The Coupling Model: A Fundamental Mechanism Governing Time Dependent Properties of Relaxations, Structural Recovery and
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THE COUPLING MODEL: A FUNDAMENTAL MECHANISM GOVERNING TIME DEPENDENT PROPERTIES OF RELAXATIONS, STRUCTURAL RECOVERY AND NONLINEAR VISCOELASTICITY +
R.W. RENDELL,* K.L. NGAI* AND A.F. YEE** * Naval Research Laboratory, Washington, DC 20375-5000 ** The University of Michigan, Department of Materials and Metallurgical Engineering, Ann Arbor, MI 48109-2136
ABSTRACT The recent renewal of interest in the time dependent response of complex material systems stems both from their increasing importance and from recent advances in theoretical tools and concepts. This paper describes one of these advances, the coupling model of relaxation. The coupling model proposes a view of how relaxation proceeds in time in which a primitive relaxation mode is coupled to its complex surroundings. Examples of the coupling model predictions for terminal relaxations, primary-segmental relaxations including physical aging, and secondary relaxations in polymers are described. It is able to confront and quantitatively explain several long-standing problems and anomalies for which traditional approaches, in their present form, such as distributions of relaxation times, free volume, configuration entropy and reptation are not successful. The coupling model response function is also appropriate for structural nonequilibrium and its predictions for volume recovery are described. The same coupling model response function is used as a timedependent kernal in a constitutive equation to discuss nonlinear viscoelasticity. The model incorporates the strain history dependence and allows for the evolution of material structure. Using information from strain-tickle experiments on polycarbonate and polyetherimide, we show that the coupling model reproduces the essential features observed experimentally for a variety of strain histories. INTRODUCTION The 1980's has seen a resurgence of interest in the time dependent relaxation properties of complex material systems such as glasses, amorphous polymers, polymer melts, viscous liquids, ionic conductors and amorphous semiconductors. Relaxations are manifested by the decay (or saturating growth) of some macroscopic variable such as stress, strain, volume, enthalpy, polarization or electric field in the appropriate material system. Many of these topics have long histories of investigation and have been characterized by accurate experimental measurements. However, these phenomena have resisted a fundamental understanding of the accompanying physics. Accordingly, methods for making quantitative predictions of the properties of these systems have not been generally successful, nor have they provided much insight into the basic aspects of the problems. The time-dependent response of the macroscopic variables following a perturbation is generally observed to be characterized by a broad asymmetric (effective) relaxation spectrum, and the position of this spectrum within the experimental time window is observed to shift, often anomalously, with physical variables relevant to the process under examination such as temperat
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