Nonlinear viscoelasticity of polystyrene solutions. I. Strain‐dependent relaxation modulus

Abstract

Abstract Strain‐dependent relaxation moduli G ( t , s ) were measured for polystyrene solutions in diethyl phthalate with a relaxometer of the cone‐and‐plate type. Ranges of molecular weight M and concentration c were from 1.23 × 10 6 to 7.62 × 10 6 and 0.112 to 0.329 g/cm 3 . Measurements were performed at various magnitudes of shear s ranging from 0.055 to 27.2. The relaxation modulus G ( t , s ) always decreased with increasing s and the relative amount of decrease (i.e.,–log[ G ( t , s )/ G ( t ,0)]) increased as t increased. However, the detailed strain dependences of G ( t , s ) could be classified into two types according to the M and c of the solution. When cM < 10 6 , the plot of log G ( t , s ) versus log t varied from a convex curve to an S‐shaped curve with increasing s. For solutions of cM > 10 6 , the curves were still convex and S‐shaped at very small and large s , respectively, but in a certain range of s (approximately 3 < s < 7) log G ( t , s ) decreased rapidly at short times and then very slowly; a peculiar inflection and a plateau appeared on the plot of log G ( t , s ) versus log t . The strain‐dependent relaxation spectrum exhibited a trough at times corresponding to the plateau of log G ( t , s ). The longest relaxation time τ 1 (s) and the corresponding relaxation strength G 1 (s) were evaluated through the “Procedure X” of Tobolsky and Murakami. The relaxation time τ 1 (s) was independent of s for all the solutions studied while G 1 (s) decreased with s . The reduced relaxation strength G 1 (s) / G 1 (0) was a simple function of s (The plot of log G 1 (s) / G 1 (0) against log s was a convex curve) and was approximately independent of M and c in the range of cM <10 6 . This behavior of G 1 (s) / G 1 (0) was in agreement with that observed for a polyisobutylene solution and seems to have wide applicability to many polymeric systems. On the other hand, log G 1 (s) / G 1 (0) as a function of log s decreased in two steps and decreased more rapidly when M or c was higher. It was suggested that in the range of cM < 10 6 , a kind of geometrical factor might be responsible for a large part of the nonlinear behavior, while in the range of cM > 10 6 , some “intrinsic” nonlinearity of the entanglement network system might be important.