Effect of non-Gaussian end-to-end distributions on shear and elastic gel moduli: theoretical and experimental approach

Despite its huge potentiality, main limitations of the ideal rubberlike elasticity theory reside in the impossibility to account for polymer chain stiffness, high-order interchain bonding terms and a non-Gaussian distribution of polymer segments, reflecting into a non-Gaussian end-to-end length statistics [1]. Especially this last aspect can play a very important role as hydrogels synthesized by bimodal chain length distributions give rise to networks [2] whose features cannot be modeled by classical rubberlike elasticity theory. Aim of this work was thus to reformulate a rubberlike elasticity theory by considering three non-Gaussian end-to-end length statistics and recalculate shear (G) and elastic (E) moduli dependencies on swelling degree and extension ratio. Particularly, attention was on achieving the configuration integral and the so-called perfect gas term at variable functionality upon Laplace, Cauchy and continuous Poisson (in exponential limit) laws, as they have the two-fold aim to formally mimic the Gaussian law but quantitatively deviate from it to a non-perturbative extent. Interestingly, despite the formal complexity coming from the statistical mechanics treatment, final equations for G and E, whatever the distribution regarded, are reasonably simple and suit to a prompt comparison with available gel data. To infer the most likely end-to-end length distribution in an arbitrary network, a theoreticalexperimental approach based on LF-NMR was devised. Application of this strategy to agar 1 %, alginate 1 % and scleroglucan 2 % hydrogels (wt %) reveals that the end-to-end distribution should be never deemed as Gaussian even if, as in agar and scleroglucan systems, the normal statistics is the best among those here regarded. Remarkably, Poisson law is proved instead to be the most realistic for alginate hydrogels.