RESUMO
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.
RESUMO
The paper is concerned with mechano-chemical effects, namely, osmosis and pressure-driven separation of ions that can be observed when a charged porous medium is placed between two electrolyte solutions. The study is focused on porous systems with low equilibrium interfacial potentials (about 30 mV or lower). At such low potentials, osmosis and pressure-driven separation of ions noticeably manifest themselves provided that the ions in the electrolyte solutions have different diffusion coefficients. The analysis is conducted by combining the irreversible thermodynamic approach and the linearized (in terms of the normalized equilibrium interfacial potential) version of the Standard Electrokinetic Model. Osmosis and the pressure-driven separation of ions are considered for an arbitrary mixed electrolyte solution and various porous space geometries. It is shown that the effects under consideration are proportional to a geometrical factor which, for all the considered geometries of porous space, can be expressed as a function of porosity and the Λ- parameter of porous medium normalized by the Debye length. For all the studied geometries, this function turns out to be weakly dependent on both the porosity and the geometry type. The latter allows for a rough evaluation of the geometrical factor from experimental data on electric conductivity and hydraulic permeability without previous knowledge of the porous space geometry. The obtained results are used to illustrate how the composition of electrolyte solution affects the mechano-chemical effects. For various examples of electrolyte solution compositions, the obtained results are capable of describing positive, negative and anomalous osmosis, positive and negative rejection of binary electrolytes, and pressure-driven separation of binary electrolyte mixtures.
