http://soft-matter.seas.harvard.edu/api.php?action=feedcontributions&user=Lauren&feedformat=atomSoft-Matter - User contributions [en]2022-12-03T17:16:20ZUser contributionsMediaWiki 1.24.2http://soft-matter.seas.harvard.edu/index.php?title=Superhydrophobic_surfaces&diff=23782Superhydrophobic surfaces2011-12-10T16:55:59Z<p>Lauren: </p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
Entry has been combined with [[Superhydrophobicity]], [[Superhydrophicity]] (misspelled) and [[Superhydrophobic]]. (LH 2011)<br />
<br />
==Introduction==<br />
A water droplet on a superhydrophobic surface has a contact angle of greater than 150 degrees and a very low roll-off angle. In nature and in man-made materials, this has been achieved with [[Structured Surfaces]]. Advantages of such surfaces include the ability to repel water and self-clean.[3] Industrial applications include "self-cleaning window glasses, paints, and textiles to low-friction surfaces for fluid flow and energy conservation."[2] To predict when a droplet will wet the surface and when it will be repelled, one can compare the contact angle for complete wetting to the contact angle for a droplet resting atop the surface structure with no penetration. When a droplet is in intimate contact with the surface, the Wenzel state, the following equation applies:<br />
<br />
<math>\cos{\theta}_c = r \cos{\theta}</math><br />
<br />
where r is the ratio of the actual area to the projected contact area and <math>\theta</math> is the contact angle of the droplet on a flat surface of the same material.. When the droplet rests atop the surface structure, it is in the Cassie-Baxter state, modeled by:<br />
<br />
<math>\cos{\theta}_{c} = \phi \left( cos \theta + 1 \right) - 1</math><br />
<br />
where <math>\phi</math> is the area fraction of the solid in contact with the liquid, and <math>\theta</math> is the contact angle of the droplet on a flat surface of the same material. Setting the two contact angles equal gives the following critical condition for the transition between the Cassie-Baxter and Wenzel states.<br />
<br />
<math>cos \theta = \frac {\phi - 1}{r -\phi}</math><br />
<br />
By this prediction, a droplet resting atop surface structures might be a lower energy state than intimate contact when the cosine of the contact angle on a flat surface is less than the right hand side of the equation. <br />
<br />
It is argued that surface structure can produce superhydrophobic effects, even on a hydrophilic surface. For example, lotus leaves have been shown to be superhydrophobic, despite the waxy, weakly hydrophilic coating on the surface.[1] It has been demonstrated that the surface of a lotus leaf is superhydrophobic in part due to the presence of hierarchical surface structures structures consisting of micro- and nano-scale features. [2] Figure 1 contrasts the state of a droplet on a flat surface and surfaces of increasingly complex structure.<br />
<br />
[[Image:Wetting_figure.png|frame|Figure from reference 1.]]<br />
<br />
Butterfly wings and parts of pitcher plants have observed superhydrophobic properties. Figure 2 shows an image of real lotus leaf structures at different scales from reference 2.<br />
<br />
[[Image:Lotus_leaf_image.png|frame|Figure from reference 2.]]<br />
<br />
==References==<br />
[1]"Design parameters for superhydrophobicity and superoleophobicity". Anish Tuteja, Wonjae Choi, Gareth H. McKinley, Robert E. Cohen, and Michael F. Rubner. ''MRS Bulletin'' 33 (8), 752-758 (August 2008)<br />
<br />
[2]"Fabrication of artificial Lotus leaves and significance of hierarchical structure for superhydrophobicity and low adhesion". Kerstin Koch, Bharat Bhushan, Yong Chae Jung and Wilhelm Barthlott. ''Soft Matter'', 2009, 5, 1386–1393.<br />
<br />
[3]"Self-cleaning materials: Lotus leaf inspired nanotechnology" Peter Forbes, ''Scientific American'' 30 July 2008.<br />
<br />
==See also==<br />
<br />
[[Effects of contact angles#Surface heterogeneity|Superhydrophobic surfaces]] in [[Effects of contact angles]] in [[Capillarity and wetting]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
==Keyword in References==<br />
<br />
[[Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity]]<br />
<br />
[[Growth of polygonal rings and wires of CuS on structured surfaces]]<br />
<br />
[[Pitcher plant inspired non-stick surface]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Creep&diff=23780Creep2011-12-10T16:53:10Z<p>Lauren: </p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
==Definition==<br />
<br />
Creep is the time dependent change in [[Strain]] of a material subject to a constant [[Stress]]. A [[Creep test]] attempts to quantify the relevant timescales and functional forms of molecular and/or atomic rearrangement that occur when a material creeps. The mechanism of creep differs depending on the material. In a crystal, mechanisms for creep include the movement of dislocations (Dislocation Creep) and the diffusion of atoms along grain boundaries (Coble Creep) or through the bulk (Nabarro-Herring creep). <br />
<br />
The general equation for describing creep is:<br />
<br />
<math> \frac{\mathrm{d}\varepsilon}{\mathrm{d}t} = \frac{C\sigma^m}{d^b} e^\frac{-Q}{kT}</math><br />
<br />
where the left hand side is the strain rate due to creep, ''Q'' is the activation energy of creep, ''d'' is the grain size, <math>\sigma</math> is the stress in the material, ''T'' is the temperature, and ''m'' and ''b'' are constants that depend on the mechanism of creep. In dislocation creep, m = 4 to 6 and b = 0. In Nabarro-Herring creep, m = 1 and b = 2. In Coble creep, m = 1 and b = 3. Depending on the mechanism being modeled, the exponents m and b can be tuned. Creep is a temperature-dependent process.<br />
<br />
For viscoelastic materials like many polymers, a number of models can be used to describe time dependent deformation. One approach is to combine two fundamental units (the spring, which represents elastic response, and the dashpot, which represents viscous response) in different configurations to create a simplified mechanical model of the system. The Zener model, for example, models a linear viscoelastic response as a "dashpot" (Newtonian flow behavior) in parallel with a spring, and spring in series with the combined unit. <br />
<br />
==Examples==<br />
<br />
Polymers can be characterized as cross-linked (where chains are chemically linked), uncross-linked (where chains are free to slide over one another), or crystalline. Uncross-linked polymers behave most like linearly viscoelastic materials, while cross-links in polymer chains limit the degree to which chains can slide past one another, and depending on the degree of cross-linking, can substantially impact the ability of the polymer to flow in a Newtonian manner. A polymer's creep behavior is often substantially more pronounced above its [[Glass Transition Temperature]], where chains more freely slide across one another. For more details, see ''Introduction to the Mechanics of a Continuous Medium'', Chapter 6.4 (linear viscoelastic response) by Malvern.<br />
<br />
==See also:==<br />
<br />
[[Creep of ice]], [[Creep test]]<br />
<br />
== Keyword in references: ==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]<br />
<br />
[[Stress Enhancement in the Delayed Yielding of Colloidal Gels]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Poisson%27s_Ratio&diff=23776Poisson's Ratio2011-12-10T16:50:38Z<p>Lauren: </p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
==Definition==<br />
<br />
When a material is elongated or compressed along one axis, the Poisson's ratio, <math>\nu</math>, of a material is the ratio of the [[Strain]] in the directions perpendicular to the axis, divided by the [[Strain]] along that axis. Essentially, this dimensionless number describes the tendency of a contraction or expansion in one dimension to cause contraction or expansion in other dimensions. Most materials have a positive Poisson's ratio, meaning other dimensions will contract in response to elongation along one dimension, and vice versa. Figure 1 demonstrates this concept. <br />
<br />
[[Image:Poissons_ratio.jpg|frame|Figure 1, from http://www.feppd.org/ICB-Dent/campus/biomechanics_in_dentistry/ldv_data/img/mech/mech_122.jpg]]<br />
<br />
<br />
Most materials have a Poisson's ratio near 0.3, with more rubbery materials approaching 0.5. [3] Auxetic materials, or materials with a negative Poisson's ratio were first reported in 1987 by Lakes.[2] Example materials of this type include some foams, honeycomb structures produced by Prall and Lakes,[3] and patterned arrays of circular and elliptical holes in an elastomer (Bertoldi).[3] In these last two cases, local buckling of the structure (i.e., repeatable collapse) leading to volume reduction is directly observed to cause a negative Poisson's ratio. Figure 1 shows a schematic of local buckling in Bertoldi's material. The material compresses uniformly until a critical applied strain is reached. At this strain, an elastic instability develops, and the structure experiences uniform, repeatable local buckling of the walls. Figures 3 and 4 show Prall and Lakes' honeycomb structures. Figure 3 shows a "regular" honeycomb shape, with a positive Poisson's ratio, and a "reentrant" honeycomb shape, with a negative Poisson's ratio. Figure 4 shows the same groups chiral honey comb structures in a) a schematic and b) a photograph of the fabricated structure. [3]<br />
<br />
''Important Limits''<br />
<br />
For an isotropic, unconstrained three dimensional elastic material, Poisson's ratio must range from -1 to 1/2.[3]<br />
<br />
[[Image:Neg_poisson_ratio_bertoldi.png|frame|none|Figure 2]]<br />
<br />
[[Image:Reentrant_honeycomb.png|frame|none|Figure 3]]<br />
<br />
[[Image:Chiral_honeycomb.png|frame|none|Figure 4]]<br />
<br />
==References==<br />
<br />
[1] http://silver.neep.wisc.edu/~lakes/PoissonIntro.html<br />
<br />
[2] '"Negative Poisson’s Ratio Behavior Induced by an Elastic Instability". Katia Bertoldi, Pedro M. Reis, Stephen Willshaw, and Tom Mullin. ''Adv. Mater''. 2009, 21, 1–6.<br />
<br />
[3] "Properties of a chiral honeycomb with a Poisson's ratio -1" D. Prall, R. S. Lakes. ''Int. J. of Mechanical Sciences'', 39, 305-314, (1996)<br />
<br />
==Keyword in References==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Strain&diff=23775Strain2011-12-10T16:50:15Z<p>Lauren: </p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
Defined along one dimension of a material, strain can be either ''normal'' or ''shear''. ''Normal strain'' is the ratio of the length change along that dimension to the length along that dimension. <br />
<br />
<math> \epsilon = \frac{\Delta L}{L}</math><br />
<br />
The engineering, or cauchy strain uses the pre-deformation length in this measure, while the true strain uses the length of the material at the time the strain is measured (this length changes as the material is deformed). ''Shear strain'' along a particular axis measures the angular displacement when the material is deformed perpendicular to this axis. For small displacements, it can be approximated as, where the indices indicate the axis of deformation and the axis of interest: <br />
<br />
<math>\gamma_{ij} = \frac {1}{2} \left( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_i}{\partial x_j} \right) </math><br />
<br />
By geometry, one can deduce that <math>\gamma_{ij} = \gamma_{ji}</math>. Figure 1 illustrates 2-D normal (top diagrams) and shear strain (bottom diagrams) in x and y.<br />
<br />
[[Image:2Dstrain.gif|frame|none|Figure 1 from http://folk.ntnu.no/stoylen/strainrate/mathemathics/2Dstrain.GIF]]<br />
<br />
<br />
== Keyword in references: ==<br />
<br />
<br />
[[An active biopolymer network controlled by molecular motors]]<br />
<br />
[[A simple model for the dynamics of adhesive failure]]<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]<br />
<br />
[[Stretchable Microfluidic Radiofrequency Antennas]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Strain&diff=23769Strain2011-12-10T16:47:32Z<p>Lauren: </p>
<hr />
<div>Defined along one dimension of a material, strain can be either ''normal'' or ''shear''. ''Normal strain'' is the ratio of the length change along that dimension to the length along that dimension. <br />
<br />
<math> \epsilon = \frac{\Delta L}{L}</math><br />
<br />
The engineering, or cauchy strain uses the pre-deformation length in this measure, while the true strain uses the length of the material at the time the strain is measured (this length changes as the material is deformed). ''Shear strain'' along a particular axis measures the angular displacement when the material is deformed perpendicular to this axis. For small displacements, it can be approximated as, where the indices indicate the axis of deformation and the axis of interest: <br />
<br />
<math>\gamma_{ij} = \frac {1}{2} \left( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_i}{\partial x_j} \right) </math><br />
<br />
By geometry, one can deduce that <math>\gamma_{ij} = \gamma_{ji}</math>. Figure 1 illustrates 2-D normal (top diagrams) and shear strain (bottom diagrams) in x and y.<br />
<br />
[[Image:2Dstrain.gif|frame|none|Figure 1 from http://folk.ntnu.no/stoylen/strainrate/mathemathics/2Dstrain.GIF]]<br />
<br />
<br />
== Keyword in references: ==<br />
<br />
<br />
[[An active biopolymer network controlled by molecular motors]]<br />
<br />
[[A simple model for the dynamics of adhesive failure]]<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]<br />
<br />
[[Stretchable Microfluidic Radiofrequency Antennas]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Strain&diff=23764Strain2011-12-10T16:45:11Z<p>Lauren: </p>
<hr />
<div>Defined along one dimension of a material, strain can be either ''normal'' or ''shear''. ''Normal strain'' is the ratio of the length change along that dimension to the length along that dimension. <br />
<br />
<math> \epsilon = \frac{\Delta L}{L}</math><br />
<br />
The engineering, or cauchy strain uses the pre-deformation length in this measure, while the true strain uses the length of the material at the time the strain is measured (this length changes as the material is deformed). ''Shear strain'' along a particular axis measures the angular displacement when the material is deformed perpendicular to this axis. For small displacements, it can be approximated as, where the indices indicate the axis of deformation and the axis of interest: <br />
<br />
<math>\gamma_{ij} = \frac {1}{2} \left( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_i}{\partial x_j} \right) </math><br />
<br />
By geometry, one can deduce that <math>\gamma_{ij} = \gamma_{ji}</math>. Figure 1 shows normal and shear strain.<br />
<br />
[[Image:2Dstrain.gif|frame|none|Figure 1 from http://folk.ntnu.no/stoylen/strainrate/mathemathics/2Dstrain.GIF]]<br />
<br />
<br />
== Keyword in references: ==<br />
<br />
<br />
[[An active biopolymer network controlled by molecular motors]]<br />
<br />
[[A simple model for the dynamics of adhesive failure]]<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]<br />
<br />
[[Stretchable Microfluidic Radiofrequency Antennas]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Strain&diff=23762Strain2011-12-10T16:42:49Z<p>Lauren: </p>
<hr />
<div>Defined along one dimension of a material, strain can be either ''normal'' or ''shear''. Normal strain is the ratio of the length change along that dimension to the length along that dimension. <br />
<br />
<math> \epsilon = \frac{\Delta L}{L}</math><br />
<br />
The engineering, or cauchy strain uses the pre-deformation length in this measure, while the true strain uses the length of the material at the time the strain is measured (this length changes as the material is deformed). Shear strain along a particular axis measures the angular displacement when the material is deformed perpendicular to this axis. For small displacements, it can be approximated as, where the indices indicate the axis of deformation and the axis of interest: <br />
<br />
<math>\gamma_{ij} = \frac {1}{2} \left( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_i}{\partial x_j} \right) </math><br />
<br />
Conservation of angular momentum requires that <math>\gamma_{ij} = \gamma_{ji}</math>. Figure 1 shows normal and shear strain.<br />
<br />
[[Image:2Dstrain.gif|frame|Figure 1 from http://folk.ntnu.no/stoylen/strainrate/mathemathics/2Dstrain.GIF]]<br />
<br />
<br />
== Keyword in references: ==<br />
<br />
<br />
[[An active biopolymer network controlled by molecular motors]]<br />
<br />
[[A simple model for the dynamics of adhesive failure]]<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]<br />
<br />
[[Stretchable Microfluidic Radiofrequency Antennas]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=File:2Dstrain.gif&diff=23761File:2Dstrain.gif2011-12-10T16:42:29Z<p>Lauren: </p>
<hr />
<div></div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Strain&diff=23759Strain2011-12-10T16:42:04Z<p>Lauren: </p>
<hr />
<div>Defined along one dimension of a material, strain can be either ''normal'' or ''shear''. Normal strain is the ratio of the length change along that dimension to the length along that dimension. <br />
<br />
<math> \epsilon = \frac{\Delta L}{L}</math><br />
<br />
The engineering, or cauchy strain uses the pre-deformation length in this measure, while the true strain uses the length of the material at the time the strain is measured (this length changes as the material is deformed). Shear strain along a particular axis measures the angular displacement when the material is deformed perpendicular to this axis. For small displacements, it can be approximated as, where the indices indicate the axis of deformation and the axis of interest: <br />
<br />
<math>\gamma_{ij} = \frac {1}{2} \left( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_i}{\partial x_j} \right) </math><br />
<br />
Conservation of angular momentum requires that <math>\gamma_{ij} = \gamma_{ji}</math>. Figure 1 shows normal and shear strain.<br />
<br />
[[Image:|frame|Figure 1 from http://folk.ntnu.no/stoylen/strainrate/mathemathics/2Dstrain.GIF]]<br />
<br />
<br />
== Keyword in references: ==<br />
<br />
<br />
[[An active biopolymer network controlled by molecular motors]]<br />
<br />
[[A simple model for the dynamics of adhesive failure]]<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]<br />
<br />
[[Stretchable Microfluidic Radiofrequency Antennas]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Strain&diff=23750Strain2011-12-10T16:29:29Z<p>Lauren: </p>
<hr />
<div>Defined along one dimension of a material, strain can be either ''normal'' or ''shear''. Normal strain is the ratio of the length change along that dimension to the length along that dimension. The engineering, or cauchy strain uses the pre-deformation length in this measure, while the true strain uses the length of the material at the time the strain is measured (this length changes as the material is deformed). Shear strain along a particular axis measures the angular displacement when the material is deformed perpendicular to this axis. For small displacements, it can be approximated as, where the indices indicate the axis of deformation and the axis of interest: <br />
<br />
<math>\gamma_{ij} = \frac {1}{2} \left( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_i}{\partial x_j} \right) </math><br />
<br />
Conservation of angular momentum requires that <math>\gamma_{ij} = \gamma_{ji}</math>. <br />
<br />
<br />
== Keyword in references: ==<br />
<br />
<br />
[[An active biopolymer network controlled by molecular motors]]<br />
<br />
[[A simple model for the dynamics of adhesive failure]]<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]<br />
<br />
[[Stretchable Microfluidic Radiofrequency Antennas]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Fulcher%E2%80%93Vogel%E2%80%93Tammann_Equation&diff=23744Fulcher–Vogel–Tammann Equation2011-12-10T16:11:33Z<p>Lauren: </p>
<hr />
<div>Entry needed.<br />
<br />
Suggested reference. "The Nature of the Glassy State and the Behavior of Liquids at Low Temperatures." Chemical reviews [0009-2665] Kauzmann yr:1948 vol:43 iss:2 pg:219<br />
<br />
==Keyword in References==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Poisson%27s_Ratio&diff=23742Poisson's Ratio2011-12-10T16:08:07Z<p>Lauren: </p>
<hr />
<div>==Definition==<br />
<br />
When a material is elongated or compressed along one axis, the Poisson's ratio, <math>\nu</math>, of a material is the ratio of the [[Strain]] in the directions perpendicular to the axis, divided by the [[Strain]] along that axis. Essentially, this dimensionless number describes the tendency of a contraction or expansion in one dimension to cause contraction or expansion in other dimensions. Most materials have a positive Poisson's ratio, meaning other dimensions will contract in response to elongation along one dimension, and vice versa. Figure 1 demonstrates this concept. <br />
<br />
[[Image:Poissons_ratio.jpg|frame|Figure 1, from http://www.feppd.org/ICB-Dent/campus/biomechanics_in_dentistry/ldv_data/img/mech/mech_122.jpg]]<br />
<br />
<br />
Most materials have a Poisson's ratio near 0.3, with more rubbery materials approaching 0.5. [3] Auxetic materials, or materials with a negative Poisson's ratio were first reported in 1987 by Lakes.[2] Example materials of this type include some foams, honeycomb structures produced by Prall and Lakes,[3] and patterned arrays of circular and elliptical holes in an elastomer (Bertoldi).[3] In these last two cases, local buckling of the structure (i.e., repeatable collapse) leading to volume reduction is directly observed to cause a negative Poisson's ratio. Figure 1 shows a schematic of local buckling in Bertoldi's material. The material compresses uniformly until a critical applied strain is reached. At this strain, an elastic instability develops, and the structure experiences uniform, repeatable local buckling of the walls. Figures 3 and 4 show Prall and Lakes' honeycomb structures. Figure 3 shows a "regular" honeycomb shape, with a positive Poisson's ratio, and a "reentrant" honeycomb shape, with a negative Poisson's ratio. Figure 4 shows the same groups chiral honey comb structures in a) a schematic and b) a photograph of the fabricated structure. [3]<br />
<br />
''Important Limits''<br />
<br />
For an isotropic, unconstrained three dimensional elastic material, Poisson's ratio must range from -1 to 1/2.[3]<br />
<br />
[[Image:Neg_poisson_ratio_bertoldi.png|frame|none|Figure 2]]<br />
<br />
[[Image:Reentrant_honeycomb.png|frame|none|Figure 3]]<br />
<br />
[[Image:Chiral_honeycomb.png|frame|none|Figure 4]]<br />
<br />
==References==<br />
<br />
[1] http://silver.neep.wisc.edu/~lakes/PoissonIntro.html<br />
<br />
[2] '"Negative Poisson’s Ratio Behavior Induced by an Elastic Instability". Katia Bertoldi, Pedro M. Reis, Stephen Willshaw, and Tom Mullin. ''Adv. Mater''. 2009, 21, 1–6.<br />
<br />
[3] "Properties of a chiral honeycomb with a Poisson's ratio -1" D. Prall, R. S. Lakes. ''Int. J. of Mechanical Sciences'', 39, 305-314, (1996)<br />
<br />
==Keyword in References==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Poisson%27s_Ratio&diff=23741Poisson's Ratio2011-12-10T16:07:07Z<p>Lauren: /* Definition */</p>
<hr />
<div>==Definition==<br />
<br />
When a material is elongated or compressed along one axis, the Poisson's ratio, <math>\nu</math>, of a material is the ratio of the [[Strain]] in the directions perpendicular to the axis, divided by the [[Strain]] along that axis. Essentially, this dimensionless number describes the tendency of a contraction or expansion in one dimension to cause contraction or expansion in other dimensions. Most materials have a positive Poisson's ratio, meaning other dimensions will contract in response to elongation along one dimension, and vice versa. Figure 1 demonstrates this concept. <br />
<br />
[[Image:Poissons_ratio.jpg|frame|Figure 1, from http://www.feppd.org/ICB-Dent/campus/biomechanics_in_dentistry/ldv_data/img/mech/mech_122.jpg]]<br />
<br />
<br />
Most materials have a Poisson's ratio near 0.3, with more rubbery materials approaching 0.5. [3] Auxetic materials, or materials with a negative Poisson's ratio were first reported in 1987 by Lakes.[2] Example materials of this type include some foams, honeycomb structures produced by Prall and Lakes,[3] and patterned arrays of circular and elliptical holes in an elastomer (Bertoldi).[3] In these last two cases, local buckling of the structure (i.e., repeatable collapse) leading to volume reduction is directly observed to cause a negative Poisson's ratio. Figure 1 shows a schematic of local buckling in Bertoldi's material. The material compresses uniformly until a critical applied strain is reached. At this strain, an elastic instability develops, and the structure experiences uniform, repeatable local buckling of the walls. Figures 3 and 4 show Prall and Lakes' honeycomb structures. Figure 3 shows a "regular" honeycomb shape, with a positive Poisson's ratio, and a "reentrant" honeycomb shape, with a negative Poisson's ratio. Figure 4 shows the same groups chiral honey comb structures in a) a schematic and b) a photograph of the fabricated structure. [3]<br />
<br />
''Important Limits''<br />
<br />
For an isotropic, unconstrained three dimensional elastic material, Poisson's ratio must range from -1 to 1/2.[3]<br />
<br />
[[Image:Neg_poisson_ratio_bertoldi.png|frame|Figure 2]]<br />
<br />
[[Image:Reentrant_honeycomb.png|frame|Figure 3]]<br />
<br />
[[Image:Chiral_honeycomb.png|frame|Figure 4]]<br />
<br />
==References==<br />
<br />
[1] http://silver.neep.wisc.edu/~lakes/PoissonIntro.html<br />
<br />
[2] '"Negative Poisson’s Ratio Behavior Induced by an Elastic Instability". Katia Bertoldi, Pedro M. Reis, Stephen Willshaw, and Tom Mullin. ''Adv. Mater''. 2009, 21, 1–6.<br />
<br />
[3] "Properties of a chiral honeycomb with a Poisson's ratio -1" D. Prall, R. S. Lakes. ''Int. J. of Mechanical Sciences'', 39, 305-314, (1996)<br />
<br />
==Keyword in References==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=File:Poissons_ratio.jpg&diff=23740File:Poissons ratio.jpg2011-12-10T16:06:52Z<p>Lauren: </p>
<hr />
<div></div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=File:Reentrant_honeycomb.png&diff=23736File:Reentrant honeycomb.png2011-12-10T16:00:58Z<p>Lauren: </p>
<hr />
<div></div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=File:Chiral_honeycomb.png&diff=23735File:Chiral honeycomb.png2011-12-10T16:00:08Z<p>Lauren: </p>
<hr />
<div></div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Poisson%27s_Ratio&diff=23725Poisson's Ratio2011-12-10T15:45:44Z<p>Lauren: /* References */</p>
<hr />
<div>==Definition==<br />
<br />
When a material is elongated or compressed along one axis, the Poisson's ratio, <math>\nu</math>, of a material is the ratio of the [[Strain]] in the directions perpendicular to the axis, divided by the [[Strain]] along that axis. Essentially, this dimensionless number describes the tendency of a contraction or expansion in one dimension to cause contraction or expansion in other dimensions. Most materials have a positive Poisson's ratio, meaning other dimensions will contract in response to elongation along one dimension, and vice versa. Most materials have a Poisson's ratio near 0.3, with more rubbery materials approaching 0.5. [3] Materials with negative Poisson's ratio were first reported in 1987 by Lakes. Example materials of this type include some foams, honeycomb structures produced by Prall and Lakes,[3] and patterned arrays of circular and elliptical holes in an elastomer (Bertoldi).[3] In these last two cases, local buckling of the structure walls leading to volume reduction is directly observed to cause a negative Poisson's ratio. Figure 1 shows a schematic of local buckling in Bertoldi's material.<br />
<br />
''Important Limits''<br />
<br />
For an isotropic, unconstrained three dimensional elastic material, Poisson's ratio must range from -1 to 1/2.[3] <br />
<br />
==References==<br />
<br />
[1] http://silver.neep.wisc.edu/~lakes/PoissonIntro.html<br />
<br />
[2] '"Negative Poisson’s Ratio Behavior Induced by an Elastic Instability". Katia Bertoldi, Pedro M. Reis, Stephen Willshaw, and Tom Mullin. ''Adv. Mater''. 2009, 21, 1–6.<br />
<br />
[3] "Properties of a chiral honeycomb with a Poisson's ratio -1" D. Prall, R. S. Lakes. ''Int. J. of Mechanical Sciences'', 39, 305-314, (1996)<br />
<br />
==Keyword in References==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=File:Neg_poisson_ratio_bertoldi.png&diff=23722File:Neg poisson ratio bertoldi.png2011-12-10T15:45:22Z<p>Lauren: </p>
<hr />
<div></div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Poisson%27s_Ratio&diff=23720Poisson's Ratio2011-12-10T15:41:08Z<p>Lauren: </p>
<hr />
<div>==Definition==<br />
<br />
When a material is elongated or compressed along one axis, the Poisson's ratio, <math>\nu</math>, of a material is the ratio of the [[Strain]] in the directions perpendicular to the axis, divided by the [[Strain]] along that axis. Essentially, this dimensionless number describes the tendency of a contraction or expansion in one dimension to cause contraction or expansion in other dimensions. Most materials have a positive Poisson's ratio, meaning other dimensions will contract in response to elongation along one dimension, and vice versa. Most materials have a Poisson's ratio near 0.3, with more rubbery materials approaching 0.5. [3] Materials with negative Poisson's ratio were first reported in 1987 by Lakes. Example materials of this type include some foams, honeycomb structures produced by Prall and Lakes,[3] and patterned arrays of circular and elliptical holes in an elastomer (Bertoldi).[3] In these last two cases, local buckling of the structure walls leading to volume reduction is directly observed to cause a negative Poisson's ratio. Figure 1 shows a schematic of local buckling in Bertoldi's material.<br />
<br />
''Important Limits''<br />
<br />
For an isotropic, unconstrained three dimensional elastic material, Poisson's ratio must range from -1 to 1/2.[3] <br />
<br />
==References==<br />
<br />
[1]http://silver.neep.wisc.edu/~lakes/PoissonIntro.html<br />
<br />
[2] '"Negative Poisson’s Ratio Behavior Induced by an Elastic Instability". Katia Bertoldi, Pedro M. Reis, Stephen Willshaw, and Tom Mullin. ''Adv. Mater''. 2009, 21, 1–6.<br />
<br />
[3] "Properties of a chiral honeycomb with a Poisson's ratio -1" D. Prall, R. S. Lakes. ''Int. J. of Mechanical Sciences'', 39, 305-314, (1996)<br />
<br />
<br />
==Keyword in References==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Creep&diff=23638Creep2011-12-10T14:18:54Z<p>Lauren: /* Definition */</p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
==Definition==<br />
<br />
Creep is the time dependent change in [[Strain]] of a material subject to a constant [[Stress]]. A [[Creep test]] attempts to quantify the relevant timescales and functional forms of molecular and/or atomic rearrangement that occur when a material creeps. The mechanism of creep differs depending on the material. In a crystal, mechanisms for creep include the movement of dislocations (Dislocation Creep) and the diffusion of atoms along grain boundaries (Coble Creep) or through the bulk (Nabarro-Herring creep). <br />
<br />
The general equation for describing creep is:<br />
<br />
<math> \frac{\mathrm{d}\varepsilon}{\mathrm{d}t} = \frac{C\sigma^m}{d^b} e^\frac{-Q}{kT}</math><br />
<br />
where the left hand side is the strain rate due to creep, ''Q'' is the activation energy of creep, ''d'' is the grain size, <math>\sigma</math> is the stress in the material, ''T'' is the temperature, and ''m'' and ''b'' are constants that depend on the mechanism of creep. In dislocation creep, m = 4 to 6 and b = 0. In Nabarro-Herring creep, m = 1 and b = 2. In Coble creep, m = 1 and b = 3. Depending on the mechanism being modeled, the exponents m and b can be tuned.<br />
<br />
For viscoelastic materials like many polymers, a number of models can be used to describe time dependent deformation. One approach is to combine two fundamental units (the spring, which represents elastic response, and the dashpot, which represents viscous response) in different configurations to create a simplified mechanical model of the system. The Zener model, for example, models a linear viscoelastic response as a "dashpot" (Newtonian flow behavior) in parallel with a spring, and spring in series with the combined unit. A polymer's creep behavior is often substantially more pronounced above its [[Glass Transition Temperature]], where chains more freely slide across one another.<br />
<br />
==Examples==<br />
<br />
Polymers can be characterized as cross-linked (where chains are chemically linked), uncross-linked (where chains are free to slide over one another), or crystalline. Uncross-linked polymers behave most like linearly viscoelastic materials, while cross-links in polymer chains limit the degree to which chains can slide past one another, and depending on the degree of cross-linking, can substantially impact the ability of the polymer to flow in a Newtonian manner. For more details, see ''Introduction to the Mechanics of a Continuous Medium'', Chapter 6.4 (linear viscoelastic response) by Malvern.<br />
<br />
==See also:==<br />
<br />
[[Creep of ice]], [[Creep test]]<br />
<br />
== Keyword in references: ==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]<br />
<br />
[[Stress Enhancement in the Delayed Yielding of Colloidal Gels]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Glass_transition&diff=23636Glass transition2011-12-10T14:17:04Z<p>Lauren: /* Specific Examples */</p>
<hr />
<div>Original entry: Ian Burgess, Fall 2009. Edited by [[Lauren Hartle]], Fall 2011.<br />
<br />
<br />
== Definition ==<br />
<br />
The glass transition describes the manner in which certain materials transition between the liquid and the [http://en.wikipedia.org/wiki/Glass glass] phases. The transition to a glass is marked by a solidification of the material without the addition of any long range order to the molecular packing. Unlike crystallization, there is also no discontinuous change in any thermodynamic property, and hence the transition is not, strictly speaking, a phase transition.[1] Figure 1, taken from [1], illustrates the discontinuous nature of a crystalline versus the smooth glassy transition. [[Image:Debenedetti_and_Stillinger_figure.png|frame|none]] Kinetics hold the key to this behavior: when a liquid is cooled faster than the timescale required for nucleation and crystallization, an amorphous solid results. The resulting material behaves mechanically like a solid on laboratory timescales, but experiences continuous, slow rearrangement moving toward its equilibrium state. The structure of some materials prohibit crystallization and hence naturally transition to a glassy state when cooled. A crystalline material can also be brought through a glass transition when the liquid state is supercooled. The precise mechanisms for this transition to solid-like behavior is not well understood.[1] The glass transition occurs at the [[Glass Transition Temperature]], <math>T_g</math>, which varies with the material and cooling rate. It should be noted that manipulating pressure, independent of temperature, can produce a glass transition.<br />
<br />
==Specific Examples==<br />
''Polymers:'' In polymers above the glass transition temperature, chains have sufficient mobility to slide past each other and reconfigure under an applied stress. This mobility is substantially reduced below the glass transition. However, at temperatures above the glass transition, but below the melting point, polymers still have a finite stiffness.<br />
<br />
''Common Materials:'' Silica, commonly used to make windows and other commercial glass products, experiences a glass transition.<br />
<br />
''Metallic Glasses:'' See [[Metallic glasses]].<br />
<br />
==See also:==<br />
<br />
[[Polymer molecules#Glass transition|Polymers - Glass transitions]] in [[Polymer molecules]] in [[Polymers and polymer solutions]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
[[Phases and Phase Diagrams#Definitions|Glass transition]] in [[Phases and Phase Diagrams]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
== References ==<br />
<br />
[1] Debenedetti and F. H. Stillinger. "Supercooled liquids and the glass transition". ''Nature'', Vol 410, 8 March 2001.<br />
<br />
[2] Z. Fakhraai and J. A. Forrest, "Measuring the Surface Dynamics of Glassy Polymers" Science 319, 600 (2008). <br />
<br />
[3] Kingery, W,D., Bowen, H.K., and Uhlmann, D.R., Introduction to Ceramics, 2nd Edn. (John Wiley & Sons, New York, 2006).</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Glass_transition&diff=23635Glass transition2011-12-10T14:15:34Z<p>Lauren: /* Definition */</p>
<hr />
<div>Original entry: Ian Burgess, Fall 2009. Edited by [[Lauren Hartle]], Fall 2011.<br />
<br />
<br />
== Definition ==<br />
<br />
The glass transition describes the manner in which certain materials transition between the liquid and the [http://en.wikipedia.org/wiki/Glass glass] phases. The transition to a glass is marked by a solidification of the material without the addition of any long range order to the molecular packing. Unlike crystallization, there is also no discontinuous change in any thermodynamic property, and hence the transition is not, strictly speaking, a phase transition.[1] Figure 1, taken from [1], illustrates the discontinuous nature of a crystalline versus the smooth glassy transition. [[Image:Debenedetti_and_Stillinger_figure.png|frame|none]] Kinetics hold the key to this behavior: when a liquid is cooled faster than the timescale required for nucleation and crystallization, an amorphous solid results. The resulting material behaves mechanically like a solid on laboratory timescales, but experiences continuous, slow rearrangement moving toward its equilibrium state. The structure of some materials prohibit crystallization and hence naturally transition to a glassy state when cooled. A crystalline material can also be brought through a glass transition when the liquid state is supercooled. The precise mechanisms for this transition to solid-like behavior is not well understood.[1] The glass transition occurs at the [[Glass Transition Temperature]], <math>T_g</math>, which varies with the material and cooling rate. It should be noted that manipulating pressure, independent of temperature, can produce a glass transition.<br />
<br />
==Specific Examples==<br />
''Polymers:'' In polymers above the glass transition temperature, chains have sufficient mobility to slide past each other and reconfigure under an applied stress. This mobility is substantially reduced below the glass transition. However, at temperatures above the glass transition, but below the melting point, polymers still have a finite stiffness.<br />
''Common Materials:'' Silica, commonly used to make windows and other commercial glass products, experiences a glass transition.<br />
<br />
''Metallic Glasses:'' See [[Metallic glasses]].<br />
<br />
==See also:==<br />
<br />
[[Polymer molecules#Glass transition|Polymers - Glass transitions]] in [[Polymer molecules]] in [[Polymers and polymer solutions]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
[[Phases and Phase Diagrams#Definitions|Glass transition]] in [[Phases and Phase Diagrams]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
== References ==<br />
<br />
[1] Debenedetti and F. H. Stillinger. "Supercooled liquids and the glass transition". ''Nature'', Vol 410, 8 March 2001.<br />
<br />
[2] Z. Fakhraai and J. A. Forrest, "Measuring the Surface Dynamics of Glassy Polymers" Science 319, 600 (2008). <br />
<br />
[3] Kingery, W,D., Bowen, H.K., and Uhlmann, D.R., Introduction to Ceramics, 2nd Edn. (John Wiley & Sons, New York, 2006).</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Creep&diff=23631Creep2011-12-10T14:12:51Z<p>Lauren: /* Examples */</p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
==Definition==<br />
<br />
Creep is the time dependent change in [[Strain]] of a material subject to a constant [[Stress]]. A [[Creep test]] attempts to quantify the relevant timescales and functional forms of molecular and/or atomic rearrangement that occur when a material creeps. The mechanism of creep differs depending on the material. In a crystal, mechanisms for creep include the movement of dislocations (Dislocation Creep) and the diffusion of atoms along grain boundaries (Coble Creep) or through the bulk (Nabarro-Herring creep). <br />
<br />
The general equation for describing creep is:<br />
<br />
<math> \frac{\mathrm{d}\varepsilon}{\mathrm{d}t} = \frac{C\sigma^m}{d^b} e^\frac{-Q}{kT}</math><br />
<br />
where the left hand side is the strain rate due to creep, ''Q'' is the activation energy of creep, ''d'' is the grain size, <math>\sigma</math> is the stress in the material, ''T'' is the temperature, and ''m'' and ''b'' are constants that depend on the mechanism of creep. In dislocation creep, m = 4 to 6 and b = 0. In Nabarro-Herring creep, m = 1 and b = 2. In Coble creep, m = 1 and b = 3. Depending on the mechanism being modeled, the exponents m and b can be tuned.<br />
<br />
For viscoelastic materials like many polymers, a number of models can be used to describe time dependent deformation. One approach is to combine two fundamental units (the spring, which represents elastic response, and the dashpot, which represents viscous response) in different configurations to create a simplified mechanical model of the system. The Zener model, for example, models a linear viscoelastic response as a "dashpot" (Newtonian flow behavior) in parallel with a spring, and spring in series with the combined unit. <br />
<br />
==Examples==<br />
<br />
Polymers can be characterized as cross-linked (where chains are chemically linked), uncross-linked (where chains are free to slide over one another), or crystalline. Uncross-linked polymers behave most like linearly viscoelastic materials, while cross-links in polymer chains limit the degree to which chains can slide past one another, and depending on the degree of cross-linking, can substantially impact the ability of the polymer to flow in a Newtonian manner. For more details, see ''Introduction to the Mechanics of a Continuous Medium'', Chapter 6.4 (linear viscoelastic response) by Malvern.<br />
<br />
==See also:==<br />
<br />
[[Creep of ice]], [[Creep test]]<br />
<br />
== Keyword in references: ==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]<br />
<br />
[[Stress Enhancement in the Delayed Yielding of Colloidal Gels]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Superhydrophobic_surfaces&diff=23627Superhydrophobic surfaces2011-12-10T14:06:59Z<p>Lauren: /* Introduction */</p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
Entry has been combined with [[Superhydrophobicity]], [[Superhydrophicity]] (misspelled) and [[Superhydrophobic]]. (LH 2011)<br />
<br />
==Introduction==<br />
A water droplet on a superhydrophobic surface has a contact angle of greater than 150 degrees and a very low roll-off angle. In nature and in man-made materials, this has been achieved with [[Structured Surfaces]]. Advantages of such surfaces include the ability to repel water and self-clean.[3] Industrial applications include "self-cleaning window glasses, paints, and textiles to low-friction surfaces for fluid flow and energy conservation."[2] To predict when a droplet will wet the surface and when it will be repelled, one can compare the contact angle for complete wetting to the contact angle for a droplet resting atop the surface structure with no penetration. When a droplet is in intimate contact with the surface, the Wenzel state, the following equation applies:<br />
<br />
<math>\cos{\theta}_c = r \cos{\theta}</math><br />
<br />
where r is the ratio of the actual area to the projected contact area and <math>\theta</math> is the contact angle of the droplet on a flat surface of the same material.. When the droplet rests atop the surface structure, it is in the Cassie-Baxter state, modeled by:<br />
<br />
<math>\cos{\theta}_{c} = \phi \left( cos \theta + 1 \right) - 1</math><br />
<br />
where <math>\phi</math> is the area fraction of the solid in contact with the liquid, and <math>\theta</math> is the contact angle of the droplet on a flat surface of the same material. Setting the two contact angles equal gives the following critical condition for the transition between the Cassie-Baxter and Wenzel states.<br />
<br />
<math>cos \theta = \frac {\phi - 1}{r -\phi}</math><br />
<br />
By this prediction, a droplet resting atop surface structures might be a lower energy state than intimate contact when the cosine of the contact angle on a flat surface is less than the right hand side of the equation. <br />
<br />
It is argued that surface structure can produce superhydrophobic effects, even on a hydrophilic surface. For example, lotus leaves have been shown to be superhydrophobic, despite the waxy, weakly hydrophilic coating on the surface.[1] It has been demonstrated that the surface of a lotus leaf is superhydrophobic in part due to the presence of hierarchical surface structures structures consisting of micro- and nano-scale features. [2] Figure 1 contrasts the state of a droplet on a flat surface and surfaces of increasingly complex structure.<br />
<br />
[[Image:Wetting_figure.png|frame|Figure from reference 1.]]<br />
<br />
Butterfly wings and parts of pitcher plants have observed superhydrophobic properties. Figure 2 shows an image of real and artificially fabricated lotus leaf structures from reference 2.<br />
<br />
[[Image:Lotus_leaf_image.png|frame|Figure from reference 2.]]<br />
<br />
==References==<br />
[1]"Design parameters for superhydrophobicity and superoleophobicity". Anish Tuteja, Wonjae Choi, Gareth H. McKinley, Robert E. Cohen, and Michael F. Rubner. ''MRS Bulletin'' 33 (8), 752-758 (August 2008)<br />
<br />
[2]"Fabrication of artificial Lotus leaves and significance of hierarchical structure for superhydrophobicity and low adhesion". Kerstin Koch, Bharat Bhushan, Yong Chae Jung and Wilhelm Barthlott. ''Soft Matter'', 2009, 5, 1386–1393.<br />
<br />
[3]"Self-cleaning materials: Lotus leaf inspired nanotechnology" Peter Forbes, ''Scientific American'' 30 July 2008.<br />
<br />
==See also==<br />
<br />
[[Effects of contact angles#Surface heterogeneity|Superhydrophobic surfaces]] in [[Effects of contact angles]] in [[Capillarity and wetting]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
==Keyword in References==<br />
<br />
[[Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity]]<br />
<br />
[[Growth of polygonal rings and wires of CuS on structured surfaces]]<br />
<br />
[[Pitcher plant inspired non-stick surface]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Superhydrophobic_surfaces&diff=23625Superhydrophobic surfaces2011-12-10T14:05:31Z<p>Lauren: </p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
Entry has been combined with [[Superhydrophobicity]], [[Superhydrophicity]] (misspelled) and [[Superhydrophobic]]. (LH 2011)<br />
<br />
==Introduction==<br />
A water droplet on a superhydrophobic surface has a contact angle of greater than 150 degrees and a very low roll-off angle. In nature and in man-made materials, this has been achieved with [[Structured Surfaces]]. Advantages of such surfaces include the ability to repel water and self-clean.[3] Industrial applications include "self-cleaning window glasses, paints, and textiles to low-friction surfaces for fluid flow and energy conservation."[2] To predict when a droplet will wet the surface and when it will be repelled, one can compare the contact angle for complete wetting to the contact angle for a droplet resting atop the surface structure with no penetration. When a droplet is in intimate contact with the surface, the Wenzel state, the following equation applies:<br />
<br />
<math>\cos{\theta}_c = r \cos{\theta}</math><br />
<br />
where r is the ratio of the actual area to the projected contact area and <math>\theta</math> is the contact angle of the droplet on a flat surface of the same material.. When the droplet rests atop the surface structure, it is in the Cassie-Baxter state, modeled by:<br />
<br />
<math>\cos{\theta}_{c} = \phi \left( cos \theta + 1 \right) - 1</math><br />
<br />
where <math>\phi</math> is the area fraction of the solid in contact with the liquid, and <math>\theta</math> is the contact angle of the droplet on a flat surface of the same material. Setting the two contact angles equal gives the following critical condition for the transition between the Cassie-Baxter and Wenzel states.<br />
<br />
<math>cos \theta = \frac {\phi - 1}{r -\phi}</math><br />
<br />
By this prediction, a droplet resting atop surface structures might be a lower energy state than intimate contact when the cosine of the contact angle on a flat surface is less than the right hand side of the equation. <br />
<br />
It is argued that surface structure can produce superhydrophobic effects, even on a hydrophilic surface. For example, lotus leaves have been shown to be superhydrophobic, despite the waxy, weakly hydrophilic coating on the surface.[1] It has been demonstrated that the surface of a lotus leaf is superhydrophobic in part due to the presence of hierarchical surface structures structures consisting of micro- and nano-scale features. [2] Figure 1 contrasts the state of a droplet on a flat surface and surfaces of increasingly complex structure. <br />
<br />
[[Image:Wetting_figure.png|frame|Figure from reference 1.]]<br />
<br />
Butterfly wings and parts of pitcher plants have observed superhydrophobic properties. Figure 2 shows an image of real and artificially fabricated lotus leaf structures from reference 2.<br />
<br />
[[Image:Lotus_leaf_image.png|frame|Figure from reference 2.]]<br />
<br />
==References==<br />
[1]"Design parameters for superhydrophobicity and superoleophobicity". Anish Tuteja, Wonjae Choi, Gareth H. McKinley, Robert E. Cohen, and Michael F. Rubner. ''MRS Bulletin'' 33 (8), 752-758 (August 2008)<br />
<br />
[2]"Fabrication of artificial Lotus leaves and significance of hierarchical structure for superhydrophobicity and low adhesion". Kerstin Koch, Bharat Bhushan, Yong Chae Jung and Wilhelm Barthlott. ''Soft Matter'', 2009, 5, 1386–1393.<br />
<br />
[3]"Self-cleaning materials: Lotus leaf inspired nanotechnology" Peter Forbes, ''Scientific American'' 30 July 2008.<br />
<br />
==See also==<br />
<br />
[[Effects of contact angles#Surface heterogeneity|Superhydrophobic surfaces]] in [[Effects of contact angles]] in [[Capillarity and wetting]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
==Keyword in References==<br />
<br />
[[Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity]]<br />
<br />
[[Growth of polygonal rings and wires of CuS on structured surfaces]]<br />
<br />
[[Pitcher plant inspired non-stick surface]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Glass_Transition_Temperature&diff=23585Glass Transition Temperature2011-12-10T07:27:49Z<p>Lauren: /* Definition */</p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
==Definition==<br />
The glass transition temperature, <math>T_g</math>, is the temperature at which an amorphous solid transitions continuously into a liquid state, and vice versa. This temperature depends on the material and the cooling rate; altering the cooling rate changes the timescale on which atoms and molecules must rearrange to reach their equilibrium configuration. Depending on the cooling rate, the resulting amorphous structure can change. For most materials, the glass transition temperature is fairly well-defined and only weakly cooling rate-dependent.<br />
<br />
There are different quantitative definitions of this temperature, detailed by Debenedetti and Stillinger [1]:<br />
<br />
1. In a plot of volume versus temperature, the intersection of the liquid and glass curves marks <math>T_g</math>. Figure 1 [1], shows this phenomenon.<br />
[[Image:Debenedetti_and_Stillinger_figure.png|frame|none]]<br />
<br />
2. Temperature at which the material viscosity reaches <math> 10^{13}</math> poise.<br />
<br />
==See also==<br />
[[Glass transition]], [[Metallic glasses]]<br />
<br />
==References==<br />
[1] Debenedetti and F. H. Stillinger. "Supercooled liquids and the glass transition". ''Nature'', Vol 410, 8 March 2001.<br />
<br />
==Keyword in References==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Creep&diff=23584Creep2011-12-10T07:26:48Z<p>Lauren: /* Definition */</p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
==Definition==<br />
<br />
Creep is the time dependent change in [[Strain]] of a material subject to a constant [[Stress]]. A [[Creep test]] attempts to quantify the relevant timescales and functional forms of molecular and/or atomic rearrangement that occur when a material creeps. The mechanism of creep differs depending on the material. In a crystal, mechanisms for creep include the movement of dislocations (Dislocation Creep) and the diffusion of atoms along grain boundaries (Coble Creep) or through the bulk (Nabarro-Herring creep). <br />
<br />
The general equation for describing creep is:<br />
<br />
<math> \frac{\mathrm{d}\varepsilon}{\mathrm{d}t} = \frac{C\sigma^m}{d^b} e^\frac{-Q}{kT}</math><br />
<br />
where the left hand side is the strain rate due to creep, ''Q'' is the activation energy of creep, ''d'' is the grain size, <math>\sigma</math> is the stress in the material, ''T'' is the temperature, and ''m'' and ''b'' are constants that depend on the mechanism of creep. In dislocation creep, m = 4 to 6 and b = 0. In Nabarro-Herring creep, m = 1 and b = 2. In Coble creep, m = 1 and b = 3. Depending on the mechanism being modeled, the exponents m and b can be tuned.<br />
<br />
For viscoelastic materials like many polymers, a number of models can be used to describe time dependent deformation. One approach is to combine two fundamental units (the spring, which represents elastic response, and the dashpot, which represents viscous response) in different configurations to create a simplified mechanical model of the system. The Zener model, for example, models a linear viscoelastic response as a "dashpot" (Newtonian flow behavior) in parallel with a spring, and spring in series with the combined unit. <br />
<br />
==Examples==<br />
<br />
Polymers can be characterized as cross-linked (where chains are chemically linked), uncross-linked (where chains are free to slide over one another), or crystalline. Uncross-linked polymers behave most like linearly viscoelastic materials, while cross-links in polymer chains can place an upper limit on the amount of stress and strain a polymer can withstand.<br />
<br />
==See also:==<br />
<br />
[[Creep of ice]], [[Creep test]]<br />
<br />
== Keyword in references: ==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]<br />
<br />
[[Stress Enhancement in the Delayed Yielding of Colloidal Gels]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Creep&diff=23430Creep2011-12-09T22:00:40Z<p>Lauren: /* Definition */</p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
==Definition==<br />
<br />
Creep is the time dependent change in [[Strain]] of a material subject to a constant [[Stress]]. A [[Creep test]] attempts to quantify the relevant timescales and functional forms of molecular and/or atomic rearrangement that occur when a material creeps. The mechanism of creep differs depending on the material. In a crystal, mechanisms for creep include the movement of dislocations (Dislocation Creep) and the diffusion of atoms along grain boundaries (Coble Creep) or through the bulk (Nabarro-Herring creep). <br />
<br />
The general equation for describing creep is:<br />
<br />
<math> \frac{\mathrm{d}\varepsilon}{\mathrm{d}t} = \frac{C\sigma^m}{d^b} e^\frac{-Q}{kT}</math><br />
<br />
where the left hand side is the strain rate due to creep, ''Q'' is the activation energy of creep, ''d'' is the grain size, <math>\sigma</math> is the stress in the material, ''T'' is the temperature, and ''m'' and ''b'' are constants that depend on the mechanism of creep. In dislocation creep, m = 4 to 6 and b = 0. In Nabarro-Herring creep, m = 1 and b = 2. In Coble creep, m = 1 and b = 3. Depending on the mechanism being modeled, the exponents m and b can be tuned.<br />
<br />
For viscoelastic materials like many polymers, a number of models can be used. An uncross<br />
<br />
==See also:==<br />
<br />
[[Creep of ice]], [[Creep test]]<br />
<br />
== Keyword in references: ==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]<br />
<br />
[[Stress Enhancement in the Delayed Yielding of Colloidal Gels]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Creep&diff=23421Creep2011-12-09T21:31:09Z<p>Lauren: /* Definition */</p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
==Definition==<br />
<br />
Creep is the time dependent change in [[Strain]] of a material subject to a constant [[Stress]]. A [[Creep test]] attempts to quantify the relevant timescales and functional forms of molecular and/or atomic rearrangement that occur when a material creeps. The mechanism of creep differs depending on the material. In a crystal, mechanisms for creep include the movement of dislocations (Dislocation Creep) and the diffusion of atoms along grain boundaries (Coble Creep) or through the bulk (Nabarro-Herring creep). <br />
<br />
The general equation for describing creep is:<br />
<br />
<math> \frac{\mathrm{d}\varepsilon}{\mathrm{d}t} = \frac{C\sigma^m}{d^b} e^\frac{-Q}{kT}</math><br />
<br />
where the left hand side is the strain rate due to creep, ''Q'' is the activation energy of creep, ''d'' is the grain size, <math>\sigma</math> is the stress in the material, ''T'' is the temperature, and ''m'' and ''b'' are constants that depend on the mechanism of creep. In dislocation creep, m = 4 to 6 and b = 0. In Nabarro-Herring creep, m = 1 and b = 2. In Coble creep, m = 1 and b = 3. Depending on the mechanism being modeled, the exponents m and b can be tuned.<br />
<br />
==See also:==<br />
<br />
[[Creep of ice]], [[Creep test]]<br />
<br />
== Keyword in references: ==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]<br />
<br />
[[Stress Enhancement in the Delayed Yielding of Colloidal Gels]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Creep&diff=23419Creep2011-12-09T21:22:19Z<p>Lauren: /* Definition */</p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
==Definition==<br />
<br />
Creep is the time dependent change in [[Strain]] of a material subject to a constant [[Stress]]. A [[Creep test]] attempts to quantify the relevant timescales and functional forms of molecular and/or atomic rearrangement that occur when a material creeps. The mechanism of creep differs depending on the material. In a crystal, mechanisms for creep include the movement of dislocations (Dislocation Creep) and the diffusion of atoms along grain boundaries (Coble Creep) or through the bulk (Nabarro-Herring creep). <br />
<br />
The general equation for describing creep is:<br />
<br />
<math> \frac{\mathrm{d}\varepsilon}{\mathrm{d}t} = \frac{C\sigma^m}{d^b} e^\frac{-Q}{kT}</math><br />
<br />
where the left hand side is the strain rate due to creep, ''Q'' is the activation energy of creep, ''d'' is the grain size, <math>\sigma</math> is the stress in the material, ''T'' is the temperature, and ''m'' and ''b'' are constants that depend on the mechanism of creep. In dislocation creep, m = 4 to 6 and b = 0. In Nabarro-Herring creep, m = 1 and b = 2. In Coble creep, m = 1 and b = 3.<br />
<br />
==See also:==<br />
<br />
[[Creep of ice]], [[Creep test]]<br />
<br />
== Keyword in references: ==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]<br />
<br />
[[Stress Enhancement in the Delayed Yielding of Colloidal Gels]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Creep&diff=23416Creep2011-12-09T21:08:26Z<p>Lauren: /* Definition */</p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
==Definition==<br />
<br />
Creep is the time dependent change in [[Strain]] of a material subject to a constant [[Stress]]. A [[Creep test]] and [[Stress relaxation]] test attempt to quantify the same material behavior: the timescale and functional form of molecular and/or atomic rearrangement that occurs when a material is irreversibly deformed. The mechanism of creep differs depending on the material. In a crystal, mechanisms for creep include the movement of dislocations and the diffusion of atoms along grain boundaries or through grains. <br />
<br />
The general equation for describing creep is:<br />
<br />
<math> \frac{\mathrm{d}\varepsilon}{\mathrm{d}t} = \frac{C\sigma^m}{d^b} e^\frac{-Q}{kT}</math><br />
<br />
where the left hand side is the strain rate due to creep, ''Q'' is the activation energy of creep, ''d'' is the grain size, <math>\sigma</math> is the stress in the material, ''T'' is the temperature, and ''m'' and ''b'' are constants that depend on the mechanism of creep.<br />
<br />
==See also:==<br />
<br />
[[Creep of ice]], [[Creep test]]<br />
<br />
== Keyword in references: ==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]<br />
<br />
[[Stress Enhancement in the Delayed Yielding of Colloidal Gels]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Superhydrophobic_surfaces&diff=23374Superhydrophobic surfaces2011-12-09T18:01:20Z<p>Lauren: /* Introduction */</p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
Entry has been combined with [[Superhydrophobicity]], [[Superhydrophicity]] (misspelled) and [[Superhydrophobic]]. (LH 2011)<br />
<br />
==Introduction==<br />
A water droplet on a superhydrophobic surface has a contact angle of greater than 150 degrees and a very low roll-off angle. In nature and in man-made materials, this has been achieved with [[Structured Surfaces]]. Advantages of such surfaces include the ability to repel water and self-clean.[3] Industrial applications include "self-cleaning window glasses, paints, and textiles to low-friction surfaces for fluid flow and energy conservation."[2] To understand why water droplets wet these surfaces so poorly, one m<br />
<br />
[[Image:Wetting_figure.png|frame|Figure from reference 1.]]<br />
<br />
Wenzel:<br />
<math>\cos{\theta}_c = r \cos{\theta}</math><br />
<br />
where r is the ratio of the actual area to the projected contact area.<br />
Cassie-Baxter:<br />
<math>\cos{\theta}_{c} = \phi \left( cos \theta + 1 \right) - 1</math><br />
<math>cos \theta < \frac {\phi - 1}{r -\phi}</math><br />
<br />
It is argued that surface structure can produce superhydrophobic effects, even on a hydrophilic surface. For example, lotus leaves have been shown to be superhydrophobic, despite the waxy, weakly hydrophilic coating on the surface.[1] It has been demonstrated that the surface of a lotus leaf is superhydrophobic in part due to the presence of hierarchical surface structures structures consisting of micro- and nano-scale features. [2] Butterfly wings and parts of pitcher plants have observed superhydrophobic properties.<br />
<br />
[[Image:Lotus_leaf_image.png|frame|Figure from reference 2.]]<br />
<br />
==References==<br />
[1]"Design parameters for superhydrophobicity and superoleophobicity". Anish Tuteja, Wonjae Choi, Gareth H. McKinley, Robert E. Cohen, and Michael F. Rubner. ''MRS Bulletin'' 33 (8), 752-758 (August 2008)<br />
<br />
[2]"Fabrication of artificial Lotus leaves and significance of hierarchical structure for superhydrophobicity and low adhesion". Kerstin Koch, Bharat Bhushan, Yong Chae Jung and Wilhelm Barthlott. ''Soft Matter'', 2009, 5, 1386–1393.<br />
<br />
[3]"Self-cleaning materials: Lotus leaf inspired nanotechnology" Peter Forbes, ''Scientific American'' 30 July 2008.<br />
<br />
==See also==<br />
<br />
[[Effects of contact angles#Surface heterogeneity|Superhydrophobic surfaces]] in [[Effects of contact angles]] in [[Capillarity and wetting]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
==Keyword in References==<br />
<br />
[[Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity]]<br />
<br />
[[Growth of polygonal rings and wires of CuS on structured surfaces]]<br />
<br />
[[Pitcher plant inspired non-stick surface]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Superhydrophobic_surfaces&diff=23373Superhydrophobic surfaces2011-12-09T18:00:23Z<p>Lauren: /* Introduction */</p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
Entry has been combined with [[Superhydrophobicity]], [[Superhydrophicity]] (misspelled) and [[Superhydrophobic]]. (LH 2011)<br />
<br />
==Introduction==<br />
A water droplet on a superhydrophobic surface has a contact angle of greater than 150 degrees and a very low roll-off angle. In nature and in man-made materials, this has been achieved with [[Structured Surfaces]]. Advantages of such surfaces include the ability to repel water and self-clean.[3] Industrial applications include "self-cleaning window glasses, paints, and textiles to low-friction surfaces for fluid flow and energy conservation."[2] To understand why water droplets wet these surfaces so poorly, one m<br />
<br />
[[Wetting_figure.png|frame|Figure from reference 1.]]<br />
<br />
Wenzel:<br />
<math>\cos{\theta}_c = r \cos{\theta}</math><br />
<br />
where r is the ratio of the actual area to the projected contact area.<br />
Cassie-Baxter:<br />
<math>\cos{\theta}_{c} = \phi \left( cos \theta + 1 \right) - 1</math><br />
<math>cos \theta < \frac {\phi - 1}{r -\phi}</math><br />
<br />
It is argued that surface structure can produce superhydrophobic effects, even on a hydrophilic surface. For example, lotus leaves have been shown to be superhydrophobic, despite the waxy, weakly hydrophilic coating on the surface.[1] It has been demonstrated that the surface of a lotus leaf is superhydrophobic in part due to the presence of hierarchical surface structures structures consisting of micro- and nano-scale features. [2] Butterfly wings and parts of pitcher plants have observed superhydrophobic properties.<br />
<br />
[[Image:Lotus_leaf_image.png]]<br />
<br />
==References==<br />
[1]"Design parameters for superhydrophobicity and superoleophobicity". Anish Tuteja, Wonjae Choi, Gareth H. McKinley, Robert E. Cohen, and Michael F. Rubner. ''MRS Bulletin'' 33 (8), 752-758 (August 2008)<br />
<br />
[2]"Fabrication of artificial Lotus leaves and significance of hierarchical structure for superhydrophobicity and low adhesion". Kerstin Koch, Bharat Bhushan, Yong Chae Jung and Wilhelm Barthlott. ''Soft Matter'', 2009, 5, 1386–1393.<br />
<br />
[3]"Self-cleaning materials: Lotus leaf inspired nanotechnology" Peter Forbes, ''Scientific American'' 30 July 2008.<br />
<br />
==See also==<br />
<br />
[[Effects of contact angles#Surface heterogeneity|Superhydrophobic surfaces]] in [[Effects of contact angles]] in [[Capillarity and wetting]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
==Keyword in References==<br />
<br />
[[Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity]]<br />
<br />
[[Growth of polygonal rings and wires of CuS on structured surfaces]]<br />
<br />
[[Pitcher plant inspired non-stick surface]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=File:Wetting_figure.png&diff=23372File:Wetting figure.png2011-12-09T17:57:45Z<p>Lauren: </p>
<hr />
<div></div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=File:Lotus_leaf_image.png&diff=23371File:Lotus leaf image.png2011-12-09T17:57:00Z<p>Lauren: </p>
<hr />
<div></div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Superhydrophobic_surfaces&diff=23370Superhydrophobic surfaces2011-12-09T17:51:28Z<p>Lauren: /* Introduction */</p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
Entry has been combined with [[Superhydrophobicity]], [[Superhydrophicity]] (misspelled) and [[Superhydrophobic]]. (LH 2011)<br />
<br />
==Introduction==<br />
A water droplet on a superhydrophobic surface has a contact angle of greater than 150 degrees and a very low roll-off angle. In nature and in man-made materials, this has been achieved with [[Structured Surfaces]]. Advantages of such surfaces include the ability to repel water and self-clean.[3] Industrial applications include "self-cleaning window glasses, paints, and textiles to low-friction surfaces for fluid flow and energy conservation."[2] To understand why water droplets wet these surfaces so poorly, one m<br />
Wenzel:<br />
<math>\cos{\theta}_c = r \cos{\theta}</math><br />
<br />
where r is the ratio of the actual area to the projected contact area.<br />
Cassie-Baxter:<br />
<math>\cos{\theta}_{c} = \phi \left( cos \theta + 1 \right) - 1</math><br />
<math>cos \theta < \frac {\phi - 1}{r -\phi}</math><br />
<br />
It is argued that surface structure can produce superhydrophobic effects, even on a hydrophilic surface. For example, lotus leaves have been shown to be superhydrophobic, despite the waxy, weakly hydrophilic coating on the surface.[1] It has been demonstrated that the surface of a lotus leaf is superhydrophobic in part due to the presence of hierarchical surface structures structures consisting of micro- and nano-scale features. [2] Butterfly wings and parts of pitcher plants have observed superhydrophobic properties.<br />
<br />
==References==<br />
[1]"Design parameters for superhydrophobicity and superoleophobicity". Anish Tuteja, Wonjae Choi, Gareth H. McKinley, Robert E. Cohen, and Michael F. Rubner. ''MRS Bulletin'' 33 (8), 752-758 (August 2008)<br />
<br />
[2]"Fabrication of artificial Lotus leaves and significance of hierarchical structure for superhydrophobicity and low adhesion". Kerstin Koch, Bharat Bhushan, Yong Chae Jung and Wilhelm Barthlott. ''Soft Matter'', 2009, 5, 1386–1393.<br />
<br />
[3]"Self-cleaning materials: Lotus leaf inspired nanotechnology" Peter Forbes, ''Scientific American'' 30 July 2008.<br />
<br />
==See also==<br />
<br />
[[Effects of contact angles#Surface heterogeneity|Superhydrophobic surfaces]] in [[Effects of contact angles]] in [[Capillarity and wetting]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
==Keyword in References==<br />
<br />
[[Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity]]<br />
<br />
[[Growth of polygonal rings and wires of CuS on structured surfaces]]<br />
<br />
[[Pitcher plant inspired non-stick surface]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Superhydrophobic_surfaces&diff=23369Superhydrophobic surfaces2011-12-09T17:36:25Z<p>Lauren: /* References */</p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
Entry has been combined with [[Superhydrophobicity]], [[Superhydrophicity]] (misspelled) and [[Superhydrophobic]]. (LH 2011)<br />
<br />
==Introduction==<br />
A water droplet on a superhydrophobic surface has a contact angle of greater than 150 degrees and a very low roll-off angle. In nature and in man-made materials, this has been achieved with [[Structured Surfaces]]. Advantages of such surfaces include the ability to repel water and self-clean.[3] Industrial applications include "self-cleaning window glasses, paints, and textiles to low-friction surfaces for fluid flow and energy conservation."[2] To understand why water droplets wet these surfaces so poorly, one m<br />
<br />
It is argued that surface structure can produce superhydrophobic effects, even on a hydrophilic surface. For example, lotus leaves have been shown to be superhydrophobic, despite the waxy, weakly hydrophilic coating on the surface.[1] It has been demonstrated that the surface of a lotus leaf is superhydrophobic in part due to the presence of hierarchical surface structures structures consisting of micro- and nano-scale features. [2] Butterfly wings and parts of pitcher plants have observed superhydrophobic properties.<br />
<br />
==References==<br />
[1]"Design parameters for superhydrophobicity and superoleophobicity". Anish Tuteja, Wonjae Choi, Gareth H. McKinley, Robert E. Cohen, and Michael F. Rubner. ''MRS Bulletin'' 33 (8), 752-758 (August 2008)<br />
<br />
[2]"Fabrication of artificial Lotus leaves and significance of hierarchical structure for superhydrophobicity and low adhesion". Kerstin Koch, Bharat Bhushan, Yong Chae Jung and Wilhelm Barthlott. ''Soft Matter'', 2009, 5, 1386–1393.<br />
<br />
[3]"Self-cleaning materials: Lotus leaf inspired nanotechnology" Peter Forbes, ''Scientific American'' 30 July 2008.<br />
<br />
==See also==<br />
<br />
[[Effects of contact angles#Surface heterogeneity|Superhydrophobic surfaces]] in [[Effects of contact angles]] in [[Capillarity and wetting]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
==Keyword in References==<br />
<br />
[[Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity]]<br />
<br />
[[Growth of polygonal rings and wires of CuS on structured surfaces]]<br />
<br />
[[Pitcher plant inspired non-stick surface]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Superhydrophobic_surfaces&diff=23368Superhydrophobic surfaces2011-12-09T17:36:12Z<p>Lauren: /* References */</p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
Entry has been combined with [[Superhydrophobicity]], [[Superhydrophicity]] (misspelled) and [[Superhydrophobic]]. (LH 2011)<br />
<br />
==Introduction==<br />
A water droplet on a superhydrophobic surface has a contact angle of greater than 150 degrees and a very low roll-off angle. In nature and in man-made materials, this has been achieved with [[Structured Surfaces]]. Advantages of such surfaces include the ability to repel water and self-clean.[3] Industrial applications include "self-cleaning window glasses, paints, and textiles to low-friction surfaces for fluid flow and energy conservation."[2] To understand why water droplets wet these surfaces so poorly, one m<br />
<br />
It is argued that surface structure can produce superhydrophobic effects, even on a hydrophilic surface. For example, lotus leaves have been shown to be superhydrophobic, despite the waxy, weakly hydrophilic coating on the surface.[1] It has been demonstrated that the surface of a lotus leaf is superhydrophobic in part due to the presence of hierarchical surface structures structures consisting of micro- and nano-scale features. [2] Butterfly wings and parts of pitcher plants have observed superhydrophobic properties.<br />
<br />
==References==<br />
[1]"Design parameters for superhydrophobicity and superoleophobicity". Anish Tuteja, Wonjae Choi, Gareth H. McKinley, Robert E. Cohen, and Michael F. Rubner. MRS Bulletin 33 (8), 752-758 (August 2008)<br />
<br />
[2]"Fabrication of artificial Lotus leaves and significance of hierarchical structure for superhydrophobicity and low adhesion". Kerstin Koch, Bharat Bhushan, Yong Chae Jung and Wilhelm Barthlott. ''Soft Matter'', 2009, 5, 1386–1393.<br />
<br />
[3]"Self-cleaning materials: Lotus leaf inspired nanotechnology" Peter Forbes, ''Scientific American'' 30 July 2008.<br />
<br />
==See also==<br />
<br />
[[Effects of contact angles#Surface heterogeneity|Superhydrophobic surfaces]] in [[Effects of contact angles]] in [[Capillarity and wetting]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
==Keyword in References==<br />
<br />
[[Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity]]<br />
<br />
[[Growth of polygonal rings and wires of CuS on structured surfaces]]<br />
<br />
[[Pitcher plant inspired non-stick surface]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Superhydrophobic_surfaces&diff=23367Superhydrophobic surfaces2011-12-09T17:34:38Z<p>Lauren: </p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
Entry has been combined with [[Superhydrophobicity]], [[Superhydrophicity]] (misspelled) and [[Superhydrophobic]]. (LH 2011)<br />
<br />
==Introduction==<br />
A water droplet on a superhydrophobic surface has a contact angle of greater than 150 degrees and a very low roll-off angle. In nature and in man-made materials, this has been achieved with [[Structured Surfaces]]. Advantages of such surfaces include the ability to repel water and self-clean.[3] Industrial applications include "self-cleaning window glasses, paints, and textiles to low-friction surfaces for fluid flow and energy conservation."[2] To understand why water droplets wet these surfaces so poorly, one m<br />
<br />
It is argued that surface structure can produce superhydrophobic effects, even on a hydrophilic surface. For example, lotus leaves have been shown to be superhydrophobic, despite the waxy, weakly hydrophilic coating on the surface.[1] It has been demonstrated that the surface of a lotus leaf is superhydrophobic in part due to the presence of hierarchical surface structures structures consisting of micro- and nano-scale features. [2] Butterfly wings and parts of pitcher plants have observed superhydrophobic properties.<br />
<br />
==References==<br />
[1]"Design parameters for superhydrophobicity and superoleophobicity". Anish Tuteja, Wonjae Choi, Gareth H. McKinley, Robert E. Cohen, and Michael F. Rubner. MRS Bulletin 33 (8), 752-758 (August 2008)<br />
[2]"Fabrication of artificial Lotus leaves and significance of hierarchical structure for superhydrophobicity and low adhesion". Kerstin Koch, Bharat Bhushan, Yong Chae Jung and Wilhelm Barthlott. ''Soft Matter'', 2009, 5, 1386–1393.<br />
[3]"Self-cleaning materials: Lotus leaf inspired nanotechnology" Peter Forbes, ''Scientific American'' 30 July 2008.<br />
<br />
==See also==<br />
<br />
[[Effects of contact angles#Surface heterogeneity|Superhydrophobic surfaces]] in [[Effects of contact angles]] in [[Capillarity and wetting]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
==Keyword in References==<br />
<br />
[[Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity]]<br />
<br />
[[Growth of polygonal rings and wires of CuS on structured surfaces]]<br />
<br />
[[Pitcher plant inspired non-stick surface]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Superhydrophobic_surfaces&diff=23366Superhydrophobic surfaces2011-12-09T17:22:21Z<p>Lauren: </p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
Suggest to combine with [[Superhydrophobicity]], [[Superhydrophicity]] (misspelled) and [[Superhydrophobic]]. (LH 2011)<br />
<br />
==Definition==<br />
A superhydrophobic surface has a contact angle of greater than 150 degrees and a very low roll-off angle. In nature and in man-made materials, this has been achieved with [[Structured Surfaces]]. <br />
<br />
It is argued that surface structure can produce superhydrophobic effects, even on a hydrophilic surface. For example, lotus leaves have been shown to be superhydrophobic, despite the waxy, weakly hydrophilic coating on the surface.[1] It has been demonstrated that the surface of a lotus leaf is superhydrophobic in part due to the presence of hierarchical surface structures structures consisting of micro- and nano-scale features. [2]<br />
<br />
==References==<br />
[1]"Design parameters for superhydrophobicity and superoleophobicity". Anish Tuteja, Wonjae Choi, Gareth H. McKinley, Robert E. Cohen, and Michael F. Rubner. MRS Bulletin 33 (8), 752-758 (August 2008)<br />
[2]"Fabrication of artificial Lotus leaves and significance of hierarchical structure for superhydrophobicity and low adhesion". Kerstin Koch, Bharat Bhushan, Yong Chae Jung and Wilhelm Barthlott. ''Soft Matter'', 2009, 5, 1386–1393.<br />
<br />
<br />
==See also==<br />
<br />
[[Effects of contact angles#Surface heterogeneity|Superhydrophobic surfaces]] in [[Effects of contact angles]] in [[Capillarity and wetting]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
==Keyword in References==<br />
<br />
[[Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity]]<br />
<br />
[[Growth of polygonal rings and wires of CuS on structured surfaces]]<br />
<br />
[[Pitcher plant inspired non-stick surface]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Superhydrophobic_surfaces&diff=23365Superhydrophobic surfaces2011-12-09T16:42:07Z<p>Lauren: /* Definition */</p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
Suggest to combine with [[Superhydrophobicity]], [[Superhydrophicity]] (misspelled) and [[Superhydrophobic]]. (LH 2011)<br />
<br />
==Definition==<br />
A superhydrophobic surface has a contact angle of greater than 150 degrees.<br />
<br />
==Examples==<br />
<br />
<br />
See also:<br />
<br />
[[Effects of contact angles#Surface heterogeneity|Superhydrophobic surfaces]] in [[Effects of contact angles]] in [[Capillarity and wetting]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
==Keyword in References==<br />
<br />
[[Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity]]<br />
<br />
[[Growth of polygonal rings and wires of CuS on structured surfaces]]<br />
<br />
[[Pitcher plant inspired non-stick surface]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Superhydrophobic_surfaces&diff=23301Superhydrophobic surfaces2011-12-08T21:28:24Z<p>Lauren: </p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
Suggest to combine with [[Superhydrophobicity]], [[Superhydrophicity]] (misspelled) and [[Superhydrophobic]]. (LH 2011)<br />
<br />
==Definition==<br />
A superhydrophobic surface has a contact angle of greater<br />
<br />
==Examples==<br />
<br />
<br />
See also:<br />
<br />
[[Effects of contact angles#Surface heterogeneity|Superhydrophobic surfaces]] in [[Effects of contact angles]] in [[Capillarity and wetting]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
==Keyword in References==<br />
<br />
[[Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity]]<br />
<br />
[[Growth of polygonal rings and wires of CuS on structured surfaces]]<br />
<br />
[[Pitcher plant inspired non-stick surface]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Superhydrophobic_surfaces&diff=23300Superhydrophobic surfaces2011-12-08T21:27:17Z<p>Lauren: </p>
<hr />
<div>Entry needed. Suggest to combine with [[Superhydrophobicity]], [[Superhydrophicity]] (misspelled) and [[Superhydrophobic]]. (LH 2011)<br />
<br />
==Definition==<br />
Hydrophobicity<br />
<br />
==Examples==<br />
<br />
<br />
See also:<br />
<br />
[[Effects of contact angles#Surface heterogeneity|Superhydrophobic surfaces]] in [[Effects of contact angles]] in [[Capillarity and wetting]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
==Keyword in References==<br />
<br />
[[Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity]]<br />
<br />
[[Growth of polygonal rings and wires of CuS on structured surfaces]]<br />
<br />
[[Pitcher plant inspired non-stick surface]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Creep&diff=23287Creep2011-12-08T21:13:49Z<p>Lauren: /* Definition */</p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
==Definition==<br />
<br />
Creep is the time dependent change in [[Strain]] of a material subject to a constant [[Stress]]. Creep is distinct from [[Plastic flow]], which is often defined as time-''independent'' permanent deformation. A [[Creep test]] and [[Stress relaxation]] test attempt to quantify the same material behavior: the timescale and functional form of molecular and/or atomic rearrangement that occurs when a material is irreversibly deformed. The mechanism of creep differs depending on the material. In a crystal, mechanisms for creep include the movement of dislocations and the diffusion of atoms along grain boundaries or through grains. <br />
<br />
The general equation for describing creep is:<br />
<br />
<math> \frac{\mathrm{d}\varepsilon}{\mathrm{d}t} = \frac{C\sigma^m}{d^b} e^\frac{-Q}{kT}</math><br />
<br />
where the left hand side is the strain rate due to creep, ''Q'' is the activation energy of creep, ''d'' is the grain size, <math>\sigma</math> is the stress in the material, ''T'' is the temperature, and ''m'' and ''b'' are constants that depend on the mechanism of creep.<br />
<br />
==See also:==<br />
<br />
[[Creep of ice]], [[Creep test]]<br />
<br />
== Keyword in references: ==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]<br />
<br />
[[Stress Enhancement in the Delayed Yielding of Colloidal Gels]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Creep&diff=23286Creep2011-12-08T21:13:34Z<p>Lauren: /* Definition */</p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
==Definition==<br />
<br />
Creep is the time dependent change in [[Strain]] of a material subject to a constant [[Stress]]. Creep is distinct from [[Plastic flow]], which is often defined as time-''independent'' permanent deformation. A [[Creep test]] and [[Stress relaxation]] test attempt to quantify the same material behavior: the timescale and functional form of molecular and/or atomic rearrangement that occurs when a material is irreversibly deformed. The mechanism of creep differs depending on the material. In a crystal, mechanisms for creep include the movement of dislocations and the diffusion of atoms along grain boundaries or through grains. <br />
<br />
The general equation for describing creep is:<br />
<br />
<math> \frac{\mathrm{d}\varepsilon}{\mathrm{d}t} = \frac{C\sigma^m}{d^b} e^\frac{-Q}{kT}</math><br />
<br />
where the left hand side is the strain rate due to creep, ''Q'' is the activation energy of creep, ''d'' is the grain size, <math>\sigma</math> is the stress in the material, ''T'' is the temperature, and ''m'' and ''b'' are constants that depend on the mechanism of creep.<br />
<br />
For a general visco-elastic material, one can use one of several material<br />
<br />
==See also:==<br />
<br />
[[Creep of ice]], [[Creep test]]<br />
<br />
== Keyword in references: ==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]<br />
<br />
[[Stress Enhancement in the Delayed Yielding of Colloidal Gels]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Creep&diff=23285Creep2011-12-08T21:08:12Z<p>Lauren: </p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
==Definition==<br />
<br />
Creep is the time dependent change in [[Strain]] of a material subject to a constant [[Stress]]. Creep is distinct from [[Plastic flow]], which is often defined as time-''independent'' permanent deformation. A [[Creep test]] and [[Stress relaxation]] test attempt to quantify the same material behavior: the timescale and functional form of molecular and/or atomic rearrangement that occurs when a material is irreversibly deformed. The mechanism of creep differs depending on the material. In a crystal, mechanisms for creep include the movement of dislocations and the diffusion of atoms along grain boundaries or through grains. <br />
<br />
The general equation for describing creep is:<br />
<br />
<math> \frac{\mathrm{d}\varepsilon}{\mathrm{d}t} = \frac{C\sigma^m}{d^b} e^\frac{-Q}{kT}</math><br />
<br />
where the left hand side is the strain rate due to creep, ''Q'' is the activation energy of creep, ''d'' is the grain size, <math>\sigma</math> is the stress in the material, ''T'' is the temperature, and ''m'' and ''b'' are constants that depend on the mechanism of creep.<br />
<br />
For a general visco-elastic material, such as a polymer, <br />
==See also:==<br />
<br />
[[Creep of ice]], [[Creep test]]<br />
<br />
== Keyword in references: ==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]<br />
<br />
[[Stress Enhancement in the Delayed Yielding of Colloidal Gels]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Creep&diff=23284Creep2011-12-08T21:07:24Z<p>Lauren: </p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
==Definition==<br />
<br />
Creep is the time dependent change in [[Strain]] of a material subject to a constant [[Stress]]. Creep is distinct from [[Plastic flow]], which is often defined as time-''independent'' permanent deformation. A [[Creep test]] and [[Stress relaxation]] test attempt to quantify the same material behavior: the timescale and functional form of molecular and/or atomic rearrangement that occurs when a material is irreversibly deformed. The mechanism of creep differs depending on the material. In a crystal, mechanisms for creep include the movement of dislocations and the diffusion of atoms along grain boundaries or through grains. <br />
<br />
The general equation for describing creep is:<br />
<br />
<math> \frac{\mathrm{d}\varepsilon}{\mathrm{d}t} = \frac{C\sigma^m}{d^b} e^\frac{-Q}{kT}</math><br />
<br />
where the left hand side is the strain rate due to creep, ''Q'' is the activation energy of creep, ''d'' is the grain size, <math>\sigma</math> is the stress in the material, ''T'' is the temperature, and ''m'' and ''b'' are constants that depend on the mechanism of creep.<br />
<br />
For a general visco-elastic material, <br />
==See also:==<br />
<br />
[[Creep of ice]], [[Creep test]]<br />
<br />
== Keyword in references: ==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]<br />
<br />
[[Stress Enhancement in the Delayed Yielding of Colloidal Gels]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Creep&diff=23246Creep2011-12-08T18:45:40Z<p>Lauren: </p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
==Definition==<br />
<br />
Creep is the time dependent change in [[Strain]] of a material subject to a constant [[Stress]]. Creep is distinct from [[Plastic flow]], which is often defined as time-''independent'' permanent deformation. A [[Creep test]] and [[Stress relaxation]] test attempt to quantify the same material behavior: the timescale and functional form of molecular and/or atomic rearrangement that occurs when a material is irreversibly deformed. The mechanism of creep differs depending on the material. In a crystal, creep<br />
<br />
<br />
==See also:==<br />
<br />
[[Creep of ice]], [[Creep test]]<br />
<br />
== Keyword in references: ==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]<br />
<br />
[[Stress Enhancement in the Delayed Yielding of Colloidal Gels]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Creep&diff=23245Creep2011-12-08T18:45:13Z<p>Lauren: </p>
<hr />
<div>Started by [[Lauren Hartle]], Fall 2011.<br />
<br />
==Definition==<br />
<br />
Creep is the time dependent change in [[Strain]] of a material subject to a constant [[Stress]]. Creep is distinct from [[Plastic flow]], which is often defined as time-''independent'' permanent deformation. A [[Creep test]] and [[Stress relaxation test]] attempt to quantify the same material behavior: the timescale and functional form of molecular and/or atomic rearrangement that occurs when a material is irreversibly deformed. The mechanism of creep differs depending on the material. In a crystal, creep<br />
<br />
<br />
==See also:==<br />
<br />
[[Creep of ice]], [[Creep test]]<br />
<br />
== Keyword in references: ==<br />
<br />
[[Homogeneous flow of metallic glasses: A free volume perspective]]<br />
<br />
[[Stress Enhancement in the Delayed Yielding of Colloidal Gels]]</div>Laurenhttp://soft-matter.seas.harvard.edu/index.php?title=Glass_transition&diff=23244Glass transition2011-12-08T18:35:00Z<p>Lauren: /* Definition */</p>
<hr />
<div>Original entry: Ian Burgess, Fall 2009. Edited by [[Lauren Hartle]], Fall 2011.<br />
<br />
<br />
== Definition ==<br />
<br />
The glass transition describes the manner in which certain materials transition between the liquid and the [http://en.wikipedia.org/wiki/Glass glass] phases. The transition to a glass is marked by a solidification of the material without the addition of any long range order to the molecular packing. Unlike crystallization, there is also no discontinuous change in any thermodynamic property, and hence the transition is not, strictly speaking, a phase transition.[1] Figure 1, taken from [1], illustrates the difference between a crystalline and glassy transition. [[Image:Debenedetti_and_Stillinger_figure.png|frame|none]] Kinetics hold the key to this behavior: when a liquid is cooled faster than the timescale required for nucleation and crystallization, an amorphous solid results. The resulting material behaves mechanically like a solid on laboratory timescales, but experiences continuous, slow rearrangement moving toward its equilibrium state. The structure of some materials prohibit crystallization and hence naturally transition to a glassy state when cooled. A crystalline material can also be brought through a glass transition when the liquid state is supercooled. The precise mechanisms for this transition to solid-like behavior is not well understood.[1] The glass transition occurs at the [[Glass Transition Temperature]], <math>T_g</math>, which varies with the material and cooling rate. It should be noted that manipulating pressure, independent of temperature, can produce a glass transition.<br />
<br />
==Specific Examples==<br />
''Polymers:'' In polymers above the glass transition temperature, chains have sufficient mobility to slide past each other and reconfigure under an applied stress. This mobility is substantially reduced below the glass transition. However, at temperatures above the glass transition, but below the melting point, polymers still have a finite stiffness.<br />
''Common Materials:'' Silica, commonly used to make windows and other commercial glass products, experiences a glass transition.<br />
<br />
''Metallic Glasses:'' See [[Metallic glasses]].<br />
<br />
==See also:==<br />
<br />
[[Polymer molecules#Glass transition|Polymers - Glass transitions]] in [[Polymer molecules]] in [[Polymers and polymer solutions]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
[[Phases and Phase Diagrams#Definitions|Glass transition]] in [[Phases and Phase Diagrams]] from [[Main Page#Lectures for AP225|Lectures for AP225]].<br />
<br />
== References ==<br />
<br />
[1] Debenedetti and F. H. Stillinger. "Supercooled liquids and the glass transition". ''Nature'', Vol 410, 8 March 2001.<br />
<br />
[2] Z. Fakhraai and J. A. Forrest, "Measuring the Surface Dynamics of Glassy Polymers" Science 319, 600 (2008). <br />
<br />
[3] Kingery, W,D., Bowen, H.K., and Uhlmann, D.R., Introduction to Ceramics, 2nd Edn. (John Wiley & Sons, New York, 2006).</div>Lauren