Incorporating dendrite growth into continuum models of electrolytes: insights from NMR measurements and inverse modelling

In this work we develop a combined experimental and inverse continuum modelling approach to the problem of determining properties of a lithium electrolyte from NMR measurements of ion concentration in a test cell. The experimental set-up consists of an enclosed, lithium-electrolyte-filled tube with lithium electrodes at either end. A constant current is passed between these electrodes and the resulting evolution of the spatial distribution of the lithium ions is monitored using NMR imaging techniques. Using the recently developed tools of inverse modelling, in combination with the concentration measurements acquired with NMR imaging, it is shown that the standard Planck-Nernst electrolyte model results in predictions of negative transference numbers. The observation of growing lithium dendrites on the cathode suggests the cause for these unphysical predictions and motivates the formulation of a generalized Planck-Nernst model that explicitly accounts for the presence of these growing lithium-metal dendrites. In this approach, lithium depletion in a dendritic region adjacent to the cathode is modelled by adding a suitably-chosen spatially distributed sink term. It is demonstrated that a model in which lithium is lost from the electrolyte uniformly throughout the dendritic region provides predictions of electrolyte data consistent with the literature and thereby remedies the shortcoming of the standard Planck-Nernst model. In addition, a state-of-the-art Bayesian technique is used to quantify the uncertainty of the inferred material properties.