A Non-Electroneutral Model for Complex Reaction-Diffusion Systems Incorporating Species Interactions

Abstract

In this study we develop a general framework for describing reaction-diffusion processes in a multi-component electrolyte in which multiple reactions of different types may occur. Our motivation for this is the need to understand how the interactions between species and processes occurring in a complex electrochemical system. We use the framework to develop a modified Poisson-Nernst-Planck model which accounts for the excluded volume interaction (EVI) and incorporates both electrochemical and chemical reactions. Using this model, we investigate how the EVI influences the reactions and how the reactions influence each other in the contexts of the equilibrium state of a system and of a simple electrochemical device under load. Complex behavior quickly emerges even in relatively simple systems, and deviations from the predictions of ideal solution theory, together with how they may influence the behavior of more complex system, are discussed. Electrochemical energy storage devices play a crucial role in the modern world, having enabled the development of a wide range of portable and mobile devices in a vast range of applications. They also have significant future potential in facilitating a shift away from environmentally damaging fossil fuels as our primary source of energy, through the electrification of transport and as load balancing for the variability suffered by most forms of renewable energy. However, modeling these systems can be challenging because the overall behavior is typically the emergent result of a large number of processes and interactions at the microscopic scale, making linking the microscopic behavior to the macroscopic performance complicated. Furthermore, individual processes may themselves be complex, so simplifications have to be made if we wish to understand the device behavior at macroscopic length and time-scales.By way of example, the particular system in which we are interested is that of a lithium-sulfur (LiS) cell, a promising post-lithium-ion technology with both an expected practical energy density of 500-600 Wh kg −1 and a lower raw materials cost. 1,2 The overall discharge process of a LiS cell involves the reduction of solid phase S 8 to solid phase Li 2 S, according to the reactionWhile the overall process is bound by the dissolution of S 8 and the precipitation of Li 2 S, the intermediate steps occur between species in the solvent/electrolyte phase, involving the electrodissolution of lithium from the anode and a range of electrochemical and chemical reactions involving a number of ionic sulfur species at the cathode. While these types of process are not uncommon in traditional (i.e. non-intercalation) battery chemistries, the sheer number of species and intermediate elementary reaction steps involved, together with the integral role played by chemical reaction processes, make understanding the LiS mechanism complex. 3The common approach to modeling LiS cells is similar to that taken for many electrochemical devices, with the reduction of the cell structure to a one-dimension...

Molecular modeling of electrolyte and polysulfide ions for lithium-sulfur batteries

“…Therefore, modeling of electrolyte and sulfide ion transport would be a useful tool for the design of cathode, separator, and electrolyte materials in Li-S batteries. A continuum ion transport model taking into account the pore size distribution [8,12,13] has been recommended for Li-S batteries [13]. Such a model requires as input data the size (minimum and maximum dimensions) of the electrolyte and polysulfide ions in desolvated and solvated forms, as well as their desolvation energy [8].…”

Lithium-Sulfur Battery Technology Readiness and Applications—A Review

“…Li-S is generally considered the post lithium-ion (Li-ion) chemistry of choice for high energy density applications. Over the past decade, there has been an ever increasing volume of Li-S academic research spanning materials development [1][2][3][4], fundamental understanding [5][6][7] and modelling [8,9], and application-based control algorithm development [10,11]. In addition, the industrial interest in developing Li-S technology has increased from two to three dedicated research companies in 2007 [12,13] to almost every global cell developer investing in their in-house Li-S research capability by 2017 [14][15][16].…”