Osmotic Pressure of Permeable Ionic Microgels

Ionic microgels are soft, permeable, colloidal particles made of crosslinked polymer networks that ionize and swell in a good solvent. Swelling of these particles is responsive to external stimuli and involves a balance of electrostatic and gel contributions to the single-particle osmotic pressure. The electrostatic contribution depends on the distributions of mobile microions and fixed charge on the polymer. Within the cell model, we derive the electrostatic contribution within Poisson-Boltzmann (PB) theory, by minimizing a free energy functional with respect to electrostatic potential, and extract the gel pressure from the pressure tensor. By varying the free energy with respect to microgel size, we also derive exact statistical mechanical relations for the electrostatic osmotic pressure for models of planar, cylindrical, and spherical microgels with fixed charge uniformly spread over their surface or volume. To validate these relations, we solve the PB equation and compute ion densities and osmotic pressures [1]. We show that microgel swelling depends on the electrostatic pressure profile inside the particle and discuss implications for interpreting experiments.

[1] A. R. Denton and M. O. Alziyadi, J. Chem. Phys. 151, 074903 (2019).