Quantifying Cell Degradation Using Thermally Corrected Differential Capacity Spectra
Thermally corrected differential capacity spectra isolate lithium loss from active material decay by subtracting entropic and kinetic overpotential shifts.
Gibbs Helmholtz Relation
Meaning
Mathematical expressions define the temperature dependence of the change in Gibbs free energy for a closed system at constant pressure. The gibbs helmholtz relation determines the enthalpy change of a reaction from the slope of a plot where the ratio of the change in Gibbs free energy to temperature is plotted against the inverse of temperature. Physicists apply these equations to predict the spontaneous direction of chemical reactions under varying thermal conditions.
Thermal Sensitivity
Battery chemists utilize the logic behind the gibbs helmholtz relation to isolate the entropic contribution to total cell heat generation during charge and discharge cycles. Measuring the open circuit voltage across a range of temperatures allows for the calculation of the entropy of the electrochemical reaction. High entropic heat values signal potential degradation or thermal management challenges within large format lithium ion packs.
Precise data gathered through this method prevents inaccurate modeling of pack thermal behavior during high current operation.
Analytical Boundary
Calculations depend strictly upon the assumption that the process remains at a constant pressure state throughout the entire temperature sweep. If the cell casing exerts significant mechanical constraint that alters internal pressure, the standard formulation loses its predictive power. Researchers treat these variances by adjusting the pressure coefficients before extracting enthalpy values from the derivative.
Error occurs when investigators ignore the volume expansion coefficients of active materials during the transition.
Energy Validation
Voltage drift data combined with these calculations verify the state of health of active materials in secondary cells. Engineers compare the measured temperature sensitivity of the potential against theoretical values for the specified chemistry to confirm material purity. Deviations from the expected slope suggest electrolyte decomposition or side reactions that consume lithium ions.
Accurate extraction of enthalpy through the gibbs helmholtz relation confirms the energy efficiency of the electrochemical interface.