Rubbers configurational relaxation

It is certain that the relaxation behavior of filled rubbers at large strains involves numerous complications beyond the phenomena of linear viscoelasticity in unfilled amorphous polymers. Breakdown of filler structure, strain amplification, failure of the polymer-filler bond, scission of highly extended network chains and changes in network chain configuration probably all play important roles in certain ranges of time, strain rate, and temperature. A clear understanding of the interplay of these effects is not yet at hand. 

The assumption that the contraction process is ideally adiabatic, while perhaps not entirely permissible practically, seems indicated by modern theory of the behavior of molecular chains, which pictures these as undergoing, when freed of restraints, a sort of segmental diffusion, much like the adiabatic expansion of an ideal gas into a vacuum (155). In the case of the molecular chain, it diffuses to the most probable, randomly coiled configuration, which is much less asymmetric, hence shorter, than an initially extended chain. Because rubber most nearly presents this ideal behavior, those fibers which develop increased tension (a measure of the tendency toward assumption of the contracted form) when held isometrically under conditions of increasing temperature (favoring the diffusion ) are said to be rubber-like. Most normal elastic solids upon stress are strained from some stable structure and relax as the temperature is raised. 

For a cured rubber, there is a unique configuration of a material element that it will always return to when the extra stress is zero, and a time when the element was in this configuration is an obvious choice for the reference time. For a melt, there is no such unique, unstrained state, so some other reference time must be selected. In a laboratory experiment in which a sample of a melt is initially in a fixed, stress-free configuration, the time at which the deformation begins is an obvious reference time. For example, for a step strain experiment, the relaxation modulus G(f) is measured as a function of the time from the instant of the initial strain (t = 0). Thus it is convenient to let the reference time be fg = 0. 

According to classical rubber elasticity theory, intermolecular forces have no effect on the equilibrium chain configurations, and thus no effect on the stress. The relaxation of rubber toward mechanical equilibrium, however, is governed by the interactions among neighboring segments. This relationship has led to various attempts to interpret the elastic properties of rubber in terms of the network dynamics [47-52],... 

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