Transport in membrane fuel cells

Transport in membrane fuel cells

Electrochimica Acta, 1971, Vol. 16, pp. 1577 to 1591. Pcrgamon Press. Printed jn Northern Ireland TRANSPORT IN MEMBRANE FUEL CELLS* F. R. FouLic...

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Electrochimica Acta, 1971, Vol. 16, pp. 1577 to 1591. Pcrgamon Press. Printed jn Northern Ireland

TRANSPORT

IN

MEMBRANE

FUEL

CELLS*

F. R. FouLicEs? and W. F. GRAYDON Department of Chemical Engineering and Applied Chemistry, University of Toronto, Toronto, Canada Abstract-The discharge characteristics of a hydrogen-oxygen ion-exchange-membrane fuel cell employing platinized screen electrodes and polystyrenesulphonic acid ion-exchange membranes of the homogeneous type were investigated at 0 and 50 psig. In ail cases an increase in the total gas pressure significantly improved the voltage/current characteristics of the cell. Discharge was generally found to be controlled by the internal resistance of the cell, and the effects on the cell internal resistance of catalyst loading, unbound acid, membrane surface-sulphonation, electrode mesh, membrane thickness, membrane capacity and membrane cross-linking were determined. The internal resistance was found to be comprised of two parts--the resistance of the membrane and a contact resistance between the membrane and the electrodes. The resistance of the membrane is controlled by the rate of diffusion of hydrogen ion through the membrane. Cells were operated for as long as 500 h with no deterioration in steady-state discharge. R&m&--Etude, B 0 psig et 50 psig, des caract&istiques de dkcharge d’une pile A combustible & membrane Bchangeuse d’ions hydroghne-oxygkne, en utilisant des 6lectrodes 2t cribles platin&s et des membranes Bchangeuses d’ions en polystyrl?ne-acide sulfonique de type [email protected] Dans tous les cas un accroisscment de la pression totale gazeuse amtliore notablement les caract6ristiques courant-tension de la cellule. La dbcharge a g&&alement et& reconnue contr616e par la r&istance interne de la cellule et on a d&ermine les influences sur Ia resistance interne de la ceIlule de la teneur en catalyseur, de l’acidit6 libre, de la sulfonation de la membrane supeticielle, de la trame de l’electrode, de l’epaisseur de la membrane, de sa capacit6 et de ses liaisons transversales. La resistance interne a Bt6 trouvke &tre composCe de deux parts: la rtsistance de la membrane et une r6sistance de contact entre la membrane et les 6lectrodes. La rksistance de la membrane est contrbl& par la vitesse de diffusion de l’ion hydrogbne & travers la membrane. Ces piles ont fonctionnd jusqu’k 500 h. sans aucune alteration de leur &at stationnaire de dkcharge. Zusammenfassung-Die Entladungscharakteristiken einer Wasserstoff/Sauerstoff-Brennstoffzelle mit Ionentauschermembran wurde zwischen 0 und 50 psig untersucht. Als Elektroden wurden platinierte Netze, als Membranen Polystyrolsulfonslure-Ionentauscher des homogenen Typs verwendet. In allen Fallen wurde die Strom/Spannungscharakteristik der Zelle durch eine Erh6hung des totalen Gasdruckes erheblich verbessert. Die Entladung war allgemein durch den innem Widerstand der Zelle kontrolliert. Die Einfliisse auf den innern Widerstand, wie Beladung des Katalysators, freie SBure, Oberfl3chensulfonierung der Membran, Maschenweite der Elektroden sowie Dicke, Kapazitlt und Vernetzung der Membranen, wurden untersucht. Der innere Widerstand seizt sich aus zwei Teilen zusammen, einem Membran-Widerstand und einem Kontaktwiderstand zwischen der Membran und den Elektroden. Die Diffusionsgeschwindigkeit der Wasserstoflionen durch die Membran kontrolliert deren Widerstand. Die Zellen wurden bis zu 500 Stunden betrieben, ohne dass sich bei der stationgren Entladung eine Verschlechterung zeigte. INTRODUCTION

membranes (IEM) prepared by the bulk co-polymerization of the of p-styrenesulphonic acid with styrene and divinylbenzene and subsequent hydrolysis to produce polystyrenesulphonic acid (pssa) are undoubtedly more homogeneous than commercial membranes of the pssa-polyethylene or pssasince the chemical, physical and transport polyfluoroethylene types. Furthermore, properties of these membranes are well understood, having been extensively studied and reported in the literature, l-l1 they ate ideally adapted to an analytical study of the ION-EXCHANGE

n-propyl

ester

* Manuscript received 12 November 1969. t Present address: Huron Chemicals, Ltd., 889 Kipling Ave., Toronto, Ontario, Canada. 1577

1578

F. R. FOUL-

and W. F. GRAYDON

operational behaviour of the IEM fuel cell. In this report, the discharge characteristics of an IEM fuel cell have been reported in terms of the properties of the membranes. EXPERIMENTAL

TECHNIQUE

Membranes

The n-propyl ester of p-styrenesulphonic acid was prepared as described previously.l* The membranes were cast between glass plates and polymerized for 3+l h at IlO”C. This was followed by removal from the plates by immersion in boiling de-ionized water and subsequent hydrolysis for 48 h in 5 % ethanolic potassium hydroxide solution at reflux temperature. Electrodes

Electrode preparation was as follows. A 1.5 in square piece of platinum gauze was cleaned for 2 min in boiling dilute aqua regia (5 ml cone HNO, + 15 ml cone HCI + 50 ml distilled water), rinsed 5 times in distilled water and transferred to a cell containing 65 ml of a platinizing solution consisting of chloroplatinic acid (3 g Pt/l) and a trace of lead acetate (0.0063 g Pb/l). Pt black was electrodeposited at 75 mA and about 2 V for 9 min. The freshly platinized electrode was then rinsed 5 times in distilled water and placed in 150 ml of aqueous 10 % H,SO, and alternately anodized and cathodized for a total of 15 min at 75 mA with current reversals every 15 s, ending on an anodic cycle for an oxygen electrode and a cathodic cycle for a hydrogen electrode. The electrode was then washed in distilled water, blotted and placed in the fuel cell. Fuel-cell runs

The experimental fuel-cell assembly, described eIsewhere,12 employed a membrane that had been pre-equilibrated in either 8 N H,S04 or distilled water and surface blotted prior to a run. Polarization data were obtained as follows: The external resistance, R,, was set,* the open circuit voltage recorded and the circuit closed. Voltage and current, which became steady after about I.5 min, were recorded after 2 min and the circuit opened. R, was changed to a new value (selected at random from amongst the 23 resistances used), the open-circuit voltage recorded and the circuit closed again. Apparent cds were based on the geometrical membrane area exposed to the reactant gases (10 cm2). RESULTS

AND

DISCUSSION

Life tests

Two cells employing leached membranes? were allowed to discharge for extended lengths of time through external resistances of 823 and 9-5 C! respectively_ The discharge was occasionally interrupted to obtain polarization data. Figure 1 shows the variation of cd and cell voltage with time and Figs. 2 and 3 show the variation of cell polarization with time. For the low-discharge case (Fig. 2) it can be seen that cell discharge was initially controlled by internal-resistance (R,). However, by 44 h a limiting diffusion current began to develop, becoming most severe after 118 h. Beyond this time it gradually l There were 23 values, ranging from 0.7 to 99,000 n. t l-50 meq/gdry H+ form, 6 mol % DVB, 11-O mol H,O/eq, O-0381 cm thick.

Transport in membrane fuel cefls

1579

0.8 0.6

0

100

200

300

Time,

400

500

h

FIG. 1. Variation of cell cd and voltage with time. 45-mesh screen, O-2 mg Pt black/cma. Membrane: leached, l-50 meqlg, 6% DVB, O-0381 cm thick. 0, discharge through an 823 fi resistor; A, discharge through a 9.5 R resistor.

25°C.

0 psig.

0.8

0.8

0

0.8

0

0

0.8

0.8 0.4 n

-0123012301234

01234012345

mA/cm’

mA/cm’

FIG. 2. Variation of cell polarization with time. Discharge through an 823 !LIresistor.

FIG. 3. Variation of cell polarization with time. Discharge through a 9.5 fi resistor.

disappeared until by 352 h discharge was once more &-controlled. Throughout the run the cell R, remained approximately constant at 25 Sk When the cell was disassembled at the termination of the run the usual water mist was observed on the oxygen

side of the membrane

but no flooding

was present.

The high-discharge cell (Fig. 3) was also initially &-controlled, but by as early as 27 h began to exhibit a limiting diffusion current which became progressively more severe until about 92 h, beyond which time it remained steady at about 1.5 mA/cm2. R1 also increased, reaching a maximum, steady value of about 40 Q by 140 h.

1580

F. R. FOULKES and W. F. GRAYDON

Disassembly of the cell revealed that the hydrogen side of the membrane was apparently bone-dry while the oxygen side was completely flooded. After the current has flowed through a cell for some time both reaction water and transported water begin to accumulate on the oxygen side. Membrane watertransport can occur via electro-osmosis, hydraulic permeation, water vapour permeation and bulk diffusion through the pores. It has been shown that electro-osmosis accounts for most of the water transported,s*ls and that except at very low current densities, this transport can not be offset by the application of pressure and relative humidity gradients favouring water transport in the opposite direction. As water is transported towards the oxygen side of the membrane the hydrogen side becomes drier. Tombalakian at aL4 have shown that electro-osmotic water transport decreases as membrane water-content decreases, and that the drier face of the membrane controls the electro-osmotic water transport. Therefore, as the hydrogen side becomes drier the water-transport rate decreases until a steady state is attained at which a further decrease (caused by further drying of the hydrogen side) in the electro-osmotic water-transport rate is prevented by the back diffusion of water. Since this in turn reaches a limiting value corresponding to flooding at the oxygen side, the hydrogen side of the membrane will be drier when larger currents flow, for larger currents cause greater amounts of water to be transported. 4 Therefore, since the steady-state current flow in the high-discharge cell was more than ten times that of the lowdischarge cell, membrane dehydration at the hydrogen side was more severe in this cell. Any dehydration of the membrane face is rather serious since a liquid film is relied upon to make contact between the eIectrocatalyst and the membrane, it having been determined from micrographs that no significant interpenetration occurs between catalyst and membrane.14 In the absence of a free electrolyte solution film on the membrane surface, the actual area of the membrane used for ionic conduction is restricted to a very narrow region surrounding the areas of contact between the electrode screens and the membrane.l” In fact, from measurements of screen imprints made in the membranes it has been calculated that in these cells only about O-016 cm2 per cm2 of membrane was actualy contacted by the catalyst. Using 50 52 cm as the specific resistivity of the (water saturated) membrane, 5 the resistance of the membrane in the cell should be about (50 Cl cm)(Oa0381 cm)/[(O*Ol6 cm2/cm2)(10 cm”)] = 11.9 !X This value is compatible with the observed values of 25 and 40 0 for the low and high discharge cell, respectively, since varying degrees of dehydration (and hence reduced contact area) were present at the hydrogen side face of the membrane in each cell. Assuming the observed cell resistances were due mostly to the membrane,ls the effective membrane areas in the low and high discharge cell are readily calculated to be O-0395 and 0.0246 cm2 respectively. This means the respective true steady state cds (assuming unidirectional ionic migration through the membrane) were about 13 and 230 mA/cmZ at O-81 and 0.12 V, an indication that this type of membrane is potentially very good for fuel-celI use. Although the amount of water transported per faraday is somewhat lower at high than at low cd, 4,17it can reasonably be assumed that the total rate of water accumulation (transport + reaction) was at least five times greater for the highdischarge cell than for the low-discharge cell. The transient limiting diffusion current

Transport in membrane fuel cells

1581

observed in the low-discharge

cell probably resulted from a gradual water film build-up on the oxygen side of the membrane, which was eventually able to level off to an acceptable, non-limiting value. However, in the high-discharge cell water accumulated so fast that the oxygen electrode became permanently flooded and cell discharge was controlled by the diffusion of oxygen through the water film to the electrode. A simple limiting-diffusion-current calculation* readily substantiates this. One advantage of operating in the absence of free electrolyte is that the active sites of the electrodes, and especially those of the oxygen electrode, remain relatively free from the absorptive blockage which is sometimes observed in the presence of sulphuric acid .ls The constancy of the cell open-circuit voltages (Figs. 2 and 3) indicates that the oxygen electrode, which is a mixed electrode,12 remained relatively free from absorptive poisoning. Although slight reductions in the specific surface areas of electrodeposited platinum blacks over great lengths of time have been reported, l9 these are probably not important with regard to IEM fuel cells since the catalytic activity of platinum black is believed to be restricted only to the exterior surface of the cata1yst,20 and therefore would not be strongly affected by any slight relaxation of its internal structure. Furthermore, no significant degradation of the membrane should be expected since pssa has been shown to be very resistant to hydrolysis.13 No losses in membrane ion-exchange capacity have ever been detected in the course of this work. There appears to be no reason why these cells cannot operate for very long periods of time. Catalyst loading and pressurization Greater loadings of electrodeposited platinum black should result in larger screen surface areas and hence better contact (ie more utilized membrane area) between the membrane and catalyst. Figure 4 shows the effect of catalyst loading on cell discharge.

O-8 > 0.6

mA/cme FIG. 4. EfYect of catalyst loading on cell polarization. 25°C. 45-mesh screen. Membranes: leached, l-50 meqlg. 6% DVB, 0.0381 cm thick. Platinum black loadings, m&mP: l O(shiny screen); a, O-26, I, l-01 ; 0, 3-21; A, 7.06; 0, 16.0. * Assuming a diffusion area of 10 cm% and film thickness equal to that of the platinum screen.

F. R. FOULKEISand W. F. GRAYDON

1582

The relationship between the cell internal resistance and the various electrochemical parameters has been shown to bela R,=_---__ d&u d1

RT

RT

BcWI

RT

&F&A,

-

nF(A&,

RT -

0 -

nF(A,i,,,

-

I) ’

(1)

where Ri is the cell internal resistance in a, I the cell current in A, B;1 the transfer coefficient, I the number of electrons transferred in the rate-controlling step of the activation, A the electrode area in cm2, iL the limiting cd in A/cm2, i. the exchange cd in A/cm2 ; “a” and “c” refer to the anode and cathode respectively and R, T and F have their usual meanings. By making the usual assumptions that fl,& = O-5, L, = J., = 1, and that concentration polarization, if present, is much more severe at one electrode than the other, then at 25°C (1) becomes Ri _

d&.;,,,

0*01;136 _ 0:025JS _ l0.a

a

O-01284 (AiL -

I) _

(2)

Since it is known that the hydrogen electrodes in these cells exhibit negligible Tafel behaviour in the current range investigated,12J3*21r22 &&A, >

(3)

(~E,,po’

Similarly, in the absence of observabIe concentration &

z

polarization,

W)E,,~~=~.

(4)

By measuring the slope of the polarization curve and the cell current at a given polarization (chosen as O-6 V), and letting &,,A, = AiL = (I)zcell=O, R, can be calculated using (2). Figure 5 shows the results of such calculations. It readily can be seen that catalyst loadings up to about 10 mg Pt/cm2 improve catalyst/membrane contact.

1

I

1

5

IO

15

mg Pt / cm’

FIG. 5. Variation of cell internal resistance with catalyst loading. 25°C. l , 0 psig; A, 50 psig.

1583

Transport in membrane fuel cells

Zeliger 12O in a study of oxygen reduction on platinum in 5N H2S04, found that beyond a certain loading additional platinum black did not increase the surface area (or current output) of the electrode. This observation supports the theory that catalytic reaction, at least in the electrochemical reduction of oxygen, occurs only near the exterior surface of the platinum catalyst. Tarasevich et ~1.~ reached a similar conclusion using 1 N H&40,. The data presented here support this conclusion even in the absence of free electrolyte. Increase in gas pressure* tightens the membrane/screen contact and hence reduces R,. Figures 6 and 7 show this effect. Increase in pressure beyond about 100 psig has been shown not to reduce Ri by much greater amounts.l*

>

0.6

0

IO

20

30

40

50

60

mA/cm* 25°C.

FIG. 6. Variation of cell polarization with total gas pressure. 45-mesh screen, 16-O mg Pt black/cm*. Membrane: leached, l-50 meqlg, 6% DVB, O-0381 cm thick. 0, 0 psig; A, 50 psig; 1, 100 psig.

0.4

o

20

60

I 80

PRESSURE,

psig

40

I 100

FIG. 7. Variation of cell internal resistance with pressure.

25°C.

Free acid

Figure 8 shows that a membrane pre-equilibrated in 8 N H,SO, gives better cell-current/voltage characteristics than a leached membrane. The main effect is the replacement of a water film with a highly conductive electrolyte solution film, thereby * In using equation (1) to calculate Ri at 50 psig, && was assumed independent of pressure. It has previously been reported *I that since the ionic distribution in the double layer is subject to an electrostatic equilibrium; pressurization should not sign&antly affect it.

F. R. FOUL=

1584

1 >

0

and

W. F. GRAYDON

psig

50

pslg

O-6 0.4 0.2 0

’ 0

I

1

IO

20

30

I

40

50 0

I

I

IO

20

30

40

50

mA/cm’ 25°C.

FIG. 8. Effect of unbound acid on cell polarization. 45-mesh screen, l-01 mg Pt black/cma. Membrane: l-50 meq/g, O-0381 cm thick. 0, leached; 0, 8 N HeS04.

6 oA DVB,

achieving better catalyst/membrane contact. Since there is Iittle catalyst/membrane interpenetration14 and the current-producing zone is limited to a very narrow region near the electrode/film contact, l5 free electrolyte bridging is an important factor in decreasing Ri- Furthermore, the improvement in performance cannot be attributed to decreased membrane resistivity resulting from free acid in the membrane pores, since these membranes exhibit Donnan exclusion towards sulphuric acid. In fact, even in low capacity commercial membranes which only contain about 25 % styrenepssa copolymer, 25the free electrolyte is much more dilute internally than externally.12 When intimate catalyst/membrane contact is achieved by means other than free eleetrolyte bridging, the presence of a free electrolyte film can be expected to have a very much reduced effect on cell performance. Van Duin and Kruissink,26 who achieved good catalyst contact using a special membrane surface treatment, have in fact reported that membranes soaked in sulphuric acid did not give higher cell outputs.

0

4

8

CONC. ACID, N FIG. 9. Effect of unbound acid on cell internal resistance. 25°C. 0,O psig; l ,50 psig.

Transport in membrane fuel cells

1585

The internal Figure 9 shows Ri as a function of pressure and acid concentration.* resistance changes can be regarded as two separate, additive effects. At either acid concentration, pressurization increases the catalyst/membrane contact by giving tighter membrane/screen continuity, but does not influence the nature of the liquid film contact. Similarly, at either pressure, increased acid concentration increases the catalyst/membrane contact through a more highly conductive liquid film, but does not influence the membrane/screen contact. 8 N H&30, is the optimum concentration to employ as free electrolyte since more dilute concentrations reduce liquid film conductivity and increase membrane water transport,4D17while greater acid concentrations increase membrane dehydration due to decreased water activity.12*27 Surface sulphonation In order to improve membrane contact several membranes were sulphonated for 2.5 min in cold (5C) chlorosulphonic acid (longer immersion attacked the membranes). The 8 per cent capacity increases so obtained are believed to be restricted to the membrane surface since appreciable penetration of chlorosulphonic acid into these membranes is unlikely. Figure 10 shows that contact was not improved at 0 psig (Ri = l-701 Q) but decreased from 04421 Q to O-728 Q at 50 psig.

0

IO

psig

0.8 >

0.6 0.4 0.2

O-

0

IO

20

30

40

50

mA/

0

IO

20

30

40

50

cm’

FIG. 10. Effect of membrane surface-sulphonation on cell polarization. Membrane: 8 N unbound HaSO,, l-50 25°C. 4%mesh screen, 1.01 mg Pt black/cm’. meq/g, 6% DVB, O-0381 cm thick. a, unsulphonated; 0, sulphonated.

At 0 psig most of the catalyst/membrane contact is probably achieved through the free electrolyte film. Since the liquid film already enjoys almost perfect interfacial contact with the membrane surface, an increased concentration of sulphonic acid groups at the surface does not further improve the nature of this contact. However, the membrane/screen contact, which has been shown to improve significantly with higher pressures, is enhanced even more by the greater number of sulphonic acid groups coming in contact with the platinum electrocatalyst. l In calculating Ri from (1) it has been assumed that &A, is independent of concentration. Transfer coefficients listed in the literature for the oxygen utilization reaction are scanty and inconclusive with respect to the effect of concentration.

16

F. R. FOULKES and W. F. GRAYDON

1586

The fact that the internal resistance of the cell at 0 psig was the same for both the treated and untreated membranes indicates that sulphonation caused no appreciable internal. capacity increases in the membranes. Membrane

thickness

Figures 11 and 12 show the effect of membrane thickness on fuel cell discharge characteristics and Ri respectively. From Fig. 12 it can be seen that Ri decreases

0.4 0.2 0

I

I

10

0

20

I

I

I

30

40

50

mA/cm’

25°C. 0 psig.

FIG. 11. Effect of membrane thickness on cell polarization. lo&mesh screen, l-01 mg Pt black/ems. Membrane: 8 N unbound HISOI, 2.58 meq/g, 6% DVB. Thickness: I, O-127 cm; A, O-0381 cm; a, O-0155 cm.

0.6 c: . 0.4 .P 0.2 0

I

0

I

I

0.02 004

o-06

MEMBRANE

0,

I

I

O-IO

0.12

THiCKNESS

, cm

0.08

0.14

FIG. 12. Effect of membrane thickness on Ceil internal resistance. data from Fig. 11; A, addition of 8 mg Pd black spread over membrane surface.

linearly with decreasing thickness and that at “zero thickness” a contact resistance of The membranes used (2-58 meqjg, 6 % DVB) have a about 0.32 Q is indicated. specific resistivity6 of about 6.81 Q cm. Since Rm,,mbrane= R, - Roontwt, the effective membrane area utilized in the case of a 0.0381-cm thick membrane was (6.81 a cm) (O-0381 cm)/@-422 - 0.32 sz> = 2-54 cm2. Therefore approximately 25 per cent of the available membrane area was being utilized.

Transport in membrane fuel cells

1587

Also shown in Fig. 12 is the Ri of a cell in which each side of the membrane was evenly coated with about 8 mg of palladium black in addition to the use of the lOOmesh platinized screen. The decrease in R, resulted from the increased membrane/ catalyst contact which gave both greater membrane area utilization and lower contact resistance. Screen mesh and membrane

capacity

Figure 13 shows the effect on Ri of varying the screen mesh and ion exchange capacity of the membrane_ I

0

I I.0

l-5

I

I

20

2.5 meq

/g

I

I

I- 5

I.0 dry

H+

2-o

I

2 5

form

FIG. 13. Effect of

screen mesh and membrane exchange capacity on cell internal resistance. Membranes: 8 N unbound HsSOI, 6% DVB, 0.0381 cm 25°C. l-01 mg pt black/cm’. thick. Screen mesh: l , 45; A, 50; I, 100.

The results for 45- and 50-mesh screens were about the same but lOO-mesh screens reduced Ri, especially at 0 psig. Increased screen mesh, like catalyst loading, has the dual effect of decreasing the screen/membrane contact resistance and increasing the utilized area of the membrane. Membrane conductance increases with capacity due to increased moisture content and increased protonic concentration. At high exchange capacities the electric fields surrounding the fixed sulphonate groups overlap, making it relatively easy for hydrogen counter-ions to migrate from one site to the next. However, at very low capacities, discrete electric fields tend to be formed about the fixed sulphonate groups, making it energetically more difficult for hydrogen ions to leave the vicinity of one for that of the next, thereby contributing to increased membrane resistance. From a knowledge of membrane moisture content and exchange capacity, the Na+-H+ interdiffusion coefficients for the membranes employed in this work can be determined using the empirical correlation developed by Stewart2 Furthermore, the following relationships (which are independent of capacity and cross-linking) between the interdiffusion coefficients and single ion diffusion coefficients have been given by Ciric,5 2&t+&*+ D Nat--H+ =

DH+ +

DN~+

F. R. FOULKES and W. F. GRAYDON

1588

and Du+/DNs+ = 7.3. Using the above information, the hydrogen-ion single-ion diffusion coefficients, DH+, can be readily evaluated. By subtracting the O-32 Sz contact resistance from Ri, the resistance of the membrane, RM, and hence the membrane conductivity, l/R,, is obtained. The NernstEinstein equation5 predicts a direct proportionality between the electrical conductivity and the singIe-ion diffusion coefficient. From Fig. 14, which is a verifying plot for the Nernst-Einstein relationship, it can be concluded that the membrane resistance is controlled by the rate of diffusion of hydrogen ion through the membrane.

0

( bM ) , mho FIG. 14. Hydrogen-ion diffusioncoefficientversusmembraneconductivity. Membrane capacity, meq/g : I, l-50; A, 2-00; a, 2.58.

Membrane cross-linking Figure 15 shows that membranes of higher cross-linking increased the internal resistance of the cell and therefore decreased the hydrogen-ion diffusion rate. This I

I

I-

I.0

c: g

0.5 /

0 0

I

i

I

1

L

2

4

6

8

IO

MOLE-V.

25°C.

DVB

FIG. 15. Effect of membrane cross-linking on cell internal resistance. IOO-mesh screen, 1.01 mg Pt black/cm8. Membrane: 8 N unbound HISO&, 2.00 meqlg, 0.0381 cm thick. 0, 0 psig; 0. 50 psig.

Transport in membrane fuel cells

1589

has also been observed by Tombalakian et al. ’ It has been shown* that the ratios of interdiffusion coefficients for univalent inorganic cation-exchange systems in these membranes are nearly the same as in aqueous solution, being quite independent of differences in porosity. This indicates that increasing the membrane cross-linking causes very little sieve effect, and tends only to increase the tortuosity, and hence lengths of the diffusion paths, in the membrane. For a system whose tortuosity is affected only by the bulk of the polymer matrix, Meares2* has shown that the diffusion coefficient is directly proportional to the quantity {VW/(2 - Vw)12, where VW is the volume fraction of water in the swollen against membrane. Figure 16 _shows a plot of membrane conductance, l/R,,

FIG. 16, Membrane conductance tts [VW/(2 Membranes 240 me&. A, 9% DVB; 1,6x DVB.

VW)]*.

It can be seen that the variation of membrane conductance, and therefore hydrogen-ion diffusion coefficient, follows Meares’ correlation. A similar plot (Fig+ 17), using the data for membranes of varying ion-exchange capacity, does not agree with the correlation. In this case the observed membrane conductances WV/(2

-

VW)}“_

0

-E

8

-pt=

6

0

0,02

0.04

0.06

FIG. 17. Membrane conductance us [VW/(2 - VW)]‘. Membranes: A, 1.50 meq/g; I, 2-00 meq/g; l , 2-58 meq/g.

6% DVB.

F. R. FOUL-

1590

and W. F. GRAYD~N

at higher values of {VW/(2 - Vw)j2 were greater than predicted, since protonic concentrationin the membrane as well as water content contributed to the conductance. In concluding it might be added that although highly cross-linked pssa membranes have lower conductivities than membranes of lower cross-linking, they have one advantage in that their water contents are much less sensitive to relative humidity changes.2s LIST

OF

SYMBOLS

A, electrode area, cm2 ZZ, fuel cell terminal voItage, V F, the faraday, 23,060 cal/eq. V i,,, exchange current density, A/cm2 iL, limiting current density, A/cm2 1, cell current, A IEM, ion-exchange membrane pssa, polystyrenesulphonic acid R, the gas constant, l-987 cal/eq. “K R,, external circuit resistance, fi Ri, cell internal resistance, Q RM, membrane resistance, C2 T, temperature, “K VW, volume fraction of water in the membrane /?, symmetry factor A, the number of electrons transferred in the rate-determining Acknowledgement-The

step

authors gratefully acknowledge financial support from the National

Research Council of Canada.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

W. F. GRA~DON and R. J. STEWART, J. pkp. R. J. STEWART and W. F. GRAYDON, J. pkys.

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59,86 (1955). 60,750 (1956).

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