Osmotic virial coefficients: Difference between revisions
Carl McBride (talk | contribs) (New page: ==Second virial coefficient== For an athermal polymer solution the osmotic second virial coefficient is given by: :<math>B_2 = \frac{1}{2} \iint f( \{ {\mathbf \Omega} \}) f( \{ {\ma...) |
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==Second virial coefficient== | ==Second virial coefficient== | ||
For an athermal polymer solution the osmotic [[second virial coefficient]] | For an athermal polymer solution the osmotic [[second virial coefficient]] | ||
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:<math>B_2 = \frac{1}{2} \iint f( \{ {\mathbf \Omega} \}) f( \{ {\mathbf \Omega}' \}) V_{\rm ex} ( \{ {\mathbf \Omega} \},\{ {\mathbf \Omega}' \}) d \{ {\mathbf \Omega} \} d \{ {\mathbf \Omega}' \}</math> | :<math>B_2 = \frac{1}{2} \iint f( \{ {\mathbf \Omega} \}) f( \{ {\mathbf \Omega}' \}) V_{\rm ex} ( \{ {\mathbf \Omega} \},\{ {\mathbf \Omega}' \}) d \{ {\mathbf \Omega} \} d \{ {\mathbf \Omega}' \}</math> | ||
where <math>V_{\rm ex} ( \{ {\mathbf \Omega} \},\{ {\mathbf \Omega}' \})</math> is the [[excluded volume]] for two polymers | |||
with conformations <math>\{ {\mathbf \Omega} \}</math> and <math>\{ {\mathbf \Omega}'\}</math>. The curly braces denotes an ensemble of molecular configurations for a single polymer. | |||
==References== | ==References== | ||
[[ | [[category: Virial coefficients]] | ||
Latest revision as of 17:19, 8 January 2008
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Second virial coefficient[edit]
For an athermal polymer solution the osmotic second virial coefficient is given by:
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle B_{2}={\frac {1}{2}}\iint f(\{{\mathbf {\Omega } }\})f(\{{\mathbf {\Omega } }'\})V_{\rm {ex}}(\{{\mathbf {\Omega } }\},\{{\mathbf {\Omega } }'\})d\{{\mathbf {\Omega } }\}d\{{\mathbf {\Omega } }'\}}
where Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle V_{\rm {ex}}(\{{\mathbf {\Omega } }\},\{{\mathbf {\Omega } }'\})} is the excluded volume for two polymers with conformations Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \{{\mathbf {\Omega } }\}} and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \{{\mathbf {\Omega } }'\}} . The curly braces denotes an ensemble of molecular configurations for a single polymer.