  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

Soft Condensed Matter;Materials Science