Flory theory of the second virial coefficient

The osmotic second virial coefficient, A2, is determined by the interaction of two polymer molecules with each other and with the solvent. This interaction can be expressed in terms of a potential of mean force, where R12 is 

The integral is twice the excluded volume for a pair of whole polymer molecules. The osmotic second virial coefficient is a direct measure of the excluded volume of the polymer chains. If the chains are modeled as hard spheres with radius R, the second virial coefficient is  

For globular protein molecules in a solution of high ionic strength at the isoelectric point, the second virial coefficient is well described by Equation 5.22. Since the volume of a globular protein is proportional to its molecular weight, the second virial coefficient decreases as 1/M. 

An approximate potential of mean force for two polymer coils in a good solvent was developed by Flory and Krigbaum. It is based on the same 

The potential is a Gaussian with range determined by the mean-squared radius of gyrahon and strength determined by the intersubunit excluded volume and the square of the number of subchains. Direct evaluation of the integral (Equation 5.21) then leads to the lowest-order soluhon for the second virial coefficient  

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