Theory of Dilute High Polymer Solutions. II

Abstract

The second virial coefficient is calculated according to the smoothed distribution method. Our treatment differs from those of Flory-Krigbaum and Isihara-Koyama through inclusion of the numerous short-range intramolecular contacts arising by virtue of the connected nature of the chain. The result is to replace the previous F(X) by F(X, ρ), where the parameter ρ depends upon the ratio of the total number of intramolecular contacts to the number of long-range contacts counted using a radial segment distribution. The number of intermolecular contacts created when two molecules overlap is estimated by the use of an additional smoothed radial segment distribution which is assumed to be uniformly expanded by intramolecular excluded volume effects. Comparison with experiment reveals that both the temperature and molecular weight dependences of A2 in the vicinity of the theta temperature are described in a reasonably quantitative fashion by the present treatment. In this case there are no adjustable parameters. Furthermore, satisfactory agreement is observed for good solvents using values for the thermodynamic interaction parameter deduced from intrinsic viscosity. In the limit ρ=1 the present treatment yields a result equivalent to those of FK and IK. We conclude that the latter underestimate the number of intramolecular contacts through neglect of the connected nature of the chain. In the other limit, ρ=0, a result approximating that of the Casassa-Markovitz treatment is obtained. We believe that their assumption of a spherical segment distribution about the initial point of contact results in an over-estimation of the number of intermolecular contacts.