Electrochimlca Acta, 1963, Vol. 8, pp. 693 to 702. Pergamon Press Ltd. Printed in Northern Ireland

T H E D I S C H A R G E C H A R A C T E R I S T I C S O F L E A D - A C I D B A T T E R Y P L A T E S *

M. I. GILLIBRAND and G. R. LOMAX Chloride Technical Service Ltd., Clifton Swinton, Manchester, England

Abstract--An apparatus was developed whereby a single battery plate could be discharged at high rates out of the environment of the accumulator. During the discharge the transient potential of the plate was measured continuously to an accuracy of 0.01 V. The results showed that the capacity of a plate was related exponentially to the current density of discharge. The discharge characteristics are discussed in terms of activation and concentration overpotentials.

R~sum~-Description d'un appareil permettant la d~charge d'un plaque unique hors de l'enceinte d'un accumulateur. Durant cette d6charge, le potentiel transitoire de la plaque a pue 6tre mesur6 continuement avec une pr6cision de 0,01 V. Les r6sultats montrent que la capacit6 de la plaque se relie exponentiellement/t la densit6 du courant de de d6charche. Les caracteristiques de la d6charge sont discut6s en termes de surtensions d'activitation et de concentration.

Zusammenfassung--Es wurde eine Anordnung entwickelt, welche gestattet, die Entladung einer Blei-Akkumulatorplatte mit hohen Str6men ausserhalb eines Akkumulators vorzunehmen, lrn Laufe der Entladung wurde das instationare Potential der Platte kontinuierlich mit einer Genauigkeit von 0,01 Volt gemessen. Die Resultate ergaben, dass die Kapazitfit einer Platte exponentieU mit der Entladungsstromst/irke verkniipft ist. Die Charakteristiken des Entladungsvorganges werden auf Grund von Aktivierungs- und Konzentrationsiiberspannung diskutiert.

I N T R O D U C T I O N

THE traditional method of measuring the capacity of an accumulator plate was to place it between two auxiliary plates of similar capacity and opposite polarity and measure the voltage across the cell during the discharge. Although this method gave some indication of the capacity of the plate it gave very little additional information, par- ticularly at high rates of discharge. It was assumed that the two auxiliary plates had a much greater total capacity than the test plate and that their potentials did not vary appreciably during the course of the discharge. The potential of the auxiliary plates, and the voltage drop across the electrolyte, were not known and consequently the discharge potential of the plate could not be calculated with any degree of accuracy.

To determine the discharge characteristics of a plate it was necessary to measure the potential independently of the auxiliary electrodes and the voltage drop in the electrolyte. An apparatus was constructed to measure this potential and consistent results accurate to 0"005 V were obtained.

E X P E R I M E N T A L The discharge cell

The cell (Fig. 1) consisted of a box (A) constructed in Perspex (I.C.I. Ltd) and containing the pure lead auxiliary electrodes (B). The experimental plate (C) was held in position in a porous pot (D) by a perspex jig (E). The cell contained 6-00 M

* Manuscript received 28 February 1963.

693

694 M.I. GILLIBRAND and G. R. LOMAX

sulphuric acid, the concentration commonly used in accumulators. During a discharge the current passing through the cell heated the electrolyte but the temperature of the acid in the porous pot was maintained constant at 21°C by a supply of cold acid on to the stirrer (F) through the tube (G). The level of the acid was maintained by the outlet tube (H).

FIG. 1. The discharge cell.

The cold acid used to cool the cell was stored in a lagged aspirator. Solid carbon dioxide was added to the acid until its temperature fell to -- 50°C. The flow of cold acid was controlled by means of a screw clip on a piece of rubber tubing which remained slightly flexible at this temperature. It was possible to keep the temperature of the cell constant to -± I°C by careful manipulation of the clip.

A Luggin capillary (I) was held against the plate at the intersection of its diagonals by the resilience of the rubber bung in which it was mounted. An electrolyte bridge containing 6.00 M sulphuric acid joined the Luggin capillary to a mercurous sulphate reference electrode also containing 6.00 M sulphuric acid. The potential of the refer- ence electrode when measured against a normal hydrogen electrode was 0.601 V and all potentials were expressed with respect to the normal hydrogen scale. The potential of the reference electrode was confirmed by calculation using the data reported by Harned and Hamer 1 for the thermodynamic properties of sulphuric acid. Assuming that the activity coefficient of the sulphate ion was equal to the mean activity coefficient of sulphuric acid the calculated potential was 0.6115 V.

The discharge circuit ~s shown in Fig. 2. The p.d. between the plate in the discharge cell (J) and the reference electrode (K) was measured by the valve voltmeter (L). The discharge cell was connected to a reversing switch (M) so that the current could be passed in either direction depending upon whether negative plates or positive plates

The discharge characteristics of lead-acid battery plates 695

were being discharged. The current was obtained from a high capacity lead acid battery (360 Ah., 12 V) (N) and controlled by a carbon-pile variable resistor (O). The value of the current was shown by the ammeter (P).

FIG. 2. The discharge circuit.

The valve voltmeter

To observe the rapid changes in potential a direct reading valve voltmeter was required. For accurate measurements a large input impedance was necessary, and details of the circuit can be seen in Fig. 3. The potential was applied across the grid of V 1 and the virtual earth of the system, the junction of R 5 and R 6. The degree of

I•24T ~-~I 3 4 V2

4 S1 I R1

FIG. 3. The valve voltmeter M 120/~A meter V,, V2 Brimar 3V4 $1 3-pole, 4-way switch $2 2-pole, 1-way switch C Standard Master Cell, 1.020 V

, I ,

t t R4

R1, R~-6.8 ohm., 3 W R3, R4-15 K ohm., 3 W Rs, R6-1 K ohm., 0.5 W VR1-240-ohm potentiometer VR~-10-K ohm potentiometer

l : 120V.

unbalance of the cathode followers V 1 and V 2 was measured on a Cambridge "Uni- pivot" microammeter. The instrument was balanced with the switch Sa in position 2, when the grid of the valve Va was connected to the virtual earth. The potentiometer VR 1 was adjusted until the deflection on the microammeter was zero. To standardize the instrument the switch $1 was turned to position. 1 which connected the standard

696 M.I. GILLIBRAND and G. R. LOMAX

Weston Cell across the input. With the switch in this position the pre-set variable resistance was adjusted until the reading on the ammeter was 1"020. The potential of the external source was the reading when the switch S 1 was in position 3. The in- strument was calibrated against a substandard voltmeter and was found to be accurate to 0.005 V over its entire scale. With the switch $1 in position 3 the full scale deflection was 1-200 V and by switching to position 4 the standard cell was placed in series with the input voltage, extending the range to 2-220 V.

Discharge of the plates Fifteen positive and fifteen negative battery plates (14 x 12 × 0-2 cm) were made

under identical conditions, care being taken to ensure that each plate contained the same weight of active material distributed evenly over its surface.

The main electrical connection to the plate (Fig. 4) was made through the lug (P)

\ m

FIG. 4. A battery plate showing electrical connections.

and as this carried a substantial current there was appreciable potential drop along its length. To avoid this potential drop being included in the measured potential of the plate, the connection to the valve voltmeter was made through a subsidiary lug (Q). This second lug was formed by welding a lead strip to the frame of the plate about 3 cm from the edge furthest away from the main lug. The plates were charged in sulphuric acid (6"00 M) at room temperature for 24 hr to ensure that they were in the fully charged state. The charging current was 0-5 A for each plate.

Before discharge, a plate was transferred as quickly as possible from the charging tank to the discharge cell (Fig. 1). It was allowed to soak for half an hour and then discharged at a constant current. The potential of the plate was recorded at regular intervals. Three negative plates and three positive plates were discharged at each o f the currents 10, 20, 40, 70 and 100 A.

RESULTS

By using the technique described above very reproducible results were obtained with different plates and typical results for three positive plates are given in Table 1. Table 2 gives corresponding results for three different negative plates.

The discharge characteristics of lead-acid battery plates

TABLE l. DISCHARGE POTENTIALS OF POSITIVE PLATES AT 40 A AND 21°C

Potential (normal hydrogen scale) Time Plate No. 1 Plate No. 2 Plate No. 3 (min) (V) (V) (V)

Open circuit 1.740 1.730 1.740 0.1 1.660 1.665 1-670 0.5 1.675 1.680 1.680 1-0 1.680 1 "680 1-680 2.0 1-675 1.680 1.680 3.0 1.675 1.675 1.675 4.0 1-670 1.670 1.670 5.0 1.660 1.665 ! -665 6.0 1-650 1.655 1.655 7.0 1-630 1.630 1.630 7.5 1.600 1.600 1.560 7-9 - - - - ! -200 8.0 1.420 1-200 -- 8.1 1.200 - - - -

697

TABLE 2. DISCHARGE POTENTIALS OF NEGATIVE PLATES AT 40 A AND 21°C

Potential (normal hydrogen scale) Time Plate No. 1 Plate No. 2 Plate No. (min) V V V

Open circuit ~0 .360 --0.355 --0.335 0.1 --0.340 -- 0-335 --0-335 0.5 --0.340 --0.335 --0-335 1.0 - 0.340 --0-335 --0-335 2.0 --0.340 --0-335 --0.335 3.0 --0.335 --0-335 --0.335 4-0 --0.335 -0.335 --0.335 5.0 --0-335 --0.335 --0.335 6.0 --0.335 --0.335 --0.335 7.0 --0.325 --0.325 --0.325 8.0 --0-325 --0.325 --0.320 9.0 --0.310 --0-315 --0-305 9"5 0.280 - - --0.275 9"7 --0"000 - - --0-000

10-0 - - --0"245 - - 10"1 - - 0.000 - -

S i m i l a r r e su l t s we re o b t a i n e d f o r t h r e e i n d e p e n d e n t p l a t e s a t t he o t h e r c u r r e n t s .

T h e a v e r a g e v a l u e s f o r t he se r e su l t s a re g i v e n g r a p h i c a l l y in Fig. 5 w h e r e t he p o t e n t i a l s

o f t he pos i t i ve p l a t e s a re g iven in t he t o p h a l f o f t he f igure a n d t he c o r r e s p o n d i n g

g r a p h s fo r t he n e g a t i v e p l a t e s in t he l o w e r ha l f . A l t h o u g h t h e n u m e r i c a l va lues d i f fe red ,

t h e g e n e r a l s h a p e o f t he g r a p h s we re t he s a m e fo r b o t h e l e c t r o d e s a t al l c u r r e n t s .

W h e n t h e c u r r e n t was s w i t c h e d on , t he p o t e n t i a l o f t he e l e c t r o d e c h a n g e d r a p i d l y f r o m

the o p e n c i r cu i t v a l u e to a r e l a t ive ly s t ab l e p o l a r i z a t i o n p o t e n t i a l r e p r e s e n t e d b y t he

f la t i n t e r m e d i a t e s ec t i on o f the cu rves . T h i s s t e a d y p o l a r i z a t i o n was a t t a i n e d a f t e r

a b o u t 5 sec f r o m s w i t c h i n g o n a n d l a s t ed f o r m o s t o f t h e d i s c h a r g e t ime . F o l l o w i n g

th i s p e r i o d t h e r e was a r a p i d i n c r e a s e in t he p o l a r i z a t i o n , g e n e r a l l y k n o w n as t h e " k n e e "

698 M. L GILLIBRAND and G. R. LOMAX

of the curve. These characteristics were similar to those obtained when complete batteries are discharged ~. Normal ly batteries are discharged to a voltage just past the knee o f the curve 2. It was desirable to adopt final voltages for the termination o f the

1,8

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1,4

o t-2 o_

"6 E_ 0

- 0 ' 2

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I 5

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Positive ptote /

o

• IOA o 2 0 A n 4 0 A x T O A

IOOA

Negative plate

° m ° ~ ° j I I ~ L

40 60

Time, min

FIG. 5. D i s c h a r g e charac te r i s t i cs .

discharge o f single plates on a similar basis. Consequently a potential o f --0.25 V for negative plates and 1-60 V for positive plates was considered as the end o f the useful discharge at all currents. Thus the general characteristic o f the discharge can be

TABLE 3. DISCHARGE PARAMETERS AT 2 1 ° C

Discharge current Discharge potential Duration Plate A V rain

Positive 10 1-690 52.3 20 1.683 19-5 40 1.665 8.0 70 1-650 3.98

100 1.635 2-50 Negative 10 --0.345 71"0

20 --0.345 26.6 40 --0-335 9.87 70 --0.330 4.97

100 --0.325 3.10

defined by the value o f the steady potential during discharge and the discharge dur- ation. The values of these parameters at various currents are given in Table 3. Each o f these results is the average o f three independent experiments in which the maximum variation o f the potentials was ~-5 mV and of the durations was ~:3 per cent.

The discharge characteristics of lead-acid battery plates 699

DISCUSSION Reproducibility of results

The causes of the variable results obtained in the initial experiments were investi- gated. Gas, either hydrogen or oxygen, depending on the polarity of the plate being discharged, was evolved in large quantities at the auxiliary electrodes. This gas formed a suspension in the electrolyte which migrated rapidly to the discharging plate. There it caused variable boundary conditions on the electrode surface and could react electro- chemically with the plate material. Stable conditions in the electrolyte in the vicinity of the plate were obtained by surrounding it with a porous pot. The temperature of the electrolyte during the discharge was another variable. In particular the tempera- ture, which was adjusted to 21°C at the beginning of the experiment, increased rapidly during the discharge at the highest current densities. Stable temperature conditions were obtained by the arrangement in which cold acid was fed into the cell and the supply could be adjusted according to the conditions of discharge.

The discharge current was carried by the conducting grid members and main lug of the plate. The design of plates is such that the ohmic resistance of this path is a minimum. However, at the larger currents used in our experiments an appreciable voltage drop would be produced. In early experiments this voltage drop was included in the measured potential when the connection to the valve voltmeter was made to the main plate lug which was also carrying the discharge current. However, the contri- bution of the ohmic voltage drop due to the discharge current to the observed potentials was reduced to a minimum by the provision of the special lug on the plate for the connection to the valve voltmeter (Fig. 4).

The position of the Luggin capillary had a marked effect oll the measured potential. When the capillary was moved to the periphery of the plate, the potential appeared to fall and the readings became less reproducible. Consistent results were obtained when the capillary was positioned at the mid-point of the plate. It was found that forcing the capillary into the porous interior of the plate gave no change in the measured potential, thus indicating that the voltage drop due to the resistance of the electrolyte in the pores was not appreciable when compared with the total polarization.

Discharge characteristics The overall reactions which occurred during discharge of each type of plate can be

represented by the following general equations:

Positive plate 2e + PbO2 + 4H + + SO42- -~ PbSO~ + 2H20 (1)

Negative plate Pb + SO42- -+ PbSO 4 + 2e. (2)

The discharge curves for both plates (Fig. 5) are composed of two parts, a more or less horizontal portion at the beginning of the discharge, followed by increasing polarization which becomes larger as the discharge progresses, until finally the potential/time curve becomes almost vertical. The difference between the open circuit potential of the electrode and the flat section of the curve is probably the activation overpotential for the corresponding reaction quoted above. As expected, the positive discharge, involving two ionic species exhibits greater overpotentials than the negative electrode.

The rapid change of plate potential at the end of the discharge could be accounted

700 M.I. GILLIBRAND and G. R. LOMAX

for either by postulating that the active material of the plate is covered by a non- conducting layer of lead sulphate or that it is caused by changes in the concentration of the sulphate ions at the surface of the electrode. If the polarization of the plate is due to the formation of a non-conducting layer of lead sulphate, the capacity of the plate would be independent of the discharge rate, for the time taken to cover the surface of the plate with a layer of lead sulphate should have no bearing on its ultimate capacity. Furthermore the conception of a sulphate layer would not explain why, after a high rate discharge, further capacity was available if the plate was allowed to rest. It appears that, in addition to the polarization resulting from the formation of the non-conducting lead sulphate, the rapid changes in potential at the end of the discharge are caused by changes in concentration of the acid at the electrode surface. For example, the potential of the negative plate during the discharge is the sum of the equilibrium potential in the concentration of sulphate ions at the surface of the plate and the activation overpotential for the reaction

R T E = E o -- ~-ff In (SO42-) + ~7, (3)

where E = the potential of the electrode, E o = the molar potential of the lead sulphate electrode and

= the activation overpotential. Thus the potential of the electrode is a function of the logarithm of the sulphate activity in the electrolyte at the surface of the plate. As the electrode reaction is taking place at constant current, the rate of removal of sulphate ions from the elec- trolyte is constant. Initially the concentration of the sulphate ions at the surface and in the interior of the porous plate is that of the bulk of the electrolyte. As the reaction progresses, the sulphate ions at the electrode interface will be removed at a greater rate than they could diffuse from the body of the electrolyte. In the case of porous electrodes the bulk of the surface is in the interior of the plate and consequently tends to be inaccessible to diffusing ions. When the concentration at the surface is large a small decrease in concentration in a given time has very little effect on the logarithmic term but at low concentrations the same decrease in concentration produces a larger change in the logarithm and hence the sharp decrease in the potential of the plate. When most of the available sulphate ions in the body of the plate have been removed, the rate of removal of ions at the outer surface will increase. In effect this is equiv- alent to an increased current density at the outer surfaces of the electrode and this in turn will increase the activation overpotential and also lead to a rapid exhaustion of sulphate ions at those surfaces. Once the sulphate ions in the body of the plate have been removed the passivation would rapidly spread to the outer surface and the increase in the overpotential would be cumulative.

Willihnganz 3 has shown that when a negative plate is discharged at a high rate the resistance of the plate increases sharply at the polarization point and falls to nearly its original value when the current is switched off. As this resistance effect is not perma- nent it cannot be due to lead sulphate and it was suggested that it is due to a decrease in the concentration of the electrolyte in the immediate vicinity of the plate. These conclusions are in agreement with the explanation which we have suggested for the discharge characteristics of a plate.

The discharge characteristics of lead-acid battery plates 701

The results given in Table 3 showed that the discharge duration decreases rapidly as the discharge current is increased. The logarithm of the discharge time was plotted against the logarithm of the discharge current and the straight lines shown in Fig. 6 were obtained. They are represented by the equation

K t - - I " ' (4)

where t = discharge duration (rain) I = discharge current (A) n = 1.39 K = a constant equal to 0.42 for negative plates and 0-35 for positive plates.

Muller and Machu 4 obtained a similar relationship for the passivation of smooth lead

2"0

c. I-5

Q; E

1.0

0 . 5

F I G . 6.

o Positive plates \ c] Negative plates

I ~ [ i ! N ] 1.0 f'5 2.0

log current, A

The relationship between polarization time and current.

surfaces in sulphuric acid at constant potential. Their results at current densities less than 0-03 A/cm 2 were represented by the equation when I was the initial current density and n and Kequal to 0.87 and 0-17 respectively. At larger current densities the values of n and K were 1-62 and 0-04 respectively. The passivation of lead sheets in sulphuric acid at a constant current density was also studied by Feitknecht and Gaumann 5 and their results agreed with an equation of the same type in which K was 0.37 and n was 0-95.

Peukert ~ has reported that the discharge performances of a lead acid battery can be represented by equation (4) in which n is equal to about 1"3. Consideration of our

702 M.I. G1LLIBRAND and G. R. LOMAX

results on the performance of single plates shows that they are compatible with Peukert 's results. The discharge durat ion o f a multi-plate cell at a constant current is not the mean of the performance of the negative plates and positive plates but is the same as the duration o f the plates with the lower capacity. Usually, the temperature o f operat ion will determine which of the plate groups limits the discharge. For ins tance at reduced temperatures the discharge duration o f the negative plates will be less than that o f the positive plates. In this case the form of the Peukert equation which will be obtained for the complete cell will be identical to equation (4) obtained for the negative plates at that temperature. Such considerations show that our results for single plates are the basis o f the Peukert relationship for complete cells or batteries.

Acknowledgement--The authors wish to thank Dr. M. Barak for helpful advice during the course of this work.

R E F E R E N C E S 1. H. S. HARNED and W. J. HAMER, J. Amer. Chem. Soc. 57, 27 (1955). 2. G. W. VINAL, Storage Batteries, Wiley, New York, p. 196 (1952). 3. E. WILLIHNGANZ, Trans. Electrochem. Soc. 79, 243 0941). 4. W. J. MULLER and W. MACHU, Monatsh.fiir Chemic 63, 347 0933). 5. W. FEITKNECHT and A. GAUMANN, J. Chim. Phys. 49, 135 0952). 6. W. PEUKERT, Elektrotech. Zeit. 18, 287 (1897).