Current-Induced Concentration Polarization of Nanoporous Media: Role of Electroosmosis

Current-induced concentration polarization of nanoporous media is explored theoretically by using approach of local thermodynamic equilibrium within nanopore cross-sections. The problem is solved in quadratures in terms of irreversible thermodynamics. The phenomenological coefficients are further specified by using capillary space-charge model for straight slit-like and cylindrical capillaries. This analysis reveals several novel features of current-induced concentration polarization related to the (electro)osmotic volume transfer. It confirms the previous finding that volume transfer can suppress the limiting-current phenomena but obtains more accurate criteria for this. In particular, it shows that the critical nanopore size and/or electrolyte concentration depend on the nanoporous-medium relative thickness. Under no-limiting-current conditions, the salt concentration at the interface between nanoporous medium and unstirred layer is a nonmonotone function of current density. This gives rise to unconventional current-voltage characteristics. Moreover, under certain conditions, the analysis predicts the existence of ranges of "prohibited" current densities where the problem does not have 1D stationary solution, which could give rise to a kind of "phase separation" with coexisting zones of different local current densities corresponding to the same voltage. Besides the advanced understanding of current-induced concentration polarization of nanoporous media, this analysis provides guidelines for the optimization of sample preconcentration systems in (bio)chemical microanalysis.