Diffusion Polarization in Air Channels

7 Diffusion Polarization in Air Channels Electrochemical Reduction of Oxygen (Air) HENRI J. R. MAGET and EUGENE A. OSTER

Downloaded by UNIV OF ALABAMA on June 18, 2016 | http://pubs.acs.org Publication Date: January 1, 1969 | doi: 10.1021/ba-1965-0047.ch007

Fuel Cell Laboratory, General Electric Co., West Lynn, Mass.

Current density distributions in electrodes operating by gas diffusion into restricted rectangular cross-sectional

channels are largely

fected by channel geometry.

af-

The ratio edge

current/center channel current can be as large as 4, resulting practically in nonuniform surface conditions—(temperature, concentration).

Semi-

empirical equations allow calculation of position-dependent current-voltage relationships.

pates of cathodic oxygen reduction—that is, cell currents—are dependent on partial pressures of the oxidant if rate-controlling steps i n volve the concentration or partial pressure of oxygen. This is likely to be observed since reaction rates w i l l be either liquid film or gas diffusion controlled. However, cases can arise where removal of the reaction product may be hindered by slow transport processes, thus resulting i n , possibly, appreciably lower rates. This could be the case of water removal from the catalyst surface of an oxygen electrode. If local current densities are either dependent on partial pressures of oxygen or water, it w i l l become necessary to establish a relationship predicting such local current densities and to design electrode geometries favorable to uniform current distribution, and as a result, uniform distribution of the main influential variables affecting oxygen electrode performance. Such considerations, however, would imply knowledge of limiting current densities. In establishing over-all oxygen electrode capabilities for fuel cell application, one of the important variables is the limiting current density. Although these limiting currents are not simply dependent on some limited parameters—that is, electrode activity, electrode structure, electrolyte properties, local temperatures, and anisotropic current density distributions—actual measurements are valuable if some reproducible 83 Young and Linden; Fuel Cell Systems Advances in Chemistry; American Chemical Society: Washington, DC, 1969.


84

FUEL CELL SYSTEMS

characteristics can be controlled—that is, catalytic activity, electrode structure, electrolyte properties. Thus, measurements are valuable for a specifically designed system, as related to limiting current densities, and very generally applicable to any air electrode current collector design, if the geometry is influential on, and descriptive of, the limiting currents. The ultimate goal—that is, quantitative description of current-voltage relationships as a function of main variables—can be, i n principle, attained from experimental studies, involving the determination of limiting current densities at discrete positions on the air electrode, placed i n a channel through which the reaction air is diffusing or flowing. Also necessary are the establishment of the rate-controlling process for known channel geometries i n the high current density range (corresponding to .85 to 0.5 volt ) ; the derivation of relationships describing the currentvoltage behavior over practical operational ranges; the transport phenomena explaining polarization potentials at these practical currents; and the experimental values of open-circuit potentials. If all these equilibrium conditions, rates, and processes are known, a reasonable analytical description of local as well as over-all currents and potentials, can be expected. It is conceivable then, that limiting currents can be associated with channel geometry and that diffusional processes i n restricted channels become small enough (rate-controlling). The purpose of the work described here was to obtain experimental results and interpretation to explain polarization i n channels of defined geometry and to establish influential parameters which would affect electrode performance. In order to establish applicability of a selfbreathing air electrode (without forced convective air-flow) for low current densities, experimental investigations were started on straight air channels. Since the diffusion polarization becomes quite severe at high current densities, these electrodes can not operate near limiting currents. To minimize large polarization contributions, the electrode must operate under forced-flow conditions. Experimental results on current distribution i n air-electrode channels under forced-flow conditions were reported elsewhere ( I ) . Experimental Equipment The system chosen for experimental investigation was based on platinum black electrodes bound to a solid-matrix electrolyte ( cation exchange membranes ). Such a system offered multiple advantages i n preparing discretely separated small electrodes and displaying good and uniform contact with the electrolyte. The individual electrodes included metallic screens to increase surface conductivity. Reference potential measurements were based on a Luggin-type

Young and Linden; Fuel Cell Systems Advances in Chemistry; American Chemical Society: Washington, DC, 1969.


7.

MAGET AND

OSTER

Polarization in Air Channels

85

capillary-saturated calomel electrode ( S C E ) system, specially developed for application to ion exchange membrane electrolytes (2). A low-leakage capillary was placed against the membrane and sulfuric acid used to establish the bridge with the calomel electrode. In all cases, the ion exchange membrane extended outside of the apparatus for potential measurements. Effects of capillary positions were investigated by placing the tip against and within the membrane. N o appreciable differences were observed. The ten segmented electrodes allowed the determination of limiting currents as a function of position and represented values for discrete electrode sizes. In many instances, the data presented represent smooth interpolation of position-dependent limiting currents. Investigations were conducted under galvanostatic operating conditions. Voltage current curves were obtained for individual electrode segments while all segments were under operating conditions. From these measurements it was possible to obtain local electrode currents of nearly uniform potential for all segments. The equipment is shown in Figure 1. A l l experimental work was conducted on air channels 6.35 cm. long and 1.27 cm. wide. Channel height could be varied by changing a removable Lucite bar placed on the channel top. Thus, channel heights could be 0.16, 0.32, 0.64, or 1.27 cm. The channel was mounted on an air electrode and placed in a large Lucite box to avoid small air flow sweeps over the air electrode. Both channel ends were open to allow for oxygen diffusion.

D I F F USION

Figure I.

PATH

HYDRO GEN

Experimental device for measuring local currents in air channels of variable geometry

To determine local current densities, the air electrode was manufactured by placing ten parallel electrode/screen strips on an ion ex-


FUEL CELL SYSTEMS


86

change membrane. Gaps of 0.16 cm. between electrodes allowed for electrical insulation of the various electrodes. Electrode dimensions were (1.27 X 0.48) sq. cm. with an actual area of 0.60 ± 0.05 sq. cm. The ion exchange membrane extended out of the channel for reference potential measurements and stainless steel rods contacted the screens for current pickup. The counter electrode (hydrogen electrode) was prepared i n a similar manner. Catalytic electrodes faced each other across the electrolyte (membrane). The two ends of the self-breathing channel were open, thus displaying planar symmetry for either side of the channel center cross-section. Closing one channel end actually corresponded to doubling the channel length. Single electrode failure would not affect results appreciably, since experimental results could be obtained from mirror-image electrode. Experimental Results Representative single electrode polarization characteristics are presented i n Figure 2 for a channel height of 0.32 cm. These polarization curves represent the largest changes from the edge to center electrodes for the smallest channel height investigated. Limiting current densities for the channel edges (edges of electrode 1 and 10) should be about 130 to 140 ma./sq. cm., as determined independently for electrodes exposed to semi-infinite air space ( 3 ) . Thus, the local limiting currents should increase very sharply, precisely at the channel edges. Figure 2 indicates that appreciable polarization is encountered as soon as measurements are conducted slightly away from the channel edge. Larger currents are observed for all electrodes for increasing channel height. F o r 1.27 cm. channels, very little polarization is observed even at current densities near limiting values—130 to 140 ma./sq. cm. Polarization is less severe for all electrodes at small local currents, as expected. Channel heights affect polarization characteristics to a large degreethat is, limiting currents for center electrodes are 22 and 35 ma. for 0.16 and 0.32 cm. channels, respectively. These currents correspond to oxygen partial pressures of 0.07 and 0.1, respectively, as determined independently b y determining the effect of oxygen partial pressure on limiting currents ( 3 ) . F o r identical polarization potentials (as determined from polarization curves) current density distributions display minima for inner electrodes and can be extrapolated to edge values of limiting currents of 130 to 140 ma./sq. cm. Current density distributions for channel heights of 0.32 and 0.16 cm. for various applied potentials are shown in Figures 3 and 4. Edge currents can become two to four times larger than center currents, but display much more uniform distribution for lower electrode polarization—


7.

MAGET AND OSTER


VOLTAGE vs. S C E

87


|. , 0

Numbers in c i r c l e s represent the position of the να rious electrode segments For actual location refer to Figure I-

TOTAL LOCAL

Figure 2.

CURRENT, m A

Polarization characteristics of individual electrodes for 10 parallel electrodes Channel height, 0.32 cm.; electrode surface, 0.6 sq. cm.

Figure 3. Current distnbution for individual electrodes in the self-breathing channel Channel height, 0.32 cm.; electrode surface, 0.6 sq. cm.


88

FUEL CELL SYSTEMS

LOCAL

CURRENT mA


40

20

Figure 4.

Current distribution for individual electrodes in the self-breathing channel Channel height, 0.16 cm.; electrode surface, 0.6 sq. cm.

POTENTIAL

Figure 5.

CHANNEL

POLARIZATION

Single-electrode diffusion polarization

i — diffusion-limited current channel poforization d

7\ — Ea-Ewce = actual voltage minus voltage in absence of channel effects d

that is, 0.5 volts vs. S C E for 0.32 cm. channel. Interpretation of Individual Folarization Curves Current potential behavior for the investigated systems is shown i n Figure 5. Figure 5A represents polarization characteristics as observed i n absence and presence of diffusion polarization (including activation polarization, in absence of ohmic contribution, which are generally eliminated ). Figure 5B represents strictly diffusion polarization terms i n absence of


7.

MAGET AND OSTER


89

other possible polarization. T h e shape of curve 5B suggests the following empirical relationship between current and channel polarization: -i/h)

(1

(1)

in which a l l variables but E° are position-dependent; i and i represent actual and limiting position-dependent currents, respectively. The con stant (a) must be evaluated. E° represents the air electrode potential in absence of channel polarization, Ε the electrode potential and E° — Ε = η represents the channel polarization. It follows from Equation 1 that: L

α

l n ( l - i/i ) = -a(E° - E) = -a Downloaded by UNIV OF ALABAMA on June 18, 2016 | http://pubs.acs.org Publication Date: January 1, 1969 | doi: 10.1021/ba-1965-0047.ch007

L

(2)

Vd

B y differentiation: dvd

1

di

ai {\ L

—

(3)

I/IL)

with oo as

ι

IL

\αι / and

*M = (£)

= (4) \ di Ji _ ο a i (x) If Equation 1 is applicable, it would follow that slope (άη /άι) at i = 0 should be inversely proportional to the limiting current for each electrode segment. In fact, these slopes can be determined and are de pendent on the electrode position. (Figure 2 does not present these voltage variations at low local currents for reasons of clarity. However, results are presented in Table I ). F r o m Equation 2 and for i = 0: L

ά

A

AE°

àE — = Rd(x) (2a) Αι Αι Αι A E /A i was determined from experimental results obtained for a channel height of 0.64 cm., which displayed no channel polarization contribution as reported in Figure 6, and for which the position independent slope was determined to be Δ Ε /A i = R = 4. The coefficient (a) can then be evaluated from: Vd

- 7 T

—

=

0

0

*

=

*-(Λ£/Δ0,·-ο

( 4 & )

The evaluation of (a) from the experimental results is reported i n Table I. Since i (x) displays a regular decrease up to channel center, E q u a L


90

FUEL CELL SYSTEMS

tion 4 is expected to display an increase from channel edge to center. Figure 6 presents smoothed experimental results for channel heights of 0.16, 0.32, and 0.64 cm. As suggested b y Equation 4 and experimentally observed, the diffusional resistance displays: • N o diffusional resistance at the channel edges, at least as related to electrode geometry. • Maximum diffusional resistance for center electrodes. • Increased resistance for reduced channel cross-section. Since the coefficient (a) has the dimensions of v o l t , it is suggested to identify (a) with anF/RT, i n which case an = 0.24 to 0.27. Downloaded by UNIV OF ALABAMA on June 18, 2016 | http://pubs.acs.org Publication Date: January 1, 1969 | doi: 10.1021/ba-1965-0047.ch007

-1

Table I. Electrode osition

Determination of (a) from Experimental Data

Limiting current, i amps

u

1/tL, amps' 1

fàV\ \Δ// ohm

β χ ρ

,

/ΔΚ_ \ \Al /' ohm

i (AV/AI — R) volts' L

1

Channel height: 0.16 cm. 1

0.041

2 3 4 5 6 7 8 9

0.028 0.024 0.022 0.025 0.027 0.030 0.050

35.8 41.7 45.5 40.0 38.0 33.3 20.0

7.3 7.8 8.2 8.1 7.9 7.3 6.1

3.3 3.8 4.2 4.1 3.9 3.3 2.1

Average ( β ) =

10.8 11.0 10.8 9.8 9.7 10.1 9.6

10.4

Channel height: 0.32 cm. 1 2 3 4 5 6 7 8

0.045 0.043 0.037 0.035 0.035 0.037 0.044

22.2 23.2 27.0 28.6 28.6 27.0 22.7

6.0 6.7 7.1 7.3 7.3 7.1 6.8

2.0 2.7 3.1 3.3 3.3 3.1 2.8

Average (a) =

11.1 8.6 9.0 8.7 8.7 9.0 8.2

9.0

A current-voltage relationship can now be obtained from Equation 1, iffaM can be obtained as a function of channel parameters. Evaluation of i (x) L

For steady state conditions, it is now necessary to approximate cur rent density distributions over the electrode surface b y assuming a mass transfer process which accounts for channel geometry and yields positiondependent transport rates simulating current distributions. This ap proach w i l l not elucidate the transport mechanism but allow evaluations of i ( x ) , which then can be used i n Equation 1 describing current-po tential behavior of the electrode. Channel conditions are not easy to define since electrode surface L



7.

MAGET AND

Figure 6.

OSTER

Slopes


(AV/AI)

91

for various électrodes in the self-breathing air electrode channel

LEGEND

\ \ \

Determined by

\\

Ο

- Ο Cole. 0

Ι Ι

- Δ Cole. H 0 diffusion

2

diffusion

2

^*' | m

n

1 17 20

2 D, c m / u c 0-21 0 29

-•-

1

^\

\\ ^

X

CHANNEL LEN3TH

Figure 7. Current distribution in 0.16 cm. channel

concentrations as well as temperature distributions are not known. H o w ever, it w i l l be assumed that the temperature is uniform; that the surface concentration of oxygen is small (equal to 0); and that the liquid water is i n equilibrium with a saturated gas phase at the electrode temperature. In the following derivations, convection w i l l be neglected, and transport


92

FUEL CELL SYSTEMS

rates w i l l be evaluated for the moving gas phase components—that is, oxygen and water. Under these conditions: V C, = 0

(5)

ZCi = 1

(6)

2

I

Ci represents the concentration i n the three component gas phase. In the two-dimensional channel, y represents the distance above the electrode surface (y = 0 at the surface and y = y at the top of the channel), and χ is the direction parallel to the electrode surface (x = 0 and χ = 2b at channel edges). Boundary conditions are: 0


Cfày)

= C (2b,y) = C t

A t the electrode surface: C ( * , 0) = 0; C (x, 0) = f(T); 0e

C ( * , 0) = 1 — / ( Γ ) Nf

w

Furthermore it w i l l be assumed that: / dCp _

rfC \ N>

2

\ dy

=

dy J , y

0

yo

Oxygen Transport Rates. W i t h these boundary conditions the con centration distribution for oxygen becomes: Co, = C° |~1 —

oc x(cosh a„y — tka^osha^)^

s i n

where A

n

and a

n

n

(7)

= -•-

The local current densities which can be associated with this concentra tion are obtained from: /Mo,

For air, with D obtained:

0

2

= -nFD ,(^)y

= 0

0

(8)

= 0.21 sq. cm./sec, the following expression has been

; W o , = 0.235 π =

Σ 1,3.

sin(/i ττ x/2b)th(n wy /2b) 0

(9)

. .

and plotted in Figure 7. The calculated values deviate appreciably from experimental results. Water Transport Rates: 1. W i t h the previous boundary conditions, i n addition to (dC /dy)y w

ay0

— 0,

similar expressions as Equations 7 a n d 9 can be derived, yielding transport rate distributions appteciably lower than measured.


7.

MAGBT AND OSTER

Polarization

93

in Air Channels

2. If the temperature at y = y is lower than at y = 0 and if gas phase saturation is assumed, the following boundary condition is introduced: (C ) _ „ = g ( T ) . For these conditions the concentration distribution for water becomes: 0

w

y

=

0

Σ

ι

Λ η sin a x n

~ f(T) cosh a jo n

sh a y

L

n

sh

+ /( T) cosh

Diffusion Polarization in Air Channels

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