1301.4449 (Jack F. Douglas)
Jack F. Douglas
Classical network elasticity theories are based on the concept of flexible volumeless polymers fixed into a network in which there are no excluded volume, or even topological interactions, and where the chains explore accessible configurations by Brownian motion. In this type of model, the elasticity of the network derives from the entropic changes arising from a displacement of the network junction positions. The shortcoming of this approach is clear from the observation that unswollen rubbery materials are nearly incompressible, reflecting the existence of strong intermolecular interactions that restrict the polymer chains to an exploration of their local tube-like molecular environments. 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 on the macroscopic elasticity of the material as a whole. Many researchers have struggled with this difficult problem, in the present paper we focus on the simple localization model of rubber elasticity of Gaylord and Douglas, which provides a simple minimal model for the network elasticity of rubbers having strong intermolecular interactions in the dense polymer state. Particular emphasis is given in the implications of this model in describing how network elasticity changes with swelling by a solvent, a phenomenon where large deviations from classical elasticity have been observed and a situation relevant to numerous applications involving rubbery materials. We also discuss the nature of entanglement based on the same packing picture and deduce general relationships for entanglement in terms of molecular parameters and we find that our predictions accord with recent experimental correlations relating chain molecular structure to the entanglement molecular mass
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http://arxiv.org/abs/1301.4449
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