The transmembrane potential across a charged nanochannel subjected to asymmetric electrolytes

TL;DR

This paper derives analytical expressions for the transmembrane potential in charged nanochannels with asymmetric electrolytes, enhancing understanding of ion transport in desalination and energy systems.

Contribution

It introduces two new models for calculating the transmembrane voltage, one for two species and another for multiple species, without relying on simplifying assumptions.

Findings

Models are verified with numerical simulations.

Interplay of diffusion coefficients and ionic valencies affects system response.

The models can improve interpretation of experimental ion transport data.

Abstract

The transmembrane voltage, $V$, which is the potential drop required to nullify the electrical current ($i=0$), is a key characteristic of water desalination and energy harvesting systems that utilize macroscopically large nanoporous membranes, as well as for physiological ion channels subjected to asymmetric salt concentrations. To date, existing analytical expressions for $V_{i=0}$ have been limited to simple scenarios or under simplifying assumptions. In this work, we derive two expressions for $V_{i=0}$. First, we consider the much simpler scenario of two species. Then, we can consider an electrolyte comprised of an arbitrary number of species. The difference in the models is that the latter solution utilizes an ad-hoc assumption of a linear concentration profile, while the former solution does not require such an ad-hoc assumption. We analyze both models and show how to reduce them to several known models. We also verify both models with numerical simulations of the one-dimensional Poisson-Nernst-Planck equations. We show how the interplay between diffusion coefficients and ionic valencies significantly varies the system response and why it is essential to account for all system parameters. Ultimately, this model can be used to improve experimental interpretation of ion transport measurements