule is made up of a water soluble (hydrophilic) and a water insoluble (hydrophobic) component.<br />
The hydrophobe is usually the equivalent of an 8 to 18 carbon hydrocarbon, and can be aliphatic, aromatic, or a mixture of both. The sources of hydrophobes are normally natural fats and oils, petroleum fractions, relatively short synthetic polymers, or relatively high molecular weight synthetic alcohols. The hydrophilic groups give the primary classification to surfactants, and are anionic, cationic and nonionic in nature. The anionic hydrophiles are the carboxylates (soaps), sulphates, sulphonates and phosphates. The cationic hydrophiles are some form of an amine product. The nonionic hydrophiles associate with water at the ether oxygens of a polyethylene glycol chain. In each case, the hydrophilic end of the surfactant is strongly attracted to the water molecules and the force of attraction between the hydrophobe and water is only slight. As a result, the surfactant molecules align themselves at the surface and internally so that the hydrophile end is toward the water and the hydrophobe is squeezed away from the water.<br />
<br />
Because of this characteristic behaviour of surfactants to orient at surfaces and to form micelles, all surfactants perform certain basic functions. However, each surfactant excels in certain functions and has others in which it is deficient.<br />
<br />
Foaming agents, emulsifiers, and dispersants are surfactants which suspend respectively, a gas, an immiscible liquid, or a solid in water or some other liquid. Although there is similarity in these functions, in practice the surfactants required to perform these functions differ widely. In emulsification, as an example - the selection of surfactant or surfactant system will depend on the materials to be used and the properties desired in the end product. An emulsion can be either oil droplets suspended in water, an oil in water (O/W) emulsion, water suspended in a continuous oil phase, water in oil (W/O) emulsion, or a mixed emulsion. Selection of surfactants, orders of addition and relative amounts of the two phases determine the class of emulsion.<br />
<br />
Each of these three functions is related to the surfactant absorbing at a surface, either gas, liquid or solid with the hydrophilic ends of the molecules oriented to the water phase. The surfactants form what amounts to a protective coating around the suspended material, and these hydrophilic ends associate with the neighbouring water molecules. In addition to surfactant effects the stability of these suspensions is related to the particle size and density of the suspended material.<br />
<br />
[[Image:Detergentgif.gif|thumb|400px|left|Simplified Illustration of Detergency]]<br />
Solubilisation is a function closely related to emulsification. As the size of the emulsified droplet becomes smaller, a condition is reached where this droplet and the surfactant micelle are the same size.<br />
<br />
At this stage, an oil droplet can be imagined as being in solution in the hydrophobic tails of the surfactant and the term solubilisation is used. Emulsions are milky in appearance and solubilised oils, for example - are clear to the eye.<br />
<br />
The function of detergency or cleaning is a complex combination of all the previous functions. The surface to be cleaned and the soil to be removed must initially be wet and the soils suspended, solubilised, dissolved or separated in some way so that the soil will not just re-deposit on the surface in question<br />
<br />
<br />
<br />
<br />
== References ==<br />
[1] http://en.wikipedia.org/wiki/Surfactant<br />
<br />
[2] http://www.chemistry.co.nz/surfactants.htm<br />
<br />
[3] [[The Science of Chocolate: interactive activities on phase transitions, emulsification, and nucleation]]<br />
<br />
<br />
<br />
<br />
== Keyword in references: ==<br />
<br />
[[Amphiphilic Crescent-Moon-Shaped Microparticles Formed by Selective Adsorption of Colloids]]<br />
<br />
[[Biomimetic Morphogenesis of Calcium Carbonate in Mixed Solutions of Surfactants and Double-Hydrophilic Block Copolymers]]<br />
<br />
[[Krafft Points, Critical Micelle Concentrations, Surface Tension, and Solubilizing Power of Aqueous Solutions of Fluorinated Surfactants]]<br />
<br />
[[Order–disorder transition induced by surfactant micelles in single-walled carbon nanotubes dispersions]]<br />
<br />
[[Patterned Colloidal Coating Using Adhesive Emulsions]]<br />
<br />
[[Reversible aggregation of responsive polymer-stabilized colloids and the pH-dependent formation of porous scaffolds]]<br />
<br />
[[Enriching libraries of high-aspect-ratio micro- or nanostructures by rapid, low-cost, benchtop nanofabrication]]<br />
<br />
[[Liquid-infused structured surfaces with exceptional anti-biofouling performance]]<br />
<br />
[[Liquid-Infused Nanostructured Surfaces with Extreme Anti-Ice and Anti-Frost Performance]]<br />
<br />
[[Dynamics of foam drainage]]<br />
<br />
[[Dynamic mechanisms for apparent slip on hydrophobic surfaces]]<br />
<br />
[[Phase diagrams for sonoluminescing bubbles]]<br />
<br />
[[Non-coalescence of oppositely charged droplets in pH-sensitive emulsions]]<br />
<br />
[[Yielding and Flow of Monodisperse Emulsions]]<br />
<br />
[[Swollen Vesicles and Multiple Emulsions from Block Copolymers]]<br />
<br />
[[Spontaneous Formation of Lipid Structures at Oil/Water/Lipid Interfaces]]<br />
<br />
[[Production of Unilamellar Vesicles Using an Inverted Emulsion]]<br />
<br />
[[Short-time self-diffusion of nearly hard spheres at an oil–water interface]]<br />
<br />
[[Hierarchical Porous Materials Made by Drying Complex Suspensions]]<br />
<br />
[[Double Emulsion Droplets as Microreactors for Synthesis of Mesoporous Hydroxyapatite]]<br />
<br />
[[Microfluidic Fabrication of Monodisperse Biocompatible and Biodegradable Polymersomes with Controlled Permeability]]<br />
<br />
[[Droplet Microfluidics for Fabrication of Non-Spherical Particles]]<br />
<br />
[[Arrested Coalescence of Particle-coated Droplets into Nonspherical Supracolloidal Structures]]<br />
<br />
[[Early development drug formulation on a chip: Fabrication of nanoparticles using a microfluidic spray dryer]]<br />
<br />
[[Fabrication of Monodisperse Toroidal Particles by Polymer Solidification in Microfluidics]]<br />
<br />
[[Asymmetric functionalization of colloidal dimer particles with gold nanoparticles]]<br />
<br />
[[Single-bubble sonoluminescence]]<br />
<br />
[[Four-phase merging in sessile compound drops]]<br />
<br />
[[Elasticity of an interfacial particle raft]]<br />
<br />
[[Dynamics of Surfactant-Driven Fracture of Particle Rafts]]<br />
<br />
[[Mechanics of Interfacial Composite Materials]]<br />
<br />
[[Gravitational Stability of Suspensions of Attractive Colloidal Particles]]<br />
<br />
[[Elastohydrodynamics of wet bristles, carpets and brushes]]<br />
<br />
[[Shock-driven jamming and periodic fracture of particulate rafts]]<br />
<br />
[[Colloidal spheres confined by liquid droplets: Geometry, physics, and physical chemistry]]<br />
<br />
[[Measuring Dynamics and Interactions of Colloidal Particles with Digital Holographic Microscopy]]<br />
<br />
[[Self-Assembly of Polyhedral Hybrid Colloidal Particles]]<br />
<br />
[[Surfactant-Assisted Synthesis of Uniform Titania Microspheres and Their Clusters]]<br />
<br />
[[Microtubule Protofilament Number Is Modulated in a Stepwise Fashion by the Charge Density of an Enveloping Layer]]<br />
<br />
[[￼Cationic liposome–microtubule complexes: Pathways to the formation of two-state lipid–protein nanotubes with open or closed ends]]<br />
<br />
[[Fluctuations in membranes with crystalline and hexatic order]]<br />
<br />
[[Biomimetic Isotropic Nanostructures for Structural Coloration]]<br />
<br />
[[Comparison of low-amplitude oscillatory shear in experimental and computational studies of model foams]]<br />
<br />
[[Short-range order and near-field effects on optical scattering and structural coloration]]<br />
<br />
[[Stable island arrays by height-constrained Stranski–Krastanov growth]]<br />
<br />
[[Nanoscale Domain Stability in Organic Monolayers on Metals]]<br />
<br />
[[New directions in mechanics]]<br />
<br />
[[Measuring the elastic modulus of microgels using microdrops]]<br />
<br />
[[Surface Energy as a Barrier to Creasing of Elastomer Films: An Elastic Analogy to Classical Nucleation]]<br />
<br />
[[Novel Colloidal Interactions in Anisotropic Fluids]]<br />
<br />
[[Surfactant-Mediated Two-Dimensional Crystallization of Colloidal Crystals]]<br />
<br />
[[High-throughput injection with microfluidics using picoinjectors]]<br />
<br />
[[Air-bubble-triggered drop formation in microfluidics]]<br />
<br />
[[Syringe-vacuum microfluidics: A portable technique to create monodisperse emulsions]]<br />
<br />
[[Monodisperse Gas-Filled Microparticles from Reactions in Double Emulsions]]<br />
<br />
[[Universal non-diffusive slow dynamics in aging soft matter]]<br />
<br />
[[THE STRUCTURE AND STRENGTH OF FLOCS OF PRECIPITATED CALCIUM CARBONATE INDUCED BY VARIOUS POLYMERS USED IN PAPERMAKING]]<br />
<br />
[[Patterned Colloidal Coating Using Adhesive Emulsions]]<br />
<br />
[[Inverted and multiple nematic emulsions]]<br />
<br />
[[Osmotic pressure and viscoelastic shear moduli of concentrated emulsions]]<br />
<br />
[[Micro!uidic fabrication of smart microgels from macromolecular precursors]]<br />
<br />
[[Functionalized glass coating for PDMS microfluidic devices]]<br />
<br />
[[Bacillus subtilis spreads by surfing on waves of surfactant]]<br />
<br />
[[Structure of adhesive emulsions]]<br />
<br />
[[Droplet-Based Microfluidics for Emulsion and Solvent Evaporation Synthesis of Monodisperse Mesoporous Silica Microspheres]]<br />
<br />
[[Rheology of attractive emulsions]]<br />
<br />
[[Colloidosomes: Selectively Permeable Capsules Composed of Colloidal Particles]]<br />
<br />
[[Interactions between surfactant-coated surfaces in hydrocarbon liquids containing functionalized polymer dispersant]]<br />
<br />
[[Self-Assembled Polymer Membrane Capsules Inflated by Osmotic Pressure]]<br />
<br />
[[Rheology of Binary Colloidal Structures Assembled via Specific Biological Cross-Linking]]<br />
<br />
[[Biocompatible surfactants for water-in-fluorocarbon emulsions]]<br />
<br />
[[Self-assembled Shells Composed of Colloidal Particles: Fabrication and Characterization]]<br />
<br />
[[Amphiphilic Crescent-Moon-Shaped Microparticles Formed by Selective Adsorption of Colloids]]<br />
<br />
[[Colloid Surfactants for Emulsion Stabilization]]<br />
<br />
[[Synthesis of Nonspherical Colloidal Particles with Anisotropic Properties]]<br />
<br />
[[Gravitational Stability of Suspensions of Attractive Colloidal Particles]]<br />
<br />
[[Surface roughness directed self-assembly of patchy particles into colloidal micelles]]<br />
<br />
[[Modeling Surfactant Adsorption on Hydrophobic Surfaces]]</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Adsorption&diff=26295Adsorption2012-11-27T06:00:54Z<p>Xingyu: /* Keyword in references: */</p>
<hr />
<div>[[Surfactants#Topics | Back to Topics.]]<br />
<br />
== What is adsorption? ==<br />
<br />
Adsorption is a process that occurs when a gas or liquid solute accumulates on the surface of a solid or a liquid (adsorbent), forming a film of molecules or atoms (the adsorbate). It is different from absorption, in which a substance diffuses into a liquid or solid to form a solution. The term sorption encompasses both processes, while desorption is the reverse process.<br />
[[Image:Fig6.gif|360px|thumb|right|Adsorption]]<br />
Adsorption is present in many natural physical, biological, and chemical systems, and is widely used in industrial applications such as activated charcoal, synthetic resins, and water purification. Adsorption, ion exchange, and chromatography are sorption processes in which certain adsorbates are selectively transferred from the fluid phase to the surface of insoluble, rigid particles suspended in a vessel or packed in a column.<br />
<br />
Similar to surface tension, adsorption is a consequence of surface energy. In a bulk material, all the bonding requirements (be they ionic, covalent, or metallic) of the constituent atoms of the material are filled by other atoms in the material. However, atoms on the surface of the adsorbent are not wholly surrounded by other adsorbent atoms and therefore can attract adsorbates. The exact nature of the bonding depends on the details of the species involved, but the adsorption process is generally classified as physisorption (characteristic of weak van der Waals forces) or chemisorption (characteristic of covalent bonding).<br />
<br />
Adsorption is usually described through isotherms, that is, the amount of adsorbate on the adsorbent as a function of its pressure (if gas) or concentration (if liquid) at constant temperature. The quantity adsorbed is nearly always normalized by the mass of the adsorbent to allow comparison of different materials.<br />
<br />
The first mathematical fit to an isotherm was published by Freundlich and Küster (1894) and is a purely empirical formula for gaseous adsorbates,<br />
<br />
<br />
:::::::::::::::::::<math>\frac{x}{m}=kP^{\frac{1}{n}}</math><br />
<br />
where <math>x</math> is the quantity adsorbed, <math>m</math> is the mass of the adsorbent, <math>P</math> is the pressure of adsorbate and <math>k</math> and <math>n</math> are empirical constants for each adsorbent-adsorbate pair at a given temperature. The function has an asymptotic maximum as pressure increases without bound. As the temperature increases, the constants <math>k</math> and <math>n</math> change to reflect the empirical observation that the quantity adsorbed rises more slowly and higher pressures are required to saturate the surface.<br />
<br />
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<br />
== Adsorption lowers surface energy ==<br />
<br />
{|-<br />
| At the air/liquid interface:<br />
| And the solid/liquid interface:<br />
|-<br />
| [[Image:SurfactantsLowerSurfaceTension.png |thumb| 200px | center | ]]<br />
| [[Image:SurfactantsAsorb.png |thumb| 200px | center | ]]<br />
|-<br />
| Lowers the surface tension.<br />
| Stabilizes dispersions.<br />
|}<br />
<br />
<br />
== Culinary applications ==<br />
* '''Mayonnaise''' is a classic example of an emulsion of an oil in water. Howard McGee gives an extensive discussion of how to prepare this well-known condiment:<br />
** The surface tension of water makes it highly-favorable for the water and oil to exist in distinct phases. Energy, in the form of vigorous mixing, needs to be added to the mixture to create a dispersion of oil droplets in water. As an order of magnitude estimate, 15 ml of oil can separate into 30 billion drops in the final product! Enthusiastic mixing by hand can achieve droplets on the order of 3 micron, but industrial-grade homogenizers can produce drops less than one micron in size. <br />
** As described in the previous section, this process of dispersing the droplets can be made easier with the presence of surfactants, also known as emulsifiers. In mayonnaise, the phospholipid lecithin in the eggs serves this purpose. The proteins in the egg yolks contain separate hydrophobic and hydrophillic regions, which is also effective. Warm, raw eggs yolks are traditionally used since they are more flexible and can flow more easily than their refrigerated or cooked counterparts. The casein in milk and cream are also sometimes used in emulsions.<br />
** However, it is not enough to simply create the droplets: something is needed to keep them from coalescing into larger drops. In mayonnaise, the polymers in mustard seeds do the job. <br />
* '''Chocolate''' is an emulsion of cocoa particles in cocoa butter. Starting in the 1930's, lecithin was used to replace some of the cocoa butter. One part lecithin can lubricate as many cocoa particles as 10 parts cocoa butter. Due to this efficiency, chocolate typically contains only 0.3 to 0.5% lecithin my weight.<br />
* '''Whisky''' may often be served "on the rocks" to enhance the flavor of the beverage, rather than just to dilute the alcohol. As the ice melts and the liquid becomes more polar, long chain esters and alcohols form micelles, which "masks" their flavor. On the other hand, ethanol becomes more soluble in water as the liquid cools, which causes it to break up existing micelles of flavor molecules. For more information, see the blog [http://blog.khymos.org/2007/06/03/new-perspectives-on-whisky-and-water/ post] on [[khymos.org]].<br />
[[Image:Diluted-whisky.jpg | 200 px ]]<br />
[[Image:Diluted-whisky-2.jpg | 300 px]]<br />
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[[Surfactants#Topics | Back to Topics.]]<br />
<br />
==Foam==<br />
Surfactants lower interfacial tension. This promotes finer dispersions. But they also keep dispersed droplets from coalescing. Surfactant coated surfaces repel each other, and merging of droplets would also require the surfactants to reorganize on the surface. "Thus, it is that two adjacent surfactant-coated droplets can coalesce only on the timescale of years." Thus, emulsions such as mayo or cold cream can have a long shelf life.<br />
<br />
Foam is just a dispersion where the solute is air. Foams can be made either by stirring or by lowering the pressure of a gas-saturated solution. The solution becomes supersaturated with gas and begins to bubble. This is what happens with shaving cream or with beer bottles when they are opened.<br />
(Witten p. 197)<br />
<br />
Great Experiment: Put some dry ice in soapy water, and you will get soap bubbles rising from the surface! <br />
<br />
http://en.wikipedia.org/wiki/Image:Foam_-_big.jpg<br />
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[[Surfactants#Topics | Back to Topics.]]<br />
<br />
== Gibbs' adsorption isotherm ==<br />
<br />
A derivation by Gibbs gives a relation between the chemical potential of a solute in solution, the surface tension of an interface and the excess concentration the solute at that interface. The interface is considered to be wide compared to the concentration gradients; the excess number of moles associated with that interface is calculated and is expressed as a surface concentration, moles per area:<br />
<br />
[[Image:MORFG1501.png |thumb| 200px | center | Morrison. Fig. 15.1]]<br />
<br />
{|-<br />
| The differential of the total energy:<br />
| <math>dU=TdS-pdV+\sigma dA+\sum{\mu _{i}dn_{i}}</math><br />
|-<br />
| Integrating to get the total energy:<br />
| <math>U=TS-pV+\sigma A+\sum{\mu _{i}n_{i}}</math><br />
|-<br />
| Taking the differential gives the Gibbs-Duhem relation<br />
| <math>SdT-Vdp+Ad\sigma +\sum{n_{i}d\mu _{i}}=0</math><br />
|-<br />
| Defining that relation for both bulk phases:<br />
| <math>S^{\alpha }dT-V^{\alpha }dp+\sum{n_{i}^{\alpha }}d\mu _{i}^{\alpha }=0</math><br />
|-<br />
| <br />
| <math>S^{\beta }dT-V^{\beta }dp+\sum{n_{i}^{\beta }}d\mu _{i}^{\beta }=0</math><br />
|-<br />
| Chemical potentials are constant:<br />
| <math>d\mu _{i}=d\mu _{i}^{\alpha }=d\mu _{i}^{\beta }</math><br />
|-<br />
| Subtracting the phases from the total:<br />
| <math>\left( S-S^{\alpha }-S^{\beta } \right)dT-\left( V-V^{\alpha }-V^{\beta } \right)dp+Ad\sigma +\sum{\left( n_{i}-n_{i}^{\alpha }-n_{i}^{\beta } \right)}d\mu _{i}=0</math><br />
|-<br />
| Defining the excess quantities:<br />
| <math>S^{\sigma }=S-S^{\alpha }-S^{\beta }</math><br />
|-<br />
| <br />
| <math>S^{\sigma }=S-S^{\alpha }-S^{\beta }</math><br />
|-<br />
| <br />
| <math>S^{\sigma }=S-S^{\alpha }-S^{\beta }</math><br />
|-<br />
| Substitution and subtraction gives:<br />
| <math>Ad\sigma +S^{\sigma }dT-V^{\sigma }dp+\sum{n_{i}^{\sigma }d\mu _{i}}</math><br />
|-<br />
|}<br />
<br />
Finally:<br />
<br />
{|-class="wikitable" border = "1"<br />
| Gibbs adsorption isotherm:<br />
| <math>-d\sigma =\sum{\frac{n_{i}^{\sigma }}{A}}d\mu _{i}=\sum{\Gamma _{i}}d\mu _{i}</math> <br />
|- <br />
| The surface excess:<br />
| <math>\Gamma _{i}=\frac{n_{i}^{\sigma }}{A}\text{ mol m}^{\text{-2}}</math><br />
|- <br />
| For a 2-component system:<br />
|<math>-d\sigma =\Gamma _{2}d\mu _{2}\simeq kT\Gamma _{2}d\ln c_{2}</math><br />
|-<br />
|}<br />
<br />
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[[Surfactants#Topics | Back to Topics.]]<br />
<br />
== Adsorption at interfaces ==<br />
<br />
<br />
{|-<br />
| Air-water surface<br />
| Air-oil surface<br />
| Oil-water interface<br />
|-<br />
|[[Image:AdsorptionAirWater.png |thumb| 400px | center | ]]<br />
|[[Image:AdsorptionAirOil.png |thumb| 400px | center | ]]<br />
|[[Image:AdsorptionOilWater.png |thumb| 400px | center | ]]<br />
|-<br />
| Strong adsorption, substantial lowering of surface tension.<br />
| Little adsorption, little lowering of surface tension.<br />
| Strong adsorption, substantial lowering of interfacial tension.<br />
|-<br />
|}<br />
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[[Surfactants#Topics | Back to Topics.]]<br />
<br />
== Adsorption on bubbles ==<br />
<br />
Ratio of the observed velocity of ascent of a bubble to the calculated Stokes’ velocity in solutions of various concentrations of<br />
<br />
* (a) polydimethylsiloxane in trimethylolpropane–heptanoate;<br />
* (b) polydimethylsiloxane in mineral oil;<br />
* (c) N-phenyl–1–1napthylamine in trimethylolpropane–heptanoate.<br />
<br />
Each figure shows the transition from the Hadamard to the Stokes regime.<br />
<br />
[[Image:BubbleRise.png |thumb| 400px | center | Suzin and Ross, 1985]]<br />
<br />
<br />
Suzin, Y.; Ross, S. Retardation of the ascent of gas bubbles by surface-active solutes in nonaqueous solutions, ''J. Colloid Interface Sci.'' '''1985''', ''103'', 578 – 585.<br />
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[[Surfactants#Topics | Back to Topics.]]<br />
<br />
== Adsorption by a solid surface ==<br />
<br />
The surfactant must be soluble in the liquid !<br />
<br />
{|-<br />
| Solid-water interface<br />
| Solid-oil interface<br />
|-<br />
| [[Image:AdsorptionSolidWater.png |thumb| 250px | center | ]]<br />
| [[Image:AdsorptionSolidOil.png |thumb| 250px | center | ]]<br />
|-<br />
| The adsorption is driven by both strong tail/solid interaction and entropy – the '''hydrophobic effect'''.<br />
| The adsorption is driven by strong head group/solid interaction.<br />
|-<br />
|}<br />
<br />
What would happen to this configuration if the water and oil were alternated at the surface? Would the molecules at the surface just keep flipping?<br />
<br />
Adsorption of surfactants on solid surfaces has significant applications. One is detergents, where a dirt particle is surrounded by adsorbed surfactant molecules. Another commercial application is solubility of solid material such as pigment or latex particles in paints. The adsorption of particles from a solution onto a solid surface is described by the Langmuir adsorption equation. At equilibrium, the adsorption rate is equal to the desorption rate, hence:<br />
<br />
<math>\frac{d\Theta}{dt} = k_ac(1-\Theta) </math> for adsorption<br />
<br />
<math>\frac{d\Theta}{dt} = k_d\Theta </math> for desorptions<br />
<br />
Where <math>\Theta </math> is the surface coverage and c is the surfactant concentration. <math>k_a </math> and <math>k_d</math> are the rates of adsorption and desorption respectively. Solving for <math>\Theta</math> at equilibrium yields:<br />
<math>\Theta = \frac{ \frac{k_a}{k_d} c}{1 + \frac{k_a}{k_d}c} = \frac{Kc}{1+Kc}</math><br />
<br />
With <math>K=\frac{k_a}{k_d}</math> being the equilibrium constant. <br />
<br />
At the limit <math>K,c >> 1</math> then <math>\Theta \approx 1</math> and the surface is saturated with surfactant. <br />
<br />
At the limit of <math>c,K << 1</math>, then <math>\Theta \approx Kc</math> and the coverage is still proportional to concentration.<br />
<br />
[Info adapted from I. W. Hamley, 'Introduction to Soft Matter', John Wiley & Sons editions, 2007 West Sussex England]<br />
<br />
== Adsorption Applications ==<br />
<br />
Adsorbents most commonly exist as spherical rods, pellets or monoliths with hydrodynamic diameters at the order 1 to 10 mm. The properties that characterize them are high abrasion resistance, high thermal stability, as well as small pore diameters. All these characteristics make the exposed surface area greater therefore enable higher surface capacity for adsorption. In addition, adsorbents must also have a specific structure which enables fast transport of the vapors.<br />
<br />
Adsorbents in industry are usually classified in three categories:<br />
<br />
* Oxygen-containing compounds – hydrophilic and polar (silica gel, zeolites).<br />
* Carbon-based compounds – hydrophobic and non-polar (activated carbon, graphite).<br />
* Polymer-based compounds - could be polar or non-polar.<br />
<br />
[[Surfactants#Topics | Back to Topics.]]<br />
<br />
== Industrial Application: Cryosorption Pumping ==<br />
<br />
The phenomenon of adsorption is very important in vacuum science, and is the physics behind a very important class of vacuum pump. A cryosorption pump (sometimes called simply a cryopump) uses cooled surfaces covered with a material that adsorbs a certain vapor. Because they have no moving parts and require no oil (only a cold surface), cryopumps are a clean, effective, and simple way to achieve a very high high vacuum.<br />
<br />
While a flat, smooth surface will cryopump most gases, helium requires a very porous material to be cryopumped. Modern cryopumps use materials with very high surface areas and internals mircopores; common materials are activated charcoal (usually made from coconut, but also made from wood, petroleum byproducts, or bone), porous metals such as copper, or solid argon.<br />
<br />
A well-constructed cryopump, cooled down to a few Kelvin, can pump several liters of helium per second per square centimeter, and has a capacity of several Torr-liters per square centimeter. In other words, the adsorbing materials can contain a few hundred times their own volume!<br />
<br />
Coconut-charcoal based cryopumps are a common tool in cryogenics labs, and are the vacuum pumps of choice in fusion reactors because of their huge pumping speeds and low contamination.<br />
<br />
[[Surfactants#Topics | Back to Topics.]]<br />
<br />
----<br />
== Adsorption of Virus ==<br />
[[Image:Adsorption_of_virus.gif|360px|thumb|center|Adsorption of virus.]]<br />
Adsorption is the first step in the viral infection cycle. The next steps are penetration, uncoating, synthesis (transcription if needed, and translation), and release. The virus replication cycle is similar, if not the same, for all types of viruses. Factors such as transcription may or may not be needed if the virus is able to integrate its genomic information in the cell's nucleus, or if the virus can replicate itself directly within the cell's cytoplasm.<br />
<br />
<br />
[[Surfactants#Topics | Back to Topics.]]<br />
<br />
----<br />
<br />
<br />
== Adsorption on catalysts ==<br />
<br />
The adsorption of molecules on certain catalytic materials can achieve or accelerate certain chemical reactions. Zarzar et al. [[Multiphoton Lithography of Nanocrystalline Platinum and Palladium for Site-Specific Catalysis in 3D Microenvironments|[1]]] introduced the use of Multiphoton Lithography (MPL) to generate arbitrary micropatterns of nanocrystallined catalysts and demonstrated the possibility to catalyze chemical reactions as well as control the flow of chemical output by certain microenvironments.<br />
<br />
== Water adsorption and desorption using zeolites==<br />
<br />
Zeolites are crystalline aluminosilicates, polar in nature, which have a periodic pore network and release water at high temperature. They are produced by hydrothermal synthesis of sodium aluminosilicate (or similar silica source) followed by an ion exchange with a cation (Na+, Li+). <br />
<br />
As we mentioned, natural zeolites are highly polar and have the property of adsorbing and desorbing water without damage to its crystal structure. This capability makes them very useful in desiccation processes. In many industrial and commercial applications, zeolites have been found highly effective in controlling moisture levels. They are able to dry the air, remove CO2 from natural gas, remove CO from reforming gas, etc.<br />
<br />
Furthermore, ability to adsorb and desorb water without change in its structure, together with a high heat of adsorption, makes zeolites effective and efficient heat energy storage for later use. Unlike other heat energy systems utilizing non-zeolite heat storage which can be very expensive, zeolites provide a low cost, efficient media for heat storage. <br />
<br />
Here are some images of zeolites:<br />
<br />
[[Image:zeolite1.png]]<br />
<br />
3D Zeolite structure<br />
<br />
[[Image:zeolite2.jpg]]<br />
<br />
Zeolite image (length ~ 2.5") <br />
<br />
== Keyword in references: ==<br />
<br />
[[Controlled Assembly of Jammed Colloidal Shells on Fluid Droplets]]<br />
<br />
[[Steering nanofibers: An integrative approach to bio-inspired fiber fabrication and assembly]]<br />
<br />
[[Fine-Tuning the Degree of Stem Cell Polarization and Alignment on Ordered Arrays of High-Aspect-Ratio Nanopillars]]<br />
<br />
[[Multiphoton Lithography of Nanocrystalline Platinum and Palladium for Site-Specific Catalysis in 3D Microenvironments]]<br />
<br />
[[Liquid-infused structured surfaces with exceptional anti-biofouling performance]]<br />
<br />
[[Wetting in Color: Colorimetric Differentiation of Organic Liquids with High Selectivity]]<br />
<br />
[[Relating microstructure to rheology of a bundled and cross-linked F-actin network in vitro]]<br />
<br />
[[Elastohydrodynamics of wet bristles, carpets and brushes]]<br />
<br />
[[Colloidal spheres confined by liquid droplets: Geometry, physics, and physical chemistry]]<br />
<br />
[[Surfactant-Assisted Synthesis of Uniform Titania Microspheres and Their Clusters]]<br />
<br />
[[Microtubule Protofilament Number Is Modulated in a Stepwise Fashion by the Charge Density of an Enveloping Layer]]<br />
<br />
[[Cationic membranes complexed with oppositely charged microtubules: hierarchical self-assembly leading to bio-nanotubes]]<br />
<br />
[[Non-coalescence of oppositely charged droplets in pH-sensitive emulsions]]<br />
<br />
[[Spontaneous Formation of Lipid Structures at Oil/Water/Lipid Interfaces]]<br />
<br />
[[Production of Unilamellar Vesicles Using an Inverted Emulsion]]<br />
<br />
[[Short-time self-diffusion of nearly hard spheres at an oil–water interface]]<br />
<br />
[[Hierarchical Porous Materials Made by Drying Complex Suspensions]]<br />
<br />
[[Double Emulsion Droplets as Microreactors for Synthesis of Mesoporous Hydroxyapatite]]<br />
<br />
[[Droplet Microfluidics for Fabrication of Non-Spherical Particles]]<br />
<br />
[[Arrested Coalescence of Particle-coated Droplets into Nonspherical Supracolloidal Structures]]<br />
<br />
[[Early development drug formulation on a chip: Fabrication of nanoparticles using a microfluidic spray dryer]]<br />
<br />
[[Asymmetric functionalization of colloidal dimer particles with gold nanoparticles]]<br />
<br />
<br />
[[￼Cationic liposome–microtubule complexes: Pathways to the formation of two-state lipid–protein nanotubes with open or closed ends]]<br />
<br />
[[Single molecule statistics and the polynucleotide unzipping transition]]<br />
<br />
[[The orientation of the self-assembled monolayer stripes on a crystalline substrate]]<br />
<br />
[[Nanoscale Domain Stability in Organic Monolayers on Metals]]<br />
<br />
[[Molecular assembly on cylindrical surfaces]]<br />
<br />
[[New directions in mechanics]]<br />
<br />
[[Dynamics of terraces on a silicon surface due to the combined action of strain and electric current]]<br />
<br />
[[Singular stress fields at corners in flip-chip packages]]<br />
<br />
[[Surfactant-Mediated Two-Dimensional Crystallization of Colloidal Crystals]]<br />
<br />
[[High-throughput injection with microfluidics using picoinjectors]]<br />
<br />
[[THE STRUCTURE AND STRENGTH OF FLOCS OF PRECIPITATED CALCIUM CARBONATE INDUCED BY VARIOUS POLYMERS USED IN PAPERMAKING]]<br />
<br />
[[Patterned Colloidal Coating Using Adhesive Emulsions]]<br />
<br />
[[Inverted and multiple nematic emulsions]]<br />
<br />
[[Functionalized glass coating for PDMS microfluidic devices]]<br />
<br />
[[Bacillus subtilis spreads by surfing on waves of surfactant]]<br />
<br />
[[Colloidosomes: Selectively Permeable Capsules Composed of Colloidal Particles]]<br />
<br />
[[Interactions between surfactant-coated surfaces in hydrocarbon liquids containing functionalized polymer dispersant]]<br />
<br />
[[Self-Assembled Polymer Membrane Capsules Inflated by Osmotic Pressure]]<br />
<br />
[[Biocompatible surfactants for water-in-fluorocarbon emulsions]]<br />
<br />
[[Self-assembled Shells Composed of Colloidal Particles: Fabrication and Characterization]]<br />
<br />
[[Amphiphilic Crescent-Moon-Shaped Microparticles Formed by Selective Adsorption of Colloids]]<br />
<br />
[[Colloid Surfactants for Emulsion Stabilization]]<br />
<br />
[[Synthesis of Nonspherical Colloidal Particles with Anisotropic Properties]]<br />
<br />
[[Surface roughness directed self-assembly of patchy particles into colloidal micelles]]<br />
<br />
[[Modeling Surfactant Adsorption on Hydrophobic Surfaces]]<br />
<br />
[[Surfactants#Topics | Back to Topics.]]</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Adsorption&diff=26294Adsorption2012-11-27T06:00:24Z<p>Xingyu: /* Keyword in references: */</p>
<hr />
<div>[[Surfactants#Topics | Back to Topics.]]<br />
<br />
== What is adsorption? ==<br />
<br />
Adsorption is a process that occurs when a gas or liquid solute accumulates on the surface of a solid or a liquid (adsorbent), forming a film of molecules or atoms (the adsorbate). It is different from absorption, in which a substance diffuses into a liquid or solid to form a solution. The term sorption encompasses both processes, while desorption is the reverse process.<br />
[[Image:Fig6.gif|360px|thumb|right|Adsorption]]<br />
Adsorption is present in many natural physical, biological, and chemical systems, and is widely used in industrial applications such as activated charcoal, synthetic resins, and water purification. Adsorption, ion exchange, and chromatography are sorption processes in which certain adsorbates are selectively transferred from the fluid phase to the surface of insoluble, rigid particles suspended in a vessel or packed in a column.<br />
<br />
Similar to surface tension, adsorption is a consequence of surface energy. In a bulk material, all the bonding requirements (be they ionic, covalent, or metallic) of the constituent atoms of the material are filled by other atoms in the material. However, atoms on the surface of the adsorbent are not wholly surrounded by other adsorbent atoms and therefore can attract adsorbates. The exact nature of the bonding depends on the details of the species involved, but the adsorption process is generally classified as physisorption (characteristic of weak van der Waals forces) or chemisorption (characteristic of covalent bonding).<br />
<br />
Adsorption is usually described through isotherms, that is, the amount of adsorbate on the adsorbent as a function of its pressure (if gas) or concentration (if liquid) at constant temperature. The quantity adsorbed is nearly always normalized by the mass of the adsorbent to allow comparison of different materials.<br />
<br />
The first mathematical fit to an isotherm was published by Freundlich and Küster (1894) and is a purely empirical formula for gaseous adsorbates,<br />
<br />
<br />
:::::::::::::::::::<math>\frac{x}{m}=kP^{\frac{1}{n}}</math><br />
<br />
where <math>x</math> is the quantity adsorbed, <math>m</math> is the mass of the adsorbent, <math>P</math> is the pressure of adsorbate and <math>k</math> and <math>n</math> are empirical constants for each adsorbent-adsorbate pair at a given temperature. The function has an asymptotic maximum as pressure increases without bound. As the temperature increases, the constants <math>k</math> and <math>n</math> change to reflect the empirical observation that the quantity adsorbed rises more slowly and higher pressures are required to saturate the surface.<br />
<br />
----<br />
<br />
== Adsorption lowers surface energy ==<br />
<br />
{|-<br />
| At the air/liquid interface:<br />
| And the solid/liquid interface:<br />
|-<br />
| [[Image:SurfactantsLowerSurfaceTension.png |thumb| 200px | center | ]]<br />
| [[Image:SurfactantsAsorb.png |thumb| 200px | center | ]]<br />
|-<br />
| Lowers the surface tension.<br />
| Stabilizes dispersions.<br />
|}<br />
<br />
<br />
== Culinary applications ==<br />
* '''Mayonnaise''' is a classic example of an emulsion of an oil in water. Howard McGee gives an extensive discussion of how to prepare this well-known condiment:<br />
** The surface tension of water makes it highly-favorable for the water and oil to exist in distinct phases. Energy, in the form of vigorous mixing, needs to be added to the mixture to create a dispersion of oil droplets in water. As an order of magnitude estimate, 15 ml of oil can separate into 30 billion drops in the final product! Enthusiastic mixing by hand can achieve droplets on the order of 3 micron, but industrial-grade homogenizers can produce drops less than one micron in size. <br />
** As described in the previous section, this process of dispersing the droplets can be made easier with the presence of surfactants, also known as emulsifiers. In mayonnaise, the phospholipid lecithin in the eggs serves this purpose. The proteins in the egg yolks contain separate hydrophobic and hydrophillic regions, which is also effective. Warm, raw eggs yolks are traditionally used since they are more flexible and can flow more easily than their refrigerated or cooked counterparts. The casein in milk and cream are also sometimes used in emulsions.<br />
** However, it is not enough to simply create the droplets: something is needed to keep them from coalescing into larger drops. In mayonnaise, the polymers in mustard seeds do the job. <br />
* '''Chocolate''' is an emulsion of cocoa particles in cocoa butter. Starting in the 1930's, lecithin was used to replace some of the cocoa butter. One part lecithin can lubricate as many cocoa particles as 10 parts cocoa butter. Due to this efficiency, chocolate typically contains only 0.3 to 0.5% lecithin my weight.<br />
* '''Whisky''' may often be served "on the rocks" to enhance the flavor of the beverage, rather than just to dilute the alcohol. As the ice melts and the liquid becomes more polar, long chain esters and alcohols form micelles, which "masks" their flavor. On the other hand, ethanol becomes more soluble in water as the liquid cools, which causes it to break up existing micelles of flavor molecules. For more information, see the blog [http://blog.khymos.org/2007/06/03/new-perspectives-on-whisky-and-water/ post] on [[khymos.org]].<br />
[[Image:Diluted-whisky.jpg | 200 px ]]<br />
[[Image:Diluted-whisky-2.jpg | 300 px]]<br />
<br />
<br />
<br />
----<br />
<br />
[[Surfactants#Topics | Back to Topics.]]<br />
<br />
==Foam==<br />
Surfactants lower interfacial tension. This promotes finer dispersions. But they also keep dispersed droplets from coalescing. Surfactant coated surfaces repel each other, and merging of droplets would also require the surfactants to reorganize on the surface. "Thus, it is that two adjacent surfactant-coated droplets can coalesce only on the timescale of years." Thus, emulsions such as mayo or cold cream can have a long shelf life.<br />
<br />
Foam is just a dispersion where the solute is air. Foams can be made either by stirring or by lowering the pressure of a gas-saturated solution. The solution becomes supersaturated with gas and begins to bubble. This is what happens with shaving cream or with beer bottles when they are opened.<br />
(Witten p. 197)<br />
<br />
Great Experiment: Put some dry ice in soapy water, and you will get soap bubbles rising from the surface! <br />
<br />
http://en.wikipedia.org/wiki/Image:Foam_-_big.jpg<br />
<br />
----<br />
<br />
[[Surfactants#Topics | Back to Topics.]]<br />
<br />
== Gibbs' adsorption isotherm ==<br />
<br />
A derivation by Gibbs gives a relation between the chemical potential of a solute in solution, the surface tension of an interface and the excess concentration the solute at that interface. The interface is considered to be wide compared to the concentration gradients; the excess number of moles associated with that interface is calculated and is expressed as a surface concentration, moles per area:<br />
<br />
[[Image:MORFG1501.png |thumb| 200px | center | Morrison. Fig. 15.1]]<br />
<br />
{|-<br />
| The differential of the total energy:<br />
| <math>dU=TdS-pdV+\sigma dA+\sum{\mu _{i}dn_{i}}</math><br />
|-<br />
| Integrating to get the total energy:<br />
| <math>U=TS-pV+\sigma A+\sum{\mu _{i}n_{i}}</math><br />
|-<br />
| Taking the differential gives the Gibbs-Duhem relation<br />
| <math>SdT-Vdp+Ad\sigma +\sum{n_{i}d\mu _{i}}=0</math><br />
|-<br />
| Defining that relation for both bulk phases:<br />
| <math>S^{\alpha }dT-V^{\alpha }dp+\sum{n_{i}^{\alpha }}d\mu _{i}^{\alpha }=0</math><br />
|-<br />
| <br />
| <math>S^{\beta }dT-V^{\beta }dp+\sum{n_{i}^{\beta }}d\mu _{i}^{\beta }=0</math><br />
|-<br />
| Chemical potentials are constant:<br />
| <math>d\mu _{i}=d\mu _{i}^{\alpha }=d\mu _{i}^{\beta }</math><br />
|-<br />
| Subtracting the phases from the total:<br />
| <math>\left( S-S^{\alpha }-S^{\beta } \right)dT-\left( V-V^{\alpha }-V^{\beta } \right)dp+Ad\sigma +\sum{\left( n_{i}-n_{i}^{\alpha }-n_{i}^{\beta } \right)}d\mu _{i}=0</math><br />
|-<br />
| Defining the excess quantities:<br />
| <math>S^{\sigma }=S-S^{\alpha }-S^{\beta }</math><br />
|-<br />
| <br />
| <math>S^{\sigma }=S-S^{\alpha }-S^{\beta }</math><br />
|-<br />
| <br />
| <math>S^{\sigma }=S-S^{\alpha }-S^{\beta }</math><br />
|-<br />
| Substitution and subtraction gives:<br />
| <math>Ad\sigma +S^{\sigma }dT-V^{\sigma }dp+\sum{n_{i}^{\sigma }d\mu _{i}}</math><br />
|-<br />
|}<br />
<br />
Finally:<br />
<br />
{|-class="wikitable" border = "1"<br />
| Gibbs adsorption isotherm:<br />
| <math>-d\sigma =\sum{\frac{n_{i}^{\sigma }}{A}}d\mu _{i}=\sum{\Gamma _{i}}d\mu _{i}</math> <br />
|- <br />
| The surface excess:<br />
| <math>\Gamma _{i}=\frac{n_{i}^{\sigma }}{A}\text{ mol m}^{\text{-2}}</math><br />
|- <br />
| For a 2-component system:<br />
|<math>-d\sigma =\Gamma _{2}d\mu _{2}\simeq kT\Gamma _{2}d\ln c_{2}</math><br />
|-<br />
|}<br />
<br />
<br />
<br />
----<br />
[[Surfactants#Topics | Back to Topics.]]<br />
<br />
== Adsorption at interfaces ==<br />
<br />
<br />
{|-<br />
| Air-water surface<br />
| Air-oil surface<br />
| Oil-water interface<br />
|-<br />
|[[Image:AdsorptionAirWater.png |thumb| 400px | center | ]]<br />
|[[Image:AdsorptionAirOil.png |thumb| 400px | center | ]]<br />
|[[Image:AdsorptionOilWater.png |thumb| 400px | center | ]]<br />
|-<br />
| Strong adsorption, substantial lowering of surface tension.<br />
| Little adsorption, little lowering of surface tension.<br />
| Strong adsorption, substantial lowering of interfacial tension.<br />
|-<br />
|}<br />
<br />
<br />
----<br />
[[Surfactants#Topics | Back to Topics.]]<br />
<br />
== Adsorption on bubbles ==<br />
<br />
Ratio of the observed velocity of ascent of a bubble to the calculated Stokes’ velocity in solutions of various concentrations of<br />
<br />
* (a) polydimethylsiloxane in trimethylolpropane–heptanoate;<br />
* (b) polydimethylsiloxane in mineral oil;<br />
* (c) N-phenyl–1–1napthylamine in trimethylolpropane–heptanoate.<br />
<br />
Each figure shows the transition from the Hadamard to the Stokes regime.<br />
<br />
[[Image:BubbleRise.png |thumb| 400px | center | Suzin and Ross, 1985]]<br />
<br />
<br />
Suzin, Y.; Ross, S. Retardation of the ascent of gas bubbles by surface-active solutes in nonaqueous solutions, ''J. Colloid Interface Sci.'' '''1985''', ''103'', 578 – 585.<br />
<br />
<br />
<br />
----<br />
[[Surfactants#Topics | Back to Topics.]]<br />
<br />
== Adsorption by a solid surface ==<br />
<br />
The surfactant must be soluble in the liquid !<br />
<br />
{|-<br />
| Solid-water interface<br />
| Solid-oil interface<br />
|-<br />
| [[Image:AdsorptionSolidWater.png |thumb| 250px | center | ]]<br />
| [[Image:AdsorptionSolidOil.png |thumb| 250px | center | ]]<br />
|-<br />
| The adsorption is driven by both strong tail/solid interaction and entropy – the '''hydrophobic effect'''.<br />
| The adsorption is driven by strong head group/solid interaction.<br />
|-<br />
|}<br />
<br />
What would happen to this configuration if the water and oil were alternated at the surface? Would the molecules at the surface just keep flipping?<br />
<br />
Adsorption of surfactants on solid surfaces has significant applications. One is detergents, where a dirt particle is surrounded by adsorbed surfactant molecules. Another commercial application is solubility of solid material such as pigment or latex particles in paints. The adsorption of particles from a solution onto a solid surface is described by the Langmuir adsorption equation. At equilibrium, the adsorption rate is equal to the desorption rate, hence:<br />
<br />
<math>\frac{d\Theta}{dt} = k_ac(1-\Theta) </math> for adsorption<br />
<br />
<math>\frac{d\Theta}{dt} = k_d\Theta </math> for desorptions<br />
<br />
Where <math>\Theta </math> is the surface coverage and c is the surfactant concentration. <math>k_a </math> and <math>k_d</math> are the rates of adsorption and desorption respectively. Solving for <math>\Theta</math> at equilibrium yields:<br />
<math>\Theta = \frac{ \frac{k_a}{k_d} c}{1 + \frac{k_a}{k_d}c} = \frac{Kc}{1+Kc}</math><br />
<br />
With <math>K=\frac{k_a}{k_d}</math> being the equilibrium constant. <br />
<br />
At the limit <math>K,c >> 1</math> then <math>\Theta \approx 1</math> and the surface is saturated with surfactant. <br />
<br />
At the limit of <math>c,K << 1</math>, then <math>\Theta \approx Kc</math> and the coverage is still proportional to concentration.<br />
<br />
[Info adapted from I. W. Hamley, 'Introduction to Soft Matter', John Wiley & Sons editions, 2007 West Sussex England]<br />
<br />
== Adsorption Applications ==<br />
<br />
Adsorbents most commonly exist as spherical rods, pellets or monoliths with hydrodynamic diameters at the order 1 to 10 mm. The properties that characterize them are high abrasion resistance, high thermal stability, as well as small pore diameters. All these characteristics make the exposed surface area greater therefore enable higher surface capacity for adsorption. In addition, adsorbents must also have a specific structure which enables fast transport of the vapors.<br />
<br />
Adsorbents in industry are usually classified in three categories:<br />
<br />
* Oxygen-containing compounds – hydrophilic and polar (silica gel, zeolites).<br />
* Carbon-based compounds – hydrophobic and non-polar (activated carbon, graphite).<br />
* Polymer-based compounds - could be polar or non-polar.<br />
<br />
[[Surfactants#Topics | Back to Topics.]]<br />
<br />
== Industrial Application: Cryosorption Pumping ==<br />
<br />
The phenomenon of adsorption is very important in vacuum science, and is the physics behind a very important class of vacuum pump. A cryosorption pump (sometimes called simply a cryopump) uses cooled surfaces covered with a material that adsorbs a certain vapor. Because they have no moving parts and require no oil (only a cold surface), cryopumps are a clean, effective, and simple way to achieve a very high high vacuum.<br />
<br />
While a flat, smooth surface will cryopump most gases, helium requires a very porous material to be cryopumped. Modern cryopumps use materials with very high surface areas and internals mircopores; common materials are activated charcoal (usually made from coconut, but also made from wood, petroleum byproducts, or bone), porous metals such as copper, or solid argon.<br />
<br />
A well-constructed cryopump, cooled down to a few Kelvin, can pump several liters of helium per second per square centimeter, and has a capacity of several Torr-liters per square centimeter. In other words, the adsorbing materials can contain a few hundred times their own volume!<br />
<br />
Coconut-charcoal based cryopumps are a common tool in cryogenics labs, and are the vacuum pumps of choice in fusion reactors because of their huge pumping speeds and low contamination.<br />
<br />
[[Surfactants#Topics | Back to Topics.]]<br />
<br />
----<br />
== Adsorption of Virus ==<br />
[[Image:Adsorption_of_virus.gif|360px|thumb|center|Adsorption of virus.]]<br />
Adsorption is the first step in the viral infection cycle. The next steps are penetration, uncoating, synthesis (transcription if needed, and translation), and release. The virus replication cycle is similar, if not the same, for all types of viruses. Factors such as transcription may or may not be needed if the virus is able to integrate its genomic information in the cell's nucleus, or if the virus can replicate itself directly within the cell's cytoplasm.<br />
<br />
<br />
[[Surfactants#Topics | Back to Topics.]]<br />
<br />
----<br />
<br />
<br />
== Adsorption on catalysts ==<br />
<br />
The adsorption of molecules on certain catalytic materials can achieve or accelerate certain chemical reactions. Zarzar et al. [[Multiphoton Lithography of Nanocrystalline Platinum and Palladium for Site-Specific Catalysis in 3D Microenvironments|[1]]] introduced the use of Multiphoton Lithography (MPL) to generate arbitrary micropatterns of nanocrystallined catalysts and demonstrated the possibility to catalyze chemical reactions as well as control the flow of chemical output by certain microenvironments.<br />
<br />
== Water adsorption and desorption using zeolites==<br />
<br />
Zeolites are crystalline aluminosilicates, polar in nature, which have a periodic pore network and release water at high temperature. They are produced by hydrothermal synthesis of sodium aluminosilicate (or similar silica source) followed by an ion exchange with a cation (Na+, Li+). <br />
<br />
As we mentioned, natural zeolites are highly polar and have the property of adsorbing and desorbing water without damage to its crystal structure. This capability makes them very useful in desiccation processes. In many industrial and commercial applications, zeolites have been found highly effective in controlling moisture levels. They are able to dry the air, remove CO2 from natural gas, remove CO from reforming gas, etc.<br />
<br />
Furthermore, ability to adsorb and desorb water without change in its structure, together with a high heat of adsorption, makes zeolites effective and efficient heat energy storage for later use. Unlike other heat energy systems utilizing non-zeolite heat storage which can be very expensive, zeolites provide a low cost, efficient media for heat storage. <br />
<br />
Here are some images of zeolites:<br />
<br />
[[Image:zeolite1.png]]<br />
<br />
3D Zeolite structure<br />
<br />
[[Image:zeolite2.jpg]]<br />
<br />
Zeolite image (length ~ 2.5") <br />
<br />
== Keyword in references: ==<br />
<br />
[[Modeling Surfactant Adsorption on Hydrophobic Surfaces]]<br />
<br />
[[Controlled Assembly of Jammed Colloidal Shells on Fluid Droplets]]<br />
<br />
[[Steering nanofibers: An integrative approach to bio-inspired fiber fabrication and assembly]]<br />
<br />
[[Fine-Tuning the Degree of Stem Cell Polarization and Alignment on Ordered Arrays of High-Aspect-Ratio Nanopillars]]<br />
<br />
[[Multiphoton Lithography of Nanocrystalline Platinum and Palladium for Site-Specific Catalysis in 3D Microenvironments]]<br />
<br />
[[Liquid-infused structured surfaces with exceptional anti-biofouling performance]]<br />
<br />
[[Wetting in Color: Colorimetric Differentiation of Organic Liquids with High Selectivity]]<br />
<br />
[[Relating microstructure to rheology of a bundled and cross-linked F-actin network in vitro]]<br />
<br />
[[Elastohydrodynamics of wet bristles, carpets and brushes]]<br />
<br />
[[Colloidal spheres confined by liquid droplets: Geometry, physics, and physical chemistry]]<br />
<br />
[[Surfactant-Assisted Synthesis of Uniform Titania Microspheres and Their Clusters]]<br />
<br />
[[Microtubule Protofilament Number Is Modulated in a Stepwise Fashion by the Charge Density of an Enveloping Layer]]<br />
<br />
[[Cationic membranes complexed with oppositely charged microtubules: hierarchical self-assembly leading to bio-nanotubes]]<br />
<br />
[[Non-coalescence of oppositely charged droplets in pH-sensitive emulsions]]<br />
<br />
[[Spontaneous Formation of Lipid Structures at Oil/Water/Lipid Interfaces]]<br />
<br />
[[Production of Unilamellar Vesicles Using an Inverted Emulsion]]<br />
<br />
[[Short-time self-diffusion of nearly hard spheres at an oil–water interface]]<br />
<br />
[[Hierarchical Porous Materials Made by Drying Complex Suspensions]]<br />
<br />
[[Double Emulsion Droplets as Microreactors for Synthesis of Mesoporous Hydroxyapatite]]<br />
<br />
[[Droplet Microfluidics for Fabrication of Non-Spherical Particles]]<br />
<br />
[[Arrested Coalescence of Particle-coated Droplets into Nonspherical Supracolloidal Structures]]<br />
<br />
[[Early development drug formulation on a chip: Fabrication of nanoparticles using a microfluidic spray dryer]]<br />
<br />
[[Asymmetric functionalization of colloidal dimer particles with gold nanoparticles]]<br />
<br />
<br />
[[￼Cationic liposome–microtubule complexes: Pathways to the formation of two-state lipid–protein nanotubes with open or closed ends]]<br />
<br />
[[Single molecule statistics and the polynucleotide unzipping transition]]<br />
<br />
[[The orientation of the self-assembled monolayer stripes on a crystalline substrate]]<br />
<br />
[[Nanoscale Domain Stability in Organic Monolayers on Metals]]<br />
<br />
[[Molecular assembly on cylindrical surfaces]]<br />
<br />
[[New directions in mechanics]]<br />
<br />
[[Dynamics of terraces on a silicon surface due to the combined action of strain and electric current]]<br />
<br />
[[Singular stress fields at corners in flip-chip packages]]<br />
<br />
[[Surfactant-Mediated Two-Dimensional Crystallization of Colloidal Crystals]]<br />
<br />
[[High-throughput injection with microfluidics using picoinjectors]]<br />
<br />
[[THE STRUCTURE AND STRENGTH OF FLOCS OF PRECIPITATED CALCIUM CARBONATE INDUCED BY VARIOUS POLYMERS USED IN PAPERMAKING]]<br />
<br />
[[Patterned Colloidal Coating Using Adhesive Emulsions]]<br />
<br />
[[Inverted and multiple nematic emulsions]]<br />
<br />
[[Functionalized glass coating for PDMS microfluidic devices]]<br />
<br />
[[Bacillus subtilis spreads by surfing on waves of surfactant]]<br />
<br />
[[Colloidosomes: Selectively Permeable Capsules Composed of Colloidal Particles]]<br />
<br />
[[Interactions between surfactant-coated surfaces in hydrocarbon liquids containing functionalized polymer dispersant]]<br />
<br />
[[Self-Assembled Polymer Membrane Capsules Inflated by Osmotic Pressure]]<br />
<br />
[[Biocompatible surfactants for water-in-fluorocarbon emulsions]]<br />
<br />
[[Self-assembled Shells Composed of Colloidal Particles: Fabrication and Characterization]]<br />
<br />
[[Amphiphilic Crescent-Moon-Shaped Microparticles Formed by Selective Adsorption of Colloids]]<br />
<br />
[[Colloid Surfactants for Emulsion Stabilization]]<br />
<br />
[[Synthesis of Nonspherical Colloidal Particles with Anisotropic Properties]]<br />
<br />
[[Surface roughness directed self-assembly of patchy particles into colloidal micelles]]<br />
<br />
[[Surfactants#Topics | Back to Topics.]]</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Surfactant&diff=26293Surfactant2012-11-27T05:59:39Z<p>Xingyu: /* Keyword in references: */</p>
<hr />
<div>Entry by Haifei Zhang, AP 225, Fall 2009<br />
<br />
== What is surfactant ==<br />
[[Image:Surfactant.png|right|thumb|A micelle—the lipophilic tails of the surfactant molecules remain on the inside of the micelle due to unfavourable interactions. ]]<br />
<br />
Surfactant is a combination of three words: Surface Active Agents. Surfactants are wetting agents that lower the surface tension of a liquid, allowing easier spreading, and lower the interfacial tension between two liquids. Surfactants are usually organic compounds that are amphiphilic, meaning they contain both hydrophobic groups (their "tails") and hydrophilic groups (their "heads"). Therefore, they are soluble in both organic solvents and water. <br />
<br />
As shown in the figure on right, the polar "heads" of the micelle, due to favourable interactions with water, form a hydrophilic outer layer that in effect protects the hydrophobic core of the micelle. The compounds that make up a micelle are typically amphiphilic in nature, meaning that not only are micelles soluble in protic solvents such as water but also in aprotic solvents as a reverse micelle<br />
<br />
== Properties ==<br />
Surfactants reduce the surface tension of water by adsorbing at the liquid-gas interface. They also reduce the interfacial tension between oil and water by adsorbing at the liquid-liquid interface. Many surfactants can also assemble in the bulk solution into aggregates. Examples of such aggregates are vesicles and micelles. The concentration at which surfactants begin to form micelles is known as the critical micelle concentration or CMC. When micelles form in water, their tails form a core that can encapsulate an oil droplet, and their (ionic/polar) heads form an outer shell that maintains favorable contact with water. When surfactants assemble in oil, the aggregate is referred to as a reverse micelle. In a reverse micelle, the heads are in the core and the tails maintain favorable contact with oil. Surfactants are also often classified into four primary groups; anionic, cationic, non-ionic, and zwitterionic (dual charge).<br />
Thermodynamics of the surfactant systems are of great importance, theoretically and practically. This is because surfactant systems represent systems between ordered and disordered states of matter. Surfactant solutions may contain an ordered phase (micelles) and a disordered phase (free surfactant molecules and/or ions in the solution).<br />
Ordinary washing up (dishwashing) detergent, for example, will promote water penetration in soil, but the effect would only last a few days (many standard laundry detergent powders contain levels of chemicals such as sodium and boron, which can be damaging to plants and should not be applied to soils). Commercial soil wetting agents will continue to work for a considerable period, but they will eventually be degraded by soil micro-organisms. Some can, however, interfere with the life-cycles of some aquatic organisms, so care should be taken to prevent run-off of these products into streams, and excess product should not be washed down.<br />
<br />
== Applications ==<br />
=== Many applications ===<br />
Surfactants play an important role in many practical applications and products, including: <br />
* Detergents<br />
* Fabric softener<br />
* Emulsifiers and Emulsions<br />
* Paints<br />
* Adhesives<br />
* Inks<br />
* Anti-fogging<br />
* Soil remediation<br />
* Dispersants<br />
* Wetting<br />
* Ski wax, snowboard wax<br />
* Deinking of recycled paper, both in flotation, washing and enzymatic processes<br />
* Foaming agents<br />
* Defoamers<br />
* Laxatives<br />
* Agrochemical formulations<br />
** Herbicides some<br />
** Insecticides<br />
* Quantum dot coating<br />
* Biocides (sanitizers)<br />
* Shampoo<br />
* Hair conditioners (after shampoo)<br />
* Spermicide (nonoxynol-9)<br />
* Firefighting<br />
* Pipeline, Liquid drag reducing agent<br />
* Alkali Surfactant Polymers (used to mobilize oil in oil wells)<br />
* Ferrofluids<br />
* Leak Detectors<br />
<br />
=== Detergent ===<br />
<br />
[[Image:Sur1.gif|thumb|300px|left|Schematic Sketch of Surfactant Molecule]]<br />
[[Image:Sur2.gif|thumb|300px|right|Schematic Sketch of Surfactant Molecules in Water]]<br />
<br />
A particular type of molecular structure performs as a surfactant. This molecule is made up of a water soluble (hydrophilic) and a water insoluble (hydrophobic) component.<br />
The hydrophobe is usually the equivalent of an 8 to 18 carbon hydrocarbon, and can be aliphatic, aromatic, or a mixture of both. The sources of hydrophobes are normally natural fats and oils, petroleum fractions, relatively short synthetic polymers, or relatively high molecular weight synthetic alcohols. The hydrophilic groups give the primary classification to surfactants, and are anionic, cationic and nonionic in nature. The anionic hydrophiles are the carboxylates (soaps), sulphates, sulphonates and phosphates. The cationic hydrophiles are some form of an amine product. The nonionic hydrophiles associate with water at the ether oxygens of a polyethylene glycol chain. In each case, the hydrophilic end of the surfactant is strongly attracted to the water molecules and the force of attraction between the hydrophobe and water is only slight. As a result, the surfactant molecules align themselves at the surface and internally so that the hydrophile end is toward the water and the hydrophobe is squeezed away from the water.<br />
<br />
Because of this characteristic behaviour of surfactants to orient at surfaces and to form micelles, all surfactants perform certain basic functions. However, each surfactant excels in certain functions and has others in which it is deficient.<br />
<br />
Foaming agents, emulsifiers, and dispersants are surfactants which suspend respectively, a gas, an immiscible liquid, or a solid in water or some other liquid. Although there is similarity in these functions, in practice the surfactants required to perform these functions differ widely. In emulsification, as an example - the selection of surfactant or surfactant system will depend on the materials to be used and the properties desired in the end product. An emulsion can be either oil droplets suspended in water, an oil in water (O/W) emulsion, water suspended in a continuous oil phase, water in oil (W/O) emulsion, or a mixed emulsion. Selection of surfactants, orders of addition and relative amounts of the two phases determine the class of emulsion.<br />
<br />
Each of these three functions is related to the surfactant absorbing at a surface, either gas, liquid or solid with the hydrophilic ends of the molecules oriented to the water phase. The surfactants form what amounts to a protective coating around the suspended material, and these hydrophilic ends associate with the neighbouring water molecules. In addition to surfactant effects the stability of these suspensions is related to the particle size and density of the suspended material.<br />
<br />
[[Image:Detergentgif.gif|thumb|400px|left|Simplified Illustration of Detergency]]<br />
Solubilisation is a function closely related to emulsification. As the size of the emulsified droplet becomes smaller, a condition is reached where this droplet and the surfactant micelle are the same size.<br />
<br />
At this stage, an oil droplet can be imagined as being in solution in the hydrophobic tails of the surfactant and the term solubilisation is used. Emulsions are milky in appearance and solubilised oils, for example - are clear to the eye.<br />
<br />
The function of detergency or cleaning is a complex combination of all the previous functions. The surface to be cleaned and the soil to be removed must initially be wet and the soils suspended, solubilised, dissolved or separated in some way so that the soil will not just re-deposit on the surface in question<br />
<br />
<br />
<br />
<br />
== References ==<br />
[1] http://en.wikipedia.org/wiki/Surfactant<br />
<br />
[2] http://www.chemistry.co.nz/surfactants.htm<br />
<br />
[3] [[The Science of Chocolate: interactive activities on phase transitions, emulsification, and nucleation]]<br />
<br />
<br />
<br />
<br />
== Keyword in references: ==<br />
<br />
[[Modeling Surfactant Adsorption on Hydrophobic Surfaces]]<br />
<br />
[[Amphiphilic Crescent-Moon-Shaped Microparticles Formed by Selective Adsorption of Colloids]]<br />
<br />
[[Biomimetic Morphogenesis of Calcium Carbonate in Mixed Solutions of Surfactants and Double-Hydrophilic Block Copolymers]]<br />
<br />
[[Krafft Points, Critical Micelle Concentrations, Surface Tension, and Solubilizing Power of Aqueous Solutions of Fluorinated Surfactants]]<br />
<br />
[[Order–disorder transition induced by surfactant micelles in single-walled carbon nanotubes dispersions]]<br />
<br />
[[Patterned Colloidal Coating Using Adhesive Emulsions]]<br />
<br />
[[Reversible aggregation of responsive polymer-stabilized colloids and the pH-dependent formation of porous scaffolds]]<br />
<br />
[[Enriching libraries of high-aspect-ratio micro- or nanostructures by rapid, low-cost, benchtop nanofabrication]]<br />
<br />
[[Liquid-infused structured surfaces with exceptional anti-biofouling performance]]<br />
<br />
[[Liquid-Infused Nanostructured Surfaces with Extreme Anti-Ice and Anti-Frost Performance]]<br />
<br />
[[Dynamics of foam drainage]]<br />
<br />
[[Dynamic mechanisms for apparent slip on hydrophobic surfaces]]<br />
<br />
[[Phase diagrams for sonoluminescing bubbles]]<br />
<br />
[[Non-coalescence of oppositely charged droplets in pH-sensitive emulsions]]<br />
<br />
[[Yielding and Flow of Monodisperse Emulsions]]<br />
<br />
[[Swollen Vesicles and Multiple Emulsions from Block Copolymers]]<br />
<br />
[[Spontaneous Formation of Lipid Structures at Oil/Water/Lipid Interfaces]]<br />
<br />
[[Production of Unilamellar Vesicles Using an Inverted Emulsion]]<br />
<br />
[[Short-time self-diffusion of nearly hard spheres at an oil–water interface]]<br />
<br />
[[Hierarchical Porous Materials Made by Drying Complex Suspensions]]<br />
<br />
[[Double Emulsion Droplets as Microreactors for Synthesis of Mesoporous Hydroxyapatite]]<br />
<br />
[[Microfluidic Fabrication of Monodisperse Biocompatible and Biodegradable Polymersomes with Controlled Permeability]]<br />
<br />
[[Droplet Microfluidics for Fabrication of Non-Spherical Particles]]<br />
<br />
[[Arrested Coalescence of Particle-coated Droplets into Nonspherical Supracolloidal Structures]]<br />
<br />
[[Early development drug formulation on a chip: Fabrication of nanoparticles using a microfluidic spray dryer]]<br />
<br />
[[Fabrication of Monodisperse Toroidal Particles by Polymer Solidification in Microfluidics]]<br />
<br />
[[Asymmetric functionalization of colloidal dimer particles with gold nanoparticles]]<br />
<br />
[[Single-bubble sonoluminescence]]<br />
<br />
[[Four-phase merging in sessile compound drops]]<br />
<br />
[[Elasticity of an interfacial particle raft]]<br />
<br />
[[Dynamics of Surfactant-Driven Fracture of Particle Rafts]]<br />
<br />
[[Mechanics of Interfacial Composite Materials]]<br />
<br />
[[Gravitational Stability of Suspensions of Attractive Colloidal Particles]]<br />
<br />
[[Elastohydrodynamics of wet bristles, carpets and brushes]]<br />
<br />
[[Shock-driven jamming and periodic fracture of particulate rafts]]<br />
<br />
[[Colloidal spheres confined by liquid droplets: Geometry, physics, and physical chemistry]]<br />
<br />
[[Measuring Dynamics and Interactions of Colloidal Particles with Digital Holographic Microscopy]]<br />
<br />
[[Self-Assembly of Polyhedral Hybrid Colloidal Particles]]<br />
<br />
[[Surfactant-Assisted Synthesis of Uniform Titania Microspheres and Their Clusters]]<br />
<br />
[[Microtubule Protofilament Number Is Modulated in a Stepwise Fashion by the Charge Density of an Enveloping Layer]]<br />
<br />
[[￼Cationic liposome–microtubule complexes: Pathways to the formation of two-state lipid–protein nanotubes with open or closed ends]]<br />
<br />
[[Fluctuations in membranes with crystalline and hexatic order]]<br />
<br />
[[Biomimetic Isotropic Nanostructures for Structural Coloration]]<br />
<br />
[[Comparison of low-amplitude oscillatory shear in experimental and computational studies of model foams]]<br />
<br />
[[Short-range order and near-field effects on optical scattering and structural coloration]]<br />
<br />
[[Stable island arrays by height-constrained Stranski–Krastanov growth]]<br />
<br />
[[Nanoscale Domain Stability in Organic Monolayers on Metals]]<br />
<br />
[[New directions in mechanics]]<br />
<br />
[[Measuring the elastic modulus of microgels using microdrops]]<br />
<br />
[[Surface Energy as a Barrier to Creasing of Elastomer Films: An Elastic Analogy to Classical Nucleation]]<br />
<br />
[[Novel Colloidal Interactions in Anisotropic Fluids]]<br />
<br />
[[Surfactant-Mediated Two-Dimensional Crystallization of Colloidal Crystals]]<br />
<br />
[[High-throughput injection with microfluidics using picoinjectors]]<br />
<br />
[[Air-bubble-triggered drop formation in microfluidics]]<br />
<br />
[[Syringe-vacuum microfluidics: A portable technique to create monodisperse emulsions]]<br />
<br />
[[Monodisperse Gas-Filled Microparticles from Reactions in Double Emulsions]]<br />
<br />
[[Universal non-diffusive slow dynamics in aging soft matter]]<br />
<br />
[[THE STRUCTURE AND STRENGTH OF FLOCS OF PRECIPITATED CALCIUM CARBONATE INDUCED BY VARIOUS POLYMERS USED IN PAPERMAKING]]<br />
<br />
[[Patterned Colloidal Coating Using Adhesive Emulsions]]<br />
<br />
[[Inverted and multiple nematic emulsions]]<br />
<br />
[[Osmotic pressure and viscoelastic shear moduli of concentrated emulsions]]<br />
<br />
[[Micro!uidic fabrication of smart microgels from macromolecular precursors]]<br />
<br />
[[Functionalized glass coating for PDMS microfluidic devices]]<br />
<br />
[[Bacillus subtilis spreads by surfing on waves of surfactant]]<br />
<br />
[[Structure of adhesive emulsions]]<br />
<br />
[[Droplet-Based Microfluidics for Emulsion and Solvent Evaporation Synthesis of Monodisperse Mesoporous Silica Microspheres]]<br />
<br />
[[Rheology of attractive emulsions]]<br />
<br />
[[Colloidosomes: Selectively Permeable Capsules Composed of Colloidal Particles]]<br />
<br />
[[Interactions between surfactant-coated surfaces in hydrocarbon liquids containing functionalized polymer dispersant]]<br />
<br />
[[Self-Assembled Polymer Membrane Capsules Inflated by Osmotic Pressure]]<br />
<br />
[[Rheology of Binary Colloidal Structures Assembled via Specific Biological Cross-Linking]]<br />
<br />
[[Biocompatible surfactants for water-in-fluorocarbon emulsions]]<br />
<br />
[[Self-assembled Shells Composed of Colloidal Particles: Fabrication and Characterization]]<br />
<br />
[[Amphiphilic Crescent-Moon-Shaped Microparticles Formed by Selective Adsorption of Colloids]]<br />
<br />
[[Colloid Surfactants for Emulsion Stabilization]]<br />
<br />
[[Synthesis of Nonspherical Colloidal Particles with Anisotropic Properties]]<br />
<br />
[[Gravitational Stability of Suspensions of Attractive Colloidal Particles]]<br />
<br />
[[Surface roughness directed self-assembly of patchy particles into colloidal micelles]]</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Modeling_Surfactant_Adsorption_on_Hydrophobic_Surfaces&diff=26292Modeling Surfactant Adsorption on Hydrophobic Surfaces2012-11-27T05:55:19Z<p>Xingyu: </p>
<hr />
<div>== General Information ==<br />
'''Authors:''' S. O. Nielsen, G. Srinivas, C. F. Lopez, and M. L. Klein.<br />
<br />
'''Publication:''' Physical Review Letters<br />
<br />
'''Keywords:''' [[Surfactant]], [[micelle]], [[adsorption]]<br />
<br />
== Summary ==<br />
As the authors mentioned, the self-assembly behavior of surfactants is useful in many contexts, including manipulation of single wall carbon nanotubes or solubilization of hydrophobic quantum dots.<br />
However, such processes are not well understood because their dimensional and temporal scales are ill-suited for experiments or atomistic simulations.<br />
This study presents a coarse grain method used to simulate surfactant (aqueous n-alkyl poly(ethylene oxide) adsorption on an hydrophobic surface (graphite).<br />
This is done by modeling the surface with an implicit potential, coarse graining for interactions using respective center masses, then returning to the explicit model for the surface.<br />
The simulation results agree with experimental measurements using atomic force microscopy and demonstrate interesting behavior for adsorption.<br />
<br />
==Theory==<br />
[[Image:msa1.jpeg|thumb|300px|right| Fig. 1: a) the probability distribution for the c.m. of two bonded particles interacting with the surface, b) the probability distribution for for z = 3.38Å, denoted by the filled circle in a), c) the potential energy for one particle, c.m. of 2 unbonded and bonded particles, d) the potential for -O-<math>CH_2</math>- in poly(ethylene oxide) due to a graphite surface From [1].]]<br />
For the implicit model, the authors used a semi-infinite geometry with the surface as a continuum for z ≤ 0 and atoms in the liquid phase in z > 0.<br />
They then used a Lennard-Jones potential, U(z), for the potential energy of the atom at a height z.<br />
For the coarse graining, groups of atoms are reparameterized by their center of masses (c.m.) for the interactions with the solid surface.<br />
Probability distributions are used for the interactions rather than potential energies to aid the coarse graining.<br />
For example, the joint probability that particle 1 is at a height <math>z_1</math> and particle 2 at height <math>z_2 </math> is given by:<br />
<math>P(z_1,z_2) = e^{-\beta U(z_1)} e^{-\beta U(z_2)}</math><br />
where <math>\beta</math> denotes the inverse of Boltzmann's constant times the temperature. <br />
So, the probability that c.m. for a pair of non-interacting particles is at height z is given by the marginal distribution:<br />
<math>P(z)=(2z)^{-1} \int_{0}^{2z} e^{-\beta U(z_1)} e^{-\beta U(2z-z_1)} dz_1 </math><br />
and similarly, for particles with some interaction <math>P_I(z_1,z_2)</math> independent of the surface, the probability that the center of mass is at height z is then<br />
<math>P(z)=\frac{\int_{0}^{2z} e^{-\beta U(z_1)}e^{-\beta U(2z-z_1)}P_I(2z_1-z) dz_1 }{\int_0^{2z}P_I(2z_1-2z) dz_1} </math><br />
which are appropriately normalized and have features visualized in Fig. 1<br />
<br />
==Simulation==<br />
Applying these probability distributions for large numbers of particles is more tricky.<br />
One issue is that pair interactions are often non-radial (e.g. conformational details for poly(ethylene oxide) mentioned in the paper).<br />
Another challenge is the large number of particles that must be incorporated in the simulation.<br />
To alleviate this, common coarse graining methods combine several (>2) heavy atoms and H atoms associated with them to a single position.<br />
The authors explained that a judicious choice for the implementation of coarse grain is required with a -O-<math>CH_2</math>- piece of poly(ethylene oxide).<br />
One method is to coarse grain <math>CH_2</math> then combine it with O.<br />
Another method is to coarse grain CHO, then combine it with H.<br />
The third method is to coarse grain HH and CO separately, then combine the pairs.<br />
Only first and third are reasonable since the first combines heavy atoms (and their associated H atoms in groups) and the third retains symmetry by first coarse graining light and heavy atoms together then combining them.<br />
The discrepancy for the second method is shown in Fig. 1d where the potential energy is different than those from the other methods.<br />
These principles are applied for a coarse grain simulation of aqueous n-alkyl poly(ethylene oxide), specifically C12E5, adsorbing on a graphite surface.<br />
The nonionic surfactant CnEm were coarse grained with 3 <math>CH_2</math> group at each hydrophobic site and one ethylene monomer at each hydrophilic site in order to observe the overall shape of the surfactant.<br />
Specific parameters such used to model details of the interactions were previously measured experimentally with bulk density, surface tension, and inter-facial surface tension.<br />
The diffusion coefficients were reported to have been calculated from mean square displacement curves for binary mixtures of C12E5 at different concentrations and water and confirmed by experiment.<br />
<br />
==Results and discussion==<br />
[[Image:msa2.jpeg|thumb|300px|left| Fig. 2: Simulation results for C12E5 adsorption onto a graphite surface at t = 0, 0.64, 3.3, 3.75, 4.3, and 6 ns (a-f) with solid-liquid interfaces at the top and bottom separated by 12 nm and 3D periodic boundary conditions. From [1].]]<br />
As the authors mentioned, the self-assembly of nonionic surfactants at graphite-liquid interfaces have been characterized using methods such as atomic force microscopy.<br />
C12E5 was found to form cylindrical micelles in solution and hemicylinders at the graphite-liquid interface.<br />
The results from the simulation (Fig. 2) what that initially, the surfactants coat the graphite surface or begin to self-assemble into spherical micelles (but never fuse completely since they are saturated) far away from the surface (Fig. 2b).<br />
However, when a micelle approaches the partly coated surface, the head groups in the micelle interact with those adsorbed to the surface.<br />
The authors describe what occurs next as "feeding," where two sets of head groups open so that the hydrophobic tails of the micelles touch those of the monolayer on the graphite surface (Fig. 2c,d)<br />
The tails then quickly disperse onto the surface and the head groups rearrange so that the entire micelle is adsorbed onto the surface (Fig. 2e).<br />
Reorganization then occurs and hemicylinders of surfactants form on the graphite surface with spacing ~5 nm which agrees with experimental data (Fig. 2f).<br />
Simulations with C9E3 gave similar feeding phenomena but the final state is that of a monolayer with the surfactants perpendicular to the surface, as predicted by the geometry of C9E3 and agrees with experiment.<br />
An explicit representation of the surface was also recovered so that more general and detailed surface geometries can be modeled.<br />
The computational techniques are also four orders of magnitude more efficient than atomistic simulations.<br />
As the authors mentioned, this holds promise for nanoscale studies of hydrophobic surfaces interacting with aqueous surfactant solutions.<br />
This includes examining how different surfactants solubilize carbon nanotubes and depositing quantum dots on a substrate.<br />
<br />
==References==<br />
[1] Nielsen, S. O., Srinivas, G., Lopez, C. F., & Klein, M. L. (2005). Modeling surfactant adsorption on hydrophobic surfaces. Physical review letters, 94(22), 228301.<br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Modeling_Surfactant_Adsorption_on_Hydrophobic_Surfaces&diff=26291Modeling Surfactant Adsorption on Hydrophobic Surfaces2012-11-27T05:51:14Z<p>Xingyu: /* Simulation */</p>
<hr />
<div>== General Information ==<br />
'''Authors:''' S. O. Nielsen, G. Srinivas, C. F. Lopez, and M. L. Klein.<br />
<br />
'''Publication:''' Physical Review Letters<br />
<br />
'''Keywords:''' [[Surfactant]], [[micelle]], [[adsorption]]<br />
<br />
== Summary ==<br />
As the authors mentioned, the self-assembly behavior of surfactants is useful in many contexts, including manipulation of single wall carbon nanotubes or solubilization of hydrophobic quantum dots.<br />
However, such processes are not well understood because their dimensional and temporal scales are ill-suited for experiments or atomistic simulations.<br />
This study presents a coarse grain method used to simulate surfactant (aqueous n-alkyl poly(ethylene oxide) adsorption on an hydrophobic surface (graphite).<br />
This is done by modeling the surface with an implicit potential, coarse graining for interactions using respective center masses, then returning to the explicit model for the surface.<br />
The simulation results agree with experimental measurements using atomic force microscopy and demonstrate interesting behavior for adsorption.<br />
<br />
==Theory==<br />
[[Image:msa1.jpeg|thumb|300px|right| Fig. 1: a) the probability distribution for the c.m. of two bonded particles interacting with the surface, b) the probability distribution for for z = 3.38Å, denoted by the filled circle in a), c) the potential energy for one particle, c.m. of 2 unbonded and bonded particles, d) the potential for -O-<math>CH_2</math>- in poly(ethylene oxide) due to a graphite surface From [1].]]<br />
For the implicit model, the authors used a semi-infinite geometry with the surface as a continuum for z ≤ 0 and atoms in the liquid phase in z > 0.<br />
They then used a Lennard-Jones potential, U(z), for the potential energy of the atom at a height z.<br />
For the coarse graining, groups of atoms are reparameterized by their center of masses (c.m.) for the interactions with the solid surface.<br />
Probability distributions are used for the interactions rather than potential energies to aid the coarse graining.<br />
For example, the joint probability that particle 1 is at a height <math>z_1</math> and particle 2 at height <math>z_2 </math> is given by:<br />
<math>P(z_1,z_2) = e^{-\beta U(z_1)} e^{-\beta U(z_2)}</math><br />
where <math>\beta</math> denotes the inverse of Boltzmann's constant times the temperature. <br />
So, the probability that c.m. for a pair of non-interacting particles is at height z is given by the marginal distribution:<br />
<math>P(z)=(2z)^{-1} \int_{0}^{2z} e^{-\beta U(z_1)} e^{-\beta U(2z-z_1)} dz_1 </math><br />
and similarly, for particles with some interaction <math>P_I(z_1,z_2)</math> independent of the surface, the probability that the center of mass is at height z is then<br />
<math>P(z)=\frac{\int_{0}^{2z} e^{-\beta U(z_1)}e^{-\beta U(2z-z_1)}P_I(2z_1-z) dz_1 }{\int_0^{2z}P_I(2z_1-2z) dz_1} </math><br />
which are appropriately normalized and have features visualized in Fig. 1<br />
<br />
==Simulation==<br />
Applying these probability distributions for large numbers of particles is more tricky.<br />
One issue is that pair interactions are often non-radial (e.g. conformational details for poly(ethylene oxide) mentioned in the paper).<br />
Another challenge is the large number of particles that must be incorporated in the simulation.<br />
To alleviate this, common coarse graining methods combine several (>2) heavy atoms and H atoms associated with them to a single position.<br />
The authors explained that a judicious choice for the implementation of coarse grain is required with a -O-<math>CH_2</math>- piece of poly(ethylene oxide).<br />
One method is to coarse grain <math>CH_2</math> then combine it with O.<br />
Another method is to coarse grain CHO, then combine it with H.<br />
The third method is to coarse grain HH and CO separately, then combine the pairs.<br />
Only first and third are reasonable since the first combines heavy atoms (and their associated H atoms in groups) and the third retains symmetry by first coarse graining light and heavy atoms together then combining them.<br />
The discrepancy for the second method is shown in Fig. 1d where the potential energy is different than those from the other methods.<br />
These principles are applied for a coarse grain simulation of aqueous n-alkyl poly(ethylene oxide), specifically C12E5, adsorbing on a graphite surface.<br />
The nonionic surfactant CnEm were coarse grained with 3 <math>CH_2</math> group at each hydrophobic site and one ethylene monomer at each hydrophilic site in order to observe the overall shape of the surfactant.<br />
Specific parameters such used to model details of the interactions were previously measured experimentally with bulk density, surface tension, and inter-facial surface tension.<br />
The diffusion coefficients were reported to have been calculated from mean square displacement curves for binary mixtures of C12E5 at different concentrations and water and confirmed by experiment.<br />
<br />
==Results and discussion==<br />
[[Image:msa2.jpeg|thumb|300px|left| Fig. 2: _ From [1].]]<br />
As the authors mentioned, the self-assembly of nonionic surfactants at graphite-liquid interfaces have been characterized using methods such as atomic force microscopy.<br />
C12E5 was found to form cylindrical micelles in solution and hemicylinders at the graphite-liquid interface.<br />
The results from the simulation (Fig. 2) what that initially, the surfactants coat the graphite surface or begin to self-assemble into spherical micelles (but never fuse completely since they are saturated) far away from the surface (Fig. 2B).<br />
However, when a micelle approaches the partly coated surface, the head groups in the micelle interact with those adsorbed to the surface.<br />
The authors describe what occurs next as "feeding," where two sets of head groups open so that the hydrophobic tails of the micelles touch those of the monolayer on the graphite surface (Fig. 2C-D)<br />
The tails then quickly disperse onto the surface and the head groups rearrange so that the entire micelle is adsorbed onto the surface (Fig. 2E).<br />
Reorganization then occurs and hemicylinders of surfactants form on the graphite surface with spacing ~5 nm which agrees with experimental data.<br />
Simulations with C9E3 gave similar feeding phenomena but the final state is that of a monolayer with the surfactants perpendicular to the surface, as predicted by the geometry of C9E3 and agrees with experiment.<br />
An explicit representation of the surface was also recovered so that more general and detailed surface geometries can be modeled.<br />
The computational techniques are also four orders of magnitude more efficient than atomistic simulations.<br />
As the authors mentioned, this holds promise for nanoscale studies of hydrophobic surfaces interacting with aqueous surfactant solutions.<br />
This includes examining how different surfactants solubilize carbon nanotubes and depositing quantum dots on a substrate.<br />
<br />
==References==<br />
[1] Nielsen, S. O., Srinivas, G., Lopez, C. F., & Klein, M. L. (2005). Modeling surfactant adsorption on hydrophobic surfaces. Physical review letters, 94(22), 228301.<br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Modeling_Surfactant_Adsorption_on_Hydrophobic_Surfaces&diff=26290Modeling Surfactant Adsorption on Hydrophobic Surfaces2012-11-27T05:49:46Z<p>Xingyu: /* Simulation */</p>
<hr />
<div>== General Information ==<br />
'''Authors:''' S. O. Nielsen, G. Srinivas, C. F. Lopez, and M. L. Klein.<br />
<br />
'''Publication:''' Physical Review Letters<br />
<br />
'''Keywords:''' [[Surfactant]], [[micelle]], [[adsorption]]<br />
<br />
== Summary ==<br />
As the authors mentioned, the self-assembly behavior of surfactants is useful in many contexts, including manipulation of single wall carbon nanotubes or solubilization of hydrophobic quantum dots.<br />
However, such processes are not well understood because their dimensional and temporal scales are ill-suited for experiments or atomistic simulations.<br />
This study presents a coarse grain method used to simulate surfactant (aqueous n-alkyl poly(ethylene oxide) adsorption on an hydrophobic surface (graphite).<br />
This is done by modeling the surface with an implicit potential, coarse graining for interactions using respective center masses, then returning to the explicit model for the surface.<br />
The simulation results agree with experimental measurements using atomic force microscopy and demonstrate interesting behavior for adsorption.<br />
<br />
==Theory==<br />
[[Image:msa1.jpeg|thumb|300px|right| Fig. 1: a) the probability distribution for the c.m. of two bonded particles interacting with the surface, b) the probability distribution for for z = 3.38Å, denoted by the filled circle in a), c) the potential energy for one particle, c.m. of 2 unbonded and bonded particles, d) the potential for -O-<math>CH_2</math>- in poly(ethylene oxide) due to a graphite surface From [1].]]<br />
For the implicit model, the authors used a semi-infinite geometry with the surface as a continuum for z ≤ 0 and atoms in the liquid phase in z > 0.<br />
They then used a Lennard-Jones potential, U(z), for the potential energy of the atom at a height z.<br />
For the coarse graining, groups of atoms are reparameterized by their center of masses (c.m.) for the interactions with the solid surface.<br />
Probability distributions are used for the interactions rather than potential energies to aid the coarse graining.<br />
For example, the joint probability that particle 1 is at a height <math>z_1</math> and particle 2 at height <math>z_2 </math> is given by:<br />
<math>P(z_1,z_2) = e^{-\beta U(z_1)} e^{-\beta U(z_2)}</math><br />
where <math>\beta</math> denotes the inverse of Boltzmann's constant times the temperature. <br />
So, the probability that c.m. for a pair of non-interacting particles is at height z is given by the marginal distribution:<br />
<math>P(z)=(2z)^{-1} \int_{0}^{2z} e^{-\beta U(z_1)} e^{-\beta U(2z-z_1)} dz_1 </math><br />
and similarly, for particles with some interaction <math>P_I(z_1,z_2)</math> independent of the surface, the probability that the center of mass is at height z is then<br />
<math>P(z)=\frac{\int_{0}^{2z} e^{-\beta U(z_1)}e^{-\beta U(2z-z_1)}P_I(2z_1-z) dz_1 }{\int_0^{2z}P_I(2z_1-2z) dz_1} </math><br />
which are appropriately normalized and have features visualized in Fig. 1<br />
<br />
==Simulation==<br />
Applying these probability distributions for large numbers of particles is more tricky.<br />
One issue is that pair interactions are often non-radial (e.g. conformational details for poly(ethylene oxide) mentioned in the paper).<br />
Another challenge is the large number of particles that must be incorporated in the simulation.<br />
To alleviate this, common coarse graining methods combine several (>2) heavy atoms and H atoms associated with them to a single position.<br />
The authors explained that a judicious choice for the implementation of coarse grain is required with a -O-<math>CH_2</math>- piece of poly(ethylene oxide).<br />
One method is to coarse grain <math>CH_2</math> then combine it with O.<br />
Another method is to coarse grain CHO, then combine it with H.<br />
The third method is to coarse grain HH and CO separately, then combine the pairs.<br />
The first and third are reasonable since the first combines heavy atoms (and their associated H atoms in groups) and the third retains symmetry by first coarse graining light and heavy atoms together then combining them.<br />
These principles are applied for a coarse grain simulation of aqueous n-alkyl poly(ethylene oxide), specifically C12E5, adsorbing on a graphite surface.<br />
The nonionic surfactant CnEm were coarse grained with 3 <math>CH_2</math> group at each hydrophobic site and one ethylene monomer at each hydrophilic site in order to observe the overall shape of the surfactant.<br />
Specific parameters such used to model details of the interactions were previously measured experimentally with bulk density, surface tension, and inter-facial surface tension.<br />
The diffusion coefficients were reported to have been calculated from mean square displacement curves for binary mixtures of C12E5 at different concentrations and water and confirmed by experiment.<br />
<br />
==Results and discussion==<br />
[[Image:msa2.jpeg|thumb|300px|left| Fig. 2: _ From [1].]]<br />
As the authors mentioned, the self-assembly of nonionic surfactants at graphite-liquid interfaces have been characterized using methods such as atomic force microscopy.<br />
C12E5 was found to form cylindrical micelles in solution and hemicylinders at the graphite-liquid interface.<br />
The results from the simulation (Fig. 2) what that initially, the surfactants coat the graphite surface or begin to self-assemble into spherical micelles (but never fuse completely since they are saturated) far away from the surface (Fig. 2B).<br />
However, when a micelle approaches the partly coated surface, the head groups in the micelle interact with those adsorbed to the surface.<br />
The authors describe what occurs next as "feeding," where two sets of head groups open so that the hydrophobic tails of the micelles touch those of the monolayer on the graphite surface (Fig. 2C-D)<br />
The tails then quickly disperse onto the surface and the head groups rearrange so that the entire micelle is adsorbed onto the surface (Fig. 2E).<br />
Reorganization then occurs and hemicylinders of surfactants form on the graphite surface with spacing ~5 nm which agrees with experimental data.<br />
Simulations with C9E3 gave similar feeding phenomena but the final state is that of a monolayer with the surfactants perpendicular to the surface, as predicted by the geometry of C9E3 and agrees with experiment.<br />
An explicit representation of the surface was also recovered so that more general and detailed surface geometries can be modeled.<br />
The computational techniques are also four orders of magnitude more efficient than atomistic simulations.<br />
As the authors mentioned, this holds promise for nanoscale studies of hydrophobic surfaces interacting with aqueous surfactant solutions.<br />
This includes examining how different surfactants solubilize carbon nanotubes and depositing quantum dots on a substrate.<br />
<br />
==References==<br />
[1] Nielsen, S. O., Srinivas, G., Lopez, C. F., & Klein, M. L. (2005). Modeling surfactant adsorption on hydrophobic surfaces. Physical review letters, 94(22), 228301.<br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Modeling_Surfactant_Adsorption_on_Hydrophobic_Surfaces&diff=26289Modeling Surfactant Adsorption on Hydrophobic Surfaces2012-11-27T05:49:27Z<p>Xingyu: /* Theory */</p>
<hr />
<div>== General Information ==<br />
'''Authors:''' S. O. Nielsen, G. Srinivas, C. F. Lopez, and M. L. Klein.<br />
<br />
'''Publication:''' Physical Review Letters<br />
<br />
'''Keywords:''' [[Surfactant]], [[micelle]], [[adsorption]]<br />
<br />
== Summary ==<br />
As the authors mentioned, the self-assembly behavior of surfactants is useful in many contexts, including manipulation of single wall carbon nanotubes or solubilization of hydrophobic quantum dots.<br />
However, such processes are not well understood because their dimensional and temporal scales are ill-suited for experiments or atomistic simulations.<br />
This study presents a coarse grain method used to simulate surfactant (aqueous n-alkyl poly(ethylene oxide) adsorption on an hydrophobic surface (graphite).<br />
This is done by modeling the surface with an implicit potential, coarse graining for interactions using respective center masses, then returning to the explicit model for the surface.<br />
The simulation results agree with experimental measurements using atomic force microscopy and demonstrate interesting behavior for adsorption.<br />
<br />
==Theory==<br />
[[Image:msa1.jpeg|thumb|300px|right| Fig. 1: a) the probability distribution for the c.m. of two bonded particles interacting with the surface, b) the probability distribution for for z = 3.38Å, denoted by the filled circle in a), c) the potential energy for one particle, c.m. of 2 unbonded and bonded particles, d) the potential for -O-<math>CH_2</math>- in poly(ethylene oxide) due to a graphite surface From [1].]]<br />
For the implicit model, the authors used a semi-infinite geometry with the surface as a continuum for z ≤ 0 and atoms in the liquid phase in z > 0.<br />
They then used a Lennard-Jones potential, U(z), for the potential energy of the atom at a height z.<br />
For the coarse graining, groups of atoms are reparameterized by their center of masses (c.m.) for the interactions with the solid surface.<br />
Probability distributions are used for the interactions rather than potential energies to aid the coarse graining.<br />
For example, the joint probability that particle 1 is at a height <math>z_1</math> and particle 2 at height <math>z_2 </math> is given by:<br />
<math>P(z_1,z_2) = e^{-\beta U(z_1)} e^{-\beta U(z_2)}</math><br />
where <math>\beta</math> denotes the inverse of Boltzmann's constant times the temperature. <br />
So, the probability that c.m. for a pair of non-interacting particles is at height z is given by the marginal distribution:<br />
<math>P(z)=(2z)^{-1} \int_{0}^{2z} e^{-\beta U(z_1)} e^{-\beta U(2z-z_1)} dz_1 </math><br />
and similarly, for particles with some interaction <math>P_I(z_1,z_2)</math> independent of the surface, the probability that the center of mass is at height z is then<br />
<math>P(z)=\frac{\int_{0}^{2z} e^{-\beta U(z_1)}e^{-\beta U(2z-z_1)}P_I(2z_1-z) dz_1 }{\int_0^{2z}P_I(2z_1-2z) dz_1} </math><br />
which are appropriately normalized and have features visualized in Fig. 1<br />
<br />
==Simulation==<br />
Applying these probability distributions for large numbers of particles is more tricky.<br />
One issue is that pair interactions are often non-radial (e.g. conformational details for poly(ethylene oxide) mentioned in the paper).<br />
Another challenge is the large number of particles that must be incorporated in the simulation.<br />
To alleviate this, common coarse graining methods combine several (>2) heavy atoms and H atoms associated with them to a single position.<br />
The authors explained that a judicious choice for the implementation of coarse grain is required with a <math>-O-CH_2-</math> piece of poly(ethylene oxide).<br />
One method is to coarse grain <math>CH_2</math> then combine it with O.<br />
Another method is to coarse grain CHO, then combine it with H.<br />
The third method is to coarse grain HH and CO separately, then combine the pairs.<br />
The first and third are reasonable since the first combines heavy atoms (and their associated H atoms in groups) and the third retains symmetry by first coarse graining light and heavy atoms together then combining them.<br />
These principles are applied for a coarse grain simulation of aqueous n-alkyl poly(ethylene oxide), specifically C12E5, adsorbing on a graphite surface.<br />
The nonionic surfactant CnEm were coarse grained with 3 <math>CH_2</math> group at each hydrophobic site and one ethylene monomer at each hydrophilic site in order to observe the overall shape of the surfactant.<br />
Specific parameters such used to model details of the interactions were previously measured experimentally with bulk density, surface tension, and inter-facial surface tension.<br />
The diffusion coefficients were reported to have been calculated from mean square displacement curves for binary mixtures of C12E5 at different concentrations and water and confirmed by experiment.<br />
<br />
==Results and discussion==<br />
[[Image:msa2.jpeg|thumb|300px|left| Fig. 2: _ From [1].]]<br />
As the authors mentioned, the self-assembly of nonionic surfactants at graphite-liquid interfaces have been characterized using methods such as atomic force microscopy.<br />
C12E5 was found to form cylindrical micelles in solution and hemicylinders at the graphite-liquid interface.<br />
The results from the simulation (Fig. 2) what that initially, the surfactants coat the graphite surface or begin to self-assemble into spherical micelles (but never fuse completely since they are saturated) far away from the surface (Fig. 2B).<br />
However, when a micelle approaches the partly coated surface, the head groups in the micelle interact with those adsorbed to the surface.<br />
The authors describe what occurs next as "feeding," where two sets of head groups open so that the hydrophobic tails of the micelles touch those of the monolayer on the graphite surface (Fig. 2C-D)<br />
The tails then quickly disperse onto the surface and the head groups rearrange so that the entire micelle is adsorbed onto the surface (Fig. 2E).<br />
Reorganization then occurs and hemicylinders of surfactants form on the graphite surface with spacing ~5 nm which agrees with experimental data.<br />
Simulations with C9E3 gave similar feeding phenomena but the final state is that of a monolayer with the surfactants perpendicular to the surface, as predicted by the geometry of C9E3 and agrees with experiment.<br />
An explicit representation of the surface was also recovered so that more general and detailed surface geometries can be modeled.<br />
The computational techniques are also four orders of magnitude more efficient than atomistic simulations.<br />
As the authors mentioned, this holds promise for nanoscale studies of hydrophobic surfaces interacting with aqueous surfactant solutions.<br />
This includes examining how different surfactants solubilize carbon nanotubes and depositing quantum dots on a substrate.<br />
<br />
==References==<br />
[1] Nielsen, S. O., Srinivas, G., Lopez, C. F., & Klein, M. L. (2005). Modeling surfactant adsorption on hydrophobic surfaces. Physical review letters, 94(22), 228301.<br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Modeling_Surfactant_Adsorption_on_Hydrophobic_Surfaces&diff=26288Modeling Surfactant Adsorption on Hydrophobic Surfaces2012-11-27T05:48:55Z<p>Xingyu: /* Theory */</p>
<hr />
<div>== General Information ==<br />
'''Authors:''' S. O. Nielsen, G. Srinivas, C. F. Lopez, and M. L. Klein.<br />
<br />
'''Publication:''' Physical Review Letters<br />
<br />
'''Keywords:''' [[Surfactant]], [[micelle]], [[adsorption]]<br />
<br />
== Summary ==<br />
As the authors mentioned, the self-assembly behavior of surfactants is useful in many contexts, including manipulation of single wall carbon nanotubes or solubilization of hydrophobic quantum dots.<br />
However, such processes are not well understood because their dimensional and temporal scales are ill-suited for experiments or atomistic simulations.<br />
This study presents a coarse grain method used to simulate surfactant (aqueous n-alkyl poly(ethylene oxide) adsorption on an hydrophobic surface (graphite).<br />
This is done by modeling the surface with an implicit potential, coarse graining for interactions using respective center masses, then returning to the explicit model for the surface.<br />
The simulation results agree with experimental measurements using atomic force microscopy and demonstrate interesting behavior for adsorption.<br />
<br />
==Theory==<br />
[[Image:msa1.jpeg|thumb|300px|right| Fig. 1: a) the probability distribution for the c.m. of two bonded particles interacting with the surface, b) the probability distribution for for z = 3.38Å, denoted by the filled circle in a), c) the potential energy for one particle, c.m. of 2 unbonded and bonded particles, d) the potential for <math>-O-CH_2-</math> in poly(ethylene oxide) due to a graphite surface From [1].]]<br />
For the implicit model, the authors used a semi-infinite geometry with the surface as a continuum for z ≤ 0 and atoms in the liquid phase in z > 0.<br />
They then used a Lennard-Jones potential, U(z), for the potential energy of the atom at a height z.<br />
For the coarse graining, groups of atoms are reparameterized by their center of masses (c.m.) for the interactions with the solid surface.<br />
Probability distributions are used for the interactions rather than potential energies to aid the coarse graining.<br />
For example, the joint probability that particle 1 is at a height <math>z_1</math> and particle 2 at height <math>z_2 </math> is given by:<br />
<math>P(z_1,z_2) = e^{-\beta U(z_1)} e^{-\beta U(z_2)}</math><br />
where <math>\beta</math> denotes the inverse of Boltzmann's constant times the temperature. <br />
So, the probability that c.m. for a pair of non-interacting particles is at height z is given by the marginal distribution:<br />
<math>P(z)=(2z)^{-1} \int_{0}^{2z} e^{-\beta U(z_1)} e^{-\beta U(2z-z_1)} dz_1 </math><br />
and similarly, for particles with some interaction <math>P_I(z_1,z_2)</math> independent of the surface, the probability that the center of mass is at height z is then<br />
<math>P(z)=\frac{\int_{0}^{2z} e^{-\beta U(z_1)}e^{-\beta U(2z-z_1)}P_I(2z_1-z) dz_1 }{\int_0^{2z}P_I(2z_1-2z) dz_1} </math><br />
which are appropriately normalized and have features visualized in Fig. 1<br />
<br />
==Simulation==<br />
Applying these probability distributions for large numbers of particles is more tricky.<br />
One issue is that pair interactions are often non-radial (e.g. conformational details for poly(ethylene oxide) mentioned in the paper).<br />
Another challenge is the large number of particles that must be incorporated in the simulation.<br />
To alleviate this, common coarse graining methods combine several (>2) heavy atoms and H atoms associated with them to a single position.<br />
The authors explained that a judicious choice for the implementation of coarse grain is required with a <math>-O-CH_2-</math> piece of poly(ethylene oxide).<br />
One method is to coarse grain <math>CH_2</math> then combine it with O.<br />
Another method is to coarse grain CHO, then combine it with H.<br />
The third method is to coarse grain HH and CO separately, then combine the pairs.<br />
The first and third are reasonable since the first combines heavy atoms (and their associated H atoms in groups) and the third retains symmetry by first coarse graining light and heavy atoms together then combining them.<br />
These principles are applied for a coarse grain simulation of aqueous n-alkyl poly(ethylene oxide), specifically C12E5, adsorbing on a graphite surface.<br />
The nonionic surfactant CnEm were coarse grained with 3 <math>CH_2</math> group at each hydrophobic site and one ethylene monomer at each hydrophilic site in order to observe the overall shape of the surfactant.<br />
Specific parameters such used to model details of the interactions were previously measured experimentally with bulk density, surface tension, and inter-facial surface tension.<br />
The diffusion coefficients were reported to have been calculated from mean square displacement curves for binary mixtures of C12E5 at different concentrations and water and confirmed by experiment.<br />
<br />
==Results and discussion==<br />
[[Image:msa2.jpeg|thumb|300px|left| Fig. 2: _ From [1].]]<br />
As the authors mentioned, the self-assembly of nonionic surfactants at graphite-liquid interfaces have been characterized using methods such as atomic force microscopy.<br />
C12E5 was found to form cylindrical micelles in solution and hemicylinders at the graphite-liquid interface.<br />
The results from the simulation (Fig. 2) what that initially, the surfactants coat the graphite surface or begin to self-assemble into spherical micelles (but never fuse completely since they are saturated) far away from the surface (Fig. 2B).<br />
However, when a micelle approaches the partly coated surface, the head groups in the micelle interact with those adsorbed to the surface.<br />
The authors describe what occurs next as "feeding," where two sets of head groups open so that the hydrophobic tails of the micelles touch those of the monolayer on the graphite surface (Fig. 2C-D)<br />
The tails then quickly disperse onto the surface and the head groups rearrange so that the entire micelle is adsorbed onto the surface (Fig. 2E).<br />
Reorganization then occurs and hemicylinders of surfactants form on the graphite surface with spacing ~5 nm which agrees with experimental data.<br />
Simulations with C9E3 gave similar feeding phenomena but the final state is that of a monolayer with the surfactants perpendicular to the surface, as predicted by the geometry of C9E3 and agrees with experiment.<br />
An explicit representation of the surface was also recovered so that more general and detailed surface geometries can be modeled.<br />
The computational techniques are also four orders of magnitude more efficient than atomistic simulations.<br />
As the authors mentioned, this holds promise for nanoscale studies of hydrophobic surfaces interacting with aqueous surfactant solutions.<br />
This includes examining how different surfactants solubilize carbon nanotubes and depositing quantum dots on a substrate.<br />
<br />
==References==<br />
[1] Nielsen, S. O., Srinivas, G., Lopez, C. F., & Klein, M. L. (2005). Modeling surfactant adsorption on hydrophobic surfaces. Physical review letters, 94(22), 228301.<br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Modeling_Surfactant_Adsorption_on_Hydrophobic_Surfaces&diff=26287Modeling Surfactant Adsorption on Hydrophobic Surfaces2012-11-27T05:42:25Z<p>Xingyu: /* Results and discussion */</p>
<hr />
<div>== General Information ==<br />
'''Authors:''' S. O. Nielsen, G. Srinivas, C. F. Lopez, and M. L. Klein.<br />
<br />
'''Publication:''' Physical Review Letters<br />
<br />
'''Keywords:''' [[Surfactant]], [[micelle]], [[adsorption]]<br />
<br />
== Summary ==<br />
As the authors mentioned, the self-assembly behavior of surfactants is useful in many contexts, including manipulation of single wall carbon nanotubes or solubilization of hydrophobic quantum dots.<br />
However, such processes are not well understood because their dimensional and temporal scales are ill-suited for experiments or atomistic simulations.<br />
This study presents a coarse grain method used to simulate surfactant (aqueous n-alkyl poly(ethylene oxide) adsorption on an hydrophobic surface (graphite).<br />
This is done by modeling the surface with an implicit potential, coarse graining for interactions using respective center masses, then returning to the explicit model for the surface.<br />
The simulation results agree with experimental measurements using atomic force microscopy and demonstrate interesting behavior for adsorption.<br />
<br />
==Theory==<br />
[[Image:msa1.jpeg|thumb|300px|right| Fig. 1: _ From [1].]]<br />
For the implicit model, the authors used a semi-infinite geometry with the surface as a continuum for z ≤ 0 and atoms in the liquid phase in z > 0.<br />
They then used a Lennard-Jones potential, U(z), for the potential energy of the atom at a height z.<br />
For the coarse graining, groups of atoms are reparameterized by their center of masses (c.m.) for the interactions with the solid surface.<br />
Probability distributions are used for the interactions rather than potential energies to aid the coarse graining.<br />
For example, the joint probability that particle 1 is at a height <math>z_1</math> and particle 2 at height <math>z_2 </math> is given by:<br />
<math>P(z_1,z_2) = e^{-\beta U(z_1)} e^{-\beta U(z_2)}</math><br />
where <math>\beta</math> denotes the inverse of Boltzmann's constant times the temperature. <br />
So, the probability that c.m. for a pair of non-interacting particles is at height z is given by the marginal distribution:<br />
<math>P(z)=(2z)^{-1} \int_{0}^{2z} e^{-\beta U(z_1)} e^{-\beta U(2z-z_1)} dz_1 </math><br />
and similarly, for particles with some interaction <math>P_I(z_1,z_2)</math> independent of the surface, the probability that the center of mass is at height z is then<br />
<math>P(z)=\frac{\int_{0}^{2z} e^{-\beta U(z_1)}e^{-\beta U(2z-z_1)}P_I(2z_1-z) dz_1 }{\int_0^{2z}P_I(2z_1-2z) dz_1} </math><br />
which are appropriately normalized and have features visualized in Fig. 1<br />
<br />
==Simulation==<br />
Applying these probability distributions for large numbers of particles is more tricky.<br />
One issue is that pair interactions are often non-radial (e.g. conformational details for poly(ethylene oxide) mentioned in the paper).<br />
Another challenge is the large number of particles that must be incorporated in the simulation.<br />
To alleviate this, common coarse graining methods combine several (>2) heavy atoms and H atoms associated with them to a single position.<br />
The authors explained that a judicious choice for the implementation of coarse grain is required with a <math>-O-CH_2-</math> piece of poly(ethylene oxide).<br />
One method is to coarse grain <math>CH_2</math> then combine it with O.<br />
Another method is to coarse grain CHO, then combine it with H.<br />
The third method is to coarse grain HH and CO separately, then combine the pairs.<br />
The first and third are reasonable since the first combines heavy atoms (and their associated H atoms in groups) and the third retains symmetry by first coarse graining light and heavy atoms together then combining them.<br />
These principles are applied for a coarse grain simulation of aqueous n-alkyl poly(ethylene oxide), specifically C12E5, adsorbing on a graphite surface.<br />
The nonionic surfactant CnEm were coarse grained with 3 <math>CH_2</math> group at each hydrophobic site and one ethylene monomer at each hydrophilic site in order to observe the overall shape of the surfactant.<br />
Specific parameters such used to model details of the interactions were previously measured experimentally with bulk density, surface tension, and inter-facial surface tension.<br />
The diffusion coefficients were reported to have been calculated from mean square displacement curves for binary mixtures of C12E5 at different concentrations and water and confirmed by experiment.<br />
<br />
==Results and discussion==<br />
[[Image:msa2.jpeg|thumb|300px|left| Fig. 2: _ From [1].]]<br />
As the authors mentioned, the self-assembly of nonionic surfactants at graphite-liquid interfaces have been characterized using methods such as atomic force microscopy.<br />
C12E5 was found to form cylindrical micelles in solution and hemicylinders at the graphite-liquid interface.<br />
The results from the simulation (Fig. 2) what that initially, the surfactants coat the graphite surface or begin to self-assemble into spherical micelles (but never fuse completely since they are saturated) far away from the surface (Fig. 2B).<br />
However, when a micelle approaches the partly coated surface, the head groups in the micelle interact with those adsorbed to the surface.<br />
The authors describe what occurs next as "feeding," where two sets of head groups open so that the hydrophobic tails of the micelles touch those of the monolayer on the graphite surface (Fig. 2C-D)<br />
The tails then quickly disperse onto the surface and the head groups rearrange so that the entire micelle is adsorbed onto the surface (Fig. 2E).<br />
Reorganization then occurs and hemicylinders of surfactants form on the graphite surface with spacing ~5 nm which agrees with experimental data.<br />
Simulations with C9E3 gave similar feeding phenomena but the final state is that of a monolayer with the surfactants perpendicular to the surface, as predicted by the geometry of C9E3 and agrees with experiment.<br />
An explicit representation of the surface was also recovered so that more general and detailed surface geometries can be modeled.<br />
The computational techniques are also four orders of magnitude more efficient than atomistic simulations.<br />
As the authors mentioned, this holds promise for nanoscale studies of hydrophobic surfaces interacting with aqueous surfactant solutions.<br />
This includes examining how different surfactants solubilize carbon nanotubes and depositing quantum dots on a substrate.<br />
<br />
==References==<br />
[1] Nielsen, S. O., Srinivas, G., Lopez, C. F., & Klein, M. L. (2005). Modeling surfactant adsorption on hydrophobic surfaces. Physical review letters, 94(22), 228301.<br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Modeling_Surfactant_Adsorption_on_Hydrophobic_Surfaces&diff=26286Modeling Surfactant Adsorption on Hydrophobic Surfaces2012-11-27T05:42:04Z<p>Xingyu: /* Theory */</p>
<hr />
<div>== General Information ==<br />
'''Authors:''' S. O. Nielsen, G. Srinivas, C. F. Lopez, and M. L. Klein.<br />
<br />
'''Publication:''' Physical Review Letters<br />
<br />
'''Keywords:''' [[Surfactant]], [[micelle]], [[adsorption]]<br />
<br />
== Summary ==<br />
As the authors mentioned, the self-assembly behavior of surfactants is useful in many contexts, including manipulation of single wall carbon nanotubes or solubilization of hydrophobic quantum dots.<br />
However, such processes are not well understood because their dimensional and temporal scales are ill-suited for experiments or atomistic simulations.<br />
This study presents a coarse grain method used to simulate surfactant (aqueous n-alkyl poly(ethylene oxide) adsorption on an hydrophobic surface (graphite).<br />
This is done by modeling the surface with an implicit potential, coarse graining for interactions using respective center masses, then returning to the explicit model for the surface.<br />
The simulation results agree with experimental measurements using atomic force microscopy and demonstrate interesting behavior for adsorption.<br />
<br />
==Theory==<br />
[[Image:msa1.jpeg|thumb|300px|right| Fig. 1: _ From [1].]]<br />
For the implicit model, the authors used a semi-infinite geometry with the surface as a continuum for z ≤ 0 and atoms in the liquid phase in z > 0.<br />
They then used a Lennard-Jones potential, U(z), for the potential energy of the atom at a height z.<br />
For the coarse graining, groups of atoms are reparameterized by their center of masses (c.m.) for the interactions with the solid surface.<br />
Probability distributions are used for the interactions rather than potential energies to aid the coarse graining.<br />
For example, the joint probability that particle 1 is at a height <math>z_1</math> and particle 2 at height <math>z_2 </math> is given by:<br />
<math>P(z_1,z_2) = e^{-\beta U(z_1)} e^{-\beta U(z_2)}</math><br />
where <math>\beta</math> denotes the inverse of Boltzmann's constant times the temperature. <br />
So, the probability that c.m. for a pair of non-interacting particles is at height z is given by the marginal distribution:<br />
<math>P(z)=(2z)^{-1} \int_{0}^{2z} e^{-\beta U(z_1)} e^{-\beta U(2z-z_1)} dz_1 </math><br />
and similarly, for particles with some interaction <math>P_I(z_1,z_2)</math> independent of the surface, the probability that the center of mass is at height z is then<br />
<math>P(z)=\frac{\int_{0}^{2z} e^{-\beta U(z_1)}e^{-\beta U(2z-z_1)}P_I(2z_1-z) dz_1 }{\int_0^{2z}P_I(2z_1-2z) dz_1} </math><br />
which are appropriately normalized and have features visualized in Fig. 1<br />
<br />
==Simulation==<br />
Applying these probability distributions for large numbers of particles is more tricky.<br />
One issue is that pair interactions are often non-radial (e.g. conformational details for poly(ethylene oxide) mentioned in the paper).<br />
Another challenge is the large number of particles that must be incorporated in the simulation.<br />
To alleviate this, common coarse graining methods combine several (>2) heavy atoms and H atoms associated with them to a single position.<br />
The authors explained that a judicious choice for the implementation of coarse grain is required with a <math>-O-CH_2-</math> piece of poly(ethylene oxide).<br />
One method is to coarse grain <math>CH_2</math> then combine it with O.<br />
Another method is to coarse grain CHO, then combine it with H.<br />
The third method is to coarse grain HH and CO separately, then combine the pairs.<br />
The first and third are reasonable since the first combines heavy atoms (and their associated H atoms in groups) and the third retains symmetry by first coarse graining light and heavy atoms together then combining them.<br />
These principles are applied for a coarse grain simulation of aqueous n-alkyl poly(ethylene oxide), specifically C12E5, adsorbing on a graphite surface.<br />
The nonionic surfactant CnEm were coarse grained with 3 <math>CH_2</math> group at each hydrophobic site and one ethylene monomer at each hydrophilic site in order to observe the overall shape of the surfactant.<br />
Specific parameters such used to model details of the interactions were previously measured experimentally with bulk density, surface tension, and inter-facial surface tension.<br />
The diffusion coefficients were reported to have been calculated from mean square displacement curves for binary mixtures of C12E5 at different concentrations and water and confirmed by experiment.<br />
<br />
==Results and discussion==<br />
As the authors mentioned, the self-assembly of nonionic surfactants at graphite-liquid interfaces have been characterized using methods such as atomic force microscopy.<br />
C12E5 was found to form cylindrical micelles in solution and hemicylinders at the graphite-liquid interface.<br />
[[Image:msa2.jpeg|thumb|300px|right| Fig. 2: _ From [1].]]<br />
The results from the simulation (Fig. 2) what that initially, the surfactants coat the graphite surface or begin to self-assemble into spherical micelles (but never fuse completely since they are saturated) far away from the surface (Fig. 2B).<br />
However, when a micelle approaches the partly coated surface, the head groups in the micelle interact with those adsorbed to the surface.<br />
The authors describe what occurs next as "feeding," where two sets of head groups open so that the hydrophobic tails of the micelles touch those of the monolayer on the graphite surface (Fig. 2C-D)<br />
The tails then quickly disperse onto the surface and the head groups rearrange so that the entire micelle is adsorbed onto the surface (Fig. 2E).<br />
Reorganization then occurs and hemicylinders of surfactants form on the graphite surface with spacing ~5 nm which agrees with experimental data.<br />
Simulations with C9E3 gave similar feeding phenomena but the final state is that of a monolayer with the surfactants perpendicular to the surface, as predicted by the geometry of C9E3 and agrees with experiment.<br />
An explicit representation of the surface was also recovered so that more general and detailed surface geometries can be modeled.<br />
The computational techniques are also four orders of magnitude more efficient than atomistic simulations.<br />
As the authors mentioned, this holds promise for nanoscale studies of hydrophobic surfaces interacting with aqueous surfactant solutions.<br />
This includes examining how different surfactants solubilize carbon nanotubes and depositing quantum dots on a substrate.<br />
<br />
==References==<br />
[1] Nielsen, S. O., Srinivas, G., Lopez, C. F., & Klein, M. L. (2005). Modeling surfactant adsorption on hydrophobic surfaces. Physical review letters, 94(22), 228301.<br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Msa2.jpeg&diff=26285File:Msa2.jpeg2012-11-27T05:41:28Z<p>Xingyu: uploaded a new version of "Image:Msa2.jpeg"</p>
<hr />
<div></div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Msa2.jpeg&diff=26284File:Msa2.jpeg2012-11-27T05:40:32Z<p>Xingyu: </p>
<hr />
<div></div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Msa1.jpeg&diff=26283File:Msa1.jpeg2012-11-27T05:40:18Z<p>Xingyu: </p>
<hr />
<div></div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Modeling_Surfactant_Adsorption_on_Hydrophobic_Surfaces&diff=26282Modeling Surfactant Adsorption on Hydrophobic Surfaces2012-11-27T05:38:54Z<p>Xingyu: </p>
<hr />
<div>== General Information ==<br />
'''Authors:''' S. O. Nielsen, G. Srinivas, C. F. Lopez, and M. L. Klein.<br />
<br />
'''Publication:''' Physical Review Letters<br />
<br />
'''Keywords:''' [[Surfactant]], [[micelle]], [[adsorption]]<br />
<br />
== Summary ==<br />
As the authors mentioned, the self-assembly behavior of surfactants is useful in many contexts, including manipulation of single wall carbon nanotubes or solubilization of hydrophobic quantum dots.<br />
However, such processes are not well understood because their dimensional and temporal scales are ill-suited for experiments or atomistic simulations.<br />
This study presents a coarse grain method used to simulate surfactant (aqueous n-alkyl poly(ethylene oxide) adsorption on an hydrophobic surface (graphite).<br />
This is done by modeling the surface with an implicit potential, coarse graining for interactions using respective center masses, then returning to the explicit model for the surface.<br />
The simulation results agree with experimental measurements using atomic force microscopy and demonstrate interesting behavior for adsorption.<br />
<br />
==Theory==<br />
For the implicit model, the authors used a semi-infinite geometry with the surface as a continuum for z ≤ 0 and atoms in the liquid phase in z > 0.<br />
They then used a Lennard-Jones potential, U(z), for the potential energy of the atom at a height z.<br />
For the coarse graining, groups of atoms are reparameterized by their center of masses (c.m.) for the interactions with the solid surface.<br />
Probability distributions are used for the interactions rather than potential energies to aid the coarse graining.<br />
For example, the joint probability that particle 1 is at a height <math>z_1</math> and particle 2 at height <math>z_2 </math> is given by:<br />
<math>P(z_1,z_2) = e^{-\beta U(z_1)} e^{-\beta U(z_2)}</math><br />
where <math>\beta</math> denotes the inverse of Boltzmann's constant times the temperature. <br />
So, the probability that c.m. for a pair of non-interacting particles is at height z is given by the marginal distribution:<br />
<math>P(z)=(2z)^{-1} \int_{0}^{2z} e^{-\beta U(z_1)} e^{-\beta U(2z-z_1)} dz_1 </math><br />
and similarly, for particles with some interaction <math>P_I(z_1,z_2)</math> independent of the surface, the probability that the center of mass is at height z is then<br />
<math>P(z)=\frac{\int_{0}^{2z} e^{-\beta U(z_1)}e^{-\beta U(2z-z_1)}P_I(2z_1-z) dz_1 }{\int_0^{2z}P_I(2z_1-2z) dz_1} </math><br />
which are appropriately normalized and have features visualized in Fig. 1<br />
[[Image:msa1.jpeg|thumb|300px|right| Fig. 1: _ From [1].]]<br />
<br />
==Simulation==<br />
Applying these probability distributions for large numbers of particles is more tricky.<br />
One issue is that pair interactions are often non-radial (e.g. conformational details for poly(ethylene oxide) mentioned in the paper).<br />
Another challenge is the large number of particles that must be incorporated in the simulation.<br />
To alleviate this, common coarse graining methods combine several (>2) heavy atoms and H atoms associated with them to a single position.<br />
The authors explained that a judicious choice for the implementation of coarse grain is required with a <math>-O-CH_2-</math> piece of poly(ethylene oxide).<br />
One method is to coarse grain <math>CH_2</math> then combine it with O.<br />
Another method is to coarse grain CHO, then combine it with H.<br />
The third method is to coarse grain HH and CO separately, then combine the pairs.<br />
The first and third are reasonable since the first combines heavy atoms (and their associated H atoms in groups) and the third retains symmetry by first coarse graining light and heavy atoms together then combining them.<br />
These principles are applied for a coarse grain simulation of aqueous n-alkyl poly(ethylene oxide), specifically C12E5, adsorbing on a graphite surface.<br />
The nonionic surfactant CnEm were coarse grained with 3 <math>CH_2</math> group at each hydrophobic site and one ethylene monomer at each hydrophilic site in order to observe the overall shape of the surfactant.<br />
Specific parameters such used to model details of the interactions were previously measured experimentally with bulk density, surface tension, and inter-facial surface tension.<br />
The diffusion coefficients were reported to have been calculated from mean square displacement curves for binary mixtures of C12E5 at different concentrations and water and confirmed by experiment.<br />
<br />
==Results and discussion==<br />
As the authors mentioned, the self-assembly of nonionic surfactants at graphite-liquid interfaces have been characterized using methods such as atomic force microscopy.<br />
C12E5 was found to form cylindrical micelles in solution and hemicylinders at the graphite-liquid interface.<br />
[[Image:msa2.jpeg|thumb|300px|right| Fig. 2: _ From [1].]]<br />
The results from the simulation (Fig. 2) what that initially, the surfactants coat the graphite surface or begin to self-assemble into spherical micelles (but never fuse completely since they are saturated) far away from the surface (Fig. 2B).<br />
However, when a micelle approaches the partly coated surface, the head groups in the micelle interact with those adsorbed to the surface.<br />
The authors describe what occurs next as "feeding," where two sets of head groups open so that the hydrophobic tails of the micelles touch those of the monolayer on the graphite surface (Fig. 2C-D)<br />
The tails then quickly disperse onto the surface and the head groups rearrange so that the entire micelle is adsorbed onto the surface (Fig. 2E).<br />
Reorganization then occurs and hemicylinders of surfactants form on the graphite surface with spacing ~5 nm which agrees with experimental data.<br />
Simulations with C9E3 gave similar feeding phenomena but the final state is that of a monolayer with the surfactants perpendicular to the surface, as predicted by the geometry of C9E3 and agrees with experiment.<br />
An explicit representation of the surface was also recovered so that more general and detailed surface geometries can be modeled.<br />
The computational techniques are also four orders of magnitude more efficient than atomistic simulations.<br />
As the authors mentioned, this holds promise for nanoscale studies of hydrophobic surfaces interacting with aqueous surfactant solutions.<br />
This includes examining how different surfactants solubilize carbon nanotubes and depositing quantum dots on a substrate.<br />
<br />
==References==<br />
[1] Nielsen, S. O., Srinivas, G., Lopez, C. F., & Klein, M. L. (2005). Modeling surfactant adsorption on hydrophobic surfaces. Physical review letters, 94(22), 228301.<br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Adsorption_Kinetics_in_Micellar_Solutions_of_Nonionic_Surfactants&diff=26268Adsorption Kinetics in Micellar Solutions of Nonionic Surfactants2012-11-26T18:44:44Z<p>Xingyu: Removing all content from page</p>
<hr />
<div></div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Modeling_Surfactant_Adsorption_on_Hydrophobic_Surfaces&diff=26267Modeling Surfactant Adsorption on Hydrophobic Surfaces2012-11-26T18:44:17Z<p>Xingyu: New page: I'll do this article.</p>
<hr />
<div>I'll do this article.</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Xingyu_Zhang&diff=26266Xingyu Zhang2012-11-26T18:44:04Z<p>Xingyu: </p>
<hr />
<div>Topic 1: [[Measuring translational, rotational, and vibrational dynamics with digital holographic microscopy]]<br />
<br />
Topic 2: [[Long-range attraction between colloidal spheres at the air-water interface: The consequence of an irregular meniscus]]<br />
<br />
Topic 3: [[Thin film photonic crystals: synthesis and characterisation]]<br />
<br />
Topic 4: [[Modeling Surfactant Adsorption on Hydrophobic Surfaces]]</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Adsorption_Kinetics_in_Micellar_Solutions_of_Nonionic_Surfactants&diff=26265Adsorption Kinetics in Micellar Solutions of Nonionic Surfactants2012-11-26T18:40:25Z<p>Xingyu: New page: I'll do this article</p>
<hr />
<div>I'll do this article</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Xingyu_Zhang&diff=26264Xingyu Zhang2012-11-26T18:40:09Z<p>Xingyu: </p>
<hr />
<div>Topic 1: [[Measuring translational, rotational, and vibrational dynamics with digital holographic microscopy]]<br />
<br />
Topic 2: [[Long-range attraction between colloidal spheres at the air-water interface: The consequence of an irregular meniscus]]<br />
<br />
Topic 3: [[Thin film photonic crystals: synthesis and characterisation]]<br />
<br />
Topic 4: [[Adsorption Kinetics in Micellar Solutions of Nonionic Surfactants]]</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Thin_film&diff=26112Thin film2012-11-17T02:27:56Z<p>Xingyu: /* Examples */</p>
<hr />
<div>== Definition ==<br />
<br />
Thin films are thin layers of a liquid in which their length is much greater than their thickness. Important examples of thin films include soap bubbles, and thin films between solids for lubrication. Capillary forces are also very important in governing the physics of thin films - for more information go to [[Capillarity and wetting]].<br />
<br />
For more information on flow in thin films, go to: [[Flow of thin films]]<br />
<br />
==Examples==<br />
<br />
The study of thin films will play a large role in [[New directions in mechanics|mechanics research in the future]].<br />
<br />
Thin films of spherical liquid crystal droplets in a polymer matrix can be stretched along one axis so that the droplets can then be solidified as elliptical particles. (See [[Optically Anisotropic Colloids of Controllable Shape]])<br />
<br />
Thin film photonic crystals can be grown using polystyrene spheres with controlled vertical drying. (See [[Thin film photonic crystals: synthesis and characterisation]])<br />
<br />
== References ==<br />
<br />
* R. Jones, "Soft Condensed Matter," Oxford University Press Inc., New York (2002).<br />
* http://en.wikipedia.org/wiki/Thin_film<br />
<br />
== Keyword in references: ==<br />
<br />
[[Contact angle associated with thin liquid films in emulsions]]<br />
<br />
[[High-throughput injection with microfluidics using picoinjectors]]<br />
<br />
[[Graphene as a subnanometre trans-electrode membrane]]<br />
<br />
[[Liquid-infused structured surfaces with exceptional anti-biofouling performance]]<br />
<br />
[[￼Buckling cascades in free sheets]]<br />
<br />
[[Biomimetic ratcheting motion of a soft, slender, sessile gel]]<br />
<br />
[[Magnetic self-assembly of three-dimensional surfaces from planar sheets]]<br />
<br />
[[Measuring the Work of Adhesion between a Soft Confined Film and a Flexible Plate]]<br />
<br />
[[Self-Organized Origami]]<br />
<br />
[[Growth, geometry, and mechanics of a blooming lily]]<br />
<br />
[[Geometric Control of Rippling in Supported Polymer Nanolines]]<br />
<br />
[[Dislocation-mediated melting in two dimensions]]<br />
<br />
[[Assembly of optical-scale dumbbells into dense photonic crystals]]<br />
<br />
[[Size-dependent phase transformations in nanoscale pure and Y-doped zirconia thin films]]<br />
<br />
[[Synthesis and Phase Stability in Ultra-thin Solid Electrolytes: The Case of Zirconia Thin Films]]<br />
<br />
[[Thin film cracking and ratcheting caused by temperature cycling]]<br />
<br />
[[Self-Organizing Nanophases on a Solid Surface]]<br />
<br />
[[Domain Dynamics in a Ferroelastic Epilayer on a Paraelastic Substrate]]<br />
<br />
[[Mechanisms Active during Fracture under Constraint]]<br />
<br />
[[Mechanics of Relaxing SiGe Islands on a Viscous Glass]]<br />
<br />
[[Reliability of Interconnect Structures]]<br />
<br />
[[Kinetics of crack initiation and growth in organic-containing integrated structures]]<br />
<br />
[[Design and Performance of Thin Metal Film Interconnects for Skin-Like Electronic Circuits]]<br />
<br />
[[Fatigue Damage Evolution in Silicon Films for Micromechanical Applications]]<br />
<br />
[[New directions in mechanics]]<br />
<br />
[[Effects of Mechanical Strain on TFTs on Spherical Domes]]<br />
<br />
[[A Continuum Theory That Couples Creep and Self-Diffusion]]<br />
<br />
[[Evolution of wrinkles in hard films on soft substrates]]<br />
<br />
[[Experimental Determination of Crack Driving Forces in Integrated Structures]]<br />
<br />
[[Deformability of thin metal films on elastomer substrates]]<br />
<br />
[[Compliant thin film patterns of stiff materials as platforms for stretchable electronics]]<br />
<br />
[[Thermomechanical criteria for overlay alignment in flexible thin-film electronic circuits]]<br />
<br />
[[Micromechanics of Macroelectronics]]<br />
<br />
[[Mechanics of thin-film transistors and solar cells on flexible substrates]]<br />
<br />
[[Metal films on polymer substrates stretched beyond 50%]]<br />
<br />
[[Failure by simultaneous grain growth, strain localization, and interface debonding in metal films on polymer substrates]]<br />
<br />
[[Inorganic islands on a highly stretchable polyimide substrate]]<br />
<br />
[[Averting cracks caused by insertion reaction in lithium–ion batteries]]<br />
<br />
[[Force generated by a swelling elastomer subject to constraint]]<br />
<br />
[[Poroelastic swelling kinetics of thin hydrogel layers: comparison of theory and experiment]]<br />
<br />
[[Inelastic hosts as electrodes for high-capacity lithium-ion batteries]]<br />
<br />
[[Large Plastic Deformation in High-Capacity Lithium-Ion Batteries Caused by Charge and Discharge]]<br />
<br />
[[Analytical Solutions of Polymeric Gel Structures under Buckling and Wrinkle]]<br />
<br />
[[Concurrent electromigration and creep in lead-free solder]]<br />
<br />
[[Model of dissipative dielectric elastomers]]<br />
<br />
[[Reactive Flow in Large-Deformation Electrodes of Lithium-Ion Batteries]]<br />
<br />
[[ Kinetics of Initial Lithiation of Crystalline Silicon Electrodes of Lithium-Ion Batteries]]<br />
<br />
[[Swelling Kinetics of a Microgel Shell]]<br />
<br />
[[Optically Anisotropic Colloids of Controllable Shape]]<br />
<br />
[[Permeability of Model Stratum Corneum Lipid Membrane Measured Using Quartz Crystal Microbalance]]<br />
<br />
[[Swollen Vesicles and Multiple Emulsions from Block Copolymers]]<br />
<br />
[[Visualization of Dislocation Dynamics in Colloidal Crystals]]<br />
<br />
[[Osmotic spreading of Bacillus subtilis biofilms driven by an extracellular matrix]]<br />
<br />
[[Hierarchical Porous Materials Made by Drying Complex Suspensions]]<br />
<br />
[[Buckling and Crumpling of Drying Droplets of Colloid-Polymer Suspensions]]<br />
<br />
[[The pressure drop along rectangular microchannels containing bubbles]]<br />
<br />
[[Electrostatic Charging Due to Separation of Ions at Interfaces: Contact Electrification of Ionic Electrets]]<br />
<br />
[[￼Fabrication of Arrays of Metal and Metal Oxide Nanotubes by Shadow Evaporation]]<br />
<br />
[[Integrated Fabrication and Magnetic Positioning of Metallic and Polymeric Nanowires Embedded in Thin Epoxy Slabs]]<br />
<br />
[[Fabrication of micrometer-scale, patterned polyhedra by self-assembly]]<br />
<br />
[[Fabrication and Wetting Properties of Metallic Half-Shells with Submicron Diameters]]<br />
<br />
[[Surface Tension-Powered Self-Assembly of Microstructures—The State-of-the-Art]]<br />
<br />
[[Self-Assembled Monolayers of Thiolates on Metals as a Form of Nanotechnology]]<br />
<br />
[[Formation of droplets and bubbles in a microfluidic T-junction—scaling and mechanism of break-up]]</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Thin_film&diff=26111Thin film2012-11-17T02:26:41Z<p>Xingyu: /* Examples */</p>
<hr />
<div>== Definition ==<br />
<br />
Thin films are thin layers of a liquid in which their length is much greater than their thickness. Important examples of thin films include soap bubbles, and thin films between solids for lubrication. Capillary forces are also very important in governing the physics of thin films - for more information go to [[Capillarity and wetting]].<br />
<br />
For more information on flow in thin films, go to: [[Flow of thin films]]<br />
<br />
==Examples==<br />
<br />
The study of thin films will play a large role in [[New directions in mechanics|mechanics research in the future]].<br />
<br />
Thin films of spherical liquid crystal droplets in a polymer matrix can be stretched along one axis so that the droplets can then be solidified as elliptical particles. (See [[Optically Anisotropic Colloids of Controllable Shape]])<br />
<br />
Thin film photonic crystals can be grown using polystyrene spheres using controlled vertical drying. (See [[Thin film photonic crystals: synthesis and characterisation]])<br />
<br />
== References ==<br />
<br />
* R. Jones, "Soft Condensed Matter," Oxford University Press Inc., New York (2002).<br />
* http://en.wikipedia.org/wiki/Thin_film<br />
<br />
== Keyword in references: ==<br />
<br />
[[Contact angle associated with thin liquid films in emulsions]]<br />
<br />
[[High-throughput injection with microfluidics using picoinjectors]]<br />
<br />
[[Graphene as a subnanometre trans-electrode membrane]]<br />
<br />
[[Liquid-infused structured surfaces with exceptional anti-biofouling performance]]<br />
<br />
[[￼Buckling cascades in free sheets]]<br />
<br />
[[Biomimetic ratcheting motion of a soft, slender, sessile gel]]<br />
<br />
[[Magnetic self-assembly of three-dimensional surfaces from planar sheets]]<br />
<br />
[[Measuring the Work of Adhesion between a Soft Confined Film and a Flexible Plate]]<br />
<br />
[[Self-Organized Origami]]<br />
<br />
[[Growth, geometry, and mechanics of a blooming lily]]<br />
<br />
[[Geometric Control of Rippling in Supported Polymer Nanolines]]<br />
<br />
[[Dislocation-mediated melting in two dimensions]]<br />
<br />
[[Assembly of optical-scale dumbbells into dense photonic crystals]]<br />
<br />
[[Size-dependent phase transformations in nanoscale pure and Y-doped zirconia thin films]]<br />
<br />
[[Synthesis and Phase Stability in Ultra-thin Solid Electrolytes: The Case of Zirconia Thin Films]]<br />
<br />
[[Thin film cracking and ratcheting caused by temperature cycling]]<br />
<br />
[[Self-Organizing Nanophases on a Solid Surface]]<br />
<br />
[[Domain Dynamics in a Ferroelastic Epilayer on a Paraelastic Substrate]]<br />
<br />
[[Mechanisms Active during Fracture under Constraint]]<br />
<br />
[[Mechanics of Relaxing SiGe Islands on a Viscous Glass]]<br />
<br />
[[Reliability of Interconnect Structures]]<br />
<br />
[[Kinetics of crack initiation and growth in organic-containing integrated structures]]<br />
<br />
[[Design and Performance of Thin Metal Film Interconnects for Skin-Like Electronic Circuits]]<br />
<br />
[[Fatigue Damage Evolution in Silicon Films for Micromechanical Applications]]<br />
<br />
[[New directions in mechanics]]<br />
<br />
[[Effects of Mechanical Strain on TFTs on Spherical Domes]]<br />
<br />
[[A Continuum Theory That Couples Creep and Self-Diffusion]]<br />
<br />
[[Evolution of wrinkles in hard films on soft substrates]]<br />
<br />
[[Experimental Determination of Crack Driving Forces in Integrated Structures]]<br />
<br />
[[Deformability of thin metal films on elastomer substrates]]<br />
<br />
[[Compliant thin film patterns of stiff materials as platforms for stretchable electronics]]<br />
<br />
[[Thermomechanical criteria for overlay alignment in flexible thin-film electronic circuits]]<br />
<br />
[[Micromechanics of Macroelectronics]]<br />
<br />
[[Mechanics of thin-film transistors and solar cells on flexible substrates]]<br />
<br />
[[Metal films on polymer substrates stretched beyond 50%]]<br />
<br />
[[Failure by simultaneous grain growth, strain localization, and interface debonding in metal films on polymer substrates]]<br />
<br />
[[Inorganic islands on a highly stretchable polyimide substrate]]<br />
<br />
[[Averting cracks caused by insertion reaction in lithium–ion batteries]]<br />
<br />
[[Force generated by a swelling elastomer subject to constraint]]<br />
<br />
[[Poroelastic swelling kinetics of thin hydrogel layers: comparison of theory and experiment]]<br />
<br />
[[Inelastic hosts as electrodes for high-capacity lithium-ion batteries]]<br />
<br />
[[Large Plastic Deformation in High-Capacity Lithium-Ion Batteries Caused by Charge and Discharge]]<br />
<br />
[[Analytical Solutions of Polymeric Gel Structures under Buckling and Wrinkle]]<br />
<br />
[[Concurrent electromigration and creep in lead-free solder]]<br />
<br />
[[Model of dissipative dielectric elastomers]]<br />
<br />
[[Reactive Flow in Large-Deformation Electrodes of Lithium-Ion Batteries]]<br />
<br />
[[ Kinetics of Initial Lithiation of Crystalline Silicon Electrodes of Lithium-Ion Batteries]]<br />
<br />
[[Swelling Kinetics of a Microgel Shell]]<br />
<br />
[[Optically Anisotropic Colloids of Controllable Shape]]<br />
<br />
[[Permeability of Model Stratum Corneum Lipid Membrane Measured Using Quartz Crystal Microbalance]]<br />
<br />
[[Swollen Vesicles and Multiple Emulsions from Block Copolymers]]<br />
<br />
[[Visualization of Dislocation Dynamics in Colloidal Crystals]]<br />
<br />
[[Osmotic spreading of Bacillus subtilis biofilms driven by an extracellular matrix]]<br />
<br />
[[Hierarchical Porous Materials Made by Drying Complex Suspensions]]<br />
<br />
[[Buckling and Crumpling of Drying Droplets of Colloid-Polymer Suspensions]]<br />
<br />
[[The pressure drop along rectangular microchannels containing bubbles]]<br />
<br />
[[Electrostatic Charging Due to Separation of Ions at Interfaces: Contact Electrification of Ionic Electrets]]<br />
<br />
[[￼Fabrication of Arrays of Metal and Metal Oxide Nanotubes by Shadow Evaporation]]<br />
<br />
[[Integrated Fabrication and Magnetic Positioning of Metallic and Polymeric Nanowires Embedded in Thin Epoxy Slabs]]<br />
<br />
[[Fabrication of micrometer-scale, patterned polyhedra by self-assembly]]<br />
<br />
[[Fabrication and Wetting Properties of Metallic Half-Shells with Submicron Diameters]]<br />
<br />
[[Surface Tension-Powered Self-Assembly of Microstructures—The State-of-the-Art]]<br />
<br />
[[Self-Assembled Monolayers of Thiolates on Metals as a Form of Nanotechnology]]<br />
<br />
[[Formation of droplets and bubbles in a microfluidic T-junction—scaling and mechanism of break-up]]</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Thin_film_photonic_crystals:_synthesis_and_characterisation&diff=26110Thin film photonic crystals: synthesis and characterisation2012-11-17T02:23:58Z<p>Xingyu: </p>
<hr />
<div>== General Information ==<br />
'''Authors:''' M. A. McLachlan, N. P. Johnson, R. M. D. L. Rue, and D. W. McComb.<br />
<br />
'''Publication:''' Journal of Materials Chemistry, 14:144–150, 2004.<br />
<br />
'''Keywords:''' [[Thin film]], [[colloids]], [[photonic crystal]], [[self-assembly]]<br />
<br />
== Summary ==<br />
[[Image:tfpc1.jpeg|thumb|300px|right| Fig. 1: Optical microscopy images of thin films at T = 25, 45, and 65˚C when grown showing cracks and domain sizes. Inset images are SEM images where the scale marker <br />
is 200 µm. From [1].]]<br />
This paper examines the factors that affect colloidal self-assembly of thin film photonic crystals.<br />
The authors found that temperature has the largest effect and determined the ideal conditions for growing low-defect photonic crystals.<br />
There are many diverse applications and methods to create photonic crystals such as synthetic opals.<br />
One method employing colloidal self-assembly is controlled vertical drying, which is the focus of this study.<br />
The technique deposits colloidal spheres along the evaporation front of a meniscus that moves along the substrate.<br />
While the technique is generally effective, this paper systematically examines and optimizes the controllable conditions: temperature, relative humidity, sphere diameter, colloidal concentration, and substrate angle to assemble colloidal crystals from polystyrene (PS) spheres in aqueous solution.<br />
The crystals are then characterized using various microscopy and spectroscopy methods.<br />
<br />
==Experimental methods==<br />
The authors synthesized highly mono-disperse PS spheres with mean diameter in the ranges of 200-750 nm with a suspension polymerization [1].<br />
Different diameters were achieved by adjusting reagent concentrations or synthesis conditions such as stirring speed.<br />
The diameters of the spheres were measured using a transmission electron microscope (TEM) and their polydisperity recorded for large number of measurements (200 spheres).<br />
<br />
The colloidal crystals were grown using controlled vertical drying for temperatures ranging from 20 and 70˚ C (error within 0.2˚ C).<br />
The substrate angles were also varied, however, the paper only reports those for the angles of 75 and 90˚.<br />
The third condition that was studied was the effect of relative humidity of water vapor in the air (RH) defined as the percentage of amount of water vapor in the air compared to the saturation capacity of water vapor in the air.<br />
Special care was taken to ensure control of this quantity (to within 2%) of the set value during the entire growth period of the crystal by placing the device in a humidity controlled incubator.<br />
The size of the sample grown was 10 x 40 mm <math>^2</math> for all temperatures and RH.<br />
Depending on the conditions, the growth times ranged from < 4 to 40 days.<br />
The thin films were then studied using optical microscopy, reflectance spectroscopy, and scanning electron microscopy (SEM) for sections of the same sample grown under each experimental setting.<br />
[[Image:tfpc2.jpeg|thumb|300px|left| Fig. 2: Reflectance spectra of thin film photonic crystal's made from 230 nm PS spheres. From [1].]]<br />
<br />
For optical microscopy, the thin films were observed using an optical microscope with a CCD camera attached.<br />
This analysis showed that large cracks in the thin film that differed in number and size for the different experimental conditions (Fig. 1).<br />
The images were digitally processed and the crack density (percentage of cracks versus total area) computed for each of the samples.<br />
This gave a measure of the "macrosctructural" quality for the samples grown under different conditions.<br />
[[Image:tfpc3.jpeg|thumb|300px|left| Fig. 3: Plot of peak wavelength squared versus the sine of incident angle for thin films made of spheres of 230, 300, and 376 nm. From [1].]]<br />
<br />
For reflectance spectroscopy, a beam of monochromatic light (selected through a single grating monochrometer) was focused on a 1 mm <math>^2</math> spot on the sample at controlled angles.<br />
The intensity of the reflected light was then collected over a range of wavelengths (300-900 nm).<br />
Since no incident light is transmitted at the stop-band wavelength, which arises when the refractive index contrast is insufficient to support a full photonic bandgap, the angular-resolved reflection spectra (e.g. reflected intensity vs. wavelength at different incident angles (Fig. 2)) gives information about the the thin films [1].<br />
As given in Fig. 2, larger angles of incidence correspond to reflectance peaks at shorter wavelengths.<br />
In Fig. 3, a plot of the peak wavelength squared versus the sine of the incident angle squared has an intercept of <math>n_{eff}^2</math>, the square of the effective refractive index and a slope of <math>1/(4d)^2</math>, where <math> d</math> is the interplanar spacing in the (111) direction.<br />
This arises form Bragg's law: <math>n \lambda = 2 d \sin \theta</math> and Snells law: <math>n_1 \sin \theta_1 = n_2 \sin \theta _2</math> to produce [1]:<br />
<br />
<math>\lambda = 2 d (n_eff^2 - sin^2 \theta)^{1/2} </math>.<br />
<br />
[[Image:tfpc4.jpeg|thumb|300px|right| Fig. 3: SEM images of cracks in the thin films at T = 25, 45, and 65˚ C showing that the directions of the cracks were the same for all temperatures.]]<br />
This type of characterization could also have been done with transmission, but was not pursued in this study since it does not provide additional information.<br />
For SEM, the regions analyzed from optical microscopy and reflectance spectroscopy were divided into smaller sections for analysis.<br />
SEM images were taken (Fig. 4) of the corners and centers of the smaller samples and fast Fourier transforms were taken of the images to check for homogeneity of <br />
growth.<br />
<br />
==Results and discussion==<br />
These three analytical methods were used to examine the effects of different growth conditions on the quality of the thin films.<br />
Temperature, T was found to have the largest effect on the growth quality of the crystals.<br />
Using optical microscopy, the authors found that domains were larger at higher T, with three to five times the lengths for domains for T at 45˚ to 65˚ C.<br />
Using SEM and optical microscopy, cracks ~5 µm wide were observed to form only along the <110> directions that became increasing anisotropic (larger domains), for higher T (e.g. 100 <math>\times</math> 300 µm at 65 ˚C).<br />
FFT's of the SEM images found increasing long-range order at higher T and showed evidence that cracks occurred after self-assembly during the drying process.<br />
The authors also noticed that the thicknesses of the crystals grown using vertical drying increased by 66% from 25 to 45 ˚C from 30 layers thick to 50 layers thick.<br />
<br />
Relative humidity was also thought to play a role since the PS colloidal spheres shrink upon drying, which increases the stresses on the crystal and increases the number of defects.<br />
In this study, most of the crystals for experiments varying T and the substrate angle were carried out at a RH of 10-20%.<br />
Higher RH (40-50%) environments at T = 45 and 65 ˚C showed the films had poor adhesion to the substrate.<br />
Hence, the results suggest that low RH is better for growing these types of crystals.<br />
For the substrate angles, 75˚ was shown to yield larger domains than those at 90˚.<br />
However, the 75˚ produces shorter films since the entire length of the substrate cannot be utilized, unlike the case for 90˚.<br />
<br />
The authors also found that higher concentrations of the PS spheres produced thicker thin films.<br />
However, they also found that when the volume fraction of the polymer was increased to 5% from 1%, the films adhered poorly to the substrate.<br />
Hence, they determined that 1% was optimal for fabrication.<br />
Sphere diameter was found to have little effect on the growth properties of the crystals.<br />
<br />
Combining all these factors, the authors used the Design of Experiments (DoE) methodology to systematically optimize all the experimental settings.<br />
They also used it to determine that temperature was most significant for optimizing the domain size.<br />
Using a number of Lenth plots, they examined the significance of the remaining factors and found that sphere diameter variation was not significant while substrate angle was.<br />
It was also found that factors, when coupled, did not produce statistically significant changes in the domain size.<br />
<br />
As mentioned by the authors of this study, the best crystals have large domain size, low defect density, well-aligned domains, good mechanical strength, and sharp reflectance peaks.<br />
They were able to optimize growth conditions (esp. temperature, which is optimized at T = 65˚) and produce high quality thin film photonic crystals made of colloidal PS using controlled vertical drying with a growth period of less than 5 days.<br />
<br />
==References==<br />
<br />
[1] McLachlan, M. A., Johnson, N. P., & Richard, M. (2004). Thin film photonic crystals: synthesis and characterisation. Journal of Materials Chemistry, 14(2), 144-150.<br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Thin_film_photonic_crystals:_synthesis_and_characterisation&diff=26109Thin film photonic crystals: synthesis and characterisation2012-11-17T02:21:21Z<p>Xingyu: </p>
<hr />
<div>_ short paragraph on keywords section<br />
<br />
== General Information ==<br />
'''Authors:''' M. A. McLachlan, N. P. Johnson, R. M. D. L. Rue, and D. W. McComb.<br />
<br />
'''Publication:''' Journal of Materials Chemistry, 14:144–150, 2004.<br />
<br />
'''Keywords:''' [[Thin film]], [[colloids]], [[photonic crystal]], [[self-assembly]]<br />
<br />
== Summary ==<br />
[[Image:tfpc1.jpeg|thumb|300px|left| Fig. 1: Optical microscopy images of thin films at T = 25, 45, and 65˚C when grown showing cracks and domain sizes. Inset images are SEM images where the scale marker <br />
This paper examines the factors that affect colloidal self-assembly of thin film photonic crystals.<br />
The authors found that temperature has the largest effect and determined the ideal conditions for growing low-defect photonic crystals.<br />
There are many diverse applications and methods to create photonic crystals such as synthetic opals.<br />
One method employing colloidal self-assembly is controlled vertical drying, which is the focus of this study.<br />
The technique deposits colloidal spheres along the evaporation front of a meniscus that moves along the substrate.<br />
While the technique is generally effective, this paper systematically examines and optimizes the controllable conditions: temperature, relative humidity, sphere diameter, colloidal concentration, and substrate angle to assemble colloidal crystals from polystyrene (PS) spheres in aqueous solution.<br />
The crystals are then characterized using various microscopy and spectroscopy methods.<br />
<br />
==Experimental methods==is 200 µm. From [1].]]<br />
The authors synthesized highly mono-disperse PS spheres with mean diameter in the ranges of 200-750 nm with a suspension polymerization [1].<br />
Different diameters were achieved by adjusting reagent concentrations or synthesis conditions such as stirring speed.<br />
The diameters of the spheres were measured using a transmission electron microscope (TEM) and their polydisperity recorded for large number of measurements (200 spheres).<br />
<br />
The colloidal crystals were grown using controlled vertical drying for temperatures ranging from 20 and 70˚ C (error within 0.2˚ C).<br />
The substrate angles were also varied, however, the paper only reports those for the angles of 75 and 90˚.<br />
The third condition that was studied was the effect of relative humidity of water vapor in the air (RH) defined as the percentage of amount of water vapor in the air compared to the saturation capacity of water vapor in the air.<br />
Special care was taken to ensure control of this quantity (to within 2%) of the set value during the entire growth period of the crystal by placing the device in a humidity controlled incubator.<br />
The size of the sample grown was 10 x 40 mm <math>^2</math> for all temperatures and RH.<br />
Depending on the conditions, the growth times ranged from < 4 to 40 days.<br />
The thin films were then studied using optical microscopy, reflectance spectroscopy, and scanning electron microscopy (SEM) for sections of the same sample grown under each experimental setting.<br />
[[Image:tfpc2.jpeg|thumb|300px|left| Fig. 2: Reflectance spectra of thin film photonic crystal's made from 230 nm PS spheres. From [1].]]<br />
<br />
For optical microscopy, the thin films were observed using an optical microscope with a CCD camera attached.<br />
This analysis showed that large cracks in the thin film that differed in number and size for the different experimental conditions (Fig. 1).<br />
The images were digitally processed and the crack density (percentage of cracks versus total area) computed for each of the samples.<br />
This gave a measure of the "macrosctructural" quality for the samples grown under different conditions.<br />
[[Image:tfpc3.jpeg|thumb|300px|right| Fig. 3: Plot of peak wavelength squared versus the sine of incident angle for thin films made of spheres of 230, 300, and 376 nm. From [1].]]<br />
<br />
For reflectance spectroscopy, a beam of monochromatic light (selected through a single grating monochrometer) was focused on a 1 mm <math>^2</math> spot on the sample at controlled angles.<br />
The intensity of the reflected light was then collected over a range of wavelengths (300-900 nm).<br />
Since no incident light is transmitted at the stop-band wavelength, which arises when the refractive index contrast is insufficient to support a full photonic bandgap, the angular-resolved reflection spectra (e.g. reflected intensity vs. wavelength at different incident angles (Fig. 2)) gives information about the the thin films [1].<br />
As given in Fig. 2, larger angles of incidence correspond to reflectance peaks at shorter wavelengths.<br />
In Fig. 3, a plot of the peak wavelength squared versus the sine of the incident angle squared has an intercept of <math>n_{eff}^2</math>, the square of the effective refractive index and a slope of <math>1/(4d)^2</math>, where <math> d</math> is the interplanar spacing in the (111) direction.<br />
This arises form Bragg's law: <math>n \lambda = 2 d \sin \theta</math> and Snells law: <math>n_1 \sin \theta_1 = n_2 \sin \theta _2</math> to produce [1]:<br />
<br />
<math>\lambda = 2 d (n_eff^2 - sin^2 \theta)^{1/2} </math>.<br />
<br />
[[Image:tfpc4.jpeg|thumb|300px|right| Fig. 3: SEM images of cracks in the thin films at T = 25, 45, and 65˚ C showing that the directions of the cracks were the same for all temperatures.]]<br />
This type of characterization could also have been done with transmission, but was not pursued in this study since it does not provide additional information.<br />
For SEM, the regions analyzed from optical microscopy and reflectance spectroscopy were divided into smaller sections for analysis.<br />
SEM images were taken (Fig. 4) of the corners and centers of the smaller samples and fast Fourier transforms were taken of the images to check for homogeneity of <br />
growth.<br />
<br />
==Results and discussion==<br />
These three analytical methods were used to examine the effects of different growth conditions on the quality of the thin films.<br />
Temperature, T was found to have the largest effect on the growth quality of the crystals.<br />
Using optical microscopy, the authors found that domains were larger at higher T, with three to five times the lengths for domains for T at 45˚ to 65˚ C.<br />
Using SEM and optical microscopy, cracks ~5 µm wide were observed to form only along the <110> directions that became increasing anisotropic (larger domains), for higher T (e.g. 100 <math>\times</math> 300 µm at 65 ˚C).<br />
FFT's of the SEM images found increasing long-range order at higher T and showed evidence that cracks occurred after self-assembly during the drying process.<br />
The authors also noticed that the thicknesses of the crystals grown using vertical drying increased by 66% from 25 to 45 ˚C from 30 layers thick to 50 layers thick.<br />
<br />
Relative humidity was also thought to play a role since the PS colloidal spheres shrink upon drying, which increases the stresses on the crystal and increases the number of defects.<br />
In this study, most of the crystals for experiments varying T and the substrate angle were carried out at a RH of 10-20%.<br />
Higher RH (40-50%) environments at T = 45 and 65 ˚C showed the films had poor adhesion to the substrate.<br />
Hence, the results suggest that low RH is better for growing these types of crystals.<br />
For the substrate angles, 75˚ was shown to yield larger domains than those at 90˚.<br />
However, the 75˚ produces shorter films since the entire length of the substrate cannot be utilized, unlike the case for 90˚.<br />
<br />
The authors also found that higher concentrations of the PS spheres produced thicker thin films.<br />
However, they also found that when the volume fraction of the polymer was increased to 5% from 1%, the films adhered poorly to the substrate.<br />
Hence, they determined that 1% was optimal for fabrication.<br />
Sphere diameter was found to have little effect on the growth properties of the crystals.<br />
<br />
Combining all these factors, the authors used the Design of Experiments (DoE) methodology to systematically optimize all the experimental settings.<br />
They also used it to determine that temperature was most significant for optimizing the domain size.<br />
Using a number of Lenth plots, they examined the significance of the remaining factors and found that sphere diameter variation was not significant while substrate angle was.<br />
It was also found that factors, when coupled, did not produce statistically significant changes in the domain size.<br />
<br />
As mentioned by the authors of this study, the best crystals have large domain size, low defect density, well-aligned domains, good mechanical strength, and sharp reflectance peaks.<br />
They were able to optimize growth conditions (esp. temperature, which is optimized at T = 65˚) and produce high quality thin film photonic crystals made of colloidal PS using controlled vertical drying with a growth period of less than 5 days.<br />
<br />
==References==<br />
<br />
[1] McLachlan, M. A., Johnson, N. P., & Richard, M. (2004). Thin film photonic crystals: synthesis and characterisation. Journal of Materials Chemistry, 14(2), 144-150.<br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Thin_film_photonic_crystals:_synthesis_and_characterisation&diff=26108Thin film photonic crystals: synthesis and characterisation2012-11-17T02:20:53Z<p>Xingyu: </p>
<hr />
<div>_ short paragraph on keywords section<br />
<br />
== General Information ==<br />
'''Authors:''' M. A. McLachlan, N. P. Johnson, R. M. D. L. Rue, and D. W. McComb.<br />
<br />
'''Publication:''' Journal of Materials Chemistry, 14:144–150, 2004.<br />
<br />
'''Keywords:''' [[Thin film]], [[colloids]], [[photonic crystal]], [[self-assembly]]<br />
<br />
== Summary ==<br />
This paper examines the factors that affect colloidal self-assembly of thin film photonic crystals.<br />
The authors found that temperature has the largest effect and determined the ideal conditions for growing low-defect photonic crystals.<br />
There are many diverse applications and methods to create photonic crystals such as synthetic opals.<br />
One method employing colloidal self-assembly is controlled vertical drying, which is the focus of this study.<br />
The technique deposits colloidal spheres along the evaporation front of a meniscus that moves along the substrate.<br />
While the technique is generally effective, this paper systematically examines and optimizes the controllable conditions: temperature, relative humidity, sphere diameter, colloidal concentration, and substrate angle to assemble colloidal crystals from polystyrene (PS) spheres in aqueous solution.<br />
The crystals are then characterized using various microscopy and spectroscopy methods.<br />
<br />
==Experimental methods==<br />
[[Image:tfpc1.jpeg|thumb|300px|left| Fig. 1: Optical microscopy images of thin films at T = 25, 45, and 65˚C when grown showing cracks and domain sizes. Inset images are SEM images where the scale marker is 200 µm. From [1].]]<br />
The authors synthesized highly mono-disperse PS spheres with mean diameter in the ranges of 200-750 nm with a suspension polymerization [1].<br />
Different diameters were achieved by adjusting reagent concentrations or synthesis conditions such as stirring speed.<br />
The diameters of the spheres were measured using a transmission electron microscope (TEM) and their polydisperity recorded for large number of measurements (200 spheres).<br />
<br />
The colloidal crystals were grown using controlled vertical drying for temperatures ranging from 20 and 70˚ C (error within 0.2˚ C).<br />
The substrate angles were also varied, however, the paper only reports those for the angles of 75 and 90˚.<br />
The third condition that was studied was the effect of relative humidity of water vapor in the air (RH) defined as the percentage of amount of water vapor in the air compared to the saturation capacity of water vapor in the air.<br />
Special care was taken to ensure control of this quantity (to within 2%) of the set value during the entire growth period of the crystal by placing the device in a humidity controlled incubator.<br />
The size of the sample grown was 10 x 40 mm <math>^2</math> for all temperatures and RH.<br />
Depending on the conditions, the growth times ranged from < 4 to 40 days.<br />
The thin films were then studied using optical microscopy, reflectance spectroscopy, and scanning electron microscopy (SEM) for sections of the same sample grown under each experimental setting.<br />
[[Image:tfpc2.jpeg|thumb|300px|left| Fig. 2: Reflectance spectra of thin film photonic crystal's made from 230 nm PS spheres. From [1].]]<br />
<br />
For optical microscopy, the thin films were observed using an optical microscope with a CCD camera attached.<br />
This analysis showed that large cracks in the thin film that differed in number and size for the different experimental conditions (Fig. 1).<br />
The images were digitally processed and the crack density (percentage of cracks versus total area) computed for each of the samples.<br />
This gave a measure of the "macrosctructural" quality for the samples grown under different conditions.<br />
[[Image:tfpc3.jpeg|thumb|300px|right| Fig. 3: Plot of peak wavelength squared versus the sine of incident angle for thin films made of spheres of 230, 300, and 376 nm. From [1].]]<br />
<br />
For reflectance spectroscopy, a beam of monochromatic light (selected through a single grating monochrometer) was focused on a 1 mm <math>^2</math> spot on the sample at controlled angles.<br />
The intensity of the reflected light was then collected over a range of wavelengths (300-900 nm).<br />
Since no incident light is transmitted at the stop-band wavelength, which arises when the refractive index contrast is insufficient to support a full photonic bandgap, the angular-resolved reflection spectra (e.g. reflected intensity vs. wavelength at different incident angles (Fig. 2)) gives information about the the thin films [1].<br />
As given in Fig. 2, larger angles of incidence correspond to reflectance peaks at shorter wavelengths.<br />
In Fig. 3, a plot of the peak wavelength squared versus the sine of the incident angle squared has an intercept of <math>n_{eff}^2</math>, the square of the effective refractive index and a slope of <math>1/(4d)^2</math>, where <math> d</math> is the interplanar spacing in the (111) direction.<br />
This arises form Bragg's law: <math>n \lambda = 2 d \sin \theta</math> and Snells law: <math>n_1 \sin \theta_1 = n_2 \sin \theta _2</math> to produce [1]:<br />
<br />
<math>\lambda = 2 d (n_eff^2 - sin^2 \theta)^{1/2} </math>.<br />
<br />
[[Image:tfpc4.jpeg|thumb|300px|right| Fig. 3: SEM images of cracks in the thin films at T = 25, 45, and 65˚ C showing that the directions of the cracks were the same for all temperatures.]]<br />
This type of characterization could also have been done with transmission, but was not pursued in this study since it does not provide additional information.<br />
For SEM, the regions analyzed from optical microscopy and reflectance spectroscopy were divided into smaller sections for analysis.<br />
SEM images were taken (Fig. 4) of the corners and centers of the smaller samples and fast Fourier transforms were taken of the images to check for homogeneity of <br />
growth.<br />
<br />
==Results and discussion==<br />
These three analytical methods were used to examine the effects of different growth conditions on the quality of the thin films.<br />
Temperature, T was found to have the largest effect on the growth quality of the crystals.<br />
Using optical microscopy, the authors found that domains were larger at higher T, with three to five times the lengths for domains for T at 45˚ to 65˚ C.<br />
Using SEM and optical microscopy, cracks ~5 µm wide were observed to form only along the <110> directions that became increasing anisotropic (larger domains), for higher T (e.g. 100 <math>\times</math> 300 µm at 65 ˚C).<br />
FFT's of the SEM images found increasing long-range order at higher T and showed evidence that cracks occurred after self-assembly during the drying process.<br />
The authors also noticed that the thicknesses of the crystals grown using vertical drying increased by 66% from 25 to 45 ˚C from 30 layers thick to 50 layers thick.<br />
<br />
Relative humidity was also thought to play a role since the PS colloidal spheres shrink upon drying, which increases the stresses on the crystal and increases the number of defects.<br />
In this study, most of the crystals for experiments varying T and the substrate angle were carried out at a RH of 10-20%.<br />
Higher RH (40-50%) environments at T = 45 and 65 ˚C showed the films had poor adhesion to the substrate.<br />
Hence, the results suggest that low RH is better for growing these types of crystals.<br />
For the substrate angles, 75˚ was shown to yield larger domains than those at 90˚.<br />
However, the 75˚ produces shorter films since the entire length of the substrate cannot be utilized, unlike the case for 90˚.<br />
<br />
The authors also found that higher concentrations of the PS spheres produced thicker thin films.<br />
However, they also found that when the volume fraction of the polymer was increased to 5% from 1%, the films adhered poorly to the substrate.<br />
Hence, they determined that 1% was optimal for fabrication.<br />
Sphere diameter was found to have little effect on the growth properties of the crystals.<br />
<br />
Combining all these factors, the authors used the Design of Experiments (DoE) methodology to systematically optimize all the experimental settings.<br />
They also used it to determine that temperature was most significant for optimizing the domain size.<br />
Using a number of Lenth plots, they examined the significance of the remaining factors and found that sphere diameter variation was not significant while substrate angle was.<br />
It was also found that factors, when coupled, did not produce statistically significant changes in the domain size.<br />
<br />
As mentioned by the authors of this study, the best crystals have large domain size, low defect density, well-aligned domains, good mechanical strength, and sharp reflectance peaks.<br />
They were able to optimize growth conditions (esp. temperature, which is optimized at T = 65˚) and produce high quality thin film photonic crystals made of colloidal PS using controlled vertical drying with a growth period of less than 5 days.<br />
<br />
==References==<br />
<br />
[1] McLachlan, M. A., Johnson, N. P., & Richard, M. (2004). Thin film photonic crystals: synthesis and characterisation. Journal of Materials Chemistry, 14(2), 144-150.<br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Thin_film_photonic_crystals:_synthesis_and_characterisation&diff=26107Thin film photonic crystals: synthesis and characterisation2012-11-17T02:20:11Z<p>Xingyu: </p>
<hr />
<div>_ short paragraph on keywords section<br />
<br />
== General Information ==<br />
'''Authors:''' M. A. McLachlan, N. P. Johnson, R. M. D. L. Rue, and D. W. McComb.<br />
<br />
'''Publication:''' Journal of Materials Chemistry, 14:144–150, 2004.<br />
<br />
'''Keywords:''' [[Thin film]], [[colloids]], [[photonic crystal]], [[self-assembly]]<br />
<br />
== Summary ==<br />
This paper examines the factors that affect colloidal self-assembly of thin film photonic crystals.<br />
The authors found that temperature has the largest effect and determined the ideal conditions for growing low-defect photonic crystals.<br />
There are many diverse applications and methods to create photonic crystals such as synthetic opals.<br />
One method employing colloidal self-assembly is controlled vertical drying, which is the focus of this study.<br />
The technique deposits colloidal spheres along the evaporation front of a meniscus that moves along the substrate.<br />
While the technique is generally effective, this paper systematically examines and optimizes the controllable conditions: temperature, relative humidity, sphere diameter, colloidal concentration, and substrate angle to assemble colloidal crystals from polystyrene (PS) spheres in aqueous solution.<br />
The crystals are then characterized using various microscopy and spectroscopy methods.<br />
<br />
==Experimental methods==<br />
[[Image:tfpc1.jpeg|thumb|300px|left| Fig. 1: Optical microscopy images of thin films at T = 25, 45, and 65˚C when grown showing cracks and domain sizes. Inset images are SEM images where the scale marker is 200 µm. From [1].]]<br />
The authors synthesized highly mono-disperse PS spheres with mean diameter in the ranges of 200-750 nm with a suspension polymerization [1].<br />
Different diameters were achieved by adjusting reagent concentrations or synthesis conditions such as stirring speed.<br />
The diameters of the spheres were measured using a transmission electron microscope (TEM) and their polydisperity recorded for large number of measurements (200 spheres).<br />
<br />
The colloidal crystals were grown using controlled vertical drying for temperatures ranging from 20 and 70˚ C (error within 0.2˚ C).<br />
The substrate angles were also varied, however, the paper only reports those for the angles of 75 and 90˚.<br />
The third condition that was studied was the effect of relative humidity of water vapor in the air (RH) defined as the percentage of amount of water vapor in the air compared to the saturation capacity of water vapor in the air.<br />
Special care was taken to ensure control of this quantity (to within 2%) of the set value during the entire growth period of the crystal by placing the device in a humidity controlled incubator.<br />
The size of the sample grown was 10 x 40 mm <math>^2</math> for all temperatures and RH.<br />
Depending on the conditions, the growth times ranged from < 4 to 40 days.<br />
The thin films were then studied using optical microscopy, reflectance spectroscopy, and scanning electron microscopy (SEM) for sections of the same sample grown under each experimental setting.<br />
<br />
For optical microscopy, the thin films were observed using an optical microscope with a CCD camera attached.<br />
This analysis showed that large cracks in the thin film that differed in number and size for the different experimental conditions (Fig. 1).<br />
The images were digitally processed and the crack density (percentage of cracks versus total area) computed for each of the samples.<br />
This gave a measure of the "macrosctructural" quality for the samples grown under different conditions.<br />
<br />
For reflectance spectroscopy, a beam of monochromatic light (selected through a single grating monochrometer) was focused on a 1 mm <math>^2</math> spot on the sample at controlled angles.<br />
The intensity of the reflected light was then collected over a range of wavelengths (300-900 nm).<br />
Since no incident light is transmitted at the stop-band wavelength, which arises when the refractive index contrast is insufficient to support a full photonic bandgap, the angular-resolved reflection spectra (e.g. reflected intensity vs. wavelength at different incident angles (Fig. 2)) gives information about the the thin films [1].<br />
As given in Fig. 2, larger angles of incidence correspond to reflectance peaks at shorter wavelengths.<br />
[[Image:tfpc2.jpeg|thumb|300px|left| Fig. 2: Reflectance spectra of thin film photonic crystal's made from 230 nm PS spheres. From [1].]]<br />
In Fig. 3, a plot of the peak wavelength squared versus the sine of the incident angle squared has an intercept of <math>n_{eff}^2</math>, the square of the effective refractive index and a slope of <math>1/(4d)^2</math>, where <math> d</math> is the interplanar spacing in the (111) direction.<br />
[[Image:tfpc3.jpeg|thumb|300px|right| Fig. 3: Plot of peak wavelength squared versus the sine of incident angle for thin films made of spheres of 230, 300, and 376 nm. From [1].]]<br />
This arises form Bragg's law: <math>n \lambda = 2 d \sin \theta</math> and Snells law: <math>n_1 \sin \theta_1 = n_2 \sin \theta _2</math> to produce [1]:<br />
<br />
<math>\lambda = 2 d (n_eff^2 - sin^2 \theta)^{1/2} </math>.<br />
<br />
This type of characterization could also have been done with transmission, but was not pursued in this study since it does not provide additional information.<br />
For SEM, the regions analyzed from optical microscopy and reflectance spectroscopy were divided into smaller sections for analysis.<br />
SEM images were taken (Fig. 4) of the corners and centers of the smaller samples and fast Fourier transforms were taken of the images to check for homogeneity of <br />
growth.<br />
[[Image:tfpc4.jpeg|thumb|300px|right| Fig. 3: SEM images of cracks in the thin films at T = 25, 45, and 65˚ C showing that the directions of the cracks were the same for all temperatures.]]<br />
<br />
==Results and discussion==<br />
These three analytical methods were used to examine the effects of different growth conditions on the quality of the thin films.<br />
Temperature, T was found to have the largest effect on the growth quality of the crystals.<br />
Using optical microscopy, the authors found that domains were larger at higher T, with three to five times the lengths for domains for T at 45˚ to 65˚ C.<br />
Using SEM and optical microscopy, cracks ~5 µm wide were observed to form only along the <110> directions that became increasing anisotropic (larger domains), for higher T (e.g. 100 <math>\times</math> 300 µm at 65 ˚C).<br />
FFT's of the SEM images found increasing long-range order at higher T and showed evidence that cracks occurred after self-assembly during the drying process.<br />
The authors also noticed that the thicknesses of the crystals grown using vertical drying increased by 66% from 25 to 45 ˚C from 30 layers thick to 50 layers thick.<br />
<br />
Relative humidity was also thought to play a role since the PS colloidal spheres shrink upon drying, which increases the stresses on the crystal and increases the number of defects.<br />
In this study, most of the crystals for experiments varying T and the substrate angle were carried out at a RH of 10-20%.<br />
Higher RH (40-50%) environments at T = 45 and 65 ˚C showed the films had poor adhesion to the substrate.<br />
Hence, the results suggest that low RH is better for growing these types of crystals.<br />
For the substrate angles, 75˚ was shown to yield larger domains than those at 90˚.<br />
However, the 75˚ produces shorter films since the entire length of the substrate cannot be utilized, unlike the case for 90˚.<br />
<br />
The authors also found that higher concentrations of the PS spheres produced thicker thin films.<br />
However, they also found that when the volume fraction of the polymer was increased to 5% from 1%, the films adhered poorly to the substrate.<br />
Hence, they determined that 1% was optimal for fabrication.<br />
Sphere diameter was found to have little effect on the growth properties of the crystals.<br />
<br />
Combining all these factors, the authors used the Design of Experiments (DoE) methodology to systematically optimize all the experimental settings.<br />
They also used it to determine that temperature was most significant for optimizing the domain size.<br />
Using a number of Lenth plots, they examined the significance of the remaining factors and found that sphere diameter variation was not significant while substrate angle was.<br />
It was also found that factors, when coupled, did not produce statistically significant changes in the domain size.<br />
<br />
As mentioned by the authors of this study, the best crystals have large domain size, low defect density, well-aligned domains, good mechanical strength, and sharp reflectance peaks.<br />
They were able to optimize growth conditions (esp. temperature, which is optimized at T = 65˚) and produce high quality thin film photonic crystals made of colloidal PS using controlled vertical drying with a growth period of less than 5 days.<br />
<br />
==References==<br />
<br />
[1] McLachlan, M. A., Johnson, N. P., & Richard, M. (2004). Thin film photonic crystals: synthesis and characterisation. Journal of Materials Chemistry, 14(2), 144-150.<br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Thin_film_photonic_crystals:_synthesis_and_characterisation&diff=26106Thin film photonic crystals: synthesis and characterisation2012-11-17T02:19:40Z<p>Xingyu: </p>
<hr />
<div>_ short paragraph on keywords section<br />
<br />
== General Information ==<br />
'''Authors:''' M. A. McLachlan, N. P. Johnson, R. M. D. L. Rue, and D. W. McComb.<br />
<br />
'''Publication:''' Journal of Materials Chemistry, 14:144–150, 2004.<br />
<br />
'''Keywords:''' [[Thin film]], [[colloids]], [[photonic crystal]], [[self-assembly]]<br />
<br />
== Summary ==<br />
This paper examines the factors that affect colloidal self-assembly of thin film photonic crystals.<br />
The authors found that temperature has the largest effect and determined the ideal conditions for growing low-defect photonic crystals.<br />
There are many diverse applications and methods to create photonic crystals such as synthetic opals.<br />
One method employing colloidal self-assembly is controlled vertical drying, which is the focus of this study.<br />
The technique deposits colloidal spheres along the evaporation front of a meniscus that moves along the substrate.<br />
While the technique is generally effective, this paper systematically examines and optimizes the controllable conditions: temperature, relative humidity, sphere diameter, colloidal concentration, and substrate angle to assemble colloidal crystals from polystyrene (PS) spheres in aqueous solution.<br />
The crystals are then characterized using various microscopy and spectroscopy methods.<br />
<br />
==Experimental methods==<br />
The authors synthesized highly mono-disperse PS spheres with mean diameter in the ranges of 200-750 nm with a suspension polymerization [1].<br />
Different diameters were achieved by adjusting reagent concentrations or synthesis conditions such as stirring speed.<br />
The diameters of the spheres were measured using a transmission electron microscope (TEM) and their polydisperity recorded for large number of measurements (200 spheres).<br />
<br />
The colloidal crystals were grown using controlled vertical drying for temperatures ranging from 20 and 70˚ C (error within 0.2˚ C).<br />
The substrate angles were also varied, however, the paper only reports those for the angles of 75 and 90˚.<br />
The third condition that was studied was the effect of relative humidity of water vapor in the air (RH) defined as the percentage of amount of water vapor in the air compared to the saturation capacity of water vapor in the air.<br />
Special care was taken to ensure control of this quantity (to within 2%) of the set value during the entire growth period of the crystal by placing the device in a humidity controlled incubator.<br />
The size of the sample grown was 10 x 40 mm <math>^2</math> for all temperatures and RH.<br />
Depending on the conditions, the growth times ranged from < 4 to 40 days.<br />
The thin films were then studied using optical microscopy, reflectance spectroscopy, and scanning electron microscopy (SEM) for sections of the same sample grown under each experimental setting.<br />
<br />
For optical microscopy, the thin films were observed using an optical microscope with a CCD camera attached.<br />
This analysis showed that large cracks in the thin film that differed in number and size for the different experimental conditions (Fig. 1).<br />
[[Image:tfpc1.jpeg|thumb|300px|left| Fig. 1: Optical microscopy images of thin films at T = 25, 45, and 65˚C when grown showing cracks and domain sizes. Inset images are SEM images where the scale marker is 200 µm. From [1].]]<br />
The images were digitally processed and the crack density (percentage of cracks versus total area) computed for each of the samples.<br />
This gave a measure of the "macrosctructural" quality for the samples grown under different conditions.<br />
<br />
For reflectance spectroscopy, a beam of monochromatic light (selected through a single grating monochrometer) was focused on a 1 mm <math>^2</math> spot on the sample at controlled angles.<br />
The intensity of the reflected light was then collected over a range of wavelengths (300-900 nm).<br />
Since no incident light is transmitted at the stop-band wavelength, which arises when the refractive index contrast is insufficient to support a full photonic bandgap, the angular-resolved reflection spectra (e.g. reflected intensity vs. wavelength at different incident angles (Fig. 2)) gives information about the the thin films [1].<br />
As given in Fig. 2, larger angles of incidence correspond to reflectance peaks at shorter wavelengths.<br />
[[Image:tfpc2.jpeg|thumb|300px|left| Fig. 2: Reflectance spectra of thin film photonic crystal's made from 230 nm PS spheres. From [1].]]<br />
In Fig. 3, a plot of the peak wavelength squared versus the sine of the incident angle squared has an intercept of <math>n_{eff}^2</math>, the square of the effective refractive index and a slope of <math>1/(4d)^2</math>, where <math> d</math> is the interplanar spacing in the (111) direction.<br />
[[Image:tfpc3.jpeg|thumb|300px|right| Fig. 3: Plot of peak wavelength squared versus the sine of incident angle for thin films made of spheres of 230, 300, and 376 nm. From [1].]]<br />
This arises form Bragg's law: <math>n \lambda = 2 d \sin \theta</math> and Snells law: <math>n_1 \sin \theta_1 = n_2 \sin \theta _2</math> to produce [1]:<br />
<br />
<math>\lambda = 2 d (n_eff^2 - sin^2 \theta)^{1/2} </math>.<br />
<br />
This type of characterization could also have been done with transmission, but was not pursued in this study since it does not provide additional information.<br />
For SEM, the regions analyzed from optical microscopy and reflectance spectroscopy were divided into smaller sections for analysis.<br />
SEM images were taken (Fig. 4) of the corners and centers of the smaller samples and fast Fourier transforms were taken of the images to check for homogeneity of <br />
growth.<br />
[[Image:tfpc4.jpeg|thumb|300px|right| Fig. 3: SEM images of cracks in the thin films at T = 25, 45, and 65˚ C showing that the directions of the cracks were the same for all temperatures.]]<br />
<br />
==Results and discussion==<br />
These three analytical methods were used to examine the effects of different growth conditions on the quality of the thin films.<br />
Temperature, T was found to have the largest effect on the growth quality of the crystals.<br />
Using optical microscopy, the authors found that domains were larger at higher T, with three to five times the lengths for domains for T at 45˚ to 65˚ C.<br />
Using SEM and optical microscopy, cracks ~5 µm wide were observed to form only along the <110> directions that became increasing anisotropic (larger domains), for higher T (e.g. 100 <math>\times</math> 300 µm at 65 ˚C).<br />
FFT's of the SEM images found increasing long-range order at higher T and showed evidence that cracks occurred after self-assembly during the drying process.<br />
The authors also noticed that the thicknesses of the crystals grown using vertical drying increased by 66% from 25 to 45 ˚C from 30 layers thick to 50 layers thick.<br />
<br />
Relative humidity was also thought to play a role since the PS colloidal spheres shrink upon drying, which increases the stresses on the crystal and increases the number of defects.<br />
In this study, most of the crystals for experiments varying T and the substrate angle were carried out at a RH of 10-20%.<br />
Higher RH (40-50%) environments at T = 45 and 65 ˚C showed the films had poor adhesion to the substrate.<br />
Hence, the results suggest that low RH is better for growing these types of crystals.<br />
For the substrate angles, 75˚ was shown to yield larger domains than those at 90˚.<br />
However, the 75˚ produces shorter films since the entire length of the substrate cannot be utilized, unlike the case for 90˚.<br />
<br />
The authors also found that higher concentrations of the PS spheres produced thicker thin films.<br />
However, they also found that when the volume fraction of the polymer was increased to 5% from 1%, the films adhered poorly to the substrate.<br />
Hence, they determined that 1% was optimal for fabrication.<br />
Sphere diameter was found to have little effect on the growth properties of the crystals.<br />
<br />
Combining all these factors, the authors used the Design of Experiments (DoE) methodology to systematically optimize all the experimental settings.<br />
They also used it to determine that temperature was most significant for optimizing the domain size.<br />
Using a number of Lenth plots, they examined the significance of the remaining factors and found that sphere diameter variation was not significant while substrate angle was.<br />
It was also found that factors, when coupled, did not produce statistically significant changes in the domain size.<br />
<br />
As mentioned by the authors of this study, the best crystals have large domain size, low defect density, well-aligned domains, good mechanical strength, and sharp reflectance peaks.<br />
They were able to optimize growth conditions (esp. temperature, which is optimized at T = 65˚) and produce high quality thin film photonic crystals made of colloidal PS using controlled vertical drying with a growth period of less than 5 days.<br />
<br />
==References==<br />
<br />
[1] McLachlan, M. A., Johnson, N. P., & Richard, M. (2004). Thin film photonic crystals: synthesis and characterisation. Journal of Materials Chemistry, 14(2), 144-150.<br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Tfpc4.jpeg&diff=26105File:Tfpc4.jpeg2012-11-17T02:18:48Z<p>Xingyu: uploaded a new version of "Image:Tfpc4.jpeg"</p>
<hr />
<div></div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Thin_film_photonic_crystals:_synthesis_and_characterisation&diff=26104Thin film photonic crystals: synthesis and characterisation2012-11-17T02:17:37Z<p>Xingyu: </p>
<hr />
<div>_ short paragraph on keywords section<br />
<br />
== General Information ==<br />
'''Authors:''' M. A. McLachlan, N. P. Johnson, R. M. D. L. Rue, and D. W. McComb.<br />
<br />
'''Publication:''' Journal of Materials Chemistry, 14:144–150, 2004.<br />
<br />
'''Keywords:''' [[Thin film]], [[colloids]], [[photonic crystal]], [[self-assembly]]<br />
<br />
== Summary ==<br />
This paper examines the factors that affect colloidal self-assembly of thin film photonic crystals.<br />
The authors found that temperature has the largest effect and determined the ideal conditions for growing low-defect photonic crystals.<br />
There are many diverse applications and methods to create photonic crystals such as synthetic opals.<br />
One method employing colloidal self-assembly is controlled vertical drying, which is the focus of this study.<br />
The technique deposits colloidal spheres along the evaporation front of a meniscus that moves along the substrate.<br />
While the technique is generally effective, this paper systematically examines and optimizes the controllable conditions: temperature, relative humidity, sphere diameter, colloidal concentration, and substrate angle to assemble colloidal crystals from polystyrene (PS) spheres in aqueous solution.<br />
The crystals are then characterized using various microscopy and spectroscopy methods.<br />
<br />
==Experimental methods==<br />
The authors synthesized highly mono-disperse PS spheres with mean diameter in the ranges of 200-750 nm with a suspension polymerization [1].<br />
Different diameters were achieved by adjusting reagent concentrations or synthesis conditions such as stirring speed.<br />
The diameters of the spheres were measured using a transmission electron microscope (TEM) and their polydisperity recorded for large number of measurements (200 spheres).<br />
<br />
The colloidal crystals were grown using controlled vertical drying for temperatures ranging from 20 and 70˚ C (error within 0.2˚ C).<br />
The substrate angles were also varied, however, the paper only reports those for the angles of 75 and 90˚.<br />
The third condition that was studied was the effect of relative humidity of water vapor in the air (RH) defined as the percentage of amount of water vapor in the air compared to the saturation capacity of water vapor in the air.<br />
Special care was taken to ensure control of this quantity (to within 2%) of the set value during the entire growth period of the crystal by placing the device in a humidity controlled incubator.<br />
The size of the sample grown was 10 x 40 mm <math>^2</math> for all temperatures and RH.<br />
Depending on the conditions, the growth times ranged from < 4 to 40 days.<br />
The thin films were then studied using optical microscopy, reflectance spectroscopy, and scanning electron microscopy (SEM) for sections of the same sample grown under each experimental setting.<br />
<br />
For optical microscopy, the thin films were observed using an optical microscope with a CCD camera attached.<br />
This analysis showed that large cracks in the thin film that differed in number and size for the different experimental conditions (Fig. 1).<br />
[[Image:tfpc1.jpeg|thumb|300px|left| Fig. 1: Optical microscopy images of thin films at T = 25, 45, and 65˚C when grown showing cracks and domain sizes. Inset images are SEM images where the scale marker is 200 µm. From [1].]]<br />
The images were digitally processed and the crack density (percentage of cracks versus total area) computed for each of the samples.<br />
This gave a measure of the "macrosctructural" quality for the samples grown under different conditions.<br />
<br />
For reflectance spectroscopy, a beam of monochromatic light (selected through a single grating monochrometer) was focused on a 1 mm <math>^2</math> spot on the sample at controlled angles.<br />
The intensity of the reflected light was then collected over a range of wavelengths (300-900 nm).<br />
Since no incident light is transmitted at the stop-band wavelength, which arises when the refractive index contrast is insufficient to support a full photonic bandgap, the angular-resolved reflection spectra (e.g. reflected intensity vs. wavelength at different incident angles (Fig. 2)) gives information about the the thin films [1].<br />
As given in Fig. 2, larger angles of incidence correspond to reflectance peaks at shorter wavelengths.<br />
[[Image:tfpc2.jpeg|thumb|300px|right| Fig. 2: Reflectance spectra of thin film photonic crystal's made from 230 nm PS spheres. From [1].]]<br />
In Fig. 3, a plot of the peak wavelength squared versus the sine of the incident angle squared has an intercept of <math>n_{eff}^2</math>, the square of the effective refractive index and a slope of <math>1/(4d)^2</math>, where <math> d</math> is the interplanar spacing in the (111) direction.<br />
[[Image:tfpc3.jpeg|thumb|300px|right| Fig. 3: Plot of peak wavelength squared versus the sine of incident angle for thin films made of spheres of 230, 300, and 376 nm. From [1].]]<br />
This arises form Bragg's law: <math>n \lambda = 2 d \sin \theta</math> and Snells law: <math>n_1 \sin \theta_1 = n_2 \sin \theta _2</math> to produce [1]:<br />
<br />
<math>\lambda = 2 d (n_eff^2 - sin^2 \theta)^{1/2} </math>.<br />
<br />
This type of characterization could also have been done with transmission, but was not pursued in this study since it does not provide additional information.<br />
For SEM, the regions analyzed from optical microscopy and reflectance spectroscopy were divided into smaller sections for analysis.<br />
SEM images were taken (Fig. 4) of the corners and centers of the smaller samples and fast Fourier transforms were taken of the images to check for homogeneity of <br />
growth.<br />
[[Image:tfpc4.jpeg|thumb|300px|left| Fig. 3: SEM images of cracks in the thin films at T = 25, 45, and 65˚ C showing that the directions of the cracks were the same for all temperatures.]]<br />
<br />
==Results and discussion==<br />
These three analytical methods were used to examine the effects of different growth conditions on the quality of the thin films.<br />
Temperature, T was found to have the largest effect on the growth quality of the crystals.<br />
Using optical microscopy, the authors found that domains were larger at higher T, with three to five times the lengths for domains for T at 45˚ to 65˚ C.<br />
Using SEM and optical microscopy, cracks ~5 µm wide were observed to form only along the <110> directions that became increasing anisotropic (larger domains), for higher T (e.g. 100 <math>\times</math> 300 µm at 65 ˚C).<br />
FFT's of the SEM images found increasing long-range order at higher T and showed evidence that cracks occurred after self-assembly during the drying process.<br />
The authors also noticed that the thicknesses of the crystals grown using vertical drying increased by 66% from 25 to 45 ˚C from 30 layers thick to 50 layers thick.<br />
<br />
Relative humidity was also thought to play a role since the PS colloidal spheres shrink upon drying, which increases the stresses on the crystal and increases the number of defects.<br />
In this study, most of the crystals for experiments varying T and the substrate angle were carried out at a RH of 10-20%.<br />
Higher RH (40-50%) environments at T = 45 and 65 ˚C showed the films had poor adhesion to the substrate.<br />
Hence, the results suggest that low RH is better for growing these types of crystals.<br />
For the substrate angles, 75˚ was shown to yield larger domains than those at 90˚.<br />
However, the 75˚ produces shorter films since the entire length of the substrate cannot be utilized, unlike the case for 90˚.<br />
<br />
The authors also found that higher concentrations of the PS spheres produced thicker thin films.<br />
However, they also found that when the volume fraction of the polymer was increased to 5% from 1%, the films adhered poorly to the substrate.<br />
Hence, they determined that 1% was optimal for fabrication.<br />
Sphere diameter was found to have little effect on the growth properties of the crystals.<br />
<br />
Combining all these factors, the authors used the Design of Experiments (DoE) methodology to systematically optimize all the experimental settings.<br />
They also used it to determine that temperature was most significant for optimizing the domain size.<br />
Using a number of Lenth plots, they examined the significance of the remaining factors and found that sphere diameter variation was not significant while substrate angle was.<br />
It was also found that factors, when coupled, did not produce statistically significant changes in the domain size.<br />
<br />
As mentioned by the authors of this study, the best crystals have large domain size, low defect density, well-aligned domains, good mechanical strength, and sharp reflectance peaks.<br />
They were able to optimize growth conditions (esp. temperature, which is optimized at T = 65˚) and produce high quality thin film photonic crystals made of colloidal PS using controlled vertical drying with a growth period of less than 5 days.<br />
<br />
==References==<br />
<br />
[1] McLachlan, M. A., Johnson, N. P., & Richard, M. (2004). Thin film photonic crystals: synthesis and characterisation. Journal of Materials Chemistry, 14(2), 144-150.<br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Tfpc4.jpeg&diff=26103File:Tfpc4.jpeg2012-11-17T02:17:18Z<p>Xingyu: </p>
<hr />
<div></div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Tfpc3.jpeg&diff=26102File:Tfpc3.jpeg2012-11-17T02:17:06Z<p>Xingyu: </p>
<hr />
<div></div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Tfpc2.jpeg&diff=26101File:Tfpc2.jpeg2012-11-17T02:16:18Z<p>Xingyu: </p>
<hr />
<div></div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Tfpc1.jpeg&diff=26100File:Tfpc1.jpeg2012-11-17T02:13:17Z<p>Xingyu: </p>
<hr />
<div></div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Thin_film_photonic_crystals:_synthesis_and_characterisation&diff=25729Thin film photonic crystals: synthesis and characterisation2012-10-31T01:10:44Z<p>Xingyu: New page: I'll do this paper: M. A. McLachlan, N. P. Johnson, R. M. D. L. Rue, and D. W. McComb. Thin film photonic crystals: synthesis and characterisation. J. Mater. Chem., 14:144–150, 200...</p>
<hr />
<div>I'll do this paper:<br />
<br />
M. A. McLachlan, N. P. Johnson, R. M. D. L. Rue, and D. W. McComb. Thin film photonic crystals: synthesis and characterisation. J. Mater. Chem., 14:144–150, 2004.<br />
<br />
-Xingyu</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Xingyu_Zhang&diff=25728Xingyu Zhang2012-10-31T01:08:55Z<p>Xingyu: </p>
<hr />
<div>Topic 1: [[Measuring translational, rotational, and vibrational dynamics with digital holographic microscopy]]<br />
<br />
Topic 2: [[Long-range attraction between colloidal spheres at the air-water interface: The consequence of an irregular meniscus]]<br />
<br />
Topic 3: [[Thin film photonic crystals: synthesis and characterisation]]</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Wetting&diff=25531Wetting2012-10-16T13:40:11Z<p>Xingyu: </p>
<hr />
<div>''Written by Grant England AP225, Fall 2011''<br />
<br />
==Introduction==<br />
Wetting refers to how well or poorly a liquid contacts a surface. Usually the term applies to water, where if a surface is [[hydrophobic]] it will not wet well while if it is [[hydrophilic]] it will wet well. The relative [[hydrophobicity]] or [[hydrophilicity]] of a substrate can be determined by measuring the [[contact angle]] of water with the surface. A liquid wets a surface better if it has a low [[contact angle]] with that surface. In general, if the contact angle is lower than 90 degrees, the liquid is considered to be wetting for that surface; while, if the contact angle is greater than 90 degrees, the liquid is non-wetting for the surface.<br />
<br />
[[Image:wetting.png|thumb|400px| Diagram showing states for a liquid on a surface with (A) little wetting, (B) moderate wetting, and (C) high wetting. (Taken from[http://en.wikipedia.org/wiki/Wetting Wikipedia Article] ) ]]<br />
<br />
<br />
<br />
==Cassie and Wenzel States==<br />
<br />
Surfaces can be made to be [[superhydrophobic]] or [[superhydrophilic]] by modification to have high aspect-ratio structures (micro-posts) on their surfaces, and chemical modification of these surfaces with [[hydrophobic]] or [[hydrophilic]] functional groups. Depending on the energetics of the surface, a drop of liquid on such a surface can be in either of two states--sitting on top of the micro-posts or sitting with the micro-posts embedded within it. The former is the [[Cassie state]] and the latter is the [[Wenzel state]].<br />
<br />
==Ways to Change Wetting==<br />
<br />
[[Surfactant]]s can change the wetting properties of a liquid, since they change the energetics of the surface of the liquid. Also, changing the properties of the surface by chemical functionalization or modification of the surface (etching or other methods of attaining high aspect-ratio structures on the surface which increase the microscopic surface area) can change a liquid-solid interaction from wetting to non-wetting or vice versa.<br />
<br />
<br />
== Applications of Wetting ==<br />
<br />
Wetting can be used for chemical sensing as different chemicals and concentrations result in different surface properties. The sensing result can be extracted by a photonic-crystal based [[Encoding complex wettability patterns in chemically functionalized 3D photonic crystals|colourimetric method (WICK)]]. The chemical selectivity can be greatly enhanced by an array of different surface functionalized WICKs, which is capable of identifying liquids as an [[Combinatorial Wetting in Colour: An Optofluidic Nose|optofluidic nose]].<br />
<br />
By changing the wetting properties of a material, one can change its contact angle hysteresis. If the contact angle hysteresis of a material is extremely small, droplets will slide off at a small incline. This has large implications for [[Liquid-Infused Nanostructured Surfaces with Extreme Anti-Ice and Anti-Frost Performance| anti-ice coatings]].<br />
<br />
<br />
== Examples ==<br />
====[[Long-range attraction between colloidal spheres at the air-water interface: The consequence of an irregular meniscus]] ====<br />
Stamou et al. showed that nonuniform wetting can explain the long-range attractive interactions between colloidal particles at an interface. It is responsible for certain favored orientations of pairs of particles and larger aggregates, as well as frustrated geometries that do not appear in the experimental results. By changing the wetting properties of the liquid, the authors showed that the aggregation behavior of the particles agreed with a model based on nonuniform wetting.<br />
<br />
==See also==<br />
<br />
[[Soft matter - Course review#Week 4 - Wetting|Wetting]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
[[Dynamics_of_forced_wetting]]<br />
<br />
[[Dynamics_of_total_wetting]]<br />
<br />
[http://aizenberglab.seas.harvard.edu/index.php?show=research_topic&top=4 Aizenberg Lab @Harvard: Wettability]<br />
<br />
[http://en.wikipedia.org/wiki/Wetting Wikipedia Article]<br />
<br />
== Keyword in references: ==<br />
<br />
[[Controlled switching of the wetting behavior of biomimetic surfaces with hydrogel-supported nanostructures]]<br />
<br />
[[Critical Casimir effect in three-dimensional Ising systems: Measurements on binary wetting films]]<br />
<br />
[[Dewetting-Induced Membrane Formation by Adhesion of Amphiphile-Laden Interface]]<br />
<br />
[[Encoding complex wettability patterns in chemically functionalized 3D photonic crystals]]<br />
<br />
[[Pitcher plant inspired non-stick surface]]<br />
<br />
[[Structural Transformation by Electrodeposition on Patterned Substrates (STEPS) - A New Versatile Nanofabrication Method]]<br />
<br />
[[Enriching libraries of high-aspect-ratio micro- or nanostructures by rapid, low-cost, benchtop nanofabrication]]<br />
<br />
[[Steering nanofibers: An integrative approach to bio-inspired fiber fabrication and assembly]]<br />
<br />
[[Fine-Tuning the Degree of Stem Cell Polarization and Alignment on Ordered Arrays of High-Aspect-Ratio Nanopillars]]<br />
<br />
[[Screening Conditions for Rationally Engineered Electrodeposition of Nanostructures (SCREEN): Electrodeposition and Applications of Polypyrrole Nanofibers using Microfluidic Gradients]]<br />
<br />
[[Combinatorial Wetting in Colour: An Optofluidic Nose]]<br />
<br />
[[Functionalized glass coating for PDMS microfluidic devices]]<br />
<br />
[[Elastic Instability in Growing Yeast Colonies]]<br />
<br />
[[Liquid-infused structured surfaces with exceptional anti-biofouling performance]]<br />
<br />
[[Liquid-Infused Nanostructured Surfaces with Extreme Anti-Ice and Anti-Frost Performance]]<br />
<br />
[[Wetting in Color: Colorimetric Differentiation of Organic Liquids with High Selectivity]]<br />
<br />
[[Electric-field-induced capillary attraction between like-charged particles at liquid interfaces]]<br />
<br />
[[Dynamics of foam drainage]]<br />
<br />
[[Dynamic mechanisms for apparent slip on hydrophobic surfaces]]<br />
<br />
[[Linear stability and transient growth in driven contact lines]]<br />
<br />
[[Spreading of Droplets on a Solid Surface]]<br />
<br />
[[The single-cell chemostat: an agarose-based, microfluidic device for high-throughput, single-cell studies of bacteria and bacterial communities]]<br />
<br />
[[DNA molecules and configurations in a solid- state nanopore microscope]]<br />
<br />
[[Graphene as a subnanometre trans-electrode membrane]]<br />
<br />
[[￼￼Non-stick water]]<br />
<br />
[[How aphids lose their marbles]]<br />
<br />
[[Elasticity of an interfacial particle raft]]<br />
<br />
[[Nested self-similar wrinkling patterns in skins]]<br />
<br />
[[The ‘‘Cheerios effect’’]]<br />
<br />
[[Soft lubrication: The elastohydrodynamics of nonconforming and conforming contacts]]<br />
<br />
[[Capillary rise between elastic sheets]]<br />
<br />
[[Dynamics of Surfactant-Driven Fracture of Particle Rafts]]<br />
<br />
[[Mechanics of Interfacial Composite Materials]]<br />
<br />
[[The Universal Dynamics of Cell Spreading]]<br />
<br />
[[Localized and extended deformations of elastic shells]]<br />
<br />
[[Self-Organization of a Mesoscale Bristle into Ordered, Hierarchical Helical Assemblies]]<br />
<br />
[[Hygromorphs: from pine cones to biomimetic bilayers]]<br />
<br />
[[Infochemistry: Encoding Information as Optical Pulses Using Droplets in a Microfluidic Device]]<br />
<br />
[[Control of Shape and Size of Nanopillar Assembly by Adhesion-Mediated Elastocapillary Interaction]]<br />
<br />
[[How wet paper curls]]<br />
<br />
[[Shock-driven jamming and periodic fracture of particulate rafts]]<br />
<br />
[[Hydrodynamics of Writing with Ink]]<br />
<br />
[[Skating on a Film of Air: Drops Impacting on a Surface]]<br />
<br />
[[Cationic liposome–microtubule complexes: Pathways to the formation of two-state lipid–protein nanotubes with open or closed ends]]<br />
<br />
[[Single molecule statistics and the polynucleotide unzipping transition]]<br />
<br />
[[Stable island arrays by height-constrained Stranski–Krastanov growth]]<br />
<br />
[[Nanoscale Domain Stability in Organic Monolayers on Metals]]<br />
<br />
[[Electromigration lifetime and critical void volume]]<br />
<br />
[[Statistics of Electromigration Lifetime Analyzed Using a Deterministic Transient Model]]<br />
<br />
[[Saturated voids in interconnect lines due to thermal strains and electromigration]]<br />
<br />
[[Drying-induced bifurcation in a hydrogel-actuated nanostructure]]<br />
<br />
[[Foldable Printed Circuit Boards on Paper Substrates]]<br />
<br />
[[One-step formation of multiple emulsions in microfluidics]]<br />
<br />
[[A new device for the generation of microbubbles]]<br />
<br />
[[Microfluidic synthesis of advanced microparticles for encapsulation and controlled release]]<br />
<br />
[[Monodisperse Gas-Filled Microparticles from Reactions in Double Emulsions]]<br />
<br />
[[Patterned Colloidal Coating Using Adhesive Emulsions]]<br />
<br />
[[Surface-Tension-Induced Synthesis of Complex Particles Using Confined Polymeric Fluids]]<br />
<br />
[[Glass coating for PDMS microfluidic channels by sol–gel methods]]<br />
<br />
[[Microfluidic fabrication of complex-shaped microfibers by liquid template-aided multiphase microflow]]<br />
<br />
[[Controllable Monodisperse Multiple Emulsions]]<br />
<br />
[[Arrested fluid-fluid phase separation in depletion systems: Implications of the characteristic length on gel formation and rheology]]<br />
<br />
[[Eutectic Gallium-Indium (EGaIn): A Liquid Metal Alloy for the Formation of Stable Structures in Microchannels at Room Temperature]]<br />
<br />
[[Surface acoustic wave (SAW) directed droplet flow in microfluidics for PDMS devices]]<br />
<br />
[[Self-Assembled Polymer Membrane Capsules Inflated by Osmotic Pressure]]<br />
<br />
[[Dewetting Instability during the Formation of Polymersomes from Block-Copolymer-Stabilized Double Emulsions]]<br />
<br />
[[Suppression of instabilities in multiphase flow by geometric confinement]]<br />
<br />
[[Double-emulsion drops with ultra-thin shells for capsule templates]]<br />
<br />
[[Amphiphilic Crescent-Moon-Shaped Microparticles Formed by Selective Adsorption of Colloids]]<br />
<br />
[[Multiple Polymersomes for Programmed Release of Multiple Components]]<br />
<br />
[[Uniform Nonspherical Colloidal Particles with Tunable Shapes]]<br />
<br />
[[Controlled production of emulsion drops using an electric field in a flow-focusing microfluidic device]]<br />
<br />
[[Drop-based microfluidic devices for encapsulation of single cells]]<br />
<br />
[[Highly monodisperse conjugated polymer particles synthesized with drop-based microfluidics]]<br />
<br />
[[Nonspherical Colloidosomes with Multiple Compartments from Double Emulsions]]<br />
<br />
[[Electric Control of Droplets in Microfluidic Devices]]<br />
<br />
[[Non-coalescence of oppositely charged droplets in pH-sensitive emulsions]]<br />
<br />
[[Protein Expression, Aggregation, and Triggered Release from Polymersomes as Artificial Cell-like Structures]]<br />
<br />
[[Electric-field-induced capillary attraction between like-charged particles at liquid interfaces]]<br />
<br />
[[Short-time self-diffusion of nearly hard spheres at an oil–water interface]]<br />
<br />
[[High throughput production of single core double emulsions in a parallelized microfluidic device]]<br />
<br />
[[Functional patterning of PDMS microfluidic devices using integrated chemo-masks]]<br />
<br />
[[Drop formation in non-planar microfluidic devices]]<br />
<br />
[[Skating on a Film of Air: Drops Impacting on a Surface]]<br />
<br />
[[Novel surface acoustic wave (SAW)-driven closed PDMS flow chamber]]<br />
<br />
[[Osmotic spreading of Bacillus subtilis biofilms driven by an extracellular matrix]]<br />
<br />
[[Polymers fit for function Making emulsions drop by drop]]<br />
<br />
[[Dewetting-Induced Membrane Formation by Adhesion of Amphiphile-Laden Interfaces]]<br />
<br />
[[Multicompartment Polymersomes from Double Emulsions]]<br />
<br />
[[Hierarchical Porous Materials Made by Drying Complex Suspensions]]<br />
<br />
[[Corrugated interfaces in multiphase core-annular flow]]<br />
<br />
[[Microfluidic Fabrication of Monodisperse Biocompatible and Biodegradable Polymersomes with Controlled Permeability]]<br />
<br />
[[Double Emulsion Templated Monodisperse Phospholipid Vesicles]]<br />
<br />
[[￼Fabrication of Polymersomes using Double-Emulsion Templates in Glass-Coated Stamped Microfluidic Devices]]<br />
<br />
[[Dripping, Jetting, Drops, and Wetting: The Magic of Microfluidics]]<br />
<br />
[[Monodisperse Double Emulsions Generated from a Microcapillary Device]]<br />
<br />
[[Mechanism for clogging of microchannels]]<br />
<br />
[[Dynamics of Drying in 3D Porous Media]]<br />
<br />
[[The pressure drop along rectangular microchannels containing bubbles]]<br />
<br />
[[Eutectic Gallium-Indium (EGaIn): A Liquid Metal Alloy for the Formation of Stable Structures in Microchannels at Room Temperature]]<br />
<br />
[[Interfacial instabilities in a microfluidic Hele-Shaw cell]]<br />
<br />
[[Integrated Fabrication and Magnetic Positioning of Metallic and Polymeric Nanowires Embedded in Thin Epoxy Slabs]]<br />
<br />
[[Basic Microfluidic and Soft Lithographic Techniques]]<br />
<br />
[[Continuously tunable microdroplet-laser in a microfluidic channel]]<br />
<br />
[[Fabrication of Micrometer-Scale, Patterned Polyhedra by Self-Assembly]]<br />
<br />
[[Fabrication and Wetting Properties of Metallic Half-Shells with Submicron Diameters]]<br />
<br />
[[Chemical Force Spectroscopy in Heterogeneous Systems: Intermolecular Interactions Involving Epoxy Polymer, Mixed Monolayers, and Polar Solvents]]<br />
<br />
[[Surface Tension-Powered Self-Assembly of Microstructures—The State-of-the-Art]]<br />
<br />
[[Self-Assembled Monolayers of Thiolates on Metals as a Form of Nanotechnology]]<br />
<br />
[[Formation of droplets and bubbles in a microfluidic T-junction—scaling and mechanism of break-up]]</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Wetting&diff=25530Wetting2012-10-16T13:32:13Z<p>Xingyu: /* Applications of Wetting */</p>
<hr />
<div>''Written by Grant England AP225, Fall 2011''<br />
<br />
==Introduction==<br />
Wetting refers to how well or poorly a liquid contacts a surface. Usually the term applies to water, where if a surface is [[hydrophobic]] it will not wet well while if it is [[hydrophilic]] it will wet well. The relative [[hydrophobicity]] or [[hydrophilicity]] of a substrate can be determined by measuring the [[contact angle]] of water with the surface. A liquid wets a surface better if it has a low [[contact angle]] with that surface. In general, if the contact angle is lower than 90 degrees, the liquid is considered to be wetting for that surface; while, if the contact angle is greater than 90 degrees, the liquid is non-wetting for the surface.<br />
<br />
[[Image:wetting.png|thumb|400px| Diagram showing states for a liquid on a surface with (A) little wetting, (B) moderate wetting, and (C) high wetting. (Taken from[http://en.wikipedia.org/wiki/Wetting Wikipedia Article] ) ]]<br />
<br />
<br />
<br />
==Cassie and Wenzel States==<br />
<br />
Surfaces can be made to be [[superhydrophobic]] or [[superhydrophilic]] by modification to have high aspect-ratio structures (micro-posts) on their surfaces, and chemical modification of these surfaces with [[hydrophobic]] or [[hydrophilic]] functional groups. Depending on the energetics of the surface, a drop of liquid on such a surface can be in either of two states--sitting on top of the micro-posts or sitting with the micro-posts embedded within it. The former is the [[Cassie state]] and the latter is the [[Wenzel state]].<br />
<br />
==Ways to Change Wetting==<br />
<br />
[[Surfactant]]s can change the wetting properties of a liquid, since they change the energetics of the surface of the liquid. Also, changing the properties of the surface by chemical functionalization or modification of the surface (etching or other methods of attaining high aspect-ratio structures on the surface which increase the microscopic surface area) can change a liquid-solid interaction from wetting to non-wetting or vice versa.<br />
<br />
<br />
== Applications of Wetting ==<br />
<br />
Wetting can be used for chemical sensing as different chemicals and concentrations result in different surface properties. The sensing result can be extracted by a photonic-crystal based [[Encoding complex wettability patterns in chemically functionalized 3D photonic crystals|colourimetric method (WICK)]]. The chemical selectivity can be greatly enhanced by an array of different surface functionalized WICKs, which is capable of identifying liquids as an [[Combinatorial Wetting in Colour: An Optofluidic Nose|optofluidic nose]].<br />
<br />
By changing the wetting properties of a material, one can change its contact angle hysteresis. If the contact angle hysteresis of a material is extremely small, droplets will slide off at a small incline. This has large implications for [[Liquid-Infused Nanostructured Surfaces with Extreme Anti-Ice and Anti-Frost Performance| anti-ice coatings]].<br />
<br />
Stamou et al. showed that [[Long-range attraction between colloidal spheres at the air-water interface: The consequence of an irregular meniscus|nonuniform wetting]] can explain the long-range attraction between colloidal particles at an interface. It is responsible for favored orientations for pairs of particles and larger aggregates, and explain how certain frustrated geometries do not appear in experimental results.<br />
<br />
==See also==<br />
<br />
[[Soft matter - Course review#Week 4 - Wetting|Wetting]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
[[Dynamics_of_forced_wetting]]<br />
<br />
[[Dynamics_of_total_wetting]]<br />
<br />
[http://aizenberglab.seas.harvard.edu/index.php?show=research_topic&top=4 Aizenberg Lab @Harvard: Wettability]<br />
<br />
[http://en.wikipedia.org/wiki/Wetting Wikipedia Article]<br />
<br />
== Keyword in references: ==<br />
<br />
[[Controlled switching of the wetting behavior of biomimetic surfaces with hydrogel-supported nanostructures]]<br />
<br />
[[Critical Casimir effect in three-dimensional Ising systems: Measurements on binary wetting films]]<br />
<br />
[[Dewetting-Induced Membrane Formation by Adhesion of Amphiphile-Laden Interface]]<br />
<br />
[[Encoding complex wettability patterns in chemically functionalized 3D photonic crystals]]<br />
<br />
[[Pitcher plant inspired non-stick surface]]<br />
<br />
[[Structural Transformation by Electrodeposition on Patterned Substrates (STEPS) - A New Versatile Nanofabrication Method]]<br />
<br />
[[Enriching libraries of high-aspect-ratio micro- or nanostructures by rapid, low-cost, benchtop nanofabrication]]<br />
<br />
[[Steering nanofibers: An integrative approach to bio-inspired fiber fabrication and assembly]]<br />
<br />
[[Fine-Tuning the Degree of Stem Cell Polarization and Alignment on Ordered Arrays of High-Aspect-Ratio Nanopillars]]<br />
<br />
[[Screening Conditions for Rationally Engineered Electrodeposition of Nanostructures (SCREEN): Electrodeposition and Applications of Polypyrrole Nanofibers using Microfluidic Gradients]]<br />
<br />
[[Combinatorial Wetting in Colour: An Optofluidic Nose]]<br />
<br />
[[Functionalized glass coating for PDMS microfluidic devices]]<br />
<br />
[[Elastic Instability in Growing Yeast Colonies]]<br />
<br />
[[Liquid-infused structured surfaces with exceptional anti-biofouling performance]]<br />
<br />
[[Liquid-Infused Nanostructured Surfaces with Extreme Anti-Ice and Anti-Frost Performance]]<br />
<br />
[[Wetting in Color: Colorimetric Differentiation of Organic Liquids with High Selectivity]]<br />
<br />
[[Electric-field-induced capillary attraction between like-charged particles at liquid interfaces]]<br />
<br />
[[Dynamics of foam drainage]]<br />
<br />
[[Dynamic mechanisms for apparent slip on hydrophobic surfaces]]<br />
<br />
[[Linear stability and transient growth in driven contact lines]]<br />
<br />
[[Spreading of Droplets on a Solid Surface]]<br />
<br />
[[The single-cell chemostat: an agarose-based, microfluidic device for high-throughput, single-cell studies of bacteria and bacterial communities]]<br />
<br />
[[DNA molecules and configurations in a solid- state nanopore microscope]]<br />
<br />
[[Graphene as a subnanometre trans-electrode membrane]]<br />
<br />
[[￼￼Non-stick water]]<br />
<br />
[[How aphids lose their marbles]]<br />
<br />
[[Elasticity of an interfacial particle raft]]<br />
<br />
[[Nested self-similar wrinkling patterns in skins]]<br />
<br />
[[The ‘‘Cheerios effect’’]]<br />
<br />
[[Soft lubrication: The elastohydrodynamics of nonconforming and conforming contacts]]<br />
<br />
[[Capillary rise between elastic sheets]]<br />
<br />
[[Dynamics of Surfactant-Driven Fracture of Particle Rafts]]<br />
<br />
[[Mechanics of Interfacial Composite Materials]]<br />
<br />
[[The Universal Dynamics of Cell Spreading]]<br />
<br />
[[Localized and extended deformations of elastic shells]]<br />
<br />
[[Self-Organization of a Mesoscale Bristle into Ordered, Hierarchical Helical Assemblies]]<br />
<br />
[[Hygromorphs: from pine cones to biomimetic bilayers]]<br />
<br />
[[Infochemistry: Encoding Information as Optical Pulses Using Droplets in a Microfluidic Device]]<br />
<br />
[[Control of Shape and Size of Nanopillar Assembly by Adhesion-Mediated Elastocapillary Interaction]]<br />
<br />
[[How wet paper curls]]<br />
<br />
[[Shock-driven jamming and periodic fracture of particulate rafts]]<br />
<br />
[[Hydrodynamics of Writing with Ink]]<br />
<br />
[[Skating on a Film of Air: Drops Impacting on a Surface]]<br />
<br />
[[Cationic liposome–microtubule complexes: Pathways to the formation of two-state lipid–protein nanotubes with open or closed ends]]<br />
<br />
[[Single molecule statistics and the polynucleotide unzipping transition]]<br />
<br />
[[Stable island arrays by height-constrained Stranski–Krastanov growth]]<br />
<br />
[[Nanoscale Domain Stability in Organic Monolayers on Metals]]<br />
<br />
[[Electromigration lifetime and critical void volume]]<br />
<br />
[[Statistics of Electromigration Lifetime Analyzed Using a Deterministic Transient Model]]<br />
<br />
[[Saturated voids in interconnect lines due to thermal strains and electromigration]]<br />
<br />
[[Drying-induced bifurcation in a hydrogel-actuated nanostructure]]<br />
<br />
[[Foldable Printed Circuit Boards on Paper Substrates]]<br />
<br />
[[One-step formation of multiple emulsions in microfluidics]]<br />
<br />
[[A new device for the generation of microbubbles]]<br />
<br />
[[Microfluidic synthesis of advanced microparticles for encapsulation and controlled release]]<br />
<br />
[[Monodisperse Gas-Filled Microparticles from Reactions in Double Emulsions]]<br />
<br />
[[Patterned Colloidal Coating Using Adhesive Emulsions]]<br />
<br />
[[Surface-Tension-Induced Synthesis of Complex Particles Using Confined Polymeric Fluids]]<br />
<br />
[[Glass coating for PDMS microfluidic channels by sol–gel methods]]<br />
<br />
[[Microfluidic fabrication of complex-shaped microfibers by liquid template-aided multiphase microflow]]<br />
<br />
[[Controllable Monodisperse Multiple Emulsions]]<br />
<br />
[[Arrested fluid-fluid phase separation in depletion systems: Implications of the characteristic length on gel formation and rheology]]<br />
<br />
[[Eutectic Gallium-Indium (EGaIn): A Liquid Metal Alloy for the Formation of Stable Structures in Microchannels at Room Temperature]]<br />
<br />
[[Surface acoustic wave (SAW) directed droplet flow in microfluidics for PDMS devices]]<br />
<br />
[[Self-Assembled Polymer Membrane Capsules Inflated by Osmotic Pressure]]<br />
<br />
[[Dewetting Instability during the Formation of Polymersomes from Block-Copolymer-Stabilized Double Emulsions]]<br />
<br />
[[Suppression of instabilities in multiphase flow by geometric confinement]]<br />
<br />
[[Double-emulsion drops with ultra-thin shells for capsule templates]]<br />
<br />
[[Amphiphilic Crescent-Moon-Shaped Microparticles Formed by Selective Adsorption of Colloids]]<br />
<br />
[[Multiple Polymersomes for Programmed Release of Multiple Components]]<br />
<br />
[[Uniform Nonspherical Colloidal Particles with Tunable Shapes]]<br />
<br />
[[Controlled production of emulsion drops using an electric field in a flow-focusing microfluidic device]]<br />
<br />
[[Drop-based microfluidic devices for encapsulation of single cells]]<br />
<br />
[[Highly monodisperse conjugated polymer particles synthesized with drop-based microfluidics]]<br />
<br />
[[Nonspherical Colloidosomes with Multiple Compartments from Double Emulsions]]<br />
<br />
[[Electric Control of Droplets in Microfluidic Devices]]<br />
<br />
[[Non-coalescence of oppositely charged droplets in pH-sensitive emulsions]]<br />
<br />
[[Protein Expression, Aggregation, and Triggered Release from Polymersomes as Artificial Cell-like Structures]]<br />
<br />
[[Electric-field-induced capillary attraction between like-charged particles at liquid interfaces]]<br />
<br />
[[Short-time self-diffusion of nearly hard spheres at an oil–water interface]]<br />
<br />
[[High throughput production of single core double emulsions in a parallelized microfluidic device]]<br />
<br />
[[Functional patterning of PDMS microfluidic devices using integrated chemo-masks]]<br />
<br />
[[Drop formation in non-planar microfluidic devices]]<br />
<br />
[[Skating on a Film of Air: Drops Impacting on a Surface]]<br />
<br />
[[Novel surface acoustic wave (SAW)-driven closed PDMS flow chamber]]<br />
<br />
[[Osmotic spreading of Bacillus subtilis biofilms driven by an extracellular matrix]]<br />
<br />
[[Polymers fit for function Making emulsions drop by drop]]<br />
<br />
[[Dewetting-Induced Membrane Formation by Adhesion of Amphiphile-Laden Interfaces]]<br />
<br />
[[Multicompartment Polymersomes from Double Emulsions]]<br />
<br />
[[Hierarchical Porous Materials Made by Drying Complex Suspensions]]<br />
<br />
[[Corrugated interfaces in multiphase core-annular flow]]<br />
<br />
[[Microfluidic Fabrication of Monodisperse Biocompatible and Biodegradable Polymersomes with Controlled Permeability]]<br />
<br />
[[Double Emulsion Templated Monodisperse Phospholipid Vesicles]]<br />
<br />
[[￼Fabrication of Polymersomes using Double-Emulsion Templates in Glass-Coated Stamped Microfluidic Devices]]<br />
<br />
[[Dripping, Jetting, Drops, and Wetting: The Magic of Microfluidics]]<br />
<br />
[[Monodisperse Double Emulsions Generated from a Microcapillary Device]]<br />
<br />
[[Mechanism for clogging of microchannels]]<br />
<br />
[[Dynamics of Drying in 3D Porous Media]]<br />
<br />
[[The pressure drop along rectangular microchannels containing bubbles]]<br />
<br />
[[Eutectic Gallium-Indium (EGaIn): A Liquid Metal Alloy for the Formation of Stable Structures in Microchannels at Room Temperature]]<br />
<br />
[[Interfacial instabilities in a microfluidic Hele-Shaw cell]]<br />
<br />
[[Integrated Fabrication and Magnetic Positioning of Metallic and Polymeric Nanowires Embedded in Thin Epoxy Slabs]]<br />
<br />
[[Basic Microfluidic and Soft Lithographic Techniques]]<br />
<br />
[[Continuously tunable microdroplet-laser in a microfluidic channel]]<br />
<br />
[[Fabrication of Micrometer-Scale, Patterned Polyhedra by Self-Assembly]]<br />
<br />
[[Fabrication and Wetting Properties of Metallic Half-Shells with Submicron Diameters]]<br />
<br />
[[Chemical Force Spectroscopy in Heterogeneous Systems: Intermolecular Interactions Involving Epoxy Polymer, Mixed Monolayers, and Polar Solvents]]<br />
<br />
[[Surface Tension-Powered Self-Assembly of Microstructures—The State-of-the-Art]]<br />
<br />
[[Self-Assembled Monolayers of Thiolates on Metals as a Form of Nanotechnology]]<br />
<br />
[[Formation of droplets and bubbles in a microfluidic T-junction—scaling and mechanism of break-up]]</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Long-range_attraction_between_colloidal_spheres_at_the_air-water_interface:_The_consequence_of_an_irregular_meniscus&diff=25529Long-range attraction between colloidal spheres at the air-water interface: The consequence of an irregular meniscus2012-10-16T13:22:26Z<p>Xingyu: </p>
<hr />
<div>== General Information ==<br />
'''Authors:''' Dimitris Stamou, Claus Duschl, and Diethelm Johannsmann<br />
<br />
'''Publication:''' Physical Review E, Vol 62, Issue 4, pp. 5263-5272 (2000)<br />
<br />
'''Keywords:''' [[Wetting]], [[Surface force]], [[Interface]], [[Capillarity]], [[Colloids]]<br />
<br />
== Summary ==<br />
<br />
This paper discusses the behavior of colloidal particles at the air-water interface and examines their long-range attraction using a model based on nonuniform wetting.<br />
The study of colloidal systems at the interface has many applications.<br />
As the authors mentioned, they include those in basic physics, such as phase behavior in different dimensions; engineering, such as those in nanofabrication; and industry, in the manufacturing of emulsions and foams.<br />
Existing models do not explain the observed attractive interactions of particles at distances ~ <math>\mu</math> m.<br />
Here, attraction based on merging of troughs from gravity is not strong enough for the polystyrene (PS) spheres (radius ~ -0.5 <math>\mu</math> m) used in the experiment.<br />
Additionally, although immersion capillary forces are strong enough to explain the results of the experiment, they're likely not present since there is likely no solvent film to cause aggregation.<br />
<br />
Therefore, a model based on the irregular meniscus is used to explain the lateral attraction between the particles at the air-water interface.<br />
Such nonuniform contact lines favor certain orientations when particles are in close proximity and give rise to an attractive force which is a function of the interparticle distance (Fig. 1).<br />
[[Image:Stamou1.jpeg|thumb|300px|left| Fig. 1: The water surface around two interacting particles is not uniform, given rise to certain favored orientations (top) which reduce the slope of the water level in between the particles, unlike the one in the bottom figure, from [1].]]<br />
Experimentally, this was observed using fluorescence microscopy for particle aggregates at the air-water surface where clusters had interparticle spacings approximately twice the particle diameters.<br />
Detergent was also added in later experiments to demonstrate the surface properties of the interface.<br />
<br />
The authors used fluorescently-labeled polystyrene microspheres (PS) with diameter 1.06 <math>\mu</math>m which were prepared to be uncharged for the experiment.<br />
For depositing monolayers of the particles at the air-water interface, a Langmuir trough was used.<br />
The PS were initially deposited in DI water, then the detergent Octylglucoside was added to the water at concentrations between 5 <math>\mu</math> M and 10 mM.<br />
This detergent was chosen since it is neutral and can be back-exchanged.<br />
The particles were then imaged using a fluorescence microscope and captured on a video camera.<br />
<br />
Time series images showing the aggregation of PS are shown in Fig. 2.<br />
[[Image:Stamou2.jpeg|thumb|300px|right| Fig. 2: Fluorescence images for the particles showing initial aggregation (a(i),(ii)), then reshaping when 40 <math>\mu</math>M of detergent is added (b). At (c), 70 <math>\mu</math>M of solution is added, the average particle distance increases to ~10 <math>\mu</math>m. When the detergent is purged, the particles re-aggregate similar to (a). From [1].]]<br />
The particles initially cluster to interparticle distances ~2 <math>\mu</math> m (Fig. 2a).<br />
This is thought to be due to the attractive interactions due to the nonuniform contact line.<br />
Then, with the addition of the detergent, the particle aggregates break up (Fig. 2 b, c).<br />
The detergent did not change the air-water surface tension, but did adsorb to the particles with hydrophobic head groups toward the water, which affected the contact angle of the water to the particles.<br />
Finally, when the detergent is purged, the particles re-aggregate and resume a state similar but not identical to the initial one (Fig. 2d). <br />
<br />
The attractive interactions and nonuniform contact line was captured in theory based on nonuniform wetting.<br />
From the shorter length scales, the authors ignore effects due to gravity and postulate that there is no pressure drop across the water surface.<br />
Then, using the Young-Laplace equation: <math> \nabla h(r,\phi) = 0 </math> , the authors expand an expression for the height of water contact line into multipoles in cylindrical coordinates locally centered at each sphere: <math> h(r_c, \phi) = \sum_{2}^{\infty} R_{m,0} r_c^{-m}\Phi_{m,0} \cos(m(\phi-\phi_m,0))</math><br />
where <math> R(m,0)</math> gives the solution in <math> r </math> and <math> \Phi</math> in <math> \phi </math> from separation of variables.<br />
Both the mono- and dipole terms are zero from the lack of external forces (e.g. gravity) or torques that would rotate spheres from the equilibrium positions on the water surface.<br />
Focusing on the dominant quadrupole term which is proportional to <math>r^{-2}</math>, the "self energy" (the difference between the contact area and that from a projection onto the surface times the surface energy) was found to have typical values of <math> 4 \times 10^{-16}</math> J or <math> \approx 10^5 k T </math>.<br />
Similarly, the interaction energy <math>\delta </math> for two particles whose centers are separated by L is given by:<br />
<math>\delta E_{AB} = \gamma(\delta S_{AB} - \delta S_A - \delta S_{B})</math> <br />
where <math>\delta S_{AB}</math> is the surface area surrounding the interacting particles, <math>\delta S_A, \delta S_B</math> is the surface area of the isolated particles.<br />
After carefully accounting for the boundary conditions, using deviations of the ideal contact line of <math>50 \text{nm} </math> and the experimental values for the particle size and their observed interparticle spacings, <math> \delta E_{AB}</math> was found to be <math> 5 \times 10^4 k T </math>.<br />
The authors describe such solutions as much akin to those of electrostatics problems and found analogies between the attraction of particles to areas of high surface curvature to those of interactions of electric multipoles to gradients of the electric field.<br />
However, this model applies only to large interparticle spacings, and ignores higher multiple terms from the quadrupole.<br />
For much shorter distances, higher multipole terms must be taken into account and other effects may influence the behavior of the particles.<br />
<br />
==Results and Discussion==<br />
The interactions between two spheres in this experimental system is due to electrostatics and capillarity, depending often on the distance scale.<br />
The repulsive dipole-dipole interaction is proportional to <math> L^{-3} </math> where <math> L </math> is the distance between the particles and dominates capillarity at longer distances.<br />
Interactions due to capillarity, which is attractive and proportional to <math> L^{-4} </math>, exceeds that of the dipole-dipole interaction at shorter distances.<br />
This combination of interactions then give an activation barrier given in Fig. 3.<br />
Anisotropy was also observed with the formation of strings and irregular clusters by the particle aggregates.<br />
A simple qualitative explanation was proposed for three particles which favor the formation of strings rather than clusters.<br />
[[Image:Stamou3.jpeg|thumb|300px|right| Fig. 3: The total potential with contributions from attraction due to capillarity which is proportional to <math> L^{-4} </math> and repulsion due to dipole-dipole interactions which is proportional to <math>L^{-3}</math> has an activation barrier. From [1].]]<br />
<br />
The results from the experiment showed that the fundamental assumption of the irregular meniscus is satisfied.<br />
Furthermore, the theory suggests that interaction strength is proportional to <math> R^4 </math> where <math> R </math> is the particle radius.<br />
This was corroborated experimentally where less clustering occurred for smaller particles.<br />
The activation barrier from the combination of interactions due to electrostatics and capillarity was also observed in the particles that did not aggregate around clusters and remained unclustered.<br />
The quadrupolar interaction model also suggested frustration of certain clustering geometries (e.g. hexagonal array) and the propensity for the formation of linear aggregates, which were observed experimentally.<br />
Although the main features of the experiments were explained with the given model, the authors do caution that nonuniform wetting does not fully explain all aspects of the interaction.<br />
Nonetheless, these results are useful for other systems which involve colloidal particles trapped at various interfaces.<br />
<br />
==References==<br />
[1] D. Stamou, C. Duschl, and D. Johannsmann. Long-range attraction between colloidal spheres at the air-water interface: The consequence of an irregular meniscus. Phys. Rev. E, 62:5263–5272, Oct 2000. <br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Long-range_attraction_between_colloidal_spheres_at_the_air-water_interface:_The_consequence_of_an_irregular_meniscus&diff=25528Long-range attraction between colloidal spheres at the air-water interface: The consequence of an irregular meniscus2012-10-16T13:13:07Z<p>Xingyu: </p>
<hr />
<div>== General Information ==<br />
'''Authors:''' Dimitris Stamou, Claus Duschl, and Diethelm Johannsmann<br />
<br />
'''Publication:''' Physical Review E, Vol 62, Issue 4, pp. 5263-5272 (2000)<br />
<br />
'''Keywords:''' [[Wetting]], [[Surface force]], [[Interface]]<br />
<br />
== Summary ==<br />
<br />
This paper discusses the behavior of colloidal particles at the air-water interface and examines their long-range attraction using a model based on nonuniform wetting.<br />
The study of colloidal systems at the interface has many applications.<br />
As the authors mentioned, they include those in basic physics, such as phase behavior in different dimensions; engineering, such as those in nanofabrication; and industry, in the manufacturing of emulsions and foams.<br />
Existing models do not explain the observed attractive interactions of particles at distances ~ <math>\mu</math> m.<br />
Here, attraction based on merging of troughs from gravity is not strong enough for the polystyrene (PS) spheres (radius ~ -0.5 <math>\mu</math> m) used in the experiment.<br />
Additionally, although immersion capillary forces are strong enough to explain the results of the experiment, they're likely not present since there is likely no solvent film to cause aggregation.<br />
<br />
Therefore, a model based on the irregular meniscus is used to explain the lateral attraction between the particles at the air-water interface.<br />
Such nonuniform contact lines favor certain orientations when particles are in close proximity and give rise to an attractive force which is a function of the interparticle distance (Fig. 1).<br />
[[Image:Stamou1.jpeg|thumb|300px|left| Fig. 1: The water surface around two interacting particles is not uniform, given rise to certain favored orientations (top) which reduce the slope of the water level in between the particles, unlike the one in the bottom figure, from [1].]]<br />
Experimentally, this was observed using fluorescence microscopy for particle aggregates at the air-water surface where clusters had interparticle spacings approximately twice the particle diameters.<br />
Detergent was also added in later experiments to demonstrate the surface properties of the interface.<br />
<br />
The authors used fluorescently-labeled polystyrene microspheres (PS) with diameter 1.06 <math>\mu</math>m which were prepared to be uncharged for the experiment.<br />
For depositing monolayers of the particles at the air-water interface, a Langmuir trough was used.<br />
The PS were initially deposited in DI water, then the detergent Octylglucoside was added to the water at concentrations between 5 <math>\mu</math> M and 10 mM.<br />
This detergent was chosen since it is neutral and can be back-exchanged.<br />
The particles were then imaged using a fluorescence microscope and captured on a video camera.<br />
<br />
Time series images showing the aggregation of PS are shown in Fig. 2.<br />
[[Image:Stamou2.jpeg|thumb|300px|right| Fig. 2: Fluorescence images for the particles showing initial aggregation (a(i),(ii)), then reshaping when 40 <math>\mu</math>M of detergent is added (b). At (c), 70 <math>\mu</math>M of solution is added, the average particle distance increases to ~10 <math>\mu</math>m. When the detergent is purged, the particles re-aggregate similar to (a). From [1].]]<br />
The particles initially cluster to interparticle distances ~2 <math>\mu</math> m (Fig. 2a).<br />
This is thought to be due to the attractive interactions due to the nonuniform contact line.<br />
Then, with the addition of the detergent, the particle aggregates break up (Fig. 2 b, c).<br />
The detergent did not change the air-water surface tension, but did adsorb to the particles with hydrophobic head groups toward the water, which affected the contact angle of the water to the particles.<br />
Finally, when the detergent is purged, the particles re-aggregate and resume a state similar but not identical to the initial one (Fig. 2d). <br />
<br />
The attractive interactions and nonuniform contact line was captured in theory based on nonuniform wetting.<br />
From the shorter length scales, the authors ignore effects due to gravity and postulate that there is no pressure drop across the water surface.<br />
Then, using the Young-Laplace equation: <math> \nabla h(r,\phi) = 0 </math> , the authors expand an expression for the height of water contact line into multipoles in cylindrical coordinates locally centered at each sphere: <math> h(r_c, \phi) = \sum_{2}^{\infty} R_{m,0} r_c^{-m}\Phi_{m,0} \cos(m(\phi-\phi_m,0))</math><br />
where <math> R(m,0)</math> gives the solution in <math> r </math> and <math> \Phi</math> in <math> \phi </math> from separation of variables.<br />
Both the mono- and dipole terms are zero from the lack of external forces (e.g. gravity) or torques that would rotate spheres from the equilibrium positions on the water surface.<br />
Focusing on the dominant quadrupole term which is proportional to <math>r^{-2}</math>, the "self energy" (the difference between the contact area and that from a projection onto the surface times the surface energy) was found to have typical values of <math> 4 \times 10^{-16}</math> J or <math> \approx 10^5 k T </math>.<br />
Similarly, the interaction energy <math>\delta </math> for two particles whose centers are separated by L is given by:<br />
<math>\delta E_{AB} = \gamma(\delta S_{AB} - \delta S_A - \delta S_{B})</math> <br />
where <math>\delta S_{AB}</math> is the surface area surrounding the interacting particles, <math>\delta S_A, \delta S_B</math> is the surface area of the isolated particles.<br />
After carefully accounting for the boundary conditions, using deviations of the ideal contact line of <math>50 \text{nm} </math> and the experimental values for the particle size and their observed interparticle spacings, <math> \delta E_{AB}</math> was found to be <math> 5 \times 10^4 k T </math>.<br />
The authors describe such solutions as much akin to those of electrostatics problems and found analogies between the attraction of particles to areas of high surface curvature to those of interactions of electric multipoles to gradients of the electric field.<br />
However, this model applies only to large interparticle spacings, and ignores higher multiple terms from the quadrupole.<br />
For much shorter distances, higher multipole terms must be taken into account and other effects may influence the behavior of the particles.<br />
<br />
==Results and Discussion==<br />
The interactions between two spheres in this experimental system is due to electrostatics and capillarity, depending often on the distance scale.<br />
The repulsive dipole-dipole interaction is proportional to <math> L^{-3} </math> where <math> L </math> is the distance between the particles and dominates capillarity at longer distances.<br />
Interactions due to capillarity, which is attractive and proportional to <math> L^{-4} </math>, exceeds that of the dipole-dipole interaction at shorter distances.<br />
This combination of interactions then give an activation barrier given in Fig. 3.<br />
Anisotropy was also observed with the formation of strings and irregular clusters by the particle aggregates.<br />
A simple qualitative explanation was proposed for three particles which favor the formation of strings rather than clusters.<br />
[[Image:Stamou3.jpeg|thumb|300px|right| Fig. 3: The total potential with contributions from attraction due to capillarity which is proportional to <math> L^{-4} </math> and repulsion due to dipole-dipole interactions which is proportional to <math>L^{-3}</math> has an activation barrier. From [1].]]<br />
<br />
The results from the experiment showed that the fundamental assumption of the irregular meniscus is satisfied.<br />
Furthermore, the theory suggests that interaction strength is proportional to <math> R^4 </math> where <math> R </math> is the particle radius.<br />
This was corroborated experimentally where less clustering occurred for smaller particles.<br />
The activation barrier from the combination of interactions due to electrostatics and capillarity was also observed in the particles that did not aggregate around clusters and remained unclustered.<br />
The quadrupolar interaction model also suggested frustration of certain clustering geometries (e.g. hexagonal array) and the propensity for the formation of linear aggregates, which were observed experimentally.<br />
Although the main features of the experiments were explained with the given model, the authors do caution that nonuniform wetting does not fully explain all aspects of the interaction.<br />
Nonetheless, these results are useful for other systems which involve colloidal particles trapped at various interfaces.<br />
<br />
=Keyword=<br />
==References==<br />
[1] D. Stamou, C. Duschl, and D. Johannsmann. Long-range attraction between colloidal spheres at the air-water interface: The consequence of an irregular meniscus. Phys. Rev. E, 62:5263–5272, Oct 2000. <br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Long-range_attraction_between_colloidal_spheres_at_the_air-water_interface:_The_consequence_of_an_irregular_meniscus&diff=25330Long-range attraction between colloidal spheres at the air-water interface: The consequence of an irregular meniscus2012-10-13T21:26:55Z<p>Xingyu: </p>
<hr />
<div>== General Information ==<br />
'''Authors:''' Dimitris Stamou, Claus Duschl, and Diethelm Johannsmann<br />
<br />
'''Publication:''' Physical Review E, Vol 62, Issue 4, pp. 5263-5272 (2000)<br />
<br />
'''Keywords:''' [[Wetting]], [[Surface force]], [[Interface]], [[Capillarity]]<br />
<br />
== Summary ==<br />
<br />
This paper discusses the behavior of colloidal particles at the air-water interface and examines their long-range attraction using a model based on nonuniform wetting.<br />
The study of colloidal systems at the interface has many applications.<br />
As the authors mentioned, they include those in basic physics, such as phase behavior in different dimensions; engineering, such as those in nanofabrication; and industry, in the manufacturing of emulsions and foams.<br />
Existing models do not explain the observed attractive interactions of particles at distances ~ <math>\mu</math> m.<br />
Here, attraction based on merging of troughs from gravity is not strong enough for the polystyrene (PS) spheres (radius ~ -0.5 <math>\mu</math> m) used in the experiment.<br />
Additionally, although immersion capillary forces are strong enough to explain the results of the experiment, they're likely not present since there is likely no solvent film to cause aggregation.<br />
<br />
Therefore, a model based on the irregular meniscus is used to explain the lateral attraction between the particles at the air-water interface.<br />
Such nonuniform contact lines favor certain orientations when particles are in close proximity and give rise to an attractive force which is a function of the interparticle distance (Fig. 1).<br />
[[Image:Stamou1.jpeg|thumb|300px|left| Fig. 1: The water surface around two interacting particles is not uniform, given rise to certain favored orientations (top) which reduce the slope of the water level in between the particles, unlike the one in the bottom figure, from [1].]]<br />
Experimentally, this was observed using fluorescence microscopy for particle aggregates at the air-water surface where clusters had interparticle spacings approximately twice the particle diameters.<br />
Detergent was also added in later experiments to demonstrate the surface properties of the interface.<br />
<br />
The authors used fluorescently-labeled polystyrene microspheres (PS) with diameter 1.06 <math>\mu</math>m which were prepared to be uncharged for the experiment.<br />
For depositing monolayers of the particles at the air-water interface, a Langmuir trough was used.<br />
The PS were initially deposited in DI water, then the detergent Octylglucoside was added to the water at concentrations between 5 <math>\mu</math> M and 10 mM.<br />
This detergent was chosen since it is neutral and can be back-exchanged.<br />
The particles were then imaged using a fluorescence microscope and captured on a video camera.<br />
<br />
Time series images showing the aggregation of PS are shown in Fig. 2.<br />
[[Image:Stamou2.jpeg|thumb|300px|right| Fig. 2: Fluorescence images for the particles showing initial aggregation (a(i),(ii)), then reshaping when 40 <math>\mu</math>M of detergent is added (b). At (c), 70 <math>\mu</math>M of solution is added, the average particle distance increases to ~10 <math>\mu</math>m. When the detergent is purged, the particles re-aggregate similar to (a). From [1].]]<br />
The particles initially cluster to interparticle distances ~2 <math>\mu</math> m (Fig. 2a).<br />
This is thought to be due to the attractive interactions due to the nonuniform contact line.<br />
Then, with the addition of the detergent, the particle aggregates break up (Fig. 2 b, c).<br />
The detergent did not change the air-water surface tension, but did adsorb to the particles with hydrophobic head groups toward the water, which affected the contact angle of the water to the particles.<br />
Finally, when the detergent is purged, the particles re-aggregate and resume a state similar but not identical to the initial one (Fig. 2d). <br />
<br />
The attractive interactions and nonuniform contact line was captured in theory based on nonuniform wetting.<br />
From the shorter length scales, the authors ignore effects due to gravity and postulate that there is no pressure drop across the water surface.<br />
Then, using the Young-Laplace equation: <math> \nabla h(r,\phi) = 0 </math> , the authors expand an expression for the height of water contact line into multipoles in cylindrical coordinates locally centered at each sphere: <math> h(r_c, \phi) = \sum_{2}^{\infty} R_{m,0} r_c^{-m}\Phi_{m,0} \cos(m(\phi-\phi_m,0))</math><br />
where <math> R(m,0)</math> gives the solution in <math> r </math> and <math> \Phi</math> in <math> \phi </math> from separation of variables.<br />
Both the mono- and dipole terms are zero from the lack of external forces (e.g. gravity) or torques that would rotate spheres from the equilibrium positions on the water surface.<br />
Focusing on the dominant quadrupole term which is proportional to <math>r^{-2}</math>, the "self energy" (the difference between the contact area and that from a projection onto the surface times the surface energy) was found to have typical values of <math> 4 \times 10^{-16}</math> J or <math> \approx 10^5 k T </math>.<br />
Similarly, the interaction energy <math>\delta </math> for two particles whose centers are separated by L is given by:<br />
<math>\delta E_{AB} = \gamma(\delta S_{AB} - \delta S_A - \delta S_{B})</math> <br />
where <math>\delta S_{AB}</math> is the surface area surrounding the interacting particles, <math>\delta S_A, \delta S_B</math> is the surface area of the isolated particles.<br />
After carefully accounting for the boundary conditions, using deviations of the ideal contact line of <math>50 \text{nm} </math> and the experimental values for the particle size and their observed interparticle spacings, <math> \delta E_{AB}</math> was found to be <math> 5 \times 10^4 k T </math>.<br />
The authors describe such solutions as much akin to those of electrostatics problems and found analogies between the attraction of particles to areas of high surface curvature to those of interactions of electric multipoles to gradients of the electric field.<br />
However, this model applies only to large interparticle spacings, and ignores higher multiple terms from the quadrupole.<br />
For much shorter distances, higher multipole terms must be taken into account and other effects may influence the behavior of the particles.<br />
<br />
==Results and Discussion==<br />
The interactions between two spheres in this experimental system is due to electrostatics and capillarity, depending often on the distance scale.<br />
The repulsive dipole-dipole interaction is proportional to <math> L^{-3} </math> where <math> L </math> is the distance between the particles and dominates capillarity at longer distances.<br />
Interactions due to capillarity, which is attractive and proportional to <math> L^{-4} </math>, exceeds that of the dipole-dipole interaction at shorter distances.<br />
This combination of interactions then give an activation barrier given in Fig. 3.<br />
Anisotropy was also observed with the formation of strings and irregular clusters by the particle aggregates.<br />
A simple qualitative explanation was proposed for three particles which favor the formation of strings rather than clusters.<br />
[[Image:Stamou3.jpeg|thumb|300px|right| Fig. 3: The total potential with contributions from attraction due to capillarity which is proportional to <math> L^{-4} </math> and repulsion due to dipole-dipole interactions which is proportional to <math>L^{-3}</math> has an activation barrier. From [1].]]<br />
<br />
The results from the experiment showed that the fundamental assumption of the irregular meniscus is satisfied.<br />
Furthermore, the theory suggests that interaction strength is proportional to <math> R^4 </math> where <math> R </math> is the particle radius.<br />
This was corroborated experimentally where less clustering occurred for smaller particles.<br />
The activation barrier from the combination of interactions due to electrostatics and capillarity was also observed in the particles that did not aggregate around clusters and remained unclustered.<br />
The quadrupolar interaction model also suggested frustration of certain clustering geometries (e.g. hexagonal array) and the propensity for the formation of linear aggregates, which were observed experimentally.<br />
Although the main features of the experiments were explained with the given model, the authors do caution that nonuniform wetting does not fully explain all aspects of the interaction.<br />
Nonetheless, these results are useful for other systems which involve colloidal particles trapped at various interfaces.<br />
<br />
==References==<br />
[1] D. Stamou, C. Duschl, and D. Johannsmann. Long-range attraction between colloidal spheres at the air-water interface: The consequence of an irregular meniscus. Phys. Rev. E, 62:5263–5272, Oct 2000. <br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Stamou3.jpeg&diff=25329File:Stamou3.jpeg2012-10-13T21:20:13Z<p>Xingyu: </p>
<hr />
<div></div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Stamou2.jpeg&diff=25328File:Stamou2.jpeg2012-10-13T20:56:30Z<p>Xingyu: </p>
<hr />
<div></div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Long-range_attraction_between_colloidal_spheres_at_the_air-water_interface:_The_consequence_of_an_irregular_meniscus&diff=25326Long-range attraction between colloidal spheres at the air-water interface: The consequence of an irregular meniscus2012-10-13T20:44:13Z<p>Xingyu: </p>
<hr />
<div>== General Information ==<br />
'''Authors:''' Dimitris Stamou, Claus Duschl, and Diethelm Johannsmann<br />
<br />
'''Publication:''' Physical Review E, Vol 62, Issue 4, pp. 5263-5272 (2000)<br />
<br />
'''Keywords:''' [[Wetting]], [[Surface force]], [[Interface]], [[Capillarity]]<br />
<br />
== Summary ==<br />
<br />
This paper discusses the behavior of colloidal particles at the air-water interface and examines their long-range attraction using a model based on nonuniform wetting.<br />
The study of colloidal systems at the interface has many applications.<br />
As the authors mentioned, they include those in basic physics, such as phase behavior in different dimensions; engineering, such as those in nanofabrication; and industry, in the manufacturing of emulsions and foams.<br />
Existing models do not explain the observed attractive interactions of particles at distances ~ <math>\mu</math> m.<br />
Here, attraction based on merging of troughs from gravity is not strong enough for the polystyrene (PS) spheres (radius ~ -0.5 <math>\mu</math> m) used in the experiment.<br />
Additionally, although immersion capillary forces are strong enough to explain the results of the experiment, they're likely not present since there is likely no tho solvent film to cause aggregation.<br />
<br />
Therefore, a model based on the irregular meniscus is used to explain the lateral attraction between the particles at the air-water interface.<br />
Such nonuniform contact lines favor certain orientations when particles are in close proximity and give rise to an attractive force which is a function of the interparticle distance (Fig. 1).<br />
[[Image:Stamou1.jpeg|thumb|300px| Fig. 1: The water surface around two interacting particles is not uniform, given rise to certain favored orientations (top) which reduce the slope of the water level in between the particles, unlike the one in the bottom figure, from [1].]]<br />
Experimentally, this was observed using fluorescence microscopy for particle aggregates at the air-water surface where clusters had interparticle spacings approximately twice the particle diameters.<br />
Detergent was also added in later experiments to demonstrate the surface properties of the interface.<br />
<br />
The authors used fluorescently-labeled polystyrene microspheres (PS) with diameter 1.06 <math>\mu</math>m which were prepared to be uncharged for the experiment.<br />
For depositing monolayers of the particles at the air-water interface, a Langmuir trough was used.<br />
The PS were initially deposited in DI water, then the detergent Octylglucoside was added to the water at concentrations between 5 <math>\mu</math> M and 10 mM.<br />
This detergent was chosen since it is neutral and can be back-exchanged.<br />
The particles were then imaged using a fluorescence microscope and captured on a video camera.<br />
<br />
Time series images showing the aggregation of PS are shown in Fig. 2.<br />
The particles initially cluster to interparticle distances ~2 <math>\mu</math> m (Fig. 2a, b).<br />
This is thought to be due to the attractive interactions due to the nonuniform contact line.<br />
Then, when the detergent is added, the clusters of particles dissociate due to changes in the (Fig. 2 b, c).<br />
The detergent did not change the air-water surface tension, but did adsorb to the particles with hydrophobic head groups toward the water, which affected the contact angle of the water to the particles.<br />
Finally, when the detergent has been purged, the particles re-aggregate and resume a state similar but not identical to the initial one (Fig. 2d). <br />
<br />
The attractive interactions and nonuniform contact line was captured in theory based on nonuniform wetting.<br />
From the shorter length scales, the authors ignore effects due to gravity and postulate that there is no pressure drop across the water surface.<br />
Then, using the Young-Laplace equation: <math> \nabla h(r,\phi) = 0 </math> , the authors expand an expression for the height of water contact line into multipoles in cylindrical coordinates locally centered at each sphere: <math> h(r_c, \phi) = \sum_{2}^{\infty} R_{m,0} r_c^{-m}\Phi_{m,0} \cos(m(\phi-\phi_m,0))</math><br />
where <math> R(m,0)</math> gives the solution in <math> r </math> and <math> \Phi</math> from separation of variables.<br />
Both the mono- and dipole terms are zero from the lack of external forces (e.g. gravity) or torques that would rotate spheres from the equilibrium positions on the water surface.<br />
Focusing on the dominant quadrupole term which is proportional to <math>r^{-2}</math>, the "self energy" (the difference between the contact area and that from a projection onto the surface times the surface energy) and has typical values of <math> 4 \times 10^{-16}</math> J or <math> \approx 10^5 \text{k T}</math>.<br />
Then, with a similar approach, the interaction energy <math>\delta </math> for two particles whose centers are separated by <math>L</math> is given by:<br />
<math>\delta E_{AB} = \gamma(\delta S_{AB} - \delta_A - \delta S_{B})</math> <br />
where <math>\delta S_{AB}</math> is the surface area surrounding the interacting particles, <math>\delta S_A, \delta S_B</math> is the surface area of the isolated particles.<br />
After carefully accounting for the boundary conditions, using deviations of the ideal contact line of <math>50 \text{nm} </math> and the experimental values for the particle size and their observed interparticle spacings, <math> \delta E_{AB}</math> was found to be <math> 5 \times 10^4 k T </math>.<br />
The authors describe such solutions much akin to the solutions to electrostatics problems and draw analogies between attraction of particles to areas of high surface curvature to that of interactions of electric multiples to gradients of the electric field.<br />
The model described above applies only to large interparticle spacings, which ignored higher multiple terms from the quadrupole.<br />
For much shorter distances, higher multipole terms must be taken into account and other effects may influence the behavior of the particles.<br />
<br />
==Results and Discussion==<br />
Hence, the interactions between two spheres is due to electrostatics and capillarity, depending often on the distance scale.<br />
The repulsive dipole-dipole interaction is proportional to <math> L^{-3} </math> where <math> L </math> is the distance between the particles and dominates capillarity at longer distances.<br />
This interaction exceeds that due to capillarity at shorter distances, which is attractive and proportional to <math> L^{-4} </math>.<br />
Such an inflection gives an activation barrier given in Fig. 3.<br />
Anisotropy was also observed with the formation of strings and irregular clusters by the particle aggregates.<br />
A simple qualitative explanation was proposed for three particles which favor the formation of strings rather than clusters.<br />
<br />
When compared with the results of the experiment, the fundamental assumption the formation of irregular menisci was satisfied.<br />
Furthermore, results from the interaction energy suggested that the interaction strength is proportional to <math> R^4 </math> where <math> R </math> is the particle radius.<br />
This was observed experimentally where there was less clustering for smaller particles.<br />
The activation barrier from the combination of interactions due to electrostatics and capillarity was also observed in the particles that did not aggregate around clusters and remained so.<br />
The quadrupolar interaction model also suggested frustration for certain clustering geometries such as hexagonal array, which were indeed rarely observed; as well as the propensity for the formation of linear aggregates.<br />
<br />
The authors also explained why the two particle correlation function was not computed for the interaction potentials since the observed disorder was static.<br />
They also cautioned that nonuniform wetting does not fully explain all aspects of the interaction although the main features of the experiments were explained with the given model.<br />
In conclusion, in this study, the authors proposed a model for the lateral attraction of colloidal particles in the air-water interface based on that of irregular meniscus shapes and the consequent distortion of the liquid surface. A net attraction proportional to the inverse fourth power of the particle pair separation.<br />
Experiments were conducted to test the model, which included the addition of detergent to change the surface properties of the water.<br />
The proposed model sufficiently accounted for the main experimental features, which included the lack of certain frustrated cluster geometries (e.g. hexagonal planar packing) and the large number of linear clusters.<br />
Such results are useful for other systems with particles trapped at various interfaces.<br />
<br />
==References==<br />
[1] D. Stamou, C. Duschl, and D. Johannsmann. Long-range attraction between colloidal spheres at the air-water interface: The consequence of an irregular meniscus. Phys. Rev. E, 62:5263–5272, Oct 2000. <br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Stamou1.jpeg&diff=25325File:Stamou1.jpeg2012-10-13T20:40:35Z<p>Xingyu: </p>
<hr />
<div></div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Long-range_attraction_between_colloidal_spheres_at_the_air-water_interface:_The_consequence_of_an_irregular_meniscus&diff=25324Long-range attraction between colloidal spheres at the air-water interface: The consequence of an irregular meniscus2012-10-13T20:36:48Z<p>Xingyu: </p>
<hr />
<div>== General Information ==<br />
'''Authors:''' Dimitris Stamou, Claus Duschl, and Diethelm Johannsmann<br />
<br />
'''Publication:''' Physical Review E, Vol 62, Issue 4, pp. 5263-5272 (2000)<br />
<br />
'''Keywords:''' [[Wetting]], [[Surface force]], [[Interface]], [[Capillarity]]<br />
<br />
== Summary ==<br />
<br />
This paper discusses the behavior of colloidal particles at the air-water interface and examines their long-attraction using a model based on nonuniform wetting that leads to irregularity of the meniscus.<br />
<br />
The study of colloidal systems at the interface has many applications.<br />
As the authors mentioned, they include those in basic physics, such as phase behavior in different dimensions; engineering, such as those in nanofabrication; and industry, such as the manufacturing of emulsions and foams.<br />
They also explained that existing models do not explain the observed attractive interactions of particles at distances ~ <math>\mu</math> m.<br />
Uncharged colloidal particles at air-water interfaces tend to aggregate due to the van der Waals interaction.<br />
Here, attraction based on merging of troughs from gravity is not strong enough for the polystyrene (PS) spheres (radius ~ -0.5 <math>\mu</math> m) used in the experiment.<br />
Additionally, although immersion capillary forces are of sufficient strength to explain the results of the experiment, they're likely not present since there is likely no tho solvent film to cause aggregation.<br />
<br />
Therefore, a model based on the irregular meniscus is used to explain the lateral attraction between the particles at the air-water interface.<br />
Such nonuniform contact lines favor certain orientations when particles are in close proximity and give rise to an attractive force which is a function of the interparticle distance (Fig. 1).<br />
[[Image:Stamou1.jpeg|thumb|300px| Fig. 1: , from [1].]]<br />
Experimentally, this was observed using fluorescence microscopy for particle aggregates at the air-water surface where clusters had interparticle spacings approximately twice the particle diameters.<br />
Detergent was also added in later experiments to demonstrate the surface properties of the interface.<br />
<br />
The authors used fluorescently-labeled polystyrene microspheres (PS) with diameter 1.06 <math>\mu</math>m which were prepared to be uncharged for the experiment.<br />
For depositing monolayers of the particles at the air-water interface, a Langmuir trough was used.<br />
The PS were initially deposited in DI water, then the detergent Octylglucoside was added to the water at concentrations between 5 <math>\mu</math> M and 10 mM.<br />
This detergent was chosen since it is neutral and can be back-exchanged.<br />
The particles were then imaged using a fluorescence microscope and captured on a video camera.<br />
<br />
Time series images showing the aggregation of PS are shown in Fig. 2.<br />
The particles initially cluster to interparticle distances ~2 <math>\mu</math> m (Fig. 2a, b).<br />
This is thought to be due to the attractive interactions due to the nonuniform contact line.<br />
Then, when the detergent is added, the clusters of particles dissociate due to changes in the (Fig. 2 b, c).<br />
The detergent did not change the air-water surface tension, but did adsorb to the particles with hydrophobic head groups toward the water, which affected the contact angle of the water to the particles.<br />
Finally, when the detergent has been purged, the particles re-aggregate and resume a state similar but not identical to the initial one (Fig. 2d). <br />
<br />
The attractive interactions and nonuniform contact line was captured in theory based on nonuniform wetting.<br />
From the shorter length scales, the authors ignore effects due to gravity and postulate that there is no pressure drop across the water surface.<br />
Then, using the Young-Laplace equation: <math> \nabla h(r,\phi) = 0 </math> , the authors expand an expression for the height of water contact line into multipoles in cylindrical coordinates locally centered at each sphere: <math> h(r_c, \phi) = \sum_{2}^{\infty} R_{m,0} r_c^{-m}\Phi_{m,0} \cos(m(\phi-\phi_m,0))</math><br />
where <math> R(m,0)</math> gives the solution in <math> r </math> and <math> \Phi</math> from separation of variables.<br />
Both the mono- and dipole terms are zero from the lack of external forces (e.g. gravity) or torques that would rotate spheres from the equilibrium positions on the water surface.<br />
Focusing on the dominant quadrupole term which is proportional to <math>r^{-2}</math>, the "self energy" (the difference between the contact area and that from a projection onto the surface times the surface energy) and has typical values of <math> 4 \times 10^{-16}</math> J or <math> \approx 10^5 \text{k T}</math>.<br />
Then, with a similar approach, the interaction energy <math>\delta </math> for two particles whose centers are separated by <math>L</math> is given by:<br />
<math>\delta E_{AB} = \gamma(\delta S_{AB} - \delta_A - \delta S_{B})</math> <br />
where <math>\delta S_{AB}</math> is the surface area surrounding the interacting particles, <math>\delta S_A, \delta S_B</math> is the surface area of the isolated particles.<br />
After carefully accounting for the boundary conditions, using deviations of the ideal contact line of <math>50 \text{nm} </math> and the experimental values for the particle size and their observed interparticle spacings, <math> \delta E_{AB}</math> was found to be <math> 5 \times 10^4 k T </math>.<br />
The authors describe such solutions much akin to the solutions to electrostatics problems and draw analogies between attraction of particles to areas of high surface curvature to that of interactions of electric multiples to gradients of the electric field.<br />
The model described above applies only to large interparticle spacings, which ignored higher multiple terms from the quadrupole.<br />
For much shorter distances, higher multipole terms must be taken into account and other effects may influence the behavior of the particles.<br />
<br />
==Results and Discussion==<br />
Hence, the interactions between two spheres is due to electrostatics and capillarity, depending often on the distance scale.<br />
The repulsive dipole-dipole interaction is proportional to <math> L^{-3} </math> where <math> L </math> is the distance between the particles and dominates capillarity at longer distances.<br />
This interaction exceeds that due to capillarity at shorter distances, which is attractive and proportional to <math> L^{-4} </math>.<br />
Such an inflection gives an activation barrier given in Fig. 3.<br />
Anisotropy was also observed with the formation of strings and irregular clusters by the particle aggregates.<br />
A simple qualitative explanation was proposed for three particles which favor the formation of strings rather than clusters.<br />
<br />
When compared with the results of the experiment, the fundamental assumption the formation of irregular menisci was satisfied.<br />
Furthermore, results from the interaction energy suggested that the interaction strength is proportional to <math> R^4 </math> where <math> R </math> is the particle radius.<br />
This was observed experimentally where there was less clustering for smaller particles.<br />
The activation barrier from the combination of interactions due to electrostatics and capillarity was also observed in the particles that did not aggregate around clusters and remained so.<br />
The quadrupolar interaction model also suggested frustration for certain clustering geometries such as hexagonal array, which were indeed rarely observed; as well as the propensity for the formation of linear aggregates.<br />
<br />
The authors also explained why the two particle correlation function was not computed for the interaction potentials since the observed disorder was static.<br />
They also cautioned that nonuniform wetting does not fully explain all aspects of the interaction although the main features of the experiments were explained with the given model.<br />
In conclusion, in this study, the authors proposed a model for the lateral attraction of colloidal particles in the air-water interface based on that of irregular meniscus shapes and the consequent distortion of the liquid surface. A net attraction proportional to the inverse fourth power of the particle pair separation.<br />
Experiments were conducted to test the model, which included the addition of detergent to change the surface properties of the water.<br />
The proposed model sufficiently accounted for the main experimental features, which included the lack of certain frustrated cluster geometries (e.g. hexagonal planar packing) and the large number of linear clusters.<br />
Such results are useful for other systems with particles trapped at various interfaces.<br />
<br />
==References==<br />
[1] D. Stamou, C. Duschl, and D. Johannsmann. Long-range attraction between colloidal spheres at the air-water interface: The consequence of an irregular meniscus. Phys. Rev. E, 62:5263–5272, Oct 2000. <br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyuhttp://soft-matter.seas.harvard.edu/index.php?title=Long-range_attraction_between_colloidal_spheres_at_the_air-water_interface:_The_consequence_of_an_irregular_meniscus&diff=25323Long-range attraction between colloidal spheres at the air-water interface: The consequence of an irregular meniscus2012-10-13T20:36:18Z<p>Xingyu: </p>
<hr />
<div>== General Information ==<br />
'''Authors:''' Dimitris Stamou, Claus Duschl, and Diethelm Johannsmann<br />
<br />
'''Publication:''' Physical Review E, Vol 62, Issue 4, pp. 5263-5272 (2000)<br />
<br />
'''Keywords:''' [[Wetting]], [[Surface force]], [[Interface]], [[Capillarity]]<br />
<br />
== Summary ==<br />
<br />
This paper discusses the behavior of colloidal particles at the air-water interface and examines their long-attraction using a model based on nonuniform wetting that leads to irregularity of the meniscus.<br />
<br />
The study of colloidal systems at the interface has many applications.<br />
As the authors mentioned, they include those in basic physics, such as phase behavior in different dimensions; engineering, such as those in nanofabrication; and industry, such as the manufacturing of emulsions and foams.<br />
They also explained that existing models do not explain the observed attractive interactions of particles at distances ~ <math>\mu</math> m.<br />
Uncharged colloidal particles at air-water interfaces tend to aggregate due to the van der Waals interaction.<br />
Here, attraction based on merging of troughs from gravity is not strong enough for the polystyrene (PS) spheres (radius ~ -0.5 <math>\mu</math> m) used in the experiment.<br />
Additionally, although immersion capillary forces are of sufficient strength to explain the results of the experiment, they're likely not present since there is likely no tho solvent film to cause aggregation.<br />
<br />
Therefore, a model based on the irregular meniscus is used to explain the lateral attraction between the particles at the air-water interface.<br />
Such nonuniform contact lines favor certain orientations when particles are in close proximity and give rise to an attractive force which is a function of the interparticle distance (Fig. 1).<br />
[[Image:stamou1.jpeg|thumb|300px| Fig. 1: , from [1].]]<br />
Experimentally, this was observed using fluorescence microscopy for particle aggregates at the air-water surface where clusters had interparticle spacings approximately twice the particle diameters.<br />
Detergent was also added in later experiments to demonstrate the surface properties of the interface.<br />
<br />
The authors used fluorescently-labeled polystyrene microspheres (PS) with diameter 1.06 <math>\mu</math>m which were prepared to be uncharged for the experiment.<br />
For depositing monolayers of the particles at the air-water interface, a Langmuir trough was used.<br />
The PS were initially deposited in DI water, then the detergent Octylglucoside was added to the water at concentrations between 5 <math>\mu</math> M and 10 mM.<br />
This detergent was chosen since it is neutral and can be back-exchanged.<br />
The particles were then imaged using a fluorescence microscope and captured on a video camera.<br />
<br />
Time series images showing the aggregation of PS are shown in Fig. 2.<br />
The particles initially cluster to interparticle distances ~2 <math>\mu</math> m (Fig. 2a, b).<br />
This is thought to be due to the attractive interactions due to the nonuniform contact line.<br />
Then, when the detergent is added, the clusters of particles dissociate due to changes in the (Fig. 2 b, c).<br />
The detergent did not change the air-water surface tension, but did adsorb to the particles with hydrophobic head groups toward the water, which affected the contact angle of the water to the particles.<br />
Finally, when the detergent has been purged, the particles re-aggregate and resume a state similar but not identical to the initial one (Fig. 2d). <br />
<br />
The attractive interactions and nonuniform contact line was captured in theory based on nonuniform wetting.<br />
From the shorter length scales, the authors ignore effects due to gravity and postulate that there is no pressure drop across the water surface.<br />
Then, using the Young-Laplace equation: <math> \nabla h(r,\phi) = 0 </math> , the authors expand an expression for the height of water contact line into multipoles in cylindrical coordinates locally centered at each sphere: <math> h(r_c, \phi) = \sum_{2}^{\infty} R_{m,0} r_c^{-m}\Phi_{m,0} \cos(m(\phi-\phi_m,0))</math><br />
where <math> R(m,0)</math> gives the solution in <math> r </math> and <math> \Phi</math> from separation of variables.<br />
Both the mono- and dipole terms are zero from the lack of external forces (e.g. gravity) or torques that would rotate spheres from the equilibrium positions on the water surface.<br />
Focusing on the dominant quadrupole term which is proportional to <math>r^{-2}</math>, the "self energy" (the difference between the contact area and that from a projection onto the surface times the surface energy) and has typical values of <math> 4 \times 10^{-16}</math> J or <math> \approx 10^5 \text{k T}</math>.<br />
Then, with a similar approach, the interaction energy <math>\delta </math> for two particles whose centers are separated by <math>L</math> is given by:<br />
<math>\delta E_{AB} = \gamma(\delta S_{AB} - \delta_A - \delta S_{B})</math> <br />
where <math>\delta S_{AB}</math> is the surface area surrounding the interacting particles, <math>\delta S_A, \delta S_B</math> is the surface area of the isolated particles.<br />
After carefully accounting for the boundary conditions, using deviations of the ideal contact line of <math>50 \text{nm} </math> and the experimental values for the particle size and their observed interparticle spacings, <math> \delta E_{AB}</math> was found to be <math> 5 \times 10^4 k T </math>.<br />
The authors describe such solutions much akin to the solutions to electrostatics problems and draw analogies between attraction of particles to areas of high surface curvature to that of interactions of electric multiples to gradients of the electric field.<br />
The model described above applies only to large interparticle spacings, which ignored higher multiple terms from the quadrupole.<br />
For much shorter distances, higher multipole terms must be taken into account and other effects may influence the behavior of the particles.<br />
<br />
==Results and Discussion==<br />
Hence, the interactions between two spheres is due to electrostatics and capillarity, depending often on the distance scale.<br />
The repulsive dipole-dipole interaction is proportional to <math> L^{-3} </math> where <math> L </math> is the distance between the particles and dominates capillarity at longer distances.<br />
This interaction exceeds that due to capillarity at shorter distances, which is attractive and proportional to <math> L^{-4} </math>.<br />
Such an inflection gives an activation barrier given in Fig. 3.<br />
Anisotropy was also observed with the formation of strings and irregular clusters by the particle aggregates.<br />
A simple qualitative explanation was proposed for three particles which favor the formation of strings rather than clusters.<br />
<br />
When compared with the results of the experiment, the fundamental assumption the formation of irregular menisci was satisfied.<br />
Furthermore, results from the interaction energy suggested that the interaction strength is proportional to <math> R^4 </math> where <math> R </math> is the particle radius.<br />
This was observed experimentally where there was less clustering for smaller particles.<br />
The activation barrier from the combination of interactions due to electrostatics and capillarity was also observed in the particles that did not aggregate around clusters and remained so.<br />
The quadrupolar interaction model also suggested frustration for certain clustering geometries such as hexagonal array, which were indeed rarely observed; as well as the propensity for the formation of linear aggregates.<br />
<br />
The authors also explained why the two particle correlation function was not computed for the interaction potentials since the observed disorder was static.<br />
They also cautioned that nonuniform wetting does not fully explain all aspects of the interaction although the main features of the experiments were explained with the given model.<br />
In conclusion, in this study, the authors proposed a model for the lateral attraction of colloidal particles in the air-water interface based on that of irregular meniscus shapes and the consequent distortion of the liquid surface. A net attraction proportional to the inverse fourth power of the particle pair separation.<br />
Experiments were conducted to test the model, which included the addition of detergent to change the surface properties of the water.<br />
The proposed model sufficiently accounted for the main experimental features, which included the lack of certain frustrated cluster geometries (e.g. hexagonal planar packing) and the large number of linear clusters.<br />
Such results are useful for other systems with particles trapped at various interfaces.<br />
<br />
==References==<br />
[1] D. Stamou, C. Duschl, and D. Johannsmann. Long-range attraction between colloidal spheres at the air-water interface: The consequence of an irregular meniscus. Phys. Rev. E, 62:5263–5272, Oct 2000. <br />
<br />
Entry by: Xingyu Zhang, AP225, Fall 2012</div>Xingyu