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Mathematical Analysis of a Zn/NiOOH Cell
H. G u *

General Motors Research Laboratory, Electrochemistry Department, Warren, Michigan 48090
ABSTRACT A mathematical model has been developed to predict the time dependent behavior ofa Zn/NiOOH cell. The model uses experimentally determined polarization expressions to describe the losses between the positive and the negative electrodes. The electronic losses in the plane of the electrode are simulated by a network of resistors. The potential distribution, the current distribution, the cell voltage, the power capability, and the energy of a cell can be predicted. The mathematical model provides an analytical tool to evaluate, for example, the trade-offs between power capability and current collector mass, needed to design an electric vehicle battery. An electrode current collector carries current from the battery terminal to active sites on the electrode where electrochemical reactions take place. With a large electrode, the electronic losses in the current collector can be appreciable such that an uneven distribution of reaction current and an uneven polarization exist on the electrode surface affecting both the specific power and the specific energy. Accelerated degradation and shorting of electrodes may result due to excessive localized gassing on the electrodes. A current collector with high conductivity will give a uniform current distribution. Most often, a high conductivity current collector is synonymous with a heavy current collector. However, one can also improve the current distribution without increasing the overall weight of the current collector by strategically orienting the members of a current collector to evenly dis, tribute the current. A mathematical model that can predict cell performance will facilitate the design of these strategic current collectors. Eventually, a computer program can be developed that will suggest.an optimized current collector design for the specific application of a battery. Tiedemann, Newman, and Desua (1) applied the resistive network model to bare lead-acid battery grids. The potential distribution on the grid was examined by assuming a uniform current density. Various grid designs were compared based on the magnitude of the maximum potential difference between the tab and the grid node. Using the same approach, Vaaler and Brooman (2) examined the current distribution of pasted positive lead-acid battery plates relative to an equipotential surface. Electrode kinetics were not included. Tiedemann and Newman (3) then expanded their earlier model to examine the transient behavior of a lead-acid cell. Cell polarization between the positive and the negative electrodes was expressed by using an empirical equation whose coefficients were determined based on the porous electrode model de, veloped by Tiedemann and Newman (4). Recently, Sunu and Burrows (5) used a resistive model to examine the potential distributions of the positive plate
* Electrochemical Society Active Member.

and the negative plate of a lead-acid cell individually under uniform current density. They compared plates with different widths based on the tab.to.corner potential difference. The plate area was not kept constant in the comparison. Good agreement was shown between their mathematically predicted and experimentally measured potential distr~butiens. The present work describes the use of a resistive model to predict the transient behavior of a Zn/NiOOH cell with current collectors of different conductivities. The polarization characteristics of the Zn/NiOOH system was determined experimentally on small electrodes and the empirical equation obtained was used in the model to predict system behavior of cells with full size electrodes. The potential distribution, the current distribution, the cell voltage, the power capability, and the energy capability can be calculated to aid in the design of a Zn/NiOOH battery. Although the mathematical model can be applied to predict both charge and discharge behaviors, only the discharge behavior of a Zn/NiOOH cell will be discussed in this paper.

The Mathematical Model
The model simulates the electrode by a network of resistors where each model node is joined to adjacent nodes by resistors. For each node on the positive current collector, there is a node directly opposite to it on the negative current collector. Between opposite nodes, the reaction current is related to the potentials at the nodes by the empirical equation obtained experimentally on a cell with small electrodes approximately the size of the unit element (area) associated with a mathematical node. With reference to Fig. 1, the equation related to node j on an electrode was obtained by applying Kirchoff's law

- - - ~ Rt

- - + - - - ~

R~

R3

--+ijAj=O R4
[1]

where r are the potentials (V), R's are the effective resistances (a) between nodes on the electrode, ij is the reaction current density (A/crn2), and Aj is the

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