Dynamic mechanical properties of concentrated polystyrene-tricresyl phosphate solutions

Abstract

The components of the complex shear modulus for polystyrene-tricresyl phosphate solutions have been measured between 6 and 1,000 c.p.s. A polystyrene of broad and known molecular weight distribution (weight average molecular weight of 434,000) was used to prepare six solutions from 5% to 67% polystyrene by weight. The method of reduced variables was found to be applicable, and the temperature dependence of relaxation times of all solutions could be described by the WLF equation with a fractional free volume at the glass temperature of 0.0255 and a thermal expansion of free volume of 7 × 10 −4 deg. −1. An equation of the WLF form was derived and used to calculate the concentration dependence of relaxation times and was applied to the transition regions of the relaxation spectra. Above a concentration of 10%, the relaxation spectra were proportional to the 2.0 power of concentration rather than the first power predicted by molecular theories. The number of bonds between entanglements was estimated from minima in the loss tangent-frequency curves and found to be proportional to the −0.75 power of concentration. The components of the complex shear modulus of the 5% solution were compared with the molecular theories of Zimm and Rouse as modified for polymolecularity by Menefee and Peticolas. Good agreement was observed between the experimental storage modulus and the theoretical Rouse curve, whereas the loss modulus occupied an intermediate position between Rouse and Zimm theories.