Osmotic virial coefficients

Second virial coefficient

For an athermal polymer solution the osmotic second virial coefficient is given by:

$B_{2}={\frac {1}{2}}\iint f(\{{\mathbf {\Omega } }\})f(\{{\mathbf {\Omega } }'\})V_{\rm {ex}}(\{{\mathbf {\Omega } }\},\{{\mathbf {\Omega } }'\})d\{{\mathbf {\Omega } }\}d\{{\mathbf {\Omega } }'\}$

where $V_{\rm {ex}}(\{{\mathbf {\Omega } }\},\{{\mathbf {\Omega } }'\})$ is the excluded volume for two polymers with conformations Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \{ {\mathbf \Omega} \}} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \{ {\mathbf \Omega}'\}} . The curly braces denotes an ensemble of molecular configurations for a single polymer.