Elucidating the Molecular Origins of the Transference Number in Battery Electrolytes Using Computer Simulations

Abstract

The rate at which rechargeable batteries can be charged and discharged is governed by the selective transport of the working ions through the electrolyte. Conductivity, the parameter commonly used to characterize ion transport in electrolytes, reflects the mobility of both cations and anions. The transference number, a parameter introduced over a century ago, sheds light on the relative rates of cation and anion transport. This parameter is, not surprisingly, affected by cation–cation, anion–anion, and cation–anion correlations. In addition, it is affected by correlations between the ions and neutral solvent molecules. Computer simulations have the potential to provide insights into the nature of these correlations. We review the dominant theoretical approaches used to predict the transference number from simulations by using a model univalent lithium electrolyte. In electrolytes of low concentration, one can obtain a quantitative model by assuming that the solution is made up of discrete ion-containing clusters–neutral ion pairs, negatively and positively charged triplets, neutral quadruplets, and so on. These clusters can be identified in simulations using simple algorithms, provided their lifetimes are sufficiently long. In concentrated electrolytes, more clusters are short-lived and more rigorous approaches that account for all correlations are necessary to quantify transference. Elucidating the molecular origin of the transference number in this limit remains an unmet challenge.

Lithium transference in electrolytes with star-shaped multivalent anions measured by electrophoretic NMR

“…Molecular-scale simulations are usually used to identify these environments, and the correspondence between the continuum and molecular approaches has been established in several previous publications. 25,46–49…”

Dynamic Heterogeneity of Solvent Motion and Ion Transport in Concentrated Electrolytes

“…However, the lifetimes of individual clusters can vary significantly, and their effect on ion transport cannot be gauged in this framework. Alternative approaches for determining t + 0 based on Onsager transport equations have also been developed. − In these approaches, it is not necessary to identify specific clusters. Instead, t + 0 is determined from correlations in the motion of different species.…”

Molecular Origin of High Cation Transference in Mixtures of Poly(pentyl malonate) and Lithium Salt

“…This set of transport coefficients can be mapped onto the three Stefan–Maxwell diffusivities ( , , and ) using the concentrated solution theory. , Commonly used transport properties, including κ, t + 0 , and (the Stefan–Maxwell salt diffusivity), are expressed as functions of L ij 0 : where F is the Faraday constant, c is the molar salt concentration, c 0 is the molar concentration of polymer chains, c t is the total molar concentration of cations, anions, and polymers, and R is the gas constant. It is worth noting that different approaches based on the Onsager transport equation may be used to quantify the transport. , Recent work has confirmed the consistency between these approaches in determining ion transport properties. ,, …”

“…50,51 Recent work has confirmed the consistency between these approaches in determining ion transport properties. 24,30,52 While κ is measured routinely for virtually all electrolytes, measurements of t + 0 and are tedious and seldom reported in the literature. However, it is common to report the current fraction of polymer electrolytes (ρ + ), following Bruce, Watanabe, and co-workers.…”

“…We propose calling the solvating structure a “solvation cage” to reflect the difference between solvation in liquids and polymers (and other solid-like materials) . The ionic conductivity (κ) in PEO/LiTFSI, which reaches a maximum value of 10 –3 S/cm (at 90 °C) at a salt concentration (molality) around 1.7 mol Li + /kg PEO, is so far higher than that of most other polymer electrolytes. − However, one issue limiting practical applications of PEO is its low cation transference number, which limits the charging rate of PEO-based rechargeable batteries. , The cation transference number, t + 0 , is defined as the fraction of current carried by the working cation with respect to the solvent velocity. − Low t + 0 in PEO is mainly a result of tight solvation cage provided by ether oxygens from a single chain. ,, The migration of Li + under applied electric fields causes the solvating PEO segments to drift with the ion, and this reduces cation flux relative to that of the solvent. The solvation cage also slows down motion of Li + ; in fact, ionic conductivity of PEO mainly reflects the free motion of anions that do not participate in the redox reactions at the electrodes.…”