http://soft-matter.seas.harvard.edu/api.php?action=feedcontributions&user=Chsu&feedformat=atomSoft-Matter - User contributions [en]2020-04-09T08:26:20ZUser contributionsMediaWiki 1.24.2http://soft-matter.seas.harvard.edu/index.php?title=Chia_Wei_Hsu&diff=15937Chia Wei Hsu2010-11-24T00:13:18Z<p>Chsu: </p>
<hr />
<div>Definitions:<br />
<br />
<br />
<br />
Weekly wiki entries:<br />
<br />
Week 1: [[The Free-Energy Landscape of Clusters of Attractive Hard Spheres]]<br />
<br />
Week 2: [[Statistical mechanics of developable ribbons]]<br />
<br />
Week 3: [[Chemotactic Patterns without Chemotaxis]]<br />
<br />
Week 4: [[Particle Segregation and Dynamics in Confined Flows]]<br />
<br />
Week 5: [[Intracellular transport by active diffusion]]<br />
<br />
Week 6: [[Equilibrating Nanoparticle Monolayers UsingWetting Films]]<br />
<br />
Week 7: [[Shear Melting of a Colloidal Glass]]<br />
<br />
Week 8: [[Onset of Buckling in Drying Droplets of Colloidal Suspensions]]<br />
<br />
Week 9: [[Percolation Model for Slow Dynamics in Glass-Forming Materials]]</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Percolation_Model_for_Slow_Dynamics_in_Glass-Forming_Materials&diff=15936Percolation Model for Slow Dynamics in Glass-Forming Materials2010-11-24T00:12:56Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010 <br />
<br />
G. Lois, J. Blawzdziewicz, and C. S. O'Hern, "Percolation Model for Slow Dynamics in Glass-Forming Materials", Phys. Rev. Lett. '''102''', 015702 (2009).<br />
<br />
== Summary ==<br />
<br />
In this work, the authors propose an alternate approach to understand the glass transition. Instead of looking at the real space, they focus on the configuration space of the system. There are mobility regions in the configuration space, and the percolation of these regions corresponds to a glass-to-liquid transition. With a mean-field description of such percolation, they show that the stretched-exponential response functions typical of glassy systems can be explained.<br />
<br />
== Background ==<br />
<br />
Glassy systems exhibit several unique properties. During a glass transition, the structural relaxation time increases by several orders of magnitude. Also, the structural correlations display an anomalous stretched-exponential time decay: <math>exp(-t/\tau_{\alpha})^{\beta}</math>, where <math>\beta</math> is called the stretching exponent, and <math>\tau_{\alpha}</math> is called the <math>\alpha</math>-relaxation time. Although the stretched-exponential relaxation is universal among glass-forming materials, <math>\beta</math> and <math>\tau_{\alpha}</math> are not. They depend on temperature and density, and they vary from one material to another.<br />
<br />
== Basic Idea ==<br />
<br />
The basic idea is that, instead of focusing on the heterogeneous dynamics and percolation in real space (the traditional approach), the authors focus on the ''configuration space'' and its connection to the anomalous dynamics.<br />
<br />
For complete relaxation, the system must be able to diffuse over the whole configuration space. That is, there has to be a path that percolates the configuration space. Thus, we can think of a "percolation transition in the configuration space," which corresponds to the glass transition in real space.<br />
<br />
== Hard spheres ==<br />
<br />
[[Image:glass_config_fig1.jpg|thumb|300px| Fig 1. Schematic of allowed regions in configuration space for hard spheres. (a) <math>\phi = \phi_J </math>, only jammed states (discrete points in the config space) are allowed. (b) <math>\phi < \phi_J </math>, motion occurs in closed mobility domains surrounding jammed states. (c) Even smaller <math>\phi</math>, bridges between mobility domains occur. (d) Even smaller <math>\phi</math>, percolation occurs (shaded yellow).]]<br />
<br />
Hard spheres interact with infinite repulsion upon contact. At small volume fraction <math>\phi</math>, hard spheres behave like fluids. As <math>\phi</math> increases to <math>\phi_J \approx 0.64</math>, the system becomes collectively jammed. In such state no motion can occur, because any particle displacement will lead to overlap. Therefore only discrete set of points in the configuration space are allowed (fig 1a).<br />
<br />
At slightly lower <math>\phi</math>, particles can move around a little bit. Therefore, the discrete points become ''mobility domains'' in the configuration space (fig 1b). Further decrease of <math>\phi</math> lead to connection between these mobility domains (fig 1c), and eventually to a percolation between these domains (fig 1d) at <math>\phi=\phi_P</math>.<br />
<br />
Denote the volume fraction of mobility domains in the configuration by <math>\Pi</math>. Percolation occurs at a critical <math>\Pi_P</math>. When <math>\Pi > \Pi_P</math>, the system can explore the whole configuration space, and it is a metastable liquid. When <math>\Pi < \Pi_P</math>, the system can only diffuse in finite regions of the configuration space, and it is a glass. The distance it can explore is set by the percolation correlation length <math>\xi</math>, which diverges to infinite at <math>\Pi_P</math>.<br />
<br />
The authors then describe the percolation with mean-field theory. Following several known scaling laws, they show that the stretching exponent varies with time and satisfies <math>1/3 \leq \beta \leq 1</math>, agreeing with experimental observations.<br />
<br />
With a few more assumptions, they further predicts the scaling of <math>\alpha</math>-relaxation time to be<br />
<br />
<math>q^2 \tau_{\alpha} \propto \left\{<br />
\begin{array}{ll} <br />
\exp\left(\frac{A \phi_J}{\phi_J-\phi}\right)(\phi_P-\phi)^{-2} & \textrm{for } \phi_P-\phi \ll \phi_J-\phi_P\\<br />
\exp\left(\frac{B \phi_J}{\phi_J-\phi}\right) & \textrm{for } \phi_P-\phi \gg \phi_J-\phi_P<br />
\end{array} \right. </math>,<br />
<br />
where <math>q</math> is the scattering wave number, and <math>A</math>, <math>B</math> are positive constants.<br />
<br />
<br />
== Finite energy barriers ==<br />
<br />
Bonds form for systems with a finite energy barrier. In such case, the configuration space can be decomposed into basins of attraction surrounding each local energy minimum. At short times the system is confined to a basin, whereas at long times it can hop from one basin to another.<br />
<br />
Again using mean-field arguments, the authors come up with analogous expression for <math>\beta</math> and for <math>\tau_{\alpha}</math>.<br />
<br />
== Soft matter discussion ==<br />
<br />
The glass transition is one of the largest outstanding questions in soft matter. The approach proposed by these authors are dramatically different from the traditional standpoint, yet explains the observed phenomena equally well. This approach may shed some light, and hopefully lead to new predictions and better understanding of the glass-formation materials.</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Percolation_Model_for_Slow_Dynamics_in_Glass-Forming_Materials&diff=15935Percolation Model for Slow Dynamics in Glass-Forming Materials2010-11-23T23:48:59Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010 <br />
<br />
G. Lois, J. Blawzdziewicz, and C. S. O'Hern, "Percolation Model for Slow Dynamics in Glass-Forming Materials", Phys. Rev. Lett. '''102''', 015702 (2009).<br />
<br />
== Summary ==<br />
<br />
In this work, the authors propose an alternate approach to understand the glass transition. Instead of looking at the real space, they focus on the configuration space of the system. There are mobility regions in the configuration space, and the percolation of these regions corresponds to a glass-to-liquid transition. With a mean-field description of such percolation, they show that the stretched-exponential response functions typical of glassy systems can be explained.<br />
<br />
== Background ==<br />
<br />
Glassy systems exhibit several unique properties. During a glass transition, the structural relaxation time increases by several orders of magnitude. Also, the structural correlations display an anomalous stretched-exponential time decay: <math>exp(-t/\tau_{\alpha})^{\beta}</math>, where <math>\beta</math> is called the stretching exponent, and <math>\tau_{\alpha}</math> is called the <math>\alpha</math>-relaxation time. Although the stretched-exponential relaxation is universal among glass-forming materials, <math>\beta</math> and <math>\tau_{\alpha}</math> are not. They depend on temperature and density, and they vary from one material to another.<br />
<br />
== Basic Idea ==<br />
<br />
The basic idea is that, instead of focusing on the heterogeneous dynamics and percolation in real space (the traditional approach), the authors focus on the ''configuration space'' and its connection to the anomalous dynamics.<br />
<br />
For complete relaxation, the system must be able to diffuse over the whole configuration space. That is, there has to be a path that percolates the configuration space. Thus, we can think of a "percolation transition in the configuration space," which corresponds to the glass transition in real space.<br />
<br />
== Hard spheres ==<br />
<br />
[[Image:glass_config_fig1.jpg|thumb|300px| Fig 1. Schematic of allowed regions in configuration space for hard spheres. (a) <math>\phi = \phi_J </math>, only jammed states (discrete points in the config space) are allowed. (b) <math>\phi < \phi_J </math>, motion occurs in closed mobility domains surrounding jammed states. (c) Even smaller <math>\phi</math>, bridges between mobility domains occur. (d) Even smaller <math>\phi</math>, percolation occurs (shaded yellow).]]<br />
<br />
Hard spheres interact with infinite repulsion upon contact. At small volume fraction <math>\phi</math>, hard spheres behave like fluids. As <math>\phi</math> increases to <math>\phi_J \approx 0.64</math>, the system becomes collectively jammed. In such state no motion can occur, because any particle displacement will lead to overlap. Therefore only discrete set of points in the configuration space are allowed (fig 1a).<br />
<br />
At slightly lower <math>\phi</math>, particles can move around a little bit. Therefore, the discrete points become ''mobility domains'' in the configuration space (fig 1b). Further decrease of <math>\phi</math> lead to connection between these mobility domains (fig 1c), and eventually to a percolation between these domains (fig 1d) at <math>\phi=\phi_P</math>.<br />
<br />
Denote the volume fraction of mobility domains in the configuration by <math>\Pi</math>. Percolation occurs at a critical <math>\Pi_P</math>. When <math>\Pi > \Pi_P</math>, the system can explore the whole configuration space, and it is a metastable liquid. When <math>\Pi < \Pi_P</math>, the system can only diffuse in finite regions of the configuration space, and it is a glass. The distance it can explore is set by the percolation correlation length <math>\xi</math>, which diverges to infinite at <math>\Pi_P</math>.<br />
<br />
The authors then describe the percolation with mean-field theory. Following several known scaling laws, they show that the stretching exponent varies with time and satisfies <math>1/3 \leq \beta \leq 1</math>, agreeing with experimental observations.<br />
<br />
With a few more assumptions, they further predicts the scaling of <math>\alpha</math>-relaxation time to be<br />
<br />
<math>q^2 \tau_{\alpha} \propto \left\{<br />
\begin{array}{ll} <br />
\exp\left(\frac{A \phi_J}{\phi_J-\phi}\right)(\phi_P-\phi)^{-2} & \textrm{for } \phi_P-\phi \ll \phi_J-\phi_P\\<br />
\exp\left(\frac{B \phi_J}{\phi_J-\phi}\right) & \textrm{for } \phi_P-\phi \gg \phi_J-\phi_P<br />
\end{array} \right. </math>,<br />
<br />
where <math>q</math> is the scattering wave number, and <math>A</math>, <math>B</math> are positive constants.<br />
<br />
<br />
== Finite energy barriers ==<br />
<br />
For systems with a finite energy barrier...<br />
<br />
These mobility domains are hyperspherical near the jammed state points. Further away they become filamentary, and the time it takes to explore these regions is large.</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Percolation_Model_for_Slow_Dynamics_in_Glass-Forming_Materials&diff=15934Percolation Model for Slow Dynamics in Glass-Forming Materials2010-11-23T23:48:04Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010 <br />
<br />
G. Lois, J. Blawzdziewicz, and C. S. O'Hern, "Percolation Model for Slow Dynamics in Glass-Forming Materials", Phys. Rev. Lett. '''102''', 015702 (2009).<br />
<br />
== Summary ==<br />
<br />
In this work, the authors propose an alternate approach to understand the glass transition. Instead of looking at the real space, they focus on the configuration space of the system. There are mobility regions in the configuration space, and the percolation of these regions corresponds to a glass-to-liquid transition. With a mean-field description of such percolation, they show that the stretched-exponential response functions typical of glassy systems can be explained.<br />
<br />
== Background ==<br />
<br />
Glassy systems exhibit several unique properties. During a glass transition, the structural relaxation time increases by several orders of magnitude. Also, the structural correlations display an anomalous stretched-exponential time decay: <math>exp(-t/\tau_{\alpha})^{\beta}</math>, where <math>\beta</math> is called the stretching exponent, and <math>\tau_{\alpha}</math> is called the <math>\alpha</math>-relaxation time. Although the stretched-exponential relaxation is universal among glass-forming materials, <math>\beta</math> and <math>\tau_{\alpha}</math> are not. They depend on temperature and density, and they vary from one material to another.<br />
<br />
== Basic Idea ==<br />
<br />
The basic idea is that, instead of focusing on the heterogeneous dynamics and percolation in real space (the traditional approach), the authors focus on the ''configuration space'' and its connection to the anomalous dynamics.<br />
<br />
For complete relaxation, the system must be able to diffuse over the whole configuration space. That is, there has to be a path that percolates the configuration space. Thus, we can think of a "percolation transition in the configuration space," which corresponds to the glass transition in real space.<br />
<br />
[[Image:glass_config_fig1.jpg|thumb|300px| Fig 1. Schematic of allowed regions in configuration space for hard spheres. (a) <math>\phi = \phi_J </math>, only jammed states (discrete points in the config space) are allowed. (b) <math>\phi < \phi_J </math>, motion occurs in closed mobility domains surrounding jammed states. (c) Even smaller <math>\phi</math>, bridges between mobility domains occur. (d) Even smaller <math>\phi</math>, percolation occurs (shaded yellow).]]<br />
<br />
== Hard spheres ==<br />
<br />
Hard spheres interact with infinite repulsion upon contact. At small volume fraction <math>\phi</math>, hard spheres behave like fluids. As <math>\phi</math> increases to <math>\phi_J \approx 0.64</math>, the system becomes collectively jammed. In such state no motion can occur, because any particle displacement will lead to overlap. Therefore only discrete set of points in the configuration space are allowed (fig 1a).<br />
<br />
At slightly lower <math>\phi</math>, particles can move around a little bit. Therefore, the discrete points become ''mobility domains'' in the configuration space (fig 1b). Further decrease of <math>\phi</math> lead to connection between these mobility domains (fig 1c), and eventually to a percolation between these domains (fig 1d) at <math>\phi=\phi_P</math>.<br />
<br />
Denote the volume fraction of mobility domains in the configuration by <math>\Pi</math>. Percolation occurs at a critical <math>\Pi_P</math>. When <math>\Pi > \Pi_P</math>, the system can explore the whole configuration space, and it is a metastable liquid. When <math>\Pi < \Pi_P</math>, the system can only diffuse in finite regions of the configuration space, and it is a glass. The distance it can explore is set by the percolation correlation length <math>\xi</math>, which diverges to infinite at <math>\Pi_P</math>.<br />
<br />
The authors then describe the percolation with mean-field theory. Following several known scaling laws, they show that the stretching exponent varies with time and satisfies <math>1/3 \leq \beta \leq 1</math>, agreeing with experimental observations.<br />
<br />
With a few more assumptions, they further predicts the scaling of <math>\alpha</math>-relaxation time to be<br />
<br />
<math>q^2 \tau_{\alpha} \propto \left\{<br />
\begin{array}{ll} <br />
\exp\left(\frac{A \phi_J}{\phi_J-\phi}\right)(\phi_P-\phi)^{-2} & \textrm{for } \phi_P-\phi \ll \phi_J-\phi_P\\<br />
\exp\left(\frac{B \phi_J}{\phi_J-\phi}\right) & \textrm{for } \phi_P-\phi \gg \phi_J-\phi_P<br />
\end{array} \right. </math>,<br />
<br />
where <math>q</math> is the scattering wave number, and <math>A</math>, <math>B</math> are positive constants.<br />
<br />
<br />
== Finite energy barriers ==<br />
<br />
These mobility domains are hyperspherical near the jammed state points. Further away they become filamentary, and the time it takes to explore these regions is large.</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Glass_config_fig1.jpg&diff=15933File:Glass config fig1.jpg2010-11-23T23:05:01Z<p>Chsu: </p>
<hr />
<div></div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Percolation_Model_for_Slow_Dynamics_in_Glass-Forming_Materials&diff=15932Percolation Model for Slow Dynamics in Glass-Forming Materials2010-11-23T22:31:39Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010 <br />
<br />
G. Lois, J. Blawzdziewicz, and C. S. O'Hern, "Percolation Model for Slow Dynamics in Glass-Forming Materials", Phys. Rev. Lett. '''102''', 015702 (2009).<br />
<br />
== Summary ==<br />
<br />
In this work, the authors propose an alternate approach to understand the glass transition. Instead of looking at the real space, they focus on the configuration space of the system. There are mobility regions in the configuration space, and the percolation of these regions corresponds to a glass-to-liquid transition. With a mean-field description of such percolation, they show that the stretched-exponential response functions typical of glassy systems can be explained.<br />
<br />
== Background ==<br />
<br />
Glassy systems exhibit several unique properties. During a glass transition, the structural relaxation time increases by several orders of magnitude. Also, the structural correlations display an anomalous stretched-exponential time decay: <math>exp(-t/\tau_{\alpha})^{\beta}</math>, where <math>\beta</math> is called the stretching exponent, and <math>\tau_{\alpha}</math> is called the <math>\alpha</math>-relaxation time. Although the stretched-exponential relaxation is universal among glass-forming materials, <math>\beta</math> and <math>\tau_{\alpha}</math> are not. They depend on temperature and density, and they vary from one material to another.<br />
<br />
== Basic Idea ==<br />
<br />
The basic idea is that, instead of focusing on the heterogeneous dynamics and percolation in real space (the traditional approach), the authors focus on the ''configuration space'' and its connection to the anomalous dynamics.<br />
<br />
For complete relaxation, the system must be able to diffuse over the whole configuration space. That is, there has to be a path that percolates the configuration space. Thus, we can think of a "percolation transition in the configuration space," which corresponds to the glass transition in real space.<br />
<br />
[[Image:glass_config_fig1.jpg|thumb|300px| Schematic of allowed regions in configuration space for hard spheres. (a) <math>\phi = \phi_J </math>system is jammed; only jammed states (discrete points in the config space) are allowed. (b) ]]<br />
<br />
== Hard spheres ==<br />
<br />
<br />
== Finite energy barriers ==</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Percolation_Model_for_Slow_Dynamics_in_Glass-Forming_Materials&diff=15931Percolation Model for Slow Dynamics in Glass-Forming Materials2010-11-23T22:23:01Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010 <br />
<br />
G. Lois, J. Blawzdziewicz, and C. S. O'Hern, "Percolation Model for Slow Dynamics in Glass-Forming Materials", Phys. Rev. Lett. '''102''', 015702 (2009).<br />
<br />
== Summary ==<br />
<br />
In this work, the authors propose an alternate approach to understand the glass transition. Instead of looking at the real space, they focus on the configuration space of the system. There are mobility regions in the configuration space, and the percolation of these regions corresponds to a glass-to-liquid transition. With a mean-field description of such percolation, they show that the stretched-exponential response functions typical of glassy systems can be explained.<br />
<br />
== Background ==<br />
<br />
Glassy systems exhibit several unique properties. During a glass transition, the structural relaxation time increases by several orders of magnitude. Also, the structural correlations display an anomalous stretched-exponential time decay: <math>exp(-t/\tau_{\alpha})^{\beta}</math>, where <math>\beta</math> is called the stretching exponent, and <math>\tau_{\alpha}</math> is called the <math>\alpha</math>-relaxation time. Although the stretched-exponential relaxation is universal among glass-forming materials, <math>\beta</math> and <math>\tau_{\alpha}</math> are not. They depend on temperature and density, and they vary from one material to another.<br />
<br />
== Theory - Hard spheres ==<br />
<br />
This paper is fairly dense in math and equations. Here we will only give an outline of the arguments made and key results.<br />
<br />
The basic idea is that, instead of focusing on the heterogeneous dynamics and percolation in real space (the traditional approach), the authors focus on the ''configuration space'' and its connection to the anomalous dynamics.</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Percolation_Model_for_Slow_Dynamics_in_Glass-Forming_Materials&diff=15930Percolation Model for Slow Dynamics in Glass-Forming Materials2010-11-23T22:11:46Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010 <br />
<br />
G. Lois, J. Blawzdziewicz, and C. S. O'Hern, "Percolation Model for Slow Dynamics in Glass-Forming Materials", Phys. Rev. Lett. '''102''', 015702 (2009).<br />
<br />
== Summary ==<br />
<br />
In this work, the authors propose an alternate approach to understand the glass transition. Instead of looking at the real space, they focus on the configuration space of the system. There are mobility regions in the configuration space, and the percolation of these regions corresponds to a glass-to-liquid transition. With a mean-field description of such percolation, they show that the stretched-exponential response functions typical of glassy systems can be explained.<br />
<br />
== Background ==<br />
<br />
Glassy systems exhibit several unique properties. During a glass transition, the structural relaxation time increases by several orders of magnitude. Also, the structural correlations display an anomalous stretched-exponential time decay: <math>exp(-t/\tau_{\alpha})^{\beta}</math>, where <math>\beta</math> is called the stretching exponent, and <math>\tau_{\alpha}</math> is called the <math>\alpha</math>-relaxation time.</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Percolation_Model_for_Slow_Dynamics_in_Glass-Forming_Materials&diff=15929Percolation Model for Slow Dynamics in Glass-Forming Materials2010-11-23T19:10:08Z<p>Chsu: New page: Entry: Chia Wei Hsu, AP 225, Fall 2010 G. Lois, J. Blawzdziewicz, and C. S. O'Hern, "Percolation Model for Slow Dynamics in Glass-Forming Materials", Phys. Rev. Lett. '''102''', 015702 (...</p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010 <br />
<br />
G. Lois, J. Blawzdziewicz, and C. S. O'Hern, "Percolation Model for Slow Dynamics in Glass-Forming Materials", Phys. Rev. Lett. '''102''', 015702 (2009).</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Chia_Wei_Hsu&diff=15860Chia Wei Hsu2010-11-17T16:22:07Z<p>Chsu: </p>
<hr />
<div>Definitions:<br />
<br />
<br />
<br />
Weekly wiki entries:<br />
<br />
Week 1: [[The Free-Energy Landscape of Clusters of Attractive Hard Spheres]]<br />
<br />
Week 2: [[Statistical mechanics of developable ribbons]]<br />
<br />
Week 3: [[Chemotactic Patterns without Chemotaxis]]<br />
<br />
Week 4: [[Particle Segregation and Dynamics in Confined Flows]]<br />
<br />
Week 5: [[Intracellular transport by active diffusion]]<br />
<br />
Week 6: [[Equilibrating Nanoparticle Monolayers UsingWetting Films]]<br />
<br />
Week 7: [[Shear Melting of a Colloidal Glass]]<br />
<br />
Week 8: [[Onset of Buckling in Drying Droplets of Colloidal Suspensions]]</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Onset_of_Buckling_in_Drying_Droplets_of_Colloidal_Suspensions&diff=15859Onset of Buckling in Drying Droplets of Colloidal Suspensions2010-11-17T16:20:28Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010 <br />
<br />
N. Tsapis, E. R. Dufresne, S. S. Sinha, C.S. Riera, J. W. Hutchinson, L. Mahadevan, and D. A. Weitz, Phys Rev Lett '''94''', 018302 (2005)<br />
<br />
== Summary ==<br />
<br />
This work studies the drying of freely suspended colloidal droplets. These droplets initially behave like pure liquids and shrink isotropically. Eventually, they buckle like elastic shells. The authors conclude the mechanism: as droplets dry, a viscoelastic shell of densely packed particles forms at its surface. Initially, the shell yields and thickens as the droplet shrinks. Eventually, the capillary forces that drive deformation of the shell overcome the electrostatic forces stabilizing the particles. At this point, the shell undergoes a sol-gel transition, becomes elastic, and buckles. <br />
<br />
== Background ==<br />
<br />
[[Image:bucklilng_fig1.jpg|thumb|300px| Fig. 1. Buckling instability. (a) experiment. Scale bar 0.5mm. (b) Simulation]]<br />
<br />
Minute concentrations of suspended particles can dramatically alter the behavior of a drying droplet. After a period of isotropic shrinkage, similar to droplets of a pure liquid, these droplets suddenly buckle like an elastic shell. While linear elasticity is able to describe the morphology of the buckled droplets, it fails to predict the onset of buckling. Also, drying suspensions can be viscoelastic, depending on the experimental time scale. Thus, dyring droplets pose a number of intriguing fundamental questions.<br />
<br />
== Experiment and observation ==<br />
<br />
The authors study drying droplets of aqueous suspensions of monodisperse carboxylate-modified polystyrene colloids, suspended through the Leidenfrost effect (ie, fluid droplets float on a thin layer of their own vapor above 150 degree C). The radii range from 0.8 to 2.2 mm (They have to be smaller than the capillary length 2.5 mm in order to remain spherical). The dynamics of drying is monitored with high-speed camera. Fig 1 shows the transition from isotropically shrinking to the sudden buckling.<br />
<br />
== Explanation ==<br />
<br />
[[Image:bucklilng_fig2.jpg|thumb|200px| Fig. 2. Dependence of (a) <math>R_B/R_i</math> and (b) <math>(T/R)_B</math> on initial volume fraction <math>\phi_i</math>. Data shown for droplets of two different sizes.]]<br />
<br />
A shell on the surface of the droplet forms, because particles pile up just inside the drying droplet's receding air-water interface. The time for the fluid to evaporate (<math>\tau_{\mathrm{dry}} \approx 60 </math> s) is much shorter than the time required for homogenizing the fluid ((<math>\tau_{\mathrm{dry}} \approx 10^3 </math> s), so the boundary between the shell and the bulk droplet is sharp. With mass conservation, the shell thickness <math>T</math> (with volume fraction <math>\phi_c</math>) can be related to the droplet radius <math>R</math> (with volume fraction <math>\phi_i</math>) by<br />
<br />
<math>\frac{T}{R} = 1 - \left[ \frac{\phi_c - \phi_i (R_i / R)^3}{\phi_c - \phi_i} \right] ^{1/3}</math><br />
<br />
Capillary forces drive the deformation of the shell, and the shell response viscoelastically. During the isotropic shrinking, the viscous nature of the shell dominates. However, buckling requires the shell to become elastic. So the onset of buckling correspond to a crossover from viscous to elastic regimes of the shell's rheology.<br />
<br />
[[Image:bucklilng_fig3.jpg|thumb|200px| Fig. 3. Dependence of pressure drop on the initial volume fraction <math>\phi_i</math>. Data shown for droplets of two different sizes.]]<br />
<br />
The ratio between the buckling radius <math>R_B</math> and the initial radius <math>R_i</math> is a constant with respect to <math>R_i</math> (fig 2a inset), and scales as <math>\phi_i^{1/3}</math> (fig 2a). Meanwhile, the ratio between the shell thickness and the droplet radius at buckling seems to be a constant (fig 2b). Furthermore, the pressure drop through the shell at buckling <math>(\Delta P)_B</math> also seems to be a constant with respect to <math>\phi_i</math>.<br />
<br />
This "critical pressure" suggests that the crossover from viscous to elastic behavior is initiated by stress. This critical pressure corresponds to a critical force <math>F_B \approx \pi a^2 (\Delta P)_B</math>. The authors found that this critical force agrees with the maximum repulsive force due to electrostatic double-layers (estimated from the DLVO theory). Therefore, they hypothesize that buckling occurs when the capillary forces driving the deformation and the flow of a shell overcome the electrostatic forces stabilizing the particles against aggregation.<br />
<br />
== Connection to Soft Matter ==<br />
<br />
This work utilizes several things we just learned in this soft matter class, including calculation of the capillary length, the Laplace pressure, and the DLVO forces. It is nice to see how these simple theory are used in real research.<br />
<br />
This work suggests that the shell formed on the surface of a drying droplet behaves both as a viscous and a elastic material, and that the onset of buckling marks the transition between the two. The transition is an interplay between many forces. Thus even phenomenon as simple as a drying droplet can be quite complex when we examine its mechanism.</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Bucklilng_fig3.jpg&diff=15858File:Bucklilng fig3.jpg2010-11-17T16:10:23Z<p>Chsu: </p>
<hr />
<div></div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Bucklilng_fig2.jpg&diff=15857File:Bucklilng fig2.jpg2010-11-17T16:10:19Z<p>Chsu: </p>
<hr />
<div></div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Bucklilng_fig1.jpg&diff=15856File:Bucklilng fig1.jpg2010-11-17T15:53:17Z<p>Chsu: </p>
<hr />
<div></div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Onset_of_Buckling_in_Drying_Droplets_of_Colloidal_Suspensions&diff=15854Onset of Buckling in Drying Droplets of Colloidal Suspensions2010-11-17T01:26:13Z<p>Chsu: New page: Entry: Chia Wei Hsu, AP 225, Fall 2010 N. Tsapis, E. R. Dufresne, S. S. Sinha, C.S. Riera, J. W. Hutchinson, L. Mahadevan, and D. A. Weitz, Phys Rev Lett '''94''', 018302 (2005)</p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010 <br />
<br />
N. Tsapis, E. R. Dufresne, S. S. Sinha, C.S. Riera, J. W. Hutchinson, L. Mahadevan, and D. A. Weitz, Phys Rev Lett '''94''', 018302 (2005)</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Shear_Melting_of_a_Colloidal_Glass&diff=15760Shear Melting of a Colloidal Glass2010-11-11T05:26:12Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010<br />
<br />
Christoph Eisenmann, Chanjoong Kim, Johan Mattsson, and David Weitz, Phys. Rev. Lett. '''104''', 035502 (2010)<br />
<br />
== Background ==<br />
<br />
Colloidal suspensions serve as a model system for glass transition. A colloidal glass exhibit cooperativity and dynamic heterogeneity that are typically seen in glass transitions, as well as its own unique properties such as shear melting. Because of the large particle size, colloids form soft solids and can be fluidized through shear. In order to understand the relationship of shear-induced melting to others (such as melting by increasing temperature or reducing volume fraction), we need to understand the microscopic behavior of shear-melting.<br />
<br />
== Experiment ==<br />
<br />
[[Image:shear_melting_fig1.jpg|thumb|300px| Fig. 1. (a)(b) MSD versus strain. (c)(d) Non-Gaussian parameter.]]<br />
<br />
The authors study sterically stabilized poly(methylmethacrylate) particles (average radius <math>R=0.6\mu m</math>) suspended in a mixture of cis-decalin and cycloheptylbromide (which matches the particle density and index of refraction) at a volume fraction of <math>\phi=0.61\pm0.03</math>. The colloid particles are fluorescently labeled, and the suspension is contained between two parallel glass plates <math>40 \mu m</math> apart in a shear cell.<br />
<br />
A symmetrical triangular time-dependent strain is applied in the <math>y</math> direction with strain amplitude up to <math>\gamma \approx 0.5</math> and strain periods between 25 and 100 <math>s</math>. At such shear rate, particle motions are dominated by the imposed shear (as opposed to diffusion). <br />
The particle positions <math>x(t)</math> and <math> y(t)</math> are tracked with confocal microscopy during shear, with data collected 2 frames per second. Then the mean displacement due to shear is subtracted.<br />
<br />
== Results ==<br />
<br />
[[Image:shear_melting_fig2.jpg|thumb|300px| Fig. 2 Dynamic cluster for an unsheared system (a) and a sheared system (b). (c) Size histogram of the dynamic clusters. Red: unsheared; blue: sheared.]]<br />
<br />
The authors first calculate an effective mean-squared-displacement (MSD), <math>\langle\Delta x^2(\Delta t)\rangle_0=\langle ( x ( t_0 + \Delta t)-x(t_0))^2\rangle</math>, where<math>t_0</math> is the initial time of a half strain-cycle. MSD is compared for different values of <math>\gamma</math> (fig 1a, b). The MSD crosses over from subdiffusive to a steady state diffusive behavior at a transition at <math>\gamma \approx 0.08</math> is observed. At the transition, the distribution of particle displacements <math>P(\Delta x (\Delta t))</math> becomes non-Gaussian, reflecting dynamic heterogeneities. This is measured by the non-Gaussian parameter <math>\alpha_2</math> (fig 1c, d).<br />
<br />
[[Image:shear_melting_fig3.jpg|thumb|300px| Fig. 3. (a) Time evolution of MSD. (b) Diffusion constant versus shear rate. Dashed line: <math>D=(2/9)R_s^2 \dot{\gamma}</math>, with <math>R_s=1.8R</math>.]]<br />
<br />
To study the cooperative motions in the sheared colloids, the authors look at the dynamic clusters in the sample, and compare it to an unsheared colloidal liquid with comparable diffusion constant (fig 2 a,b). To be more quantitative, they compare the dynamic cluster size distribution of the two (fig 2 c). The sheared glass has a longer tail of larger dynamic clusters. Integrating the data, they obtain an average dynamic cluster size about 2-3 particles, setting the scale of cooperative motion.<br />
<br />
Lastly, they measure the diffusion constant<math>D</math> with a linear fit of the MSD data: <math>\langle \Delta x^2(t)\rangle_y=2Dt</math> (fig 3). Interestingly, <math>D</math> is linear with the shear rate <math>\dot{\gamma}</math>. They propose to explain this relation with a modified version of the Stokes-Einstein relation. Replace the thermal energy <math>k_B T</math> with the shear energy <math>(4\pi R_s^3/3)\eta \dot{\gamma}</math>, the Stokes-Einstein relation becomes <math>D=(2/9)R_s^2 \dot{\gamma}</math>. Here <math>R_s</math> is a characteristic radius. In the data <math>R_s=1.8R</math>, agreeing with the observation that a cluster contains about 3 particles.<br />
<br />
== Soft Matter discussion ==<br />
<br />
Explanation of the glass transition is one of the biggest mysteries in soft matter. Shear melting of a colloidal glass provides another way to investigate this phenomenon. Here strain plays a role similar to temperature, and the critical strain <math>\gamma \approx 0.08</math> is analogous to the glass transition temperature <math>T_g</math>. Indeed, under external shear, the particle dynamics is not determined by thermal fluctuation but by the imposed shear. That is also why we can simply swap the thermal energy with shear energy, and modify the Stokes-Einstein relation (which is just an example of fluctuation-dissipation<br />
) to explain the diffusion constant of the sheared system. Further, we note that in this example, shearing enhances the mobility of the particles, and that in similar to the role of active transport in biological systems (see [[Intracellular transport by active diffusion]]).</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Chia_Wei_Hsu&diff=15759Chia Wei Hsu2010-11-11T05:02:19Z<p>Chsu: </p>
<hr />
<div>Definitions:<br />
<br />
<br />
<br />
Weekly wiki entries:<br />
<br />
Week 1: [[The Free-Energy Landscape of Clusters of Attractive Hard Spheres]]<br />
<br />
Week 2: [[Statistical mechanics of developable ribbons]]<br />
<br />
Week 3: [[Chemotactic Patterns without Chemotaxis]]<br />
<br />
Week 4: [[Particle Segregation and Dynamics in Confined Flows]]<br />
<br />
Week 5: [[Intracellular transport by active diffusion]]<br />
<br />
Week 6: [[Equilibrating Nanoparticle Monolayers UsingWetting Films]]<br />
<br />
Week 7: [[Shear Melting of a Colloidal Glass]]</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Shear_Melting_of_a_Colloidal_Glass&diff=15753Shear Melting of a Colloidal Glass2010-11-11T04:37:19Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010<br />
<br />
Christoph Eisenmann, Chanjoong Kim, Johan Mattsson, and David Weitz, Phys. Rev. Lett. '''104''', 035502 (2010)<br />
<br />
== Background ==<br />
<br />
Colloidal suspensions serve as a model system for glass transition. A colloidal glass exhibit cooperativity and dynamic heterogeneity that are typically seen in glass transitions, as well as its own unique properties such as shear melting. Because of the large particle size, colloids form soft solids and can be fluidized through shear. In order to understand the relationship of shear-induced melting to others (such as melting by increasing temperature or reducing volume fraction), we need to understand the microscopic behavior of shear-melting.<br />
<br />
== Experiment ==<br />
<br />
[[Image:shear_melting_fig1.jpg|thumb|300px| Fig. 1. (a)]]<br />
<br />
The authors study sterically stabilized poly(methylmethacrylate) particles (average radius <math>R=0.6\mu m</math>) suspended in a mixture of cis-decalin and cycloheptylbromide (which matches the particle density and index of refraction) at a volume fraction of <math>\phi=0.61\pm0.03</math>. The colloid particles are fluorescently labeled, and the suspension is contained between two parallel glass plates <math>40 \mu m</math> apart in a shear cell.<br />
<br />
A symmetrical triangular time-dependent strain is applied in the <math>y</math> direction with strain amplitude up to <math>\gamma \approx 0.5</math> and strain periods between 25 and 100 <math>s</math>. At such shear rate, particle motions are dominated by the imposed shear (as opposed to diffusion). <br />
The particle positions <math>x(t)</math> and <math> y(t)</math> are tracked with confocal microscopy during shear, with data collected 2 frames per second. Then the mean displacement due to shear is subtracted.<br />
<br />
== Results ==<br />
<br />
[[Image:shear_melting_fig2.jpg|thumb|300px| Fig. 2 (a)]]<br />
<br />
The authors first calculate an effective mean-squared-displacement (MSD), <math>\langle\Delta x^2(\Delta t)\rangle_0=\langle ( x ( t_0 + \Delta t)-x(t_0))^2\rangle</math>, where<math>t_0</math> is the initial time of a half strain-cycle. MSD is compared for different values of <math>\gamma</math> (fig 1a, b). The MSD crosses over from subdiffusive to a steady state diffusive behavior at a transition at <math>\gamma \approx 0.08</math> is observed. At the transition, the distribution of particle displacements <math>P(\Delta x (\Delta t))</math> becomes non-Gaussian, reflecting dynamic heterogeneities. This is measured by the non-Gaussian parameter <math>\alpha_2</math> (fig 1c, d).<br />
<br />
[[Image:shear_melting_fig3.jpg|thumb|300px| Fig. 3. (a)]]</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Shear_melting_fig3.jpg&diff=15752File:Shear melting fig3.jpg2010-11-11T04:36:17Z<p>Chsu: </p>
<hr />
<div></div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Shear_melting_fig2.jpg&diff=15751File:Shear melting fig2.jpg2010-11-11T04:36:04Z<p>Chsu: </p>
<hr />
<div></div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Shear_melting_fig1.jpg&diff=15750File:Shear melting fig1.jpg2010-11-11T04:29:53Z<p>Chsu: </p>
<hr />
<div></div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Shear_Melting_of_a_Colloidal_Glass&diff=15747Shear Melting of a Colloidal Glass2010-11-11T04:06:42Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010<br />
<br />
Christoph Eisenmann, Chanjoong Kim, Johan Mattsson, and David Weitz, Phys. Rev. Lett. '''104''', 035502 (2010)<br />
<br />
== Background ==<br />
<br />
Colloidal suspensions serve as a model system for glass transition. A colloidal glass exhibit cooperativity and dynamic heterogeneity that are typically seen in glass transitions, as well as its own unique properties such as shear melting. Because of the large particle size, colloids form soft solids and can be fluidized through shear. In order to understand the relationship of shear-induced melting to others (such as melting by increasing temperature or reducing volume fraction), we need to understand the microscopic behavior of shear-melting.<br />
<br />
== Experiment ==<br />
<br />
The authors study sterically stabilized poly(methylmethacrylate) particles (average radius <math>R=0.6\mu m</math>) suspended in a mixture of cis-decalin and cycloheptylbromide (which matches the particle density and index of refraction) at a volume fraction of <math>\phi=0.61\pm0.03</math>. The colloid particles are fluorescently labeled, and the suspension is contained between two parallel glass plates <math>40 \mu m</math> apart, in a shear cell.<br />
<br />
A symmetrical triangular time-dependent strain is applied in the <math>y</math> direction with strain amplitude up to <math>\gamma \approx 0.5</math> and strain periods between 25 and 100 <math>s</math>. At such shear rate, particle motions are dominated by the imposed shear (as opposed to diffusion). <br />
The particle positions <math>x(t) and y(t)</math> are tracked with confocal microscopy during shear, with data collected 2 frames per second. Then the mean displacement due to shear is subtracted.<br />
<br />
== Results ==</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Shear_Melting_of_a_Colloidal_Glass&diff=15672Shear Melting of a Colloidal Glass2010-11-10T05:16:37Z<p>Chsu: New page: Entry: Chia Wei Hsu, AP 225, Fall 2010 Christoph Eisenmann, Chanjoong Kim, Johan Mattsson, and David Weitz, Phys. Rev. Lett. '''104''', 035502 (2010)</p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010<br />
<br />
Christoph Eisenmann, Chanjoong Kim, Johan Mattsson, and David Weitz, Phys. Rev. Lett. '''104''', 035502 (2010)</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Chia_Wei_Hsu&diff=15536Chia Wei Hsu2010-11-03T15:34:55Z<p>Chsu: </p>
<hr />
<div>Definitions:<br />
<br />
<br />
<br />
Weekly wiki entries:<br />
<br />
Week 1: [[The Free-Energy Landscape of Clusters of Attractive Hard Spheres]]<br />
<br />
Week 2: [[Statistical mechanics of developable ribbons]]<br />
<br />
Week 3: [[Chemotactic Patterns without Chemotaxis]]<br />
<br />
Week 4: [[Particle Segregation and Dynamics in Confined Flows]]<br />
<br />
Week 5: [[Intracellular transport by active diffusion]]<br />
<br />
Week 6: [[Equilibrating Nanoparticle Monolayers UsingWetting Films]]</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Equilibrating_Nanoparticle_Monolayers_UsingWetting_Films&diff=15535Equilibrating Nanoparticle Monolayers UsingWetting Films2010-11-03T15:32:08Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010 <br />
<br />
D. Pontoni, K. Alvine, A. Checco, O. Gang, B. Ocko, and P. Pershan, Equilibrating Nanoparticle Monolayers Using Wetting Films, Phys. Rev. Lett. 102, 016101 (2009).<br />
<br />
== Summary ==<br />
<br />
[[Image:monolayer_fig1.jpg|thumb|300px| Fig. 1. (a) Illustration of the nanoparticles used. (b) Gold core size distribution histogram from TEM with double Gaussian ﬁt (line). (c) Bright ﬁeld TEM (contrast enhanced) and (d) AFM images of preannealing nanoparticle monolayers (scale bars 300 A˚ ).]]<br />
<br />
The authors study monolayers of gold nanoparticles (NP) formed on silicon substrate. The gold NPs consist of mostly small NPs and some large ones. They pre-assemble the NPs on the silicon substrate, and then use controlled under-saturated toluene solvent vapors to re-assemble the monolayer. The nanoscale packing structure closely resembles those observed in micron-sized binary hard-sphere systems.<br />
<br />
== Experimental Procedure ==<br />
<br />
Thiol-stabilized gold NPs are prepared in a solution of octane-thiol and mercaptopropionic acid. The coating thickness <math>t</math> is about 12 <math>\AA</math> (Fig 1a). The distribution of the particle size (<math>s</math>) is bimodal, with the two peaks at 17 <math>\AA</math> for small particles and 76 <math>\AA</math> for large particles (fig 1b). About 85% of the particles are small. These gold NPs are hydrophobic and disperse readily in toluene.<br />
<br />
The authors first prepare a dry monolayer of particles on silicon surface using the Langmuir-Schaefer approach. The resulting structure shows correlated regions of the more abundant small particles surrounded by ribbon-like structure of larger particles (TEM image in fig 1c and AFM image in fig 1d).<br />
<br />
[[Image:monolayer_fig2.jpg|thumb|300px| Fig. 2. Pictorial summary of various system conditions. Top to bottom: Initial dry sample, thickest wetting liquid, annealed sample in thin liquid, redried sample after annealing.]]<br />
<br />
Then, toluene vapor is used for the controlled wetting of the NP monolayer. They achieve so by accurate control of the chemical potential of the toluene. They first inject toluene vapor at <math>\Delta T=15K</math>, where <math>\Delta T=T_s-T_r</math> is the temperature difference between the substrate and the toluene vapor reservoir. This creates a thin wetting film of about 1 nm thick. They they slowly cool the substrate to decrease <math>\Delta T</math> to 15 mK. In such process the film thickness grows to 10 nm. Finally, they slowly heat up (anneal) the substrate back to <math>\Delta T</math> = 15K (the wetting film get back to 1 nm thin in the process). In the end they re-dry the sample. Fig 2 provides a pictorial summary of the particle conditions of the systems in such process, based on observations.<br />
<br />
X-ray diffraction is used to study the structure of the sample through out the whole process, and microscopy is used to examine the initial dry monolayer and the final re-dried monolayer.<br />
<br />
== Results ==<br />
<br />
Within the 10 nm thick solvent, the small particles experience a nearly 3D environment, while the large particles are still confined to a 2D geometry. This is supported by scattering data. Such confinement imbalance facilitate the preferential diffusion of small particles into initially empty cracks. Indeed, in the re-assembled monolayer, small particles cover more substrate area then before (a factor of 1.24). This suggests that when the solvents are not dried yet, the particles are mobile and explore the entire area by diffusion. Another consequence is that the re-dried sample exhibit enhanced size-segregation of particles.<br />
<br />
Before wetting, the system's correlation function is dominated by the small particles, similar to predictions for a model of binary hard-sphere mixtures with predominantly small hard-spheres. After solvent annealing, the small particles still dominate the system's correlation function.<br />
<br />
== Connection to Soft Matter ==<br />
<br />
This study provides a method to systematically investigate size and solvent effects on the structure and dynamics of NP assembly, with the confinement varying continuously between purely 2D to nearly 3D. The wetting-induced restructuring provides possibility for controlled assembly with varying degrees of order. These might eventually lead to technological applications.</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Equilibrating_Nanoparticle_Monolayers_UsingWetting_Films&diff=15534Equilibrating Nanoparticle Monolayers UsingWetting Films2010-11-03T15:05:34Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010 <br />
<br />
D. Pontoni, K. Alvine, A. Checco, O. Gang, B. Ocko, and P. Pershan, Equilibrating Nanoparticle Monolayers Using Wetting Films, Phys. Rev. Lett. 102, 016101 (2009).<br />
<br />
== Summary ==<br />
<br />
[[Image:monolayer_fig1.jpg|thumb|300px| Fig. 1. (a) Illustration of the nanoparticles used. (b) Gold core size distribution histogram from TEM with double Gaussian ﬁt (line). (c) Bright ﬁeld TEM (contrast enhanced) and (d) AFM images of preannealing nanoparticle monolayers (scale bars 300 A˚ ).]]<br />
<br />
The authors study monolayers of gold nanoparticles (NP) formed on silicon substrate. The gold NPs consist of mostly small NPs and some large ones. They pre-assemble the NPs on the silicon substrate, and then use controlled under-saturated toluene solvent vapors to re-assemble the monolayer. The nanoscale packing structure closely resembles those observed in micron-sized binary hard-sphere systems.<br />
<br />
== Experimental Method ==<br />
<br />
Thiol-stabilized gold NPs are prepared in a solution of octane-thiol and mercaptopropionic acid. The coating thickness <math>t</math> is about 12 <math>\AA</math> (Fig 1a). The distribution of the particle size (<math>s</math>) is bimodal, with the two peaks at 17 <math>\AA</math> for small particles and 76 <math>\AA</math> for large particles (fig 1b). About 85% of the particles are small. These gold NPs are hydrophobic and disperse readily in toluene.<br />
<br />
The authors first prepare a dry monolayer of particles on silicon surface using the Langmuir-Schaefer approach. The resulting structure shows correlated regions of the more abundant small particles surrounded by ribbon-like structure of larger particles (TEM image in fig 1c and AFM image in fig 1d).<br />
<br />
[[Image:monolayer_fig2.jpg|thumb|300px| Fig. 2. Pictorial summary of various system conditions. Top to bottom: Initial dry sample, thickest wetting liquid, annealed sample in thin liquid, redried sample after annealing.]]<br />
<br />
Then, toluene vapor is used for the controlled wetting of the NP monolayer. They achieve so by accurate control of the chemical potential of the toluene. They first inject toluene vapor at <math>\Delta T=15K</math>, where <math>\Delta T=T_s-T_r</math> is the temperature difference between the substrate and the toluene vapor reservoir. This creates a thin wetting film of about 1 nm thick. They they slowly cool the substrate to decrease <math>\Delta T</math> to 15 mK. In such process the film thickness grows to 10 nm. Finally, they slowly heat up the substrate back to <math>\Delta T</math> = 15K (the wetting film get back to 1 nm thin in the process). In the end they re-dry the sample. Fig 2 provides a pictorial summary of the condition of the systems in such process.<br />
<br />
X-ray diffraction is used to study the structure of the sample through out the whole process, and microscopy is used to examine the initial dry monolayer and the final re-dried monolayer.<br />
<br />
== Results ==</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Monolayer_fig2.jpg&diff=15533File:Monolayer fig2.jpg2010-11-03T15:01:42Z<p>Chsu: </p>
<hr />
<div></div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Monolayer_fig1.jpg&diff=15532File:Monolayer fig1.jpg2010-11-03T15:01:36Z<p>Chsu: </p>
<hr />
<div></div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Equilibrating_Nanoparticle_Monolayers_UsingWetting_Films&diff=15531Equilibrating Nanoparticle Monolayers UsingWetting Films2010-11-03T03:21:47Z<p>Chsu: New page: Entry: Chia Wei Hsu, AP 225, Fall 2010 D. Pontoni, K. Alvine, A. Checco, O. Gang, B. Ocko, and P. Pershan, Equilibrating Nanoparticle Monolayers Using Wetting Films, Phys. Rev. Lett. 102...</p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010 <br />
<br />
D. Pontoni, K. Alvine, A. Checco, O. Gang, B. Ocko, and P. Pershan, Equilibrating Nanoparticle Monolayers Using Wetting Films, Phys. Rev. Lett. 102, 016101 (2009).</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Chia_Wei_Hsu&diff=15286Chia Wei Hsu2010-10-25T02:10:30Z<p>Chsu: </p>
<hr />
<div>Definitions:<br />
<br />
<br />
<br />
Weekly wiki entries:<br />
<br />
Week 1: [[The Free-Energy Landscape of Clusters of Attractive Hard Spheres]]<br />
<br />
Week 2: [[Statistical mechanics of developable ribbons]]<br />
<br />
Week 3: [[Chemotactic Patterns without Chemotaxis]]<br />
<br />
Week 4: [[Particle Segregation and Dynamics in Confined Flows]]<br />
<br />
Week 5: [[Intracellular transport by active diffusion]]</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Intracellular_transport_by_active_diffusion&diff=15285Intracellular transport by active diffusion2010-10-25T01:43:59Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010<br />
<br />
Clifford P. Brangwynne, Gijsje H. Koenderink, Frederick C. MacKintosh and David A. Weitz, "Intracellular transport by active diffusion" , Trends in Cell Biology 19 (9), 423-427 (2009).<br />
<br />
<br />
== Summary ==<br />
<br />
This article concerns cell mechanics. The main point of this article is that active transports in cells can result in significant random fluctuations of particles that resemble thermal fluctuations. These particles undergo an enhanced diffusion, which the authors refer to as "active diffusion".<br />
<br />
<br />
== Background: Thermal diffusion and random intracellular motion ==<br />
<br />
Thermal agitation causes molecules or small particles to perform random walk in a solution. This is referred to as Brownian motion or diffusive motion. Although diffusion is not directional, it acts as an important mechanism for short-distanced transports in cells and provides the basis for signal transduction networks.<br />
<br />
Thermal-driven diffusion follows well-known physical laws. The diffusion constant increases with temperature, and decreases with the particle size and the medium viscosity. However, a number of intracellular motions appear to be random and diffusive-like, but do not follow these basic properties of thermal diffusion. This suggests that there must be other mechanism that contributes to the random transport of particles in cells.<br />
<br />
In cells, there is another kind of transport. These are active, directional transports driven by either the motion of motor proteins along cytoskeletal filaments (kinesins and dyneins run on microtubules; myosins run on actin), or the polymerization/de-polymerization of these filaments. These directed transports are distinct from the random diffusive transport.<br />
<br />
This article discusses how the active transports can drive random diffusive-like transports.<br />
<br />
<br />
== Coupling between mechanics and diffusivity ==<br />
<br />
[[Image:active_duffusion.jpg|thumb|300px| Fig. 1. Schematic plots for active and thermal fluctuation motion of an inert probe particle in cell.]]<br />
<br />
The authors discuss how diffusivity is connected to the mechanics, by the example of actin networks. At low actin concentrations, the solution behaves as a viscous liquid, and the mean-square-displacement (MSD) of the filaments grows linearly with time. At high actin concentration, filaments cross-link and behaves like an elastic solid, and MSD remains at a small fixed value. At intermediate actin concentrations, the filaments behaves as a viscoelastic material and undergo sub-diffusive motion with MSD increases with time but slower than linear.<br />
<br />
== Thermal diffusion vs active diffusion ==<br />
<br />
Without other activities in cells, an inert probe particle is expected to undergo sub-diffusive motion on short time scales (t ~ 1 sec), hindered motion for longer time scales (t ~ 10 sec), and diffusive motion on even-longer time scales (t > 100 sec). This expected curve is described by the blue line in fig 1.<br />
<br />
With active motions in cells, the motion of an inert probe particle is actually better described by the red line in fig 1. For example, the myosin motors can "fluidize" the actin network by enhancing the ability of filaments to slide past one another. Thus the probe particles are less hindered, and undergoes diffusive-like motion at short time scales. At long time scales, the motors actively remodels the filament network, which also enhances the mobility of the probe particle. These observations are supported by both in vitro and in situ experiments.<br />
<br />
== Connection to soft matter ==<br />
<br />
In soft matter, we frequently treat thermal fluctuations as the source of diffusion, and use the Stokes-Einstein relation <math>D=k_B T / 6 \pi \eta R</math> to estimate the diffusion constant of a particle with Stokes radius <math>R</math> in a medium with viscosity <math>\eta</math>. However, this article tells us that such approach will be fundamentally incorrect when we look at the motion of particles in cell, where active transport motions are constantly going on. The motion of such particles are random on average, but can no longer be described by simple physical laws. This is another reason why it is so hard to quantify cell mechanics.</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Active_duffusion.jpg&diff=15284File:Active duffusion.jpg2010-10-25T01:22:16Z<p>Chsu: </p>
<hr />
<div></div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Intracellular_transport_by_active_diffusion&diff=15283Intracellular transport by active diffusion2010-10-25T01:15:49Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010<br />
<br />
Clifford P. Brangwynne, Gijsje H. Koenderink, Frederick C. MacKintosh and David A. Weitz, "Intracellular transport by active diffusion" , Trends in Cell Biology 19 (9), 423-427 (2009).<br />
<br />
<br />
== Summary ==<br />
<br />
This article concerns cell mechanics. The main point of this article is that active transports in cells can result in significant random fluctuations of particles that resemble thermal fluctuations. These particles undergo an enhanced diffusion, which the authors refer to as "active diffusion".<br />
<br />
<br />
== Background: Thermal diffusion and random intracellular motion ==<br />
<br />
Thermal agitation causes molecules or small particles to perform random walk in a solution. This is referred to as Brownian motion or diffusive motion. Although diffusion is not directional, it acts as an important mechanism for short-distanced transports in cells and provides the basis for signal transduction networks.<br />
<br />
Thermal-driven diffusion follows well-known physical laws. The diffusion constant increases with temperature, and decreases with the particle size and the medium viscosity. However, a number of intracellular motions appear to be random and diffusive-like, but do not follow these basic properties of thermal diffusion. This suggests that there must be other mechanism that contributes to the random transport of particles in cells.<br />
<br />
In cells, there is another kind of transport. These are active, directional transports driven by either the motion of motor proteins along cytoskeletal filaments (kinesins and dyneins run on microtubules; myosins run on actin), or the polymerization/de-polymerization of these filaments. These directed transports are distinct from the random diffusive transport.<br />
<br />
This article discusses how the active transports can drive random diffusive-like transports.<br />
<br />
<br />
== Coupling between mechanics and diffusivity ==<br />
<br />
The authors discuss how diffusivity is connected to the mechanics, by the example of actin networks. At low actin concentrations, the solution behaves as a viscous liquid, and the mean-square-displacement (MSD) of the filaments grows linearly with time. At high actin concentration, filaments cross-link and behaves like an elastic solid, and MSD remains at a small fixed value. At intermediate actin concentrations, the filaments behaves as a viscoelastic material and undergo sub-diffusive motion with MSD increases with time but slower than linear.<br />
<br />
== Thermal diffusion vs active diffusion ==<br />
<br />
[[Image:active_duffusion.jpg|thumb|300px| Fig. 1. Schematic plots for active and thermal fluctuation motion of an inert probe particle in cell.]]<br />
<br />
Without other activities in cells, an inert probe particle is expected to undergo sub-diffusive motion on short time scales (t ~ 1 sec), hindered motion for longer time scales (t ~ 10 sec), and diffusive motion on even-longer time scales (t > 100 sec). This expected curve is described by the blue line in fig 1.<br />
<br />
With active motions in cells, the motion of an inert probe particle is actually better described by the red line in fig 1. For example, the myosin motors can "fluidize" the actin network by enhancing the ability of filaments to slide past one another. Thus the probe particles are less hindered, and undergoes diffusive-like motion at short time scales. At long time scales, the motors actively remodels the filament network, which also enhances the mobility of the probe particle. These observations are supported by both in vitro experiments and in situ experiments.<br />
<br />
== Connection to soft matter ==</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Intracellular_transport_by_active_diffusion&diff=15282Intracellular transport by active diffusion2010-10-25T00:35:15Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010<br />
<br />
Clifford P. Brangwynne, Gijsje H. Koenderink, Frederick C. MacKintosh and David A. Weitz, "Intracellular transport by active diffusion" , Trends in Cell Biology 19 (9), 423-427 (2009).<br />
<br />
<br />
== Summary ==<br />
<br />
This article concerns cell mechanics. The main point of this article is that active transports in cells can result in significant random fluctuations of particles that resemble thermal fluctuations. These particles undergo an enhanced diffusion, which the authors refer to as "active diffusion".<br />
<br />
<br />
== Background: Thermal diffusion and random intracellular motion ==<br />
<br />
Thermal agitation causes molecules or small particles to perform random walk in a solution. This is referred to as Brownian motion or diffusive motion. Although diffusion is not directional, it acts as an important mechanism for short-distanced transports in cells and provides the basis for signal transduction networks.<br />
<br />
Thermal-driven diffusion follows well-known physical laws. The diffusion constant increases with temperature, and decreases with the particle size and the medium viscosity. However, a number of intracellular motions appear to be random and diffusive-like, but do not follow these basic properties of thermal diffusion. This suggests that there must be other mechanism that contributes to the random transport of particles in cells.<br />
<br />
In cells, there is another kind of transport. These are active, directional transports driven by either the motion of motor proteins along cytoskeletal filaments (kinesins and dyneins run on microtubules; myosins run on actin), or the polymerization/de-polymerization of these filaments. These directed transports are distinct from the random diffusive transport.<br />
<br />
This article discusses how the active transports can drive random diffusive-like transports.<br />
<br />
<br />
== Coupling between mechanics and diffusivity ==</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Intracellular_transport_by_active_diffusion&diff=15258Intracellular transport by active diffusion2010-10-22T15:13:54Z<p>Chsu: New page: Entry: Chia Wei Hsu, AP 225, Fall 2010 Clifford P. Brangwynne, Gijsje H. Koenderink, Frederick C. MacKintosh and David A. Weitz, "Intracellular transport by active diffusion" , Trends in ...</p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010<br />
<br />
Clifford P. Brangwynne, Gijsje H. Koenderink, Frederick C. MacKintosh and David A. Weitz, "Intracellular transport by active diffusion" , Trends in Cell Biology 19 (9), 423-427 (2009).</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Particle_Segregation_and_Dynamics_in_Confined_Flows&diff=15147Particle Segregation and Dynamics in Confined Flows2010-10-18T01:15:37Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010<br />
<br />
D. Di Carlo, J. F. Edd, K. J. Humphry, H. A. Stone, and M. Toner, "Particle Segregation and Dynamics in Confined Flows," Phys Rev Lett '''102''', 094503 (2009)<br />
<br />
<br />
== Summary ==<br />
<br />
<br />
Rigid spherical particles exhibit lateral migration in cylindrical pipes. Such phenomenon cannot be explained by the Stokes equation (ie. linearized Navier-Stokes equation at low Reynolds number). Thus the inertial contribution of the particles must be taken into account, and the full Navier-Stokes equations must be used. In order to simplify the complexity of this problem, previous studies have focused on cases when particles dimension (<math>a</math>) is much smaller than the channel cross section dimension (<math>H</math>). In this paper, the authors show that such "point-particle" assumption is not valid when <math>a</math> approaches <math>H</math>.<br />
<br />
<br />
== Method ==<br />
<br />
The authors examine rectangular cross-section microchannels. They compare experimental observations with numerical calculations based on finite element method. Fig 1 (a) shows the schematic of the system studied.<br />
<br />
The experimental system is prepared using soft-lithography fabrication. They consist of microchannels (length 5 cm; width and height <math>H</math>=20-50 µm) with dilute polystyrene particles (<math>a</math>=5-20 µm) suspended in water. The polystyrene particles flow at controlled rates using a syringe pump.<br />
<br />
== Results ==<br />
<br />
[[Image:channel_fig1.jpg|thumb|300px| Fig. 1. (a) Schematic of the channel and particle geometry. (b) Lift forces simulated for a quarter of the channel. Fixed points indicated by circles. (c) confocal cross section image. Bright spots indicate fixed points. ]]<br />
<br />
Both numerical calculations (fig 1(b)) and experiments (fig 1(c)) reveal four attractors that correspond to the equilibrium position of particles. The authors then study how the location of these fixed points depend on <math>a/H</math>, for the range <math>a/H</math>=0.1~0.9. They observe that particles shift toward channel center as <math>a/H</math> increases. Further, they found that particles rotate at a rate that is slower when <math>a/H</math> increases. Numerical calculations agree quantitatively with experiments.<br />
<br />
Then, the authors use numerical calculations to study how the lifting forces scale with <math>a/H</math> across different locations in the channel. They found that the lifting forces depend on <math>a/H</math> and location in a more complex way than the prediction of previous theoretical studies using point-particle assumption (fig 2).<br />
<br />
[[Image:channel_fig2.jpg|thumb|300px| Fig. 2. Parameters affecting the inertial lift force. ]]<br />
<br />
<br />
== Connection to Soft Matter ==<br />
<br />
The lateral migration of particles in confined flows is a common phenomenon. It occurs not only for rigid spherical particles, but also for soft deformable particles (such as blood cells) and polymers. It is important for many technical applications and for biology. This works points out that the size of the particles can play an important role in this inertial migration phenomenon, and so that the point-particle assumption should be revisited.</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Channel_fig2.jpg&diff=15146File:Channel fig2.jpg2010-10-18T01:04:40Z<p>Chsu: </p>
<hr />
<div></div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Channel_fig1.jpg&diff=15145File:Channel fig1.jpg2010-10-18T00:52:15Z<p>Chsu: </p>
<hr />
<div></div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=File:Channel_schematic.jpg&diff=15143File:Channel schematic.jpg2010-10-18T00:44:21Z<p>Chsu: </p>
<hr />
<div></div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Particle_Segregation_and_Dynamics_in_Confined_Flows&diff=15141Particle Segregation and Dynamics in Confined Flows2010-10-18T00:21:46Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010<br />
<br />
D. Di Carlo, J. F. Edd, K. J. Humphry, H. A. Stone, and M. Toner, "Particle Segregation and Dynamics in Confined Flows," Phys Rev Lett '''102''', 094503 (2009)<br />
<br />
<br />
== Summary ==<br />
<br />
<br />
Rigid spherical particles exhibit lateral migration in cylindrical pipes. Such phenomenon cannot be explained by the Stokes equation (ie. linearized Navier-Stokes equation at low Reynolds number). Thus the inertial contribution of the particles must be taken into account, and the full Navier-Stokes equations must be used. In order to simplify the complexity of this problem, previous studies have focused on cases when particles dimension (<math>a</math>) is much smaller than the channel cross section dimension (<math>H</math>). In this paper, the authors show that such "point-particle" approximation is not valid when <math>a</math> approaches <math>H</math>.<br />
<br />
<br />
== Method ==<br />
<br />
The authors examine rectangular cross-section microchannels. They compare experimental observations with numerical calculations based on finite element method.<br />
<br />
The experimental system is prepared using soft-lithography fabrication. They consist of microchannels (length 5 cm; width and height 20-50 µm) with dilute polystyrene particles (<math>a</math>=5-20 µm) suspended in water. The polystyrene particles flow at controlled rates using a syringe pump.<br />
<br />
<br />
== Results ==<br />
<br />
<br />
<br />
<br />
<br />
== Connection to Soft Matter ==</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Chia_Wei_Hsu&diff=15123Chia Wei Hsu2010-10-17T21:24:11Z<p>Chsu: </p>
<hr />
<div>Definitions:<br />
<br />
<br />
<br />
Weekly wiki entries:<br />
<br />
Week 1: [[The Free-Energy Landscape of Clusters of Attractive Hard Spheres]]<br />
<br />
Week 2: [[Statistical mechanics of developable ribbons]]<br />
<br />
Week 3: [[Chemotactic Patterns without Chemotaxis]]<br />
<br />
Week 4: [[Particle Segregation and Dynamics in Confined Flows]]</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Particle_Segregation_and_Dynamics_in_Confined_Flows&diff=15122Particle Segregation and Dynamics in Confined Flows2010-10-17T21:23:33Z<p>Chsu: New page: Entry: Chia Wei Hsu, AP 225, Fall 2010 D. Di Carlo, J. F. Edd, K. J. Humphry, H. A. Stone, and M. Toner, "Particle Segregation and Dynamics in Confined Flows," Phys Rev Lett '''102''', 09...</p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010<br />
<br />
D. Di Carlo, J. F. Edd, K. J. Humphry, H. A. Stone, and M. Toner, "Particle Segregation and Dynamics in Confined Flows," Phys Rev Lett '''102''', 094503 (2009)</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Chia_Wei_Hsu&diff=14895Chia Wei Hsu2010-10-03T20:12:52Z<p>Chsu: </p>
<hr />
<div>Definitions:<br />
<br />
<br />
<br />
Weekly wiki entries:<br />
<br />
Week 1: [[The Free-Energy Landscape of Clusters of Attractive Hard Spheres]]<br />
<br />
Week 2: [[Statistical mechanics of developable ribbons]]<br />
<br />
Week 3: [[Chemotactic Patterns without Chemotaxis]]</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Chemotactic_Patterns_without_Chemotaxis&diff=14894Chemotactic Patterns without Chemotaxis2010-10-03T20:09:48Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010<br />
<br />
M.P. Brenner, Chemotactic Patterns without Chemotaxis, Proc. Natl. Acad. Sci, '''107''', 11653–11654 (2010).<br />
<br />
== Summary ==<br />
<br />
This commentary addresses the study by Cates et al (ref 1) where an effective model is used to describe the pattern formation in chemotaxis. In particular, the effective model considers not the mechanisms of the chemotaxis but the averaged effect of it, thus greatly reducing the complexity of the modeling. Brenner uses this study as an example to show the promise of using effective models to understand biological systems.<br />
<br />
<br />
== Pattern Formation in Chemotaxis ==<br />
<br />
Chemotaxis is the phenomenon where bacteria and other organisms direct their motion based on the environment. For example, bacteria can swim up the food concentration gradient to get to a region with more food, or swim down the poison concentration gradient to avoid poisoning. <br />
<!--The fundamental idea is that bacteria perform biased random walks, in which “runs,” periods in which the bacteria swim straight with constant velocity <math>v</math>, are interrupted by “tumbles,” in which the bacteria turn randomly. By measuring a time-weighted average of chemo-attractant binding to their receptors, bacteria such as E. coli can modulate changes in the frequencies of run and tumble and hence control ascent of a gradient.--><br />
<br />
The chemotaxis phenomenon results in pattern formation. Is has been found that (ref 2) when chemotactic bacteria swim through a small tube of rich medium, the bacteria form a dense band that moves at constant velocity. Subsequent theoretical works concluded that in order to qualitatively reproduce this behavior, detailed knowledge of the nutrient consumption and the production/depletion of chemo-attractant is required. It is disturbing that such a simple collective behavior requires such a detailed level of understanding. This motivates the research for a simpler description.<br />
<br />
== Effective Model ==<br />
<br />
The model of Cates et al (ref 1) boldly ignores the direct interaction between bacteria and attractant fields. Rather, they assume a density-dependent swim speed <math>v=v(\rho)</math>, where <math>\rho</math> is the density of bacteria. This swim speed is assumed to decrease with increasing <math>\rho</math>. Thus, there is a net drift in the direction of increasing bacteria density. Since bacteria density tends to be higher in regions with more attractant, this models creates the same effect: that bacteria drift toward high attractant concentration. However, there is a fundamental difference in the modeling: this effective model neglects chemotaxis completely and instead asserts that the fundamental quantity is the density-dependent velocity <math>v=v(\rho)</math>.<br />
<br />
Cates et al demonstrate that this model quantitatively reproduces the results of a set of experiments on bacteria pattern formation. Same agreement can be found in more detailed modeling, but this effective model reduces the complexity of the model to only two dimensionless parameters.<br />
<br />
<br />
== Connection to Soft Matter ==<br />
<br />
Brenner's comment and this study by Cates et al point out the potential strength of effective modeling. With effective modeling, we can understand the most important underpinning driving forces in phenomenon we observe, rather than being overwhelmed by the complexity of the modeling and only being able to examine the numbers we get out of the simulations or numerical solutions. Such approach can help us to understand many biological and soft matter systems. But there is a catch. Such effective models have to be tested more rigorously in order to ascertain that it not only captures the correct result, but also have the right assumption. <br />
<br />
<br />
<br />
== References ==<br />
<br />
[1] Cates ME, Marenduzzo D, Pagonabarraga I, and Tailleur J, "Arrested phase separation in reproducing bacteria: A generic route to pattern formation," Proc Natl Acad Sci USA '''107''', 11715–11720 (2010).<br />
<br />
[2] Adler J, "Chemotaxis in bacteria," Science '''153''', 708–716 (1966).</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Chemotactic_Patterns_without_Chemotaxis&diff=14893Chemotactic Patterns without Chemotaxis2010-10-03T20:08:57Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010<br />
<br />
M.P. Brenner, Chemotactic Patterns without Chemotaxis, Proc. Natl. Acad. Sci, '''107''', 11653–11654 (2010).<br />
<br />
== Summary ==<br />
<br />
This commentary addresses the study by Cates et al (ref 1) where an effective model is used to describe the pattern formation in chemotaxis. In particular, the effective model considers not the mechanisms of the chemotaxis but the averaged effect of it, thus greatly reducing the complexity of the modeling. Brenner uses this study as an example to show the promise of using effective models to understand biological systems.<br />
<br />
<br />
== Pattern Formation in Chemotaxis ==<br />
<br />
Chemotaxis is the phenomenon where bacteria and other organisms direct their motion based on the environment. For example, bacteria can swim up the food concentration gradient to get to a region with more food, or swim down the poison concentration gradient to avoid poisoning. <br />
<!--The fundamental idea is that bacteria perform biased random walks, in which “runs,” periods in which the bacteria swim straight with constant velocity <math>v</math>, are interrupted by “tumbles,” in which the bacteria turn randomly. By measuring a time-weighted average of chemo-attractant binding to their receptors, bacteria such as E. coli can modulate changes in the frequencies of run and tumble and hence control ascent of a gradient.--><br />
<br />
The chemotaxis phenomenon results in pattern formation. Is has been found that (ref 2) when chemotactic bacteria swim through a small tube of rich medium, the bacteria form a dense band that moves at constant velocity. Subsequent theoretical works concluded that in order to qualitatively reproduce this behavior, detailed knowledge of the nutrient consumption and the production/depletion of chemo-attractant is required. It is disturbing that such a simple collective behavior requires such a detailed level of understanding. This motivates the research for a simpler description.<br />
<br />
== Effective Model ==<br />
<br />
The model of Cates et al (ref 1) boldly ignores the direct interaction between bacteria and attractant fields. Rather, they assume a density-dependent swim speed <math>v=v(\rho)</math>, where <math>\rho</math> is the density of bacteria. This swim speed is assumed to decrease with increasing <math>\rho</math>. Thus, there is a net drift in the direction of increasing bacteria density. Since bacteria density tends to be higher in regions with more attractant, this models creates the same effect: that bacteria drift toward high attractant concentration. However, there is a fundamental difference in the modeling: this effective model neglects chemotaxis completely and instead asserts that the fundamental quantity is the density-dependent velocity <math>v=v(\rho)</math>.<br />
<br />
Cates et al demonstrate that this model quantitatively reproduces the results of a set of experiments on bacteria pattern formation. Same agreement can be found in more detailed modeling, but this effective model reduces the complexity of the model to only two dimensionless parameters.<br />
<br />
<br />
== Connection to Soft Matter ==<br />
<br />
Brenner's comment and this study by Cates et al point out the potential strength of effective modeling. With effective modeling, we can understand the most important underpinning driving forces in phenomenon we observe, rather than being overwhelmed by the complexity of the modeling and only being able to examine the numbers we get out of the simulations or numerical solutions. Such approach can help us to understand many biological and soft matter systems. Of course there is a trade-off. Such effective models have to be tested more rigorously in order to ascertain that it not only captures the correct result, but also have the right assumption. <br />
<br />
<br />
<br />
== References ==<br />
<br />
[1] Cates ME, Marenduzzo D, Pagonabarraga I, and Tailleur J, "Arrested phase separation in reproducing bacteria: A generic route to pattern formation," Proc Natl Acad Sci USA '''107''', 11715–11720 (2010).<br />
<br />
[2] Adler J, "Chemotaxis in bacteria," Science '''153''', 708–716 (1966).</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Chemotactic_Patterns_without_Chemotaxis&diff=14892Chemotactic Patterns without Chemotaxis2010-10-03T20:07:44Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010<br />
<br />
M.P. Brenner, Chemotactic Patterns without Chemotaxis, Proc. Natl. Acad. Sci, '''107''', 11653–11654 (2010).<br />
<br />
== Summary ==<br />
<br />
This commentary addresses the study by Cates et al (ref 1) where an effective model is used to describe the pattern formation in chemotaxis. In particular, the effective model considers not the mechanisms of the chemotaxis but the averaged effect of it, thus greatly reducing the complexity of the modeling. Brenner uses this study as an example to show the promise of using effective models to understand biological systems.<br />
<br />
<br />
== Pattern Formation in Chemotaxis ==<br />
<br />
Chemotaxis is the phenomenon where bacteria and other organisms direct their motion based on the environment. For example, bacteria can swim up the food concentration gradient to get to a region with more food, or swim down the poison concentration gradient to avoid poisoning. <br />
<!--The fundamental idea is that bacteria perform biased random walks, in which “runs,” periods in which the bacteria swim straight with constant velocity <math>v</math>, are interrupted by “tumbles,” in which the bacteria turn randomly. By measuring a time-weighted average of chemo-attractant binding to their receptors, bacteria such as E. coli can modulate changes in the frequencies of run and tumble and hence control ascent of a gradient.--><br />
<br />
The chemotaxis phenomenon results in pattern formation. Is has been found that (ref 2) when chemotactic bacteria swim through a small tube of rich medium, the bacteria form a dense band that moves at constant velocity. Subsequent theoretical works concluded that in order to qualitatively reproduce this behavior, detailed knowledge of the nutrient consumption and the production/depletion of chemo-attractant is required. It is disturbing that such a simple collective behavior requires such a detailed level of understanding. This motivates the research for a simpler description.<br />
<br />
== Effective Model ==<br />
<br />
The model of Cates et al (ref 1) boldly ignores the direct interaction between bacteria and attractant fields. Rather, they assume a density-dependent swim speed <math>v=v(\rho)</math>, where <math>\rho</math> is the density of bacteria. This swim speed is assumed to decrease with increasing <math>\rho</math>. Thus, there is a net drift in the direction of increasing bacteria density. Since bacteria density tends to be higher in regions with more attractant, this models creates the same effect: that bacteria drift toward high attractant concentration. However, there is a fundamental difference in the modeling: this effective model neglects chemotaxis completely and instead asserts that the fundamental quantity is the density-dependent velocity <math>v=v(\rho)</math>.<br />
<br />
Cates et al demonstrate that this model quantitatively reproduces the results of a set of experiments on bacteria pattern formation. Same agreement can be found in more detailed modeling, but this effective model reduces the complexity of the model to only two dimensionless parameters.<br />
<br />
<br />
== Connection to Soft Matter ==<br />
<br />
Brenner's comment and this study by Cates et al point out the potential strength of effective modeling. With effective modeling, we can understand the most important underpinning driving forces in phenomenon we observe, rather than being overwhelmed by the complexity of the modeling and only being able to examine the numbers we get out of the simulations or numerical solutions. Of course there is a trade-off. Such effective models have to be tested more rigorously in order to ascertain that it not only captures the correct result, but also have the right assumption. <br />
<br />
<br />
<br />
== References ==<br />
<br />
[1] Cates ME, Marenduzzo D, Pagonabarraga I, and Tailleur J, "Arrested phase separation in reproducing bacteria: A generic route to pattern formation," Proc Natl Acad Sci USA '''107''', 11715–11720 (2010).<br />
<br />
[2] Adler J, "Chemotaxis in bacteria," Science '''153''', 708–716 (1966).</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Chemotactic_Patterns_without_Chemotaxis&diff=14891Chemotactic Patterns without Chemotaxis2010-10-03T19:54:12Z<p>Chsu: </p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010<br />
<br />
M.P. Brenner, Chemotactic Patterns without Chemotaxis, Proc. Natl. Acad. Sci, '''107''', 11653–11654 (2010).<br />
<br />
== Summary ==<br />
<br />
This commentary addresses the study by Cates et al (ref 1) where an effective model is used to describe the pattern formation in chemotaxis. In particular, the effective model considers not the mechanisms of the chemotaxis but the averaged effect of it, thus greatly reducing the complexity of the modeling. Brenner uses this study as an example to show the promise of using effective models to understand biological systems.<br />
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== Pattern Formation in Chemotaxis ==<br />
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Chemotaxis is the phenomenon where bacteria and other organisms direct their motion based on the environment. For example, bacteria can swim up the food concentration gradient to get to a region with more food, or swim down the poison concentration gradient to avoid poisoning. <br />
<!--The fundamental idea is that bacteria perform biased random walks, in which “runs,” periods in which the bacteria swim straight with constant velocity <math>v</math>, are interrupted by “tumbles,” in which the bacteria turn randomly. By measuring a time-weighted average of chemo-attractant binding to their receptors, bacteria such as E. coli can modulate changes in the frequencies of run and tumble and hence control ascent of a gradient.--><br />
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The chemotaxis phenomenon results in pattern formation. Is has been found that (ref 2) when chemotactic bacteria swim through a small tube of rich medium, the bacteria form a dense band that moves at constant velocity. Subsequent theoretical works concluded that in order to qualitatively reproduce this behavior, detailed knowledge of the nutrient consumption and the production/depletion of chemo-attractant is required. It is disturbing that such a simple collective behavior requires such a detailed level of understanding. This motivates the research for a simpler description.<br />
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== Effective Model ==<br />
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The model of Cates et al (ref 1) boldly ignores the direct interaction between bacteria and attractant fields. Rather, they assume a density-dependent swim speed <math>v=v(\rho)</math>, where <math>\rho</math> is the density of bacteria. This swim speed is assumed to decrease with increasing <math>\rho</math>. Thus, there is a net drift in the direction of increasing bacteria density. Since bacteria density tends to be higher in regions with more attractant, this models creates the same effect: that bacteria drift toward high attractant concentration.<br />
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== Connection to Soft Matter ==<br />
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== References ==<br />
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[1] Cates ME, Marenduzzo D, Pagonabarraga I, and Tailleur J, "Arrested phase separation in reproducing bacteria: A generic route to pattern formation," Proc Natl Acad Sci USA '''107''', 11715–11720 (2010).<br />
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[2] Adler J, "Chemotaxis in bacteria," Science '''153''', 708–716 (1966).</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Chemotactic_Patterns_without_Chemotaxis&diff=14890Chemotactic Patterns without Chemotaxis2010-10-03T19:35:33Z<p>Chsu: </p>
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<div>Entry: Chia Wei Hsu, AP 225, Fall 2010<br />
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M.P. Brenner, Chemotactic Patterns without Chemotaxis, Proc. Natl. Acad. Sci, '''107''', 11653–11654 (2010).<br />
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== Summary ==<br />
<br />
This commentary addresses the study by Cates et al (ref 1) where an effective model is used to describe the pattern formation in chemotaxis. In particular, the effective model ignores the details of the chemotactic mechanisms but focuses on averaged effect, thus greatly reducing the complexity of the modeling. Brenner uses this study as an example to show the promise of using effective models to understand biological systems.<br />
<br />
<br />
== Pattern Formation in Chemotaxis ==<br />
<br />
Chemotaxis is the phenomenon where bacteria and other organisms direct their motion based on the environment. For example, bacteria can swim up the food concentration gradient to get to a region with more food, or swim down the poison concentration gradient to avoid poisoning. <br />
<!--The fundamental idea is that bacteria perform biased random walks, in which “runs,” periods in which the bacteria swim straight with constant velocity <math>v</math>, are interrupted by “tumbles,” in which the bacteria turn randomly. By measuring a time-weighted average of chemo-attractant binding to their receptors, bacteria such as E. coli can modulate changes in the frequencies of run and tumble and hence control ascent of a gradient.--><br />
<br />
The chemotaxis phenomenon results in pattern formation. Is has been found that (ref 2) when chemotactic bacteria swim through a small tube of rich medium, the bacteria form a dense band that moves at constant velocity. <br />
<br />
== Effective Model ==<br />
<br />
<br />
== Connection to Soft Matter ==<br />
<br />
<br />
== References ==<br />
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[1] Cates ME, Marenduzzo D, Pagonabarraga I, and Tailleur J, "Arrested phase separation in reproducing bacteria: A generic route to pattern formation," Proc Natl Acad Sci USA '''107''', 11715–11720 (2010).<br />
<br />
[2] Adler J, "Chemotaxis in bacteria," Science '''153''', 708–716 (1966).</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Chemotactic_Patterns_without_Chemotaxis&diff=14889Chemotactic Patterns without Chemotaxis2010-10-03T17:00:11Z<p>Chsu: New page: Entry: Chia Wei Hsu, AP 225, Fall 2010 M.P. Brenner, Chemotactic Patterns without Chemotaxis, Proc. Natl. Acad. Sci, '''107''', 11653–11654 (2010).</p>
<hr />
<div>Entry: Chia Wei Hsu, AP 225, Fall 2010<br />
<br />
M.P. Brenner, Chemotactic Patterns without Chemotaxis, Proc. Natl. Acad. Sci, '''107''', 11653–11654 (2010).</div>Chsuhttp://soft-matter.seas.harvard.edu/index.php?title=Chia_Wei_Hsu&diff=14672Chia Wei Hsu2010-09-19T19:11:30Z<p>Chsu: </p>
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<div>Definitions:<br />
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Weekly wiki entries:<br />
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Week 1: [[The Free-Energy Landscape of Clusters of Attractive Hard Spheres]]<br />
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Week 2: [[Statistical mechanics of developable ribbons]]</div>Chsu