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. log 10 time. Application 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. Stress Relaxation and General Elastoviscous BehaviorThe simplest type of elastoviscous behavior was postulated by Maxwell to obey the equation where s is a component of strain (e.g., simple tensile strain), f is a component of stress (e.g., tensile stress), E is the elastic modulus, and T is the socalled relaxation time of the system. A mechanical model which behaves in the manner defined by equation (1) is a spring and dashpot connected in series, if the elastic constant of the spring is taken as E and the damping constant or viscosity of the dashpot is taken as TE. This mechanical system is known as the Maxwell model. If a substance which obeys equation (1) is rapidly extended to a fixed strain so and maintained at that strain, the stress will decay according to the law Certain substances exist whose relaxation behavior approximates equation (2)-e.g., Hevea gum vulcanizate [16~ and polysulfide rubbers [12~ at high temperatures, where the elastoviscous behavior is controlled by chemical reactions. In relaxation curves obeying this equation, the decay of stress occurs almost completely within two cycles of logarithmic time. When this relaxation function is plotted against logarithmic time as abscissa, a change in the value of the relaxation time, T, merely shifts the relaxation curve horizontally along the logarithmic time axis.The decay of stress in polyisobutylenes maintained at constant extension and temperature does * This article is based on a thesis submitted by Basil A.Dunell in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Princeton University.

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