A statistical mechanics theory of rubber-like elasticity in hydrogels
characterized by explicitly non-Gaussian distribution functions (Laplace’s, Cauchy’s,
and continuous Poisson’s in the exponential limit) of the end to end distribution is
presented. Despite its formal complexity, the outcome of this approach leads to
the formulation of reasonably simple models easily comparable with experimental
data on polymer networks. In order to identify the most likely end-to-end length
distribution in an arbitrary network, a theoretical-experimental approach based on
Low Field NMR (LF-NMR) is proposed. Three different hydrogels are considered:
agar 1 %, alginate 1 %, and scleroglucan 2 %.
