Long time dynamics of swollen rubbers: Optical and mechanical properties

Abstract

The low frequency dynamics of a swollen network is investigated by means of a many-body Langevin equation which treats the junctions like slowly moving structural units, as suggested by recent improvements of the equilibrium theory of rubber elasticity. Both the viscoelastic constitutive equation and the optical autocorrelation function S (k, t) of a junction-labeled network are then calculated for a model system with very long circuits. Deviations of S (k, t) from exponential behavior and quadratic linewidth are predicted to occur if the scattering wavelength is not much larger than the average distance between adjacent crosslinks. Calculated deviations are shown to be strongly dependent on functionality and swelling ratio. In particular, we predict a remarkable difference between trifunctional and tetrafunctional networks.