Scaling for rectification of bipolar nanopores as a function of a modified Dukhin number: the case of 1:1 electrolytes

The scaling behaviour for the rectification of bipolar nanopores is studied using the Nernst-Planck equation coupled to the Local Equilibrium Monte Carlo method. The bipolar nanopore's wall carries sigma and -sigma surface charge densities in its two half regions axially. Scaling means that the device function (rectification) depends on the system parameters (pore length, H, pore radius, R, concentration, c, voltage, U, and surface charge density, sigma) via a single scaling parameter that is a smooth analytical function of the system parameters. Here, we suggest using a modified Dukhin number, mDu = vertical bar sigma vertical bar l(B)*lambda DHU/(RU0), where l(B)* = 8 pi l(B), l(B) is the Bjerrum length, lambda(D) is the Debye length, and U-0 is a reference voltage. We show how scaling depends on H, U, and sigma and through what mechanisms these parameters influence the pore's behaviour.