UC Berkeley

Li-ion batteries are among the leading technologies for electric vehicles and grid-scale renewable electricity storage, making them a crucial element in building a sustainable energy future. The performance of current Li-ion batteries is limited in large part by the properties of the electrolyte, which is responsible for transporting ions through the battery. Sluggish motion of Li-ions through the electrolyte restricts the rate at which the battery can be charged or discharged and lowers the energy efficiency of the system. Design of improved electrolyte formulations is hindered by our inability to connect our theoretical understanding of electrolyte transport across length scales, that is, to relate the macroscopic transport behavior probed experimentally to the molecular-level mechanisms governing ion motion. 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. This presents significant challenges in deciphering the mechanisms of ion motion from experimental measurements and understanding the physical phenomena that may be limiting battery performance.

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 the governing equations of irreversible thermodynamics in electrolytes, including balance laws and internal entropy production. These relations yield 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. We demonstrate how the theory presented here may be directly related to existing frameworks for continuum-level modeling such as the Stefan-Maxwell equations and the Nernst-Planck equation for transport at infinite dilution. We further relate the Onsager transport coefficients to experimentally-measurable quantities such as the conductivity, transference number, and salt diffusion coefficient.

We demonstrate application of the Onsager transport framework by investigating the transport properties of potential next-generation battery electrolytes. In conventional batteries, the energy and power densities are limited by electrolytes with low Li-ion transference numbers, in which the majority of the electrolyte conductivity comes from motion of the anion, rather than the electrochemically-active Li-ion. Nonaqueous polyelectrolyte solutions, in which anion motion is slowed through covalent attachment to a polymer, have been recently suggested as high transference number alternatives to conventional Li-ion battery electrolytes. Initial experimental evidence on these nonaqueous polyelectrolyte solutions has been promising, with transference numbers reported to be at least twice that of conventional battery electrolytes. These experimental transference number measurements, however, are typically based on ideal solution approximations, i.e., the assumption that there no correlations between ions. Prior to this work, we lacked insight into the extent to which these assumptions hold for polyelectrolytes as well as the true transference number of these solutions. The non-idealities (ion correlations) contributing to the true transference number are very challenging to quantify experimentally yet are easily accessible through molecular dynamics simulations via the theoretical framework presented herein. Using this framework, we demonstrate that ion correlations are substantial in polyelectrolytes such that the rigorously computed transference number is actually lower than that of a conventional electrolyte. These efforts have thus suggested that --- contrary to intuition --- nonaqueous polyelectrolytes may not be promising for next-generation batteries, and they more broadly call into question some of the conventional paradigms employed for understanding and characterizing transport in polyelectrolytes. In this work, we first present detailed characterization of a specific polyelectrolyte which had been presented in the literature as particularly promising based on experimental ideal solution approximations. We subsequently construct a more general simulation model, which is agnostic to any specific polymer chemistry, and show that these surprising results hold universally across a broad range of polyelectrolytes. Finally, we present perspectives on how analyzing ion correlations in this manner has the potential to yield valuable insights across a wide class of electrolytes for energy storage applications.