A Mathematical Model of the Self‐Discharge of a Ni ‐ H 2 Battery

A simple mathematical model is presented and used to characterize the self-discharge of a nickel oxyhydroxide (NiOOH) electrode in a hydrogen environment. This model includes diffusion of dissolved hydrogen in an electrolyte film which covers a flooded electrode, electrochemical oxidation of hydrogen, reduction of nickel oxyhydroxide, and changes of surface area and of porosity of the electrode during the self-discharge process. Although the self-discharge process is complicated, the predictions of the model are consistent with experimental results reported in the literature, which include linear relationships between the logarithm of hydrogen pressure and time and between the logarithm of the capacity remaining and time. The model predictions indicate that hydrogen oxidation takes place predominantly near the front side of the electrode, but the reduction of nickel oxyhydroxide to nickel hydroxide takes place uniformly throughout the electrode. It is a commonly known that the self-discharge rate of a Ni H2 battery is many times higher than that of other batteries which use a NiOOH/Ni(OH)2 electrode as the positive electrode, such as Ni-Cd, Ni~Fe, Ni-Zn, etc. This high self-discharge has imposed limits on applications of this battery, a problem which needs to be overcome. Previous investigations (1-5) into this area have contributed significantly to understanding of the self-discharge process, but discrepancies in interpretation of the phenomena exist from different experiments. Markin and Dell (3) reported that the diffusion of dissolved hydrogen has a significant effect on the self-discharge rate. They demonstrated that the self-discharge rate was substantially decreased when * Electrochemical Society Active Member. the nickel electrode was fully immersed in the electrolyte. The microcalorimetric measurements by Mao et al. (6) also showed such an effect of the electrolyte. However, Holleck (1) suggested that some kind of an interface reaction is the controlling step, because his theoretical calculation indicated that the self-discharge rate under diffusion control would be two orders of magnitude higher than that experimentally measured. Holleck's view on the self-discharge process was shared by many researchers in the Ni-H2 battery community. That is, the self-discharge is a kinetically controlled process. However, the mechanism of hydrogen oxidation is far from being well understood. There are few investigations reported on this subject. Tsenter and Sluzhevskii (5) presented a set of kinetic equations to correlate self-discharge with the hydrogen pressure and the amount Downloaded 14 Jun 2011 to 129.252.106.20. Redistribution subject to ECS license or copyright; see http://www.ecsdl.org/terms_use.jsp J. Electrochem. Soc., Vol. 138, No. 11, November 1991 9 The Electrochemical Society, Inc. 3355 of undischarged NiOOH in the battery, with little attention being paid to the mechanism. By measuring the heat generation rate of ~-NiOOH powder as well as a mixture of 13-NiOOH and pure nickel powders in a hydrogen environment, Kim et al. (4) concluded that the mechanism of hydrogen oxidation is direct chemical reaction between hydrogen and nickel oxide material. More work is needed to characterize the self-discharge of a nickel electrode in hydrogen envi ronment and to determine the mechanism. In this work, a simple mathematical model is presented to simulate the self-discharge process. The objective of this work is to gain a better understanding of the process so that an effective means can be taken to reduce the selfdischarge rate. Since the self-discharge always results in a corresponding drop of the hydrogen pressure in the cell, the overall reaction may be written as Hs + 2NiOOH ~ 2Ni(OH)2 [1] This reaction involves the transfer of two moles of electrons from H2 to two moles of Ni a§ It is possible that this reaction occurs via two electrochemical reactions as follows H~ + 2 OH2e---> 2H20 [2] 2NiOOH + 2H20 + 2e --> 2Ni(OH)~ + 2 OH[3] According to reaction [3], the reduction of nickel oxyhydroxide will occur regardless of the presence of hydrogen if the electrode potential is below the equilibrium potential of NiOOH/Ni(OH)2. According to reaction [2], the oxidation of hydrogen does not depend on the availability of NiOOH if the electrode potential is high enough for hydrogen oxidation. If the self-discharge process is due to a chemical reaction between hydrogen and NiOOH as shown in reaction [1], the local reaction rate in the nickel electrode would depend on the local hydrogen concentration and the local amount of NiOOH. The electrode potential would not affect the reaction rate, even though the potential of the electrode would change with the ratio of the amount of NiOOH to Ni(OH)2 in the electrode. This chemical mechanism would be limited only to direct reaction between hydrogen and nickel oxyhydroxide; consequently, the local hydrogen oxidation rate would be exactly equal to the local reduction rate of nickel oxyhydroxide. If the self-discharge occurs electrochemically as shown by reactions [2] and [3], the local reaction rates of reactions [2] and [3] would depend on the local dissolved hydrogen concentration, the state of charge of the nickel electrode, and the electrode potential. The measured potential of the nickel oxyhydroxide electrode would be a mixed potential balanced by the polarizations of reactions [2] and [3] under the constraint of zero total current, depending on state of charge, self-discharge rate, and the reversibility of reaction [2] and [3]. In this work, the electrochemical mechanism is assumed to apply. Mathemat ica l Model In the model presented here, the self-discharge process consists of the following steps (see Fig. 1). Hydrogen gas dissolves into the electrolyte and diffuses to the nickel electrode, where it is oxidized to form H20 with OH-. The nickel electrode is flooded and covered by a layer of electrolyte. Since the electrolyte is highly concentrated with potassium hydroxide (about 26-31 weight percent KOH), the solubility of hydrogen gas is small (about 10 -4 M/atm). On the other hand, the self-discharge rate is also known to be small, which should not cause an appreciable change in KOH concentration. Therefore, the transport of dissolved hydrogen can be considered to be simple diffusion according to Fick's law ~EsCH2 (:} 0CH2 DH2e ~ [4] at ox Ox where e~ is the porosity of this electrolyte region which could represent the separator of the battery, and DH~ is the II