Ternary Cluster Integral for Polystyrene in trans-Decalin near the ϑ Point

Abstract

Light scattering measurements have been made on 10 polystyrene samples with weight-average molecular weights Mw of 1.2 × 103 to 3.1 × 106 in trans-decalin at temperatures T between 13 and 55 °C to determine the second and third virial coefficients (A2 and A3) as functions of Mw and T. The former coefficient at the ϑ point (21 °C), where it vanishes for high Mw, is found to become negative and then sharply increase to positive with decreasing Mw. This molecular weight dependence of A2 is similar to that recently observed for atactic poly(methyl methacrylate) in acetonitrile at the ϑ temperature. The data of A3 for high Mw plotted against T have a broad positive minimum around the ϑ point in contrast to the two-parameter theory prediction that A3 vanishes at ϑ and becomes negative below ϑ, thus demonstrating the breakdown of the binary cluster approximation to A3 of polystyrene in trans-decalin near ϑ. For low molecular weights, A3 is insensitive to T and larger for lower Mw. The latter feature is ascribable to the effect from chain ends. From an analysis of the A3 data for low Mw at T between 17 and 35 °C the ternary cluster integral is estimated to be about 4 × 10-45 cm6, almost regardless of T. Its T-insensitive behavior bears some analogy with the temperature dependence of the third virial coefficient for imperfect monatomic gases near the Boyle point.