Transport coefficients for ion and solvent coupling. The case of the lithium-ion battery electrolyte

Abstract

Transport properties are essential for the understanding and modeling of electrochemical cells, in particular complex systems like lithium-ion batteries. In this study, we demonstrate how a certain degree of freedom in the choice of variables allows us to efficiently determine a complete set of transport properties. We apply the entropy production invariance condition to different sets of electrolyte variables and obtain a general set of formulas. We demonstrate the application of these formulas to an electrolyte typical for lithium-ion batteries, 1M lithium hexafluoro-phosphate in a 1:1 wt. % mixture of ethylene and diethyl carbonates. While simplifications can be introduced, they provide inadequate predictions of conductivity and transport numbers, and we argue that a full matrix of Onsager coefficients is needed for adequate property predictions. Our findings highlight the importance of a complete set of transport coefficients for accurate modeling of complex electrochemical systems and the need for careful consideration of the choice of variables used to determine these properties.

Effect of the Ion, Solvent, and Thermal Interaction Coefficients on Battery Voltage

“…The reaction conveys two ways of viewing the electrolyte: as composed of a mixture of ionic and neutral components (right side) or as a mixture of neutral components only (left-hand side). The transport coefficients of the electrolyte can be formulated using either set of components, and they are connected via the Rules for Coupling of Fluxes, see Kjelstrup et al 6 Both sets of components (of mixed and neutral components) were used to find the relevant sets of transport coefficients.…”

“…The expression 1 originates in the entropy production of the cell, when neutral components are used to describe the entropy production. We describe transport in the bulk electrolyte under polarization conditions by .25ex2ex lefttrue J q ′ N = l q q ∇ true( 1 T true) − l q L 1 T ∇ μ L , T − l q D 1 T ∇ μ D , T + L q φ L φ φ j J L = l L q ∇ true( 1 T true) − l L L 1 T ∇ μ L , T − l L D 1 T …”

“…Transport in the electrolyte can be described in two ways, by the mixed (ions and solvents) or by the neutral (salt and solvents) component scenario . The transport coefficients in the mixed component scenario (Λ ij ) are obtained directly from the fluctuation dissipation theorems using molecular dynamics (MD) simulations, see further explanation in the Supporting Information and in ref . The coefficients of the neutral component scenario, used in the equations above, can be obtained by converting the set of Λ ij using the Rules for Coupling of Fluxes …”

Coupled ion transport in concentrated PEO–LiTFSI polymer electrolytes

“…The magnitude of the coupling coefficient L +− is considerable relative to the main coefficients, L ++ and L −− , when compared to common carbonate-based battery electrolytes. 33 However, the relation L ii L jj ≥ L ij 2 holds for all systems. 27 The trend of the ionic conductivity is a consequence of the balance between the number of free charge carriers and their mobility, which is tightly coupled to the polymer segmental motion, as shown in several studies.…”

“…The thermodynamic factor, Γ , is a way of quantifying the ideality of a mixture. In a binary electrolyte, it can be defined as: 9,33 where γ ± is the molar activity coefficient of the salt and x is the mole fraction of the salt. For an ideal mixture, γ ± = 1 and Γ = 1.…”