http://soft-matter.seas.harvard.edu/api.php?action=feedcontributions&user=Mcilwee&feedformat=atomSoft-Matter - User contributions [en]2020-12-01T09:37:09ZUser contributionsMediaWiki 1.24.2http://soft-matter.seas.harvard.edu/index.php?title=Myosin&diff=13816Myosin2009-12-04T21:59:58Z<p>Mcilwee: </p>
<hr />
<div>Myosin II is a motor protein found in the cytoskeleton in the cytoplasm of cells. It is responsible for empowering actin to contract. <br />
<br />
In "[[A quantitative analysis of contractility in active cytoskeletal protein networks]]" by Weitz ''et al''. Show the role of myosin in actin contraction. It was shown that without appropriate amounts of <math>alpha</math>-actinin, myosin cannot produce contraction.<br />
<br />
==References==<br />
http://en.wikipedia.org/wiki/Myosin<br />
<br />
A quantitative analysis of contractility in active cytoskeletal protein networks P. Bendix, G. Koenderink, D. Cuvelier, Z. Dogic, B. Koeleman, W. Brieher, C. Field, L. Mahadevan and D. Weitz, Biophysical Journal, 94, 3126, 2008.</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Myosin&diff=13815Myosin2009-12-04T21:56:27Z<p>Mcilwee: </p>
<hr />
<div>Myosin II is a motor protein found in the cytoskeleton in the cytoplasm of cells. It is responsible for empowering actin to contract. <br />
<br />
In "[[A quantitative analysis of contractility in active cytoskeletal protein networks]]" by Weitz ''et al''. Show the role of myosin in actin contraction. It was shown that without appropriate amounts of <math>alpha</math>-actinin, myosin cannot produce contraction.<br />
<br />
==References==<br />
http://en.wikipedia.org/wiki/Myosin</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Myosin&diff=13813Myosin2009-12-04T21:56:01Z<p>Mcilwee: </p>
<hr />
<div>Myosin II is a motor protein found in the cytoskeleton in the cytoplasm of cells. It is responsible for enpowering actin to contract. <br />
<br />
In "[[A quantitative analysis of contractility in active cytoskeletal protein networks]]" by Weitz ''et al''. Show the role of myosin in actin contraction. It was shown that without appropriate amounts of <math>alpha</math>-actinin, myosin cannot produce contraction.<br />
<br />
==References==<br />
http://en.wikipedia.org/wiki/Myosin</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Myosin&diff=13812Myosin2009-12-04T21:55:24Z<p>Mcilwee: </p>
<hr />
<div>Myosin II is a motor protein found in the cytoskeleton in the cytoplasm of cells. It is responsible for enpowering actin to contract. <br />
<br />
In "[[A Quantitative Analysis of Contractility in Active Cytoskeletal Protein Networks]]" by Weitz ''et al''. Show the role of myosin in actin contraction. It was shown that without appropriate amounts of <math>alpha</math>-actinin, myosin cannot produce contraction.<br />
<br />
==References==<br />
http://en.wikipedia.org/wiki/Myosin</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=A_quantitative_analysis_of_contractility_in_active_cytoskeletal_protein_networks&diff=13809A quantitative analysis of contractility in active cytoskeletal protein networks2009-12-04T21:43:13Z<p>Mcilwee: </p>
<hr />
<div>Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
A quantitative analysis of contractility in active cytoskeletal protein networks P. Bendix, G. Koenderink, D. Cuvelier, Z. Dogic, B. Koeleman, W. Brieher, C. Field, L. Mahadevan and D. Weitz, Biophysical Journal, 94, 3126, 2008. <br />
<br />
== Paper Abstract ==<br />
Cells actively produce contractile forces for a variety of processes including cytokinesis and motility. Contractility is<br />
known to rely on myosin II motors which convert chemical energy from ATP hydrolysis into forces on actin filaments. However, the<br />
basic physical principles of cell contractility remain poorly understood. We reconstitute contractility in a simplified model system of purified F-actin, muscle myosin II motors, and a-actinin cross-linkers. We show that contractility occurs above a threshold motor concentration and within a window of cross-linker concentrations. We also quantify the pore size of the bundled networks and find contractility to occur at a critical distance between the bundles. We propose a simple mechanism of contraction based on myosin filaments pulling neighboring bundles together into an aggregated structure. Observations of this reconstituted system in both bulk and low-dimensional geometries show that the contracting gels pull on and deform their surface with a contractile force of 1mN, or 100 pN per F-actin bundle. Cytoplasmic extracts contracting in identical environments show a similar behavior and dependence on myosin as the reconstituted system. Our results suggest that cellular contractility can be sensitively regulated by tuning the (local) activity of molecular motors and the cross-linker density and binding affinity.<br />
<br />
== Keywords ==<br />
[[myosin]], actin, cellular contraction<br />
<br />
== Soft Matter ==<br />
Contractile forces are important for cell function. Forces are transmitted by the cytoskeleton, a dynamic scaffold of protein filaments throughout the cytoplasm connected to the plasma membrane. Actin and Myosin II have been identified as the main components in this contraction. F-actin provides the structure upon which myosin performs its job, powered by ATP hydrolysis. Contraction of cross-linked actin-myosin networks is mediated by internal stresses that are actively generated by the myosin motors. Myosin assembles and generates gliding of actin filaments past one another. Though there have been many successful attempts to model the contractile actin cortex, there is still a limited understanding of the dependence of contractility and pattern formation in actin-myosin gels on microscopic parameters such as the number, activity, and processivity of the myosin motors or the local cross-linker density and actin network connectivity.<br />
<br />
[[Image:McIlwee_Rheology_3.jpg|thumb|center|700px|alt=Figure 1.|Figure 1.]]<br />
<br />
Experiments have shown that contraction is accelerated by proteins that crosslink the actin filaments, but systematic and quantitative investigation of contraction is difficult because of the complexity of the system. Contraction has been studied in simplified systems and even then the importance of F-actin crosslinker was apparent. It was also shown that myosin cannot adequately do its job without the crosslinks. <br />
<br />
[[Image:McIlwee_Rheology_2.jpg|thumb|center|700px|alt=Figure 2.|Figure 2.]]<br />
<br />
Here Weitz ''et al''. focus on <math>alpha</math>-actinin, a protein expressed in contractile cytoskeletal assemblies, for example muscle myofibrils. A simplified model of actin, myosin, and <math>alpha</math>-actinin was used. Microstructure and macroscopic behavior is imaged using confocal microscopy. The number of crosslinks and myosin motors per actin filament is varied. It is sown that contractility is achieved at a critical concentration of <math>alpha</math>-actinin. It is concluded that contractility is caused by myosin filaments pulling on actin bundles without changing the bundle dimensions. The results reveal the molecular mechanisms underlying macroscopic force generation by a collection of myosin motors embedded in a random network of actin filaments.<br />
<br />
[[Image:McIlwee_Rheology_1.jpg|thumb|center|700px|alt=Figure 3.|Figure 3.]]<br />
<br />
Biological systems can give us many cues to take when building synthetic systems. It is important to study the soft matter of biology in order to realize its potentials in synthetic or biohybrid systems. You can imagine a contractile system like this being translated into an actuator for instance. <br />
<br />
== References ==<br />
P. Bendix, G. Koenderink, D. Cuvelier, Z. Dogic, B. Koeleman, W. Brieher, C. Field, L. Mahadevan and D. Weitz, A quantitative analysis of contractility in active cytoskeletal protein networks, Biophysical Journal, 94, 3126, 2008.</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=A_quantitative_analysis_of_contractility_in_active_cytoskeletal_protein_networks&diff=13804A quantitative analysis of contractility in active cytoskeletal protein networks2009-12-04T21:31:10Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
A quantitative analysis of contractility in active cytoskeletal protein networks P. Bendix, G. Koenderink, D. Cuvelier, Z. Dogic, B. Koeleman, W. Brieher, C. Field, L. Mahadevan and D. Weitz, Biophysical Journal, 94, 3126, 2008. <br />
<br />
== Abstract ==<br />
Cells actively produce contractile forces for a variety of processes including cytokinesis and motility. Contractility is<br />
known to rely on myosin II motors which convert chemical energy from ATP hydrolysis into forces on actin filaments. However, the<br />
basic physical principles of cell contractility remain poorly understood. We reconstitute contractility in a simplified model system of<br />
purified F-actin, muscle myosin II motors, and a-actinin cross-linkers. We show that contractility occurs above a threshold motor<br />
concentration and within a window of cross-linker concentrations. We also quantify the pore size of the bundled networks and find<br />
contractility to occur at a critical distance between the bundles. We propose a simple mechanism of contraction based on myosin<br />
filaments pulling neighboring bundles together into an aggregated structure. Observations of this reconstituted system in both bulk<br />
and low-dimensional geometries show that the contracting gels pull on and deform their surface with a contractile force of;1mN, or<br />
;100 pN per F-actin bundle. Cytoplasmic extracts contracting in identical environments show a similar behavior and dependence<br />
on myosin as the reconstituted system. Our results suggest that cellular contractility can be sensitively regulated by tuning the<br />
(local) activity of molecular motors and the cross-linker density and binding affinity.<br />
<br />
== Keywords ==<br />
[[myosin]], actin, cellular contraction<br />
<br />
== Soft Matter ==<br />
Contractile forces are important for cell function. Forces are transmitted by the cytoskeleton, a dynamic scaffold of protein filaments throughout the cytoplasm connected to the plasma membrane. Actin and Myosin II have been identified as the main components in this contraction. F-actin provides the structure upon which myosin performs its job, powered by ATP hydrolysis. Contraction of cross-linked actin-myosin networks is mediated by internal stresses that are actively generated by the myosin motors. Myosin assembles and generates gliding of actin filaments past one another. Though there have been many successful attempts to model the contractile actin cortex, there is still a limited understanding of the dependence of contractility and pattern formation in actin-myosin gels on microscopic parameters such as the number, activity, and processivity of the myosin motors or the local cross-linker density and actin network connectivity.<br />
<br />
[[Image:McIlwee_Rheology_3.jpg|thumb|center|700px|alt=Figure 1.|Figure 1.]]<br />
<br />
Experiments have shown that contraction is accelerated by proteins that crosslink the actin filaments, but systematic and quantitative investigation of contraction is difficult because of the complexity of the system. Contraction has been studied in simplified systems and even then the importance of F-actin crosslinker was apparent. It was also shown that myosin cannot adequately do its job without the crosslinks. <br />
<br />
[[Image:McIlwee_Rheology_2.jpg|thumb|center|700px|alt=Figure 2.|Figure 2.]]<br />
<br />
Here Weitz ''et al''. focus on <math>alpha</math>-actinin, a protein expressed in contractile cytoskeletal assemblies, for example muscle myofibrils. A simplified model of actin, myosin, and <math>alpha</math>-actinin was used. Microstructure and macroscopic behavior is imaged using confocal microscopy. The number of crosslinks and myosin motors per actin filament is varied. It is sown that contractility is achieved at a critical concentration of <math>alpha</math>-actinin. It is concluded that contractility is caused by myosin filaments pulling on actin bundles without changing the bundle dimensions. The results reveal the molecular mechanisms underlying macroscopic force generation by a collection of myosin motors embedded in a random network of actin filaments.<br />
<br />
[[Image:McIlwee_Rheology_1.jpg|thumb|center|700px|alt=Figure 3.|Figure 3.]]<br />
<br />
== References ==</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=A_quantitative_analysis_of_contractility_in_active_cytoskeletal_protein_networks&diff=13803A quantitative analysis of contractility in active cytoskeletal protein networks2009-12-04T21:30:46Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
A quantitative analysis of contractility in active cytoskeletal protein networks P. Bendix, G. Koenderink, D. Cuvelier, Z. Dogic, B. Koeleman, W. Brieher, C. Field, L. Mahadevan and D. Weitz, Biophysical Journal, 94, 3126, 2008. <br />
<br />
== Abstract ==<br />
Cells actively produce contractile forces for a variety of processes including cytokinesis and motility. Contractility is<br />
known to rely on myosin II motors which convert chemical energy from ATP hydrolysis into forces on actin filaments. However, the<br />
basic physical principles of cell contractility remain poorly understood. We reconstitute contractility in a simplified model system of<br />
purified F-actin, muscle myosin II motors, and a-actinin cross-linkers. We show that contractility occurs above a threshold motor<br />
concentration and within a window of cross-linker concentrations. We also quantify the pore size of the bundled networks and find<br />
contractility to occur at a critical distance between the bundles. We propose a simple mechanism of contraction based on myosin<br />
filaments pulling neighboring bundles together into an aggregated structure. Observations of this reconstituted system in both bulk<br />
and low-dimensional geometries show that the contracting gels pull on and deform their surface with a contractile force of;1mN, or<br />
;100 pN per F-actin bundle. Cytoplasmic extracts contracting in identical environments show a similar behavior and dependence<br />
on myosin as the reconstituted system. Our results suggest that cellular contractility can be sensitively regulated by tuning the<br />
(local) activity of molecular motors and the cross-linker density and binding affinity.<br />
<br />
== Keywords ==<br />
[[myosin]], actin, cellular contraction<br />
<br />
== Soft Matter ==<br />
Contractile forces are important for cell function. Forces are transmitted by the cytoskeleton, a dynamic scaffold of protein filaments throughout the cytoplasm connected to the plasma membrane. Actin and Myosin II have been identified as the main components in this contraction. F-actin provides the structure upon which myosin performs its job, powered by ATP hydrolysis. Contraction of cross-linked actin-myosin networks is mediated by internal stresses that are actively generated by the myosin motors. Myosin assembles and generates gliding of actin filaments past one another. Though there have been many successful attempts to model the contractile actin cortex, there is still a limited understanding of the dependence of contractility and pattern formation in actin-myosin gels on microscopic parameters such as the number, activity, and processivity of the myosin motors or the local cross-linker density and actin network connectivity.<br />
<br />
[[Image:McIlwee_Rheology_3.jpg|thumb|center|600px|alt=Figure 1.|Figure 1.]]<br />
<br />
Experiments have shown that contraction is accelerated by proteins that crosslink the actin filaments, but systematic and quantitative investigation of contraction is difficult because of the complexity of the system. Contraction has been studied in simplified systems and even then the importance of F-actin crosslinker was apparent. It was also shown that myosin cannot adequately do its job without the crosslinks. <br />
<br />
[[Image:McIlwee_Rheology_2.jpg|thumb|center|600px|alt=Figure 2.|Figure 2.]]<br />
<br />
Here Weitz ''et al''. focus on <math>alpha</math>-actinin, a protein expressed in contractile cytoskeletal assemblies, for example muscle myofibrils. A simplified model of actin, myosin, and <math>alpha</math>-actinin was used. Microstructure and macroscopic behavior is imaged using confocal microscopy. The number of crosslinks and myosin motors per actin filament is varied. It is sown that contractility is achieved at a critical concentration of <math>alpha</math>-actinin. It is concluded that contractility is caused by myosin filaments pulling on actin bundles without changing the bundle dimensions. The results reveal the molecular mechanisms underlying macroscopic force generation by a collection of myosin motors embedded in a random network of actin filaments.<br />
<br />
[[Image:McIlwee_Rheology_1.jpg|thumb|center|600px|alt=Figure 3.|Figure 3.]]<br />
<br />
== References ==</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=A_quantitative_analysis_of_contractility_in_active_cytoskeletal_protein_networks&diff=13802A quantitative analysis of contractility in active cytoskeletal protein networks2009-12-04T21:30:31Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
A quantitative analysis of contractility in active cytoskeletal protein networks P. Bendix, G. Koenderink, D. Cuvelier, Z. Dogic, B. Koeleman, W. Brieher, C. Field, L. Mahadevan and D. Weitz, Biophysical Journal, 94, 3126, 2008. <br />
<br />
== Abstract ==<br />
Cells actively produce contractile forces for a variety of processes including cytokinesis and motility. Contractility is<br />
known to rely on myosin II motors which convert chemical energy from ATP hydrolysis into forces on actin filaments. However, the<br />
basic physical principles of cell contractility remain poorly understood. We reconstitute contractility in a simplified model system of<br />
purified F-actin, muscle myosin II motors, and a-actinin cross-linkers. We show that contractility occurs above a threshold motor<br />
concentration and within a window of cross-linker concentrations. We also quantify the pore size of the bundled networks and find<br />
contractility to occur at a critical distance between the bundles. We propose a simple mechanism of contraction based on myosin<br />
filaments pulling neighboring bundles together into an aggregated structure. Observations of this reconstituted system in both bulk<br />
and low-dimensional geometries show that the contracting gels pull on and deform their surface with a contractile force of;1mN, or<br />
;100 pN per F-actin bundle. Cytoplasmic extracts contracting in identical environments show a similar behavior and dependence<br />
on myosin as the reconstituted system. Our results suggest that cellular contractility can be sensitively regulated by tuning the<br />
(local) activity of molecular motors and the cross-linker density and binding affinity.<br />
<br />
== Keywords ==<br />
[[myosin]], actin, cellular contraction<br />
<br />
== Soft Matter ==<br />
Contractile forces are important for cell function. Forces are transmitted by the cytoskeleton, a dynamic scaffold of protein filaments throughout the cytoplasm connected to the plasma membrane. Actin and Myosin II have been identified as the main components in this contraction. F-actin provides the structure upon which myosin performs its job, powered by ATP hydrolysis. Contraction of cross-linked actin-myosin networks is mediated by internal stresses that are actively generated by the myosin motors. Myosin assembles and generates gliding of actin filaments past one another. Though there have been many successful attempts to model the contractile actin cortex, there is still a limited understanding of the dependence of contractility and pattern formation in actin-myosin gels on microscopic parameters such as the number, activity, and processivity of the myosin motors or the local cross-linker density and actin network connectivity.<br />
<br />
[[Image:McIlwee_Rheology_3.jpg|thumb|center|500px|alt=Figure 1.|Figure 1.]]<br />
<br />
Experiments have shown that contraction is accelerated by proteins that crosslink the actin filaments, but systematic and quantitative investigation of contraction is difficult because of the complexity of the system. Contraction has been studied in simplified systems and even then the importance of F-actin crosslinker was apparent. It was also shown that myosin cannot adequately do its job without the crosslinks. <br />
<br />
[[Image:McIlwee_Rheology_2.jpg|thumb|center|500px|alt=Figure 2.|Figure 2.]]<br />
<br />
Here Weitz ''et al''. focus on <math>alpha</math>-actinin, a protein expressed in contractile cytoskeletal assemblies, for example muscle myofibrils. A simplified model of actin, myosin, and <math>alpha</math>-actinin was used. Microstructure and macroscopic behavior is imaged using confocal microscopy. The number of crosslinks and myosin motors per actin filament is varied. It is sown that contractility is achieved at a critical concentration of <math>alpha</math>-actinin. It is concluded that contractility is caused by myosin filaments pulling on actin bundles without changing the bundle dimensions. The results reveal the molecular mechanisms underlying macroscopic force generation by a collection of myosin motors embedded in a random network of actin filaments.<br />
<br />
[[Image:McIlwee_Rheology_1.jpg|thumb|center|500px|alt=Figure 3.|Figure 3.]]<br />
<br />
== References ==</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=A_quantitative_analysis_of_contractility_in_active_cytoskeletal_protein_networks&diff=13801A quantitative analysis of contractility in active cytoskeletal protein networks2009-12-04T21:30:13Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
A quantitative analysis of contractility in active cytoskeletal protein networks P. Bendix, G. Koenderink, D. Cuvelier, Z. Dogic, B. Koeleman, W. Brieher, C. Field, L. Mahadevan and D. Weitz, Biophysical Journal, 94, 3126, 2008. <br />
<br />
== Abstract ==<br />
Cells actively produce contractile forces for a variety of processes including cytokinesis and motility. Contractility is<br />
known to rely on myosin II motors which convert chemical energy from ATP hydrolysis into forces on actin filaments. However, the<br />
basic physical principles of cell contractility remain poorly understood. We reconstitute contractility in a simplified model system of<br />
purified F-actin, muscle myosin II motors, and a-actinin cross-linkers. We show that contractility occurs above a threshold motor<br />
concentration and within a window of cross-linker concentrations. We also quantify the pore size of the bundled networks and find<br />
contractility to occur at a critical distance between the bundles. We propose a simple mechanism of contraction based on myosin<br />
filaments pulling neighboring bundles together into an aggregated structure. Observations of this reconstituted system in both bulk<br />
and low-dimensional geometries show that the contracting gels pull on and deform their surface with a contractile force of;1mN, or<br />
;100 pN per F-actin bundle. Cytoplasmic extracts contracting in identical environments show a similar behavior and dependence<br />
on myosin as the reconstituted system. Our results suggest that cellular contractility can be sensitively regulated by tuning the<br />
(local) activity of molecular motors and the cross-linker density and binding affinity.<br />
<br />
== Keywords ==<br />
[[myosin]], actin, cellular contraction<br />
<br />
== Soft Matter ==<br />
Contractile forces are important for cell function. Forces are transmitted by the cytoskeleton, a dynamic scaffold of protein filaments throughout the cytoplasm connected to the plasma membrane. Actin and Myosin II have been identified as the main components in this contraction. F-actin provides the structure upon which myosin performs its job, powered by ATP hydrolysis. Contraction of cross-linked actin-myosin networks is mediated by internal stresses that are actively generated by the myosin motors. Myosin assembles and generates gliding of actin filaments past one another. Though there have been many successful attempts to model the contractile actin cortex, there is still a limited understanding of the dependence of contractility and pattern formation in actin-myosin gels on microscopic parameters such as the number, activity, and processivity of the myosin motors or the local cross-linker density and actin network connectivity.<br />
<br />
[[Image:McIlwee_Rheology_3.jpg|thumb|center|400px|alt=Figure 1.|Figure 1.]]<br />
<br />
Experiments have shown that contraction is accelerated by proteins that crosslink the actin filaments, but systematic and quantitative investigation of contraction is difficult because of the complexity of the system. Contraction has been studied in simplified systems and even then the importance of F-actin crosslinker was apparent. It was also shown that myosin cannot adequately do its job without the crosslinks. <br />
<br />
[[Image:McIlwee_Rheology_2.jpg|thumb|center|400px|alt=Figure 2.|Figure 2.]]<br />
<br />
Here Weitz ''et al''. focus on <math>alpha</math>-actinin, a protein expressed in contractile cytoskeletal assemblies, for example muscle myofibrils. A simplified model of actin, myosin, and <math>alpha</math>-actinin was used. Microstructure and macroscopic behavior is imaged using confocal microscopy. The number of crosslinks and myosin motors per actin filament is varied. It is sown that contractility is achieved at a critical concentration of <math>alpha</math>-actinin. It is concluded that contractility is caused by myosin filaments pulling on actin bundles without changing the bundle dimensions. The results reveal the molecular mechanisms underlying macroscopic force generation by a collection of myosin motors embedded in a random network of actin filaments.<br />
<br />
[[Image:McIlwee_Rheology_1.jpg|thumb|center|400px|alt=Figure 3.|Figure 3.]]<br />
<br />
== References ==</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=File:McIlwee_Rheology_3.jpg&diff=13797File:McIlwee Rheology 3.jpg2009-12-04T21:27:55Z<p>Mcilwee: </p>
<hr />
<div></div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=File:McIlwee_Rheology_2.jpg&diff=13796File:McIlwee Rheology 2.jpg2009-12-04T21:27:06Z<p>Mcilwee: </p>
<hr />
<div></div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=A_quantitative_analysis_of_contractility_in_active_cytoskeletal_protein_networks&diff=13795A quantitative analysis of contractility in active cytoskeletal protein networks2009-12-04T21:26:54Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
A quantitative analysis of contractility in active cytoskeletal protein networks P. Bendix, G. Koenderink, D. Cuvelier, Z. Dogic, B. Koeleman, W. Brieher, C. Field, L. Mahadevan and D. Weitz, Biophysical Journal, 94, 3126, 2008. <br />
<br />
== Abstract ==<br />
Cells actively produce contractile forces for a variety of processes including cytokinesis and motility. Contractility is<br />
known to rely on myosin II motors which convert chemical energy from ATP hydrolysis into forces on actin filaments. However, the<br />
basic physical principles of cell contractility remain poorly understood. We reconstitute contractility in a simplified model system of<br />
purified F-actin, muscle myosin II motors, and a-actinin cross-linkers. We show that contractility occurs above a threshold motor<br />
concentration and within a window of cross-linker concentrations. We also quantify the pore size of the bundled networks and find<br />
contractility to occur at a critical distance between the bundles. We propose a simple mechanism of contraction based on myosin<br />
filaments pulling neighboring bundles together into an aggregated structure. Observations of this reconstituted system in both bulk<br />
and low-dimensional geometries show that the contracting gels pull on and deform their surface with a contractile force of;1mN, or<br />
;100 pN per F-actin bundle. Cytoplasmic extracts contracting in identical environments show a similar behavior and dependence<br />
on myosin as the reconstituted system. Our results suggest that cellular contractility can be sensitively regulated by tuning the<br />
(local) activity of molecular motors and the cross-linker density and binding affinity.<br />
<br />
== Keywords ==<br />
[[myosin]], actin, cellular contraction<br />
<br />
== Soft Matter ==<br />
Contractile forces are important for cell function. Forces are transmitted by the cytoskeleton, a dynamic scaffold of protein filaments throughout the cytoplasm connected to the plasma membrane. Actin and Myosin II have been identified as the main components in this contraction. F-actin provides the structure upon which myosin performs its job, powered by ATP hydrolysis.Contraction of cross-linked actin-myosin networks is mediated by internal stresses that are actively generated by the<br />
myosin motors. Myosin assembles and generates gliding of actin filaments past one another. Though there have been many successful attempts to model the contractile actin cortex, there is still a limited understanding of the dependence of contractility and pattern formation in actin-myosin gels on microscopic parameters such as the number, activity, and processivity of the myosin motors or the local cross-linker density and actin network connectivity.<br />
<br />
Experiments have shown that contraction is accelerated by proteins that crosslink the actin filaments, but systematic and quantitative investigation of contraction is difficult because of the complexity of the system. Contraction has been studied in simplified systems and even then the importance of F-actin crosslinker was apparent. It was also shown that myosin cannot adequately do its job without the crosslinks. <br />
<br />
Here Weitz ''et al''. focus on <math>alpha</math>-actinin, a protein expressed in contractile cytoskeletal assemblies, for example muscle myofibrils. A simplified model of actin, myosin, and <math>alpha</math>-actinin was used. Microstructure and macroscopic behavior is imaged using confocal microscopy. The number of crosslinks and myosin motors per actin filament is varied. It is sown that contractility is achieved at a critical concentration of <math>alpha</math>-actinin. It is concluded that contractility is caused by myosin filaments pulling on actin bundles without changing the bundle dimensions. The results reveal the molecular mechanisms underlying macroscopic force generation by a collection of myosin motors embedded in a random network of actin filaments.<br />
<br />
McIlwee_Rheology_1.jpg<br />
<br />
McIlwee_Rheology_2.jpg<br />
<br />
== References ==</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=File:McIlwee_Rheology_1.jpg&diff=13794File:McIlwee Rheology 1.jpg2009-12-04T21:24:25Z<p>Mcilwee: </p>
<hr />
<div></div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=A_quantitative_analysis_of_contractility_in_active_cytoskeletal_protein_networks&diff=13793A quantitative analysis of contractility in active cytoskeletal protein networks2009-12-04T21:24:04Z<p>Mcilwee: /* Keywords */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
A quantitative analysis of contractility in active cytoskeletal protein networks P. Bendix, G. Koenderink, D. Cuvelier, Z. Dogic, B. Koeleman, W. Brieher, C. Field, L. Mahadevan and D. Weitz, Biophysical Journal, 94, 3126, 2008. <br />
<br />
== Abstract ==<br />
Cells actively produce contractile forces for a variety of processes including cytokinesis and motility. Contractility is<br />
known to rely on myosin II motors which convert chemical energy from ATP hydrolysis into forces on actin filaments. However, the<br />
basic physical principles of cell contractility remain poorly understood. We reconstitute contractility in a simplified model system of<br />
purified F-actin, muscle myosin II motors, and a-actinin cross-linkers. We show that contractility occurs above a threshold motor<br />
concentration and within a window of cross-linker concentrations. We also quantify the pore size of the bundled networks and find<br />
contractility to occur at a critical distance between the bundles. We propose a simple mechanism of contraction based on myosin<br />
filaments pulling neighboring bundles together into an aggregated structure. Observations of this reconstituted system in both bulk<br />
and low-dimensional geometries show that the contracting gels pull on and deform their surface with a contractile force of;1mN, or<br />
;100 pN per F-actin bundle. Cytoplasmic extracts contracting in identical environments show a similar behavior and dependence<br />
on myosin as the reconstituted system. Our results suggest that cellular contractility can be sensitively regulated by tuning the<br />
(local) activity of molecular motors and the cross-linker density and binding affinity.<br />
<br />
== Keywords ==<br />
[[myosin]], actin, cellular contraction<br />
<br />
== Soft Matter ==<br />
Contractile forces are important for cell function. Forces are transmitted by the cytoskeleton, a dynamic scaffold of protein filaments throughout the cytoplasm connected to the plasma membrane. Actin and Myosin II have been identified as the main components in this contraction. F-actin provides the structure upon which myosin performs its job, powered by ATP hydrolysis.Contraction of cross-linked actin-myosin networks is mediated by internal stresses that are actively generated by the<br />
myosin motors. Myosin assembles and generates gliding of actin filaments past one another. Though there have been many successful attempts to model the contractile actin cortex, there is still a limited understanding of the dependence of contractility and pattern formation in actin-myosin gels on microscopic parameters such as the number, activity, and processivity of the myosin motors or the local cross-linker density and actin network connectivity.<br />
<br />
Experiments have shown that contraction is accelerated by proteins that crosslink the actin filaments, but systematic and quantitative investigation of contraction is difficult because of the complexity of the system. Contraction has been studied in simplified systems and even then the importance of F-actin crosslinker was apparent. It was also shown that myosin cannot adequately do its job without the crosslinks. <br />
<br />
Here Weitz ''et al''. focus on <math>alpha</math>-actinin, a protein expressed in contractile cytoskeletal assemblies, for example muscle myofibrils. A simplified model of actin, myosin, and <math>alpha</math>-actinin was used. Microstructure and macroscopic behavior is imaged using confocal microscopy. The number of crosslinks and myosin motors per actin filament is varied. It is sown that contractility is achieved at a critical concentration of <math>alpha</math>-actinin. It is concluded that contractility is caused by myosin filaments pulling on actin bundles without changing the bundle dimensions. The results reveal the molecular mechanisms underlying macroscopic force generation by a collection of myosin motors embedded in a random network of actin filaments.<br />
<br />
== References ==</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=A_quantitative_analysis_of_contractility_in_active_cytoskeletal_protein_networks&diff=13792A quantitative analysis of contractility in active cytoskeletal protein networks2009-12-04T21:23:53Z<p>Mcilwee: /* Keywords */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
A quantitative analysis of contractility in active cytoskeletal protein networks P. Bendix, G. Koenderink, D. Cuvelier, Z. Dogic, B. Koeleman, W. Brieher, C. Field, L. Mahadevan and D. Weitz, Biophysical Journal, 94, 3126, 2008. <br />
<br />
== Abstract ==<br />
Cells actively produce contractile forces for a variety of processes including cytokinesis and motility. Contractility is<br />
known to rely on myosin II motors which convert chemical energy from ATP hydrolysis into forces on actin filaments. However, the<br />
basic physical principles of cell contractility remain poorly understood. We reconstitute contractility in a simplified model system of<br />
purified F-actin, muscle myosin II motors, and a-actinin cross-linkers. We show that contractility occurs above a threshold motor<br />
concentration and within a window of cross-linker concentrations. We also quantify the pore size of the bundled networks and find<br />
contractility to occur at a critical distance between the bundles. We propose a simple mechanism of contraction based on myosin<br />
filaments pulling neighboring bundles together into an aggregated structure. Observations of this reconstituted system in both bulk<br />
and low-dimensional geometries show that the contracting gels pull on and deform their surface with a contractile force of;1mN, or<br />
;100 pN per F-actin bundle. Cytoplasmic extracts contracting in identical environments show a similar behavior and dependence<br />
on myosin as the reconstituted system. Our results suggest that cellular contractility can be sensitively regulated by tuning the<br />
(local) activity of molecular motors and the cross-linker density and binding affinity.<br />
<br />
== Keywords ==<br />
[[myosin]], Actin, Cellular contraction<br />
<br />
== Soft Matter ==<br />
Contractile forces are important for cell function. Forces are transmitted by the cytoskeleton, a dynamic scaffold of protein filaments throughout the cytoplasm connected to the plasma membrane. Actin and Myosin II have been identified as the main components in this contraction. F-actin provides the structure upon which myosin performs its job, powered by ATP hydrolysis.Contraction of cross-linked actin-myosin networks is mediated by internal stresses that are actively generated by the<br />
myosin motors. Myosin assembles and generates gliding of actin filaments past one another. Though there have been many successful attempts to model the contractile actin cortex, there is still a limited understanding of the dependence of contractility and pattern formation in actin-myosin gels on microscopic parameters such as the number, activity, and processivity of the myosin motors or the local cross-linker density and actin network connectivity.<br />
<br />
Experiments have shown that contraction is accelerated by proteins that crosslink the actin filaments, but systematic and quantitative investigation of contraction is difficult because of the complexity of the system. Contraction has been studied in simplified systems and even then the importance of F-actin crosslinker was apparent. It was also shown that myosin cannot adequately do its job without the crosslinks. <br />
<br />
Here Weitz ''et al''. focus on <math>alpha</math>-actinin, a protein expressed in contractile cytoskeletal assemblies, for example muscle myofibrils. A simplified model of actin, myosin, and <math>alpha</math>-actinin was used. Microstructure and macroscopic behavior is imaged using confocal microscopy. The number of crosslinks and myosin motors per actin filament is varied. It is sown that contractility is achieved at a critical concentration of <math>alpha</math>-actinin. It is concluded that contractility is caused by myosin filaments pulling on actin bundles without changing the bundle dimensions. The results reveal the molecular mechanisms underlying macroscopic force generation by a collection of myosin motors embedded in a random network of actin filaments.<br />
<br />
== References ==</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=A_quantitative_analysis_of_contractility_in_active_cytoskeletal_protein_networks&diff=13790A quantitative analysis of contractility in active cytoskeletal protein networks2009-12-04T21:23:00Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
A quantitative analysis of contractility in active cytoskeletal protein networks P. Bendix, G. Koenderink, D. Cuvelier, Z. Dogic, B. Koeleman, W. Brieher, C. Field, L. Mahadevan and D. Weitz, Biophysical Journal, 94, 3126, 2008. <br />
<br />
== Abstract ==<br />
Cells actively produce contractile forces for a variety of processes including cytokinesis and motility. Contractility is<br />
known to rely on myosin II motors which convert chemical energy from ATP hydrolysis into forces on actin filaments. However, the<br />
basic physical principles of cell contractility remain poorly understood. We reconstitute contractility in a simplified model system of<br />
purified F-actin, muscle myosin II motors, and a-actinin cross-linkers. We show that contractility occurs above a threshold motor<br />
concentration and within a window of cross-linker concentrations. We also quantify the pore size of the bundled networks and find<br />
contractility to occur at a critical distance between the bundles. We propose a simple mechanism of contraction based on myosin<br />
filaments pulling neighboring bundles together into an aggregated structure. Observations of this reconstituted system in both bulk<br />
and low-dimensional geometries show that the contracting gels pull on and deform their surface with a contractile force of;1mN, or<br />
;100 pN per F-actin bundle. Cytoplasmic extracts contracting in identical environments show a similar behavior and dependence<br />
on myosin as the reconstituted system. Our results suggest that cellular contractility can be sensitively regulated by tuning the<br />
(local) activity of molecular motors and the cross-linker density and binding affinity.<br />
<br />
== Keywords ==<br />
<br />
<br />
== Soft Matter ==<br />
Contractile forces are important for cell function. Forces are transmitted by the cytoskeleton, a dynamic scaffold of protein filaments throughout the cytoplasm connected to the plasma membrane. Actin and Myosin II have been identified as the main components in this contraction. F-actin provides the structure upon which myosin performs its job, powered by ATP hydrolysis.Contraction of cross-linked actin-myosin networks is mediated by internal stresses that are actively generated by the<br />
myosin motors. Myosin assembles and generates gliding of actin filaments past one another. Though there have been many successful attempts to model the contractile actin cortex, there is still a limited understanding of the dependence of contractility and pattern formation in actin-myosin gels on microscopic parameters such as the number, activity, and processivity of the myosin motors or the local cross-linker density and actin network connectivity.<br />
<br />
Experiments have shown that contraction is accelerated by proteins that crosslink the actin filaments, but systematic and quantitative investigation of contraction is difficult because of the complexity of the system. Contraction has been studied in simplified systems and even then the importance of F-actin crosslinker was apparent. It was also shown that myosin cannot adequately do its job without the crosslinks. <br />
<br />
Here Weitz ''et al''. focus on <math>alpha</math>-actinin, a protein expressed in contractile cytoskeletal assemblies, for example muscle myofibrils. A simplified model of actin, myosin, and <math>alpha</math>-actinin was used. Microstructure and macroscopic behavior is imaged using confocal microscopy. The number of crosslinks and myosin motors per actin filament is varied. It is sown that contractility is achieved at a critical concentration of <math>alpha</math>-actinin. It is concluded that contractility is caused by myosin filaments pulling on actin bundles without changing the bundle dimensions. The results reveal the molecular mechanisms underlying macroscopic force generation by a collection of myosin motors embedded in a random network of actin filaments.<br />
<br />
== References ==</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=A_quantitative_analysis_of_contractility_in_active_cytoskeletal_protein_networks&diff=13789A quantitative analysis of contractility in active cytoskeletal protein networks2009-12-04T21:22:40Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
A quantitative analysis of contractility in active cytoskeletal protein networks P. Bendix, G. Koenderink, D. Cuvelier, Z. Dogic, B. Koeleman, W. Brieher, C. Field, L. Mahadevan and D. Weitz, Biophysical Journal, 94, 3126, 2008. <br />
<br />
== Abstract ==<br />
Cells actively produce contractile forces for a variety of processes including cytokinesis and motility. Contractility is<br />
known to rely on myosin II motors which convert chemical energy from ATP hydrolysis into forces on actin filaments. However, the<br />
basic physical principles of cell contractility remain poorly understood. We reconstitute contractility in a simplified model system of<br />
purified F-actin, muscle myosin II motors, and a-actinin cross-linkers. We show that contractility occurs above a threshold motor<br />
concentration and within a window of cross-linker concentrations. We also quantify the pore size of the bundled networks and find<br />
contractility to occur at a critical distance between the bundles. We propose a simple mechanism of contraction based on myosin<br />
filaments pulling neighboring bundles together into an aggregated structure. Observations of this reconstituted system in both bulk<br />
and low-dimensional geometries show that the contracting gels pull on and deform their surface with a contractile force of;1mN, or<br />
;100 pN per F-actin bundle. Cytoplasmic extracts contracting in identical environments show a similar behavior and dependence<br />
on myosin as the reconstituted system. Our results suggest that cellular contractility can be sensitively regulated by tuning the<br />
(local) activity of molecular motors and the cross-linker density and binding affinity.<br />
<br />
== Keywords ==<br />
<br />
<br />
== Soft Matter ==<br />
Contractile forces are important for cell function. Forces are transmitted by the cytoskeleton, a dynamic scaffold of protein filaments throughout the cytoplasm connected to the plasma membrane. Actin and Myosin II have been identified as the main components in this contraction. F-actin provides the structure upon which myosin performs its job, powered by ATP hydrolysis.Contraction of cross-linked actin-myosin networks is mediated by internal stresses that are actively generated by the<br />
myosin motors. Myosin assembles and generates gliding of actin filaments past one another. Though there have been many successful attempts to model the contractile actin cortex, there is still a limited understanding of the dependence of contractility and pattern formation in actin-myosin gels on microscopic parameters such as the number, activity, and processivity of the myosin motors or the local cross-linker density and actin network connectivity.<br />
<br />
Experiments have shown that contraction is accelerated by proteins that crosslink the actin filaments, but systematic and quantitative investigation of contraction is difficult because of the complexity of the system. Contraction has been studied in simplified systems and even then the importance of F-actin crosslinker was apparent. It was also shown that myosin cannot adequately do its job without the crosslinks. <br />
<br />
Here Weitz ''et al''. focus on <math>alpha<\math>-actinin, a protein expressed in contractile cytoskeletal assemblies, for example muscle myofibrils. A simplified model of actin, myosin, and <math>alpha<\math>-actinin was used. Microstructure and macroscopic behavior is imaged using confocal microscopy. The number of crosslinks and myosin motors per actin filament is varied. It is sown that contractility is achieved at a critical concentration of <math>alpha<\math>-actinin. It is concluded that contractility is caused by myosin filaments pulling on actin bundles without changing the bundle dimensions. The results reveal the molecular mechanisms underlying macroscopic force generation by a collection of myosin motors embedded in a random network of actin filaments.<br />
<br />
== References ==</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Isotropic&diff=13768Isotropic2009-12-04T19:18:53Z<p>Mcilwee: </p>
<hr />
<div>Isotropic simply means uniform in all directions. Because of this, an isotropic material is described as one in which the materials properties are the same in all crystallograohic directions.<br />
<br />
==References==<br />
http://en.wikipedia.org/wiki/Isotropy</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=A_quantitative_analysis_of_contractility_in_active_cytoskeletal_protein_networks&diff=13763A quantitative analysis of contractility in active cytoskeletal protein networks2009-12-04T19:05:40Z<p>Mcilwee: /* Abstract */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
A quantitative analysis of contractility in active cytoskeletal protein networks P. Bendix, G. Koenderink, D. Cuvelier, Z. Dogic, B. Koeleman, W. Brieher, C. Field, L. Mahadevan and D. Weitz, Biophysical Journal, 94, 3126, 2008. <br />
<br />
== Abstract ==<br />
Cells actively produce contractile forces for a variety of processes including cytokinesis and motility. Contractility is<br />
known to rely on myosin II motors which convert chemical energy from ATP hydrolysis into forces on actin filaments. However, the<br />
basic physical principles of cell contractility remain poorly understood. We reconstitute contractility in a simplified model system of<br />
purified F-actin, muscle myosin II motors, and a-actinin cross-linkers. We show that contractility occurs above a threshold motor<br />
concentration and within a window of cross-linker concentrations. We also quantify the pore size of the bundled networks and find<br />
contractility to occur at a critical distance between the bundles. We propose a simple mechanism of contraction based on myosin<br />
filaments pulling neighboring bundles together into an aggregated structure. Observations of this reconstituted system in both bulk<br />
and low-dimensional geometries show that the contracting gels pull on and deform their surface with a contractile force of;1mN, or<br />
;100 pN per F-actin bundle. Cytoplasmic extracts contracting in identical environments show a similar behavior and dependence<br />
on myosin as the reconstituted system. Our results suggest that cellular contractility can be sensitively regulated by tuning the<br />
(local) activity of molecular motors and the cross-linker density and binding affinity.<br />
<br />
== Keywords ==<br />
<br />
<br />
== Soft Matter ==<br />
<br />
<br />
== References ==</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Nematic_Phase_transitions_in_Mixtures_of_Thin_and_Thick_Colloidal_Rods&diff=13761Nematic Phase transitions in Mixtures of Thin and Thick Colloidal Rods2009-12-04T19:01:57Z<p>Mcilwee: /* References */</p>
<hr />
<div>Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Nematic Phase transitions in Mixtures of Thin and Thick Colloidal Rods. K. R. Purdy, S. Varga, A. Galindo, G. Jackson, and S. Fraden. Phys. Rev. Lett. 94, 057801 (2005).<br />
<br />
== Abstract ==<br />
Fraden ''et al''. report experimental measurements of the phase behavior of mixtures of thin (charged semiflexible ''fd'' virus) and thick (''fd''-PEG, ''fd'' virus covalently coated with polyethylene glycol) rods with diameter ratio varying from 3.7 to 1.1. The phase diagrams of the rod mixtures reveal isotropic-nematic, isotropic-nematic- nematic, and nematic-nematic coexisting phases with increasing concentration. In stark contrast to predictions from earlier theoretical work, a nematic-nematic coexistence region bound by a lower critical point is observed. Moreover, it is shown that a rescaled Onsager-type theory for binary hard-rod mixtures<br />
qualitatively describes the observed phase behavior.<br />
<br />
== Keywords ==<br />
[[Isotropic]], Nematic, Phase Diagram<br />
<br />
== Soft Matter ==<br />
Fraden ''et al''. and Teramoto ''et al''. have studied the entropy driven phase transition of monodisperse suspensions of purely repulsive rods from an isotropic to an aligned nematic phase experimentally. [1-2] The phase transition has also been studied theoretically and computationally. [3-5] For Fraden ''et al''. the motivation to study hard particle binary mixtures of multiple aspect ratios stems from the desire to ultimately understand the impact of polydispersity on the phase separation of concentrated suspensions of rodlike macromolecules. <br />
<br />
F-actin, microtubules, and DNA are all examples of biological rodlike particles in which length and diameter polydispersity are common. Theoretical studies of binary hard-rod mixtures predict that in addition to isotropicnematic (I-N) coexistence, isotropic-nematic-nematic (I-N-N), isotropic-isotropic (I-I), and nematic-nematic (N-N) coexistence are possible when the length or diameter<br />
ratios of the particles are large enough [6 –12]. <br />
<br />
Fraden et al. have presented here phase behavior measurements of binary mixtures of rods of varying diameter and equal length up to high nematic concentrations. Phase behavior of varying diameter and length have been studied. [7-9,14] Previously they were unable to look at phase diagrams in the nemaic region and therefore only now have they found a lower critical point in the N-N coexisitence. The results were then compared to predictions of a scaled Onsager theory. [12] Onsager's theory predicts isotropic to nematic phase transitions in suspensions of hard rods. Here Onsager's theory has been extended to binary mixtures. But Onsager's second virial expansion is not accurate for high concentrations and therefore a Parsons-Lee (PL) free energy has been adopted. Here higher virial coefficients are approximated by interpolating between the Carnahan-Starling free energy for hard spheres and the Onsager free energy for long hard rods. As mentioned, in previous studies where length was varied, measurements could only be made near the I-N region. It is thought that this may be the result of a few different properties: polydispersity in particle size, high solution viscosity, and/or weak attractions. [2,15,17] <br />
<br />
Mixtures of charged ''fd'' virus (representing thin rods) and ''fd'' virus coated in polyethylene glycol (representing the thick rod) were studied experimentally. The observed phase separations, viewed under crossed polarizers, are depicted in Fig. 1. These include an isotropic phase (I) coexisting with a nematic (N) phase, I-N-N three-phase coexistence, or N-N coexistence. These findings confirm the theoretical predictions for the stable coexisting phases for such a system. In Figs. 1(c) and 1(d) the ''fd''-PEG-rich nematic phase floats above the ''fd''-rich isotropic phase. Even though the volume fraction of rods is higher in the nematic phase, the mass density of the ''fd''-rich isotropic phase is greater than that of the ''fd''-PEG-rich nematic phase. <br />
<br />
[[Image:McIlwee_Nematic_Phase_Transitions.jpg|thumb|center|400px|alt=Figure 1.|Figure 1.]]<br />
<br />
When the evolution of experimental phase behavior is compared to ''d'' for the long rods with PL predictions it qualitatively follows the phase behavior predicted for short rigid rods. Fraden ''et al''. expected the long flexible rods to exhibits phase behavior similar to that predicted for short rigid rods because of previous studies which have shown that the excluded volume for such groups is essentially the same. This was observed. It was also seen that the experimental I-N-N coexistence is stable at much lower diameter ratios than predicted. It is thought that this is because the thin-thick rod interactions are nonadditive.<br />
<br />
It was concluded by Fraden ''et al''., one of the challenges that remains is to incorporate nonadditivity and flexibility into theories for the binary rod phase behavior. The experimental and theoretical results show that an I-N-N coexistence region is not required for the existence of a region of N-N coexistence in contrast to past predictions. However, the N-N upper critical point, which is predicted for very long rods in both the SVT and Parsons-Lee theory has not yet been observed experimentally; further experimental or computational studies of binary mixtures of longer, more rigid rods, may reveal this upper critical point.<br />
<br />
== References ==<br />
[1] J. Tang and S. Fraden, Liq. Cryst. 19, 459 (1995).<br />
<br />
[2] T. Sato and A. Teramoto, Adv. Polym. Sci. 126, 85 (1996).<br />
<br />
[3] L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949).<br />
<br />
[4] G. J. Vroege and H. N.W. Lekkerkerker, Rep. Prog. Phys. 55, 1241 (1992).<br />
<br />
[5] P. G. Bolhuis and D. Frenkel, J. Chem. Phys. 106, 668 (1997).<br />
<br />
[6] A. Abe and P. J. Flory, Macromolecules 11, 1122 (1978).<br />
<br />
[7] H. N.W. Lekkerkerker et al., J. Chem. Phys. 80, 3427 (1984).<br />
<br />
[8] G. J. Vroege and H. N.W. Lekkerkerker, J. Phys. Chem. 97, 3601 (1993).<br />
<br />
[9] R. van Roij, B. Mulder, and M. Dijkstra, Physica A (Amsterdam) 261, 374 (1998).<br />
<br />
[10] P. C.Hemmer, Mol. Phys. 96, 1153 (1999).<br />
<br />
[11] A. Speranza and P. Sollich, J. Chem. Phys. 117, 5421 (2002).<br />
<br />
[12] S. Varga, A. Galindo, and G. Jackson, Mol. Phys. 101, 817 (2003).<br />
<br />
[14] S. Varga and I. Szalai, Chem. Phys. 2, 1955 (2000).</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Nematic_Phase_transitions_in_Mixtures_of_Thin_and_Thick_Colloidal_Rods&diff=13760Nematic Phase transitions in Mixtures of Thin and Thick Colloidal Rods2009-12-04T19:01:32Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Nematic Phase transitions in Mixtures of Thin and Thick Colloidal Rods. K. R. Purdy, S. Varga, A. Galindo, G. Jackson, and S. Fraden. Phys. Rev. Lett. 94, 057801 (2005).<br />
<br />
== Abstract ==<br />
Fraden ''et al''. report experimental measurements of the phase behavior of mixtures of thin (charged semiflexible ''fd'' virus) and thick (''fd''-PEG, ''fd'' virus covalently coated with polyethylene glycol) rods with diameter ratio varying from 3.7 to 1.1. The phase diagrams of the rod mixtures reveal isotropic-nematic, isotropic-nematic- nematic, and nematic-nematic coexisting phases with increasing concentration. In stark contrast to predictions from earlier theoretical work, a nematic-nematic coexistence region bound by a lower critical point is observed. Moreover, it is shown that a rescaled Onsager-type theory for binary hard-rod mixtures<br />
qualitatively describes the observed phase behavior.<br />
<br />
== Keywords ==<br />
[[Isotropic]], Nematic, Phase Diagram<br />
<br />
== Soft Matter ==<br />
Fraden ''et al''. and Teramoto ''et al''. have studied the entropy driven phase transition of monodisperse suspensions of purely repulsive rods from an isotropic to an aligned nematic phase experimentally. [1-2] The phase transition has also been studied theoretically and computationally. [3-5] For Fraden ''et al''. the motivation to study hard particle binary mixtures of multiple aspect ratios stems from the desire to ultimately understand the impact of polydispersity on the phase separation of concentrated suspensions of rodlike macromolecules. <br />
<br />
F-actin, microtubules, and DNA are all examples of biological rodlike particles in which length and diameter polydispersity are common. Theoretical studies of binary hard-rod mixtures predict that in addition to isotropicnematic (I-N) coexistence, isotropic-nematic-nematic (I-N-N), isotropic-isotropic (I-I), and nematic-nematic (N-N) coexistence are possible when the length or diameter<br />
ratios of the particles are large enough [6 –12]. <br />
<br />
Fraden et al. have presented here phase behavior measurements of binary mixtures of rods of varying diameter and equal length up to high nematic concentrations. Phase behavior of varying diameter and length have been studied. [7-9,14] Previously they were unable to look at phase diagrams in the nemaic region and therefore only now have they found a lower critical point in the N-N coexisitence. The results were then compared to predictions of a scaled Onsager theory. [12] Onsager's theory predicts isotropic to nematic phase transitions in suspensions of hard rods. Here Onsager's theory has been extended to binary mixtures. But Onsager's second virial expansion is not accurate for high concentrations and therefore a Parsons-Lee (PL) free energy has been adopted. Here higher virial coefficients are approximated by interpolating between the Carnahan-Starling free energy for hard spheres and the Onsager free energy for long hard rods. As mentioned, in previous studies where length was varied, measurements could only be made near the I-N region. It is thought that this may be the result of a few different properties: polydispersity in particle size, high solution viscosity, and/or weak attractions. [2,15,17] <br />
<br />
Mixtures of charged ''fd'' virus (representing thin rods) and ''fd'' virus coated in polyethylene glycol (representing the thick rod) were studied experimentally. The observed phase separations, viewed under crossed polarizers, are depicted in Fig. 1. These include an isotropic phase (I) coexisting with a nematic (N) phase, I-N-N three-phase coexistence, or N-N coexistence. These findings confirm the theoretical predictions for the stable coexisting phases for such a system. In Figs. 1(c) and 1(d) the ''fd''-PEG-rich nematic phase floats above the ''fd''-rich isotropic phase. Even though the volume fraction of rods is higher in the nematic phase, the mass density of the ''fd''-rich isotropic phase is greater than that of the ''fd''-PEG-rich nematic phase. <br />
<br />
[[Image:McIlwee_Nematic_Phase_Transitions.jpg|thumb|center|400px|alt=Figure 1.|Figure 1.]]<br />
<br />
When the evolution of experimental phase behavior is compared to ''d'' for the long rods with PL predictions it qualitatively follows the phase behavior predicted for short rigid rods. Fraden ''et al''. expected the long flexible rods to exhibits phase behavior similar to that predicted for short rigid rods because of previous studies which have shown that the excluded volume for such groups is essentially the same. This was observed. It was also seen that the experimental I-N-N coexistence is stable at much lower diameter ratios than predicted. It is thought that this is because the thin-thick rod interactions are nonadditive.<br />
<br />
It was concluded by Fraden ''et al''., one of the challenges that remains is to incorporate nonadditivity and flexibility into theories for the binary rod phase behavior. The experimental and theoretical results show that an I-N-N coexistence region is not required for the existence of a region of N-N coexistence in contrast to past predictions. However, the N-N upper critical point, which is predicted for very long rods in both the SVT and Parsons-Lee theory has not yet been observed experimentally; further experimental or computational studies of binary mixtures of longer, more rigid rods, may reveal this upper critical point.<br />
<br />
== References ==<br />
[1] J. Tang and S. Fraden, Liq. Cryst. 19, 459 (1995).<br />
[2] T. Sato and A. Teramoto, Adv. Polym. Sci. 126, 85 (1996).<br />
[3] L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949).<br />
[4] G. J. Vroege and H. N.W. Lekkerkerker, Rep. Prog. Phys. 55, 1241 (1992).<br />
[5] P. G. Bolhuis and D. Frenkel, J. Chem. Phys. 106, 668 (1997).<br />
[6] A. Abe and P. J. Flory, Macromolecules 11, 1122 (1978).<br />
[7] H. N.W. Lekkerkerker et al., J. Chem. Phys. 80, 3427 (1984).<br />
[8] G. J. Vroege and H. N.W. Lekkerkerker, J. Phys. Chem. 97, 3601 (1993).<br />
[9] R. van Roij, B. Mulder, and M. Dijkstra, Physica A (Amsterdam) 261, 374 (1998).<br />
[10] P. C.Hemmer, Mol. Phys. 96, 1153 (1999).<br />
[11] A. Speranza and P. Sollich, J. Chem. Phys. 117, 5421 (2002).<br />
[12] S. Varga, A. Galindo, and G. Jackson, Mol. Phys. 101, 817 (2003).<br />
[14] S. Varga and I. Szalai, Chem. Phys. 2, 1955 (2000).</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Nematic_Phase_transitions_in_Mixtures_of_Thin_and_Thick_Colloidal_Rods&diff=13754Nematic Phase transitions in Mixtures of Thin and Thick Colloidal Rods2009-12-04T18:45:06Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Nematic Phase transitions in Mixtures of Thin and Thick Colloidal Rods. K. R. Purdy, S. Varga, A. Galindo, G. Jackson, and S. Fraden. Phys. Rev. Lett. 94, 057801 (2005).<br />
<br />
== Abstract ==<br />
Fraden ''et al''. report experimental measurements of the phase behavior of mixtures of thin (charged semiflexible ''fd'' virus) and thick (''fd''-PEG, ''fd'' virus covalently coated with polyethylene glycol) rods with diameter ratio varying from 3.7 to 1.1. The phase diagrams of the rod mixtures reveal isotropic-nematic, isotropic-nematic- nematic, and nematic-nematic coexisting phases with increasing concentration. In stark contrast to predictions from earlier theoretical work, a nematic-nematic coexistence region bound by a lower critical point is observed. Moreover, it is shown that a rescaled Onsager-type theory for binary hard-rod mixtures<br />
qualitatively describes the observed phase behavior.<br />
<br />
== Keywords ==<br />
[[Isotropic]], Nematic, Phase Diagram<br />
<br />
== Soft Matter ==<br />
Fraden ''et al''. and Teramoto ''et al''. have studied the entropy driven phase transition of monodisperse suspensions of purely repulsive rods from an isotropic to an aligned nematic phase experimentally. [1-2] The phase transition has also been studied theoretically and computationally. [3-5] For Fraden ''et al''. the motivation to study hard particle binary mixtures of multiple aspect ratios stems from the desire to ultimately understand the impact of polydispersity on the phase separation of concentrated suspensions of rodlike macromolecules. <br />
<br />
F-actin, microtubules, and DNA are all examples of biological rodlike particles in which length and diameter polydispersity are common. Theoretical studies of binary hard-rod mixtures predict that in addition to isotropicnematic (I-N) coexistence, isotropic-nematic-nematic (I-N-N), isotropic-isotropic (I-I), and nematic-nematic (N-N) coexistence are possible when the length or diameter<br />
ratios of the particles are large enough [6 –12]. <br />
<br />
Fraden et al. have presented here phase behavior measurements of binary mixtures of rods of varying diameter and equal length up to high nematic concentrations. Phase behavior of varying diameter and length have been studied. [7-9,14] Previously they were unable to look at phase diagrams in the nemaic region and therefore only now have they found a lower critical point in the N-N coexisitence. The results were then compared to predictions of a scaled Onsager theory. [12] Onsager's theory predicts isotropic to nematic phase transitions in suspensions of hard rods. Here Onsager's theory has been extended to binary mixtures. But Onsager's second virial expansion is not accurate for high concentrations and therefore a Parsons-Lee (PL) free energy has been adopted. Here higher virial coefficients are approximated by interpolating between the Carnahan-Starling free energy for hard spheres and the Onsager free energy for long hard rods. As mentioned, in previous studies where length was varied, measurements could only be made near the I-N region. It is thought that this may be the result of a few different properties: polydispersity in particle size, high solution viscosity, and/or weak attractions. [2,15,17] <br />
<br />
Mixtures of charged ''fd'' virus (representing thin rods) and ''fd'' virus coated in polyethylene glycol (representing the thick rod) were studied experimentally. The observed phase separations, viewed under crossed polarizers, are depicted in Fig. 1. These include an isotropic phase (I) coexisting with a nematic (N) phase, I-N-N three-phase coexistence, or N-N coexistence. These findings confirm the theoretical predictions for the stable coexisting phases for such a system. In Figs. 1(c) and 1(d) the ''fd''-PEG-rich nematic phase floats above the ''fd''-rich isotropic phase. Even though the volume fraction of rods is higher in the nematic phase, the mass density of the ''fd''-rich isotropic phase is greater than that of the ''fd''-PEG-rich nematic phase. The mass density difference arises in part because of the difference in single particle densities.<br />
<br />
[[Image:McIlwee_Nematic_Phase_Transitions.jpg|thumb|center|400px|alt=Figure 1.|Figure 1.]]<br />
<br />
When the evolution of experimental phase behavior is compared to ''d'' for the long rods with PL predictions it qualitatively follows the phase behavior predicted for short rigid rods. It has been shown in simulations that the excluded volume of a flexible<br />
rod is equivalent to the excluded volume of a shorter but thicker rigid rod [25]. Thus we expect long flexible rods to exhibit a phase behavior similar to that predicted for shorter rigid rods, as observed. Additionally, it was observed that the experimental I-N-N coexistence is stable to much lower diameter ratios than predicted. It is thought that this is because the thin-thick rod interactions are nonadditive.<br />
<br />
Theoretically, one of the challenges that remains is to incorporate nonadditivity and flexibility into theories for the binary rod<br />
phase behavior. In conclusion, we have studied the first experimental system of mixtures of thick and thin rods. Onsager’s second<br />
virial theory qualitatively reproduces the main features of the experimental binary rod phase diagram at large d, but does not accurately capture the evolution of the phase behavior from a totally miscible nematic to a demixed nematic-nematic state with increasing d. The Parsons- Lee scaling of the hard-rod free energy, which incorporates end effects and higher virial coefficients in an approximate fashion [12] does qualitatively describes the experimental findings. Our experimental and theoretical results show<br />
that an I-N-N coexistence region is not required for the existence of a region of N-N coexistence in contrast to past<br />
predictions. However, the N-N upper critical point, which is predicted for very long rods in both the SVT and Parsons-Lee theory has not yet been observed experimentally; further experimental or computational studies of binary mixtures of longer, more rigid rods, may reveal this upper critical point.<br />
<br />
== References ==<br />
[1] J. Tang and S. Fraden, Liq. Cryst. 19, 459 (1995).<br />
[2] T. Sato and A. Teramoto, Adv. Polym. Sci. 126, 85 (1996).<br />
[3] L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949).<br />
[4] G. J. Vroege and H. N.W. Lekkerkerker, Rep. Prog. Phys. 55, 1241 (1992).<br />
[5] P. G. Bolhuis and D. Frenkel, J. Chem. Phys. 106, 668 (1997).<br />
[6] A. Abe and P. J. Flory, Macromolecules 11, 1122 (1978).<br />
[7] H. N.W. Lekkerkerker et al., J. Chem. Phys. 80, 3427 (1984).<br />
[8] G. J. Vroege and H. N.W. Lekkerkerker, J. Phys. Chem. 97, 3601 (1993).<br />
[9] R. van Roij, B. Mulder, and M. Dijkstra, Physica A (Amsterdam) 261, 374 (1998).<br />
[10] P. C.Hemmer, Mol. Phys. 96, 1153 (1999).<br />
[11] A. Speranza and P. Sollich, J. Chem. Phys. 117, 5421 (2002).<br />
[12] S. Varga, A. Galindo, and G. Jackson, Mol. Phys. 101, 817 (2003).<br />
[14] S. Varga and I. Szalai, Chem. Phys. 2, 1955 (2000).</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Nematic_Phase_transitions_in_Mixtures_of_Thin_and_Thick_Colloidal_Rods&diff=13753Nematic Phase transitions in Mixtures of Thin and Thick Colloidal Rods2009-12-04T18:43:04Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Nematic Phase transitions in Mixtures of Thin and Thick Colloidal Rods. K. R. Purdy, S. Varga, A. Galindo, G. Jackson, and S. Fraden. Phys. Rev. Lett. 94, 057801 (2005).<br />
<br />
== Abstract ==<br />
Fraden ''et al''. report experimental measurements of the phase behavior of mixtures of thin (charged semiflexible ''fd'' virus) and thick (''fd''-PEG, ''fd'' virus covalently coated with polyethylene glycol) rods with diameter ratio varying from 3.7 to 1.1. The phase diagrams of the rod mixtures reveal isotropic-nematic, isotropic-nematic- nematic, and nematic-nematic coexisting phases with increasing concentration. In stark contrast to predictions from earlier theoretical work, a nematic-nematic coexistence region bound by a lower critical point is observed. Moreover, it is shown that a rescaled Onsager-type theory for binary hard-rod mixtures<br />
qualitatively describes the observed phase behavior.<br />
<br />
== Keywords ==<br />
[[Isotropic]], Nematic, Phase Diagram<br />
<br />
== Soft Matter ==<br />
Fraden ''et al''. and Teramoto ''et al''. have studied the entropy driven phase transition of monodisperse suspensions of purely repulsive rods from an isotropic to an aligned nematic phase experimentally. [1-2] The phase transition has also been studied theoretically and computationally. [3-5] For Fraden ''et al''. the motivation to study hard particle binary mixtures of multiple aspect ratios stems from the desire to ultimately understand the impact of polydispersity on the phase separation of concentrated suspensions of rodlike macromolecules. <br />
<br />
F-actin, microtubules, and DNA are all examples of biological rodlike particles in which length and diameter polydispersity are common. Theoretical studies of binary hard-rod mixtures predict that in addition to isotropicnematic (I-N) coexistence, isotropic-nematic-nematic (I-N-N), isotropic-isotropic (I-I), and nematic-nematic (N-N) coexistence are possible when the length or diameter<br />
ratios of the particles are large enough [6 –12]. <br />
<br />
Fraden et al. have presented here phase behavior measurements of binary mixtures of rods of varying diameter and equal length up to high nematic concentrations. Phase behavior of varying diameter and length have been studied. [7-9,14] Previously they were unable to look at phase diagrams in the nemaic region and therefore only now have they found a lower critical point in the N-N coexisitence. The results were then compared to predictions of a scaled Onsager theory. [12] Onsager's theory predicts isotropic to nematic phase transitions in suspensions of hard rods. Here Onsager's theory has been extended to binary mixtures. But Onsager's second virial expansion is not accurate for high concentrations and therefore a Parsons-Lee (PL) free energy has been adopted. Here higher virial coefficients are approximated by interpolating between the Carnahan-Starling free energy for hard spheres and the Onsager free energy for long hard rods. As mentioned, in previous studies where length was varied, measurements could only be made near the I-N region. It is thought that this may be the result of a few different properties: polydispersity in particle size, high solution viscosity, and/or weak attractions. [2,15,17] <br />
<br />
Mixtures of charged ''fd'' virus (representing thin rods) and ''fd'' virus coated in polyethylene glycol (representing the thick rod) were studied experimentally. The observed phase separations, viewed under crossed polarizers, are depicted in Fig. 1. These include an isotropic phase (I) coexisting with a nematic (N) phase, I-N-N three-phase coexistence, or N-N coexistence. These findings confirm the theoretical predictions for the stable coexisting phases for such a system. In Figs. 1(c) and 1(d) the ''fd''-PEG-rich nematic phase floats above the ''fd''-rich isotropic phase. Even though the volume fraction of rods is higher in the nematic phase, the mass density of the ''fd''-rich isotropic phase is greater than that of the ''fd''-PEG-rich nematic phase. The mass density difference arises in part because of the difference in single particle densities.<br />
<br />
McIlwee_Nematic_Phase_Transitions.jpg<br />
<br />
When the evolution of experimental phase behavior is compared to ''d'' for the long rods with PL predictions it qualitatively follows the phase behavior predicted for short rigid rods. It has been shown in simulations that the excluded volume of a flexible<br />
rod is equivalent to the excluded volume of a shorter but thicker rigid rod [25]. Thus we expect long flexible rods to exhibit a phase behavior similar to that predicted for shorter rigid rods, as observed. Additionally, it was observed that the experimental I-N-N coexistence is stable to much lower diameter ratios than predicted. It is thought that this is because the thin-thick rod interactions are nonadditive.<br />
<br />
Theoretically, one of the challenges that remains is to incorporate nonadditivity and flexibility into theories for the binary rod<br />
phase behavior. In conclusion, we have studied the first experimental system of mixtures of thick and thin rods. Onsager’s second<br />
virial theory qualitatively reproduces the main features of the experimental binary rod phase diagram at large d, but does not accurately capture the evolution of the phase behavior from a totally miscible nematic to a demixed nematic-nematic state with increasing d. The Parsons- Lee scaling of the hard-rod free energy, which incorporates end effects and higher virial coefficients in an approximate fashion [12] does qualitatively describes the experimental findings. Our experimental and theoretical results show<br />
that an I-N-N coexistence region is not required for the existence of a region of N-N coexistence in contrast to past<br />
predictions. However, the N-N upper critical point, which is predicted for very long rods in both the SVT and Parsons-Lee theory has not yet been observed experimentally; further experimental or computational studies of binary mixtures of longer, more rigid rods, may reveal this upper critical point.<br />
<br />
== References ==<br />
[1] J. Tang and S. Fraden, Liq. Cryst. 19, 459 (1995).<br />
[2] T. Sato and A. Teramoto, Adv. Polym. Sci. 126, 85 (1996).<br />
[3] L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949).<br />
[4] G. J. Vroege and H. N.W. Lekkerkerker, Rep. Prog. Phys. 55, 1241 (1992).<br />
[5] P. G. Bolhuis and D. Frenkel, J. Chem. Phys. 106, 668 (1997).<br />
[6] A. Abe and P. J. Flory, Macromolecules 11, 1122 (1978).<br />
[7] H. N.W. Lekkerkerker et al., J. Chem. Phys. 80, 3427 (1984).<br />
[8] G. J. Vroege and H. N.W. Lekkerkerker, J. Phys. Chem. 97, 3601 (1993).<br />
[9] R. van Roij, B. Mulder, and M. Dijkstra, Physica A (Amsterdam) 261, 374 (1998).<br />
[10] P. C.Hemmer, Mol. Phys. 96, 1153 (1999).<br />
[11] A. Speranza and P. Sollich, J. Chem. Phys. 117, 5421 (2002).<br />
[12] S. Varga, A. Galindo, and G. Jackson, Mol. Phys. 101, 817 (2003).<br />
[14] S. Varga and I. Szalai, Chem. Phys. 2, 1955 (2000).</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=File:McIlwee_Nematic_Phase_Transitions.jpg&diff=13752File:McIlwee Nematic Phase Transitions.jpg2009-12-04T18:42:33Z<p>Mcilwee: </p>
<hr />
<div></div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Nematic_Phase_transitions_in_Mixtures_of_Thin_and_Thick_Colloidal_Rods&diff=13751Nematic Phase transitions in Mixtures of Thin and Thick Colloidal Rods2009-12-04T18:42:07Z<p>Mcilwee: </p>
<hr />
<div>Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Nematic Phase transitions in Mixtures of Thin and Thick Colloidal Rods. K. R. Purdy, S. Varga, A. Galindo, G. Jackson, and S. Fraden. Phys. Rev. Lett. 94, 057801 (2005).<br />
<br />
== Abstract ==<br />
Fraden ''et al''. report experimental measurements of the phase behavior of mixtures of thin (charged semiflexible ''fd'' virus) and thick (''fd''-PEG, ''fd'' virus covalently coated with polyethylene glycol) rods with diameter ratio varying from 3.7 to 1.1. The phase diagrams of the rod mixtures reveal isotropic-nematic, isotropic-nematic- nematic, and nematic-nematic coexisting phases with increasing concentration. In stark contrast to predictions from earlier theoretical work, a nematic-nematic coexistence region bound by a lower critical point is observed. Moreover, it is shown that a rescaled Onsager-type theory for binary hard-rod mixtures<br />
qualitatively describes the observed phase behavior.<br />
<br />
== Keywords ==<br />
[[Isotropic]], Nematic, Phase Diagram<br />
<br />
== Soft Matter ==<br />
Fraden ''et al''. and Teramoto ''et al''. have studied the entropy driven phase transition of monodisperse suspensions of purely repulsive rods from an isotropic to an aligned nematic phase experimentally. [1-2] The phase transition has also been studied theoretically and computationally. [3-5] For Fraden ''et al''. the motivation to study hard particle binary mixtures of multiple aspect ratios stems from the desire to ultimately understand the impact of polydispersity on the phase separation of concentrated suspensions of rodlike macromolecules. <br />
<br />
F-actin, microtubules, and DNA are all examples of biological rodlike particles in which length and diameter polydispersity are common. Theoretical studies of binary hard-rod mixtures predict that in addition to isotropicnematic (I-N) coexistence, isotropic-nematic-nematic (I-N-N), isotropic-isotropic (I-I), and nematic-nematic (N-N) coexistence are possible when the length or diameter<br />
ratios of the particles are large enough [6 –12]. <br />
<br />
Fraden et al. have presented here phase behavior measurements of binary mixtures of rods of varying diameter and equal length up to high nematic concentrations. Phase behavior of varying diameter and length have been studied. [7-9,14] Previously they were unable to look at phase diagrams in the nemaic region and therefore only now have they found a lower critical point in the N-N coexisitence. The results were then compared to predictions of a scaled Onsager theory. [12] Onsager's theory predicts isotropic to nematic phase transitions in suspensions of hard rods. Here Onsager's theory has been extended to binary mixtures. But Onsager's second virial expansion is not accurate for high concentrations and therefore a Parsons-Lee (PL) free energy has been adopted. Here higher virial coefficients are approximated by interpolating between the Carnahan-Starling free energy for hard spheres and the Onsager free energy for long hard rods. As mentioned, in previous studies where length was varied, measurements could only be made near the I-N region. It is thought that this may be the result of a few different properties: polydispersity in particle size, high solution viscosity, and/or weak attractions. [2,15,17] <br />
<br />
Mixtures of charged ''fd'' virus (representing thin rods) and ''fd'' virus coated in polyethylene glycol (representing the thick rod) were studied experimentally. The observed phase separations, viewed under crossed polarizers, are depicted in Fig. 1. These include an isotropic phase (I) coexisting with a nematic (N) phase, I-N-N three-phase coexistence, or N-N coexistence. These findings confirm the theoretical predictions for the stable coexisting phases for such a system. In Figs. 1(c) and 1(d) the ''fd''-PEG-rich nematic phase floats above the ''fd''-rich isotropic phase. Even though the volume fraction of rods is higher in the nematic phase, the mass density of the ''fd''-rich isotropic phase is greater than that of the ''fd''-PEG-rich nematic phase. The mass density difference arises in part because of the difference in single particle densities.<br />
<br />
When the evolution of experimental phase behavior is compared to ''d'' for the long rods with PL predictions it qualitatively follows the phase behavior predicted for short rigid rods. It has been shown in simulations that the excluded volume of a flexible<br />
rod is equivalent to the excluded volume of a shorter but thicker rigid rod [25]. Thus we expect long flexible rods to exhibit a phase behavior similar to that predicted for shorter rigid rods, as observed. Additionally, it was observed that the experimental I-N-N coexistence is stable to much lower diameter ratios than predicted. It is thought that this is because the thin-thick rod interactions are nonadditive.<br />
<br />
Theoretically, one of the challenges that remains is to incorporate nonadditivity and flexibility into theories for the binary rod<br />
phase behavior. In conclusion, we have studied the first experimental system of mixtures of thick and thin rods. Onsager’s second<br />
virial theory qualitatively reproduces the main features of the experimental binary rod phase diagram at large d, but does not accurately capture the evolution of the phase behavior from a totally miscible nematic to a demixed nematic-nematic state with increasing d. The Parsons- Lee scaling of the hard-rod free energy, which incorporates end effects and higher virial coefficients in an approximate fashion [12] does qualitatively describes the experimental findings. Our experimental and theoretical results show<br />
that an I-N-N coexistence region is not required for the existence of a region of N-N coexistence in contrast to past<br />
predictions. However, the N-N upper critical point, which is predicted for very long rods in both the SVT and Parsons-Lee theory has not yet been observed experimentally; further experimental or computational studies of binary mixtures of longer, more rigid rods, may reveal this upper critical point.<br />
<br />
<br />
== References ==<br />
[1] J. Tang and S. Fraden, Liq. Cryst. 19, 459 (1995).<br />
[2] T. Sato and A. Teramoto, Adv. Polym. Sci. 126, 85 (1996).<br />
[3] L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949).<br />
[4] G. J. Vroege and H. N.W. Lekkerkerker, Rep. Prog. Phys. 55, 1241 (1992).<br />
[5] P. G. Bolhuis and D. Frenkel, J. Chem. Phys. 106, 668 (1997).<br />
[6] A. Abe and P. J. Flory, Macromolecules 11, 1122 (1978).<br />
[7] H. N.W. Lekkerkerker et al., J. Chem. Phys. 80, 3427 (1984).<br />
[8] G. J. Vroege and H. N.W. Lekkerkerker, J. Phys. Chem. 97, 3601 (1993).<br />
[9] R. van Roij, B. Mulder, and M. Dijkstra, Physica A (Amsterdam) 261, 374 (1998).<br />
[10] P. C.Hemmer, Mol. Phys. 96, 1153 (1999).<br />
[11] A. Speranza and P. Sollich, J. Chem. Phys. 117, 5421 (2002).<br />
[12] S. Varga, A. Galindo, and G. Jackson, Mol. Phys. 101, 817 (2003).<br />
[14] S. Varga and I. Szalai, Chem. Phys. 2, 1955 (2000).</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Nematic_Phase_transitions_in_Mixtures_of_Thin_and_Thick_Colloidal_Rods&diff=13750Nematic Phase transitions in Mixtures of Thin and Thick Colloidal Rods2009-12-04T18:32:43Z<p>Mcilwee: /* Keywords */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Nematic Phase transitions in Mixtures of Thin and Thick Colloidal Rods. K. R. Purdy, S. Varga, A. Galindo, G. Jackson, and S. Fraden. Phys. Rev. Lett. 94, 057801 (2005).<br />
<br />
== Abstract ==<br />
Fraden ''et al''. report experimental measurements of the phase behavior of mixtures of thin (charged semiflexible<br />
''fd'' virus) and thick (''fd''-PEG, ''fd'' virus covalently coated with polyethylene glycol) rods with diameter<br />
ratio varying from 3.7 to 1.1. The phase diagrams of the rod mixtures reveal isotropic-nematic, isotropic-nematic-<br />
nematic, and nematic-nematic coexisting phases with increasing concentration. In stark contrast<br />
to predictions from earlier theoretical work, a nematic-nematic coexistence region bound by a<br />
lower critical point is observed. Moreover, it is shown that a rescaled Onsager-type theory for binary hard-rod mixtures<br />
qualitatively describes the observed phase behavior.<br />
<br />
== Keywords ==<br />
[[Isotropic]], Nematic, Phase Diagram<br />
<br />
== Soft Matter ==<br />
Fraden ''et al''. and Teramoto ''et al''. have studied the entropy driven phase transition of monodisperse suspensions of purely repulsive rods from an isotropic to an aligned nematic phase experimentally. [1-2] The phase trasition has also been studied theoretically and computationally. [3-5] For Fraden ''et al''. the motivation to study binary mixtures of hard particles of multiple aspect ratios comes from the desire to ultimately understand the impact of polydispersity on the phase separation of concentrated suspensions of rodlike macromolecules. <br />
<br />
F-actin, microtubules, and DNA are all examples of biological rodlike particles in which length and diameter polydispersity are common. Theoretical studies of binary hard-rod mixtures predict that in addition to isotropicnematic (I-N) coexistence, isotropic-nematic-nematic (I-N-N), isotropic-isotropic (I-I), and nematic-nematic (N-N) coexistence are possible when the length or diameter<br />
ratio of the particles is large enough [6 –12]. <br />
<br />
Fraden et al. have presented here measurements of phase behavior of binary mixtures of rods of varying diameter and equal length up to high nematic concentrations. Previously they were unable to look at the phase diagrams inthe nemaic region and therefore only now have they found a lower critical point in the N-N coexisitence. The results were then compared to predictions of a scaled Onsager theory. [12] Onsager's theory predicts isotropic to nematic phase transitions in suspensionsof hard rods. Here Onsager's theory has been extended to binary mixtures. Phase behavior of varying diameter and length have previously been studied. [7-9,14] But Onsager's second virial expansion is not accurate for high concentrations and therefore a Parsons-Lee (PL) free energy has been adopted. Here higher virial coefficients are approximated by interpolating between the Carnahan-Starling free energy for hard spheres and the Onsager free energy for long hard rods. As mentioned, in previous studies where length was varied, mesurements could only be made near the I-N region. It is thought that this may be because of a number of reasons: polydispersity in particle size, high solution viscosity, and/or eak attractions. [2,15,17] <br />
<br />
Mixtures of charged ''fd'' virus (representing thin rods) and ''fd'' virus coated in polyethylene glycol (representing the thick rod) were studied experimentally. The observed phase separations, viewed under crossed polarizers, are depicted in Fig. 1. These include an isotropic phase (I) coexisting with a nematic (N) phase, I-N-N three-phase coexistence, or N-N coexistence. These findings confirm the theoretical predictions for the stable coexisting phases for such a system. In Figs. 1(c) and 1(d) the ''fd''-PEG-rich nematic phase floats above the ''fd''-rich isotropic phase. Even though the volume fraction of rods is higher in the nematic phase, the mass density of the ''fd''-rich isotropic phase is greater than that of the ''fd''-PEG-rich nematic phase. The mass density difference arises in part because of the difference in single particle densities.<br />
<br />
When the evolution of experimental phase behavior is compared to ''d'' for the long rods with PL predictions it qualitatively follows the phase behavior predicted for short rigid rods. It has been shown in simulations that the excluded volume of a flexible<br />
rod is equivalent to the excluded volume of a shorter but thicker rigid rod [25]. Thus we expect long flexible rods to exhibit a phase behavior similar to that predicted for shorter rigid rods, as observed. Additionally, it was observed that the experimental I-N-N coexistence is stable to much lower diameter ratios than predicted. It is thought that this is because the thin-thick rod interactions are nonadditive.<br />
<br />
Theoretically, one of the challenges that remains is to incorporate nonadditivity and flexibility into theories for the binary rod<br />
phase behavior. In conclusion, we have studied the first experimental system of mixtures of thick and thin rods. Onsager’s second<br />
virial theory qualitatively reproduces the main features of the experimental binary rod phase diagram at large d, but does not accurately capture the evolution of the phase behavior from a totally miscible nematic to a demixed nematic-nematic state with increasing d. The Parsons- Lee scaling of the hard-rod free energy, which incorporates end effects and higher virial coefficients in an approximate fashion [12] does qualitatively describes the experimental findings. Our experimental and theoretical results show<br />
that an I-N-N coexistence region is not required for the existence of a region of N-N coexistence in contrast to past<br />
predictions. However, the N-N upper critical point, which is predicted for very long rods in both the SVT and Parsons-Lee theory has not yet been observed experimentally; further experimental or computational studies of binary mixtures of longer, more rigid rods, may reveal this upper critical point.<br />
<br />
[1] J. Tang and S. Fraden, Liq. Cryst. 19, 459 (1995).<br />
[2] T. Sato and A. Teramoto, Adv. Polym. Sci. 126, 85 (1996).<br />
[3] L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949).<br />
[4] G. J. Vroege and H. N.W. Lekkerkerker, Rep. Prog. Phys. 55, 1241 (1992).<br />
[5] P. G. Bolhuis and D. Frenkel, J. Chem. Phys. 106, 668 (1997).<br />
[6] A. Abe and P. J. Flory, Macromolecules 11, 1122 (1978).<br />
[7] H. N.W. Lekkerkerker et al., J. Chem. Phys. 80, 3427 (1984).<br />
[8] G. J. Vroege and H. N.W. Lekkerkerker, J. Phys. Chem. 97, 3601 (1993).<br />
[9] R. van Roij, B. Mulder, and M. Dijkstra, Physica A (Amsterdam) 261, 374 (1998).<br />
[10] P. C.Hemmer, Mol. Phys. 96, 1153 (1999).<br />
[11] A. Speranza and P. Sollich, J. Chem. Phys. 117, 5421 (2002).<br />
[12] S. Varga, A. Galindo, and G. Jackson, Mol. Phys. 101, 817 (2003).<br />
[14] S. Varga and I. Szalai, Chem. Phys. 2, 1955 (2000).<br />
<br />
== References ==</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Nematic_Phase_transitions_in_Mixtures_of_Thin_and_Thick_Colloidal_Rods&diff=13749Nematic Phase transitions in Mixtures of Thin and Thick Colloidal Rods2009-12-04T18:31:52Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Nematic Phase transitions in Mixtures of Thin and Thick Colloidal Rods. K. R. Purdy, S. Varga, A. Galindo, G. Jackson, and S. Fraden. Phys. Rev. Lett. 94, 057801 (2005).<br />
<br />
== Abstract ==<br />
Fraden ''et al''. report experimental measurements of the phase behavior of mixtures of thin (charged semiflexible<br />
''fd'' virus) and thick (''fd''-PEG, ''fd'' virus covalently coated with polyethylene glycol) rods with diameter<br />
ratio varying from 3.7 to 1.1. The phase diagrams of the rod mixtures reveal isotropic-nematic, isotropic-nematic-<br />
nematic, and nematic-nematic coexisting phases with increasing concentration. In stark contrast<br />
to predictions from earlier theoretical work, a nematic-nematic coexistence region bound by a<br />
lower critical point is observed. Moreover, it is shown that a rescaled Onsager-type theory for binary hard-rod mixtures<br />
qualitatively describes the observed phase behavior.<br />
<br />
== Keywords ==<br />
<br />
<br />
== Soft Matter ==<br />
Fraden ''et al''. and Teramoto ''et al''. have studied the entropy driven phase transition of monodisperse suspensions of purely repulsive rods from an isotropic to an aligned nematic phase experimentally. [1-2] The phase trasition has also been studied theoretically and computationally. [3-5] For Fraden ''et al''. the motivation to study binary mixtures of hard particles of multiple aspect ratios comes from the desire to ultimately understand the impact of polydispersity on the phase separation of concentrated suspensions of rodlike macromolecules. <br />
<br />
F-actin, microtubules, and DNA are all examples of biological rodlike particles in which length and diameter polydispersity are common. Theoretical studies of binary hard-rod mixtures predict that in addition to isotropicnematic (I-N) coexistence, isotropic-nematic-nematic (I-N-N), isotropic-isotropic (I-I), and nematic-nematic (N-N) coexistence are possible when the length or diameter<br />
ratio of the particles is large enough [6 –12]. <br />
<br />
Fraden et al. have presented here measurements of phase behavior of binary mixtures of rods of varying diameter and equal length up to high nematic concentrations. Previously they were unable to look at the phase diagrams inthe nemaic region and therefore only now have they found a lower critical point in the N-N coexisitence. The results were then compared to predictions of a scaled Onsager theory. [12] Onsager's theory predicts isotropic to nematic phase transitions in suspensionsof hard rods. Here Onsager's theory has been extended to binary mixtures. Phase behavior of varying diameter and length have previously been studied. [7-9,14] But Onsager's second virial expansion is not accurate for high concentrations and therefore a Parsons-Lee (PL) free energy has been adopted. Here higher virial coefficients are approximated by interpolating between the Carnahan-Starling free energy for hard spheres and the Onsager free energy for long hard rods. As mentioned, in previous studies where length was varied, mesurements could only be made near the I-N region. It is thought that this may be because of a number of reasons: polydispersity in particle size, high solution viscosity, and/or eak attractions. [2,15,17] <br />
<br />
Mixtures of charged ''fd'' virus (representing thin rods) and ''fd'' virus coated in polyethylene glycol (representing the thick rod) were studied experimentally. The observed phase separations, viewed under crossed polarizers, are depicted in Fig. 1. These include an isotropic phase (I) coexisting with a nematic (N) phase, I-N-N three-phase coexistence, or N-N coexistence. These findings confirm the theoretical predictions for the stable coexisting phases for such a system. In Figs. 1(c) and 1(d) the ''fd''-PEG-rich nematic phase floats above the ''fd''-rich isotropic phase. Even though the volume fraction of rods is higher in the nematic phase, the mass density of the ''fd''-rich isotropic phase is greater than that of the ''fd''-PEG-rich nematic phase. The mass density difference arises in part because of the difference in single particle densities.<br />
<br />
When the evolution of experimental phase behavior is compared to ''d'' for the long rods with PL predictions it qualitatively follows the phase behavior predicted for short rigid rods. It has been shown in simulations that the excluded volume of a flexible<br />
rod is equivalent to the excluded volume of a shorter but thicker rigid rod [25]. Thus we expect long flexible rods to exhibit a phase behavior similar to that predicted for shorter rigid rods, as observed. Additionally, it was observed that the experimental I-N-N coexistence is stable to much lower diameter ratios than predicted. It is thought that this is because the thin-thick rod interactions are nonadditive.<br />
<br />
Theoretically, one of the challenges that remains is to incorporate nonadditivity and flexibility into theories for the binary rod<br />
phase behavior. In conclusion, we have studied the first experimental system of mixtures of thick and thin rods. Onsager’s second<br />
virial theory qualitatively reproduces the main features of the experimental binary rod phase diagram at large d, but does not accurately capture the evolution of the phase behavior from a totally miscible nematic to a demixed nematic-nematic state with increasing d. The Parsons- Lee scaling of the hard-rod free energy, which incorporates end effects and higher virial coefficients in an approximate fashion [12] does qualitatively describes the experimental findings. Our experimental and theoretical results show<br />
that an I-N-N coexistence region is not required for the existence of a region of N-N coexistence in contrast to past<br />
predictions. However, the N-N upper critical point, which is predicted for very long rods in both the SVT and Parsons-Lee theory has not yet been observed experimentally; further experimental or computational studies of binary mixtures of longer, more rigid rods, may reveal this upper critical point.<br />
<br />
[1] J. Tang and S. Fraden, Liq. Cryst. 19, 459 (1995).<br />
[2] T. Sato and A. Teramoto, Adv. Polym. Sci. 126, 85 (1996).<br />
[3] L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949).<br />
[4] G. J. Vroege and H. N.W. Lekkerkerker, Rep. Prog. Phys. 55, 1241 (1992).<br />
[5] P. G. Bolhuis and D. Frenkel, J. Chem. Phys. 106, 668 (1997).<br />
[6] A. Abe and P. J. Flory, Macromolecules 11, 1122 (1978).<br />
[7] H. N.W. Lekkerkerker et al., J. Chem. Phys. 80, 3427 (1984).<br />
[8] G. J. Vroege and H. N.W. Lekkerkerker, J. Phys. Chem. 97, 3601 (1993).<br />
[9] R. van Roij, B. Mulder, and M. Dijkstra, Physica A (Amsterdam) 261, 374 (1998).<br />
[10] P. C.Hemmer, Mol. Phys. 96, 1153 (1999).<br />
[11] A. Speranza and P. Sollich, J. Chem. Phys. 117, 5421 (2002).<br />
[12] S. Varga, A. Galindo, and G. Jackson, Mol. Phys. 101, 817 (2003).<br />
[14] S. Varga and I. Szalai, Chem. Phys. 2, 1955 (2000).<br />
<br />
== References ==</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Nematic_Phase_transitions_in_Mixtures_of_Thin_and_Thick_Colloidal_Rods&diff=13734Nematic Phase transitions in Mixtures of Thin and Thick Colloidal Rods2009-12-04T17:14:38Z<p>Mcilwee: /* Abstract */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Nematic Phase transitions in Mixtures of Thin and Thick Colloidal Rods. K. R. Purdy, S. Varga, A. Galindo, G. Jackson, and S. Fraden. Phys. Rev. Lett. 94, 057801 (2005).<br />
<br />
== Abstract ==<br />
Fraden ''et al''. report experimental measurements of the phase behavior of mixtures of thin (charged semiflexible<br />
''fd'' virus) and thick (''fd''-PEG, ''fd'' virus covalently coated with polyethylene glycol) rods with diameter<br />
ratio varying from 3.7 to 1.1. The phase diagrams of the rod mixtures reveal isotropic-nematic, isotropic-nematic-<br />
nematic, and nematic-nematic coexisting phases with increasing concentration. In stark contrast<br />
to predictions from earlier theoretical work, a nematic-nematic coexistence region bound by a<br />
lower critical point is observed. Moreover, it is shown that a rescaled Onsager-type theory for binary hard-rod mixtures<br />
qualitatively describes the observed phase behavior.<br />
<br />
== Keywords ==<br />
<br />
<br />
== Soft Matter ==<br />
<br />
<br />
== References ==</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Surface_tension&diff=13733Surface tension2009-12-04T17:08:03Z<p>Mcilwee: /* Units */</p>
<hr />
<div>==Definition==<br />
Surface tension is a property of liquid surfaces caused by cohesion. Cohesion is the physical property resulting from the intermolecular forces attracting like-molecules. The molecules on the surface of a liquid have a greater attraction to like-molecules around them than to unlike-molecules.<br />
<br />
Molecules on the surface of a liquid experience an inward force balanced by the resistance to compression. Another important point in understanding surface tension is the liquid molecules seek the lowest possible surface area. This is the reason that liquids form droplets on hydrophobic surfaces. The interface of lke-molecules has a lower energy than the interface of unlike-molecules, therefore surface molecules seek to have as many like-molecule interfaces as possible resulting in the lowest surface area.<br />
<br />
==Units==<br />
Surface tension (<math>\gamma</math>) has dimensions of force per unit length, <math>\frac{F} {L}</math>.<br />
<br />
==References==<br />
<br />
http://en.wikipedia.org/wiki/Cohesion_%28chemistry%29<br />
<br />
http://en.wikipedia.org/wiki/Surface_tension</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Surface_tension&diff=13732Surface tension2009-12-04T17:07:39Z<p>Mcilwee: /* Units */</p>
<hr />
<div>==Definition==<br />
Surface tension is a property of liquid surfaces caused by cohesion. Cohesion is the physical property resulting from the intermolecular forces attracting like-molecules. The molecules on the surface of a liquid have a greater attraction to like-molecules around them than to unlike-molecules.<br />
<br />
Molecules on the surface of a liquid experience an inward force balanced by the resistance to compression. Another important point in understanding surface tension is the liquid molecules seek the lowest possible surface area. This is the reason that liquids form droplets on hydrophobic surfaces. The interface of lke-molecules has a lower energy than the interface of unlike-molecules, therefore surface molecules seek to have as many like-molecule interfaces as possible resulting in the lowest surface area.<br />
<br />
==Units==<br />
Surface tension (<math>\gamma</math>) has dimensions of force per unit length (<math>\frac{F} {L}</math>.<br />
<br />
==References==<br />
<br />
http://en.wikipedia.org/wiki/Cohesion_%28chemistry%29<br />
<br />
http://en.wikipedia.org/wiki/Surface_tension</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Surface_tension&diff=13731Surface tension2009-12-04T17:06:41Z<p>Mcilwee: /* Units */</p>
<hr />
<div>==Definition==<br />
Surface tension is a property of liquid surfaces caused by cohesion. Cohesion is the physical property resulting from the intermolecular forces attracting like-molecules. The molecules on the surface of a liquid have a greater attraction to like-molecules around them than to unlike-molecules.<br />
<br />
Molecules on the surface of a liquid experience an inward force balanced by the resistance to compression. Another important point in understanding surface tension is the liquid molecules seek the lowest possible surface area. This is the reason that liquids form droplets on hydrophobic surfaces. The interface of lke-molecules has a lower energy than the interface of unlike-molecules, therefore surface molecules seek to have as many like-molecule interfaces as possible resulting in the lowest surface area.<br />
<br />
==Units==<br />
Surface tension (<math>\gamma</math>) has dimensions of force per unit length (<math>frac{F} {L}</math>.<br />
<br />
==References==<br />
<br />
http://en.wikipedia.org/wiki/Cohesion_%28chemistry%29<br />
<br />
http://en.wikipedia.org/wiki/Surface_tension</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Surface_tension&diff=13730Surface tension2009-12-04T17:06:24Z<p>Mcilwee: /* Units */</p>
<hr />
<div>==Definition==<br />
Surface tension is a property of liquid surfaces caused by cohesion. Cohesion is the physical property resulting from the intermolecular forces attracting like-molecules. The molecules on the surface of a liquid have a greater attraction to like-molecules around them than to unlike-molecules.<br />
<br />
Molecules on the surface of a liquid experience an inward force balanced by the resistance to compression. Another important point in understanding surface tension is the liquid molecules seek the lowest possible surface area. This is the reason that liquids form droplets on hydrophobic surfaces. The interface of lke-molecules has a lower energy than the interface of unlike-molecules, therefore surface molecules seek to have as many like-molecule interfaces as possible resulting in the lowest surface area.<br />
<br />
==Units==<br />
Surface tension (<math>\gamma</math>) has dimensions of force per unit length (<math>Frac{F} {L}</math>.<br />
<br />
==References==<br />
<br />
http://en.wikipedia.org/wiki/Cohesion_%28chemistry%29<br />
<br />
http://en.wikipedia.org/wiki/Surface_tension</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Surface_tension&diff=13729Surface tension2009-12-04T17:05:33Z<p>Mcilwee: </p>
<hr />
<div>==Definition==<br />
Surface tension is a property of liquid surfaces caused by cohesion. Cohesion is the physical property resulting from the intermolecular forces attracting like-molecules. The molecules on the surface of a liquid have a greater attraction to like-molecules around them than to unlike-molecules.<br />
<br />
Molecules on the surface of a liquid experience an inward force balanced by the resistance to compression. Another important point in understanding surface tension is the liquid molecules seek the lowest possible surface area. This is the reason that liquids form droplets on hydrophobic surfaces. The interface of lke-molecules has a lower energy than the interface of unlike-molecules, therefore surface molecules seek to have as many like-molecule interfaces as possible resulting in the lowest surface area.<br />
<br />
==Units==<br />
Surface tension (<math>\gamma</math>) has dimensions of force per unit length (<math>Fract {F} {L}</math>.<br />
<br />
==References==<br />
<br />
http://en.wikipedia.org/wiki/Cohesion_%28chemistry%29<br />
<br />
http://en.wikipedia.org/wiki/Surface_tension</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Surface_tension&diff=13728Surface tension2009-12-04T16:45:18Z<p>Mcilwee: </p>
<hr />
<div>Currently being edited by Holly McIlwee<br />
<br />
<math>\gamma</math><br />
<br />
<br />
==References==<br />
<br />
http://en.wikipedia.org/wiki/Cohesion_%28chemistry%29</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Like_charged_particles_at_liquid_interfaces&diff=13721Like charged particles at liquid interfaces2009-12-04T16:33:41Z<p>Mcilwee: </p>
<hr />
<div>Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Like charged particles at liquid interfaces, M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. Brief Communications, Nature, 424, August, (2003).<br />
<br />
== Abstract ==<br />
Joanna Aizenberg ''et al''. wrote a communication in response to an article Nikolaids ''et al''. published in Nature in 2002. In the original paper, it was proposed that the attraction between micron-sized particles and an aqueous interface they are absorbed on is caused by a distortion of the liquid interface due to the dipolar electric field of the particles inducing capillary action. Aizenberg ''et al''. were compelled to challenge this claim on the basis that they believed that this explanation for the observed attraction does not adhere to force balance laws. <br />
<br />
== Keywords ==<br />
[[Surface tension]], Electric field, Capillary action<br />
<br />
== Soft Matter ==<br />
Nikolaides ''et al.'' assume that the sum of electrostatic pressure acting on the liquid interface is equal to an external force, F, acting on the particle resulting in:<br />
<br />
U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/<math>r_o</math>)<br />
<br />
Where: <br />
<math>\gamma</math> is surface tension<br />
r is particle distance<br />
<math>r_o</math> is a constant<br />
<br />
This equation implies that the force acts on the particle and water at the same time. As Aizenberg ''et al.'' explains, this cannot be the case because the force is balanced by surface tension creating a dimple in the water (as seen in Figure 1) which is governed by the Young-LaPlace equation:<br />
<br />
[(1/<math>R_1</math>) + (1/<math>R_2</math>)]<math>\gamma</math> = <math>\Delta</math>p<br />
<br />
[[Image:McIlwee_Like_Charged_Particles.jpg|thumb|center|400px|alt=Figure 1. |Figure 1. ]]<br />
<br />
They go on to say that capillary attraction between spheres is caused by the overlap of their dimples reducing the total surface area of the water. This results in, for large (r):<br />
<br />
U(r) = -(<math>F^ 2</math>/<math>\pi</math><math>\gamma</math>)(<math>r_c</math>/r)^6<br />
<br />
This is much shorter range than, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/<math>r_o</math>), and shorter than dipole-dipole repulsion between like-charged particles proportional to 1/<math>r^ 3</math>, revealing that no attraction exists and is thermodynamically insignificant, contributing 1.8 x <math>10^-5</math>kT to interaction potential. In conclusion, they believe that the mystery of the origin of the attraction remains unsolved.<br />
<br />
In their rebuttal, it is admitted that, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/<math>r_o</math>) accounts for the electrostatic stressed while neglecting the force that the electric field exerts on the particle itself. Detailed calculations, not shown, reveal the interfacial force pulling the particle out of the fluid is canceled by the electrical force pushing the particle into the fluid.<br />
<br />
The data does show that there is a long range repulsive interaction because of charges. Also the attractive interactions balances the electrostatic repulsion. If it decays as a power law it must be slower than 1/<math>r^ 3</math>. Still, the most likely interaction with sufficient range is capillary distortion at the interface. This can only occur if there is an imbalance between the forces pushing the particle into the water and the interface outwards towards the oil. <br />
<br />
The interesting factor left is the charge on the particles on the oil side. The density of free charges is much less in oil than water and the screening length is larger. These factors extend the range of force imbalance and can account for the experimental observations. The capillary distortion remains electrostatic in nature.<br />
<br />
Further experiments confirm the measurable charge in oil increasing the screening length to values greater than particle separation allowing force imbalance to persist far enough for significant interfacial distortion to exist at scales comparable to interparticle separation.<br />
<br />
Therefore it is believed that electric-field-induced capillary distortion remains the likely culprit for the attractive interaction between like-charged interfacial particles.<br />
<br />
== References ==<br />
M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. ''Nature'', '''424''', August, (2003).<br />
<br />
M. G. Nikolaides ''et al''. ''Nature'' '''420''', 299-301 (2002).<br />
<br />
Stamou, D., Dushi, C. and Johannsmann, D. ''Phys. Rev E'' '''54''', 5263-5272, (2000).<br />
<br />
Aveyard, R ''et al. Phys. Rev. Lett''. '''88''', 246102-1-4 (2002).</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Like_charged_particles_at_liquid_interfaces&diff=13720Like charged particles at liquid interfaces2009-12-04T16:33:26Z<p>Mcilwee: /* Keywords */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Like charged particles at liquid interfaces, M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. Brief Communications, Nature, 424, August, (2003).<br />
<br />
== Abstract ==<br />
Joanna Aizenberg ''et al''. wrote a communication in response to an article Nikolaids ''et al''. published in Nature in 2002. In the original paper, it was proposed that the attraction between micron-sized particles and an aqueous interface they are absorbed on is caused by a distortion of the liquid interface due to the dipolar electric field of the particles inducing capillary action. Aizenberg ''et al''. were compelled to challenge this claim on the basis that they believed that this explanation for the observed attraction does not adhere to force balance laws. <br />
<br />
== Keywords ==<br />
[[Surface tension]], Electric field, Capillary action<br />
<br />
== Soft Matter ==<br />
Nikolaides ''et al.'' assume that the sum of electrostatic pressure acting on the liquid interface is equal to an external force, F, acting on the particle resulting in:<br />
<br />
U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/<math>r_o</math>)<br />
<br />
Where: <br />
<math>\gamma</math> is surface tension<br />
r is particle distance<br />
<math>r_o</math> is a constant<br />
<br />
This equation implies that the force acts on the particle and water at the same time. As Aizenberg ''et al.'' explains, this cannot be the case because the force is balanced by surface tension creating a dimple in the water (as seen in Figure 1) which is governed by the Young-LaPlace equation:<br />
<br />
[(1/<math>R_1</math>) + (1/<math>R_2</math>)]<math>\gamma</math> = <math>\Delta</math>p<br />
<br />
[[Image:McIlwee_Like_Charged_Particles.jpg|thumb|center|400px|alt=Figure 1. |Figure 1. ]]<br />
<br />
They go on to say that capillary attraction between spheres is caused by the overlap of their dimples reducing the total surface area of the water. This results in, for large (r):<br />
<br />
U(r) = -(<math>F^ 2</math>/<math>\pi</math><math>\gamma</math>)(<math>r_c</math>/r)^6<br />
<br />
This is much shorter range than, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/<math>r_o</math>), and shorter than dipole-dipole repulsion between like-charged particles proportional to 1/<math>r^ 3</math>, revealing that no attraction exists and is thermodynamically insignificant, contributing 1.8 x <math>10^-5</math>kT to interaction potential. In conclusion, they believe that the mystery of the origin of the attraction remains unsolved.<br />
<br />
In their rebuttal, it is admitted that, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/<math>r_o</math>) accounts for the electrostatic stressed while neglecting the force that the electric field exerts on the particle itself. Detailed calculations, not shown, reveal the interfacial force pulling the particle out of the fluid is canceled by the electrical force pushing the particle into the fluid.<br />
<br />
The data does show that there is a long range repulsive interaction because of charges. Also the attractive interactions balances the electrostatic repulsion. If it decays as a power law it must be slower than 1/<math>r^ 3</math>. Still, the most likely interaction with sufficient range is capillary distortion at the interface. This can only occur if there is an imbalance between the forces pushing the particle into the water and the interface outwards towards the oil. <br />
<br />
The interesting factor left is the charge on the particles on the oil side. The density of free charges is much less in oil than water and the screening length is larger. These factors extend the range of force imbalance and can account for the experimental observations. The capillary distortion remains electrostatic in nature.<br />
<br />
Further experiments confirm the measurable charge in oil increasing the screening length to values greater than particle separation allowing force imbalance to persist far enough for significant interfacial distortion to exist at scales comparable to interparticle separation.<br />
<br />
Therefore it is believed that electric-field-induced capillary distortion remains the likely culprit for the attractive interaction between like-charged interfacial particles.<br />
<br />
== References ==<br />
M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. ''Nature'', '''424''', August, (2003).<br />
<br />
M. G. Nikolaides ''et al''. ''Nature'' '''420''', 299-301 (2002).<br />
<br />
Stamou, D., Dushi, C. and Johannsmann, D. ''Phys. Rev E'' '''54''', 5263-5272, (2000).<br />
<br />
Aveyard, R ''et al. Phys. Rev. Lett''. '''88''', 246102-1-4 (2002).</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Like_charged_particles_at_liquid_interfaces&diff=13718Like charged particles at liquid interfaces2009-12-04T16:30:08Z<p>Mcilwee: /* Keywords */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Like charged particles at liquid interfaces, M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. Brief Communications, Nature, 424, August, (2003).<br />
<br />
== Abstract ==<br />
Joanna Aizenberg ''et al''. wrote a communication in response to an article Nikolaids ''et al''. published in Nature in 2002. In the original paper, it was proposed that the attraction between micron-sized particles and an aqueous interface they are absorbed on is caused by a distortion of the liquid interface due to the dipolar electric field of the particles inducing capillary action. Aizenberg ''et al''. were compelled to challenge this claim on the basis that they believed that this explanation for the observed attraction does not adhere to force balance laws. <br />
<br />
== Keywords ==<br />
[[Surface tension]], [[Electric field]], [[Capillary action]]<br />
<br />
== Soft Matter ==<br />
Nikolaides ''et al.'' assume that the sum of electrostatic pressure acting on the liquid interface is equal to an external force, F, acting on the particle resulting in:<br />
<br />
U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/<math>r_o</math>)<br />
<br />
Where: <br />
<math>\gamma</math> is surface tension<br />
r is particle distance<br />
<math>r_o</math> is a constant<br />
<br />
This equation implies that the force acts on the particle and water at the same time. As Aizenberg ''et al.'' explains, this cannot be the case because the force is balanced by surface tension creating a dimple in the water (as seen in Figure 1) which is governed by the Young-LaPlace equation:<br />
<br />
[(1/<math>R_1</math>) + (1/<math>R_2</math>)]<math>\gamma</math> = <math>\Delta</math>p<br />
<br />
[[Image:McIlwee_Like_Charged_Particles.jpg|thumb|center|400px|alt=Figure 1. |Figure 1. ]]<br />
<br />
They go on to say that capillary attraction between spheres is caused by the overlap of their dimples reducing the total surface area of the water. This results in, for large (r):<br />
<br />
U(r) = -(<math>F^ 2</math>/<math>\pi</math><math>\gamma</math>)(<math>r_c</math>/r)^6<br />
<br />
This is much shorter range than, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/<math>r_o</math>), and shorter than dipole-dipole repulsion between like-charged particles proportional to 1/<math>r^ 3</math>, revealing that no attraction exists and is thermodynamically insignificant, contributing 1.8 x <math>10^-5</math>kT to interaction potential. In conclusion, they believe that the mystery of the origin of the attraction remains unsolved.<br />
<br />
In their rebuttal, it is admitted that, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/<math>r_o</math>) accounts for the electrostatic stressed while neglecting the force that the electric field exerts on the particle itself. Detailed calculations, not shown, reveal the interfacial force pulling the particle out of the fluid is canceled by the electrical force pushing the particle into the fluid.<br />
<br />
The data does show that there is a long range repulsive interaction because of charges. Also the attractive interactions balances the electrostatic repulsion. If it decays as a power law it must be slower than 1/<math>r^ 3</math>. Still, the most likely interaction with sufficient range is capillary distortion at the interface. This can only occur if there is an imbalance between the forces pushing the particle into the water and the interface outwards towards the oil. <br />
<br />
The interesting factor left is the charge on the particles on the oil side. The density of free charges is much less in oil than water and the screening length is larger. These factors extend the range of force imbalance and can account for the experimental observations. The capillary distortion remains electrostatic in nature.<br />
<br />
Further experiments confirm the measurable charge in oil increasing the screening length to values greater than particle separation allowing force imbalance to persist far enough for significant interfacial distortion to exist at scales comparable to interparticle separation.<br />
<br />
Therefore it is believed that electric-field-induced capillary distortion remains the likely culprit for the attractive interaction between like-charged interfacial particles.<br />
<br />
== References ==<br />
M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. ''Nature'', '''424''', August, (2003).<br />
<br />
M. G. Nikolaides ''et al''. ''Nature'' '''420''', 299-301 (2002).<br />
<br />
Stamou, D., Dushi, C. and Johannsmann, D. ''Phys. Rev E'' '''54''', 5263-5272, (2000).<br />
<br />
Aveyard, R ''et al. Phys. Rev. Lett''. '''88''', 246102-1-4 (2002).</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Like_charged_particles_at_liquid_interfaces&diff=13717Like charged particles at liquid interfaces2009-12-04T16:27:47Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Like charged particles at liquid interfaces, M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. Brief Communications, Nature, 424, August, (2003).<br />
<br />
== Abstract ==<br />
Joanna Aizenberg ''et al''. wrote a communication in response to an article Nikolaids ''et al''. published in Nature in 2002. In the original paper, it was proposed that the attraction between micron-sized particles and an aqueous interface they are absorbed on is caused by a distortion of the liquid interface due to the dipolar electric field of the particles inducing capillary action. Aizenberg ''et al''. were compelled to challenge this claim on the basis that they believed that this explanation for the observed attraction does not adhere to force balance laws. <br />
<br />
== Keywords ==<br />
<br />
<br />
== Soft Matter ==<br />
Nikolaides ''et al.'' assume that the sum of electrostatic pressure acting on the liquid interface is equal to an external force, F, acting on the particle resulting in:<br />
<br />
U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/<math>r_o</math>)<br />
<br />
Where: <br />
<math>\gamma</math> is surface tension<br />
r is particle distance<br />
<math>r_o</math> is a constant<br />
<br />
This equation implies that the force acts on the particle and water at the same time. As Aizenberg ''et al.'' explains, this cannot be the case because the force is balanced by surface tension creating a dimple in the water (as seen in Figure 1) which is governed by the Young-LaPlace equation:<br />
<br />
[(1/<math>R_1</math>) + (1/<math>R_2</math>)]<math>\gamma</math> = <math>\Delta</math>p<br />
<br />
[[Image:McIlwee_Like_Charged_Particles.jpg|thumb|center|400px|alt=Figure 1. |Figure 1. ]]<br />
<br />
They go on to say that capillary attraction between spheres is caused by the overlap of their dimples reducing the total surface area of the water. This results in, for large (r):<br />
<br />
U(r) = -(<math>F^ 2</math>/<math>\pi</math><math>\gamma</math>)(<math>r_c</math>/r)^6<br />
<br />
This is much shorter range than, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/<math>r_o</math>), and shorter than dipole-dipole repulsion between like-charged particles proportional to 1/<math>r^ 3</math>, revealing that no attraction exists and is thermodynamically insignificant, contributing 1.8 x <math>10^-5</math>kT to interaction potential. In conclusion, they believe that the mystery of the origin of the attraction remains unsolved.<br />
<br />
In their rebuttal, it is admitted that, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/<math>r_o</math>) accounts for the electrostatic stressed while neglecting the force that the electric field exerts on the particle itself. Detailed calculations, not shown, reveal the interfacial force pulling the particle out of the fluid is canceled by the electrical force pushing the particle into the fluid.<br />
<br />
The data does show that there is a long range repulsive interaction because of charges. Also the attractive interactions balances the electrostatic repulsion. If it decays as a power law it must be slower than 1/<math>r^ 3</math>. Still, the most likely interaction with sufficient range is capillary distortion at the interface. This can only occur if there is an imbalance between the forces pushing the particle into the water and the interface outwards towards the oil. <br />
<br />
The interesting factor left is the charge on the particles on the oil side. The density of free charges is much less in oil than water and the screening length is larger. These factors extend the range of force imbalance and can account for the experimental observations. The capillary distortion remains electrostatic in nature.<br />
<br />
Further experiments confirm the measurable charge in oil increasing the screening length to values greater than particle separation allowing force imbalance to persist far enough for significant interfacial distortion to exist at scales comparable to interparticle separation.<br />
<br />
Therefore it is believed that electric-field-induced capillary distortion remains the likely culprit for the attractive interaction between like-charged interfacial particles.<br />
<br />
== References ==<br />
M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. ''Nature'', '''424''', August, (2003).<br />
<br />
M. G. Nikolaides ''et al''. ''Nature'' '''420''', 299-301 (2002).<br />
<br />
Stamou, D., Dushi, C. and Johannsmann, D. ''Phys. Rev E'' '''54''', 5263-5272, (2000).<br />
<br />
Aveyard, R ''et al. Phys. Rev. Lett''. '''88''', 246102-1-4 (2002).</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Like_charged_particles_at_liquid_interfaces&diff=13715Like charged particles at liquid interfaces2009-12-04T16:27:06Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Like charged particles at liquid interfaces, M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. Brief Communications, Nature, 424, August, (2003).<br />
<br />
== Abstract ==<br />
Joanna Aizenberg ''et al''. wrote a communication in response to an article Nikolaids ''et al''. published in Nature in 2002. In the original paper, it was proposed that the attraction between micron-sized particles and an aqueous interface they are absorbed on is caused by a distortion of the liquid interface due to the dipolar electric field of the particles inducing capillary action. Aizenberg ''et al''. were compelled to challenge this claim on the basis that they believed that this explanation for the observed attraction does not adhere to force balance laws. <br />
<br />
== Keywords ==<br />
<br />
<br />
== Soft Matter ==<br />
Nikolaides ''et al.'' assume that the sum of electrostatic pressure acting on the liquid interface is equal to an external force, F, acting on the particle resulting in:<br />
<br />
U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/<math>r_o</math>)<br />
<br />
Where: <br />
<math>\gamma</math> is surface tension<br />
r is particle distance<br />
<math>r_o</math> is a constant<br />
<br />
This equation implies that the force acts on the particle and water at the same time. As Aizenberg ''et al.'' explains, this cannot be the case because the force is balanced by surface tension creating a dimple in the water (as seen in Figure 1) which is governed by the Young-LaPlace equation:<br />
<br />
[(1/<math>R_1</math>) + (1/<math>R_2</math>)]<math>\gamma</math> = <math>\Delta</math>p<br />
<br />
[[Image:McIlwee_Like_Charged_Particles.jpg|thumb|center|400px|alt=Figure 1. |Figure 1. ]]<br />
<br />
They go on to say that capillary attraction between spheres is caused by the overlap of their dimples reducing the total surface area of the water. This results in, for large (r):<br />
<br />
U(r) = -(<math>F^ 2</math>/<math>\pi</math><math>\gamma</math>)(<math>r_c</math>/r)^6<br />
<br />
This is much shorter range than, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/<math>r_o</math>), and shorter than dipole-dipole repulsion between like-charged particles proportional to 1/<math>r^ 3</math>, revealing that no attraction exists and is thermodynamically insignificant, contributing 1.8 x <math>10^(-5)</math>kT to interaction potential. In conclusion, they believe that the mystery of the origin of the attraction remains unsolved.<br />
<br />
In their rebuttal, it is admitted that, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/<math>r_o</math>) accounts for the electrostatic stressed while neglecting the force that the electric field exerts on the particle itself. Detailed calculations, not shown, reveal the interfacial force pulling the particle out of the fluid is canceled by the electrical force pushing the particle into the fluid.<br />
<br />
The data does show that there is a long range repulsive interaction because of charges. Also the attractive interactions balances the electrostatic repulsion. If it decays as a power law it must be slower than 1/<math>r^ 3</math>. Still, the most likely interaction with sufficient range is capillary distortion at the interface. This can only occur if there is an imbalance between the forces pushing the particle into the water and the interface outwards towards the oil. <br />
<br />
The interesting factor left is the charge on the particles on the oil side. The density of free charges is much less in oil than water and the screening length is larger. These factors extend the range of force imbalance and can account for the experimental observations. The capillary distortion remains electrostatic in nature.<br />
<br />
Further experiments confirm the measurable charge in oil increasing the screening length to values greater than particle separation allowing force imbalance to persist far enough for significant interfacial distortion to exist at scales comparable to interparticle separation.<br />
<br />
Therefore it is believed that electric-field-induced capillary distortion remains the likely culprit for the attractive interaction between like-charged interfacial particles.<br />
<br />
== References ==<br />
M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. ''Nature'', '''424''', August, (2003).<br />
<br />
M. G. Nikolaides ''et al''. ''Nature'' '''420''', 299-301 (2002).<br />
<br />
Stamou, D., Dushi, C. and Johannsmann, D. ''Phys. Rev E'' '''54''', 5263-5272, (2000).<br />
<br />
Aveyard, R ''et al. Phys. Rev. Lett''. '''88''', 246102-1-4 (2002).</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Like_charged_particles_at_liquid_interfaces&diff=13714Like charged particles at liquid interfaces2009-12-04T16:25:08Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Like charged particles at liquid interfaces, M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. Brief Communications, Nature, 424, August, (2003).<br />
<br />
== Abstract ==<br />
Joanna Aizenberg ''et al''. wrote a communication in response to an article Nikolaids ''et al''. published in Nature in 2002. In the original paper, it was proposed that the attraction between micron-sized particles and an aqueous interface they are absorbed on is caused by a distortion of the liquid interface due to the dipolar electric field of the particles inducing capillary action. Aizenberg ''et al''. were compelled to challenge this claim on the basis that they believed that this explanation for the observed attraction does not adhere to force balance laws. <br />
<br />
== Keywords ==<br />
<br />
<br />
== Soft Matter ==<br />
Nikolaides ''et al.'' assume that the sum of electrostatic pressure acting on the liquid interface is equal to an external force, F, acting on the particle resulting in:<br />
<br />
U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/<math>r_o</math>)<br />
<br />
Where: <br />
<math>\gamma</math> is surface tension<br />
r is particle distance<br />
rsub0 is a constant<br />
<br />
This equation implies that the force acts on the particle and water at the same time. As Aizenberg ''et al.'' explains, this cannot be the case because the force is balanced by surface tension creating a dimple in the water (as seen in Figure 1) which is governed by the Young-LaPlace equation:<br />
<br />
[(1/R1) + (1/R2)]<math>\gamma</math> = <math>\Delta</math>p<br />
<br />
[[Image:McIlwee_Like_Charged_Particles.jpg|thumb|center|400px|alt=Figure 1. |Figure 1. ]]<br />
<br />
They go on to say that capillary attraction between spheres is caused by the overlap of their dimples reducing the total surface area of the water. This results in, for large (r):<br />
<br />
U(r) = -(<math>F^ 2</math>/<math>\pi</math><math>\gamma</math>)(rsubc/r)^6<br />
<br />
This is much shorter range than, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo), and shorter than dipole-dipole repulsion between like-charged particles proportional to 1/<math>r^ 3</math>, revealing that no attraction exists and is thermodynamically insignificant, contributing 1.8 x <math>10^(-5)</math>kT to interaction potential. In conclusion, they believe that the mystery of the origin of the attraction remains unsolved.<br />
<br />
In their rebuttal, it is admitted that, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo) accounts for the electrostatic stressed while neglecting the force that the electric field exerts on the particle itself. Detailed calculations, not shown, reveal the interfacial force pulling the particle out of the fluid is canceled by the electrical force pushing the particle into the fluid.<br />
<br />
The data does show that there is a long range repulsive interaction because of charges. Also the attractive interactions balances the electrostatic repulsion. If it decays as a power law it must be slower than 1/<math>r^ 3</math>. Still, the most likely interaction with sufficient range is capillary distortion at the interface. This can only occur if there is an imbalance between the forces pushing the particle into the water and the interface outwards towards the oil. <br />
<br />
The interesting factor left is the charge on the particles on the oil side. The density of free charges is much less in oil than water and the screening length is larger. These factors extend the range of force imbalance and can account for the experimental observations. The capillary distortion remains electrostatic in nature.<br />
<br />
Further experiments confirm the measurable charge in oil increasing the screening length to values greater than particle separation allowing force imbalance to persist far enough for significant interfacial distortion to exist at scales comparable to interparticle separation.<br />
<br />
Therefore it is believed that electric-field-induced capillary distortion remains the likely culprit for the attractive interaction between like-charged interfacial particles.<br />
<br />
== References ==<br />
M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. ''Nature'', '''424''', August, (2003).<br />
<br />
M. G. Nikolaides ''et al''. ''Nature'' '''420''', 299-301 (2002).<br />
<br />
Stamou, D., Dushi, C. and Johannsmann, D. ''Phys. Rev E'' '''54''', 5263-5272, (2000).<br />
<br />
Aveyard, R ''et al. Phys. Rev. Lett''. '''88''', 246102-1-4 (2002).</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Like_charged_particles_at_liquid_interfaces&diff=13713Like charged particles at liquid interfaces2009-12-04T16:23:06Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Like charged particles at liquid interfaces, M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. Brief Communications, Nature, 424, August, (2003).<br />
<br />
== Abstract ==<br />
Joanna Aizenberg ''et al''. wrote a communication in response to an article Nikolaids ''et al''. published in Nature in 2002. In the original paper, it was proposed that the attraction between micron-sized particles and an aqueous interface they are absorbed on is caused by a distortion of the liquid interface due to the dipolar electric field of the particles inducing capillary action. Aizenberg ''et al''. were compelled to challenge this claim on the basis that they believed that this explanation for the observed attraction does not adhere to force balance laws. <br />
<br />
== Keywords ==<br />
<br />
<br />
== Soft Matter ==<br />
Nikolaides ''et al.'' assume that the sum of electrostatic pressure acting on the liquid interface is equal to an external force, F, acting on the particle resulting in:<br />
<br />
U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo)<br />
<br />
Where: <br />
<math>\gamma</math> is surface tension<br />
r is particle distance<br />
rsub0 is a constant<br />
<br />
This equation implies that the force acts on the particle and water at the same time. As Aizenberg ''et al.'' explains, this cannot be the case because the force is balanced by surface tension creating a dimple in the water (as seen in Figure 1) which is governed by the Young-LaPlace equation:<br />
<br />
[(1/R1) + (1/R2)]<math>\gamma</math> = <math>\Delta</math>p<br />
<br />
[[Image:McIlwee_Like_Charged_Particles.jpg|thumb|center|400px|alt=Figure 1. |Figure 1. ]]<br />
<br />
They go on to say that capillary attraction between spheres is caused by the overlap of their dimples reducing the total surface area of the water. This results in, for large (r):<br />
<br />
U(r) = -(<math>F^ 2</math>/<math>\pi</math><math>\gamma</math>)(rsubc/r)^6<br />
<br />
This is much shorter range than, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo), and shorter than dipole-dipole repulsion between like-charged particles proportional to 1/<math>r^ 3</math>, revealing that no attraction exists and is thermodynamically insignificant, contributing 1.8 x <math>10^(-5)</math>kT to interaction potential. In conclusion, they believe that the mystery of the origin of the attraction remains unsolved.<br />
<br />
In their rebuttal, it is admitted that, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo) accounts for the electrostatic stressed while neglecting the force that the electric field exerts on the particle itself. Detailed calculations, not shown, reveal the interfacial force pulling the particle out of the fluid is canceled by the electrical force pushing the particle into the fluid.<br />
<br />
The data does show that there is a long range repulsive interaction because of charges. Also the attractive interactions balances the electrostatic repulsion. If it decays as a power law it must be slower than 1/<math>r^ 3</math>. Still, the most likely interaction with sufficient range is capillary distortion at the interface. This can only occur if there is an imbalance between the forces pushing the particle into the water and the interface outwards towards the oil. <br />
<br />
The interesting factor left is the charge on the particles on the oil side. The density of free charges is much less in oil than water and the screening length is larger. These factors extend the range of force imbalance and can account for the experimental observations. The capillary distortion remains electrostatic in nature.<br />
<br />
Further experiments confirm the measurable charge in oil increasing the screening length to values greater than particle separation allowing force imbalance to persist far enough for significant interfacial distortion to exist at scales comparable to interparticle separation.<br />
<br />
Therefore it is believed that electric-field-induced capillary distortion remains the likely culprit for the attractive interaction between like-charged interfacial particles.<br />
<br />
== References ==<br />
M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. ''Nature'', '''424''', August, (2003).<br />
<br />
M. G. Nikolaides ''et al''. ''Nature'' '''420''', 299-301 (2002).<br />
<br />
Stamou, D., Dushi, C. and Johannsmann, D. ''Phys. Rev E'' '''54''', 5263-5272, (2000).<br />
<br />
Aveyard, R ''et al. Phys. Rev. Lett''. '''88''', 246102-1-4 (2002).</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Like_charged_particles_at_liquid_interfaces&diff=13712Like charged particles at liquid interfaces2009-12-04T16:21:16Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Like charged particles at liquid interfaces, M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. Brief Communications, Nature, 424, August, (2003).<br />
<br />
== Abstract ==<br />
Joanna Aizenberg ''et al''. wrote a communication in response to an article Nikolaids ''et al''. published in Nature in 2002. In the original paper, it was proposed that the attraction between micron-sized particles and an aqueous interface they are absorbed on is caused by a distortion of the liquid interface due to the dipolar electric field of the particles inducing capillary action. Aizenberg ''et al''. were compelled to challenge this claim on the basis that they believed that this explanation for the observed attraction does not adhere to force balance laws. <br />
<br />
== Keywords ==<br />
<br />
<br />
== Soft Matter ==<br />
Nikolaides ''et al.'' assume that the sum of electrostatic pressure acting on the liquid interface is equal to an external force, F, acting on the particle resulting in:<br />
<br />
<math>U(r)=\frac{<math>F^ 2</math>}{2} \gamma \theta^2_E \vert q \vert u^2_q </math><br />
<br />
= *<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo)<br />
<br />
Where: <br />
<math>\gamma</math> is surface tension<br />
r is particle distance<br />
rsub0 is a constant<br />
<br />
This equation implies that the force acts on the particle and water at the same time. As Aizenberg ''et al.'' explains, this cannot be the case because the force is balanced by surface tension creating a dimple in the water (as seen in Figure 1) which is governed by the Young-LaPlace equation:<br />
<br />
[(1/R1) + (1/R2)]<math>\gamma</math> = <math>\Delta</math>p<br />
<br />
[[Image:McIlwee_Like_Charged_Particles.jpg|thumb|center|400px|alt=Figure 1. |Figure 1. ]]<br />
<br />
They go on to say that capillary attraction between spheres is caused by the overlap of their dimples reducing the total surface area of the water. This results in, for large (r):<br />
<br />
U(r) = -(<math>F^ 2</math>/<math>\pi</math><math>\gamma</math>)(rsubc/r)^6<br />
<br />
This is much shorter range than, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo), and shorter than dipole-dipole repulsion between like-charged particles proportional to 1/<math>r^ 3</math>, revealing that no attraction exists and is thermodynamically insignificant, contributing 1.8 x <math>10^(-5)</math>kT to interaction potential. In conclusion, they believe that the mystery of the origin of the attraction remains unsolved.<br />
<br />
In their rebuttal, it is admitted that, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo) accounts for the electrostatic stressed while neglecting the force that the electric field exerts on the particle itself. Detailed calculations, not shown, reveal the interfacial force pulling the particle out of the fluid is canceled by the electrical force pushing the particle into the fluid.<br />
<br />
The data does show that there is a long range repulsive interaction because of charges. Also the attractive interactions balances the electrostatic repulsion. If it decays as a power law it must be slower than 1/<math>r^ 3</math>. Still, the most likely interaction with sufficient range is capillary distortion at the interface. This can only occur if there is an imbalance between the forces pushing the particle into the water and the interface outwards towards the oil. <br />
<br />
The interesting factor left is the charge on the particles on the oil side. The density of free charges is much less in oil than water and the screening length is larger. These factors extend the range of force imbalance and can account for the experimental observations. The capillary distortion remains electrostatic in nature.<br />
<br />
Further experiments confirm the measurable charge in oil increasing the screening length to values greater than particle separation allowing force imbalance to persist far enough for significant interfacial distortion to exist at scales comparable to interparticle separation.<br />
<br />
Therefore it is believed that electric-field-induced capillary distortion remains the likely culprit for the attractive interaction between like-charged interfacial particles.<br />
<br />
== References ==<br />
M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. ''Nature'', '''424''', August, (2003).<br />
<br />
M. G. Nikolaides ''et al''. ''Nature'' '''420''', 299-301 (2002).<br />
<br />
Stamou, D., Dushi, C. and Johannsmann, D. ''Phys. Rev E'' '''54''', 5263-5272, (2000).<br />
<br />
Aveyard, R ''et al. Phys. Rev. Lett''. '''88''', 246102-1-4 (2002).</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Like_charged_particles_at_liquid_interfaces&diff=13707Like charged particles at liquid interfaces2009-12-04T16:18:45Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Like charged particles at liquid interfaces, M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. Brief Communications, Nature, 424, August, (2003).<br />
<br />
== Abstract ==<br />
Joanna Aizenberg ''et al''. wrote a communication in response to an article Nikolaids ''et al''. published in Nature in 2002. In the original paper, it was proposed that the attraction between micron-sized particles and an aqueous interface they are absorbed on is caused by a distortion of the liquid interface due to the dipolar electric field of the particles inducing capillary action. Aizenberg ''et al''. were compelled to challenge this claim on the basis that they believed that this explanation for the observed attraction does not adhere to force balance laws. <br />
<br />
== Keywords ==<br />
<br />
<br />
== Soft Matter ==<br />
Nikolaides ''et al.'' assume that the sum of electrostatic pressure acting on the liquid interface is equal to an external force, F, acting on the particle resulting in:<br />
<br />
U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo)<br />
<br />
Where: <br />
<math>\gamma</math> is surface tension<br />
r is particle distance<br />
rsub0 is a constant<br />
<br />
This equation implies that the force acts on the particle and water at the same time. As Aizenberg ''et al.'' explains, this cannot be the case because the force is balanced by surface tension creating a dimple in the water (as seen in Figure 1) which is governed by the Young-LaPlace equation:<br />
<br />
[(1/R1) + (1/R2)]<math>\gamma</math> = <math>\Delta</math>p<br />
<br />
[[Image:McIlwee_Like_Charged_Particles.jpg|thumb|center|400px|alt=Figure 1. |Figure 1. ]]<br />
<br />
They go on to say that capillary attraction between spheres is caused by the overlap of their dimples reducing the total surface area of the water. This results in, for large (r):<br />
<br />
U(r) = -(<math>F^ 2</math>/<math>\pi</math><math>\gamma</math>)(rsubc/r)^6<br />
<br />
This is much shorter range than, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo), and shorter than dipole-dipole repulsion between like-charged particles proportional to 1/<math>r^ 3</math>, revealing that no attraction exists and is thermodynamically insignificant, contributing 1.8 x <math>10^(-5)</math>kT to interaction potential. In conclusion, they believe that the mystery of the origin of the attraction remains unsolved.<br />
<br />
In their rebuttal, it is admitted that, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo) accounts for the electrostatic stressed while neglecting the force that the electric field exerts on the particle itself. Detailed calculations, not shown, reveal the interfacial force pulling the particle out of the fluid is canceled by the electrical force pushing the particle into the fluid.<br />
<br />
The data does show that there is a long range repulsive interaction because of charges. Also the attractive interactions balances the electrostatic repulsion. If it decays as a power law it must be slower than 1/<math>r^ 3</math>. Still, the most likely interaction with sufficient range is capillary distortion at the interface. This can only occur if there is an imbalance between the forces pushing the particle into the water and the interface outwards towards the oil. <br />
<br />
The interesting factor left is the charge on the particles on the oil side. The density of free charges is much less in oil than water and the screening length is larger. These factors extend the range of force imbalance and can account for the experimental observations. The capillary distortion remains electrostatic in nature.<br />
<br />
Further experiments confirm the measurable charge in oil increasing the screening length to values greater than particle separation allowing force imbalance to persist far enough for significant interfacial distortion to exist at scales comparable to interparticle separation.<br />
<br />
Therefore it is believed that electric-field-induced capillary distortion remains the likely culprit for the attractive interaction between like-charged interfacial particles.<br />
<br />
== References ==<br />
M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. ''Nature'', '''424''', August, (2003).<br />
<br />
M. G. Nikolaides ''et al''. ''Nature'' '''420''', 299-301 (2002).<br />
<br />
Stamou, D., Dushi, C. and Johannsmann, D. ''Phys. Rev E'' '''54''', 5263-5272, (2000).<br />
<br />
Aveyard, R ''et al. Phys. Rev. Lett''. '''88''', 246102-1-4 (2002).</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Like_charged_particles_at_liquid_interfaces&diff=13705Like charged particles at liquid interfaces2009-12-04T16:17:44Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Like charged particles at liquid interfaces, M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. Brief Communications, Nature, 424, August, (2003).<br />
<br />
== Abstract ==<br />
Joanna Aizenberg ''et al''. wrote a communication in response to an article Nikolaids ''et al''. published in Nature in 2002. In the original paper, it was proposed that the attraction between micron-sized particles and an aqueous interface they are absorbed on is caused by a distortion of the liquid interface due to the dipolar electric field of the particles inducing capillary action. Aizenberg ''et al''. were compelled to challenge this claim on the basis that they believed that this explanation for the observed attraction does not adhere to force balance laws. <br />
<br />
== Keywords ==<br />
<br />
<br />
== Soft Matter ==<br />
Nikolaides ''et al.'' assume that the sum of electrostatic pressure acting on the liquid interface is equal to an external force, F, acting on the particle resulting in:<br />
<br />
U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo)<br />
<br />
Where: <br />
<math>\gamma</math> is surface tension<br />
r is particle distance<br />
rsub0 is a constant<br />
<br />
This equation implies that the force acts on the particle and water at the same time. As Aizenberg ''et al.'' explains, this cannot be the case because the force is balanced by surface tension creating a dimple in the water (as seen in Figure 1) which is governed by the Young-LaPlace equation:<br />
<br />
[(1/R1) + (1/R2)]<math>\gamma</math> = <math>\Delta</math>p<br />
<br />
[[Image:McIlwee_Like_Charged_Particles.jpg|thumb|center|400px|alt=Figure 1. |Figure 1. ]]<br />
<br />
They go on to say that capillary attraction between spheres is caused by the overlap of their dimples reducing the total surface area of the water. This results in, for large (r):<br />
<br />
U(r) = -(<math>F^ 2</math>/<math>\pi</math><math>\gamma</math>)(rsubc/r)^6<br />
<br />
This is much shorter range than, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo), and shorter than dipole-dipole repulsion between like-charged particles proportional to 1/<math>r^ 3</math>, revealing that no attraction exists and is thermodynamically insignificant, contributing 1.8 x <math>10^(-5)</math>kT to interaction potential. In conclusion, they believe that the mystery of the origin of the attraction remains unsolved.<br />
<br />
In their rebuttal, it is admitted that, U(r) = <math>F^ 2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo) accounts for the electrostatic stressed while neglecting the force that the electric field exerts on the particle itself. Detailed calculations, not shown, reveal the interfacial force pulling the particle out of the fluid is canceled by the electrical force pushing the particle into the fluid.<br />
<br />
The data does show that there is a long range repulsive interaction because of charges. Also the attractive interactions balances the electrostatic repulsion. If it decays as a power law it must be slower than 1/r^3. Still, the most likely interaction with sufficient range is capillary distortion at the interface. This can only occur if there is an imbalance between the forces pushing the particle into the water and the interface outwards towards the oil. <br />
<br />
The interesting factor left is the charge on the particles on the oil side. The density of free charges is much less in oil than water and the screening length is larger. These factors extend the range of force imbalance and can account for the experimental observations. The capillary distortion remains electrostatic in nature.<br />
<br />
Further experiments confirm the measurable charge in oil increasing the screening length to values greater than particle separation allowing force imbalance to persist far enough for significant interfacial distortion to exist at scales comparable to interparticle separation.<br />
<br />
Therefore it is believed that electric-field-induced capillary distortion remains the likely culprit for the attractive interaction between like-charged interfacial particles.<br />
<br />
== References ==<br />
M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. ''Nature'', '''424''', August, (2003).<br />
<br />
M. G. Nikolaides ''et al''. ''Nature'' '''420''', 299-301 (2002).<br />
<br />
Stamou, D., Dushi, C. and Johannsmann, D. ''Phys. Rev E'' '''54''', 5263-5272, (2000).<br />
<br />
Aveyard, R ''et al. Phys. Rev. Lett''. '''88''', 246102-1-4 (2002).</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Like_charged_particles_at_liquid_interfaces&diff=13700Like charged particles at liquid interfaces2009-12-04T16:15:51Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Like charged particles at liquid interfaces, M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. Brief Communications, Nature, 424, August, (2003).<br />
<br />
== Abstract ==<br />
Joanna Aizenberg ''et al''. wrote a communication in response to an article Nikolaids ''et al''. published in Nature in 2002. In the original paper, it was proposed that the attraction between micron-sized particles and an aqueous interface they are absorbed on is caused by a distortion of the liquid interface due to the dipolar electric field of the particles inducing capillary action. Aizenberg ''et al''. were compelled to challenge this claim on the basis that they believed that this explanation for the observed attraction does not adhere to force balance laws. <br />
<br />
== Keywords ==<br />
<br />
<br />
== Soft Matter ==<br />
Nikolaides ''et al.'' assume that the sum of electrostatic pressure acting on the liquid interface is equal to an external force, F, acting on the particle resulting in:<br />
<br />
U(r) = <math>F^2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo)<br />
<br />
Where: <br />
<math>\gamma</math> is surface tension<br />
r is particle distance<br />
rsub0 is a constant<br />
<br />
This equation implies that the force acts on the particle and water at the same time. As Aizenberg ''et al.'' explains, this cannot be the case because the force is balanced by surface tension creating a dimple in the water (as seen in Figure 1) which is governed by the Young-LaPlace equation:<br />
<br />
[(1/R1) + (1/R2)]<math>\gamma</math> = <math>\Delta</math>p<br />
<br />
[[Image:McIlwee_Like_Charged_Particles.jpg|thumb|center|400px|alt=Figure 1. |Figure 1. ]]<br />
<br />
They go on to say that capillary attraction between spheres is caused by the overlap of their dimples reducing the total surface area of the water. This results in, for large (r):<br />
<br />
U(r) = -(F^2/<math>\pi</math><math>\gamma</math>)(rsubc/r)^6<br />
<br />
This is much shorter range than, U(r) = F^2/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo), and shorter than dipole-dipole repulsion between like-charged particles proportional to 1/r^3, revealing that no attraction exists and is thermodynamically insignificant, contributing 1.8 x 10^(-5)kT to interaction potential. In conclusion, they believe that the mystery of the origin of the attraction remains unsolved.<br />
<br />
In their rebuttal, it is admitted that, U(r) = F^2/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo) accounts for the electrostatic stressed while neglecting the force that the electric field exerts on the particle itself. Detailed calculations, not shown, reveal the interfacial force pulling the particle out of the fluid is canceled by the electrical force pushing the particle into the fluid.<br />
<br />
The data does show that there is a long range repulsive interaction because of charges. Also the attractive interactions balances the electrostatic repulsion. If it decays as a power law it must be slower than 1/r^3. Still, the most likely interaction with sufficient range is capillary distortion at the interface. This can only occur if there is an imbalance between the forces pushing the particle into the water and the interface outwards towards the oil. <br />
<br />
The interesting factor left is the charge on the particles on the oil side. The density of free charges is much less in oil than water and the screening length is larger. These factors extend the range of force imbalance and can account for the experimental observations. The capillary distortion remains electrostatic in nature.<br />
<br />
Further experiments confirm the measurable charge in oil increasing the screening length to values greater than particle separation allowing force imbalance to persist far enough for significant interfacial distortion to exist at scales comparable to interparticle separation.<br />
<br />
Therefore it is believed that electric-field-induced capillary distortion remains the likely culprit for the attractive interaction between like-charged interfacial particles.<br />
<br />
== References ==<br />
M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. ''Nature'', '''424''', August, (2003).<br />
<br />
M. G. Nikolaides ''et al''. ''Nature'' '''420''', 299-301 (2002).<br />
<br />
Stamou, D., Dushi, C. and Johannsmann, D. ''Phys. Rev E'' '''54''', 5263-5272, (2000).<br />
<br />
Aveyard, R ''et al. Phys. Rev. Lett''. '''88''', 246102-1-4 (2002).</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Like_charged_particles_at_liquid_interfaces&diff=13698Like charged particles at liquid interfaces2009-12-04T16:15:27Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Like charged particles at liquid interfaces, M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. Brief Communications, Nature, 424, August, (2003).<br />
<br />
== Abstract ==<br />
Joanna Aizenberg ''et al''. wrote a communication in response to an article Nikolaids ''et al''. published in Nature in 2002. In the original paper, it was proposed that the attraction between micron-sized particles and an aqueous interface they are absorbed on is caused by a distortion of the liquid interface due to the dipolar electric field of the particles inducing capillary action. Aizenberg ''et al''. were compelled to challenge this claim on the basis that they believed that this explanation for the observed attraction does not adhere to force balance laws. <br />
<br />
== Keywords ==<br />
<br />
<br />
== Soft Matter ==<br />
Nikolaides ''et al.'' assume that the sum of electrostatic pressure acting on the liquid interface is equal to an external force, F, acting on the particle resulting in:<br />
<br />
U(r) = <math>\F^2</math>/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo)<br />
<br />
Where: <br />
<math>\gamma</math> is surface tension<br />
r is particle distance<br />
rsub0 is a constant<br />
<br />
This equation implies that the force acts on the particle and water at the same time. As Aizenberg ''et al.'' explains, this cannot be the case because the force is balanced by surface tension creating a dimple in the water (as seen in Figure 1) which is governed by the Young-LaPlace equation:<br />
<br />
[(1/R1) + (1/R2)]<math>\gamma</math> = <math>\Delta</math>p<br />
<br />
[[Image:McIlwee_Like_Charged_Particles.jpg|thumb|center|400px|alt=Figure 1. |Figure 1. ]]<br />
<br />
They go on to say that capillary attraction between spheres is caused by the overlap of their dimples reducing the total surface area of the water. This results in, for large (r):<br />
<br />
U(r) = -(F^2/<math>\pi</math><math>\gamma</math>)(rsubc/r)^6<br />
<br />
This is much shorter range than, U(r) = F^2/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo), and shorter than dipole-dipole repulsion between like-charged particles proportional to 1/r^3, revealing that no attraction exists and is thermodynamically insignificant, contributing 1.8 x 10^(-5)kT to interaction potential. In conclusion, they believe that the mystery of the origin of the attraction remains unsolved.<br />
<br />
In their rebuttal, it is admitted that, U(r) = F^2/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo) accounts for the electrostatic stressed while neglecting the force that the electric field exerts on the particle itself. Detailed calculations, not shown, reveal the interfacial force pulling the particle out of the fluid is canceled by the electrical force pushing the particle into the fluid.<br />
<br />
The data does show that there is a long range repulsive interaction because of charges. Also the attractive interactions balances the electrostatic repulsion. If it decays as a power law it must be slower than 1/r^3. Still, the most likely interaction with sufficient range is capillary distortion at the interface. This can only occur if there is an imbalance between the forces pushing the particle into the water and the interface outwards towards the oil. <br />
<br />
The interesting factor left is the charge on the particles on the oil side. The density of free charges is much less in oil than water and the screening length is larger. These factors extend the range of force imbalance and can account for the experimental observations. The capillary distortion remains electrostatic in nature.<br />
<br />
Further experiments confirm the measurable charge in oil increasing the screening length to values greater than particle separation allowing force imbalance to persist far enough for significant interfacial distortion to exist at scales comparable to interparticle separation.<br />
<br />
Therefore it is believed that electric-field-induced capillary distortion remains the likely culprit for the attractive interaction between like-charged interfacial particles.<br />
<br />
== References ==<br />
M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. ''Nature'', '''424''', August, (2003).<br />
<br />
M. G. Nikolaides ''et al''. ''Nature'' '''420''', 299-301 (2002).<br />
<br />
Stamou, D., Dushi, C. and Johannsmann, D. ''Phys. Rev E'' '''54''', 5263-5272, (2000).<br />
<br />
Aveyard, R ''et al. Phys. Rev. Lett''. '''88''', 246102-1-4 (2002).</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Like_charged_particles_at_liquid_interfaces&diff=13696Like charged particles at liquid interfaces2009-12-04T16:13:17Z<p>Mcilwee: </p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Like charged particles at liquid interfaces, M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. Brief Communications, Nature, 424, August, (2003).<br />
<br />
== Abstract ==<br />
Joanna Aizenberg ''et al''. wrote a communication in response to an article Nikolaids ''et al''. published in Nature in 2002. In the original paper, it was proposed that the attraction between micron-sized particles and an aqueous interface they are absorbed on is caused by a distortion of the liquid interface due to the dipolar electric field of the particles inducing capillary action. Aizenberg ''et al''. were compelled to challenge this claim on the basis that they believed that this explanation for the observed attraction does not adhere to force balance laws. <br />
<br />
== Keywords ==<br />
<br />
<br />
== Soft Matter ==<br />
Nikolaides ''et al.'' assume that the sum of electrostatic pressure acting on the liquid interface is equal to an external force, F, acting on the particle resulting in:<br />
<br />
U(r) = F^2/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo)<br />
<br />
Where: <br />
<math>\gamma</math> is surface tension<br />
r is particle distance<br />
rsub0 is a constant<br />
<br />
This equation implies that the force acts on the particle and water at the same time. As Aizenberg ''et al.'' explains, this cannot be the case because the force is balanced by surface tension creating a dimple in the water (as seen in Figure 1) which is governed by the Young-LaPlace equation:<br />
<br />
[(1/R1) + (1/R2)]<math>\gamma</math> = <math>\delta</math>p<br />
<br />
[[Image:McIlwee_Like_Charged_Particles.jpg|thumb|center|400px|alt=Figure 1. |Figure 1. ]]<br />
<br />
They go on to say that capillary attraction between spheres is caused by the overlap of their dimples reducing the total surface area of the water. This results in, for large (r):<br />
<br />
U(r) = -(F^2/<math>\pi</math><math>\gamma</math>)(rsubc/r)^6<br />
<br />
This is much shorter range than, U(r) = F^2/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo), and shorter than dipole-dipole repulsion between like-charged particles proportional to 1/r^3, revealing that no attraction exists and is thermodynamically insignificant, contributing 1.8 x 10^(-5)kT to interaction potential. In conclusion, they believe that the mystery of the origin of the attraction remains unsolved.<br />
<br />
In their rebuttal, it is admitted that, U(r) = F^2/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo) accounts for the electrostatic stressed while neglecting the force that the electric field exerts on the particle itself. Detailed calculations, not shown, reveal the interfacial force pulling the particle out of the fluid is canceled by the electrical force pushing the particle into the fluid.<br />
<br />
The data does show that there is a long range repulsive interaction because of charges. Also the attractive interactions balances the electrostatic repulsion. If it decays as a power law it must be slower than 1/r^3. Still, the most likely interaction with sufficient range is capillary distortion at the interface. This can only occur if there is an imbalance between the forces pushing the particle into the water and the interface outwards towards the oil. <br />
<br />
The interesting factor left is the charge on the particles on the oil side. The density of free charges is much less in oil than water and the screening length is larger. These factors extend the range of force imbalance and can account for the experimental observations. The capillary distortion remains electrostatic in nature.<br />
<br />
Further experiments confirm the measurable charge in oil increasing the screening length to values greater than particle separation allowing force imbalance to persist far enough for significant interfacial distortion to exist at scales comparable to interparticle separation.<br />
<br />
Therefore it is believed that electric-field-induced capillary distortion remains the likely culprit for the attractive interaction between like-charged interfacial particles.<br />
<br />
== References ==<br />
M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. ''Nature'', '''424''', August, (2003).<br />
<br />
M. G. Nikolaides ''et al''. ''Nature'' '''420''', 299-301 (2002).<br />
<br />
Stamou, D., Dushi, C. and Johannsmann, D. ''Phys. Rev E'' '''54''', 5263-5272, (2000).<br />
<br />
Aveyard, R ''et al. Phys. Rev. Lett''. '''88''', 246102-1-4 (2002).</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Like_charged_particles_at_liquid_interfaces&diff=13695Like charged particles at liquid interfaces2009-12-04T16:12:51Z<p>Mcilwee: /* References */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Like charged particles at liquid interfaces, M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. Brief Communications, Nature, 424, August, (2003).<br />
<br />
== Abstract ==<br />
<br />
<br />
== Keywords ==<br />
<br />
<br />
== Soft Matter ==<br />
Joanna Aizenberg ''et al''. wrote a communication in response to an article Nikolaids ''et al''. published in Nature in 2002. In the original paper, it was proposed that the attraction between micron-sized particles and an aqueous interface they are absorbed on is caused by a distortion of the liquid interface due to the dipolar electric field of the particles inducing capillary action. Aizenberg ''et al''. were compelled to challenge this claim on the basis that they believed that this explanation for the observed attraction does not adhere to force balance laws. <br />
<br />
Nikolaides ''et al.'' assume that the sum of electrostatic pressure acting on the liquid interface is equal to an external force, F, acting on the particle resulting in:<br />
<br />
U(r) = F^2/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo)<br />
<br />
Where: <br />
<math>\gamma</math> is surface tension<br />
r is particle distance<br />
rsub0 is a constant<br />
<br />
This equation implies that the force acts on the particle and water at the same time. As Aizenberg ''et al.'' explains, this cannot be the case because the force is balanced by surface tension creating a dimple in the water (as seen in Figure 1) which is governed by the Young-LaPlace equation:<br />
<br />
[(1/R1) + (1/R2)]<math>\gamma</math> = <math>\delta</math>p<br />
<br />
[[Image:McIlwee_Like_Charged_Particles.jpg|thumb|center|400px|alt=Figure 1. |Figure 1. ]]<br />
<br />
They go on to say that capillary attraction between spheres is caused by the overlap of their dimples reducing the total surface area of the water. This results in, for large (r):<br />
<br />
U(r) = -(F^2/<math>\pi</math><math>\gamma</math>)(rsubc/r)^6<br />
<br />
This is much shorter range than, U(r) = F^2/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo), and shorter than dipole-dipole repulsion between like-charged particles proportional to 1/r^3, revealing that no attraction exists and is thermodynamically insignificant, contributing 1.8 x 10^(-5)kT to interaction potential. In conclusion, they believe that the mystery of the origin of the attraction remains unsolved.<br />
<br />
In their rebuttal, it is admitted that, U(r) = F^2/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo) accounts for the electrostatic stressed while neglecting the force that the electric field exerts on the particle itself. Detailed calculations, not shown, reveal the interfacial force pulling the particle out of the fluid is canceled by the electrical force pushing the particle into the fluid.<br />
<br />
The data does show that there is a long range repulsive interaction because of charges. Also the attractive interactions balances the electrostatic repulsion. If it decays as a power law it must be slower than 1/r^3. Still, the most likely interaction with sufficient range is capillary distortion at the interface. This can only occur if there is an imbalance between the forces pushing the particle into the water and the interface outwards towards the oil. <br />
<br />
The interesting factor left is the charge on the particles on the oil side. The density of free charges is much less in oil than water and the screening length is larger. These factors extend the range of force imbalance and can account for the experimental observations. The capillary distortion remains electrostatic in nature.<br />
<br />
Further experiments confirm the measurable charge in oil increasing the screening length to values greater than particle separation allowing force imbalance to persist far enough for significant interfacial distortion to exist at scales comparable to interparticle separation.<br />
<br />
Therefore it is believed that electric-field-induced capillary distortion remains the likely culprit for the attractive interaction between like-charged interfacial particles.<br />
<br />
== References ==<br />
M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. ''Nature'', '''424''', August, (2003).<br />
<br />
M. G. Nikolaides ''et al''. ''Nature'' '''420''', 299-301 (2002).<br />
<br />
Stamou, D., Dushi, C. and Johannsmann, D. ''Phys. Rev E'' '''54''', 5263-5272, (2000).<br />
<br />
Aveyard, R ''et al. Phys. Rev. Lett''. '''88''', 246102-1-4 (2002).</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Like_charged_particles_at_liquid_interfaces&diff=13693Like charged particles at liquid interfaces2009-12-04T16:12:26Z<p>Mcilwee: /* References */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Like charged particles at liquid interfaces, M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. Brief Communications, Nature, 424, August, (2003).<br />
<br />
== Abstract ==<br />
<br />
<br />
== Keywords ==<br />
<br />
<br />
== Soft Matter ==<br />
Joanna Aizenberg ''et al''. wrote a communication in response to an article Nikolaids ''et al''. published in Nature in 2002. In the original paper, it was proposed that the attraction between micron-sized particles and an aqueous interface they are absorbed on is caused by a distortion of the liquid interface due to the dipolar electric field of the particles inducing capillary action. Aizenberg ''et al''. were compelled to challenge this claim on the basis that they believed that this explanation for the observed attraction does not adhere to force balance laws. <br />
<br />
Nikolaides ''et al.'' assume that the sum of electrostatic pressure acting on the liquid interface is equal to an external force, F, acting on the particle resulting in:<br />
<br />
U(r) = F^2/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo)<br />
<br />
Where: <br />
<math>\gamma</math> is surface tension<br />
r is particle distance<br />
rsub0 is a constant<br />
<br />
This equation implies that the force acts on the particle and water at the same time. As Aizenberg ''et al.'' explains, this cannot be the case because the force is balanced by surface tension creating a dimple in the water (as seen in Figure 1) which is governed by the Young-LaPlace equation:<br />
<br />
[(1/R1) + (1/R2)]<math>\gamma</math> = <math>\delta</math>p<br />
<br />
[[Image:McIlwee_Like_Charged_Particles.jpg|thumb|center|400px|alt=Figure 1. |Figure 1. ]]<br />
<br />
They go on to say that capillary attraction between spheres is caused by the overlap of their dimples reducing the total surface area of the water. This results in, for large (r):<br />
<br />
U(r) = -(F^2/<math>\pi</math><math>\gamma</math>)(rsubc/r)^6<br />
<br />
This is much shorter range than, U(r) = F^2/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo), and shorter than dipole-dipole repulsion between like-charged particles proportional to 1/r^3, revealing that no attraction exists and is thermodynamically insignificant, contributing 1.8 x 10^(-5)kT to interaction potential. In conclusion, they believe that the mystery of the origin of the attraction remains unsolved.<br />
<br />
In their rebuttal, it is admitted that, U(r) = F^2/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo) accounts for the electrostatic stressed while neglecting the force that the electric field exerts on the particle itself. Detailed calculations, not shown, reveal the interfacial force pulling the particle out of the fluid is canceled by the electrical force pushing the particle into the fluid.<br />
<br />
The data does show that there is a long range repulsive interaction because of charges. Also the attractive interactions balances the electrostatic repulsion. If it decays as a power law it must be slower than 1/r^3. Still, the most likely interaction with sufficient range is capillary distortion at the interface. This can only occur if there is an imbalance between the forces pushing the particle into the water and the interface outwards towards the oil. <br />
<br />
The interesting factor left is the charge on the particles on the oil side. The density of free charges is much less in oil than water and the screening length is larger. These factors extend the range of force imbalance and can account for the experimental observations. The capillary distortion remains electrostatic in nature.<br />
<br />
Further experiments confirm the measurable charge in oil increasing the screening length to values greater than particle separation allowing force imbalance to persist far enough for significant interfacial distortion to exist at scales comparable to interparticle separation.<br />
<br />
Therefore it is believed that electric-field-induced capillary distortion remains the likely culprit for the attractive interaction between like-charged interfacial particles.<br />
<br />
== References ==<br />
M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. Like charged particles at liquid interfaces, Brief Communications, ''Nature'', '''424''', August, (2003).<br />
<br />
M. G. Nikolaides ''et al''. ''Nature'' '''420''', 299-301 (2002).<br />
<br />
Stamou, D., Dushi, C. and Johannsmann, D. ''Phys. Rev E'' '''54''', 5263-5272, (2000).<br />
<br />
Aveyard, R ''et al. Phys. Rev. Lett''. '''88''', 246102-1-4 (2002).</div>Mcilweehttp://soft-matter.seas.harvard.edu/index.php?title=Like_charged_particles_at_liquid_interfaces&diff=13687Like charged particles at liquid interfaces2009-12-04T16:07:01Z<p>Mcilwee: /* Soft Matter */</p>
<hr />
<div>UNDER CONSTRUCTION -- Original Entry by Holly McIlwee, AP225 Fall 09<br />
<br />
== Overview ==<br />
Like charged particles at liquid interfaces, M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M. P. Brenner, C. Gay, D. A. Weitz. Brief Communications, Nature, 424, August, (2003).<br />
<br />
== Abstract ==<br />
<br />
<br />
== Keywords ==<br />
<br />
<br />
== Soft Matter ==<br />
Joanna Aizenberg ''et al''. wrote a communication in response to an article Nikolaids ''et al''. published in Nature in 2002. In the original paper, it was proposed that the attraction between micron-sized particles and an aqueous interface they are absorbed on is caused by a distortion of the liquid interface due to the dipolar electric field of the particles inducing capillary action. Aizenberg ''et al''. were compelled to challenge this claim on the basis that they believed that this explanation for the observed attraction does not adhere to force balance laws. <br />
<br />
Nikolaides ''et al.'' assume that the sum of electrostatic pressure acting on the liquid interface is equal to an external force, F, acting on the particle resulting in:<br />
<br />
U(r) = F^2/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo)<br />
<br />
Where: <br />
<math>\gamma</math> is surface tension<br />
r is particle distance<br />
rsub0 is a constant<br />
<br />
This equation implies that the force acts on the particle and water at the same time. As Aizenberg ''et al.'' explains, this cannot be the case because the force is balanced by surface tension creating a dimple in the water (as seen in Figure 1) which is governed by the Young-LaPlace equation:<br />
<br />
[(1/R1) + (1/R2)]<math>\gamma</math> = <math>\delta</math>p<br />
<br />
[[Image:McIlwee_Like_Charged_Particles.jpg|thumb|center|400px|alt=Figure 1. |Figure 1. ]]<br />
<br />
They go on to say that capillary attraction between spheres is caused by the overlap of their dimples reducing the total surface area of the water. This results in, for large (r):<br />
<br />
U(r) = -(F^2/<math>\pi</math><math>\gamma</math>)(rsubc/r)^6<br />
<br />
This is much shorter range than, U(r) = F^2/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo), and shorter than dipole-dipole repulsion between like-charged particles proportional to 1/r^3, revealing that no attraction exists and is thermodynamically insignificant, contributing 1.8 x 10^(-5)kT to interaction potential. In conclusion, they believe that the mystery of the origin of the attraction remains unsolved.<br />
<br />
In their rebuttal, it is admitted that, U(r) = F^2/2*<math>\pi</math>*<math>\gamma</math>)ln(r/rsubo) accounts for the electrostatic stressed while neglecting the force that the electric field exerts on the particle itself. Detailed calculations, not shown, reveal the interfacial force pulling the particle out of the fluid is canceled by the electrical force pushing the particle into the fluid.<br />
<br />
The data does show that there is a long range repulsive interaction because of charges. Also the attractive interactions balances the electrostatic repulsion. If it decays as a power law it must be slower than 1/r^3. Still, the most likely interaction with sufficient range is capillary distortion at the interface. This can only occur if there is an imbalance between the forces pushing the particle into the water and the interface outwards towards the oil. <br />
<br />
The interesting factor left is the charge on the particles on the oil side. The density of free charges is much less in oil than water and the screening length is larger. These factors extend the range of force imbalance and can account for the experimental observations. The capillary distortion remains electrostatic in nature.<br />
<br />
Further experiments confirm the measurable charge in oil increasing the screening length to values greater than particle separation allowing force imbalance to persist far enough for significant interfacial distortion to exist at scales comparable to interparticle separation.<br />
<br />
Therefore it is believed that electric-field-induced capillary distortion remains the likely culprit for the attractive interaction between like-charged interfacial particles.<br />
<br />
== References ==</div>Mcilwee