Limiting mechanism on rapid charging NiMH batteries

Electrochimica Acta 47 (2001) 875– 884 www.elsevier.com/locate/electacta

Limiting mechanism on rapid charging NiMH batteries Bor Yann Liaw *, Xiao-Guang Yang Hawaii Natural Energy Institute, School of Ocean and Earth Science and Technology, Uni6ersity of Hawaii at Manoa, 2540 Dole Street, Holmes Hall 246, Honolulu, HI 96822, USA Received 10 April 2001; received in revised form 8 August 2001

Abstract Nickel metal hydride (NiMH) battery systems are emerging as a competitive technology in the power electronics and tool market and for electric and hybrid vehicle applications. The ability to rapid charging the NiMH batteries can greatly enhance their market acceptance and penetration. We have demonstrated the possibility of rapid charging a commercial NiMH traction battery system at high rates. This paper will discuss the mechanism that limits the rapid charging capability of the system. We will further discuss how to control the charging process. © 2001 Elsevier Science Ltd. All rights reserved. Keywords: Rapid charging; NiMH battery; Limiting mechanism; Charge control; Hydrogen diffusion

1. Introduction Rapid charging NiMH batteries is a very complicated process and a difficult challenge to the industry. Often a sophisticated charge algorithm has to be used. Typically, the charge control unit has to monitor the voltage and temperature of the battery and the rate of the change of these parameters with time to control the charging process. Even so, it is still very difficult to determine the termination condition of the charging process with the above method during a high-rate transient condition. Therefore, the NiMH battery life will largely depend on not only the power profile applied to the battery but also the charging process and the algorithm used. This is particularly true for electric and hybrid vehicle applications, where the use of power is quite sporadic and spontaneous in nature. Rapid charging, on the other hand, allows ‘opportunity charging’ that can significantly benefit a greater utilization of the battery energy and capacity, therefore increasing the useful life of the battery. In electric vehicle applications, for example, our experience told us that, due to limited range of the vehicle, the operator tends to utilize only a fraction of the battery capacity,

* Corresponding author. Tel.: + 1-808-9562339; fax: +1-8089562335. E-mail address: [email protected] (B.Y. Liaw).

and thus resulting in frequent recharges. Our experience also showed that this usage pattern and the low-power on-board charging actually create more adverse effects to the battery performance and its life. It is because that the low-power on-board charging typically ran like a trickle charging that often caused excessive overcharge of the battery, resulting in venting of gas, and subsequent reduction of the battery life due to partial dry-out and premature failure. Rapid charging can drastically reverse this practice, since the vehicle operator now can access frequent fast recharges and fully utilize most of the battery capacity. The rapid recharge can quickly refill most of the capacity to extend the range, thus greatly enhance the mobility of the vehicle. In short, rapid charge can provide the following potential benefits: (i) reduced charging time; (ii) increased utilization of the battery energy and capacity, thus enhanced vehicle mobility; (iii) prolonged battery cycle life; and therefore, (iv) reduced overall ownership costs. The trade-off for the rapid charging, compared to plug-in low-power on-board charging, is that it usually requires installation of costly rapid charging facility and infrastructure. Recently, advanced battery modeling and simulation capability has been developed in our laboratory [1–3], which allows us to conduct more careful study, from

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Fig. 1. Experimental setup for rapid charging investigations.

first principles, to understand battery performance under dynamic cycling conditions. This approach is particularly useful in the study of charging behavior of the battery. Since, with valid experimental data, the simulation can be used to show the limiting process in the battery system in any charging regime. This type of information was not typically available in the test data from the experiments. From such a modeling effort, we found that solid-state diffusion in the electrodes play a significant role in the battery performance. Our results shown in this paper will provide evidence of this limitation. In addition, we will illustrate the limiting process of rapid charging and show how to develop a viable control strategy for the charging algorithm. More detailed discussion of the rapid charge development on the NiMH system will be published elsewhere [4].

2. Experimental aspects The NiMH battery modules used in this experiment were obtained from Ovonic Battery Company in Troy, Michigan. The MH electrode is typically made of AB2type hydrogen storage alloys. Typically, the open circuit voltage (OCV) of the cell is in the vicinity of 1.478 V when measured immediately after it is fully charged. The OCV will gradually decline as a result of self-discharge. After a 5-h rest the OCV of the cell is in the vicinity of 1.413 V. The test module consists of 11 cells in series, and 19 cells in parallel. The nominal capacity of the battery was rated at C3 =85 Ah for the 3-h rate and C1 =80 Ah for the 1-h rate. Fig. 1 shows the experimental setup. A Windows NT-4.0 workstation was used to control the ABC-150 battery test station (AeroVironment, Monrovia, California). A data acquisition system, including a pressure transducer (Measurement Specialties, Inc., Fairfield, New Jersey),

thermocouples (Omega Engineering, Inc., Stamford, Connecticut), an SCXI-1121 signal conditioning unit, and a 16-bit NIDAQ PCI-MIO-16XE-50 card, (National Instruments, Austin, Texas), was used to monitor the cell voltage, external temperature, and internal gas pressure changes during charge and discharge cycles. The software used to control the ABC-150 also supports NIDAQ interface, therefore the cell voltage, temperature and pressure measured by the NIDAQ data acquisition system can be used in the control of the tests, thus facilitating the algorithm development. The battery module was placed in a temperature-controlled test chamber with adequate ventilation for thermal control. The conditions used in the charge tests are shown in Table 1. Both constant current (CC) and constant power (CP) regimes were applied. Typical termination condition is also listed in the table. Interestingly, the pressure lid used in the tests was shown of paramount Table 1 Summary of rapid charge test parameters and termination conditions for CC and CP charge regimes Charging parameters Constant current (CC) charging Charging rate 1C, 1.6C, 2C, 2.4C, 2.7C and 3C (i.e. 85–255 A) Initial SOC 0, 20, 40 and 60% SOC Constant power (CP) charging Charging power 1.49, 2.50 and 5.30 kW level Termination conditions (for all tests) Maximum charge input Pressure lid Voltage lid Temperature lid

B88 Ah 80–150 psi (or 5.4–10.2 atm) 18.5 V/module with temperature compensation B45 °C

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Fig. 2. A typical C1/4 charge and C1/3 discharge regime.

importance. Therefore, most of the test data were obtained under the control of the gas pressure in the cell, in order to obtain reproducible results. It should be noted that the termination pressure for charge control is typically set at 150 psi or lower. This cut-off pressure of about 10 atm is below the venting pressure (12.2 atm) of the release valve set by the manufacturer. To characterize the battery performance, we usually performed C/3 discharge to determine the C3 capacity for comparison.

3. Results Fig. 2 shows a typical constant current (CC) charge regime at 20 A (i.e. C1/4 rate). The termination condition was based on the maximum charge input control set at 88 Ah. The discharge gave a C3 =84.7 Ah. The temperature rise during the charge was quite minimal, only 2–3 °C, accompanied by a pressure increase to about 6 atm (or 88 psi). This simple experiment demonstrated that a simple CC charging with the charge-input control was sufficient to return a full capacity. Similar experiments conducted at higher rates, however, indicated that the charge-input control is not sufficient any more, since the pressure increase will exceed the pressure lid used in the control scripts. This situation is illustrated in Fig. 3, where the battery voltage and pressure profiles under different charge rates at C1/4, C1/2 and 1C are shown. In the C1/4 charge regime, the maximum charge input of 88 Ah was used as the termination condition, whereas the cell pressure reached 88 psi (or 6 atm). In the C1/2 charge regime, the same termination condition was used, and the cell pressure now reached almost 100 psi (or 6.8 atm). Further test using the 1C rate showed that the same termination condition could not be valid any more, since the pressure increase was so immense that,

beyond 73 Ah of charge input, venting would be inevitable. In other words, if we set the pressure lid at 100 psi, the cell could only be charged to about 73 Ah, 83% of the charge input in the previous two tests with lower rates. The shift of the termination condition in the charge control revealed one of the most important aspects of this work, leading to our emphasis on the pressure-controlled strategy in the rapid charge algorithm. More systematic study of the rapid charging behavior at high rates was then conducted. Table 2 summarizes the rapid charging results with a battery starting from a completely discharged state in various constant current (CC) and constant power (CP) tests. The results include the charge input, C3 capacity, charge efficiency, final SOC, charge time, temperature change, and the end-ofcharge (terminal) voltage. The termination was based on the pressure lid set at 85 psi. The % SOC values

Fig. 3. Cell voltage and pressure profiles under different charge rates. Two termination regimes are shown, separated by the dashed line. At the low rates, the pressure increase does not impact on the termination, therefore a charge-input control can be used. At high rates, pressure termination is preferred.

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Table 2 Summary of rapid charging test results for both CC and CP regimes Charging mode

Charge input (Ah)

Capacity (Ah)

Efficiency (%)

Final SOC (%)

Charge time (h) Temperature change (°C)

Terminal voltage (V)

Constant current 1C 67.4 65.03 1.6C 55.44 55.55 2C 41.99 3C 31.66 31.12

63.55 65.22 52.27 53.65 41.44 31.04 31.13

94.3 100.0 94.3 96.6 98.7 98.0 100

74.8 76.7 61.5 63.1 48.7 36.5 36.6

0.793 0.781 0.406 0.408 0.239 0.123 0.123

3 4 8 7 8 9 10

16.778 16.734 17.236 17.308 17.491 18.144 18.119

Constant power (kW) 1.49 64.24 2.50 50.34 5.30 32.64

62.27 48.32 31.14

96.9 96.0 95.4

73.3 56.8 36.6

0.742 0.370 0.130

4 7 11

16.746 17.166 18.157

reported in Table 2 represents the resulting state of charge after different levels of fast charge. For example, at the 3C charge rate, it took 0.123 h to charge the battery module from its fully discharge state to 36.5% SOC. It was found that the charge input depended on the charge rate. The final SOC (or the capacity) versus the charge rate follows a logarithmic relationship with the charge time. The Coulombic efficiency of the charge process at all rates was very high, at least above 94%. The temperature rise, even at 3C, was about 10– 12 °C the most. As the charge rate increased, the terminal voltage of the cell seemed to reach a constant value at about 18.2 V. We also found that there is no noticeable difference between the constant current or comparable constant power mode in the charge results; i.e. charge time, charge efficiency and energy efficiency are very similar.

When the study of the charge performance was conducted over a range of initial SOC, we found that the final SOC of the cell (or the capacity) depends on the initial SOC and the charge rate. This relationship is depicted in Fig. 4, where the contours of the final SOC are plotted against the initial SOC and the charge rate as the result of pressure termination at 150 psi (or 10.2 atm).

4. Discussions Fig. 3 depicts a very important aspect of rapid charging the NiMH batteries in this work. It shows that, under the constant current charging regime, as we increase the charge rate from the more commonly-used C/4 rate to above 1C, the gas evolution reaction and the resulting pressure buildup in the cell are becoming a

Fig. 4. Rapid charge performance chart, showing that the final SOC of the cell depends on the initial SOC and the charge rate. The values on the contours present the final state of charge after the fast charge.

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predominant consideration in the charging control. Without proper monitoring and control of this aspect, the rapid charging could result in significant venting of gas and loss of electrolyte. The consequence will be a partial dryout in the cell and increased impedance. It will not only reduce the capacity but also degrade the performance of the cell. Proper control of the charge termination based on pressure lid seems to be crucial and beneficial to the cell performance and cycle life. To understand the limiting mechanism of the highrate rapid charging process and the associated gas evolution and pressure profile, we conducted the following analysis of the cell characteristics during charging. Particularly, we focused on the analysis of the pressure profile and the transport properties of the system in the charging regime. The following possible gas-evolution reactions were considered:

generation rate is negligible compared to the hydrogen evolution rate, as follows:

&

i PV dt = F RT

(1)

On the negative MH electrode: MH + H2O +e− “ M +OH− +H2

(2)

or, 2MH “ 2M+H2

(3)

Because the potential for the oxygen evolution reaction Eq. (1) is below that of the main half-cell reaction for the nickel electrode, Bourgault and Conway [5] found experimentally that the surface reaction of oxygen evolution occurs throughout the charging and discharging regimes. The oxygen evolution reaction Eq. (1) ought to occur first as the charging progresses. The oxygen evolution is assumed to follow the Tafel type behavior and can be generally described by the Butler– Volmer equation [6], with an exchange current density of the order of 4.5× 10 − 9 A/cm2. Furthermore, the oxygen evolution reaction rate depends on the Ni electrode surface property, and reaches a steady finite value if the electrode is held at a constant potential. The hydrogen evolution reaction occurring on the MH electrode exhibits more complex nature. Yang et al. [7,8] found in their half-cell tests that the hydrogen gas evolves on the surface of the MH electrode in the middle stage of the charge process even at a low C/4 rate. Inevitably, hydrogen evolution would take place in any high-rate charging. Inoue et al. [9] asserted that the hydrogen evolution on the MH electrode is attributed to most likely Eq. (2) and assumed that it behaves like a reversible hydrogen electrode that follows the Tafel equation. The pressure buildup is a result of gas generation from the electrochemical side reaction, and the amount of charge consumed by the side reaction can be related to the internal pressure, if we assume that the oxygen

(4)

where i is the current of the side reaction Eq. (2); P, V and T are the internal pressure, headspace volume and temperature, respectively; and, F and R are the Faraday constant and universal gas constant, respectively. The differentiation of the above equation by time gives, dP RTi = dt VF

(5)

The current of the gas generation can be written in the form of Tafel equation. i= io exp

On the positive Ni electrode: 4OH− “ 2H2O +O2 +4e−

879

  Fp RT

(6)

where io is the exchange current density and p is the overpotential for the hydrogen generation, which can be simplified as, p= bt

(7)

where b is a constant and t is the charge time, according to experimental results. The linear dependence also represents that the polarization is more likely concentration dependent in nature. Combining Eqs. (5)–(7) gives,

 

dP RTio Fbt = exp dt VF RT

(8)

Fig. 5 compares our experimental data with the calculated values from the Tafel equation in Eq. (8) using an exchange current density of 6.9×10 − 5 A/(g MH alloy), an overpotential constant b of 1.2× 10 − 4 V/s, and a headspace volume of 20 ml. Good agreement was found, showing that the pressure buildup follows an exponential curve with the charge time under a constant current charging regime. The exponential relationship also depicts that the pressure increases exponentially with the charge input or the state of charge. Because the headspace volume of the battery is very small, the amount of hydrogen accumulated in this space is trivial compared to the total charge input. Using a typical diffusion model and assuming proper diffusion length and hydrogen diffusivity in the hydride, we should be able to calculate the surface hydrogen concentration as the charge progresses. We therefore analyzed the surface hydrogen concentration on the MH electrode by solving Fick’s second law of diffusion,



#C 1 # #C = rD #t r #r #r



(9)

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with a boundary condition depicting a constant flux of hydrogen arriving at the MH particle surface according to: D=

#C i = = constant at r = ro #r F

(10)

In the equation, D is the chemical diffusion coefficient of hydrogen in the MH matrix, C the hydrogen concentration, r the distance from the center of an average MH grain, which has an average radius of ro (which we also assume to be the diffusion length in the MH particles). In the constant current charging regime, we can rewrite the constant flux of hydrogen atoms being deposited onto the MH surface with, i=

Iz =constant mAMH

(11)

where I is the applied current, m is the mass of the MH, z is the density of the MH, and AMH is the specific surface area of the MH electrode, which is often considered reciprocal to the particle size as AMH 8 1/ro. The solution for Eqs. (9)–(11), which represents the hydrogen surface concentration, C, at time t, can be expressed by [10], Co +C=



iro 3Dt r 2 3 + 2− FD r 2o 2r o 10 −

n

2 2ro sin(hnr) % 2 2 e − Dhnt r n = 1 h nr o sin(hnro)

(12)

where Co is the initial hydrogen surface concentration and the rohn values are the positive roots of rohn cot(rohn )= 1. The maximum hydrogen concentration, Cmax, can be depicted by,

Cmax =

xHmaxz W

(13)

where xHmax is the maximum hydrogen content in the MH and W is the molecular weight of the specific MH composition. The maximum hydrogen content can be extracted from the pressure–composition–temperature (p–c –T) curve, if the MH electrode composition is known. Fig. 6A shows the typical p–c–T curve of the MH. The p –c–T curve is a smooth uprising curve showing that hydrogen partial pressure (and activity) smoothly increases with the hydrogen content in the MH. No constant pressure plateau was observed. It is very likely that the composition range involved in the electrochemical reaction was in a (pseudo-)single phase solid-solution region, although the alloy is often considered of multi-components in nature. Since there is no pressure plateau appeared in the composition range, it suggests that there is no phase transformation involved during the battery operation. In-situ determination of the MH electrode composition within a battery is difficult experimentally. According to the pressure excursion we measured in the cell, we however can estimate the hydrogen composition change in the MH during the charging and discharge cycles. The values are indicated in Fig. 6A. Presumably, it is safe to assume that there is a finite (or quasi) equilibrium between the gas composition and the hydrogen surface concentration on the MH electrode. This assumption allows us to correlate the corresponding maximum surface hydrogen concentration on the MH electrode with the cut-off pressure at the end of the charge. As the charge progresses, the ‘relative’ hydrogen content, q, at the surface of the MH electrode can be expressed by the ratio of the surface concentration C to the maximum concentration Cmax by,

Fig. 5. Comparison of the pressure profiles based on the Tafel behavior of the MH electrode in the charging regime. Open circles are experimental data, while the solid line represents the calculated values from the Tafel equation, as depicted in Eq. (8).

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f(q)=

881

d ln aH 1 d ln fH2 1 d ln PH2 = = d ln xH 2 d ln xH 2 d ln xH

(16)

where aH is the activity of hydrogen in the hydride alloy, fH2 and PH2 are the fugacity and partial pressure of hydrogen in equilibrium with the alloy, respectively. The thermodynamic factor can be calculated from the experimental p–c–T data of the alloy system, as depicted in Fig. 6B. In the hydrogen content range of interest, f(q) varies in the range of 0.4–4.1. We have determined the hydrogen diffusion coefficient in the AB2 type electrode as a function of state of charge using in-situ galvanostatic intermittent titration techniques (GITT). The results were reported in [13]. The chemical diffusion coefficients are of the order of 10 − 15 m2/s and remain relatively constant in the composition range of interest. Knowing the chemical diffusion coefficients and the thermodynamic factors in such a composition range, we then calculated the intrinsic diffusion coefficients D* as a function of MH composition, as shown in Fig. 6C. Assuming that Co equals to zero when the battery is in the fully discharged state, we can combine Eqs. (12)–(16) to give the relative hydrogen content q at the surface of the MH electrode as, q=



IW r 2o 3t+ mxHmaxF 5Df(q) −

Fig. 6. (A) The pressure –composition –temperature (p – c–T) curve of the MH electrode at 25 °C. (B) Thermodynamic factor calculated from the p – c– T curve varying with the hydrogen content in the MH. (C) Calculated intrinsic diffusion coefficient of hydrogen as a function of the MH composition.

C q= ×100% Cmax

(14)

Some publications [11,12] discussed in-depth the theoretical considerations on the hydrogen diffusion coefficient varying with the concentration of hydrogen in the hydride alloys. The (measured) chemical diffusion coefficient D is related to the intrinsic diffusion coefficient D* by the thermodynamic factor f(q), D= D*f(q) The thermodynamic factor, f(q), is defined as,

(15)

2 2r 2o sin(h r) % 2 2 n e − Df(q)hnt Df(q) n = 1 h nr o sin(hnro)

n

(17)

at r= ro. We then take n= 4 to simplify the summation expression in Eq. (17). Table 3 lists the values of the parameters required in the above equation for the calculation of the relative hydrogen content at the MH surface. The relative surface hydrogen content q varies with the charge time at 1C, 2C and 3C rates, respectively, as shown in Fig. 7A. The duration that corresponds to the time that the relative hydrogen content at the MH surface reaches the maximum value (q]100%) is compared with the charge time determined by the pressure cut-off for each charge rate. Good agreement is obtained, as shown in Fig. 7B, indicating that the termination with the pressure cut-off corresponds to the Table 3 Parameters pertinent to the MH electrode in an 85-Ah battery for the estimation of charge performance Radius of MH particles, ro Chemical diffusion coefficient of H, D Thermodynamic factor, f(q) Maximum hydrogen content in MH alloy, xHmax in MHx Density, z Molecular weight of MH, W Weight of MH in a battery, m Applied discharge current, I

5 mm 2×10−15 m2/s 3 3 5.5 g/cm3 185 g/mol 450 g 85 A

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Fig. 7. (A) Calculated relative surface hydrogen content as a function of charge time at three C rates. (B) Comparison of charge time estimated by the duration of which the surface hydrogen content reaches the maximum and those determined by the pressure cut-off control.

condition that the surface hydrogen content on MH has reached the maximum. Further imposition of the charge current will only result in significant gas evolution with almost no charge benefit. It also indicates that the solid-state diffusion is limiting the charging process at high charge rates, reflecting that the hydrogen partial pressure increases as the hydrogen activity on the surface of the MH electrode approaches unity. The above analysis confirmed that the hydrogen diffusion in the MH determines the extent of charge return during the fast recharge. In other words, under a constant temperature, we can extrapolate the pressure to the corresponding hydrogen content on the surface of the MH composition, as the probing of the ability to accept charge, or ‘rechargeability’. Based on this approach, we can then assess how chemical diffusion of

hydrogen and the MH particle size can affect the rapid ‘rechargeability’ of the battery. Fig. 8 shows hypothetical changes of hydrogen chemical diffusion coefficient and their influence on the surface hydrogen content of MH during a 1C rate charging with the same particle size of 5 mm. Increasing the diffusion coefficient from 10 − 15 to 10 − 13 m2/s will result in much reduced surface hydrogen content increase as well as pressure buildup, thus facilitate rapid charge. We estimated that a corresponding charge return increase from 55.5 to 95.5% SOC can be achieved if the chemical diffusion coefficient does increase from 10 − 15 to 10 − 13 m2/s. Fig. 9 shows the effect of the particle size of the MH alloy on the charge behavior with the assumption of a constant diffusion coefficient of D= 2.0×10 − 15 m2/s

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Fig. 8. Calculated relative surface hydrogen content on the MH electrode as a function of diffusion coefficient with 1C charge rate and ro = 5 mm. The higher the diffusion rate, the slower the hydrogen surface concentration buildup. The longer the charge time, the better the charge return.

as we usually measured for the MH electrode material. The surface hydrogen content on the MH electrode does depend on the particle size of the alloy, as depicted in Eq. (17). A larger particle size like 10 mm will result in a weaker chemical potential field than a smaller particle size such as 1– 3 mm, under a constant current charging regime, thus reduce the hydrogen diffusion flux in the bulk of the MH and lead to increased surface hydrogen content, which would have a negative effect on rapid charge. Depending on the actual chemical diffusivity of hydrogen at each composition, there is a corresponding diffusion length that can effectively remove hydrogen from the surface. When the particle size is much larger than the diffusion length, the MH’s ability to receive charge (or its ‘rechargeability’) will be compromised. Under a 1C rate charge, Fig. 9 shows that when the particle size changed from 10 to 5 mm and 1 mm, the MH ‘rechargeability’ can be enhanced from 18% SOC return (from 0%) to 73% and over 96%, respectively. The temperature variation in the cell during charging and discharging and its influence on the pressure profile and charging behavior is of concern, of course. In our experimental setup we placed one of the temperature probes on the metal surface of the canister very close to the terminal of the MH electrode. Because of good thermal conductivity at the contact, the measured temperature was supposed to be closely related to the internal temperature of the MH. However, due to limited access to the cell interior, we could not determine if there was any significant deviation from the above assumption. Although the MH will give off more gaseous hydrogen upon a noticeable temperature rise leading to an accelerated pressure buildup, our excellent correlation of the experimental charge time with the calculated duration of which the maximum hydrogen

content would be reached (under a constant temperature condition) seems to suggest that such a temperature deviation is quite likely negligible. This is also consistent with our observation of very minimal temperature excursions in the experiment under various charging conditions (e.g. about 10–12 °C rise at 3C rate); therefore the temperature effect on our estimation is small if not negligible.

5. Conclusion We have demonstrated that the commercial NiMH traction batteries can be rapidly recharged at high rates. The termination is best controlled by a pressure cut-off

Fig. 9. Calculated relative surface hydrogen content as a function of particle size of the MH alloy under 1C charge and with a chemical diffusion coefficient of 2 ×10 − 15 m2/s. The smaller the particle size, the slower the hydrogen surface concentration buildup. The longer the charge time, the better the charge return.

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approach. The capacity return and terminal SOC depend on the charge rate and the initial SOC. Further analysis shows that the solid-state hydrogen diffusion in MH is the limiting step in determining the capacity return and charge efficiency. The charge time determined by the pressure cut-off is associated with the duration of which the surface hydrogen content on the MH reaches the maximum. There are two possible methods to improve ‘rechargeability’ of the battery: one by enhancing the chemical diffusion of hydrogen in MH and the other by reducing the particle size.

Acknowledgements The authors would like to thank the Defense Advanced Research Projects Agency (DARPA) and the US Department of Transportation Advanced Vehicle Technology Program in supporting this work under the Federal Cooperative Agreement MDA972-95-0009 through the Hawaii Electric Vehicle Demonstration Project (HEVDP) administrated under the High Technology Development Corporation. We are also indebt to Dr Dennis Corrigan of Ovonic Battery Company

who provided the test cells and other technical assistance. References [1] W.B. Gu, C.Y. Wang, S.M. Li, M.M. Geng, B.Y. Liaw, Electrochim. Acta 44 (1999) 4525. [2] W.B. Gu, C.Y. Wang, B.Y. Liaw, J. Electrochem. Soc. 145 (1998) 3418. [3] W.B. Gu, C.Y. Wang, B.Y. Liaw, J. Power Sources 75 (1998) 151. [4] X.G. Yang, B.Y. Liaw, J. Power Sources 101 (2001) 158. [5] P.L. Bourgault, B.E. Conway, Can. J. Chem. 37 (1959) 292. [6] K.P. Ta, J. Newman, J. Electrochem. Soc. 146 (1999) 2769. [7] X.G. Yang, G.L. Tan, X.B. Zhang, K.Y. Shu, Q.A. Zhang, X.J. Wu, Y.Q. Lei, Q.D. Wang, Mater. Chem. Phys. 61 (1999) 130. [8] X.G. Yang, W.K. Zhang, Y.Q. Lei, Q.D. Wang, J. Electrochem. Soc. 146 (1999) 1245. [9] H. Inoue, K. Yamataka, Y. Fukumoto, C. Iwakura, J. Electrochem. Soc. 143 (1996) 2527. [10] J. Crank, The Mathematics of Diffusion, Oxford Press, London, 1957. [11] E. Wicke, H. Brodowski, Topics in applied physics, in: G. Alefeld, J. Volkl (Eds.), Hydrogen in Metals II, vol. 29, Springer-Verlag, New York, 1978, p. 148. [12] S.W. Feldberg, J.J. Reilly, J. Electrochem. Soc. 14 (1997) 4260. [13] X.G. Yang, B.Y. Liaw, J. Power Sources 102 (2001) 186.