Incorporating ionic size in the transport equations for charged nanopores

Abstract

Nanopores with fixed charges show ionic selectivity because of the high surface potential and the small pore radius. In this limit, the size of the ions could no longer be ignored because they occupy a significant fraction of the pore and, in addition, they would reach unrealistic concentrations at the surface if treated as point charges. However, most models of selectivity assume point ions and ignore this fact. Although this approach shows the essential qualitative trends of the problem, it is not strictly valid for high surface potentials and low nanopore radii, which is just the case where a high ionic selectivity should be expected. We consider the effect of ion size on the electrical double layer within a charged cylindrical nanopore using an extended Poisson-Boltzmann equation, paying special attention to (non-equilibrium) transport properties such as the streaming potential, the counter-ion transport number, and the electrical conductance. The first two quantities are related to the nanopore selectivity while the third one characterizes the conductive properties. We discuss the nanopore characteristics in terms of the ratio between the electrolyte and fixed charge concentrations and the ratio between the ionic and nanopore radii showing the experimental range where the point ion model can still be useful. Even for relatively small inorganic ions at intermediate concentrations, ion size effects could be significant for a quantitative estimation of the nanopore selectivity in the case of high surface charge densities.

Energy conversion from external fluctuating signals based on asymmetric nanopores

“…These results confirm that <I> arises from the rectification of the external fluctuating signal by the asymmetric nanostructure and is not disturbed significantly by other internal noise sources of the electrical equipment [1]. Note also that the output electric current I(t) is slave of the input potential V R (t) because the period of this potential is much longer than the relaxation time characteristic of the small solution volumes found in nanopores [17][18][19] and ion channels [12]. This (adiabatic) limit is valid for low enough frequency signals [1,12,[18][19][20][21].…”

“…The charging process was described by the gives an asymmetrically distributed, negative charge along the axis of the conical pore. This charge is due to the ionized carboxylate (COO¯) groups on the pore surface, which explains the rectification observed in the I -V N curves [2,[15][16][17].…”

“…3b; a maximum rectification is achieved at c 0 = 0.05 0.1 M, as previously reported for single pore membranes [16]). It is well-known that the nanopore selectivity and rectification characteristics can be optimized at intermediate electrolyte concentrations [16,17] because these concentrations are high enough for the absolute currents to be significant but low enough for electrical rectification to be significant [16].…”

Rectification properties of conically shaped nanopores: consequences of miniaturization

“…The first successful PNP simulations for rectifying current-voltage curves of conically shaped nanopores were reported by Cervera et al 19,[27][28][29][30] . The simulations were performed using a one-dimensional (1D) reduction of the PNP model together with the Donnan equilibrium values for boundary conditions, and the local electroneutrality requirement.…”

Steric effects on electrokinetic flow of non-linear biofluids

“…There has been an increasing interest in recent years in developing the theoretical framework required for studying the steric effects on the electrokinetic phenomena [15,[18][19][20]. The results of these research works have been used to study the ionic size effects on the hydrodynamic and thermal features of electrokinetic flow [14,[21][22][23][24][25][26].…”