Induced-Charge Enhancement of the Diffusion Potential in Membranes with Polarizable Nanopores

When a charged membrane separates two salt solutions of different concentrations, a potential difference appears due to interfacial Donnan equilibrium and the diffusion junction. Here, we report a new mechanism for the generation of a membrane potential in polarizable conductive membranes via an induced surface charge. It results from an electric field generated by the diffusion of ions with different mobilities. For uncharged membranes, this effect strongly enhances the diffusion potential and makes it highly sensitive to the ion mobilities ratio, electrolyte concentration, and pore size. Theoretical predictions on the basis of the space-charge model extended to polarizable nanopores fully agree with experimental measurements in KCl and NaCl aqueous solutions.

Figure 1

The cross-sectionally averaged potential (a), concentrations (b), pressure (c), and surface charge density (d) for nonpolarizable ($\sigma =0$, dashed curves) and polarizable ($\overline{\sigma }=0$, solid curves) nanopores in NaCl solution. $R_p=8\mathrm{nm}$, $L_p=400\mu \mathrm{m}$, $C_L=10\mathrm{mM}$, and $C_R=1\mathrm{mM}$.

Figure 2

The potential (a) and concentration (b) fields in a polarizable nanopore with $\overline{\sigma }=0$ in NaCl solution (for parameters, see Fig. 1).

Figure 3

Membrane potential of Nafen (blue lines) and C-Nafen (red lines) membranes in KCl (a) and NaCl (b) aqueous solutions. Experimental data (points), calculations for uncharged nonpolarizable (blue) and polarizable (red) pores (dashed curves), fitting of experimental data (solid curves), and ideal anion selectivity (solid black line). Error bars, 1 s.d.

Figure 4

The effect of concentration $C_R$ (a) and pore radius $R_p$ (b) on the membrane potential in NaCl aqueous solution for $\overline{\sigma }=0$ (blue curves). Membrane potential for $\sigma =0$ (dashed line) and ideal anion selectivity (solid black line). The effect of the diffusion coefficients ratio on the membrane potential (c) for uncharged nonpolarizable (dashed curves) and polarizable (solid curves) nanopores.