Statistical Thermodynamics of Polymer Solutions. IV. The Second Virial Coefficient for Comblike Branched Molecules

The statistical method of Zimm is used to derive the osmotic second virial coefficient A2 for branched polymer chains with the ``regular comb'' architecture; i.e., with branches of equal length attached at uniform intervals along the main chain. Calculations are carried as far as the ``double contact'' approximation, so that volume exclusion effects are neglected for configurations of two molecules in which there exist more than two intermolecular contacts. The treatment is, therefore, strictly applicable only near the Flory temperature (where A2 vanishes). The most significant conclusion, qualitatively, is that the behavior of A2 at this limit, for molecules of a given mass, depends on branched structure primarily through the variation of the mean-square radius of the molecule with branching. The utilization of the results in an approximate development for polymers in good solvents is discussed briefly.