Lattice-Gas Model for Energy Storage Materials: Phase Diagram and Equilibrium Potential as a Function of Nanoparticle Size

Insertion reactions are of key importance for Li/Na-ion batteries and hydrogen storage materials. Nanosizing of these energy storage materials has been shown to have a fundamental impact on the storage properties. Predicting these properties based on rather simple thermodynamic grounds is of high importance for fundamental understanding, achieving the optimal performance of nanomaterials, as well as for the practical ability to manage battery systems. Here we report on the development of a new thermodynamic lattice gas model based on the equation of state of the energy carrier that is able to describe the impact of particle size on fundamental physical-chemical characteristics, such as the phase diagram and equilibrium potentials of energy storage materials that exhibit a first-order phase transition upon Li or H insertion. The model is based on the first-principles of chemical and statistical thermodynamics and takes into account complex structural changes taking place in energy storage materials and because of its general nature can be adapted to describe the influence of any state variable (particle size, temperature, etc.). The model is applied and validated using experimental data on different particle sizes of the LiFePO₄ battery electrode material resulting in excellent agreement. The model can be used to simulate phase diagrams and predict equilibrium potential isotherms with respect to the electrode nanoparticle size. The relative simplicity of the model allows easy prediction of material properties as required by for instance advanced battery management systems.