Modelling of Conductive Nanoporous Membranes with Switchable Ionic Selectivity

Abstract

An interesting area of modern membrane science is the development of "smart" membranes, which can affect the transport properties of selected components via external tuning. When the target components are ions, such a tuning can be realized with the help of electric field created by the conductive pore surface. We have proposed in this work a mathematical model of ions transport in a cylindrical nanopore with the electronic charge at the conductive surface and the chemical charge, which is separated from the surface by the Stern layer. The model is based on one-dimensional equations for potential, ion concentrations, and pressure in the diffuse layer. It is applied for describing the membrane potential at zero current, which characterizes the type and strength of ionic selectivity. It is shown that the change of surface potential in the direction from negative to positive results in the continuous change of pore selectivity from cation to anion. The decrease in the Stern layer capacitance and increase in the pore radius lead to the decrease in ionic selectivity. The presence of positive (negative) chemical charge causes the shift of potential value, at which the selectivity is switched, in the direction of negative (positive) values. At this value of potential, the membrane becomes non-selective, the diffusive flux of ions reaches maximum, and the osmotic flow ceases. The suggested model provides a qualitative and quantitative description of experimental results on switchable selectivity of tracketched membranes modified by the gold coating.

Modelling the Ionic Conductivity of Nanopores with Electrically Conductive Surface

“…In the Stern layer, there are no ions, and only water molecules can be present. The relation between the charge σ induced on the diffuse layer boundary and the surface potential Φ s is given by [26,27]…”

“…Here Φ is the potential of the diffuse layer, which is radially uniform in the 1D model, and C s is the capacitance of the Stern layer. For a cylindrical nanopore, the latter is given by [27]…”

“…The extension of UP model to the presence of both electronic and pH-dependent chemical charges was proposed in [26]. It was successfully employed in [27] for describing the experimental results of [14] on switchable ionic selectivity. It should be noted that the studies of carbon nanotube [13] and gold nanotube [14,15] membranes rise interest in the theoretical analysis of ionic conductivity on the basis of SC and UP models with constant surface potential boundary condition.…”

Glass/Au Composite Membranes with Gold Nanoparticles Synthesized inside Pores for Selective Ion Transport

“…The theoretical description of experimental results for ion transport through the membranes is performed with the help of the uniform potential model, which is based on the Navier-Stokes, Nernst-Planck, and Poisson equations [45,46]. The main assumptions of the model, problem statement, and calculation procedure are described below.…”

“…Further, the pressure in both reservoirs is considered to be zero. We write the conditions inside the pore at the inlet from the side of the reservoir with a higher concentration (at z = 0) [45,46]:…”