Osmotic virial coefficients

Second virial coefficient

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

$B_2=\frac{1}{2}\iint f(\{\mathrm{\Omega }\})f(\{{{\mathrm{\Omega }}^{\prime }}^{\prime }\})V_{\mathrm{e}\mathrm{x}}(\{\mathrm{\Omega }\},\{{{\mathrm{\Omega }}^{\prime }}^{\prime }\})d\{\mathrm{\Omega }\}d\{{{\mathrm{\Omega }}^{\prime }}^{\prime }\}$

where $V_{\mathrm{e}\mathrm{x}}(\{\mathrm{\Omega }\},\{{{\mathrm{\Omega }}^{\prime }}^{\prime }\})$ is the excluded volume for two polymers with conformations $\{\mathrm{\Omega }\}$ and $\{{{\mathrm{\Omega }}^{\prime }}^{\prime }\}$. The curly braces denotes an ensemble of molecular configurations for a single polymer.