Elasticity of Rubber-like Polymers

Abstract Polymers are rubber-like when amorphous, crosslinked and above their glass transition temperature. Their hyperelasticity results from deformation perturbing molecular thermal motion, modelled physically in terms of entropy or by empirical mathematical models. Entropy can be quantified in terms of a probability density function for the end-to-end distance of chains between crosslinks. The Gaussian chain model then predicts stiffness being proportional to the number of these chains per unit volume and to absolute temperature. It fits compression data well. However, tensile data to moderate extensions are better described by the empirical Mooney equation. At very high extensions, there is strong strain-stiffening because of limited extensibility of the chains. The empirical Gent equation then provides a better fit to data. In some cases, hysteresis intervenes at the highest extensions, because of stress-induced crystallization (SIC). In addition to natural rubber, there is now a range of engineering elastomers available, which are rubber-like at room temperature.