Qingzhi Guo

Parameter Estimation and Model Discrimination for a Lithium-Ion Cell

Two different models were used to obtain transport and kinetic parameters using nonlinear regression from experimental charge/ discharge curves of a lithium-ion cell measured at 35°C under four rates, C/5, C/2, 1C, and 2C, where the C rate is 1.656 A. The Levenberg-Marquardt method was used to estimate parameters in the models such as the diffusion of lithium ions in the positive electrode. A confidence interval for each parameter was also presented. The parameter values lie within their confidence intervals. The use of statistical weights to correct for the scatter in experimental data as well as to treat one set of data in preference to other is illustrated. An F-test was performed to discriminate between the goodness of fit obtained from the two models.

A Steady-State Impedance Model for a PEMFC Cathode

A model for the simulation of the steady-state impedance response of a polymer electrolyte membrane fuel cell (PEMFC) cathode is presented. The catalyst layer of the electrode is assumed to consist of many flooded spherical agglomerate particles surrounded by a small volume fraction of gas pores. Stefan-Maxwell equations are used to describe the multicomponent gas-phase transport occurring in both the gas diffusion layer and the catalyst layer of the electrode. Liquid-phase diffusion of O 2 is assumed to take place in the flooded agglomerate particles. Newmans porous electrode theory is applied to determine over-potential distributions.

Study of Ionic Conductivity Profiles of the Air Cathode of a PEMFC by AC Impedance Spectroscopy

A characterization of the ionic conduction of the active layer of a polymer electrolyte membrane fuel cell ~PEMFC! cathode by ac impedance measurement at open-circuit potential conditions was conducted. Porous electrode theory was used to derive a compact equation, ] 2 F & 2 /]y 2 1 ] ln f(y)/]y 3 ]F & 2 /]y 2 R/ f ( y)(1 1 jV)F & 2 5 0, to solve for the impedance response of a cathode at open-circuit potential conditions. This equation includes a parameter R, the ratio of an ionic resistance ~evaluated at the active layer/membrane interface!, to the total charge-transfer resistance of the active layer. The influence of an assumed ionic conductivity distribution profile f ( y) on the error in the estimation of total double-layer capacitance of the active layer from the 21/(ZImv) vs. ZRe plot was also investigated in this work. The increase of ionic conductivity in the active layer of an air cathode with an increase in the ionomer loading was revealed from both impedance data and surface area measurements. A nonlinear parameter estimation method was used to extract the ionic resistance from the high-frequency region of the impedance data at open-circuit potential conditions. The assumed ionic conductivity distribution profile in the active layer was found to vary with ionomer loadings.

Parameter Estimates for a PEMFC Cathode

Five parameters of a model of a polymer electrolyte membrane fuel cell ~PEMFC! cathode ~the volume fraction of gas pores in the gas diffusion layer, the volume fraction of gas pores in the catalyst layer, the exchange current density of the oxygen reduction reaction, the effective ionic conductivity of the electrolyte, and the ratio of the effective diffusion coefficient of oxygen in a flooded spherical agglomerate particle to the square of that particle radius ! were determined by least-squares fitting of experimental polarization curves. The values of parameters obtained in this work indicate that ionic conduction and gas-phase transport are two processes significantly influencing the performance of PEMFC air cathodes. While ionic conduction influences cathode performance over a wide range of current densities, gas-phase transport influences cathode performance only at high current densities. The air cathode in a polymer electrolyte membrane fuel cell ~PEMFC! is the largest source of voltage loss due to limitations of ionic ~proton! conduction, multicomponent gas transport, and liquidphase O2 diffusion. 1-3 To obtain a better understanding of these limitations, several models have been presented. 1-8 Two different pictures of the catalyst layer ~CAL! have been used to model the steady-state polarization performance of a PEMFC cathode: the flooded CAL and the CAL with the existence of gas pores. The assumption of a flooded CAL was found to overestimate the product of the diffusion coefficient and the concentration of O2 in the liquid electrolyte, 1 whereas a steady-state polarization model including gas pores in the CAL was found to be more realistic. 3,5,8Five parameters of a model of a polymer electrolyte membrane fuel cell cathode (the porosity of the gas diffusion layer, the porosity of the catalyst layer, the exchange current density of the oxygen reduction reaction, the effective ionic conductivity of the electrolyte, and the ratio of the effective diffusion coefficient of oxygen in a flooded spherical agglomerate particle to the squared particle radius) were determined by the least square fitting of experimental polarization curves. The values of parameters obtained in this work indicate that ionic conduction and gas-phase transport are two processes significantly influencing the performance of PEMFC air cathodes. While ionic conduction influences cathode performance over a wide range of current densities, gas-phase transport influences cathode performance only at high current densities.

Estimation of Diffusion Coefficient of Lithium in Carbon Using AC Impedance Technique

The validity of estimating the solid phase diffusion coefficient, Ds , of a lithium intercalation electrode from impedance measurement by a modified electrochemical impedance spectroscopy~EIS! method is studied. A macroscopic porous electrode model and concentrated electrolyte theory are used to simulate the synthetic impedance data. The modified EIS method is applied for estimating Ds . The influence of parameters such as the exchange current density, radius of active material particle, solid phase conductivity, porosity, volume fraction of inert material, and thickness of the porous carbon intercalation electrode, the solution phase diffusion coefficient, and transference number, on the validity of Ds estimation, is evaluated. A simple dimensionless group is developed to correlate all the results. It shows that the accurate estimation of Ds requires large particle size, small electrode thickness, large solution diffusion coefficient, and low active material loading. Finally, a ‘‘full model’’ method is developed for the

A New Kinetic Equation for Intercalation Electrodes

The kinetic equation used to predict the current being passed in an intercalation electrode depends on the overpotential and the composition of the intercalating species. The overpotential depends on the difference between the potential in the solid phase and in the solution phase, both of which depend on the composition of the intercalation species in the solid and solution phases, respectively. Furthermore, the overpotential depends on the local open circuit potential (OCP) of the intercalation electrode. Consequently, the kinetic equation and the OCP equation are coupled and must be written accordingly; that is, they must be written in a consistent way. In this work, a new kinetic equation, which is derived along with a thermodynamic (OCP) equation from the same reaction rate expression, is presented for intercalation electrodes. The thermodynamic equation is used to fit the OCP data of carbon (MCMB-2528) and LiCoO 2 electrodes. Comparison of the predictions from the new kinetic equation and the traditional Butler-Volmer equation used in the literature indicates that the new kinetic equation better describes the kinetic current-potential relationship for intercalation electrodes.

Cubic Spline Regression for the Open-Circuit Potential Curves of a Lithium-Ion Battery

A cubic spline regression model was used to fit the experimental open-circuit potential (OCP) curves of two intercalation electrodes of a lithium-ion battery. All the details of an OCP curve were accurately predicted by the resulting model. The number of regression intervals used to fit an OCP curve was determined in a way such that in each regression interval the OCP exhibits a profile predictable by a third-order polynomial. The locations of the data points used to separate regression intervals were optimized. Compared to a polynomial model with the same number of fitting parameters, the cubic spline regression model is more accurate. The cubic spline regression model presented here can be used conveniently to fit complicated profiles such as the OCP curves of lithium-ion battery electrodes.