Elasticity at Swelling Equilibrium of Ultrasoft Polyelectrolyte Gels: Comparisons of Theory and Experiments

We have studied the elasticity of low volume fraction hyaluronic acid polyelectrolyte gels in swelling equilibrium as a function of salt concentration and strand length. By measuring the shear modulus at different salt concentrations for a constant volume fraction, and for different volume fractions at constant salt concentrations, we uniquely identify the physical parameters responsible for swelling, the chain hydrophobicity, χ, and the degree of ionization of the network, α, for our experimental conditions. Using these parameters, we predict the complex relationship between the elasticity of the network and the polymer volume fraction. The relationship is nonmonotonic due to the internal pressure of the system, and we predict that even in the equilibrium linear-elastic regime, polyelectrolyte gels stiffen as they swell in low salt solutions. For higher salt concentrations, the relationship is reversed, and the modulus increases with polymer volume fraction as expected. Using dynamic light scattering and water permeation experiments, we find that the longitudinal modulus deduced from gel relaxations is proportional to the shear modulus measured directly from rheological experiments. We find that classical formulas of swelling equilibrium are adequate to capture the measured properties of swollen polyelectrolyte gels and that the various scaling predictions for the moduli are inadequate. The present work explains polyelectrolyte gel behavior using existing swelling equilibrium theories and establishes an experimental protocol for the determination of the physical parameters required to fully describe highly swollen polyelectrolyte hydrogels in high salt environments.