Effect of Proton Diffusion, Electron Conductivity, and Charge-Transfer Resistance on Nickel Hydroxide Discharge Curves

ABSTRACT Constant-current discharge curves for the nickel hydroxide electrode are simulated assuming resistances due to diffusion of protons and conduction of electrons through the nickel hydroxide film, and charge-transfer resistance at the film/electrolyte interface contribute to the polarization losses of the electrode. Good qualitative agreement is observed between the model predictions and experimental discharge curves. The results suggest that polarization losses due to diffusional limitations of protons is a critical factor in determining the characteristics of the discharge curve. Ohmic resistance has a significant effect on the discharge curves at the end of discharge, and charge-transfer resistance is a minor contributor to the polarization losses. These findings indicate that accurately measuring the diffusion coefficient of protons, the thickness of the hydroxide film, the initial state-of-charge, and the electronic conductivity as a function of state-of-charge towards the end of discharge are critical in accurately predicting the discharge characteristics of nickel hydroxide. Physical constants which were shown to have minor influence on the discharge curves are the film conductivity at the beginning of discharge, and the exchange current density and cathodic transfer coefficient for the reaction. The time-dependent, one-dimensional diffusion equation has been solved analytically which should provide a computationally efficient means of accounting for proton diffusion and variable electronic conductivity in a macrohomogeneous battery model without sacrificing accuracy. Battery models that can predict the effect of operating conditions on battery life and performance are extremely valuable to battery users and manufacturers. Model predictions can provide quality assurance that the batteries being manufactured are of consistently high quality, and provide indicators well in advance of failure so that steps can be taken to adjust operating condition and prolong battery life. In addition, a variety of design parameters can be investigated to aid an electrode development program. Theoretical discharge curves for nickel hydroxide have been generated by a number of investigators 1-5 using a onedimensional, macrohomogencous model. The spatial dimension of interest is in the direction perpendicular to the current collectors, and therefore the polarization losses caused by the NiOOH/Ni(OH)2 film is assumed to be due solely to a pseudocharge-transfer resistance. Although these models reveal the importance of transport limitations in the electrolyte phase, they predict nickel electrode potentials as a function of time which are more positive and flatter than experimental data. They also predict material utilization on discharge which is unrealistically high. Sinha 6 developed a model of a porous electrode in which the solid material was described using semiconductor the-* Electrochemical Society Active Member. ory. This model, however, contains many parameters that cannot be obtained experimentally. Experimentally it has been suggested that resistance due to diffusion of protons and/or conduction of electrons may contribute appreciably to overall polarization losses at the nickel hydroxide film. 7-1~ Two-dimensional, macrohomogeneous models have been developed to account for the diffusion of protons in the active nickel hydroxide film n and diffusion coupled with variable electronic resistance of the film. 1~ One of the rationales for including variable electronic resistance in the later model is that nickel hydroxide is an electrical insulator in the reduced state and a conductor in the oxidized state. The drawback of these models is that the solution procedure requires a large amount of computer memory and computational time. In this paper, an analytical solution to the time-dependent, one-dimensional diffusion equation is incorporated into a discharge model which accounts for proton diffusion and variable electronic conductivity in the film, and charge-transfer resistance at the film/electrolyte interface. The governing equations are presented in such a manner that they can be used in conjunction with a one-dimensional, macrohomogeneous model in order to predict the behavior of an entire nickel battery. The results presented here though ignore: (i) the interaction among the positiv