Diffusive dynamics of charge regulated macro-ion solutions

TL;DR

This paper extends Onsager's variational principle to model the diffusive behavior of charge-regulated macro-ion solutions, revealing how charge regulation influences macro-ion distribution and effective charge in non-equilibrium states.

Contribution

It introduces a unified theoretical framework combining charge regulation with electrolyte dynamics using Onsager's principle, including modified Poisson-Nernst-Planck equations.

Findings

Charge regulation significantly affects macro-ion distribution.

Effective macro-ion charge deviates from equilibrium values.

The model unifies various charge dynamics processes.

Abstract

Onsager's variational principle is generalized to address the diffusive dynamics of an electrolyte solution composed of charge-regulated macro-ions and counterions. The free energy entering the Rayleighian corresponds to the Poisson-Boltzmann theory augmented by the charge-regulation mechanism. The dynamical equations obtained by minimizing the Rayleighian include the classical Poisson-Nernst-Planck equations, the Debye-Falkenhagen equation, and their modifications in the presence of charge regulation. By analyzing the steady state, we show that the charge regulation has an important impact on the non-equilibrium macro-ion spatial distribution and their effective charge, deviating significantly from their equilibrium values. Our model, based on Onsager's variational principle offers a unified approach to the diffusive dynamics of electrolytes containing components that undergo various charge association/dissociation processes.