Accurate modeling of the internal battery resistance is imperative in predicting the state of charge and state of health. A mathematical model has been developed that, in addition to the ionic transport, introduces an accurate description of the electronic transport in the porous semiconducting LiFePO₄ electrodes. The model is based on the fundamental principles of electrochemistry, electrochemical kinetics, and semiconductor physics, combining them in an efficient model. This framework provides for the non-ohmic nature of semiconductor electrode materials and their current dependent conductivity. The model is validated by comparison with experimental data of Li-ion concentration profiles. It is demonstrated that the mass transport of the electrons, typically simplified or considered negligible in calculation models, have a significant influence on the electrode kinetics and therefore on the current dependent internal resistance of the battery. The accurate description of the internal resistance and the related heat production under various cycling conditions allows the design of safer battery electrode architectures. Additionally, the model allows optimization of the electrode components for various loading regime, increasing the effective energy density leading to decreasing demand for materials and costs. The present model, its principles, and methods are generally applicable and can be used for the description of the wide range of energy storage materials and systems where combined ion and electron transport takes place.

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.