Stress Relaxation and Dynamic Properties of Polymers

Abstract

The mechanical behavior of an idealized linear polymer is discussed in terms of the Maxwell relaxation theory. When a simple rectangular distribution of relaxation times is assumed, it is shown that the dynamic properties can be related to those deduced from stress relaxation data by the equation: where ηdyn is the dynamically measured internal friction or viscosity, ω the radian frequency, and E° the negative slope of the relaxation curve plotted as reduced stress vs. log₁₀ time. Appli cation of this equation to values of ωη_dyn and stress relaxation data on rubbers obtained by Dillon, Prettyman, and Hall [5] and data on textile fibers by Dunell and Dillon [6] is made. Better than order-of-magnitude agreement was obtained between dynamically measured values of ωη_dyn and those calculated by the above equation for the series of rubber stocks and fibers considered. The theory presented has interesting implications in regard to the structures of the various polymers studied, most of which would not a priori be considered linear in the sense of the idealized model. The relationships deduced from the "box" distribution are extended to other broad distributions of relaxation times.