Binary cluster integrals in the theory of dilute polymer solutions

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Abstract
The binary cluster integral β for polymer segments is evaluated on the basis of the very crude smoothed‐potential cell model, regarding it as equivalent to the second virial coefficient for a binary liquid mixture of small molecules. For polystyrene and polyisobutylene in various solvents at various temperatures, it is shown that the model can interpret qualitatively the behavior of β in terms of intermolecular forces. However, the calculated values of β are about one order of magnitude greater than the observed values, which are one order of magnitude smaller than the values expected from second virial coefficients observed for small molecules. This indicates that interactions between polymer segments in dilute solution are different from those between small molecules. It is pointed out that the difference arises from the fact that polymer segments bound in the chain have fewer degrees of freedom, translational and rotational, than free small molecules.