Interplay between Microscopic and Macroscopic Properties of Charged Hydrogels

We have investigated aqueous charged poly(acrylamide-co-acrylate) gels by varying polymer concentrations at fixed concentrations of added sodium chloride salt. Using a combination of static and dynamic light scattering, rheology, and water permeation experiments, we have made independent measurements of shear modulus, friction coefficient, diffusion coefficient, and mesh size of the gel. We have also derived a generalized mean field theory for charged gels by including electrostatic interactions between polymer segments, in addition to the contributions from free energy of mixing, elasticity, and the Donnan equilibrium. The measured dependencies of modulus, friction coefficient, and gel diffusion coefficient on polymer concentration are in accordance with the predictions of the generalized mean field theory, enabling a reliable bridge between the macroscopic and microscopic properties of polyelectrolyte gels. When the contributions to free energy of the gel from fluctuations in polymer concentration and conformations are ignored, experimentally observed results self-consistently satisfy the scaling laws among mesh size, moduli, gel friction coefficient, and gel diffusion coefficient, with an effective polymer size exponent of 2/3 in the presence of salt. Our systematic observations suggest the validity and utility of closed-form analytical formulas from the generalized mean field theory to adequately describe swollen charged gels, while opening further work on determination of fluctuation effects.