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