Viscoelasticity

Abstract

A broad view of polymer viscoelasticity is presented. The article first discusses the basic definitions of stress and strain and the material modulus and compliance properties that relate the two in linear elasticity theory. The time‐dependent analogues in viscoelasticity are presented. The beginnings of polymer viscoelasticity concepts are then presented by building mechanical analogues of springs (elastic) and dashpots (viscous) elements that can capture the general features of polymeric behavior. A brief discussion of the elastic–viscoelastic correspondence principle is also provided. The general viscoelastic response of polymeric materials is presented by emphasizing the amorphous state and how the isochronal modulus changes with temperature. This is analyzed within the context of time–temperature superposition ideas and the Williams, Landel, and Ferry equation. In particular, it is interesting to divide the behavior into that below and far above the glass‐transition temperature. In the former case the local segmental motions of the polymer dominate behavior, while in the latter the long‐chain nature of the polymer dominates behavior. Molecular rheology ideas are briefly presented where the idea of the chain length or molecular weight dependence of the viscosity is introduced. This is extended by considering the scaling of viscosity and plateau modulus due to concentration as well as the introduction of time–concentration superposition principles similar to time–temperature principles. The nonlinear rheological response of polymers far above the glass‐transition temperature is handled within a combined framework of the phenomenological K‐BKZ model and the Doi–Edwards (DE) tube model, which is based on the reptation ideas of de Gennes. The K‐BKZ framework is particularly useful because it looks much like time‐dependent finite elasticity theory that has been widely and successfully applied to rubber network polymers. Extensive discussion is presented of the comparison between theory and experiment of both K‐BKZ and DE models for polymer nonlinear viscoelastic behavior in the melt and solution states. Below the glass‐transition temperature, measurements of the nonlinear viscoelastic response are examined within the framework of the BKZ model, but also considering compressibility. Emphasis is given to torsional experiments in which both the torque and the normal force are measured. This exposition is followed by a description of several other nonlinear viscoelastic models that have been used for describing solid polymers. This article ends with a brief mention of plasticity models for the behavior of polymeric solids.

Soft matter: rubber and networks

“…On the Mooney-Rivlin plot, the material would exhibit a reduced stress that is constant and independent of deformation. Figures 2(a) and (b) [30] show stress versus stretch (λ) and reduced stress versus reciprocal stretch (1/λ), respectively. The stress-deformation curves of figure 2(a) look very much like the data presented in figure 1 for both the neo-Hookean and the Mooney-Rivlin materials.…”