Open-Circuit Voltage Models Should Be Thermodynamically Consistent

Open-circuit voltage (OCV) models as a function of state-of-charge (SOC) are fundamental to modeling the performance of batteries. The second law of thermodynamics enforces that the OCV should be monotonic with respect to the SOC. In this Perspective, we first review some of the currently popular empirical OCV fitting methods which compromise thermodynamics for the flexibility of empirical fitting. We propose a simple thermodynamically consistent OCV model enabled by differentiable thermodynamic modeling, which obeys the second law of thermodynamics. We cast the common-tangent condition derived from the second law of thermodynamics as a fixed-point solving problem and use implicit function theorem to enable efficient gradient-based parameters optimization. We demonstrate this on the OCV of 12 popular electrode materials, and this is integrated with open-source battery modeling software PyBaMM. We perform pseudo-2D discharge simulations to show the seamless integration of the above OCV models with battery modeling software. Given the simplicity of integration and implementation, we believe that thermodynamically consistent OCV models should be a requirement for future Li-ion battery models.