# Multiscale modeling of a rectifying bipolar nanopore: Comparing Poisson-Nernst-Planck to Monte Carlo

## TL;DR

This study compares continuum Poisson-Nernst-Planck and particle Monte Carlo methods to model ion transport in a bipolar rectifying nanopore, demonstrating that PNP effectively captures key behaviors like rectification.

## Contribution

It introduces a multiscale modeling framework combining PNP and LEMC methods to analyze bipolar nanopores, highlighting the validity of mean-field approximation in such systems.

## Key findings

- PNP accurately reproduces rectification behavior.
- Crowding effects can be incorporated with a non-linear PNP.
- Simulation results provide detailed profiles of ion concentration and potentials.

## Abstract

In the framework of a multiscale modeling approach, we present a systematic study of a bipolar rectifying nanopore using a continuum and a particle simulation method. The common ground in the two methods is the application of the Nernst-Planck (NP) equation to compute ion transport in the framework of the implicit-water electrolyte model. The difference is that the Poisson-Boltzmann theory is used in the Poisson-Nernst-Planck (PNP) approach, while the Local Equilibrium Monte Carlo (LEMC) method is used in the particle simulation approach (NP+LEMC) to relate the concentration profile to the electrochemical potential profile. Since we consider a bipolar pore which is short and narrow, we perform simulations using two-dimensional PNP. In addition, results of a non-linear version of PNP that takes crowding of ions into account are shown. We observe that the mean field approximation applied in PNP is appropriate to reproduce the basic behavior of the bipolar nanopore (e.g., rectification) for varying parameters of the system (voltage, surface charge, electrolyte concentration, and pore radius). We present current data that characterize the nanopore's behavior as a device, as well as concentration, electrical potential, and electrochemical potential profiles.