filmsurroundingagglomerateshavebeenpresentedandcomparedwiththeexperimentalresults.OnthebasisofthesimulationsandtheSEMstudyofthestructureoftheactivecatalystlayerithasbeenconcludedthattheagglomeratemodelisabetterrepresentationoftheactivecatalystlayerthanthep

Modelling the PEM fuel cell cathode

K. BROKA, P. EKDUNGE

Department of Chemical Engineering and Technology, Applied Electrochemistry, Royal Institute of Technology, S-100 44 Stockholm, Sweden

Received 1 November 1995; revised 3 July 1996

Two models of the cathode of the proton exchange membrane fuel cell, a pseudohomogeneous ®lm model and an agglomerate model, have been compared. The in¯uence of di€erent parameters on the shape of the polarization curves has been shown. Curves simulated by use of the two models and di€erent values of oxygen permeability, e€ective conductivity and thickness of the active layer as well as thickness of the Na®on

®lm surrounding agglomerates have been presented and compared with the experimental results. On the basis of the simulations and the SEM study of the structure of the active catalyst layer it has been concluded that the agglomerate model is a better representation of the active catalyst layer than the pseudohomogeneous ®lm model.

1. Introduction

Environmental concern has led to a renewed interest in the electric vehicle, however, its short driving range and long recharging time have prohibited its commercialization. An attractive solution of these problems is the use of fuel cells instead of batteries as a power source. The most suitable fuel cells for transport applications are ones with a solid polymer electrolyte due to their high power density, simple and safe construction and fast start-up even at low temperatures. For the commercial introduction of the proton exchange membrane (PEM) fuel cell as a power source for traction application, it is essential to improve its performance and to reduce its cost.

Also, the speci®c power density of the fuel cell should be increased to reduce the size of the cell for it to ®t within the restricted space available in a passenger car. The price of the fuel cell has to be competitive with the price of the internal combustion engine.

Low cost and high performance fuel cells require high performance three-dimensional electrodes that combine large active surface area with optimized utilization of the platinum catalyst. Recently, new methods for production of electrodes with low pla- tinum loading and high performance have been pre- sented [1±4]. This has been accomplished by the extension of the reaction zone by means of the pen- etration of the electrolyte phase into the porous electrode which increases the active surface area and the utilization of the catalyst. This can be achieved by impregnating the porous electrode with a solution of the electrolyte [1, 2] or by casting the catalyst layer from suspended Pt/C catalyst and Na®on^Òsolution [3, 4]. By means of these methods, a three-dimen- sional active catalyst layer consisting of the electro- lyte and the porous electrode is obtained. The

performance of the fuel cell largely depends on the structure of this active layer which should possess several important properties, such as high proton conductivity, high oxygen permeability and high electrochemical activity.

Mathematical models are a useful tool for analysis and optimization of the performance of the fuel cell and, particularly, of the cathode. Several models of di€erent degree of complexity have been presented for the PEM fuel cell [5±13]. These models have been developed to study di€erent aspects of the PEM fuel cell, such as transport properties of the membrane [5, 6], transport properties of the electrodes [7±10], or heat and water management [11±13]. The most de- tailed models of the cathode have been presented in [8±10]. In these models, the active layer has been treated as a pseudohomogenous ®lm. In a recent work of Springer et al. [10], the in¯uence of di€erent parameters on the performance of the cathode has been shown. In other models, where the active layer has not been the main point of interest, it has been described as an ultrathin ®lm of negligible thickness.

Usually the structure of the active layer is, however, regarded to consist of areas containing Pt/C catalyst and ionomer, and gas pores [10, 14].

An agglomerate structure model has been pre- sented by Ridge et al. [15] for the PEM fuel cell under electrolyte supported conditions (i.e., the membrane was saturated with an electrolyte, sulfuric acid, which penetrates into the membrane and ®lls some pores of the catalytic layer forming agglomerates). Agglom- erate structure models have also been developed for alkaline fuel cells [16] and phosphoric acid fuel cells [17].

The aim of this work was to investigate the structure of the active catalytic layer, its in¯uence on the performance of the fuel cell and to compare the structure models with experimental data.

0021-891X Ó1997 Chapman & Hall 281

2. Experimental details

2.1. Preparation of membrane±electrode assemblies, construction of the fuel cell system, experimental pro- cedure of electrochemical measurements

The membrane±electrode assembly was prepared ac- cording to the procedure described in [1]. 5 % Na-

®on^Ò solution was brushed onto catalysed gas di€usion electrodes from E±TEK Inc. with a Pt con- tent of 0.35 mg cm⁾²followed by evaporation of the solvent from the Na®on^Òsolution. The impregnated electrodes were hot-pressed to both sides of a puri®ed Na®on^Òmembrane at 50 atm pressure and 125 °C for 1 min. A small piece of the electrode was pressed on the anode side of the membrane for use as a reference electrode. The amount of the impregnated Na®on^Ò was about 1 mg cm⁾². Na®on^Ò 117 membrane was pretreated as follows [1]. It was boiled in 3 % H2O2

solution for 1 h, and repeatedly rinsed in boiling deionized water. This was followed by boiling in 0.5MM H2SO4 for 1 h and rinsing several times in boiling water. The membrane was then stored in deionized water.

The membrane±electrode assembly was in- corporated in a single test cell from Globe Technol- ogies. The fuel cell test station (Fig. 1) was equipped with a temperature-controlled humidi®cation system of the reactant gases and temperature control of the cell. Flow rates of oxygen and hydrogen were con- trolled by means of ¯owmeters from Brooks Instru- ment B.V. Atmospheric pressure and ¯ow rate of gases of about 150 ml min⁾¹ was used. Polarization curves were recorded in a galvanostatic manner by means of equipment consisting of a power supply 8701 D Oltronix, model 800 iR measurement system, The Electrosynthesis Company and several multi- meters 3468 B, Hewlet Packard for measurement of the potential at the cathode, the anode and also the cell voltage. To minimize the in¯uence of mass transport in the electrode backing, pure oxygen was used in the experiments.

2.2. SEM studies

SEM studies were performed on the membrane±

electrode assembly that was obtained as described above. Samples of the membrane±electrode assembly were prepared either by freeze-fracturing or freezing followed by cutting with a glass knife. The micro- scope used was a Jeol JSM-5400 scanning electron microscope.

3. Model

A mathematical model for the cathode of the PEM fuel cell, based on the assumption that the active layer can be described by a pseudohomogenous ®lm, has been developed and compared with a model, where the active layer of the cathode is described by an agglomerate structure.

Both models are steady-state, one dimensional isothermal models of the kinetics and transport of reactants in the active layer of the cathode of the PEM fuel cell. The active layer is assumed to consist of carbon black supported platinum catalyst, where the electrochemical reaction:

O2‡ 4H^‡‡ 4e^ÿÿ! 2H2O …1†

takes place and the pores between the carbon parti- cles contain recast Na®on^Ò.

Basic assumptions in both models are that: (i) the ionomer phase is an ion-conductive medium with e€ective proton conductivity je€; (ii) the transport of the reactants to active sites occurs by di€usion through the gas pores and/or through the ionomer in dissolved form; (iii) the catalyst is uniformly dis- persed in the active layer; (iv) there is no potential gradient in the electrode phase, since the conductivity of the carbon structure is much higher than that of the ionomer phase; and (v) any excess water in the cathode exists in liquid form.

3.1. Pseudohomogeneous ®lm model

In this model it is assumed that the catalytic layer can be described as a macropseudohomogeneous ®lm, consisting of four superimposed media: a di€usion medium where the transport of the reaction reactants and products takes place, an ionic conduction med- ium which transports protons, an electrical conduc- tion medium which conducts electrons and a catalytic medium where the electrochemical reaction takes place. A similar model has been presented by Springer et al. [10].

The oxygen concentration gradient changes with the local current density in the active layer as:

@C

@x ˆ I ÿ i

C_O^₂D_effnF …2†

where C_O^₂ is the saturation concentration of oxygen in Na®on^Ò, C is the dimensionless oxygen con- centration in the Na®on^Ò, CO2=C^_O2, I is the total geometric current density, i is the geometric current

Fig. 1. Fuel cell test station: (1) ¯owmeters, (2) gas humidi®ers, (3) fuel cell, (4) cathode, (5) membrane, (6) anode.

density in the ionomer phase, and D_e€is the e€ective di€usion coecient of oxygen in the active layer.

The kinetic expression for the oxygen reduction rate per unit volume can be described by a simpli®ed Butler±Volmer expression:

@i

@xˆ j ˆ j₀ACexp ÿ gbF RT

!

…3†

where j0is the exchange current density, and A is the speci®c active surface area.

Since the matrix phase can be regarded as equi- potential, changes in overvoltage in the electrolyte phase follow Ohms law:

@g

@xˆ i

jeff …4†

where j_e€ is the e€ective conductivity of the active layer.

Equations 2, 3 and 4 describe the catalytic layer according to the pseudo-homogeneous ®lm model.

3.2. Agglomerate model

In the agglomerate model, the active layer is assumed to contain small agglomerates consisting of carbon, platinum and Na®on^Ò mixture, which are separated by gas pores. These pores facilitate the transport of oxygen over the whole depth of the active layer. As in the pseudohomogeneous ®lm model, the potential gradient in the active layer can be described by Ohms law (Equation 4) for the ion transport in the ag- glomerates. In the agglomerate model, the con- centration gradient for oxygen is perpendicular to the potential gradient in the agglomerate, since the oxy- gen is di€using from the gas pores into the agglom- erate. The e€ect of the material transport limitation due to the oxygen di€usion in the agglomerates can simply be characterized by an e€ectiveness factor, in the same way as for porous catalyst particles in het- erogeneous catalysis [18]. For a ®rst order irreversible reaction the eciency factor is given by:

E ˆtanh…mL†

mL …5a†

where mL is Thiele's modulus:

mL ˆ L



k C_O^₂D_eff s

…5b†

L is the characteristic length of the agglomerate. For a sphere, L ˆ R/3 and for a cylinder it is L ˆ R/2, for other geometries L can be approximated by V/S where V is the volume and S is the exterior surface of the agglomerate.

The reaction rate constant can be calculated from the simpli®ed Butler±Volmer equation (Equation 3), which gives

k ˆAj0

nF exp ÿ gbF RT

!

…6†

If the agglomerate is covered by a layer of Na®on^Ò, through which oxygen di€uses into the agglomerate, the current density is given by

@i

@xˆ nF 1

aC^_O2dDeff‡_kE¹ 2

4

3

5 …7†

where a is the speci®c external surface area of the agglomerates and d is the thickness of the Na®on^Ò

®lm surrounding the agglomerates. Di€erential Equations 4 and 7 describe the cathode according to the agglomerate model.

For both models the set of nonlinear di€erential Equations with appropriate boundary conditions was solved by a Runge±Kutta procedure.

3.3. Model parameters

The thermodynamic open-circuit potential for the reaction

1

2O2‡ H2()H2O …8†

was estimated from the relation [9]

U_Thˆ 1:23 ÿ 0:9  10^ÿ3…T ÿ 289†

‡RT

4F log…P_H²₂P_O2† …9†

The kinetic parameters of the oxygen reduction on the platinum±Na®on^Ò interface have been in- vestigated as a function of temperature by Partha- sarathy et al. [19]. They found a change in Tafel slope from low to high at the voltage of 0.75±0.8 V. We used the highest Tafel slope in the simulations since almost the whole of our experimental polarization curve was in the voltage region below 0.8 V.

The exchange current density was determined by Parthasarathy et al. [19] for oxygen with 100 % re- lative humidity at a pressure of 5 atm. The value of exchange current used in the simulations was re- calculated for oxygen of 1 atm pressure and 100 % relative humidity assuming that Henry's law was valid.

The speci®c active surface area was estimated by dividing the platinum surface area for the electrode [20] by the thickness of the active catalyst layer. In reality, the active surface area is smaller than the total platinum surface area owing to poor utilization of the catalyst. The high value of the parameter Aj0 was, nevertheless, used in the simulations, since lower va- lues gave a poorer agreement with the experimental polarization curve.

The oxygen permeability for recast Na®on^Ò ®lm [21] and the proton conductivity for Na®on^Ò[22] as a function of temperature and relative humidity has been recently investigated in our laboratory under conditions close to those in the fuel cell. Since water is produced in the cathode reaction, the permeability and conductivity of the Na®on^Òphase were assumed to be the same as for Na®on^Òin equilibrium with gas of 100 % relative humidity at the actual temperature.

The thickness of the active layer and the size of the agglomerate was estimated from the SEM micro- graphs.

The parameter values used in the base-case simu- lation are summarized in Table 1.

The e€ective conductivity and di€usivity were calculated from the Bruggmann relation:

D_effˆ De^1:5 …10†

jeffˆ je^1:5 …11†

with an assumed porosity of 0.5 in the active layer.

4. Results and discussion 4.1. SEM observation

The structure of the active catalyst layer was studied by means of a scanning electron microscope. This study was carried out on the membrane±electrode assembly that was obtained by impregnating the electrode with Na®on^Ò solution and hot-pressing to the Na®on^Òmembrane.

Figures 2±5 present SEM micrographs of samples obtained by two di€erent methods: freeze-fracturing and cutting by a glass knife. It can be observed that the method of sample preparation in¯uenced the appearance of the structure. By analysis and com- parison of the micrographs of the samples obtained by these two methods, a good understanding of the structure of the active layer can be achieved.

Figures 2±5 show parts of the membrane±electrode assembly where the membrane is hot-pressed to the impregnated electrode. The SEM micrographs show a very good attachment between the electrode and the membrane. The impregnated Na®on^Ò layer is more clearly distinguished in the SEM micrograph of the sample that was prepared by cutting with the glass knife. In this case, Na®on^Òin the form of thin `®bres' was stretched along the cut surface. The impregnated layer exhibits pores and voids, which is particularly apparent in the samples prepared by knife-cutting (Figs 4 and 5). The microstructure of the active layer

Table 1. Base case parameter values

Parameter Value Source

Open circuit potential, UTh 1.16 V Calculated

Speci®c exchange current density, Aj₀ 5 ´ 10⁴A m⁾³ Calculated

Tafel slope, b 113 mV decade⁾¹ [19]

Oxygen permeability in the Na®on^Òphase, D ´ C* 1 ´ 10⁾¹¹mol cm⁾¹s⁾¹ [20]

Ion conductivity of the Na®on^Òphase, j 0.07 S cm⁾¹ [21]

Thickness of the active layer, l 15 lm SEM study

Characteristic length of the agglomerate, L 3 lm SEM study

Temperature of the fuel cell 343 K

Fig. 2. Freeze-fractured cross section of the membrane±electrode assembly: (a) Na®on^Ò117 membrane, (b) gas di€usion electrode with the impregnated active catalyst layer.

Fig. 3. Freeze-fractured cross section of the membrane-electrode assembly: (a) Na®on^Ò117 membrane, (b) impregnated active cat- alyst layer.

Fig. 4. Cross section of the membrane-electrode assembly (cut by a glass knife): (a) Na®on^Ò 117 membrane, (b) electrode with the impregnated active catalyst layer.

of the membrane±electrode assemblies supports the idea stated on the basis of permeability measurements [21] that the catalyst layer is porous with channels for gas transport and therefore the agglomerate model of the catalyst layer gives a better representation of the reaction zone than the pseudohomogeneous ®lm model. The agglomerate size is about 1±5 lm which can be seen in Figs 4 and 5. The thickness of the active layer was estimated to be 10±20 lm.

4.2. Simulations

Current and concentration pro®les over the active layer as well as polarization curves have been calcu- lated and compared for the two models.

If the same values are used for e€ective perme- ability and the same thickness of the active layer is assumed for both models, the agglomerate model gives the lowest overvoltage, see Fig. 6. The relatively high overvoltage for the curve obtained by the pseudohomogeneous ®lm model is due to the fact that at high current densities, oxygen does not pe-

netrate into the inner part of the active layer, which results in a very uneven current distribution. At 1000 mA cm⁾²the entire electrochemical reaction is concentrated within the outermost 1/20 of the active layer (see Fig. 7).

Fig. 5. Cross section of the membrane-electrode assembly (cut by a glass knife): (a) Na®on^Ò 117 membrane, (b) impregnated active catalyst layer, (c) electrode.

Fig. 6. Polarization curves for the cathode calculated by use of agglomerate (- - - -) and pseudohomogeneous (ÐÐÐ) ®lm models (base-case parameter values).

Fig. 7. Current (a), concentration (b) and overvoltage (c) dis- tribution in the active catalyst layer for the ®lm model at di€erent current densities (base-case parameter values):(


) 250, (- - -) 500, (± ± ±) 750 and (ÐÐÐ) 1000 mA cm⁾².

From the comparison of the simulated curves with the experimental polarization curve, it can be seen that the ®lm model predicts considerably higher overvoltages. By increasing the value of the e€ective permeability, a lower overvoltage can be obtained for the ®lm model curves. Figure 8 shows the in¯uence of the e€ective permeability on the performance of the electrode. With a value of e€ective permeability that is 100 times higher than the measured one [21] a good agreement between the experimental and simulated polarization curve is obtained up to about 600 mA cm⁾². This high value of the oxygen permeability was also used by Springer et al. [5, 10] in the simu- lation of the active layer of the cathode in the PEM fuel cell. They justi®ed the usage of this high perme- ability value by considering the di€usion of oxygen into micro pores of the carbon particles within the active layer [5].

The experimental polarization curve exhibit a change of shape at about 600 mA cm⁾². It has been shown that by decreasing the e€ective conductivity similar changes in polarization curve shape can be obtained with the pseudohomogeneous ®lm model [10]. The in¯uence of the e€ective conductivity on the polarization curves is shown in Fig. 9. A decrease of the e€ective conductivity by a factor of four gives a form of the polarization curve similar to that of the experimental curve, but at a lower potential.

The oxygen concentration pro®le, and hence cur- rent density, is more evenly distributed over the active layer in the ®lm model with 100 times higher oxygen permeability than in the model where the measured permeability value was used. The current and over- voltage distribution in the active layer for the two models are compared in Figs 10 and 11. These ®gures illustrate a great in¯uence of oxygen di€usion in the active catalytic layer on the performance of the electrode in the ®lm model. Even with the highest value of oxygen permeability, the limited oxygen transport in the active layer results in a very uneven current distribution which is more pronounced at high current densities. The agglomerate model gives a more uniformly distributed current over the whole depth of the active layer, since the oxygen is evenly distributed in the active layer. In contrast to the ®lm model, the highest values of the current density are obtained in the inner part of the electrode, where the values of overvoltage are highest (see Fig. 11).

In the agglomerate model, the oxygen concentra- tion is constant over the whole depth of the active layer. The decreased utilization of the catalyst due to the restricted oxygen di€usion manifests itself in a decreased e€ectiveness factor, which is illustrated in Fig. 12. The utilization of the inner parts of the ag- glomerates decreases with increasing current density, but alteration of the value of the e€ectiveness factor over the depth of the active layer is rather small even at high current densities.

The agglomerate model predicts a limiting current at about 1300 A cm⁾² for the base-case conditions.

The limiting current is dependent on the mass transport restriction in the ®lm surrounding the ag- glomerates, and hence proportional to the factor d/a.

The in¯uence of the factor d/a on the polarization curves is shown in Fig. 13. In the base-case, the value of the factor d/a was chosen in such a way that the best ®t with the experimental curve was ob- tained.

The two models predict a di€erent in¯uence of the thickness of the active layer. The ®lm model gives an increased overvoltage with increasing thickness at high current densities, due to an increased barrier of mass transport and limited proton conductivity (see Fig. 14). For the agglomerate model, this limiting current is proportional to the total external surface of the agglomerates. An increase in the thickness therefore gives an increase in the limiting current density if the speci®c external surface of the ag- glomerates is constant (see Fig. 15).

Fig. 8. Polarization curves for the cathode calculated by use of the

®lm model for di€erent values of oxygen permeability: (ÐÐÐ) 1 ´ 10⁾⁹, (±± ±±) 5 ´ 10⁾¹⁰, (- - - -) 2.5 ´ 10⁾¹⁰ and (


) 1 ´ 10⁾¹⁰ mol cm⁾¹s⁾¹; (h) experimental values.

Fig. 9. Polarization curves for the cathode calculated by use of the

®lm model for di€erent values of e€ective conductivity: (ÐÐÐ) 0.07, (±± ±±) 0.035 and (- - - -) 0.0175 S cm⁾¹; (h) experimental values.

5. Conclusions

The structure of the active layer of the cathode has a great in¯uence on the performance of the PEM fuel

cell. SEM studies show that the active layer produced by impregnating the electrode with Na®on^Òsolution exhibits regions of Na®on^Ò and electrode material separated by voids and pores.

Fig. 10. Current (a), concentration (b) and overvoltage (c) dis- tribution in the active catalyst layer for the ®lm model at di€erent current densities (oxygen permeability 1 ´ 10⁾⁹mol cm⁾¹s⁾¹): (


) 250, (- - - -) 500, (± ± ± ±) 750 and (ÐÐÐ) 1000 mA cm⁾².

Fig. 11. Current distribution (a), current generation (b) and over- voltage distribution (c) in the active catalyst layer for the ag- glomerate model at di€erent current densities (base-case parameter values): (


) 250, (- - - -) 500, (±± ±±) 750 and (ÐÐÐ) 1000 mA cm⁾².

Polarization curves for cathodes running on pure oxygen exhibit a change in shape at about 600 mA cm⁾² indicating mass transport limitation.

These polarization curves cannot be satisfactorily si- mulated by use of a simple pseudohomogeneous ®lm model. By means of the agglomerate model, a good agreement with the experimental curves can be achieved.

For cathodes running on air, the similar shapes of polarization curve can be explained by mass trans- port limitation in the electrode backing [10]. For oxygen cathodes, the ®lm model has to be extended by introducing an extra di€usion restriction. This di€usion restriction could be a water ®lm covering the active layer. However, the SEM study and perme- ability measurements of the electrodes impregnated by Na®on^Ò[21] indicate an agglomerate structure.

Both the simulation of the structure of the active layer as well as the SEM observations indicate that

the active layer of the electrodes possess agglomerate structure. The active layer consists of agglomerates with a size of a few micrometres. The high perfor- mance of these electrodes is due to the gas pores which enables the utilization of the entire depth of the active layer even at high current densities. In the process of manufacturing of a membrane±electrode assembly, the active layer of the electrode is im- pregnated with a solution containing about 5 % Na-

®on^Ò in alcohols. After drying, the volume of the Na®on^Òphase decreases by about 95 %. Taking this into account, it is reasonable to believe that voids in the active layer are produced during the evaporation of the solvent. By changing drying temperature and pressure, it may be possible to control the drying rate and the size of the agglomerates, and hence optimize the structure of the active layer.

Fig. 12. E€ectiveness factor as a function of the position in the active layer for the agglomerate model at di€erent current densities:

(


) 250, (- - - -) 500, (±± ±±) 750 and (ÐÐÐ) 1000 mA cm⁾².

Fig. 13. Polarization curves for the agglomerate model for di€erent values of thickness of the Na®on^Ò®lm surrounding agglomerates:

(- - - -) d ˆ x/2, (±± ±±) d ˆ x, (ÐÐÐ) d ˆ 2x.

Fig. 14. The in¯uence of the thickness of the active catalyst layer on the curves calculated by use of the ®lm model: (- - - -) l ˆ 7.5, (±± ±±) l ˆ 15 and (ÐÐÐ) l ˆ 30 lm.

Fig. 15. The in¯uence of the thickness of the active catalyst layer on the curves calculated by use of the agglomerate model: (- - - -) l ˆ 7.5, (±± ±±) l ˆ 15 and (ÐÐÐ) l ˆ 30 lm.

Acknowledgements

NUTEK, the Swedish National Board for Technical and Industrial Development, is gratefully acknowl- edged for the ®nancial support of this work.

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