Dynamic mechanical properties of moderately concentrated polystyrene solutions

Abstract

AbstractThe storage (G′) and loss (G″) shear moduli have been measured in the frequency range from 0.04 to 630 Hz for solutions of narrow distribution polystyrenes with molecular weights (M) 19,800 to 860,000, and a few of poly(vinyl acetate), M = 240,000. The concentration (c) range was 0.014–0.40 g/ml and the viscosities of the solvents (diethyl phthalate and chlorinated diphenyls) ranged from 0.12 to 70 poise. Data at different temperatures (0–40°C) were combined by the method of reduced variables. Two types of behavior departing from the usual frequency dependence describable by the Rouse‐Zimm‐Tschoegl theories were observed. First, for M ≅ 20,000, the ratio (G″ − ωηs)/G′ in the neighborhood of ωτ1 = 1 was abnormally large and the steady‐state compliance J was abnormally small, especially at the lowest concentrations studied. Here ω is circular frequency, ηs solvent viscosity, and τ1 terminal relaxation time. Related anomalies have been observed by others in undiluted polymers at still lower molecular weights. Second, at the highest concentrations and molecular weights, a “crossover” region of the logarithmic frequency scale appeared in which G″ − ωηs < G′. The width of this region is a linear function of log c; the frequency dependence under these conditions can be represented by a sequence of Rouse relaxation times grafted on to a sequence of Zimm relaxation times. For each molecular weight, the terminal relaxation time τ1 was approximately a single function of c for different solvents of widely different ηs. At lower concentrations, τ1 was close to the Rouse prediction of 6ηM/π2cRT, where η is the steady‐flow viscosity; but at higher concentrations, τ1 was proportional to η/c2 and corresponded, according to a recent theory of Graessley, to an average molecular weight of 20,000 between entanglement coupling points in the undiluted polymer.