Mathematical Description of Nucleation and Precipitation Processes in Li-Sulfur Batteries with Organic Electrolyte
Authors: Andrei Petru , Shen Chao , Zheng Jim P. 
Published: February 2020

There is much work in the literature trying to understand the discharge mechanism and the reasons for the rate-dependent capacity limitation in Li-sulfur (Li-S) batteries. Most of the existing work attributes the rate-dependent capacity limitation to the surface coverage of the cathode with insulating lithium sulfide or lithium polysulfides. Currently, there are two coverage mechanisms widely used to explain the sudden death of the Li-S batteries. The first mechanism assumes that the lithium sulfide grows uniformly as a thin layer on the surface of carbon. Due to the high resistivity of the Li2S, the electron transport through lithium sulfide is dominated by quantum tunneling. As we will discuss in this presentation, this mechanism cannot entirely explain the capacity limitations of Li-S batteries and are not supported by scanning electron microscopy (SEM) and atomic force microscopy (AFM) images taken by many authors, which show that the reaction product can grow in shapes as large as 500 nm [1, 2] or even 1 µm and above [3-5]. Another coverage mechanism that has recently received significant attention in the literature, is to assume that the coverage of the cathode is a two-step process involving nucleation and growth of Li2S in the form of “islands” on the surface of the carbon [1, 6]. In this presentation we propose a rate-dependent nucleation theory appropriate for the solid reaction products in Li-S batteries and use this theory to explain qualitatively the capacity variation as a function of the discharge rate. The theory is similar to the model developed in [1] in the sense that it attributes the death of Li-S batteries to surface passivation by Li2S nuclei, however, in our presentation, the mathematical equations are framed entirely in the form of a system of partial differential equations that can be implemented easily in ordinary or partial differential equation solvers. We also derive a closed-form equation for the nucleation rate and apply this equation to explain the discharge characteristics of Li-S batteries with cathodes made of free-standing carbon nanotube foams [7]. At the meeting we will present details about the physio-chemical processes that take place during discharge and a comprehensive mathematical description of the nucleation and growth of Li2S nuclei.
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