Lithium Sulfur Battery Modeling with Microscopic Kinetics Formulation
Authors: Chung Jui-Hui , Chen Hsun-Yi 
Published: February 2020

Lithium sulfur (Li-S) batteries are considered a promising energy storage technology for that its theoretical specific capacity can be over five folds of the currently commercialized lithium-ion batteries. The charge/discharge processes of Li-S batteries, however, involve complex reactions of sulfur species and are not yet fully understood. Physical models are crucial to elucidate these mechanisms occurring in Li-S batteries in assisting a multitude of experimental investigations. Model equations based on macroscopic theory are often used to simulate the Li-S system, but this methodology may collapse when unattainable parameters are assumed or parameterized, which in turn gives only qualitative, or even unphysical, simulation results. Our study focuses on reformulating existing equations of Li-S models to microscopic theory based ones, where parameters are accounted quantum mechanically and attained through first principal calculations. In particular, we substitute Marcus microscopic theory on charge transfer kinetics for the Butler-Volmer equations.
To date system-level models for Li-S batteries primarily employ fundamental equations based on macroscopic concepts, e.g. the Nernst-Planck and Butler-Volmer equations, in which they are expressed in terms of the phenomenological parameters, such as diffusion coefficients and exchange current densities. With established electrochemical experimental methods, such equations readily give rise to fitted parameter and are useful for design and prediction. However, it is exceedingly difficult to perform experiments to determine parameters on complex system such as a Li-S cell, which is known for its various polysulfide phase transformation, complex crystallization of solid precipitations and growth of solid phases. Kumaresan et al proposed a lithium-sulfur cell model based on porous electrode theory, with more than 50 assumed parameters. While the simulated discharge profile matches the experiment qualitatively, the model system cannot be charged. Neidhardt et al improves upon the previous work by adding extra structure and mechanisms at the anode, and successfully simulate the polysulfide shuttle. However, a large number of their parameters are attained through unphysical parameterization to the experimental data.
Moreover, such an approach cannot be employed to predict how the transport rates or the kinetics are affected by the microscopic constituents of the electrodes and electrolyte. To obtain such information, it is preferable to employ models based on microscopic physical parameters. These parameters in Li-S batteries are often unattainable through experiments; therefore, there is growing interest in using quantum mechanical computational method, such as density functional theory, to predict material properties. We aim to develop a general theory of charge-transfer and faradaic reaction kinetics based on microscopic theories, with parameters determined by ab initio calculations. A happy marriage between microscopic theory derived equations and first principal calculated parameters would provide more powerful and constructive insight to Li-S battery design.