Abstract

Improved understanding of transport phenomena in electrolyte solutions has important implications in the fields of energy storage, water purification, biological applications, and more. This understanding should ideally persist across length scales: we desire both continuum-level insight into macroscopic concentration and electric potential profiles as well as a molecular-level understanding of the mechanisms governing ion motion. However, the most commonly used theories to describe continuum-level electrolyte transport, namely the Stefan-Maxwell equations, yield transport coefficients which lack clear physical interpretation at the atomistic level and cannot be easily computed from molecular simulations. Herein, we present the theoretical development and application of the Onsager transport framework to analyze transport at both the continuum and molecular levels. We discuss the integration of continuum mechanics, nonequilibrium thermodynamics, and electromagnetism to derive internal entropy production in electrolytes, yielding the Onsager transport equations: linear laws relating the electrochemical potential gradients and fluxes of each species in solution. At the atomistic level, the transport coefficients emerging from this theory directly quantify ion correlations in the electrolyte; we show how these transport coefficients may be computed directly from molecular simulations using Green-Kubo relations derived from Onsager’s regression hypothesis. At the continuum level, the Onsager transport framework provides the governing equations for solving macroscopic boundary value problems in an electrochemical cell. This work presents a framework for rigorously analyzing transport across length scales in complex electrolyte solutions.