LINEAR VISCOELASTICITY OF LIVING POLYMERS - A QUANTITATIVE PROBE OF CHEMICAL RELAXATION-TIMES

Stress relaxation in wormlike micelles and other "living polymers" is governed by an interplay between simple reptation and the ability of the micelles to break and recombine. A simple model of the relaxation is available for which the linear viscoelastic functions can be written as averages over a one-dimensional stochastic process. Detailed results from a numerical simulation of this process are presented for various values of zeta = tau-break/tau-rep, where tau-break is the time taken for a micelle of the mean length to break and tau-rep is its (hypothetical) reptation time. First the stress relaxation modulus G(t) is calculated and then this is transformed to give the frequency-dependent modulus G*(omega). The terminal stress relation time for the system-tau is also found. When zeta is small, the stress relaxation is exponential. However, for zeta of order unity, there are clear departures from exponential relaxation which are most clearly seen in a Cole-Cole representation. Comparison of our calculated plots with those measured experimentally allows a direct estimate of the parameter-zeta-BAR = tau-break/tau. This enables the chemical relaxation time tau-break (which is hard to measure directly in concentrated systems) to be estimated purely from linear viscoelastic data. In one system where an independent measurement of tau-break is available, we find agreement to within the experimental error.