A Time-Dependent Finite Element Algorithm for Simulations of Ion Current Rectification and Hysteresis Properties of 3D Nanopore System

This paper focuses on a three-dimensional (3-D) charged conical nanopore, vertically centered in a cuboid domain, with an action boundary condition set for the applied bias voltage on the upper surface. In order to study the time-dependent I-V characteristics, we use an algorithm consisting of the backward Euler method and the finite element method to solve the 3-D time-dependent Poisson-Nernst-Planck equations. An analytical solution with varying voltage is first used to test the reliability and accuracy of the algorithm. Then, the influence of the area of charged surface and the distance from the pore to outer boundary on ion current rectification are studied and qualitatively explained by analyzing the ion concentration and electrostatic field at the nanopore tip. Besides, the ionic current hysteresis phenomena is also observed in the numerical simulation.