Ionic conductivity and hydrodynamic permeability of inhomogeneous (cavity doped) polyelectrolyte hydrogels

Ion transport in polyelectrolyte membranes (charged hydrogels) is of significant technological (and biological) importance, but little known how micro-structural inhomogeneity affects ionic conductivity. Whereas a uniform electric field drives uni-directional electro-migrative and electro-osmotic ion fluxes perfectly microstructures, this study considers the influence spherical inclusions/cavities on hydrodynamic permeability charged hydrogels. Such cavities have high permeability, they can bear much lower conductivity due to partitioning counter-ions between cavity bulk hydrogel phases, also inducing micro-scale flow. To understand these, perturbations from nonlinear Poisson–Boltzmann equilibrium state are used compute velocity disturbances, electrostatic ion-concentration polarization. These furnish three independent Onsager coefficients: one which effective all contribute two principal electrical conductivities (distinguished by electrode configuration). Cavities with diameters range $10$ – $1000$ nm found be readily polarized, decreasing an otherwise polyelectrolyte. In highly permeable hydrogels, however, electro-osmosis may enhance when flow blocked impenetrable electrodes. Explicit formulas for provided, complementing simplified (Maxwell–Donnan) analysis conductivity, neglects diffuse double-layer effects perturbations.