http://soft-matter.seas.harvard.edu/api.php?action=feedcontributions&user=Datta&feedformat=atomSoft-Matter - User contributions [en]2022-12-03T08:16:32ZUser contributionsMediaWiki 1.24.2http://soft-matter.seas.harvard.edu/index.php?title=Bulk_modulus&diff=13318Bulk modulus2009-11-30T04:38:45Z<p>Datta: </p>
<hr />
<div>The bulk (or compressional) modulus K of a material is a measure of its resistance to uniform compression. Similar to an inverse compressibility, it can be derived from the osmotic pressure <math>\Pi</math> of a sample as a function of the volume fraction <math>\phi</math> via <math>K=\phi\cdot d\Pi/d\phi</math>.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Bulk_modulus&diff=13305Bulk modulus2009-11-30T04:01:40Z<p>Datta: </p>
<hr />
<div>The bulk (or compressional) modulus K of a material is a measure of its resistance to uniform compression. Similar to a compressibility, it can be derived from the osmotic pressure <math>\Pi</math> of a sample as a function of the volume fraction <math>\phi</math> via <math>K=\phi\cdot d\Pi/d\phi</math>.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Sujit_Sankar_Datta&diff=13303Sujit Sankar Datta2009-11-30T03:57:37Z<p>Datta: </p>
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<div>'''Definitions:'''<br />
<br />
[[Percolation]]<br />
<br />
[[Coalescence]]<br />
<br />
[[Splashing]]<br />
<br />
[[Rigidity]]<br />
<br />
[[Pickering emulsion]]<br />
<br />
[[Quasicrystal]]<br />
<br />
[[Wigner crystal]]<br />
<br />
[[Critical Casimir effect]]<br />
<br />
[[Bulk modulus]]<br />
<br />
<br />
<br />
'''Weekly wiki entries:'''<br />
<br />
[[Strain-Rate Frequency Superposition: A Rheological Probe of Structural Relaxation in Soft Materials]]<br />
<br />
[[Non-coalescence of oppositely charged drops]]<br />
<br />
[[Making a splash with water repellency]]<br />
<br />
[[The packing of granular polymer chains]]<br />
<br />
[[Limited coalescence]]<br />
<br />
[[Quasicrystalline order in self-assembled binary nanoparticle superlattices]]<br />
<br />
[[Electrostatics at the oil–water interface, stability, and order in emulsions and colloids]]<br />
<br />
[[Direct observation of colloidal aggregation by critical casimir forces]]<br />
<br />
[[Elasticity of compressed emulsions]]</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Bulk_modulus&diff=13301Bulk modulus2009-11-30T03:57:04Z<p>Datta: New page: The bulk modulus K of a material is a measure of its resistance to uniform compression. Similar to a compressibility, it can be derived from the osmotic pressure <math>\Pi</math> of a samp...</p>
<hr />
<div>The bulk modulus K of a material is a measure of its resistance to uniform compression. Similar to a compressibility, it can be derived from the osmotic pressure <math>\Pi</math> of a sample as a function of the volume fraction <math>\phi</math> via <math>K=\phi\cdot d\Pi/d\phi</math>.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Elasticity_of_compressed_emulsions&diff=13297Elasticity of compressed emulsions2009-11-30T03:55:02Z<p>Datta: </p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
T. G. Mason, J. Bibette, and D. A. Weitz, ''PRL'' '''75,''' 2051 (1995). <br />
<br />
T. G. Mason, M. D. Lacasse, G. S. Grest, D. Levine, J. Bibette, and D. A. Weitz, ''PRE'' '''56,''' 3150 (1997).<br />
<br />
== Keywords ==<br />
<br />
[[emulsions]], osmotic pressure, [[rigidity percolation]], shear modulus, [[bulk modulus]], rheology, [[jamming]]<br />
<br />
== Key Points ==<br />
<br />
An emulsion is a metastable suspension of droplets of one fluid within another fluid, with the two fluids being immiscible. Emulsion droplets are stabilized against coalescence upon contact by a range of surfactants; typically, surfactants are ionic, imparting stability due to electrostatic repulsions at the droplet interfaces. <br />
<br />
For low volume fractions, a Brownian emulsion is liquid-like; as the volume fraction of droplets increases, the viscosity of the emulsion may diverge (at the colloidal glass transition, volume fraction ~ 58%), similar to a hard-sphere suspension. However, while a disordered hard-sphere suspension can only be packed up to a maximum volume fraction of 64% (random close packing), a disordered emulsion can be packed past random close packing, due to the deformability of the emulsion droplets. When the droplets first begin to touch (at random close packing), the system 'jams': it becomes solid-like, and develops an elastic modulus. <br />
<br />
A good deal of work in the past decade has focused on understanding this jamming transition, in a variety of ways. This set of papers were among the first to provide quantitative data motivating current ideas on jamming. In them, Mason et al. describe very systematic experiments on disordered, Brownian oil-in-water emulsions stabilized by an ionic surfactant, providing two measures of the elasticity of the emulsion (the bulk modulus, a measure of the material's resistance to uniform compression, and the shear modulus, a measure of the material's resistance to uniform shear) as the emulsions are compressed, and the volume fraction is increased from below random close packing up to nearly 100% (the limit of a biliquid foam). The bulk modulus K is measured by measuring the osmotic pressure <math>\Pi</math> of the emulsion as a function of the volume fraction (K is defined as <math>\phi\cdot d\Pi/d\phi</math>); experimentally, the osmotic pressure of a sample is set using dialysis, and the corresponding volume fraction is measured by evaporating off the water. The zero-frequency shear modulus is measured using linear rheology; Mason et al. find that the linear elastic modulus G' plateaus at low frequencies, consistent with other [[soft glass]]es, and use this value (G'p) as the zero-frequency shear modulus.<br />
<br />
These experiments yielded a number of key results:<br />
<br />
* Both bulk modulus and shear modulus measurements for droplets of different sizes collapsed onto a single dataset when rescaled by the Laplace pressure, <math>\sigma/r</math>, where <math>\sigma</math> is the interfacial tension between the two phases and r is the droplet radius. This shows that the emulsion elasticity is set by the Laplace pressure, and is purely due to energy storage in the interfaces of the deformed droplets.<br />
* As a function of volume fraction <math>\phi>\phi_{RCP}</math>, <math>G'_{p}\sim \phi\cdot(\phi-\phi_{RCP})</math> and <math>K\sim \phi^2+\phi\cdot(\phi-\phi_{RCP})</math>. This has a number of important implications:<br />
**The scaling of G' near random close packing is reminiscent of scaling near a critical point. This observation has motivated a good deal of recent theories of jamming that treat it as a critical phenomenon.<br />
**The onset of the shear modulus at random close packing is gradual, while the onset of the bulk modulus at random close packing is very sharp. This is very surprising -- two measures of the elasticity of compressed emulsions have very different behavior as a function of the volume fraction. Mason et al. explain this with the help of numerical simulations. They suggest that the shear modulus is much smaller than the bulk modulus because (i) the droplet structure is disordered, (ii) the droplets are 'slippery' -- they slide over each other without friction. As a result, when subjected to shear, 'pockets' form in the disordered droplet structure at which most of the shear stress is relieved: this weakens the material in shear and makes the shear modulus much smaller than the bulk modulus.<br />
<br />
While practical applications of this work are not immediately clear, the fundamental implications are profound: these experiments and simulations motivated much of the current work on jamming, and highlight the importance of inter-droplet interactions and disorder in determining the elasticity of compressed emulsions.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Elasticity_of_compressed_emulsions&diff=13295Elasticity of compressed emulsions2009-11-30T03:54:28Z<p>Datta: </p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
T. G. Mason, J. Bibette, and D. A. Weitz, ''PRL'' '''75,''' 2051 (1995). <br />
<br />
T. G. Mason, M. D. Lacasse, G. S. Grest, D. Levine, J. Bibette, and D. A. Weitz, ''PRE'' '''56,''' 3150 (1997).<br />
<br />
== Keywords ==<br />
<br />
[[emulsions]], osmotic pressure, [[rigidity percolation]], shear modulus, rheology, [[jamming]]<br />
<br />
== Key Points ==<br />
<br />
An emulsion is a metastable suspension of droplets of one fluid within another fluid, with the two fluids being immiscible. Emulsion droplets are stabilized against coalescence upon contact by a range of surfactants; typically, surfactants are ionic, imparting stability due to electrostatic repulsions at the droplet interfaces. <br />
<br />
For low volume fractions, a Brownian emulsion is liquid-like; as the volume fraction of droplets increases, the viscosity of the emulsion may diverge (at the colloidal glass transition, volume fraction ~ 58%), similar to a hard-sphere suspension. However, while a disordered hard-sphere suspension can only be packed up to a maximum volume fraction of 64% (random close packing), a disordered emulsion can be packed past random close packing, due to the deformability of the emulsion droplets. When the droplets first begin to touch (at random close packing), the system 'jams': it becomes solid-like, and develops an elastic modulus. <br />
<br />
A good deal of work in the past decade has focused on understanding this jamming transition, in a variety of ways. This set of papers were among the first to provide quantitative data motivating current ideas on jamming. In them, Mason et al. describe very systematic experiments on disordered, Brownian oil-in-water emulsions stabilized by an ionic surfactant, providing two measures of the elasticity of the emulsion (the bulk modulus, a measure of the material's resistance to uniform compression, and the shear modulus, a measure of the material's resistance to uniform shear) as the emulsions are compressed, and the volume fraction is increased from below random close packing up to nearly 100% (the limit of a biliquid foam). The bulk modulus K is measured by measuring the osmotic pressure <math>\Pi</math> of the emulsion as a function of the volume fraction (K is defined as <math>\phi\cdot d\Pi/d\phi</math>); experimentally, the osmotic pressure of a sample is set using dialysis, and the corresponding volume fraction is measured by evaporating off the water. The zero-frequency shear modulus is measured using linear rheology; Mason et al. find that the linear elastic modulus G' plateaus at low frequencies, consistent with other [[soft glass]]es, and use this value (G'p) as the zero-frequency shear modulus.<br />
<br />
These experiments yielded a number of key results:<br />
<br />
* Both bulk modulus and shear modulus measurements for droplets of different sizes collapsed onto a single dataset when rescaled by the Laplace pressure, <math>\sigma/r</math>, where <math>\sigma</math> is the interfacial tension between the two phases and r is the droplet radius. This shows that the emulsion elasticity is set by the Laplace pressure, and is purely due to energy storage in the interfaces of the deformed droplets.<br />
* As a function of volume fraction <math>\phi>\phi_{RCP}</math>, <math>G'_{p}\sim \phi\cdot(\phi-\phi_{RCP})</math> and <math>K\sim \phi^2+\phi\cdot(\phi-\phi_{RCP})</math>. This has a number of important implications:<br />
**The scaling of G' near random close packing is reminiscent of scaling near a critical point. This observation has motivated a good deal of recent theories of jamming that treat it as a critical phenomenon.<br />
**The onset of the shear modulus at random close packing is gradual, while the onset of the bulk modulus at random close packing is very sharp. This is very surprising -- two measures of the elasticity of compressed emulsions have very different behavior as a function of the volume fraction. Mason et al. explain this with the help of numerical simulations. They suggest that the shear modulus is much smaller than the bulk modulus because (i) the droplet structure is disordered, (ii) the droplets are 'slippery' -- they slide over each other without friction. As a result, when subjected to shear, 'pockets' form in the disordered droplet structure at which most of the shear stress is relieved: this weakens the material in shear and makes the shear modulus much smaller than the bulk modulus.<br />
<br />
While practical applications of this work are not immediately clear, the fundamental implications are profound: these experiments and simulations motivated much of the current work on jamming, and highlight the importance of inter-droplet interactions and disorder in determining the elasticity of compressed emulsions.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Elasticity_of_compressed_emulsions&diff=13294Elasticity of compressed emulsions2009-11-30T03:53:48Z<p>Datta: </p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
T. G. Mason, J. Bibette, and D. A. Weitz, ''PRL'' '''75,''' 2051 (1995). <br />
<br />
T. G. Mason, M. D. Lacasse, G. S. Grest, D. Levine, J. Bibette, and D. A. Weitz, ''PRE'' '''56,''' 3150 (1997).<br />
<br />
== Keywords ==<br />
<br />
[[emulsions]], osmotic pressure, rigidity percolation, shear modulus, rheology, [[jamming]]<br />
<br />
== Key Points ==<br />
<br />
An emulsion is a metastable suspension of droplets of one fluid within another fluid, with the two fluids being immiscible. Emulsion droplets are stabilized against coalescence upon contact by a range of surfactants; typically, surfactants are ionic, imparting stability due to electrostatic repulsions at the droplet interfaces. <br />
<br />
For low volume fractions, a Brownian emulsion is liquid-like; as the volume fraction of droplets increases, the viscosity of the emulsion may diverge (at the colloidal glass transition, volume fraction ~ 58%), similar to a hard-sphere suspension. However, while a disordered hard-sphere suspension can only be packed up to a maximum volume fraction of 64% (random close packing), a disordered emulsion can be packed past random close packing, due to the deformability of the emulsion droplets. When the droplets first begin to touch (at random close packing), the system 'jams': it becomes solid-like, and develops an elastic modulus. <br />
<br />
A good deal of work in the past decade has focused on understanding this jamming transition, in a variety of ways. This set of papers were among the first to provide quantitative data motivating current ideas on jamming. In them, Mason et al. describe very systematic experiments on disordered, Brownian oil-in-water emulsions stabilized by an ionic surfactant, providing two measures of the elasticity of the emulsion (the bulk modulus, a measure of the material's resistance to uniform compression, and the shear modulus, a measure of the material's resistance to uniform shear) as the emulsions are compressed, and the volume fraction is increased from below random close packing up to nearly 100% (the limit of a biliquid foam). The bulk modulus K is measured by measuring the osmotic pressure <math>\Pi</math> of the emulsion as a function of the volume fraction (K is defined as <math>\phi\cdot d\Pi/d\phi</math>); experimentally, the osmotic pressure of a sample is set using dialysis, and the corresponding volume fraction is measured by evaporating off the water. The zero-frequency shear modulus is measured using linear rheology; Mason et al. find that the linear elastic modulus G' plateaus at low frequencies, consistent with other [[soft glass]]es, and use this value (G'p) as the zero-frequency shear modulus.<br />
<br />
These experiments yielded a number of key results:<br />
<br />
* Both bulk modulus and shear modulus measurements for droplets of different sizes collapsed onto a single dataset when rescaled by the Laplace pressure, <math>\sigma/r</math>, where <math>\sigma</math> is the interfacial tension between the two phases and r is the droplet radius. This shows that the emulsion elasticity is set by the Laplace pressure, and is purely due to energy storage in the interfaces of the deformed droplets.<br />
* As a function of volume fraction <math>\phi>\phi_{RCP}</math>, <math>G'_{p}\sim \phi\cdot(\phi-\phi_{RCP})</math> and <math>K\sim \phi^2+\phi\cdot(\phi-\phi_{RCP})</math>. This has a number of important implications:<br />
**The scaling of G' near random close packing is reminiscent of scaling near a critical point. This observation has motivated a good deal of recent theories of jamming that treat it as a critical phenomenon.<br />
**The onset of the shear modulus at random close packing is gradual, while the onset of the bulk modulus at random close packing is very sharp. This is very surprising -- two measures of the elasticity of compressed emulsions have very different behavior as a function of the volume fraction. Mason et al. explain this with the help of numerical simulations. They suggest that the shear modulus is much smaller than the bulk modulus because (i) the droplet structure is disordered, (ii) the droplets are 'slippery' -- they slide over each other without friction. As a result, when subjected to shear, 'pockets' form in the disordered droplet structure at which most of the shear stress is relieved: this weakens the material in shear and makes the shear modulus much smaller than the bulk modulus.<br />
<br />
While practical applications of this work are not immediately clear, the fundamental implications are profound: these experiments and simulations motivated much of the current work on jamming, and highlight the importance of inter-droplet interactions and disorder in determining the elasticity of compressed emulsions.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Elasticity_of_compressed_emulsions&diff=13293Elasticity of compressed emulsions2009-11-30T03:52:22Z<p>Datta: </p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
T. G. Mason, J. Bibette, and D. A. Weitz, ''PRL'' '''75,''' 2051 (1995). <br />
<br />
T. G. Mason, M. D. Lacasse, G. S. Grest, D. Levine, J. Bibette, and D. A. Weitz, ''PRE'' '''56,''' 3150 (1997).<br />
<br />
== Keywords ==<br />
<br />
[[emulsions]], osmotic pressure, rigidity percolation, shear modulus, rheology, [[jamming]]<br />
<br />
== Key Points ==<br />
<br />
An emulsion is a metastable suspension of droplets of one fluid within another fluid, with the two fluids being immiscible. Emulsion droplets are stabilized against coalescence upon contact by a range of surfactants; typically, surfactants are ionic, imparting stability due to electrostatic repulsions at the droplet interfaces. <br />
<br />
For low volume fractions, a Brownian emulsion is liquid-like; as the volume fraction of droplets increases, the viscosity of the emulsion may diverge (at the colloidal glass transition, volume fraction ~ 58%), similar to a hard-sphere suspension. However, while a disordered hard-sphere suspension can only be packed up to a maximum volume fraction of 64% (random close packing), a disordered emulsion can be packed past random close packing, due to the deformability of the emulsion droplets. When the droplets first begin to touch (at random close packing), the system 'jams': it becomes solid-like, and develops an elastic modulus. <br />
<br />
A good deal of work in the past decade has focused on understanding this jamming transition, in a variety of ways. This set of papers were among the first to provide quantitative data motivating current ideas on jamming. In them, Mason et al. describe very systematic experiments on disordered, Brownian oil-in-water emulsions stabilized by an ionic surfactant, providing two measures of the elasticity of the emulsion (the bulk modulus, a measure of the material's resistance to uniform compression, and the shear modulus, a measure of the material's resistance to uniform shear) as the emulsions are compressed, and the volume fraction is increased from below random close packing up to nearly 100% (the limit of a biliquid foam). The bulk modulus K is measured by measuring the osmotic pressure <math>\Pi</math> of the emulsion as a function of the volume fraction (K is defined as <math>\phi\cdot d\Pi/d\phi</math>); experimentally, the osmotic pressure of a sample is set using dialysis, and the corresponding volume fraction is measured by evaporating off the water. The zero-frequency shear modulus is measured using linear rheology; Mason et al. find that the linear elastic modulus G' plateaus at low frequencies, consistent with other [[soft glass]]es, and use this value (G'p) as the zero-frequency shear modulus.<br />
<br />
These experiments yielded a number of key results:<br />
<br />
* Both bulk modulus and shear modulus measurements for droplets of different sizes collapsed onto a single dataset when rescaled by the Laplace pressure, <math>\sigma/r</math>, where <math>\sigma</math> is the interfacial tension between the two phases and r is the droplet radius. This shows that the emulsion elasticity is set by the Laplace pressure, and is purely due to energy storage in the interfaces of the deformed droplets.<br />
* As a function of volume fraction <math>\phi>\phi_{RCP}</math>, <math>G'_{p}\sim \phi\cdot(\phi-\phi_{RCP})</math> and <math>K\sim \phi^2+\phi\cdot(\phi-\phi_{RCP})</math>. This has a number of important implications:<br />
**The scaling of G' near random close packing is reminiscent of scaling near a critical point. This observation has motivated a good deal of recent theories of jamming that treat it as a critical phenomenon.<br />
**The onset of the shear modulus at random close packing is gradual, while the onset of the bulk modulus at random close packing is very sharp. This is very surprising -- two measures of the elasticity of compressed emulsions have very different behavior as a function of the volume fraction. Mason et al. explain this with the help of numerical simulations. They suggest that the shear modulus is much smaller than the bulk modulus because (i) the droplet structure is disordered, (ii) the droplets are 'slippery' -- they slide over each other without friction. As a result, when subjected to shear, 'pockets' form in the disordered droplet structure at which most of the shear stress is relieved: this weakens the material in shear and makes the shear modulus much smaller than the bulk modulus.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Elasticity_of_compressed_emulsions&diff=13291Elasticity of compressed emulsions2009-11-30T03:45:23Z<p>Datta: </p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
T. G. Mason, J. Bibette, and D. A. Weitz, ''PRL'' '''75,''' 2051 (1995). <br />
<br />
T. G. Mason, M. D. Lacasse, G. S. Grest, D. Levine, J. Bibette, and D. A. Weitz, ''PRE'' '''56,''' 3150 (1997).<br />
<br />
== Keywords ==<br />
<br />
[[emulsions]], osmotic pressure, rigidity percolation, shear modulus, rheology, [[jamming]]<br />
<br />
== Key Points ==<br />
<br />
An emulsion is a metastable suspension of droplets of one fluid within another fluid, with the two fluids being immiscible. Emulsion droplets are stabilized against coalescence upon contact by a range of surfactants; typically, surfactants are ionic, imparting stability due to electrostatic repulsions at the droplet interfaces. <br />
<br />
For low volume fractions, a Brownian emulsion is liquid-like; as the volume fraction of droplets increases, the viscosity of the emulsion may diverge (at the colloidal glass transition, volume fraction ~ 58%), similar to a hard-sphere suspension. However, while a disordered hard-sphere suspension can only be packed up to a maximum volume fraction of 64% (random close packing), a disordered emulsion can be packed past random close packing, due to the deformability of the emulsion droplets. When the droplets first begin to touch (at random close packing), the system 'jams': it becomes solid-like, and develops an elastic modulus. <br />
<br />
A good deal of work in the past decade has focused on understanding this jamming transition, in a variety of ways. This set of papers were among the first to provide quantitative data motivating current ideas on jamming. In them, Mason et al. describe very systematic experiments on disordered, Brownian oil-in-water emulsions stabilized by an ionic surfactant, providing two measures of the elasticity of the emulsion (the bulk modulus, a measure of the material's resistance to uniform compression, and the shear modulus, a measure of the material's resistance to uniform shear) as the emulsions are compressed, and the volume fraction is increased from below random close packing up to nearly 100% (the limit of a biliquid foam). The bulk modulus K is measured by measuring the osmotic pressure <math>\Pi</math> of the emulsion as a function of the volume fraction (K is defined as <math>\phi\cdot d\Pi/d\phi</math>); experimentally, the osmotic pressure of a sample is set using dialysis, and the corresponding volume fraction is measured by evaporating off the water. The zero-frequency shear modulus is measured using linear rheology; Mason et al. find that the linear elastic modulus G' plateaus at low frequencies, consistent with other [[soft glass]]es, and use this value (G'p) as the zero-frequency shear modulus.<br />
<br />
These experiments yielded a number of key results:<br />
<br />
* Both bulk modulus and shear modulus measurements for droplets of different sizes collapsed onto a single dataset when rescaled by the Laplace pressure, <math>\sigma/r</math>, where <math>\sigma</math> is the interfacial tension between the two phases and r is the droplet radius. This shows that the emulsion elasticity is set by the Laplace pressure, and is purely due to energy storage in the interfaces of the deformed droplets.<br />
* As a function of volume fraction <math>\phi>\phi_{RCP}</math>, <math>G'_{p}\sim \phi\cdot(\phi-\phi_{RCP})</math> and <math>K\sim \phi^2+\phi\cdot(\phi-\phi_{RCP})</math>. This has a number of important implications:<br />
**The scaling of G' near random close packing is reminiscent of scaling near a critical point. This observation has motivated a good deal of recent theories of jamming that treat it as a critical phenomenon.<br />
**The onset of the shear modulus at random close packing is gradual, while the onset of the bulk modulus at random close packing is very sharp.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Elasticity_of_compressed_emulsions&diff=13289Elasticity of compressed emulsions2009-11-30T03:40:59Z<p>Datta: </p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
T. G. Mason, J. Bibette, and D. A. Weitz, ''PRL'' '''75,''' 2051 (1995). <br />
<br />
T. G. Mason, M. D. Lacasse, G. S. Grest, D. Levine, J. Bibette, and D. A. Weitz, ''PRE'' '''56,''' 3150 (1997).<br />
<br />
== Keywords ==<br />
<br />
[[emulsions]], osmotic pressure, rigidity percolation, shear modulus, rheology<br />
<br />
== Key Points ==<br />
<br />
An emulsion is a metastable suspension of droplets of one fluid within another fluid, with the two fluids being immiscible. Emulsion droplets are stabilized against coalescence upon contact by a range of surfactants; typically, surfactants are ionic, imparting stability due to electrostatic repulsions at the droplet interfaces. <br />
<br />
For low volume fractions, a Brownian emulsion is liquid-like; as the volume fraction of droplets increases, the viscosity of the emulsion may diverge (at the colloidal glass transition, volume fraction ~ 58%), similar to a hard-sphere suspension. However, while a disordered hard-sphere suspension can only be packed up to a maximum volume fraction of 64% (random close packing), a disordered emulsion can be packed past random close packing, due to the deformability of the emulsion droplets. When the droplets first begin to touch (at random close packing), the system 'jams': it becomes solid-like, and develops an elastic modulus. <br />
<br />
A good deal of work in the past decade has focused on understanding this jamming transition, in a variety of ways. This set of papers were among the first to provide quantitative data motivating current ideas on jamming. In them, Mason et al. describe very systematic experiments on disordered, Brownian oil-in-water emulsions stabilized by an ionic surfactant, providing two measures of the elasticity of the emulsion (the bulk modulus, a measure of the material's resistance to uniform compression, and the shear modulus, a measure of the material's resistance to uniform shear) as the emulsions are compressed, and the volume fraction is increased from below random close packing up to nearly 100% (the limit of a biliquid foam). The bulk modulus K is measured by measuring the osmotic pressure <math>\Pi</math> of the emulsion as a function of the volume fraction (K is defined as <math>\phi\cdot d\Pi/d\phi</math>); experimentally, the osmotic pressure of a sample is set using dialysis, and the corresponding volume fraction is measured by evaporating off the water. The zero-frequency shear modulus is measured using linear rheology; Mason et al. find that the linear elastic modulus G' plateaus at low frequencies, consistent with other [[soft glass]]es, and use this value (G'p) as the zero-frequency shear modulus.<br />
<br />
These experiments yielded a number of key results:<br />
<br />
* Both bulk modulus and shear modulus measurements for droplets of different sizes collapsed onto a single dataset when rescaled by the Laplace pressure, <math>\sigma/r</math>, where <math>\sigma</math> is the interfacial tension between the two phases and r is the droplet radius. This shows that the emulsion elasticity is set by the Laplace pressure, and is purely due to energy storage in the interfaces of the deformed droplets.<br />
* As a function of volume fraction <math>\phi>\phi_{RCP}</math>, <math>G'_{p}\sim \phi\cdot(\phi-\phi_{RCP})</math> and <math>K\sim \phi^2+\phi\cdot(\phi-\phi_{RCP})</math></div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Elasticity_of_compressed_emulsions&diff=13278Elasticity of compressed emulsions2009-11-30T03:15:47Z<p>Datta: </p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
T. G. Mason, J. Bibette, and D. A. Weitz, ''PRL'' '''75,''' 2051 (1995). <br />
<br />
T. G. Mason, M. D. Lacasse, G. S. Grest, D. Levine, J. Bibette, and D. A. Weitz, ''PRE'' '''56,''' 3150 (1997).<br />
<br />
== Keywords ==<br />
<br />
[[emulsions]], osmotic pressure, rigidity percolation, shear modulus, rheology<br />
<br />
== Key Points ==<br />
<br />
Test</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Elasticity_of_compressed_emulsions&diff=13277Elasticity of compressed emulsions2009-11-30T03:15:39Z<p>Datta: New page: Original entry: Sujit S. Datta, APPHY 225, Fall 2009. == Reference == T. G. Mason, J. Bibette, and D. A. Weitz, ''PRL'' '''75,''' 2051 (1995). T. G. Mason, M. D. Lacasse, G. S. Grest...</p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
T. G. Mason, J. Bibette, and D. A. Weitz, ''PRL'' '''75,''' 2051 (1995). <br />
T. G. Mason, M. D. Lacasse, G. S. Grest, D. Levine, J. Bibette, and D. A. Weitz, ''PRE'' '''56,''' 3150 (1997).<br />
<br />
== Keywords ==<br />
<br />
[[emulsions]], osmotic pressure, rigidity percolation, shear modulus, rheology<br />
<br />
== Key Points ==<br />
<br />
Test</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Sujit_Sankar_Datta&diff=13027Sujit Sankar Datta2009-11-24T01:38:33Z<p>Datta: </p>
<hr />
<div>'''Definitions:'''<br />
<br />
[[Percolation]]<br />
<br />
[[Coalescence]]<br />
<br />
[[Splashing]]<br />
<br />
[[Rigidity]]<br />
<br />
[[Pickering emulsion]]<br />
<br />
[[Quasicrystal]]<br />
<br />
[[Wigner crystal]]<br />
<br />
[[Critical Casimir effect]]<br />
<br />
<br />
<br />
'''Weekly wiki entries:'''<br />
<br />
[[Strain-Rate Frequency Superposition: A Rheological Probe of Structural Relaxation in Soft Materials]]<br />
<br />
[[Non-coalescence of oppositely charged drops]]<br />
<br />
[[Making a splash with water repellency]]<br />
<br />
[[The packing of granular polymer chains]]<br />
<br />
[[Limited coalescence]]<br />
<br />
[[Quasicrystalline order in self-assembled binary nanoparticle superlattices]]<br />
<br />
[[Electrostatics at the oil–water interface, stability, and order in emulsions and colloids]]<br />
<br />
[[Direct observation of colloidal aggregation by critical casimir forces]]</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Sujit_Sankar_Datta&diff=13026Sujit Sankar Datta2009-11-24T01:38:18Z<p>Datta: </p>
<hr />
<div>Definitions:<br />
<br />
[[Percolation]]<br />
<br />
[[Coalescence]]<br />
<br />
[[Splashing]]<br />
<br />
[[Rigidity]]<br />
<br />
[[Pickering emulsion]]<br />
<br />
[[Quasicrystal]]<br />
<br />
[[Wigner crystal]]<br />
<br />
[[Critical Casimir effect]]<br />
<br />
Weekly wiki entries:<br />
<br />
[[Strain-Rate Frequency Superposition: A Rheological Probe of Structural Relaxation in Soft Materials]]<br />
<br />
[[Non-coalescence of oppositely charged drops]]<br />
<br />
[[Making a splash with water repellency]]<br />
<br />
[[The packing of granular polymer chains]]<br />
<br />
[[Limited coalescence]]<br />
<br />
[[Quasicrystalline order in self-assembled binary nanoparticle superlattices]]<br />
<br />
[[Electrostatics at the oil–water interface, stability, and order in emulsions and colloids]]<br />
<br />
[[Direct observation of colloidal aggregation by critical casimir forces]]</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Critical_Casimir_effect&diff=13025Critical Casimir effect2009-11-24T01:38:00Z<p>Datta: </p>
<hr />
<div>In analogy to the quantum Casimir effect, in which two uncharged dielectric plates in a vacuum can attract or repel each other due to zero-point fluctuations of the quantized electromagnetic field, the critical Casimir effect describes the possibility of attractive or repulsive forces between two surfaces due to confined density or concentration fluctuations. This effect occurs when the lengthscale <math>\xi</math> of these fluctuations is on the order of the separation between the two surfaces; while this lengthscale is typically very small, it can often be relevant to colloidal systems -- for example, for colloidal particles suspended in a binary mixture near its critical point, at which <math>\xi</math> can be very large.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Critical_Casimir_effect&diff=13024Critical Casimir effect2009-11-24T01:37:25Z<p>Datta: New page: In analogy to the quantum Casimir effect, in which two uncharged dielectric plates in a vacuum can attract or repel each other due to zero-point fluctuations of the quantized electromagnet...</p>
<hr />
<div>In analogy to the quantum Casimir effect, in which two uncharged dielectric plates in a vacuum can attract or repel each other due to zero-point fluctuations of the quantized electromagnetic field, the critical Casimir effect describes the possibility of attractive or repulsive forces between two surfaces due to confined density or concentration fluctuations. This effect occurs when the lengthscale <math>\xi</math> of these fluctuations is on the order of the separation between the two surfaces; while this lengthscale is typically very small, it can often be relevant to colloidal systems. This paper discusses the first direct observation of colloidal aggregation and disaggregation by tuning the critical Casimir effect.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Direct_observation_of_colloidal_aggregation_by_critical_casimir_forces&diff=13023Direct observation of colloidal aggregation by critical casimir forces2009-11-24T01:37:08Z<p>Datta: </p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
D. Bonn, J. Otwinowski, S. Sacanna, H. Guo, G. Wegdam, and P. Schall, ''PRL'' '''103,''' 156101 (2009).<br />
<br />
== Keywords ==<br />
<br />
[[critical Casimir effect]], flocculation, colloidal stability<br />
<br />
== Key Points ==<br />
<br />
In analogy to the quantum Casimir effect, in which two uncharged dielectric plates in a vacuum can attract or repel each other due to zero-point fluctuations of the quantized electromagnetic field, the critical Casimir effect describes the possibility of attractive or repulsive forces between two surfaces due to confined density or concentration fluctuations. This effect occurs when the lengthscale <math>\xi</math> of these fluctuations is on the order of the separation between the two surfaces; while this lengthscale is typically very small, it can often be relevant to colloidal systems. This paper discusses the first direct observation of colloidal aggregation and disaggregation by tuning the critical Casimir effect. <br />
<br />
Bonn et al. study a refractive index-matched suspension of colloidal latex particles in a binary mixture of water and the organic compound 3-methylpyridine. The index match of the system allows the microstructure of the system to be studied dynamically using confocal microscopy. The particular mixture is used because by tuning the composition and temperature of the system, one can approach a critical point between having a homogeneous mixture and undergoing phase separation. As with critical points in general, this point involves a very large correlation length <math>\xi</math> -- thus making the critical Casimir effect strong enough to observe. <br />
<br />
Indeed, Bonn et al. find that, for a suitable composition of the binary mixture, upon increasing the temperature close to the critical point, the colloidal particles -- which previously were stably suspended due to their charge -- aggregated and sedimented out of solution. Importantly, this process was reversible. Confocal microscopy analysis suggests that this aggregation process occurs by diffusion-limited cluster aggregation.<br />
<br />
The most straightforward explanation for this effect is due to competition between the attractive critical Casimir effect, and a "typical" screened Coulomb repulsion. Bonn et al. test this hypothesis by altering the salt concentration in their system, thus tuning the Debye length; this leads to a quantitative prediction of the interparticle interaction potential, in agreement with the superposition of an attractive Casimir force and a screened Coulomb repulsion. <br />
<br />
While this work is interesting on purely fundamental grounds -- it directly studies the effect of critical Casimir interactions in colloidal systems -- it may also have potential applications in systems of colloidal particles suspended in binary mixtures, in which Casimir interactions may be important, and may be tuned to have a stabilizing or destabilizing effect.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Direct_observation_of_colloidal_aggregation_by_critical_casimir_forces&diff=13022Direct observation of colloidal aggregation by critical casimir forces2009-11-24T01:36:57Z<p>Datta: </p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
D. Bonn, J. Otwinowski, S. Sacanna, H. Guo, G. Wegdam, and P. Schall, ''PRL'' '''103,''' 156101 (2009).<br />
<br />
== Keywords ==<br />
<br />
critical Casimir force, flocculation, colloidal stability<br />
<br />
== Key Points ==<br />
<br />
In analogy to the quantum Casimir effect, in which two uncharged dielectric plates in a vacuum can attract or repel each other due to zero-point fluctuations of the quantized electromagnetic field, the critical Casimir effect describes the possibility of attractive or repulsive forces between two surfaces due to confined density or concentration fluctuations. This effect occurs when the lengthscale <math>\xi</math> of these fluctuations is on the order of the separation between the two surfaces; while this lengthscale is typically very small, it can often be relevant to colloidal systems. This paper discusses the first direct observation of colloidal aggregation and disaggregation by tuning the critical Casimir effect. <br />
<br />
Bonn et al. study a refractive index-matched suspension of colloidal latex particles in a binary mixture of water and the organic compound 3-methylpyridine. The index match of the system allows the microstructure of the system to be studied dynamically using confocal microscopy. The particular mixture is used because by tuning the composition and temperature of the system, one can approach a critical point between having a homogeneous mixture and undergoing phase separation. As with critical points in general, this point involves a very large correlation length <math>\xi</math> -- thus making the critical Casimir effect strong enough to observe. <br />
<br />
Indeed, Bonn et al. find that, for a suitable composition of the binary mixture, upon increasing the temperature close to the critical point, the colloidal particles -- which previously were stably suspended due to their charge -- aggregated and sedimented out of solution. Importantly, this process was reversible. Confocal microscopy analysis suggests that this aggregation process occurs by diffusion-limited cluster aggregation.<br />
<br />
The most straightforward explanation for this effect is due to competition between the attractive critical Casimir effect, and a "typical" screened Coulomb repulsion. Bonn et al. test this hypothesis by altering the salt concentration in their system, thus tuning the Debye length; this leads to a quantitative prediction of the interparticle interaction potential, in agreement with the superposition of an attractive Casimir force and a screened Coulomb repulsion. <br />
<br />
While this work is interesting on purely fundamental grounds -- it directly studies the effect of critical Casimir interactions in colloidal systems -- it may also have potential applications in systems of colloidal particles suspended in binary mixtures, in which Casimir interactions may be important, and may be tuned to have a stabilizing or destabilizing effect.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Sujit_Sankar_Datta&diff=13021Sujit Sankar Datta2009-11-24T01:36:08Z<p>Datta: </p>
<hr />
<div>Definitions:<br />
<br />
[[Percolation]]<br />
<br />
[[Coalescence]]<br />
<br />
[[Splashing]]<br />
<br />
[[Rigidity]]<br />
<br />
[[Pickering emulsion]]<br />
<br />
[[Quasicrystal]]<br />
<br />
[[Wigner crystal]]<br />
<br />
<br />
Weekly wiki entries:<br />
<br />
[[Strain-Rate Frequency Superposition: A Rheological Probe of Structural Relaxation in Soft Materials]]<br />
<br />
[[Non-coalescence of oppositely charged drops]]<br />
<br />
[[Making a splash with water repellency]]<br />
<br />
[[The packing of granular polymer chains]]<br />
<br />
[[Limited coalescence]]<br />
<br />
[[Quasicrystalline order in self-assembled binary nanoparticle superlattices]]<br />
<br />
[[Electrostatics at the oil–water interface, stability, and order in emulsions and colloids]]<br />
<br />
[[Direct observation of colloidal aggregation by critical casimir forces]]</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Direct_observation_of_colloidal_aggregation_by_critical_casimir_forces&diff=12971Direct observation of colloidal aggregation by critical casimir forces2009-11-23T18:37:51Z<p>Datta: New page: Original entry: Sujit S. Datta, APPHY 225, Fall 2009. == Reference == D. Bonn, J. Otwinowski, S. Sacanna, H. Guo, G. Wegdam, and P. Schall, ''PRL'' '''103,''' 156101 (2009). == Keywo...</p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
D. Bonn, J. Otwinowski, S. Sacanna, H. Guo, G. Wegdam, and P. Schall, ''PRL'' '''103,''' 156101 (2009).<br />
<br />
== Keywords ==<br />
<br />
critical casimir, flocculation, colloidal stability<br />
<br />
== Key Points ==<br />
<br />
In analogy to the quantum Casimir effect, in which two uncharged dielectric plates in a vacuum can attract or repel each other due to zero-point fluctuations of the quantized electromagnetic field, the critical Casimir effect describes the possibility of attractive or repulsive forces between two surfaces due to confined density or concentration fluctuations. This effect occurs when the lengthscale <math>\xi</math> of these fluctuations is on the order of the separation between the two surfaces; while this lengthscale is typically very small, it can often be relevant to colloidal systems. This paper discusses the first direct observation of colloidal aggregation and disaggregation by tuning the critical Casimir effect. <br />
<br />
Bonn et al. study a refractive index-matched suspension of colloidal latex particles in a binary mixture of water and the organic compound 3-methylpyridine. The index match of the system allows the microstructure of the system to be studied dynamically using confocal microscopy. The particular mixture is used because by tuning the composition and temperature of the system, one can approach a critical point between having a homogeneous mixture and undergoing phase separation. As with critical points in general, this point involves a very large correlation length <math>\xi</math> -- thus making the critical Casimir effect strong enough to observe. <br />
<br />
Indeed, Bonn et al. find that, for a suitable composition of the binary mixture, upon increasing the temperature close to the critical point, the colloidal particles -- which previously were stably suspended due to their charge -- aggregated and sedimented out of solution. Importantly, this process was reversible. Confocal microscopy analysis suggests that this aggregation process occurs by diffusion-limited cluster aggregation.<br />
<br />
The most straightforward explanation for this effect is due to competition between the attractive critical Casimir effect, and a "typical" screened Coulomb repulsion. Bonn et al. test this hypothesis by altering the salt concentration in their system, thus tuning the Debye length; this leads to a quantitative prediction of the interparticle interaction potential, in agreement with the superposition of an attractive Casimir force and a screened Coulomb repulsion. <br />
<br />
While this work is interesting on purely fundamental grounds -- it directly studies the effect of critical Casimir interactions in colloidal systems -- it may also have potential applications in systems of colloidal particles suspended in binary mixtures, in which Casimir interactions may be important, and may be tuned to have a stabilizing or destabilizing effect.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Sujit_Sankar_Datta&diff=12609Sujit Sankar Datta2009-11-16T23:13:04Z<p>Datta: </p>
<hr />
<div>Definitions:<br />
<br />
[[Percolation]]<br />
<br />
[[Coalescence]]<br />
<br />
[[Splashing]]<br />
<br />
[[Rigidity]]<br />
<br />
[[Pickering emulsion]]<br />
<br />
[[Quasicrystal]]<br />
<br />
[[Wigner crystal]]<br />
<br />
<br />
Weekly wiki entries:<br />
<br />
[[Strain-Rate Frequency Superposition: A Rheological Probe of Structural Relaxation in Soft Materials]]<br />
<br />
[[Non-coalescence of oppositely charged drops]]<br />
<br />
[[Making a splash with water repellency]]<br />
<br />
[[The packing of granular polymer chains]]<br />
<br />
[[Limited coalescence]]<br />
<br />
[[Quasicrystalline order in self-assembled binary nanoparticle superlattices]]<br />
<br />
[[Electrostatics at the oil–water interface, stability, and order in emulsions and colloids]]</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Wigner_crystal&diff=12608Wigner crystal2009-11-16T23:12:42Z<p>Datta: New page: In a charged colloid system, a Wigner crystal is a crystalline lattice formed by the mutual repulsions of many charged colloidal particles, at relatively low volume fractions.</p>
<hr />
<div>In a charged colloid system, a Wigner crystal is a crystalline lattice formed by the mutual repulsions of many charged colloidal particles, at relatively low volume fractions.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Electrostatics_at_the_oil%E2%80%93water_interface,_stability,_and_order_in_emulsions_and_colloids&diff=12607Electrostatics at the oil–water interface, stability, and order in emulsions and colloids2009-11-16T23:12:08Z<p>Datta: /* Keywords */</p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
M. E. Leunissen, A. van Blaaderen, A. D. Hollingsworth, M. T. Sullivan, P. M. Chaikin, ''PNAS'' '''104,''' 2585 (2007).<br />
<br />
== Keywords ==<br />
<br />
electrostatics, apolar, charging, emulsion, [[Wigner crystal]]<br />
<br />
== Key Points ==<br />
<br />
A significant amount of recent work has begun to focus on the electrostatics of colloidal systems in non-polar media, such as various oils with low dielectric constants (e.g. 2-6, versus 80 for water). Because of this low dielectric constant, the energy needed to separate unlike charges is much larger in an apolar medium than in a polar medium, like water -- at equilibrium, this energy is thermal (kT). This leads to a number of rich effects: (i) for very apolar media, colloidal particles will tend to be uncharged, since spontaneous dissociation of charged species at the colloidal surface requires more energy than is available by kT; (ii) at equilibrium, apolar media tend to have a very small concentration of free ions, because the energy required to separate the charges is much larger than kT. This leads to large (from several to hundreds of micrometers) screening lengths.<br />
<br />
In this work, the dielectric constant of the solvent (~5.6) is sufficiently large such that spontaneous colloidal charging does occur, and the screening length is on the order of micrometers. However, when the suspension was placed in contact with water, colloidal particles in the solvent near the water-apolar solvent interface formed Wigner crystals with lattice constants up to tens of micrometers, suggesting an effective screening length over an order of magnitude larger than one would expect. <br />
<br />
The explanation for this effect comes from the simple observation that the energy required to place a charged ion of size a and charge q (the "self energy") in a dielectric medium is given by <math>q^{2}/2\epsilon_{r}\epsilon_{0} a</math>, where <math>\epsilon_{r}</math> is the dielectric constant of the medium. Thus, the ions in the solvent of dielectric constant 5.6 can greatly reduce their energy by "partitioning" into the water phase with dielectric constant 80 -- that is, the water phase will act as an "ion sink", reducing the ionic concentration in the apolar solvent even further and leading to a much larger effective screening length. <br />
<br />
There are subtleties which make the physics even richer. <br />
<br />
1. Because of the details of the interactions between the water and the free ions in the apolar solvent, the water "ion sink" tends to take up more positive ions, and thus the water phase becomes charged. Indeed, Leunissen et al. use this effect to produce colloid particle-free water-in-oil emulsions that are stable against coalescence, due to the fact that the water droplets are charged. This is a unique emulsion system that is free of any (surfactant or particle) stabilizers, leading to potential applications of emulsion systems that do not require any stabilizer.<br />
<br />
2. Because the water phase is charged, a region spanning tens of micrometers in the oil phase, right next to the oil-water interface, exists from which colloidal particles are depleted. This is due to electrostatic repulsion. However, colloidal particles were bound right at the interface; this is because they are attracted to their image charges in the water phase. This could have potential insight into the mechanisms behind particles binding to oil-water interfaces in "Pickering" emulsions, since the particles used in these experiments had wetting properties that do ''not'' favor their binding to the oil-water interface.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Electrostatics_at_the_oil%E2%80%93water_interface,_stability,_and_order_in_emulsions_and_colloids&diff=12606Electrostatics at the oil–water interface, stability, and order in emulsions and colloids2009-11-16T23:11:44Z<p>Datta: /* Key Points */</p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
M. E. Leunissen, A. van Blaaderen, A. D. Hollingsworth, M. T. Sullivan, P. M. Chaikin, ''PNAS'' '''104,''' 2585 (2007).<br />
<br />
== Keywords ==<br />
<br />
electrostatics, apolar, charging, emulsion, wigner crystals<br />
<br />
== Key Points ==<br />
<br />
A significant amount of recent work has begun to focus on the electrostatics of colloidal systems in non-polar media, such as various oils with low dielectric constants (e.g. 2-6, versus 80 for water). Because of this low dielectric constant, the energy needed to separate unlike charges is much larger in an apolar medium than in a polar medium, like water -- at equilibrium, this energy is thermal (kT). This leads to a number of rich effects: (i) for very apolar media, colloidal particles will tend to be uncharged, since spontaneous dissociation of charged species at the colloidal surface requires more energy than is available by kT; (ii) at equilibrium, apolar media tend to have a very small concentration of free ions, because the energy required to separate the charges is much larger than kT. This leads to large (from several to hundreds of micrometers) screening lengths.<br />
<br />
In this work, the dielectric constant of the solvent (~5.6) is sufficiently large such that spontaneous colloidal charging does occur, and the screening length is on the order of micrometers. However, when the suspension was placed in contact with water, colloidal particles in the solvent near the water-apolar solvent interface formed Wigner crystals with lattice constants up to tens of micrometers, suggesting an effective screening length over an order of magnitude larger than one would expect. <br />
<br />
The explanation for this effect comes from the simple observation that the energy required to place a charged ion of size a and charge q (the "self energy") in a dielectric medium is given by <math>q^{2}/2\epsilon_{r}\epsilon_{0} a</math>, where <math>\epsilon_{r}</math> is the dielectric constant of the medium. Thus, the ions in the solvent of dielectric constant 5.6 can greatly reduce their energy by "partitioning" into the water phase with dielectric constant 80 -- that is, the water phase will act as an "ion sink", reducing the ionic concentration in the apolar solvent even further and leading to a much larger effective screening length. <br />
<br />
There are subtleties which make the physics even richer. <br />
<br />
1. Because of the details of the interactions between the water and the free ions in the apolar solvent, the water "ion sink" tends to take up more positive ions, and thus the water phase becomes charged. Indeed, Leunissen et al. use this effect to produce colloid particle-free water-in-oil emulsions that are stable against coalescence, due to the fact that the water droplets are charged. This is a unique emulsion system that is free of any (surfactant or particle) stabilizers, leading to potential applications of emulsion systems that do not require any stabilizer.<br />
<br />
2. Because the water phase is charged, a region spanning tens of micrometers in the oil phase, right next to the oil-water interface, exists from which colloidal particles are depleted. This is due to electrostatic repulsion. However, colloidal particles were bound right at the interface; this is because they are attracted to their image charges in the water phase. This could have potential insight into the mechanisms behind particles binding to oil-water interfaces in "Pickering" emulsions, since the particles used in these experiments had wetting properties that do ''not'' favor their binding to the oil-water interface.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Electrostatics_at_the_oil%E2%80%93water_interface,_stability,_and_order_in_emulsions_and_colloids&diff=12605Electrostatics at the oil–water interface, stability, and order in emulsions and colloids2009-11-16T23:02:49Z<p>Datta: /* Key Points */</p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
M. E. Leunissen, A. van Blaaderen, A. D. Hollingsworth, M. T. Sullivan, P. M. Chaikin, ''PNAS'' '''104,''' 2585 (2007).<br />
<br />
== Keywords ==<br />
<br />
electrostatics, apolar, charging, emulsion, wigner crystals<br />
<br />
== Key Points ==<br />
<br />
A significant amount of recent work has begun to focus on the electrostatics of colloidal systems in non-polar media, such as various oils with low dielectric constants (e.g. 2-6, versus 80 for water). Because of this low dielectric constant, the energy needed to separate unlike charges is much larger in an apolar medium than in a polar medium, like water -- at equilibrium, this energy is thermal (kT). This leads to a number of rich effects: (i) for very apolar media, colloidal particles will tend to be uncharged, since spontaneous dissociation of charged species at the colloidal surface requires more energy than is available by kT; (ii) at equilibrium, apolar media tend to have a very small concentration of free ions, because the energy required to separate the charges is much larger than kT. This leads to large (from several to hundreds of micrometers) screening lengths.<br />
<br />
In this work, the dielectric constant of the solvent (~5.6) is sufficiently large such that spontaneous colloidal charging does occur, and the screening length is on the order of micrometers. However, when the suspension was placed in contact with water, colloidal particles in the solvent formed Wigner crystals with lattice constants up to tens of micrometers, suggesting an effective screening length over an order of magnitude larger than one would expect. <br />
<br />
The explanation for this effect comes from the simple observation that the energy required to place a charged ion of size a and charge q (the "self energy") in a dielectric medium is given by <math>q^{2}/2\epsilon_{r}\epsilon_{0} a</math>, where <math>\epsilon_{r}</math> is the dielectric constant of the medium. Thus, the ions in the solvent of dielectric constant 5.6 can greatly reduce their energy by "partitioning" into the water phase with dielectric constant 80.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Electrostatics_at_the_oil%E2%80%93water_interface,_stability,_and_order_in_emulsions_and_colloids&diff=12602Electrostatics at the oil–water interface, stability, and order in emulsions and colloids2009-11-16T22:55:06Z<p>Datta: /* Key Points */</p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
M. E. Leunissen, A. van Blaaderen, A. D. Hollingsworth, M. T. Sullivan, P. M. Chaikin, ''PNAS'' '''104,''' 2585 (2007).<br />
<br />
== Keywords ==<br />
<br />
electrostatics, apolar, charging, emulsion, wigner crystals<br />
<br />
== Key Points ==<br />
<br />
A significant amount of recent work has begun to focus on the electrostatics of colloidal systems in non-polar media, such as various oils with low dielectric constants (e.g. 2-6, versus 80 for water). Because of this low dielectric constant, the energy needed to separate unlike charges is much larger in an apolar medium than in a polar medium, like water -- at equilibrium, this energy is thermal (kT). This leads to a number of rich effects: (i) For very apolar media, colloidal particles will tend to be uncharged, since spontaneous dissociation of charged species at the colloidal surface requires more energy than is available by kT; (ii) at equilibrium, apolar media tend to have a very small concentration of free ions, because the energy required to separate the charges is much larger than kT. This leads to large (from several to hundreds of micrometers) screening lengths.<br />
<br />
In this work, the dielectric constant of the solvent (~5.6) is sufficiently large such that spontaneous colloidal charging does occur, and the screening length is on the order of micrometers. However, when the suspension was placed in contact with water, colloidal particles in the solvent formed Wigner crystals with lattice constants up to tens of micrometers, suggesting an effective screening length over an order of magnitude larger than one would expect. <br />
<br />
The explanation for this effect comes from the simple observation that</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Electrostatics_at_the_oil%E2%80%93water_interface,_stability,_and_order_in_emulsions_and_colloids&diff=12593Electrostatics at the oil–water interface, stability, and order in emulsions and colloids2009-11-16T22:19:24Z<p>Datta: New page: Original entry: Sujit S. Datta, APPHY 225, Fall 2009. == Reference == M. E. Leunissen, A. van Blaaderen, A. D. Hollingsworth, M. T. Sullivan, P. M. Chaikin, ''PNAS'' '''104,''' 2585 (...</p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
M. E. Leunissen, A. van Blaaderen, A. D. Hollingsworth, M. T. Sullivan, P. M. Chaikin, ''PNAS'' '''104,''' 2585 (2007).<br />
<br />
== Keywords ==<br />
<br />
electrostatics, apolar, charging, emulsion, wigner crystals<br />
<br />
== Key Points ==<br />
<br />
In progress...</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Sujit_Sankar_Datta&diff=11928Sujit Sankar Datta2009-11-05T16:38:16Z<p>Datta: </p>
<hr />
<div>Definitions:<br />
<br />
[[Percolation]]<br />
<br />
[[Coalescence]]<br />
<br />
[[Splashing]]<br />
<br />
[[Rigidity]]<br />
<br />
[[Pickering emulsion]]<br />
<br />
[[Quasicrystal]]<br />
<br />
<br />
Weekly wiki entries:<br />
<br />
[[Strain-Rate Frequency Superposition: A Rheological Probe of Structural Relaxation in Soft Materials]]<br />
<br />
[[Non-coalescence of oppositely charged drops]]<br />
<br />
[[Making a splash with water repellency]]<br />
<br />
[[The packing of granular polymer chains]]<br />
<br />
[[Limited coalescence]]<br />
<br />
[[Quasicrystalline order in self-assembled binary nanoparticle superlattices]]</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Quasicrystal&diff=11927Quasicrystal2009-11-05T16:37:27Z<p>Datta: New page: A quasicrystal is an ordered structure that fills space, but lacks translational symmetry, unlike crystals. This often results from non-crystallographic rotational symmetry, such as five-f...</p>
<hr />
<div>A quasicrystal is an ordered structure that fills space, but lacks translational symmetry, unlike crystals. This often results from non-crystallographic rotational symmetry, such as five-fold or twelve-fold symmetry.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Quasicrystalline_order_in_self-assembled_binary_nanoparticle_superlattices&diff=11926Quasicrystalline order in self-assembled binary nanoparticle superlattices2009-11-05T16:35:19Z<p>Datta: /* Key Points */</p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
D. V. Talapin, E. V. Schevchenko, M. I. Bodnarchuk, X. Ye, J. Chen, and C. B. Murray, ''Nature'' '''461,''' 964 (2009).<br />
<br />
== Keywords ==<br />
<br />
[[quasicrystal]], self-assembly, packing<br />
<br />
== Key Points ==<br />
<br />
Equilibrium phase transformations are ubiquitous in nature. Because of their complexity, it is often useful to focus on the 'simple' case of hard spheres, whose equilibrium phase diagram is dictated purely on entropic grounds. For monodisperse Brownian spheres with purely hard-sphere interactions, volume fraction is the only control parameter: for small volume fractions, the system is fluid-like; for intermediate volume fractions (between ~49% and 55%), a fluid and crystal phase coexist; for volume fractions larger than ~55%, up to the maximum FCC packing fraction of ~74%, the system is crystalline. For binary systems consisting of particles of two different sizes, the equilibrium phase diagram is much richer (e.g. see "Entropy-driven formation of a superlattice in a hard-sphere binary mixture" by Daan Frenkel's group in 2003), with three control parameters now - the volume fraction of each size particle, and the relative size difference between them. Further complexity develops in the equilibrium phase diagram with deviations from hard sphere behavior, such as the incorporation of van der Waals, Coulombic, and dipolar interactions. Different crystalline phases of nanoparticle systems have been experimentally observed (and theoretically predicted) as a result. This work is the first to demonstrate an equilibrium quasicrystalline phase, with clues suggesting that the phase is solely a general result of entropy, ''not'' the interparticle interactions.<br />
<br />
The nanoparticles used in this study are made of two different materials, and have two different sizes, respectively (with size ratio ~2.7:1). Because of their surface chemistry, they do not aggregate due to van der Waals interactions, but have additional short range steric repulsions. Thus, the key control parameter in this system is the relative composition of the different nanoparticle components. Consistent with previous work, Talapin et al. found that "normal" crystalline superlattices of different structures form when one component dominates the composition of the system. These themselves have intriguing structures, resembling regular 2D Archimedean tilings of squares and triangles. More surprisingly, Talapin et al. found that for intermediate composition ranges, superlattices with ''quasicrystalline'' order formed -- specifically, the superlattices consisting of square and triangle packing motifs organized into a dodecagonal quasicrystal (possessing 12-fold rotational symmetry, and no translational symmetry). The three-dimensional material then consists of periodic stacks of these quasicrystalline layers, making their structure straightforward to analyze using transmission electron microscopy, as is done in this work.<br />
<br />
Another clue towards understanding the formation mechanism of the DDQC phase is the observation that such phases tended to coexist with "normal" crystalline superlattices, with a sharp interface between the two. This is possible because the fundamental units of both phases are the same: either square or triangular tiles. <br />
<br />
Intriguingly, nanoparticles of slightly smaller sizes or different materials (with a similar size ratio ~2.7:1 or ~3:1, respectively) also assembled into the dodecagonal quasicrystal (DDQC) phase, often extending up to thousands of particles on a side. This suggests that interparticle interactions (which would change for different materials and different particle sizes) do not play a significant role in the formation of the DDQC phase -- furthermore, the possible dependence on particle size ratio suggests that the formation of the DDQC phase may, in fact, be due to purely entropic considerations. However, it is important to note that whether or not the hard-sphere DDQC phase is a thermodynamically-stable phase is an open question, and may be strongly dependent on the manner in which the structures are formed (in this case, by slow evaporation of the suspending liquid). Further work exploring many different particle sizes, size ratios, compositions, and sample preparation mechanisms, as well as simulations of binary hard sphere systems, should help to elucidate the mechanisms driving the formation of this unique phase of matter.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Quasicrystalline_order_in_self-assembled_binary_nanoparticle_superlattices&diff=11925Quasicrystalline order in self-assembled binary nanoparticle superlattices2009-11-05T16:29:35Z<p>Datta: /* Key Points */</p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
D. V. Talapin, E. V. Schevchenko, M. I. Bodnarchuk, X. Ye, J. Chen, and C. B. Murray, ''Nature'' '''461,''' 964 (2009).<br />
<br />
== Keywords ==<br />
<br />
[[quasicrystal]], self-assembly, packing<br />
<br />
== Key Points ==<br />
<br />
Equilibrium phase transformations are ubiquitous in nature. Because of their complexity, it is often useful to focus on the 'simple' case of hard spheres, whose equilibrium phase diagram is dictated purely on entropic grounds. For monodisperse Brownian spheres with purely hard-sphere interactions, volume fraction is the only control parameter: for small volume fractions, the system is fluid-like; for intermediate volume fractions (between ~49% and 55%), a fluid and crystal phase coexist; for volume fractions larger than ~55%, up to the maximum FCC packing fraction of ~74%, the system is crystalline. For binary systems consisting of particles of two different sizes, the equilibrium phase diagram is much richer (e.g. see "Entropy-driven formation of a superlattice in a hard-sphere binary mixture" by Daan Frenkel's group in 2003), with three control parameters now - the volume fraction of each size particle, and the relative size difference between them. Further complexity develops in the equilibrium phase diagram with deviations from hard sphere behavior, such as the incorporation of van der Waals, Coulombic, and dipolar interactions. Different crystalline phases of nanoparticle systems have been experimentally observed (and theoretically predicted) as a result. This work is the first to demonstrate an equilibrium quasicrystalline phase, with clues suggesting that the phase is solely a general result of entropy, ''not'' the interparticle interactions.<br />
<br />
The nanoparticles used in this study are made of two different materials, and have two different sizes, respectively (with size ratio ~2.7:1). Because of their surface chemistry, they do not aggregate due to van der Waals interactions, but have additional short range steric repulsions. Thus, the key control parameter in this system is the relative composition of the different nanoparticle components. Consistent with previous work, Talapin et al. found that "normal" crystalline superlattices of different structures form when one component dominates the composition of the system. These themselves have intriguing structures, resembling regular 2D Archimedean tilings of squares and triangles. More surprisingly, Talapin et al. found that for intermediate composition ranges, superlattices with ''quasicrystalline'' order formed -- specifically, the superlattices consisting of square and triangle packing motifs organized into a dodecagonal quasicrystal (possessing 12-fold rotational symmetry, and no translational symmetry). The three-dimensional material then consists of periodic stacks of these quasicrystalline layers, making their structure straightforward to analyze using transmission electron microscopy, as is done in this work.<br />
<br />
Intriguingly, nanoparticles of slightly smaller sizes or different materials (with a similar size ratio ~2.7:1 or ~3:1, respectively) also assembled into the dodecagonal quasicrystal (DDQC) phase, often extending up to thousands of particles on a side. This suggests that interparticle interactions (which would change for different materials and different particle sizes) do not play a significant role in the formation of the DDQC phase -- this may, in fact, be due to purely entropic considerations. However, it is important to note that whether or not the hard-sphere DDQC phase is a thermodynamically-stable phase is an open question, and may be strongly dependent on the manner in which the structures are formed (in this case, by slow evaporation of the suspending liquid).<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
*IN PROGRESS*</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Quasicrystalline_order_in_self-assembled_binary_nanoparticle_superlattices&diff=11924Quasicrystalline order in self-assembled binary nanoparticle superlattices2009-11-05T16:26:12Z<p>Datta: /* Key Points */</p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
D. V. Talapin, E. V. Schevchenko, M. I. Bodnarchuk, X. Ye, J. Chen, and C. B. Murray, ''Nature'' '''461,''' 964 (2009).<br />
<br />
== Keywords ==<br />
<br />
[[quasicrystal]], self-assembly, packing<br />
<br />
== Key Points ==<br />
<br />
Equilibrium phase transformations are ubiquitous in nature. Because of their complexity, it is often useful to focus on the 'simple' case of hard spheres, whose equilibrium phase diagram is dictated purely on entropic grounds. For monodisperse Brownian spheres with purely hard-sphere interactions, volume fraction is the only control parameter: for small volume fractions, the system is fluid-like; for intermediate volume fractions (between ~49% and 55%), a fluid and crystal phase coexist; for volume fractions larger than ~55%, up to the maximum FCC packing fraction of ~74%, the system is crystalline. For binary systems consisting of particles of two different sizes, the equilibrium phase diagram is much richer (e.g. see "Entropy-driven formation of a superlattice in a hard-sphere binary mixture" by Daan Frenkel's group in 2003), with three control parameters now - the volume fraction of each size particle, and the relative size difference between them. Further complexity develops in the equilibrium phase diagram with deviations from hard sphere behavior, such as the incorporation of van der Waals, Coulombic, and dipolar interactions. Different crystalline phases of nanoparticle systems have been experimentally observed (and theoretically predicted) as a result. This work is the first to demonstrate an equilibrium quasicrystalline phase, with clues suggesting that the phase is solely a general result of entropy, ''not'' the interparticle interactions.<br />
<br />
The nanoparticles used in this study are made of two different materials, and have two different sizes, respectively (with size ratio ~2.7:1). Because of their surface chemistry, they do not aggregate due to van der Waals interactions, but have additional short range steric repulsions. Thus, the key control parameter in this system is the relative composition of the different nanoparticle components. Consistent with previous work, Talapin et al. found that "normal" crystalline superlattices of different structures form when one component dominates the composition of the system. These themselves have intriguing structures, resembling regular 2D Archimedean tilings of squares and triangles. More surprisingly, Talapin et al. found that for intermediate composition ranges, superlattices with ''quasicrystalline'' order formed -- specifically, the superlattices consisting of square and triangle packing motifs organized into a dodecagonal quasicrystal (possessing 12-fold rotational symmetry, and no translational symmetry). The three-dimensional material then consists of periodic stacks of these quasicrystalline layers, making their structure straightforward to analyze using transmission electron microscopy, as is done in this work.<br />
<br />
Intriguingly, nanoparticles of slightly smaller sizes or different materials (with a similar size ratio ~2.7:1 or ~3:1, respectively) also assembled into the dodecagonal quasicrystal (DDQC) phase, often extending up to thousands of particles on a side.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
superlattices<br />
crystals, etc. by relative composition<br />
slow evaporation<br />
saw dodecagonal quasicrystal!<br />
interface, wetting layer<br />
<br />
<br />
*IN PROGRESS*</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Quasicrystalline_order_in_self-assembled_binary_nanoparticle_superlattices&diff=11923Quasicrystalline order in self-assembled binary nanoparticle superlattices2009-11-05T16:20:45Z<p>Datta: </p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
D. V. Talapin, E. V. Schevchenko, M. I. Bodnarchuk, X. Ye, J. Chen, and C. B. Murray, ''Nature'' '''461,''' 964 (2009).<br />
<br />
== Keywords ==<br />
<br />
[[quasicrystal]], self-assembly, packing<br />
<br />
== Key Points ==<br />
<br />
Equilibrium phase transformations are ubiquitous in nature. Because of their complexity, it is often useful to focus on the 'simple' case of hard spheres, whose equilibrium phase diagram is dictated purely on entropic grounds. For monodisperse Brownian spheres with purely hard-sphere interactions, volume fraction is the only control parameter: for small volume fractions, the system is fluid-like; for intermediate volume fractions (between ~49% and 55%), a fluid and crystal phase coexist; for volume fractions larger than ~55%, up to the maximum FCC packing fraction of ~74%, the system is crystalline. For binary systems consisting of particles of two different sizes, the equilibrium phase diagram is much richer (e.g. see "Entropy-driven formation of a superlattice in a hard-sphere binary mixture" by Daan Frenkel's group in 2003), with three control parameters now - the volume fraction of each size particle, and the relative size difference between them. Further complexity develops in the equilibrium phase diagram with deviations from hard sphere behavior, such as the incorporation of van der Waals, Coulombic, and dipolar interactions. Different crystalline phases of nanoparticle systems have been experimentally observed (and theoretically predicted) as a result. This work is the first to demonstrate an equilibrium quasicrystalline phase, with clues suggesting that the phase is solely a general result of entropy, ''not'' the interparticle interactions.<br />
<br />
The nanoparticles used in this study are made of two different materials, and have two different sizes, respectively (with size ratio ~2.7:1). Because of their surface chemistry, they do not aggregate due to van der Waals interactions, but have additional short range steric repulsions. Thus, the key control parameter in this system is the relative composition of the different nanoparticle components. Consistent with previous work, Talapin et al. found that "normal" crystalline superlattices of different structures form when one component dominates the composition of the system. These themselves have intriguing structures, resembling regular 2D Archimedean tilings of squares and triangles. More surprisingly, Talapin et al. found that for intermediate composition ranges, superlattices with ''quasicrystalline'' order formed -- specifically, the superlattices consisting of square and triangle packing motifs organized into a dodecagonal quasicrystal (possessing 12-fold rotational symmetry, and no translational symmetry).<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
superlattices<br />
crystals, etc. by relative composition<br />
slow evaporation<br />
saw dodecagonal quasicrystal!<br />
interface, wetting layer<br />
<br />
<br />
*IN PROGRESS*</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Quasicrystalline_order_in_self-assembled_binary_nanoparticle_superlattices&diff=11922Quasicrystalline order in self-assembled binary nanoparticle superlattices2009-11-05T16:19:27Z<p>Datta: /* Key Points */</p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
D. V. Talapin, E. V. Schevchenko, M. I. Bodnarchuk, X. Ye, J. Chen, and C. B. Murray, ''Nature'' '''461,''' 964 (2009).<br />
<br />
== Keywords ==<br />
<br />
[[quasicrystal]], self-assembly, packing<br />
<br />
== Key Points ==<br />
<br />
Equilibrium phase transformations are ubiquitous in nature. Because of their complexity, it is often useful to focus on the 'simple' case of hard spheres, whose equilibrium phase diagram is dictated purely on entropic grounds. For monodisperse Brownian spheres with purely hard-sphere interactions, volume fraction is the only control parameter: for small volume fractions, the system is fluid-like; for intermediate volume fractions (between ~49% and 55%), a fluid and crystal phase coexist; for volume fractions larger than ~55%, up to the maximum FCC packing fraction of ~74%, the system is crystalline. For binary systems consisting of particles of two different sizes, the equilibrium phase diagram is much richer (e.g. see "Entropy-driven formation of a superlattice in a hard-sphere binary mixture" by Daan Frenkel's group in 2003), with three control parameters now - the volume fraction of each size particle, and the relative size difference between them. Further complexity develops in the equilibrium phase diagram with deviations from hard sphere behavior, such as the incorporation of van der Waals, Coulombic, and dipolar interactions. Different crystalline phases of nanoparticle systems have been experimentally observed (and theoretically predicted) as a result. This work is the first to demonstrate an equilibrium quasicrystalline phase, with clues suggesting that the phase is solely a general result of entropy, ''not'' the interparticle interactions.<br />
<br />
The nanoparticles used in this study are made of two different materials, and have two different sizes, respectively (with size ratio ~2.7:1). Because of their surface chemistry, they do not aggregate due to van der Waals interactions, but have additional short range steric repulsions. Thus, the key control parameter in this system is the relative composition of the different nanoparticle components. Consistent with previous work, Talapin et al. found that "normal" crystalline superlattices of different structures form when one component dominates the composition of the system. These themselves have intriguing structures, resembling regular 2D Archimedean tilings of squares and triangles. More surprisingly, Talapin et al. found that for intermediate composition ranges, superlattices with ''quasicrystalline'' order formed. <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
superlattices<br />
crystals, etc. by relative composition<br />
slow evaporation<br />
saw dodecagonal quasicrystal!<br />
interface, wetting layer<br />
<br />
<br />
*IN PROGRESS*</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Quasicrystalline_order_in_self-assembled_binary_nanoparticle_superlattices&diff=11881Quasicrystalline order in self-assembled binary nanoparticle superlattices2009-11-04T20:55:39Z<p>Datta: /* Key Points */</p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
D. V. Talapin, E. V. Schevchenko, M. I. Bodnarchuk, X. Ye, J. Chen, and C. B. Murray, ''Nature'' '''461,''' 964 (2009).<br />
<br />
== Keywords ==<br />
<br />
[[quasicrystal]], self-assembly, packing<br />
<br />
== Key Points ==<br />
<br />
Equilibrium phase transformations are ubiquitous in nature. Because of their complexity, it is often useful to focus on the 'simple' case of hard spheres, whose equilibrium phase diagram is dictated purely on entropic grounds. For monodisperse Brownian spheres with purely hard-sphere interactions, volume fraction is the only control parameter: for small volume fractions, the system is fluid-like; for intermediate volume fractions (between ~49% and 55%), a fluid and crystal phase coexist; for volume fractions larger than ~55%, up to the maximum FCC packing fraction of ~74%, the system is crystalline. For binary systems consisting of particles of two different sizes, the equilibrium phase diagram is much richer (e.g. see "Entropy-driven formation of a superlattice in a hard-sphere binary mixture" by Daan Frenkel's group in 2003), with three control parameters now - the volume fraction of each size particle, and the relative size difference between them. Further complexity develops in the equilibrium phase diagram with deviations from hard sphere behavior, such as the incorporation of van der Waals, Coulombic, and dipolar interactions. Different crystalline phases of nanoparticle systems have been experimentally observed (and theoretically predicted) as a result. This work is the first to demonstrate an equilibrium quasicrystalline phase, with clues suggesting that the phase is solely a general result of entropy, ''not'' the interparticle interactions.<br />
<br />
The nanoparticles used in this study are made of two different materials, and have two different sizes, respectively (with size ratio ~2.7:1). Because of their surface chemistry, they do not aggregate due to van der Waals interactions, but have additional short range steric repulsions. Thus, the key control parameter in this system is the relative composition of the different nanoparticle components. Consistent with previous work, Talapin et al. found that "normal" crystalline superlattices of different structures form when one component dominates the composition of the system; however, quite surprisingly, they found that for intermediate composition ranges, superlattices with quasicrystalline order can form. <br />
<br />
<br />
superlattices<br />
crystals, etc. by relative composition<br />
slow evaporation<br />
archimidean tilings<br />
frank kasper alloys<br />
saw dodecagonal quasicrystal!<br />
interface, wetting layer<br />
<br />
<br />
*IN PROGRESS*</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Quasicrystalline_order_in_self-assembled_binary_nanoparticle_superlattices&diff=11880Quasicrystalline order in self-assembled binary nanoparticle superlattices2009-11-04T20:52:38Z<p>Datta: /* Key Points */</p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
D. V. Talapin, E. V. Schevchenko, M. I. Bodnarchuk, X. Ye, J. Chen, and C. B. Murray, ''Nature'' '''461,''' 964 (2009).<br />
<br />
== Keywords ==<br />
<br />
[[quasicrystal]], self-assembly, packing<br />
<br />
== Key Points ==<br />
<br />
Equilibrium phase transformations are ubiquitous in nature. Because of their complexity, it is often useful to focus on the 'simple' case of hard spheres, whose equilibrium phase diagram is dictated purely on entropic grounds. For monodisperse Brownian spheres with purely hard-sphere interactions, volume fraction is the only control parameter: for small volume fractions, the system is fluid-like; for intermediate volume fractions (between ~49% and 55%), a fluid and crystal phase coexist; for volume fractions larger than ~55%, up to the maximum FCC packing fraction of ~74%, the system is crystalline. For binary systems consisting of particles of two different sizes, the equilibrium phase diagram is much richer (e.g. see "Entropy-driven formation of a superlattice in a hard-sphere binary mixture" by Daan Frenkel's group in 2003), with three control parameters now - the volume fraction of each size particle, and the relative size difference between them. Further complexity develops in the equilibrium phase diagram with deviations from hard sphere behavior, such as the incorporation of van der Waals, Coulombic, and dipolar interactions. Different crystalline phases of nanoparticle systems have been experimentally observed (and theoretically predicted) as a result. This work is the first to demonstrate an equilibrium quasicrystalline phase, with clues suggesting that the phase is solely a general result of entropy, ''not'' the interparticle interactions.<br />
<br />
The nanoparticles used in this study are made of two different materials, and have two different sizes, respectively (with size ratio ~2.7:1). Because of their surface chemistry, they do not aggregate due to van der Waals interactions, but have additional short range steric repulsions. Thus, the key control parameter in this system is the relative composition of the different nanoparticle components. Consistent with previous work, Talapin et al. found that "normal" crystalline superlattices of different structures form when one component dominates the composition of the system; however, quite surprisingly, they found that for intermediate composition ranges, superlattices with quasicrystalline order can form. <br />
<br />
<br />
superlattices<br />
crystals, etc. by relative composition<br />
slow evaporation<br />
archimidean tilings<br />
frank kasper alloys<br />
<br />
<br />
*IN PROGRESS*</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Quasicrystalline_order_in_self-assembled_binary_nanoparticle_superlattices&diff=11879Quasicrystalline order in self-assembled binary nanoparticle superlattices2009-11-04T20:52:12Z<p>Datta: /* Key Points */</p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
D. V. Talapin, E. V. Schevchenko, M. I. Bodnarchuk, X. Ye, J. Chen, and C. B. Murray, ''Nature'' '''461,''' 964 (2009).<br />
<br />
== Keywords ==<br />
<br />
[[quasicrystal]], self-assembly, packing<br />
<br />
== Key Points ==<br />
<br />
Equilibrium phase transformations are ubiquitous in nature. Because of their complexity, it is often useful to focus on the 'simple' case of hard spheres, whose equilibrium phase diagram is dictated purely on entropic grounds. For monodisperse Brownian spheres with purely hard-sphere interactions, volume fraction is the only control parameter: for small volume fractions, the system is fluid-like; for intermediate volume fractions (between ~49% and 55%), a fluid and crystal phase coexist; for volume fractions larger than ~55%, up to the maximum FCC packing fraction of ~74%, the system is crystalline. For binary systems consisting of particles of two different sizes, the equilibrium phase diagram is much richer (e.g. see "Entropy-driven formation of a superlattice in a hard-sphere binary mixture" by Daan Frenkel's group in 2003), with three control parameters now - the volume fraction of each size particle, and the relative size difference between them. Further complexity develops in the equilibrium phase diagram with deviations from hard sphere behavior, such as the incorporation of van der Waals, Coulombic, and dipolar interactions. Different crystalline phases of nanoparticle systems have been experimentally observed (and theoretically predicted) as a result. This work is the first to demonstrate an equilibrium quasicrystalline phase, with clues suggesting that the phase is solely a general result of entropy, ''not'' the interparticle interactions.<br />
<br />
The nanoparticles used in this study are made of two different materials, and have two different sizes, respectively (with size ratio ~2.7:1). Because of their surface chemistry, they do not aggregate due to van der Waals interactions, but have additional short range steric repulsions. Thus, the key control parameter in this system is the relative composition of the different nanoparticle components. Consistent with previous work, Talapin et al. found that "normal" crystalline superlattices of different structures form when one component dominates the composition of the system; however, quite surprisingly, they found that for intermediate composition ranges, superlattices with quasicrystalline order can form. <br />
<br />
<br />
superlattices<br />
crystals, etc. by relative composition<br />
slow evaporation<br />
archimidean tilings<br />
<br />
*IN PROGRESS*</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Quasicrystalline_order_in_self-assembled_binary_nanoparticle_superlattices&diff=11878Quasicrystalline order in self-assembled binary nanoparticle superlattices2009-11-04T20:14:16Z<p>Datta: /* Key Points */</p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
D. V. Talapin, E. V. Schevchenko, M. I. Bodnarchuk, X. Ye, J. Chen, and C. B. Murray, ''Nature'' '''461,''' 964 (2009).<br />
<br />
== Keywords ==<br />
<br />
[[quasicrystal]], self-assembly, packing<br />
<br />
== Key Points ==<br />
<br />
Equilibrium phase transformations are ubiquitous in nature. Because of their complexity, it is often useful to focus on the 'simple' case of hard spheres, whose equilibrium phase diagram is dictated purely on entropic grounds. For monodisperse Brownian spheres with purely hard-sphere interactions, volume fraction is the only control parameter: for small volume fractions, the system is fluid-like; for intermediate volume fractions (between ~49% and 55%), a fluid and crystal phase coexist; for volume fractions larger than ~55%, up to the maximum FCC packing fraction of ~74%, the system is crystalline. For binary systems consisting of particles of two different sizes, the equilibrium phase diagram is much richer (e.g. see "Entropy-driven formation of a superlattice in a hard-sphere binary mixture" by Daan Frenkel's group in 2003), with three control parameters now - the volume fraction of each size particle, and the relative size difference between them. Further complexity develops in the equilibrium phase diagram with deviations from hard sphere behavior, such as the incorporation of van der Waals, Coulombic, and dipolar interactions. Different crystalline phases of nanoparticle systems have been experimentally observed (and theoretically predicted) as a result. This work is the first to demonstrate an equilibrium quasicrystalline phase, with clues suggesting that the phase is solely a general result of entropy, ''not'' the interparticle interactions.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Quasicrystalline_order_in_self-assembled_binary_nanoparticle_superlattices&diff=11877Quasicrystalline order in self-assembled binary nanoparticle superlattices2009-11-04T20:12:02Z<p>Datta: </p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
D. V. Talapin, E. V. Schevchenko, M. I. Bodnarchuk, X. Ye, J. Chen, and C. B. Murray, ''Nature'' '''461,''' 964 (2009).<br />
<br />
== Keywords ==<br />
<br />
[[quasicrystal]], self-assembly, packing<br />
<br />
== Key Points ==<br />
<br />
Equilibrium phase transformations are ubiquitous in nature. Because of their complexity, it is often useful to focus on the 'simple' case of hard spheres, whose equilibrium phase diagram is dictated purely on entropic grounds. For monodisperse Brownian spheres with purely hard-sphere interactions, volume fraction is the only control parameter: for small volume fractions, the system is fluid-like; for intermediate volume fractions (between ~49% and 55%), a fluid and crystal phase coexist; for volume fractions larger than ~55%, up to the maximum FCC packing fraction of ~74%, the system is crystalline. For binary systems consisting of particles of two different sizes, the equilibrium phase diagram is much richer (e.g. see "Entropy-driven formation of a superlattice in a hard-sphere binary mixture" by Daan Frenkel's group in 2003), with three control parameters now - the volume fraction of each size particle, and the relative size difference between them. Further complexity develops in the equilibrium phase diagram with deviations from hard sphere behavior, such as the incorporation of van der Waals, Coulombic, and dipolar interactions.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Quasicrystalline_order_in_self-assembled_binary_nanoparticle_superlattices&diff=11876Quasicrystalline order in self-assembled binary nanoparticle superlattices2009-11-04T19:57:04Z<p>Datta: </p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
D. V. Talapin, E. V. Schevchenko, M. I. Bodnarchuk, X. Ye, J. Chen, and C. B. Murray, ''Nature'' '''461,''' 964 (2009).<br />
<br />
== Keywords ==<br />
<br />
[[quasicrystal]], self-assembly, packing<br />
<br />
== Key Points ==<br />
<br />
Equilibrium phase transformations are ubiquitous in nature. Because of their complexity, it is often useful to focus on the 'simple' case of hard spheres, whose equilibrium phase diagram is dictated purely on entropic grounds. For monodisperse Brownian spheres with purely hard-sphere interactions, volume fraction is the only control parameter: for small volume fractions, the system is fluid-like; for intermediate volume fractions (between ~49% and 55%), a fluid and crystal phase coexist; for volume fractions larger than ~55%, up to the maximum FCC packing fraction of ~74%, the system is crystalline.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Quasicrystalline_order_in_self-assembled_binary_nanoparticle_superlattices&diff=11875Quasicrystalline order in self-assembled binary nanoparticle superlattices2009-11-04T19:49:18Z<p>Datta: New page: Original entry: Sujit S. Datta, APPHY 225, Fall 2009. == Reference == D. V. Talapin, E. V. Schevchenko, M. I. Bodnarchuk, X. Ye, J. Chen, and C. B. Murray, ''Nature'' '''461,''' 964 (...</p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
D. V. Talapin, E. V. Schevchenko, M. I. Bodnarchuk, X. Ye, J. Chen, and C. B. Murray, ''Nature'' '''461,''' 964 (2009).<br />
<br />
== Keywords ==<br />
<br />
[[quasicrystal]], self-assembly, packing<br />
<br />
== Key Points ==<br />
<br />
In progress by Sujit.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Soft_colloids_make_strong_glasses&diff=11873Soft colloids make strong glasses2009-11-04T19:41:54Z<p>Datta: Removing all content from page</p>
<hr />
<div></div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Soft_colloids_make_strong_glasses&diff=11869Soft colloids make strong glasses2009-11-04T19:23:31Z<p>Datta: </p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
J. Mattsson, H. M. Wyss, A. Fernandez-Nieves, K. Miyazaki, Z. Hu, D. R. Reichman, and D. A. Weitz, ''Nature'' '''462,''' 83 (2009).<br />
<br />
== Keywords ==<br />
<br />
glass transition, fragility, elasticity<br />
<br />
== Key Points ==<br />
<br />
In progress by Sujit.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Soft_colloids_make_strong_glasses&diff=11868Soft colloids make strong glasses2009-11-04T19:20:57Z<p>Datta: New page: In progress by Sujit</p>
<hr />
<div>In progress by Sujit</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Sujit_Sankar_Datta&diff=11282Sujit Sankar Datta2009-10-28T04:47:10Z<p>Datta: </p>
<hr />
<div>Definitions:<br />
<br />
[[Percolation]]<br />
<br />
[[Coalescence]]<br />
<br />
[[Splashing]]<br />
<br />
[[Rigidity]]<br />
<br />
[[Pickering emulsion]]<br />
<br />
<br />
Weekly wiki entries:<br />
<br />
[[Strain-Rate Frequency Superposition: A Rheological Probe of Structural Relaxation in Soft Materials]]<br />
<br />
[[Non-coalescence of oppositely charged drops]]<br />
<br />
[[Making a splash with water repellency]]<br />
<br />
[[The packing of granular polymer chains]]<br />
<br />
[[Limited coalescence]]</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Limited_coalescence&diff=11281Limited coalescence2009-10-28T04:46:30Z<p>Datta: /* Key Points */</p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
S. Arditty, C. P. Whitby, B. P. Binks, V. Schmitt, F. Leal-Calderon, ''Eur. Phys. J. E'' '''11,''' 273 (2003).<br />
<br />
== Keywords ==<br />
<br />
emulsion, [[Pickering emulsion]], interface, coalescence<br />
<br />
== Key Points ==<br />
<br />
Unlike "conventional" surfactant-stabilized emulsions (dispersions of droplets of one immiscible fluid in another), "Pickering" emulsion droplets are stabilized by solid particles (typically much smaller than the droplet size) adsorbed at the droplet interface. (Note: here, "stabilized" means "stabilized against coalescence". While the mechanisms behind this are not fully understood, and depend on the nature of the components of the particular system under consideration, Pickering emulsion stabilization is generally thought to result from a combination of steric hindrance and the formation of a thin film within the pore space of the particles, whose draining properties will depend on the structure and mechanical properties of the particle network.)<br />
<br />
The particle wetting properties determine the bulk properties of the emulsion in two crucial ways:<br />
<br />
- The continuous phase of the emulsion tends to be the phase that preferentially wets the particles. This can be understood in analogy to surfactants - a particle at the interface between the two fluid phases will sit deeper in the wetting phase, and the effective "packing shape" (Israelachvili, page 381) will be similar to a cone, with tapered end inside the non-wetting phase. That is to say, the majority of the particle volume prefers to be immersed in the wetting phase.<br />
<br />
- Unless particles very significantly prefer one phase over the other, they will tend to be irreversibly adsorbed at the interface between the two fluids. This potential energy well is due to the reduced bare surface area in contact between the two fluids, and is given by <math>\pi R^{2} \gamma_{12}(1+cos\theta)^{2}</math>, where R is the particle radius, <math>\gamma</math> is the interfacial tension between the two fluids, and <math>\theta</math> is the contact angle at the particle surface. For contact angles between ~20-160 degrees, this is many times larger than kT.<br />
<br />
Because they are stabilized by irreversibly-adsorbed solid particles, Pickering emulsions show a unique phenomenon - that of limited coalescence. While this phenomenon has been known dating back to the 1950's, this work by Arditty et al. explores it in depth. Simply put, Pickering emulsion droplets only coalesce to a limited extent, increasing the total droplet surface area until their surfaces are completely covered with solid particles. This gives rise to tremendous stability, as well as droplet dispersions of relatively low size polydispersity. The average droplet size is tuned by the concentration of stabilizing particles - verifying this is a key result of this paper. The derivation of this is straightforward (in the following, r = droplet radius, a = particle radius, <math>\phi</math> = particle volume fraction with respect to dispersed phase):<br />
<br />
Droplets will coalesce until the total surface area of droplets is equal to the total cross-sectional area of stabilizing particles (here, we assume that the effects of polydispersity or a contact angle different from 90 degrees are small). Letting N be the total number of droplets in the system, we have<br />
<br />
<math>N\times 4\pi r^{2}=N\times\phi\pi r^{3}/a</math>, and so <math>r=4a/\phi</math>. This relationship is quite elegant: the average droplet size of the emulsion is directly tuned by the concentration of stabilizing particles.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Limited_coalescence&diff=11280Limited coalescence2009-10-28T04:46:08Z<p>Datta: </p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
S. Arditty, C. P. Whitby, B. P. Binks, V. Schmitt, F. Leal-Calderon, ''Eur. Phys. J. E'' '''11,''' 273 (2003).<br />
<br />
== Keywords ==<br />
<br />
emulsion, [[Pickering emulsion]], interface, coalescence<br />
<br />
== Key Points ==<br />
<br />
Unlike "conventional" surfactant-stabilized emulsions (dispersions of droplets of one immiscible fluid in another), "Pickering" emulsion droplets are stabilized by solid particles (typically much smaller than the droplet size) adsorbed at the droplet interface. (Note: here, "stabilized" means "stabilized against coalescence". While the mechanisms behind this are not fully understood, and depend on the nature of the components of the particular system under consideration, Pickering emulsion stabilization is generally thought to result from a combination of steric hindrance and the formation of a thin film within the pore space of the particles, whose draining properties will depend on the structure and mechanical properties of the particle network.)<br />
<br />
The particle wetting properties determine the bulk properties of the emulsion in two crucial ways:<br />
<br />
- The continuous phase of the emulsion tends to be the phase that preferentially wets the particles. This can be understood in analogy to surfactants - a particle at the interface between the two fluid phases will sit deeper in the wetting phase, and the effective "packing shape" (Israelachvili, page 381) will be similar to a cone, with tapered end inside the non-wetting phase. That is to say, the majority of the particle volume prefers to be immersed in the wetting phase.<br />
<br />
- Unless particles very significantly prefer one phase over the other, they will tend to be irreversibly adsorbed at the interface between the two fluids. This potential energy well is due to the reduced bare surface area in contact between the two fluids, and is given by <math>\pi R^{2} \gamma_{12}(1+cos\theta)^{2}</math>, where R is the particle radius, <math>\gamma</math> is the interfacial tension between the two fluids, and <math>\theta</math> is the contact angle at the particle surface. For contact angles between ~20-160 degrees, this is many times larger than kT.<br />
<br />
Because they are stabilized by irreversibly-adsorbed solid particles, Pickering emulsions show a unique phenomenon - that of limited coalescence. While this phenomenon has been known dating back to the 1950's, this work by Arditty et al. explores it in depth. Simply put, Pickering emulsion droplets only coalesce to a limited extent, increasing the total droplet surface area until their surfaces are completely covered with solid particles. This gives rise to tremendous stability, as well as droplet dispersions of relatively low size polydispersity. The average droplet size is tuned by the concentration of stabilizing particles - this is a key result of this paper. The derivation of this is straightforward (in the following, r = droplet radius, a = particle radius, <math>\phi</math> = particle volume fraction with respect to dispersed phase):<br />
<br />
Droplets will coalesce until the total surface area of droplets is equal to the total cross-sectional area of stabilizing particles (here, we assume that the effects of polydispersity or a contact angle different from 90 degrees are small). Letting N be the total number of droplets in the system, we have<br />
<br />
<math>N\times 4\pi r^{2}=N\times\phi\pi r^{3}/a</math>, and so <math>r=4a/\phi</math>. This relationship is quite elegant: the average droplet size of the emulsion is directly tuned by the concentration of stabilizing particles.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Limited_coalescence&diff=11279Limited coalescence2009-10-28T04:45:24Z<p>Datta: </p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
S. Arditty, C. P. Whitby, B. P. Binks, V. Schmitt, F. Leal-Calderon, ''Eur. Phys. J. E'' '''11,''' 273 (2003).<br />
<br />
== Keywords ==<br />
<br />
emulsion, [[Pickering emulsion]], interface, coalescence<br />
<br />
== Key Points ==<br />
<br />
Unlike "conventional" surfactant-stabilized emulsions (dispersions of droplets of one immiscible fluid in another), "Pickering" emulsion droplets are stabilized by solid particles (typically much smaller than the droplet size) adsorbed at the droplet interface. (Note: here, "stabilized" means "stabilized against coalescence". While the mechanisms behind this are not fully understood, and depend on the nature of the components of the particular system under consideration, Pickering emulsion stabilization is generally thought to result from a combination of steric hindrance and the formation of a thin film within the pore space of the particles, whose draining properties will depend on the structure and mechanical properties of the particle network.)<br />
<br />
The particle wetting properties determine the bulk properties of the emulsion in two crucial ways:<br />
<br />
- The continuous phase of the emulsion tends to be the phase that preferentially wets the particles. This can be understood in analogy to surfactants - a particle at the interface between the two fluid phases will sit deeper in the wetting phase, and the effective "packing shape" (Israelachvili, page 381) will be similar to a cone, with tapered end inside the non-wetting phase. That is to say, the majority of the particle volume prefers to be immersed in the wetting phase.<br />
<br />
- Unless particles very significantly prefer one phase over the other, they will tend to be irreversibly adsorbed at the interface between the two fluids. This potential energy well is due to the reduced bare surface area in contact between the two fluids, and is given by <math>\pi R^{2} \gamma_{12}(1+cos\theta)^{2}</math>, where R is the particle radius, <math>\gamma</math> is the interfacial tension between the two fluids, and <math>\theta</math> is the contact angle at the particle surface. For contact angles between ~20-160 degrees, this is many times larger than kT.<br />
<br />
Because they are stabilized by irreversibly-adsorbed solid particles, Pickering emulsions show a unique phenomenon - that of limited coalescence. While this phenomenon has been known dating back to the 1950's, this work by Arditty et al. explores it in depth. Simply put, Pickering emulsion droplets only coalesce to a limited extent, increasing the total droplet surface area until their surfaces are completely covered with solid particles. This gives rise to tremendous stability, as well as droplet dispersions of relatively low size polydispersity. The average droplet size is tuned by the concentration of stabilizing particles - this is a key result of this paper. The derivation of this is straightforward (in the following, r = droplet radius, a = particle radius, <math>\phi</math> = particle volume fraction with respect to dispersed phase):<br />
<br />
Droplets will coalesce until the total surface area of droplets is equal to the total cross-sectional area of stabilizing particles (here, we assume that the effects of polydispersity or a contact angle different from 90 degrees are small). Letting N be the total number of droplets in the system, we have<br />
<br />
<math>N\times 4\pi r^{2}=N\times\phi\pi r^{3}/a</math>, and so <math>r=4a/\phi</math>.</div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Limited_coalescence&diff=11278Limited coalescence2009-10-28T04:44:56Z<p>Datta: </p>
<hr />
<div>Original entry: Sujit S. Datta, APPHY 225, Fall 2009.<br />
<br />
== Reference ==<br />
<br />
S. Arditty, C. P. Whitby, B. P. Binks, V. Schmitt, F. Leal-Calderon, ''Eur. Phys. J. E'' '''11,''' 273 (2003).<br />
<br />
== Keywords ==<br />
<br />
emulsion, [[Pickering emulsion]], interface, coalescence<br />
<br />
== Key Points ==<br />
<br />
Unlike "conventional" surfactant-stabilized emulsions (dispersions of droplets of one immiscible fluid in another), "Pickering" emulsion droplets are stabilized by solid particles (typically much smaller than the droplet size) adsorbed at the droplet interface. (Note: here, "stabilized" means "stabilized against coalescence". While the mechanisms behind this are not fully understood, and depend on the nature of the components of the particular system under consideration, Pickering emulsion stabilization is generally thought to result from a combination of steric hindrance and the formation of a thin film within the pore space of the particles, whose draining properties will depend on the structure and mechanical properties of the particle network.)<br />
<br />
The particle wetting properties determine the bulk properties of the emulsion in two crucial ways:<br />
<br />
- The continuous phase of the emulsion tends to be the phase that preferentially wets the particles. This can be understood in analogy to surfactants - a particle at the interface between the two fluid phases will sit deeper in the wetting phase, and the effective "packing shape" (Israelachvili, page 381) will be similar to a cone, with tapered end inside the non-wetting phase. That is to say, the majority of the particle volume prefers to be immersed in the wetting phase.<br />
<br />
- Unless particles very significantly prefer one phase over the other, they will tend to be irreversibly adsorbed at the interface between the two fluids. This potential energy well is due to the reduced bare surface area in contact between the two fluids, and is given by <math>\pi R^{2} \gamma_{12}(1+cos\theta)^{2}</math>, where R is the particle radius, <math>\gamma</math> is the interfacial tension between the two fluids, and <math>\theta</math> is the contact angle at the particle surface. For contact angles between ~20-160 degrees, this is many times larger than kT.<br />
<br />
Because they are stabilized by irreversibly-adsorbed solid particles, Pickering emulsions show a unique phenomenon - that of limited coalescence. While this phenomenon has been known dating back to the 1950's, this work by Arditty et al. explores it in depth. Simply put, Pickering emulsion droplets only coalesce to a limited extent, increasing the total droplet surface area until their surfaces are completely covered with solid particles. This gives rise to tremendous stability, as well as droplet dispersions of relatively low size polydispersity. The average droplet size is tuned by the concentration of stabilizing particles - this is a key result of this paper. The derivation of this is straightforward (in the following, r = droplet radius, a = particle radius, <math>\phi</math> = particle volume fraction with respect to dispersed phase):<br />
<br />
Droplets will coalesce until the total surface area of droplets is equal to the total cross-sectional area of stabilizing particles (here, we assume that the effects of polydispersity or a contact angle different from 90 degrees are small). Letting N be the total number of droplets in the system, we have<br />
<br />
<math>N\times 4\pi r^{2}=N\times\phi\pi r^{3}/a</math></div>Dattahttp://soft-matter.seas.harvard.edu/index.php?title=Pickering_emulsion&diff=11276Pickering emulsion2009-10-28T04:34:24Z<p>Datta: </p>
<hr />
<div>Unlike "conventional" surfactant-stabilized emulsions (dispersions of droplets of one immiscible fluid in another), "Pickering" emulsion droplets are stabilized by solid particles (typically much smaller than the droplet size) adsorbed at the droplet interface. (Note: here, "stabilized" means "stabilized against coalescence". While the mechanisms behind this are not fully understood, and depend on the nature of the components of the particular system under consideration, Pickering emulsion stabilization is generally thought to result from a combination of steric hindrance and the formation of a thin film within the pore space of the particles, whose draining properties will depend on the structure and mechanical properties of the particle network.)<br />
<br />
The particle wetting properties determine the bulk properties of the emulsion in two crucial ways:<br />
<br />
- The continuous phase of the emulsion tends to be the phase that preferentially wets the particles. This can be understood in analogy to surfactants - a particle at the interface between the two fluid phases will sit deeper in the wetting phase, and the effective "packing shape" (Israelachvili, page 381) will be similar to a cone, with tapered end inside the non-wetting phase. That is to say, the majority of the particle volume prefers to be immersed in the wetting phase.<br />
<br />
- Unless particles very significantly prefer one phase over the other, they will tend to be irreversibly adsorbed at the interface between the two fluids. This potential energy well is due to the reduced bare surface area in contact between the two fluids, and is given by <math>\pi R^{2} \gamma_{12}(1+cos\theta)^{2}</math>, where R is the particle radius, <math>\gamma</math> is the interfacial tension between the two fluids, and <math>\theta</math> is the contact angle at the particle surface. For contact angles between ~20-160 degrees, this is many times larger than kT.</div>Datta