Some Comments on the Analysis of the Third Virial Coefficient for Polymer Chains

Abstract

An analysis is made of experimental data for the third virial coefficient A3 of atactic oligo- and poly(α-methylstyrene)s (a-PαMS) in the Θ solvent cyclohexane at 30.5 °C and in three good solvents, toluene, 4-tert-butyltoluene, and n-butyl chloride, at 25.0 °C on the basis of the helical wormlike (HW) chain model. It is found that A3 at Θ, which is denoted by A3,Θ, becomes a constant of 5.0×10−4 cm6 mol/g3 independent of the weight-average molecular weight Mw for Mw ≳ 104 and deviates from it for Mw ≲ 104 because of effects of chain ends. The observed dependence of A3,Θ on Mw may be well explained by the HW theory that takes account of the effects. For the three good-solvent systems, the behavior of the factor g defined by A3/[A2(HW)]2Mw is examined as a function of the cubed gyration-radius expansion factor αS3, where A2(HW) is the part of the second virial coefficient A2 without the effects of chain ends. It is found that the data points for a-PαMS samples with Mw ≳ 105 in all the three good solvents form nearly a single-composite curve, as predicted by the HW theory, and that they follow the Stockmayer–Casassa theoretical curve for αS3 ≳ 2 but deviate upward from it for αS3 ≲ 2 because of effects of three-segment interactions. Effects of chain stiffness are of minor importance for an explanation of this deviation. Some literature data for polystyrene are also examined.