First Steps Towards a Continuum Model of Mg-S Batteries
Authors: Richter Raphael , Lück Jessica , Danner Timo , Latz Arnulf 
Published: February 2020

Modern Lithium-ion batteries based on intercalation chemistry hold more than twice as much energy by weight and are ten times cheaper as the first commercial versions sold by Sony. But today they are near its limits. The use of Lithium-metal for ‘beyond Li-Ion’ batteries, such as Lithium-sulfur, promises higher energy density and lower costs. However, dendrite formation and battery safety still is an issue. In recent years Magnesium-sulfur batteries are discussed as an attractive next-generation energy storage system. Magnesium can be directly used as anode material due to its dendrite-free deposition and thus increases the safety as well as energy density of such a cell. Two electrons are stored per Mg atom which compensates the rather low discharge potential of Magnesium-sulfur cells of 1.7 V and provides a high capacity of 3832 mAh/cm3 and 2230 mAh/g with an energy density of over 3200 Wh/l [1]. Such an energy density is beyond that of Lithium-sulfur batteries and is therefore very promising for automotive and stationary applications. Furthermore magnesium and sulfur are both naturally abundant, low in price and non-toxic.
However, Magnesium-sulfur batteries are in a very early stage of research and development. The reactions at both positive and negative electrode are not yet fully understood. At the Sulfur electrode a mechanism analogous to Lithium-sulfur batteries was proposed. Recently a new electrolyte was developed by Zhao-Karger et al. [2]. In combination with a micro-porous Sulfur-Carbon composite, they were able to demonstrate a lifetime of more than 50 cycles. However, analogous to Lithium-sulfur batteries Magnesium-sulfur batteries show polarization effects during charging, low cyclic stability, initial capacity fading, and a polysulfide shuttle.
To the best of our knowledge there are no continuum models of Magnesium-sulfur batteries in the literature. Therefore, we present the first step towards a mechanistic model of Magnesium-sulfur cells. We use a coupled particle and cell model to take into account cell layouts suggested in the literature. First the Sulfur-Carbon particles at the cathode are described by a 1D particle model that includes the sulfur kinetics via a reduced reaction mechanism which was able to reproduce the key experimental results for Li-S batteries [3]. As mentioned the particle model is coupled to a cell model describing the macroscopic transport of dissolved species. In both models the species transport is described by the Nernst-Planck equation where transport occurs via diffusion and migration. The model intrinsically takes into account the polysulfide shuttle which allows us to describe side reactions at the negative electrode and the resulting decrease in coulombic efficiency. In this work we additionally take into account adsorption and desolvation effects that take place on the surface of the carbonaceous material. This effect is expected to be prominent for Mg-S batteries [4] due to the divalent nature of the Mg cation. The process of stripping and deposition at the Anode is much more complex than the process known from Li-S batteries. In order to take this into account we developed a detailed model of the Mg-metal anode which can be coupled to our cell model [5]. Within our simulation framework we are able to simulate charge and discharge curves as well as Electrochemical Impedance Spectroscopy measurements. In close collaboration with experimentalists we aim at guiding new developments of the Mg-S system.
References:
[1] H. D. Yoo. et al., Energy Environ. Sci. 6, 2265 (2013)
[2] Z. Zhao-Karger et al., Adv Energy Mater. 5, 140155 (2015)
[3] T. Danner et al., Electrochimica Acta, 184, 127-133, (2015)
[4] J. Lück et al., Phys. Chem. Chem. Phys., 18, 17799-17804 (2016)
[5] A. Benmayza et al., J. Phys. Chem. C, 117, 26881 - 26888 (2013)