Investigation of Thermodynamic Nonideality of Solid Li-ion Electrodes Using Concentrated Solution Theory
Authors: Jin Xinfang 
Published: February 2020

Li-Ion batteries (LIBs) is poised to dominate the energy storage market of electric vehicles (EVs) and renewable-energy-integrated grids over the next few decades. To address safety and lifetime concerns of the technology, significant efforts have been devoted to advancing online battery diagnostic tools and evolving charging/discharging protocols to enhance their stability and elongate their lifetime, and both have been found to be highly amenable to physics-based models (PBMs). With the continuous improvements and breakthroughs of computer technology, PBMs in substitute of equivalent circuit models (ECMs) have been employed to produce high-fidelity, low-computational-cost reduced-order-models (ROMs) for battery management system (BMS), despite the fact that simplifications have regularly been made. For example, in a general PBM of LIBs, Li-ion diffusion is governed by Fick’s second law of diffusion in a dilute solution (Fig. 1), which neglected the thermodynamic nonideality of a solid active material which experiences large concentration variation in electrochemical processes.
Though the above fact likely indicates that such PBMs contain some battery physics to represent the key electrochemical processes, it does not exclude the possibility that important correlations could be associated with physics that have been neglected. For example, although both ks (solid/liquid interface reaction rate) and D (diffusivity of Li-ion in a solid phase) exhibited correlations with battery State-Of-Charge (SOC), especially at the end of discharge, they have been assumed to be constants over the entire range of SOC. In fact, their values reported from different researchers show variation spanning over 2 to 5 order of magnitude. With this large variation, both battery SOC and State-Of-Health (SOH) will remain unpredictable, which means that ultimately the battery management and diagnosis remains uncertain.
Numerous theoretical and experimental studies support the inevitable Li-Li interactions when Li-ion deintercalation/intercalation from/into the active materials, especially with a sufficiently large concentration. This Li-Li interaction introduces thermodynamic nonideality which could not be described by the Fick’s second law of diffusion. Consequently, critical electrochemical kinetic and transport properties such as ks and D will have a strong correlation with the SOC. In this research, we will try to understand the nonideality of a solid Li-ion solution by the concentrated solution theory, as shown in Fig.1. We will use nonequilibrium thermodynamics in a concentrated solution to correlate ks/D with the activity coefficient of the solid solution γ and elaborate new governing equations for D and ks. Then, utilize the new correlations to process experimental data tested by EIS method and to regress the experimental activity coefficient γ. Furthermore, a methodology in determining the most appropriate constants for ks and D with a minimum discrepancy for a full charge/discharge cycle will be provided.

Figure 1. (a) Inconsistency in KsS and D values between dilute solution model prediction and experimental results; (b) Ks and D comparison between dilute solution theory and concentrated solution theory; (c) Experimental and model prediction based on concentrated solution theory.

Figure 1