Influence of Chain Structure and Swelling on the Elasticity of Rubbery Materials: Localization Model Description. Issue 1 (23rd August 2013) - Douglas, Jack F.; Bowman, Christopher N.; Horkay, Ferenc
Summary Classical network elasticity theories are based on the concept of flexible volumeless network chains fixed into a network in which there are no excluded volume, or even topological, interactions between the chains and where the chains explore accessible configurations by Brownian motion. In this type of 'classical' model of rubber elasticity, the elasticity of the deformed network derives from the entropic changes that arise from a deformation of the network junction positions. The shortcoming of this approach is evident from the observation that unswollen rubbery materials are nearly incompressible, reflecting the existence of strong intermolecular interactions that restrict the polymer chains to the exploration of their local tube‐like molecular environments along their chain contours. The imposition of a deformation of these solid rubbery materials then necessitates a consideration of how the local molecular packing constraints become modified under deformation and the impact of these changes in chain confinement on the macroscopic elasticity of the material as a whole. Many researchers have struggled with this difficult many‐body problem. The present paper focuses on the simple 'localization model' (LM) of rubber elasticity of Gaylord and Douglas (GD), which provides a simple minimal model for the network elasticity of rubbery materials in the dense polymer state. Particular emphasis in the present paper is given to the implications of this model for describing how network elasticity changes with solvent swelling, a phenomenon for which large deviations from classical elasticity have been observed and a situation highly relevant to numerous applications that involve rubbery materials. We also discuss the physical nature of 'entanglement' based on the same molecular packing picture and deduce general conditions for entanglement in terms of molecular parameters. Our predictions accord rather well with experimental correlations relating chain molecular structure to the entanglement molecular mass, changing elasticity with swelling, etc.