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 $\{{\mathbf {\Omega } }\}$ and $\{{\mathbf {\Omega } }'\}$. The curly braces denotes an ensemble of molecular configurations for a single polymer.