Transport phenomena in electrolyte solutions: Nonequilibrium thermodynamics and statistical mechanics

Abstract

The theory of transport phenomena in multicomponent electrolyte solutions is presented here through the integration of continuum mechanics, electromagnetism, and nonequilibrium thermodynamics. The governing equations of irreversible thermodynamics, including balance laws, Maxwell's equations, internal entropy production, and linear laws relating the thermodynamic forces and fluxes, are derived. Green-Kubo relations for the transport coefficients connecting electrochemical potential gradients and diffusive fluxes are obtained in terms of the flux-flux time correlations. The relationship between the derived transport coefficients and those of the Stefan-Maxwell and infinitely dilute frameworks are presented, and the connection between the transport matrix and experimentally measurable quantities is described. To exemplify the application of the derived Green-Kubo relations in molecular simulations, the matrix of transport coefficients for lithium and chloride ions in dimethyl sulfoxide is computed using classical molecular dynamics and compared with experimental measurements. K E Y W O R D S electrochemistry, nonequilibrium thermodynamics, thermodynamics/statistical, transport where c i is the concentration of species i and K ij are the Stefan-Maxwell transport coefficients. These equations may be interpreted

Interfacial Effects on Transport Coefficient Measurements in Li-ion Battery Electrolytes

“…While we believe that some of these methods likely also suffer from interfacial effects that interfere with accurate extraction of transport properties, our group has determined transference numbers with reference to the center of mass velocity for a 1 molar LiPF 6 in 3:7 EC:EMC systems using molecular dynamics (MD) simulations and electrophoretic nuclear magnetic resonance spectroscopy (eNMR) and observe only positive transference numbers on the order 0.25 -0.30. [19,35,36] We believe that the calculated negative transference numbers are actually due to errors in the current ratio measurement that resulted from the analysis unsuccessfully decoupling interface and bulk electrolyte processes. The sensitivity of the measurement to ρ + can be easily demonstrated by replacing ρ + as calculated in Eqn.…”

“…Using the framework of non-equilibrium thermodynamics and entropy production we can derive the governing equations for transport in electrochemical systems. [18,19] The electrochemical potential of a species (μ i ) can be split into electrical and chemical potential contributions according tô…”

Onsager Transport Coefficients and Transference Numbers in Polyelectrolyte Solutions and Polymerized Ionic Liquids

“…The reader may be more familiar with the Stefan-Maxwell equations for multicomponent diffusion, and by extension Newman's concentrated electrolyte theory, 2 rather than the Onsager equations presented in this work. As discussed in Fong et al, 22 both frameworks are thermodynamically consistent, and it is possible to map between the transport coefficients from the two approaches. 22,23 However, the Onsager transport coefficients L ij have a more direct physical interpretation in terms of ion correlations, and only L ij may be computed directly from molecular simulations using Green-Kubo relations.…”

“…As discussed in Fong et al, 22 both frameworks are thermodynamically consistent, and it is possible to map between the transport coefficients from the two approaches. 22,23 However, the Onsager transport coefficients L ij have a more direct physical interpretation in terms of ion correlations, and only L ij may be computed directly from molecular simulations using Green-Kubo relations. Furthermore, while it is possible to obtain experimental quantities from the Stefan-Maxwell coefficients K ij , the expressions for doing so are more complex than with L ij , especially for systems with more than two ionic species.…”

“…Herein, we analyze transport in electrolytes using the Onsager transport coefficients. The theoretical framework required to define these transport equations is derived and discussed in detail in Fong et al 22 Here we summarize only the main components of the theory.…”