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Simulation studies on the fuel electrode of a H2O2 polymer electrolyte fuel cell
Ekctrochimica Acta, Vol. 37, No. 15, pp. 2737-2745, Printed in Great Britain.
1992 0
0013~4686/92 55.&l + 0.00 1992. Pergamon Press Ltd.
SIMULATION STUDIES ON THE FUEL ELECTRODE OF A Hz-O2 POLYMER ELECTROLYTE FUEL CELL JIANG-TAOWANG and ROBERTF. SAMNELL* Department of Chemical Engineering, Case Western Reserve University, Cleveland, OH 44106, U.S.A. (Received 3 February 1992; in revisedform 5 May 1992) Abstract-The macro-homogeneous porous electrode theory is used to develop a model which describes the catalyst layer of the hydrogen electrode formed by catalyst particles that are bonded to the membrane. The water transport in the catalyst layer and polymer electrolyte membrane is considered. The effects of catalyst layer structure parameters such as polymer volume fraction, catalyst layer thickness, platinum loading and reactant gas humidity as well as CO poison on the hydrogen electrode behavior are examined. The results show that the catalyst layer thickness has a significant effect on the electrode performance. A thicker catalyst layer will result in a larger ohmic voltage loss and higher catalyst cost. The optimal polymer volume fraction and catalyst layer thickness are 0.5 and 1.54ym, respectively, for
this electrode. An optimal platinum surface coverage on carbon need not exceed 20% (20wt% Pt/C). Larger platinum coverage will increase the cost, but only slightly enhance the electrode performance. Key words: PEM cell, modeling, electrode structures, gas diffusion electrodes and water transport.
NOTATION a
c H2 c l4+ Clb0
G DHz DEl+ DHZ0 E EO E=I F i w
1
i” i”co
k Ha nd NW
P P Hz PW P sat r, xp RH cb
ld
T
E
specific surface area of catalyst phase, cm- 1 concentration of hydrogen, mol/cm3 concentration of proton, mol/cm3 concentration of water, mol/cm3 concentration of fixed function group, mol/cm3 diffusion coefficient of hydrogen, cm2/s diffusion coefficient of proton, cm2/s diffusion coefficient of water, cm’/s electrode potential, V standard electrode potential of hydrogen, V equilibrium electrode potential, V Faraday’s constant, 96 487 C/equiv total current density, A/cm2 local current density, A/cm2 exchange current density, A/cm2 exchange current density in the presence of CO, A/cm2 Henry’s constant of hydrogen, atm cm3/mol drag coefficient, dimensionless flux of water at x = td , mol/cm2 s reactant gas pressure, atm partial pressure of hydrogen, atm partial pressure of water vapor, atm saturated pressure of water vapor, atm radius of carbon particle, cm radius of platinum particle, cm universal gas constant, 8.314 J/moldeg relative humidity, % thickness of polymer electrolyte membrane, cm thickness of catalyst layer, cm absolute temperature, deg K mobility of proton, cm2/V s activity of water vapor, dimensionless fraction number, dimensionless platinum coverage, dimensionless
*Author to whom correspondence should be addresed.
4 tlobm e”
eM e MH
eco
n”
PC
volume fraction of polymer phase, dimensionless overpotential, V ohmic voltage loss in polymer defined as equal to I$~ - &.j, V equilibrium coverage of adsorbed hydrogen, dimensionless fraction of platinum surface area, dimensionless fraction of platinum surface area adsorbed by H, , dimensionless fraction of platinum surface area adsorbed by CO, dimensionless conductivity of polymer phase, mho/cm water content, ie the ratio of CuzO/Crr dimensionless density of carbon, g/cm3 density of platinum, g/cm3 potential at catalyst phase, V potential at polymer electrolyte phase, V.
INTRODUCTION Fuel cells employing a solid polymer electrolyte membrane recently have been receiving more and more attention[l] due to their promise for high energy density power plants for both stationary or mobile applications. The main features of this kind of fuel cell are pollution-free operation, low operating temperature, less corrosion problems and high power density. However, there still are several unsolved problems, such as membrane dehydration due to water transport in the fuel cell, and high catalyst cost. There have been a number of reported studies on both of these issues[2-111. Extensive modeling of transport properties in perfluorsulfonate ionomers based on dilute solution theory have been presented by Verbrugge and Hill[2-41. Fales et aI.[5] reports an isothermal water map based on hydraulic permeability and electro-
2731
2738
J. T. WANG and R. F. SAVINELL
osmotic drag data. Fuller and Newman[6] applied concentrated solution theory and employed literature data on transport properties to produce a general description of water transport in a fuel cell membrane. Bernardi[7] developed a membrane water transport model which suggests optima1 conditions to operate a hydrogen/oxygen fuel cell. Bernardi and Verbrugge[8] model a PEM fuel cell taking into account gas and water transport, porous electrode theory at the anode and the cathode and transport through the gas diffusers. With only two adjustable parameters they were able to reproduce the trends in experimental polarization curves. They conclude that oxygen and water transport are factors which limit fuel cell electrode performance. Springer et al. reports two model studies on the polymer electrolyte fuel cell[9, lo]. One model is a steady-state description of a complete polymer electrolyte fuel ce11[9]. In this model the water transported by diffusion and electro-osmosis are considered with water sorption isotherms and membrane conductivity data as a function of membrane water content. In the other model[lO] the cathode catalyst layer in a polymer electrolyte fuel cell is the focus of attention. This model explains certain observed polarization curve features at high current densities. In order to reduce the catalyst cost and at same time maintain high power density, much effort has been directed at using new catalyst materials, and changing electrode fabrication procedures[ 111. The electrode performance is not only dependent on operating conditions such as gas pressure and gas humidity, but also strongly dependent on the electrode structure and catalyst loading. Therefore it is necessary to acquire a deeper understanding about the effects of the electrode structure parameters on the electrode performance. To address this issue, we apply the macro-homogeneous porous electrode theory to develop a one-dimensional mode1 which describes the performance of electrodes formed by imbedding catalyzed carbon particles that are bonded to a membrane of a proton conductive polymer. The effects of basic electrode structure parameters such as polymer volume fraction, catalyst layer thickness, platinum loading, reactant gas humidity, CO poisoning and hydrogen effective diffusion coefficients on the hydrogen electrode behavior are examined. In this model, axial variations in gas composition are neglected but should be considered in a description of a full-size fuel cell electrode.
MODEL
DEVELOPMENT
A schematic illustration of the model system of Hz-O2 polymer electrolyte fuel cell is shown in Fig. 1. Macro-homogeneous porous electrode theory[12] is used to describe the electrodes formed by the catalyst particles that are bonded to the membrane. In this model, two phases are assumed to exist in the catalyst layer. The polymer phase is assumed to be a continuum of the fluorocarbon backbone, polymer ions, and absorbed water. The second phase is the platinum covered carbon particles which are assumed to be uniformly dispersed throughout the
Catalyst
Layer
Catalyst
Membrane
Layer
Carnode
A”CdG?
0 t.3 t, + L Fig. 1. Schematic illustration of the model system of HZ-O, polymer electrolyte fuel cell.
catalyst layer. Also assumed is that the platinum is uniformly loaded on the carbon particles. This assumption agrees well with reported transmission electron microscopy (TEM) analysis results[ 111. If we consider the carbon particle to be a sphere, the specific surface area of the catalyst phase a can be expressed by the following equation &l-E) rc
(1)
where E is the volume fraction of polymer and r, is the radius of carbon particle. On the anode side of the polymer electrolyte fuel cell, the reactant gas is humidified hydrogen. Here we assume the dissolved hydrogen in polymer phase is in equilibrium with the partial pressure of hydrogen in gas phase, and Henry’s law can be used to determine the concentration of dissolved hydrogen. Since the model is one-dimensional, the gas phase composition is assumed to be constant and thus gas flow rates and reaction stoichiometry are not considered. The diffusion of dissolved hydrogen in the catalyst layer and its subsequent reaction can be described by the following mass balance equation
a%
ai” = 2cFD,, -
ax2
where i” is the local current density based on the specific surface area of the catalyst phase (A/cm2). The boundary conditions for equation (2) are x = 0, CHI = c;,
(3)
x=td,rac,,= 2%. ax
tb
In equation (3) Ci, can be determined by (5) where kH2 is Henry’s constant, and P,, is the partial pressure of hydrogen. At x = t,, we assume the flux of H, is equal to that of H2 in the membrane, and the concentration of H, at x = t, + t, is negligible. In the polymer phase, the protons associated with the fixed functional groups are the only movable charge species which carry the current. Therefore, there is no concentration gradient of proton and its
Hr-0, polymer fuel cells concentration is constant which is equal to the concentration of fixed functional groups Cr. The charge balance equation for this situation becomes ai” = - F2uH+C,.,+e
z
2739
In this model, an empirical equation relating DHzO (cm2/s) with water content Iz from experimental results[9] is used. 1 1 - 303 273 + T
D rl,d = 10m6 exp
or
)I
x (2.563 - 0.331 + 0.02641’ ai”
av2
=
- 0.00067113)
-KEdX2
where K is the conductivity of polymer electrolyte. Here we have simplified the charge balance equation by neglecting the term of the gradient of rc. However, we still consider that K is a function of the water content of the polymer, and assume k is constant locally. This will be discussed more fully in the following section. Gottesfeld et al. have reported an empirical equation describing the relationship of K with water content 1[9].
(13) 1 1 - 303 273 + T
D 311<4 = 10e6 exp
>I
x (6.89 - 1.331) 1 --p 303
D 2<1<3 = 10m6 exp
x (-3.1
(14) 1 273 + T
(15)
+ 2.02).
At the boundary x = 0, rc=exp
cHI0 (0.005139A - 0.00326)
where 1 = Cu,o/Cr. equation (7) are
The boundary
x=0,-=
x =
84, ax
conditions
(8) for
o
fa, (b2 = &.
(10)
The water balance plays a critical role in the performance of a polymer electrolyte fuel cell. In order to acquire a deeper understanding about water effects on the electrochemical behavior of electrodes, the water transport in the catalyst layer is considered. When a current passes through the external circuit, the equivalent coulombs of proton are transported from anode side to cathode side. Since in this electrolyte protons always combine with water molecules in the proton transport process, water is also moved toward the cathode direction which produces a concentration gradient of water in the polymer phase. Since the water concentration is low (C lo-’ M), dilute solution theory is applicable, and the water mass balance equation can be described by -
o + n,ai”/F %,o a=c,
2
ax2
(16)
1’ = 0.043 + 17.81~ - 39.85a’ + 36.0a3
(17)
a = P,lp.,, .
(18)
where
P, and P,,, are the partial pressures of water and saturated pressure of water at a given temperature, respectively. At the other boundary x = t,, the flux of water N, can be expressed by the following equation
-tnd i/F.
X=fd
the concentration
gradient
(19)
is
(11)going to be a function of the water production rate
In equation (1 l), DHIO is the water diffusion coefftcient and nd is the drag coellicient, ie the number of water molecules dragged per proton transported. Similar to the charge balance equation, we consider both DHZOand n,, to be the function of water content 1 and constant locally. The first term of equation (11) describes the diffusion effect due to the concentration gradient of water, and the other term illustrates the water transport due to the drag of protons. LaConti et aL[13] and Gottesfeld et a/.[91 have measured n, and assumed that it is linearly proportional to the water content of the polymer according to the following equation : nd = 2.512122.
Go
where C&, can be determined . _by the _ activity . _ of water vapor at the gas and catalyst layer interface. Zawodzinski et al.[9] have measured the membrane water content as a function of humidity for the Nafion 117 membrane. Based on their data, an empirical relationship of 1 vs. water vapor activity a at 30°C is used in this model (assuming it can be used at 80°C due to absence of data at this temperature).
In this expression,
= 0.
=
(12)
at the cathode and the transport conditions between the membrane and the adjacent gas phases. In order to solve the differential equation, we assume that N, is proportional to the total current density, N, = Bi/2F, where /3 is a fraction number. The more water moving across the interface at x = t,+, the larger b becomes. According to equation (19), when /l> 2n,, the concentration gradient of water will become negative, indicating that the movement of water by diffusion has the same direction with the water transported by electro-osmosis. This will intensify membrane dehydration. Hence, at the desired operating condition, the maximum value of fi should not be larger than 3.2 (nd = 1.6, when water content 1 = 14) in order to minimize a membrane dehydration effect. Taking into account the dependence of transport
J.T. WANG and R. F. SAVINELL
2740
properties on the level of hydration, the simulation results show that the concentration gradient of water becomes negative when /? > 1.5. On the other hand, since the current passing through the cell is usually large, water diffusion by water concentration gradient will not be large enough to balance water transported by proton migration, thus fl will usually not be negative. Therefore, it is believed that fi should vary from about 0 to 1. The total current density i is calculated by integrating the local density throughout the catalyst layer X=ld X’l.j i=a i.dx=;(l -e) i” dx. (20) c I x=0 I x=0 The mechanism for the electrochemical oxidation of molecular hydrogen on the platinum in acid electrolyte is believed to proceed according to the TafelVolmer sequence which involves a slow dissociation of adsorbed hydrogen molecule to hydrogen atoms, followed by fast electrochemical oxidation of adsorbed hydrogen atoms to protons[l4, 151. Hz+2M+2MH
(slow reaction) (fast reaction)
2MH-+2M+2H++2em
The surface coverage of adsorbed hydrogen is governed by the electrode potential as
E=E’+yln-$
(21)
MH At the equilibrium potential, i = 0 RT
E,, = E” + yin,
l-0,
(22)
0
where 8, is the equilibrium coverage of hydrogen. E” is the standard electrode potential, which is equal to zero for the hydrogen reaction. The current given by hydrogen dissociation reaction can be described by i” = i’r[&, + (1 - 6,) exp(Fq/RT)]-2 x
3
exp(ZFq/RT) HZ
1
- 1
(23)
SIMULATION
The equations of the model described in the previous section were made dimensionless to simplify programming and then were cast into finite difference form. The resulting matrix was solved using the BAND program, an iterative, implicit method developed by Newman[l7]. As mentioned previously, since in this model we consider K, DHIO and nd are functions of water content, so the charge balance and water balance equations should include the gradients of these properties. This makes both of the charge balance and water balance equations become complex, and results in the program approaching a convergence only very slowly when they are solved by implicit techniques. To simplify calculation without sacrificing accuracy, we assume the K, DHzO and nd are constant locally, and neglect their gradient terms. Since in each iteration, the program corrects the estimated values of the rc, DHzO and n,, based on the water distribution obtained from the previous iteration, it can be expected that this simplification will not result in significant calculation error. By comparison with the calculation results obtained from using the charge balance and water balance equations with or without simplification, it is found that the calculation error is within l-4% by using simplified equations, furthermore the program converges 4-10 times faster. Therefore, all the simulation results presented here are obtained by using simplified charge balance and water balance equations. Because of the many interdependencies in the model operatives, boundary conditions and property relationships, the discussion here will only illustrate the effect of several parameters as varied about a reasonable base case. The base case parameters used in the simulations are given in the Table 1. Most of the data are from[8]. Water transport
The hydrogen fuel is usually saturated or over saturated humidified gas. Since water is consumed by proton migration during hydrogen oxidation, the humidity of hydrogen gas will decrease if the gas flow rate is not large enough to compensate for water depletion. The effect of humidity of hydrogen
where r is the platinum coverage on carbon which is related to the platinum loading on the carbon and q is the overpotential. TJ=E-E_,=&-(~~.
RESULTS
0.50
,
(24)
The exchange current i” is based on the platinum surface area. Vogel et a1.[15] have found the hydrogen electrochemical oxidation on either platinum, platinum black and carbon supported platinum has no dependence on the platinum particle size down to 3 nm. Although this may still be a controversial issue[16], in this model we do not consider the effect of platinum particle size on i”. Equations (2) (6), (11) and (23) constitute the basic equations which described the hydrogen electrode of the HZ-O, polymer electrolyte fuel cell. Solving these equations, we can obtain the distributions of CHIO, Cul, i” and 42. Then using equation (20), the total current density can be calculated.
60
80
70 RH
Fig. 2. Model calculations function
/
90
100
%
of the total current density as a of reactant gas humidity. Except for humidity, conditions are for the base case.
Hz-O, polymer fuel cells
2741
Table 1. Base case parameters used in the modeling calculations Carbon particle radius, rc Platinum coverage, 6 Volume of polymer, c Catalyst layer thickness, t,[24] Membrane thickness t,,[8] Fixed charge concentration, C,[S] Hydrogen diffusion coefficient, 0,[8] H, Henry’s constant, k,,[S] Exchange current density, i”[15] Temperature, T Total pressure, P Relative humidity, RH Potential (at x = t& 4: Current collector potential, +r Fraction number, fi l
16 x lo-‘cm 5% 0.5 1 x lo-sun 0.023 cm 1.2 x 10-3mol/cm3 2.59 x lo-ecmx/s 4.5 x 104atmcm3/mol 0.055 A/cm2* 353 K 3atm 80% - 0.050 v 0.00 v 0.4
Data from[lSJ at 22°C corrected to 80°C.
gas on the electrode
performance is demonstrated by Fig. 2. It can be seen, at the same polarization potential, the total current density is linear with the humidity. By incre&ng the humidity from 60% to lOO%, the total current density increases by about 40%. The distributions of the local current density, the hydrogen concentration, the water content and the ohmic overpotential are shown in Figs 3-6,
---
w=1005 PC=-
R(
-.-
Since the hydrogen electrochemical oxidation on the platinum is very fast, the reaction is mainly under molecular hydrogen diffusion control. From Figs 3 and 4, it can be seen that the reaction takes place mostly within a very thin layer (about 1.5-2.0pm for the base case) near the hydrogen gas phase. The local current density decreases rapidly into the electrode because the hydrogen diffusing respectively.
FH=
=
7ou 6ou
d
a!-
I
6 .-.---.
D - 702 ______.__-. RI--I
.-.-.---
__-_-.-.-
J
0.00
0.04
0.08
0.12
x
0.16
0.20
9
0.20
I t,
0.40
0.60 x
Fig. 3. Model calculations of the distributions of the local current density at different humidity. Except for humidity, conditions are for the base case I
0.00
I
0.80
1 .oo
t,
Fig. 5. Model calculations of the distributions of the water content at different humidity. Except for humidity, conditions are for the base case.
.oo
0.60
“u 3
0.40
II 0.00
0.20
0.40
0.60
0.80
1 .oo
Fig. 4. Model calculations of the concentration distributions of the hydrogen at different humidity. Except for humidity, conditions are for the base case.
0.00
0.20
0.40
0.60
0.80
i.cO
Fig. 6. Model calculations of the distributions of the ohmic overpotential at different humidity. Except for humidity, conditions are for the base case.
2142
J.T. WANG
and R. F. SAVINELL
into the electrode from the gas phase side is not fast enough to compensate for the hydrogen consumed by the oxidation reaction. When the humidity is reduced from 100% to 60%, the water content of membrane i decreases from 14 to about 4 (Fig. 5). Since the conductivity of membrane is also related to the water content, the total current density also decreases with lower humidity due to larger ohmic loss in the polymer electrolyte phase (see Fig. 6). From equation (ll), it can be predicted that the gradient of the water concentration in the catalyst layer is related to the total current density. Figure 5 reflects this and shows the gradient of water is larger at higher humidity due to larger total current density which draws more water to the cathode. As mentioned previously, the flux of water transported in the fuel cell depends on the humidity of reactant gas and the gas flow rate both for the fuel and the oxidant, as well as on the total current density passing through the cell. The effect of water flux in the fuel cell electrode on the electrode performance is examined. It is found that varying b from 0.2 to 1.0 has no significant effect on the total current density. From Fig. 7, it can be seen that different values of p mainly change the water content at x = t,. Larger /3 values means more water is drawn out of the catalyst layer to the oxidation gas phase, resulting in lower water content. However, it only has little effect on water content at the side near the gas phase since in this region the water content is assumed to be in equilibrium with the water vapor in the reactant gas. Since the oxidation reaction occurs within a narrow region near the gas phase, it is reasonable to conclude that fl has no significant effect on total current density. Catalyst loading
The effect of the platinum coverage on the total current density is shown in Fig. 8. With increasing coverage, the total current density increases rapidly at first, then only slowly at coverages larger than
about 20%. If keeping all other conditions constant, the electrode with a larger platinum coverage has a larger electrochemical surface area, and thus a larger total current density can be obtained. As expected, Fig. 9 shows that the higher platinum surface cover-
I
L
0.60
0.80
7.001
0.00
0.20
0.40
1.20
4
,
0.60
. -
0.40
I/
0.20 t! 0.00
:
0
20
40
60
60
100
r-/%
Fig. 8. Model calculations of the total current density as a function of the platinum coverage r. Except for r, conditions are for the base case.
age gives a larger local current density, and also a narrower reaction region. This means larger platinum coverages will result in poorer catalyst material utilization. From an economical view, this analysis suggests that an optimal platinum coverage occurs at about 20%. The increase in total current density with platinum surface coverage greater than 20% is chiefly an outcome from increasing the electrochemical surface area near the gas phase, not the whole electrode. The literature often reports platinum surface coverages on carbon in term of a wt% loading. Reported TEM analysis by Ticianelli et al.[ll] shows that platinum particle sizes on the carbon is dependent on the Pt/C weight ratio; ie the higher the ratio, the larger the average particle size. These investigators also found the platinum crystallites are homogeneously dispersed and adhered on the carbon particles. If we assume the platinum particle on the carbon particle is in the shape of semisphere, the platinum coverage F has a relationship with the Pt/C weight ratio wt% according to the following equation: wt% py=‘rc (25) a 2 rppp 1 - wt%
LI
where I~, r and pc, pp are the particle radii and specific de&y of carbon and platinum, respectively.
’ 1.oo
x / t, Fig. 7. Model calculations of the distributions of the water content with different 8. Except for j?, conditions are for the base case.
Fig. 9. Model calculations of the distributions of the local current density with the platinum coverage r. Except for r, conditions are for the base case.
HZ-O, polymer fuel cells Table 2. The relationship of the average platinum particle size and the datinum ccveraac with WC weiaht ratio Pt/C weight
ratio
Average sii (nm)
Platinum coverage
10% 20% 40%
2.2 2.9 3.9
8.5% 14.5% 28.7%
2743
or i” = if0 r[eo + (1 - 0,) exp(Fn/RT)] - 2
x
2
1
exp(ZFq/RT) - 1 n1
where if0 = io(1 - 6JccJ2.
The average platinum diameters and the platinum surface coverages corresponding to different PtfC weight ratios are summarized in Table 2. These results indicate that the optimal Pt/C weight ratio occurs at about 2Owt%. Ticianelli et al.[ll] reported the effect of Pt/C ratio on the electrode performance of a PEM fuel cell. They prepared electrodes with different Pt/C ratios, but maintained the same platinum loading (0.4mgcm-‘). Thus the thickness of catalyst layers decreased in the electrodes with high Pt/C ratio. The experimental results show that the total current density increases with higher Pt/C ratio, but not in a linear manner. These results are consistent with our simulation results. The effect of catalyst layer thickness seems not to be significant here because calculation estimates show the catalyst layer thickness for their experimental conditions are about 32pm, 14~ and 5~ for lOwt%, 20wt% and 40 wt % Pt/C, respectively. These values are much greater than the active reaction region estimated here (see Fig. 3). Catalyst poisoning
Carbon monoxide has been reported[18] to be a serious poison for hydrogen oxidation on a platinum electrode. Hydrogen produced by reforming hydrocarbons usually contains 0.1-l% carbon monoxide[19]. Even though before passing into fuel cell the fuel is conditioned to reduce the CO content, there is still 2-10ppm CO present. Hence when hydrogen reformed hydrocarbon fuel is used, the effect of CO on the performance of electrode should be considered. The poisoning of CO on platinum can be described by a site-elimination effect for hydrogen dissociation[lS]. If we assume that the number of Pt sites has been reduced by 0,) ie the coverage of CO, so that 6, = i -
e,, - eMH
RT Fin
8MH
(27)
’
Coupled with the equilibrium condition of equation (22), one can obtain a kinetic expression for current given by the hydrogen dissociation reaction in the presence of adsorbed CO as i”
=
pr B.
+
(1
-
0,)
x
EA 37:15-F
Catalyst layer thickness and polymer volume fraction
The simulation results show the thickness of the catalyst layer influences the total current density as shown in Figs 10 and 11. Even though a thinner catalyst layer will decrease the total electrochemical surface area the total current density increases. This is related to the fact that the hydrogen oxidation only takes place within a very thin region near the gas phase, thus a thicker electrode will not increase
0.60
,
Y
I
0.40
1
Q . 0.20
0.00 0.00
2
exp(Fq/RT)
Comparing equations (29) with (23), it can be seen that the effect of adsorbed CO can be expressed simply by multiplying i” by a factor of (1 - 9,,)‘. Dhar et al.[20] reports an empirical equation relating equilibrium CO coverage &, on platinum to the gas ratio of Pc-JP,, at different temperatures. Vogel[l4] also reports experimental results of CO adsorption isotherms on Pt. Their results show that the coverage of CO is dependent on the CO concentration and temperature. In the real situation, the coverage of CO varies with time and position within the catalyst layer. As a first order of approximation, we assume the coverage of CO is uniform in the catalyst layer. As shown in Fig. 10, the total current density decreases with 0, increase. It has been reported[19] that when hydrogen gas contains 0.3% CO, the total current density will decrease by 50%. According to Fig. 10, this corresponds to where nearly 50% platinum surface is adsorbed by CO. Therefore, we can conclude that the electrode performance is very sensitive to CO poison. In Fig. 10, the total current density is not linear with (1 - &J2, indicating that the hydrogen oxidation within the electrode is complex with mix control by kinetics, hydrogen diffusion and migration.
E,
1 -f&-&n
i-e,
(30)
(26)
then the potential determined by hydrogen atom coverage in the presence of adsorbed CO is given by:
E=P+
(29)
0.20
0.40 (1 -
1
exp(ZFq/RT) - 1
(28)
0.60
0.80
1.00
e, )*
Fig. 10. Model calculations of the total current density as a function of 0, with different catalyst layer thicknesses. Except for 0, and t, , conditions are for the base case.
2144
J.T. WANG and R.F.SAVINELL 0.60
1
0.00’ . 0
’
’
’
’
1
2
4
6
8
10
0
10
the total current density very much, but will contribute to a large ohmic voltage loss. This is clearly indicated in Fig. 12 which shows the ohmic overpotential distribution with different catalyst
1
0.015,
0.20
0.40
0.60
0.80
1.oo
x I t, Fig. 12. Model calculations of the distributions of the ohmic overpotential with different electrode thicknesses. Except for t, , conditions are for the base case.
mV
layer thickness. When the catalyst layer thickness is reduced from 1Opm to 1.25~m, the ohmic voltage loss at x = 0 decreases from 24% to 4% of the total polarization potential. Also, as shown in Fig. 11 the effect of catalyst layer thickness is dependent on the magnitude of izo. The total current density decreases when catalyst layer thickness is less than 2pm because the electrochemical surface area becomes too small and its effect on total current density predominates over the ohmic voltage loss. The simulation indicates that there is an optimal value of polymer volume fraction which depends on the catalyst layer thickness. The optimum value is related to the fact that a tradeoff exists between gas diffusion as a controlling factor and ohmic losses becoming important for thicker catalyst layers. Calculation results are shown in Fig. 13 which demonstrates the maximum values of e are around 0.4 to 0.7. The maximum total current density appears at E = 0.5 and t, = 1.25pm with all other conditions given in Table 1. In general, the simulation results show that the optimal E is 0.5, and the optimal electrode thickness is around 1.25-4.Opm and is
I
T 5 Q .
50
Fig. 14. Model calculations of the polarization curves with different effective diffusion coefficient of hydrogen. Except for Du, , conditions are for the base case.
1.25
\
0.40
40
30
(9,- @I ) /
t, l/m Fig. 11. Model calculations of the total current density as a function of the catalyst layer thickness with different iL. (a) 0.055, (b) 0.025, (c) 0.01, (d) 0.005, (e) 0.001 A/cm’. Except for t, and iz,,, conditions are for the base case.
0.00
20
a
,
.:
.oo
h
0.75
i
!
0.30
0.20 0.00 0.10 0.00
0.20
0.40
0.60
0.00
1 .oo
E
Fig. 13. Model calculations of the total current density as a function of the fraction of polymer l with different electrode thicknesses. Except for c, t, and i: = 0.025A/cm2, conditions are for the base case.
0.20
0.40
0.60
0.80
1.oo
x I t, Fig. 15. Model calculations of local current density distribution for the different effective diffusion coeflicients DuI. (a) 2.59x 10m6, (b) 5.18 x 10e6, (c) 1.03 x lo-‘, (d) 2.59 x lo-‘, (e) 5.18 x 10-scm2/s. Inset, effective reaction zone thickness as a function of effective diffusion coefficient. Except for DHz, conditions are for the base case.
Hz-G, polymer fuel cells
dependent on izO (see Fig. 11). The latter result is consistent with the experimental findings of Wilson and Gottesfeld[Zl]. Finally, as noted earlier, the performance of the electrode structure is largely controlled by hydrogen diffusion into the polymer. It should be possible to enhance this diffusion rate by incorporating gas permeable fibers such as teflon into the catalyst layer structure. The catalyst layer then becomes similar to the agglomerated structureC22, 231. Utilizing this method, it may be possible to enhance the effective diffusion coefficient by an order of magnitude. This will have a significant effect on electrode performance as demonstrated in the calculated polarization curves shown in Fig. 14. The local current density with different effective diffusion coefficients is shown in Fig. 15. We define an effective reaction zone thickness as the region where the local current density is greater than 4% of the current at x = 0. The inset in Fig. 15 shows the increase in effective reaction zone thickness as a function of effective diffusion coefficients. The larger the effective diffusion coefftcient, the thicker the effective reaction zone, as well as a more efficient utilization of the catalyst.
CONCLUSIONS Macro-homogeneous porous electrode theory was used to develop a model of hydrogen oxidation electrodes formed by catalyst particles embedded into a proton conducting membrane film. The effects of humidity, platinum coverage, CO poison, catalyst layer thickness, polymer volume fraction and hydrogen effective diffusion coefficients on the electrode performance are examined. From simulation results, several conclusions can be drawn. 1. The hydrogen oxidation at an electrode formed by bonding the catalyst particles to the membrane is primarily under diffusion control, The reaction takes place within a very thin region near the gas phase. Electrode performance can be enhanced significantly if the effective diffusion coefficient of hydrogen could be increased. 2. The humidity of the reactant gas has a significant effect on the electrode performance. Increasing the humidity of the reactant gas can significantly increase the total current density. 3. From an economical view, an optimal platinum coverage need not exceed 20% (or 20wt% Pt/C). Larger platinum coverage will increase the cost, but only slightly enhance the electrode performance. 4. Since the platinum catalyst can be seriously poisoned by CO, the electrode performance is sensitive to reactant gas containing CO. The total current density decreases as Oco increases. 5. Electrode structure parameters of catalyst layer thickness and polymer volume fraction have a significant effect on the electrode performance. A thicker catalyst layer will result in a larger ohmic voltage
loss and higher
catalyst
cost. The optimal
2745
polymer volume fraction and catalyst layer thickness are 0.5 and 1.5-4.0pm, respectively, for the hydrogen electrode.
REFERENCES 1. D. G. Lovering, J. power Sources 29 (1990). 2. M. Verbrugge and R. Hill, J. phys. Chem. 92, 6778 (1988). 3. M. Verbrugge, J. electrochem. Sot. 136,417 (1989). 4. R. Hill and M. Verbrugge, J. electrochem. Sot. 137, 886 (1990). 5. J. L. Fales, N. E. Vanderborgh and P. Strceve, in Diaphragms,
Separators,
and Ion-Exchange
Membranes,
(Edited by J. W. van Zee, R. E. White, K. Kinoshita and H. S. Bumey), PV 86-13, p. 179. Softbound Proceedings Series, The Electrochemical Society, Pennington, NJ (1986). 6. T. Fuller and J. Newman, in Fuel Cells (Edited by R. E. White and A. J. Aoulebv) PV 89-14. D. 25. Softbound Proceedings Series: ‘The’ ‘Electroche&al, Pennington, NJ (1989). 7. D. Bemardi, .I. electrochem. Sot. 137,3344 (1990). 8. D. Bemardi and M. Verbrugge, in Proceedings of the Symposium on Modeling
of Batteries and Fuel Cell,
(Edited by R. E. White, M. W. Verbrugge and J. F. Stroke]) PV 91-10. D. 240. The Electrochemical Societv. _I Pennington, NJ (1991). 9. T. E. Springer, T. A. Zawodzinski and S. Gottesfeld, J. electrochem. Sot. 1X$2334 (1991). 10. T. E. Springer and S. Gottesfeld, in Proceedings of the Symposium on Modeling
of Batteries ana’ Fuel Cell,
(Edited by R. E. White, M. W. Verbrugge and J. F. Stroke]) PV 91-10, p. 197. The Electrochemical Society, Pennington, NJ (1991). 11. E Ticianelli, J. Beery and Supramaniam Srinivasan, J. appt. Electrochem. 21,597 (1991). 12. J. Newman and W. Tiedemann, AIChE J. 21,25 (1975). 13. A. B. LaConti, A. R. Fragala and J. R Boyack, Electrode Materials and Processes for Energy Conservation and Storage p. 354. Softbound Proceedings Series, The
Electrochemical Society, Pennington, NJ (1977). 14. K. J. Vetter, Electrochemical Kinetics, p. 522. Academic Press, New York (1967). 15. W. Vogel, J. Lundquist, P. Ross and P. Stonehart, Electrochim. Acta 20,79 (1975). 16. S. Mukerjee, J. appl. Electrochem. 20,537 (1990). 17. J. Newman, Electrochemical Systems. Prentice-Hall, NJ (1973). 18. P. Stonehart and G. Kohlmayr, Electrochim. Acta 17, 369 (1972).
19. K. Prater, J. power Sources 29,239 (1990). 20. H. Dhar, A. Kush, D. Pate1 and L. Christner, in Proceedings of the Symposium on Electrochemical and Thermal Modeling of Battery, Fuel Cell, and Photoenergy Conversion Systems (Edited by J. Selman and H.
Maru) PV 86-12, p. 284. The Electrochemical Society, Pennington, NJ (1986). 21. M. S. Wilson and S. Gottesfeld, J. electrochem. Sot. 139, 128 (1992). 22. J. Giner and C. Hunter, .I. electrochem Sot. 116, 1124 (1969). 23. R. P. Iczkowski and M. B. Cutlip, J. electrochem Sot. 127, 1433 (1980).
24. M. W. Verbrugge and R. F. Hill, J. electrochem. Sot. 137,377o (1990).
1992 0
0013~4686/92 55.&l + 0.00 1992. Pergamon Press Ltd.
SIMULATION STUDIES ON THE FUEL ELECTRODE OF A Hz-O2 POLYMER ELECTROLYTE FUEL CELL JIANG-TAOWANG and ROBERTF. SAMNELL* Department of Chemical Engineering, Case Western Reserve University, Cleveland, OH 44106, U.S.A. (Received 3 February 1992; in revisedform 5 May 1992) Abstract-The macro-homogeneous porous electrode theory is used to develop a model which describes the catalyst layer of the hydrogen electrode formed by catalyst particles that are bonded to the membrane. The water transport in the catalyst layer and polymer electrolyte membrane is considered. The effects of catalyst layer structure parameters such as polymer volume fraction, catalyst layer thickness, platinum loading and reactant gas humidity as well as CO poison on the hydrogen electrode behavior are examined. The results show that the catalyst layer thickness has a significant effect on the electrode performance. A thicker catalyst layer will result in a larger ohmic voltage loss and higher catalyst cost. The optimal polymer volume fraction and catalyst layer thickness are 0.5 and 1.54ym, respectively, for
this electrode. An optimal platinum surface coverage on carbon need not exceed 20% (20wt% Pt/C). Larger platinum coverage will increase the cost, but only slightly enhance the electrode performance. Key words: PEM cell, modeling, electrode structures, gas diffusion electrodes and water transport.
NOTATION a
c H2 c l4+ Clb0
G DHz DEl+ DHZ0 E EO E=I F i w
1
i” i”co
k Ha nd NW
P P Hz PW P sat r, xp RH cb
ld
T
E
specific surface area of catalyst phase, cm- 1 concentration of hydrogen, mol/cm3 concentration of proton, mol/cm3 concentration of water, mol/cm3 concentration of fixed function group, mol/cm3 diffusion coefficient of hydrogen, cm2/s diffusion coefficient of proton, cm2/s diffusion coefficient of water, cm’/s electrode potential, V standard electrode potential of hydrogen, V equilibrium electrode potential, V Faraday’s constant, 96 487 C/equiv total current density, A/cm2 local current density, A/cm2 exchange current density, A/cm2 exchange current density in the presence of CO, A/cm2 Henry’s constant of hydrogen, atm cm3/mol drag coefficient, dimensionless flux of water at x = td , mol/cm2 s reactant gas pressure, atm partial pressure of hydrogen, atm partial pressure of water vapor, atm saturated pressure of water vapor, atm radius of carbon particle, cm radius of platinum particle, cm universal gas constant, 8.314 J/moldeg relative humidity, % thickness of polymer electrolyte membrane, cm thickness of catalyst layer, cm absolute temperature, deg K mobility of proton, cm2/V s activity of water vapor, dimensionless fraction number, dimensionless platinum coverage, dimensionless
*Author to whom correspondence should be addresed.
4 tlobm e”
eM e MH
eco
n”
PC
volume fraction of polymer phase, dimensionless overpotential, V ohmic voltage loss in polymer defined as equal to I$~ - &.j, V equilibrium coverage of adsorbed hydrogen, dimensionless fraction of platinum surface area, dimensionless fraction of platinum surface area adsorbed by H, , dimensionless fraction of platinum surface area adsorbed by CO, dimensionless conductivity of polymer phase, mho/cm water content, ie the ratio of CuzO/Crr dimensionless density of carbon, g/cm3 density of platinum, g/cm3 potential at catalyst phase, V potential at polymer electrolyte phase, V.
INTRODUCTION Fuel cells employing a solid polymer electrolyte membrane recently have been receiving more and more attention[l] due to their promise for high energy density power plants for both stationary or mobile applications. The main features of this kind of fuel cell are pollution-free operation, low operating temperature, less corrosion problems and high power density. However, there still are several unsolved problems, such as membrane dehydration due to water transport in the fuel cell, and high catalyst cost. There have been a number of reported studies on both of these issues[2-111. Extensive modeling of transport properties in perfluorsulfonate ionomers based on dilute solution theory have been presented by Verbrugge and Hill[2-41. Fales et aI.[5] reports an isothermal water map based on hydraulic permeability and electro-
2731
2738
J. T. WANG and R. F. SAVINELL
osmotic drag data. Fuller and Newman[6] applied concentrated solution theory and employed literature data on transport properties to produce a general description of water transport in a fuel cell membrane. Bernardi[7] developed a membrane water transport model which suggests optima1 conditions to operate a hydrogen/oxygen fuel cell. Bernardi and Verbrugge[8] model a PEM fuel cell taking into account gas and water transport, porous electrode theory at the anode and the cathode and transport through the gas diffusers. With only two adjustable parameters they were able to reproduce the trends in experimental polarization curves. They conclude that oxygen and water transport are factors which limit fuel cell electrode performance. Springer et al. reports two model studies on the polymer electrolyte fuel cell[9, lo]. One model is a steady-state description of a complete polymer electrolyte fuel ce11[9]. In this model the water transported by diffusion and electro-osmosis are considered with water sorption isotherms and membrane conductivity data as a function of membrane water content. In the other model[lO] the cathode catalyst layer in a polymer electrolyte fuel cell is the focus of attention. This model explains certain observed polarization curve features at high current densities. In order to reduce the catalyst cost and at same time maintain high power density, much effort has been directed at using new catalyst materials, and changing electrode fabrication procedures[ 111. The electrode performance is not only dependent on operating conditions such as gas pressure and gas humidity, but also strongly dependent on the electrode structure and catalyst loading. Therefore it is necessary to acquire a deeper understanding about the effects of the electrode structure parameters on the electrode performance. To address this issue, we apply the macro-homogeneous porous electrode theory to develop a one-dimensional mode1 which describes the performance of electrodes formed by imbedding catalyzed carbon particles that are bonded to a membrane of a proton conductive polymer. The effects of basic electrode structure parameters such as polymer volume fraction, catalyst layer thickness, platinum loading, reactant gas humidity, CO poisoning and hydrogen effective diffusion coefficients on the hydrogen electrode behavior are examined. In this model, axial variations in gas composition are neglected but should be considered in a description of a full-size fuel cell electrode.
MODEL
DEVELOPMENT
A schematic illustration of the model system of Hz-O2 polymer electrolyte fuel cell is shown in Fig. 1. Macro-homogeneous porous electrode theory[12] is used to describe the electrodes formed by the catalyst particles that are bonded to the membrane. In this model, two phases are assumed to exist in the catalyst layer. The polymer phase is assumed to be a continuum of the fluorocarbon backbone, polymer ions, and absorbed water. The second phase is the platinum covered carbon particles which are assumed to be uniformly dispersed throughout the
Catalyst
Layer
Catalyst
Membrane
Layer
Carnode
A”CdG?
0 t.3 t, + L Fig. 1. Schematic illustration of the model system of HZ-O, polymer electrolyte fuel cell.
catalyst layer. Also assumed is that the platinum is uniformly loaded on the carbon particles. This assumption agrees well with reported transmission electron microscopy (TEM) analysis results[ 111. If we consider the carbon particle to be a sphere, the specific surface area of the catalyst phase a can be expressed by the following equation &l-E) rc
(1)
where E is the volume fraction of polymer and r, is the radius of carbon particle. On the anode side of the polymer electrolyte fuel cell, the reactant gas is humidified hydrogen. Here we assume the dissolved hydrogen in polymer phase is in equilibrium with the partial pressure of hydrogen in gas phase, and Henry’s law can be used to determine the concentration of dissolved hydrogen. Since the model is one-dimensional, the gas phase composition is assumed to be constant and thus gas flow rates and reaction stoichiometry are not considered. The diffusion of dissolved hydrogen in the catalyst layer and its subsequent reaction can be described by the following mass balance equation
a%
ai” = 2cFD,, -
ax2
where i” is the local current density based on the specific surface area of the catalyst phase (A/cm2). The boundary conditions for equation (2) are x = 0, CHI = c;,
(3)
x=td,rac,,= 2%. ax
tb
In equation (3) Ci, can be determined by (5) where kH2 is Henry’s constant, and P,, is the partial pressure of hydrogen. At x = t,, we assume the flux of H, is equal to that of H2 in the membrane, and the concentration of H, at x = t, + t, is negligible. In the polymer phase, the protons associated with the fixed functional groups are the only movable charge species which carry the current. Therefore, there is no concentration gradient of proton and its
Hr-0, polymer fuel cells concentration is constant which is equal to the concentration of fixed functional groups Cr. The charge balance equation for this situation becomes ai” = - F2uH+C,.,+e
z
2739
In this model, an empirical equation relating DHzO (cm2/s) with water content Iz from experimental results[9] is used. 1 1 - 303 273 + T
D rl,d = 10m6 exp
or
)I
x (2.563 - 0.331 + 0.02641’ ai”
av2
=
- 0.00067113)
-KEdX2
where K is the conductivity of polymer electrolyte. Here we have simplified the charge balance equation by neglecting the term of the gradient of rc. However, we still consider that K is a function of the water content of the polymer, and assume k is constant locally. This will be discussed more fully in the following section. Gottesfeld et al. have reported an empirical equation describing the relationship of K with water content 1[9].
(13) 1 1 - 303 273 + T
D 311<4 = 10e6 exp
>I
x (6.89 - 1.331) 1 --p 303
D 2<1<3 = 10m6 exp
x (-3.1
(14) 1 273 + T
(15)
+ 2.02).
At the boundary x = 0, rc=exp
cHI0 (0.005139A - 0.00326)
where 1 = Cu,o/Cr. equation (7) are
The boundary
x=0,-=
x =
84, ax
conditions
(8) for
o
fa, (b2 = &.
(10)
The water balance plays a critical role in the performance of a polymer electrolyte fuel cell. In order to acquire a deeper understanding about water effects on the electrochemical behavior of electrodes, the water transport in the catalyst layer is considered. When a current passes through the external circuit, the equivalent coulombs of proton are transported from anode side to cathode side. Since in this electrolyte protons always combine with water molecules in the proton transport process, water is also moved toward the cathode direction which produces a concentration gradient of water in the polymer phase. Since the water concentration is low (C lo-’ M), dilute solution theory is applicable, and the water mass balance equation can be described by -
o + n,ai”/F %,o a=c,
2
ax2
(16)
1’ = 0.043 + 17.81~ - 39.85a’ + 36.0a3
(17)
a = P,lp.,, .
(18)
where
P, and P,,, are the partial pressures of water and saturated pressure of water at a given temperature, respectively. At the other boundary x = t,, the flux of water N, can be expressed by the following equation
-tnd i/F.
X=fd
the concentration
gradient
(19)
is
(11)going to be a function of the water production rate
In equation (1 l), DHIO is the water diffusion coefftcient and nd is the drag coellicient, ie the number of water molecules dragged per proton transported. Similar to the charge balance equation, we consider both DHZOand n,, to be the function of water content 1 and constant locally. The first term of equation (11) describes the diffusion effect due to the concentration gradient of water, and the other term illustrates the water transport due to the drag of protons. LaConti et aL[13] and Gottesfeld et a/.[91 have measured n, and assumed that it is linearly proportional to the water content of the polymer according to the following equation : nd = 2.512122.
Go
where C&, can be determined . _by the _ activity . _ of water vapor at the gas and catalyst layer interface. Zawodzinski et al.[9] have measured the membrane water content as a function of humidity for the Nafion 117 membrane. Based on their data, an empirical relationship of 1 vs. water vapor activity a at 30°C is used in this model (assuming it can be used at 80°C due to absence of data at this temperature).
In this expression,
= 0.
=
(12)
at the cathode and the transport conditions between the membrane and the adjacent gas phases. In order to solve the differential equation, we assume that N, is proportional to the total current density, N, = Bi/2F, where /3 is a fraction number. The more water moving across the interface at x = t,+, the larger b becomes. According to equation (19), when /l> 2n,, the concentration gradient of water will become negative, indicating that the movement of water by diffusion has the same direction with the water transported by electro-osmosis. This will intensify membrane dehydration. Hence, at the desired operating condition, the maximum value of fi should not be larger than 3.2 (nd = 1.6, when water content 1 = 14) in order to minimize a membrane dehydration effect. Taking into account the dependence of transport
J.T. WANG and R. F. SAVINELL
2740
properties on the level of hydration, the simulation results show that the concentration gradient of water becomes negative when /? > 1.5. On the other hand, since the current passing through the cell is usually large, water diffusion by water concentration gradient will not be large enough to balance water transported by proton migration, thus fl will usually not be negative. Therefore, it is believed that fi should vary from about 0 to 1. The total current density i is calculated by integrating the local density throughout the catalyst layer X=ld X’l.j i=a i.dx=;(l -e) i” dx. (20) c I x=0 I x=0 The mechanism for the electrochemical oxidation of molecular hydrogen on the platinum in acid electrolyte is believed to proceed according to the TafelVolmer sequence which involves a slow dissociation of adsorbed hydrogen molecule to hydrogen atoms, followed by fast electrochemical oxidation of adsorbed hydrogen atoms to protons[l4, 151. Hz+2M+2MH
(slow reaction) (fast reaction)
2MH-+2M+2H++2em
The surface coverage of adsorbed hydrogen is governed by the electrode potential as
E=E’+yln-$
(21)
MH At the equilibrium potential, i = 0 RT
E,, = E” + yin,
l-0,
(22)
0
where 8, is the equilibrium coverage of hydrogen. E” is the standard electrode potential, which is equal to zero for the hydrogen reaction. The current given by hydrogen dissociation reaction can be described by i” = i’r[&, + (1 - 6,) exp(Fq/RT)]-2 x
3
exp(ZFq/RT) HZ
1
- 1
(23)
SIMULATION
The equations of the model described in the previous section were made dimensionless to simplify programming and then were cast into finite difference form. The resulting matrix was solved using the BAND program, an iterative, implicit method developed by Newman[l7]. As mentioned previously, since in this model we consider K, DHIO and nd are functions of water content, so the charge balance and water balance equations should include the gradients of these properties. This makes both of the charge balance and water balance equations become complex, and results in the program approaching a convergence only very slowly when they are solved by implicit techniques. To simplify calculation without sacrificing accuracy, we assume the K, DHzO and nd are constant locally, and neglect their gradient terms. Since in each iteration, the program corrects the estimated values of the rc, DHzO and n,, based on the water distribution obtained from the previous iteration, it can be expected that this simplification will not result in significant calculation error. By comparison with the calculation results obtained from using the charge balance and water balance equations with or without simplification, it is found that the calculation error is within l-4% by using simplified equations, furthermore the program converges 4-10 times faster. Therefore, all the simulation results presented here are obtained by using simplified charge balance and water balance equations. Because of the many interdependencies in the model operatives, boundary conditions and property relationships, the discussion here will only illustrate the effect of several parameters as varied about a reasonable base case. The base case parameters used in the simulations are given in the Table 1. Most of the data are from[8]. Water transport
The hydrogen fuel is usually saturated or over saturated humidified gas. Since water is consumed by proton migration during hydrogen oxidation, the humidity of hydrogen gas will decrease if the gas flow rate is not large enough to compensate for water depletion. The effect of humidity of hydrogen
where r is the platinum coverage on carbon which is related to the platinum loading on the carbon and q is the overpotential. TJ=E-E_,=&-(~~.
RESULTS
0.50
,
(24)
The exchange current i” is based on the platinum surface area. Vogel et a1.[15] have found the hydrogen electrochemical oxidation on either platinum, platinum black and carbon supported platinum has no dependence on the platinum particle size down to 3 nm. Although this may still be a controversial issue[16], in this model we do not consider the effect of platinum particle size on i”. Equations (2) (6), (11) and (23) constitute the basic equations which described the hydrogen electrode of the HZ-O, polymer electrolyte fuel cell. Solving these equations, we can obtain the distributions of CHIO, Cul, i” and 42. Then using equation (20), the total current density can be calculated.
60
80
70 RH
Fig. 2. Model calculations function
/
90
100
%
of the total current density as a of reactant gas humidity. Except for humidity, conditions are for the base case.
Hz-O, polymer fuel cells
2741
Table 1. Base case parameters used in the modeling calculations Carbon particle radius, rc Platinum coverage, 6 Volume of polymer, c Catalyst layer thickness, t,[24] Membrane thickness t,,[8] Fixed charge concentration, C,[S] Hydrogen diffusion coefficient, 0,[8] H, Henry’s constant, k,,[S] Exchange current density, i”[15] Temperature, T Total pressure, P Relative humidity, RH Potential (at x = t& 4: Current collector potential, +r Fraction number, fi l
16 x lo-‘cm 5% 0.5 1 x lo-sun 0.023 cm 1.2 x 10-3mol/cm3 2.59 x lo-ecmx/s 4.5 x 104atmcm3/mol 0.055 A/cm2* 353 K 3atm 80% - 0.050 v 0.00 v 0.4
Data from[lSJ at 22°C corrected to 80°C.
gas on the electrode
performance is demonstrated by Fig. 2. It can be seen, at the same polarization potential, the total current density is linear with the humidity. By incre&ng the humidity from 60% to lOO%, the total current density increases by about 40%. The distributions of the local current density, the hydrogen concentration, the water content and the ohmic overpotential are shown in Figs 3-6,
---
w=1005 PC=-
R(
-.-
Since the hydrogen electrochemical oxidation on the platinum is very fast, the reaction is mainly under molecular hydrogen diffusion control. From Figs 3 and 4, it can be seen that the reaction takes place mostly within a very thin layer (about 1.5-2.0pm for the base case) near the hydrogen gas phase. The local current density decreases rapidly into the electrode because the hydrogen diffusing respectively.
FH=
=
7ou 6ou
d
a!-
I
6 .-.---.
D - 702 ______.__-. RI--I
.-.-.---
__-_-.-.-
J
0.00
0.04
0.08
0.12
x
0.16
0.20
9
0.20
I t,
0.40
0.60 x
Fig. 3. Model calculations of the distributions of the local current density at different humidity. Except for humidity, conditions are for the base case I
0.00
I
0.80
1 .oo
t,
Fig. 5. Model calculations of the distributions of the water content at different humidity. Except for humidity, conditions are for the base case.
.oo
0.60
“u 3
0.40
II 0.00
0.20
0.40
0.60
0.80
1 .oo
Fig. 4. Model calculations of the concentration distributions of the hydrogen at different humidity. Except for humidity, conditions are for the base case.
0.00
0.20
0.40
0.60
0.80
i.cO
Fig. 6. Model calculations of the distributions of the ohmic overpotential at different humidity. Except for humidity, conditions are for the base case.
2142
J.T. WANG
and R. F. SAVINELL
into the electrode from the gas phase side is not fast enough to compensate for the hydrogen consumed by the oxidation reaction. When the humidity is reduced from 100% to 60%, the water content of membrane i decreases from 14 to about 4 (Fig. 5). Since the conductivity of membrane is also related to the water content, the total current density also decreases with lower humidity due to larger ohmic loss in the polymer electrolyte phase (see Fig. 6). From equation (ll), it can be predicted that the gradient of the water concentration in the catalyst layer is related to the total current density. Figure 5 reflects this and shows the gradient of water is larger at higher humidity due to larger total current density which draws more water to the cathode. As mentioned previously, the flux of water transported in the fuel cell depends on the humidity of reactant gas and the gas flow rate both for the fuel and the oxidant, as well as on the total current density passing through the cell. The effect of water flux in the fuel cell electrode on the electrode performance is examined. It is found that varying b from 0.2 to 1.0 has no significant effect on the total current density. From Fig. 7, it can be seen that different values of p mainly change the water content at x = t,. Larger /3 values means more water is drawn out of the catalyst layer to the oxidation gas phase, resulting in lower water content. However, it only has little effect on water content at the side near the gas phase since in this region the water content is assumed to be in equilibrium with the water vapor in the reactant gas. Since the oxidation reaction occurs within a narrow region near the gas phase, it is reasonable to conclude that fl has no significant effect on total current density. Catalyst loading
The effect of the platinum coverage on the total current density is shown in Fig. 8. With increasing coverage, the total current density increases rapidly at first, then only slowly at coverages larger than
about 20%. If keeping all other conditions constant, the electrode with a larger platinum coverage has a larger electrochemical surface area, and thus a larger total current density can be obtained. As expected, Fig. 9 shows that the higher platinum surface cover-
I
L
0.60
0.80
7.001
0.00
0.20
0.40
1.20
4
,
0.60
. -
0.40
I/
0.20 t! 0.00
:
0
20
40
60
60
100
r-/%
Fig. 8. Model calculations of the total current density as a function of the platinum coverage r. Except for r, conditions are for the base case.
age gives a larger local current density, and also a narrower reaction region. This means larger platinum coverages will result in poorer catalyst material utilization. From an economical view, this analysis suggests that an optimal platinum coverage occurs at about 20%. The increase in total current density with platinum surface coverage greater than 20% is chiefly an outcome from increasing the electrochemical surface area near the gas phase, not the whole electrode. The literature often reports platinum surface coverages on carbon in term of a wt% loading. Reported TEM analysis by Ticianelli et al.[ll] shows that platinum particle sizes on the carbon is dependent on the Pt/C weight ratio; ie the higher the ratio, the larger the average particle size. These investigators also found the platinum crystallites are homogeneously dispersed and adhered on the carbon particles. If we assume the platinum particle on the carbon particle is in the shape of semisphere, the platinum coverage F has a relationship with the Pt/C weight ratio wt% according to the following equation: wt% py=‘rc (25) a 2 rppp 1 - wt%
LI
where I~, r and pc, pp are the particle radii and specific de&y of carbon and platinum, respectively.
’ 1.oo
x / t, Fig. 7. Model calculations of the distributions of the water content with different 8. Except for j?, conditions are for the base case.
Fig. 9. Model calculations of the distributions of the local current density with the platinum coverage r. Except for r, conditions are for the base case.
HZ-O, polymer fuel cells Table 2. The relationship of the average platinum particle size and the datinum ccveraac with WC weiaht ratio Pt/C weight
ratio
Average sii (nm)
Platinum coverage
10% 20% 40%
2.2 2.9 3.9
8.5% 14.5% 28.7%
2743
or i” = if0 r[eo + (1 - 0,) exp(Fn/RT)] - 2
x
2
1
exp(ZFq/RT) - 1 n1
where if0 = io(1 - 6JccJ2.
The average platinum diameters and the platinum surface coverages corresponding to different PtfC weight ratios are summarized in Table 2. These results indicate that the optimal Pt/C weight ratio occurs at about 2Owt%. Ticianelli et al.[ll] reported the effect of Pt/C ratio on the electrode performance of a PEM fuel cell. They prepared electrodes with different Pt/C ratios, but maintained the same platinum loading (0.4mgcm-‘). Thus the thickness of catalyst layers decreased in the electrodes with high Pt/C ratio. The experimental results show that the total current density increases with higher Pt/C ratio, but not in a linear manner. These results are consistent with our simulation results. The effect of catalyst layer thickness seems not to be significant here because calculation estimates show the catalyst layer thickness for their experimental conditions are about 32pm, 14~ and 5~ for lOwt%, 20wt% and 40 wt % Pt/C, respectively. These values are much greater than the active reaction region estimated here (see Fig. 3). Catalyst poisoning
Carbon monoxide has been reported[18] to be a serious poison for hydrogen oxidation on a platinum electrode. Hydrogen produced by reforming hydrocarbons usually contains 0.1-l% carbon monoxide[19]. Even though before passing into fuel cell the fuel is conditioned to reduce the CO content, there is still 2-10ppm CO present. Hence when hydrogen reformed hydrocarbon fuel is used, the effect of CO on the performance of electrode should be considered. The poisoning of CO on platinum can be described by a site-elimination effect for hydrogen dissociation[lS]. If we assume that the number of Pt sites has been reduced by 0,) ie the coverage of CO, so that 6, = i -
e,, - eMH
RT Fin
8MH
(27)
’
Coupled with the equilibrium condition of equation (22), one can obtain a kinetic expression for current given by the hydrogen dissociation reaction in the presence of adsorbed CO as i”
=
pr B.
+
(1
-
0,)
x
EA 37:15-F
Catalyst layer thickness and polymer volume fraction
The simulation results show the thickness of the catalyst layer influences the total current density as shown in Figs 10 and 11. Even though a thinner catalyst layer will decrease the total electrochemical surface area the total current density increases. This is related to the fact that the hydrogen oxidation only takes place within a very thin region near the gas phase, thus a thicker electrode will not increase
0.60
,
Y
I
0.40
1
Q . 0.20
0.00 0.00
2
exp(Fq/RT)
Comparing equations (29) with (23), it can be seen that the effect of adsorbed CO can be expressed simply by multiplying i” by a factor of (1 - 9,,)‘. Dhar et al.[20] reports an empirical equation relating equilibrium CO coverage &, on platinum to the gas ratio of Pc-JP,, at different temperatures. Vogel[l4] also reports experimental results of CO adsorption isotherms on Pt. Their results show that the coverage of CO is dependent on the CO concentration and temperature. In the real situation, the coverage of CO varies with time and position within the catalyst layer. As a first order of approximation, we assume the coverage of CO is uniform in the catalyst layer. As shown in Fig. 10, the total current density decreases with 0, increase. It has been reported[19] that when hydrogen gas contains 0.3% CO, the total current density will decrease by 50%. According to Fig. 10, this corresponds to where nearly 50% platinum surface is adsorbed by CO. Therefore, we can conclude that the electrode performance is very sensitive to CO poison. In Fig. 10, the total current density is not linear with (1 - &J2, indicating that the hydrogen oxidation within the electrode is complex with mix control by kinetics, hydrogen diffusion and migration.
E,
1 -f&-&n
i-e,
(30)
(26)
then the potential determined by hydrogen atom coverage in the presence of adsorbed CO is given by:
E=P+
(29)
0.20
0.40 (1 -
1
exp(ZFq/RT) - 1
(28)
0.60
0.80
1.00
e, )*
Fig. 10. Model calculations of the total current density as a function of 0, with different catalyst layer thicknesses. Except for 0, and t, , conditions are for the base case.
2144
J.T. WANG and R.F.SAVINELL 0.60
1
0.00’ . 0
’
’
’
’
1
2
4
6
8
10
0
10
the total current density very much, but will contribute to a large ohmic voltage loss. This is clearly indicated in Fig. 12 which shows the ohmic overpotential distribution with different catalyst
1
0.015,
0.20
0.40
0.60
0.80
1.oo
x I t, Fig. 12. Model calculations of the distributions of the ohmic overpotential with different electrode thicknesses. Except for t, , conditions are for the base case.
mV
layer thickness. When the catalyst layer thickness is reduced from 1Opm to 1.25~m, the ohmic voltage loss at x = 0 decreases from 24% to 4% of the total polarization potential. Also, as shown in Fig. 11 the effect of catalyst layer thickness is dependent on the magnitude of izo. The total current density decreases when catalyst layer thickness is less than 2pm because the electrochemical surface area becomes too small and its effect on total current density predominates over the ohmic voltage loss. The simulation indicates that there is an optimal value of polymer volume fraction which depends on the catalyst layer thickness. The optimum value is related to the fact that a tradeoff exists between gas diffusion as a controlling factor and ohmic losses becoming important for thicker catalyst layers. Calculation results are shown in Fig. 13 which demonstrates the maximum values of e are around 0.4 to 0.7. The maximum total current density appears at E = 0.5 and t, = 1.25pm with all other conditions given in Table 1. In general, the simulation results show that the optimal E is 0.5, and the optimal electrode thickness is around 1.25-4.Opm and is
I
T 5 Q .
50
Fig. 14. Model calculations of the polarization curves with different effective diffusion coefficient of hydrogen. Except for Du, , conditions are for the base case.
1.25
\
0.40
40
30
(9,- @I ) /
t, l/m Fig. 11. Model calculations of the total current density as a function of the catalyst layer thickness with different iL. (a) 0.055, (b) 0.025, (c) 0.01, (d) 0.005, (e) 0.001 A/cm’. Except for t, and iz,,, conditions are for the base case.
0.00
20
a
,
.:
.oo
h
0.75
i
!
0.30
0.20 0.00 0.10 0.00
0.20
0.40
0.60
0.00
1 .oo
E
Fig. 13. Model calculations of the total current density as a function of the fraction of polymer l with different electrode thicknesses. Except for c, t, and i: = 0.025A/cm2, conditions are for the base case.
0.20
0.40
0.60
0.80
1.oo
x I t, Fig. 15. Model calculations of local current density distribution for the different effective diffusion coeflicients DuI. (a) 2.59x 10m6, (b) 5.18 x 10e6, (c) 1.03 x lo-‘, (d) 2.59 x lo-‘, (e) 5.18 x 10-scm2/s. Inset, effective reaction zone thickness as a function of effective diffusion coefficient. Except for DHz, conditions are for the base case.
Hz-G, polymer fuel cells
dependent on izO (see Fig. 11). The latter result is consistent with the experimental findings of Wilson and Gottesfeld[Zl]. Finally, as noted earlier, the performance of the electrode structure is largely controlled by hydrogen diffusion into the polymer. It should be possible to enhance this diffusion rate by incorporating gas permeable fibers such as teflon into the catalyst layer structure. The catalyst layer then becomes similar to the agglomerated structureC22, 231. Utilizing this method, it may be possible to enhance the effective diffusion coefficient by an order of magnitude. This will have a significant effect on electrode performance as demonstrated in the calculated polarization curves shown in Fig. 14. The local current density with different effective diffusion coefficients is shown in Fig. 15. We define an effective reaction zone thickness as the region where the local current density is greater than 4% of the current at x = 0. The inset in Fig. 15 shows the increase in effective reaction zone thickness as a function of effective diffusion coefficients. The larger the effective diffusion coefftcient, the thicker the effective reaction zone, as well as a more efficient utilization of the catalyst.
CONCLUSIONS Macro-homogeneous porous electrode theory was used to develop a model of hydrogen oxidation electrodes formed by catalyst particles embedded into a proton conducting membrane film. The effects of humidity, platinum coverage, CO poison, catalyst layer thickness, polymer volume fraction and hydrogen effective diffusion coefficients on the electrode performance are examined. From simulation results, several conclusions can be drawn. 1. The hydrogen oxidation at an electrode formed by bonding the catalyst particles to the membrane is primarily under diffusion control, The reaction takes place within a very thin region near the gas phase. Electrode performance can be enhanced significantly if the effective diffusion coefficient of hydrogen could be increased. 2. The humidity of the reactant gas has a significant effect on the electrode performance. Increasing the humidity of the reactant gas can significantly increase the total current density. 3. From an economical view, an optimal platinum coverage need not exceed 20% (or 20wt% Pt/C). Larger platinum coverage will increase the cost, but only slightly enhance the electrode performance. 4. Since the platinum catalyst can be seriously poisoned by CO, the electrode performance is sensitive to reactant gas containing CO. The total current density decreases as Oco increases. 5. Electrode structure parameters of catalyst layer thickness and polymer volume fraction have a significant effect on the electrode performance. A thicker catalyst layer will result in a larger ohmic voltage
loss and higher
catalyst
cost. The optimal
2745
polymer volume fraction and catalyst layer thickness are 0.5 and 1.5-4.0pm, respectively, for the hydrogen electrode.
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