Interactions between Polyelectrolyte Gel Surfaces

Surfaces formed by charged polymeric species are highly abundant in both synthetic and biological systems, for which maintaining an optimum contact distance and a pressure balance is paramount. Here we investigate interactions between surfaces of two same-charged and highly swollen polyelectrolyte gels, using extensive molecular dynamic simulations and minimal analytical methods. The external-pressure responses of the gels and the polymer-free ionic solvent layer separating two surfaces are considered. Simulations confirmed that the surfaces are held apart by osmotic pressure resulting from excess charges diffusing out of the network. At a threshold pressure, the counterion-induced osmotic pressure in the gel interiors becomes nearly equal to that in solvent gap, and the gels begin to deform. At the threshold pressure, the distance between surfaces is equivalent to the electrostatic screening length imposed by excess charges. Both the solvent layer and pressure dependence are well described by an analytical model based on the Poisson-Boltzmann solution for low and moderate electrostatic strengths. Scaling descriptions for the threshold pressure and critical distance compare well with the simulations. The threshold pressure decreases with increasing polymerization degree of network chains, similar to sparsely grafted polyelectrolyte brushes. As the electrostatic coupling strength is increased, the deviations from the analytical model also increase due to condensed counterions. Our results are of great importance for systems where charged gels or gel-like structures interact in various solvents, including systems encapsulated by gels and microgels in confinement.