Scaling for Selectivity in Finite Nanopores for 1:1 Electrolytes: the Dependence of Predictability of Device Behavior on System Parameters

The scaling properties of a cation selective nanopore mean that the device function (selectivity) depends on the input parameters (pore radius, pore length, surface charge density, electrolyte concentration, voltage) via a single scaling parameter that is a simple analytical function of the input parameters. In our previous study (Sarkadi et al., (2022) [5]), we showed that a parameter inspired by the Dukhin number (therefore, we also call it a Dukhin number) is an appropriate scaling parameter for infinitely long nanopores. Here, we extend that study to finite pores in a membrane and provide a detailed analyzes over a large parameter space for 1:1 electrolytes obtained from the Nernst-Planck transport equation coupled either to the Local Equilibrium Monte Carlo method or to the Poisson-Botzmann theory. Scaling is exact in a limiting case, where an analytical solution, such as Linearized Poisson-Boltzmann, is available (infinite pore). Here we show that scaling can work even if the solution is numerical or provided by computer simulations (finite pore). We discuss how these cases approach the limiting case as functions of the system parameters.