Statistical Thermodynamics of Polymer Solutions. III. The Second Virial Coefficient for Branched Star Molecules

The effect of branching on the osmotic second virial coefficient is calculated for a homogeneous solute of ``star'' molecules, each composed of a number of identical, flexible, linear, polymeric, chain elements joined together at one end through a common junction. The perturbation method of Zimm, familiar for linear chains, is generalized slightly to include the star molecule of arbitrary functionality. This calculation, applicable to thermodynamic interactions in poor solvents, is then combined with a method developed in the first paper of this series, to obtain an approximate theory for the virial coefficient in good solvents where thermodynamic interactions between solute molecules are large.