Oxygen gain analysis for proton exchange membrane fuel cells

Oxygen gain analysis for proton exchange membrane fuel cells

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 3 7 3 e3 8 2 Available online at www.sciencedirect.com journ...

679KB Sizes 0 Downloads 74 Views

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 3 7 3 e3 8 2

Available online at www.sciencedirect.com

journal homepage: www.elsevier.com/locate/he

Oxygen gain analysis for proton exchange membrane fuel cells Kevin O’Neil a, Jeremy P. Meyers a,*, Robert M. Darling b, Michael L. Perry b a b

The University of Texas at Austin, Mechanical Engineering, 1 University Station, C2200, ETC 9.154, Austin, TX 78712, USA United Technologies Research Center, 411 Silver Lane, East Hartford, CT 06108, USA

article info

abstract

Article history:

Oxygen gain is the difference in hydrogen fuel cell performance operating on oxygen-

Received 30 July 2011

depleted and oxygen-rich cathode fuel streams. Oxygen gain experiments provide

Received in revised form

insight into the degree of oxygen mass-transport resistance within a fuel cell. By taking

26 August 2011

these measurements under different operating conditions, or over time, one can determine

Accepted 27 August 2011

how oxygen mass transport varies with operating modes and/or aging. This paper provides

Available online 11 October 2011

techniques to differentiate between mass-transport resistance within the catalyst layer and within the gas-diffusion medium for a polymer-electrolyte membrane fuel cell. Two

Keywords:

extreme cases are treated in which all mass transfer limitations are located only (i) within

Fuel cell

the catalyst layer or (ii) outside the catalyst layer in the gas-diffusion medium. These two

Performance analysis

limiting cases are treated using a relatively simple model of the cathode potential and

Modeling

common oxygen gain experimental techniques. This analysis demonstrates decisively

Mass transport

different oxygen gain behavior for the two limiting cases. For catalyst layer mass transfer resistance alone, oxygen gain values are limited to a finite range of values. However, for gas-diffusion layer mass transfer resistance alone, the oxygen gain is not confined to a finite range of values. Therefore, this work provides a straightforward diagnostic method for locating the prominent source of mass transfer degradation in a PEMFC cathode. Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

1.

Introduction

Proton exchange membrane fuel cell (PEFC) cathodes require efficient mass transport of oxygen for the oxygen-reduction reaction (ORR) to occur, especially at high current densities where losses due to mass-transport resistance are significant. To improve overall performance and to ensure efficient conversion of chemical energy stored in hydrogen into electrical energy, one must identify the limiting transport properties within a given PEMFC cathode; diagnostics must pinpoint the limiting source of oxygen transport and characterize how it may be changing with time. Specific design improvements to the cathode structure can then be made to improve overall cell performance and durability.

Numerous models have been proposed to describe the oxygen mass transport processes within a PEMFC cathode [1e3]. From these models, experimental diagnostics may be used to quantify the degree of oxygen mass transport resistance within the cathode. For example, Nonoyama et al. developed expressions for different oxygen mass transport resistances present along the oxygen diffusion pathway that show differing sensitivities toward operating conditions such as temperature, gas pressure, and balance gas [3]. Other studies have used electrochemical impedance spectroscopy (EIS) to evaluate oxygen mass transfer properties in the cathode catalyst and gas-diffusion layers [4e6]. Bultel et al. introduced a model that allows for qualitative analysis of experimental polarization curves and corresponding EIS

* Corresponding author. Tel.: þ1 512 232 5276. E-mail address: [email protected] (J.P. Meyers). 0360-3199/$ e see front matter Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2011.08.085

374

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 3 7 3 e3 8 2

Numerous works use the Thiele modulus approach to treat PEMFC systems [1,2,18]. Thus, only a brief derivation is outlined here, essentially to introduce the notation used later. The Thiele modulus approach relies upon the key assumption that ohmic resistance within the electrode is negligible. At higher current densities, this assumption may break down as ohmic effects become more important. Analysis of when this assumption is allowable is provided below. The governing equation is a material balance on oxygen in the catalyst layer at steady-state: 2

D

d c ain ¼0  dx2 4F

(1)

where D is the diffusion coefficient of oxygen, c is the concentration of oxygen, x is distance, a is the catalyst area per unit volume of the electrode, in is the local current density, 4 is the number of electrons transferred by the ORR, and F is Faraday’s constant. The boundary conditions are:  dc  ¼0 dxx¼0

(2)

cjx¼L ¼ cL

(3)

where x ¼ 0 is the interface between the catalyst layer and the membrane, x ¼ L is the interface between the catalyst layer and the gas-diffusion medium, and cL is the oxygen concentration at this interface. Fig. 1 provides a schematic of the cathode and relevant boundaries. The ORR is assumed to follow Tafel kinetics, first order in oxygen concentration: in ¼ i0

     c aF  exp  V  Uq cr RT

where i0 is the exchange current density, cr is a reference oxygen concentration, a is the cathodic transfer coefficient, V is the interfacial potential drop, and Uq is the standard reversible potential of the ORR at the temperature of interest. The governing equation for the material balance of oxygen then becomes:

Cathode Catalyst Layer

Membrane

2.

Model development

2.1.

Cathode potential

To treat catalytic reactions occurring in porous media where both kinetics and diffusion occur, a Thiele modulus approach proves useful. The Thiele modulus, f, is a ratio of the kinetic rate of the reaction to the diffusion rate of the reactant. Thus, a small Thiele modulus indicates relatively negligible diffusion limitations and a kinetically controlled rate of reaction. Conversely, a large Thiele modulus indicates relatively negligible kinetic limitations and a diffusion-controlled rate of reaction. In other treatments in the literature, the Thiele modulus is used to assess the effectiveness at the agglomerate level; in the treatment in this paper, we consider only the effectiveness of the overall catalyst layer.

(4)

H+

Gas Diffusion Medium

O2

x=0

x=L

Outlet

Gas Flow Channel

curves to highlight the relevant oxygen mass transport processes within both the catalyst layer and gas-diffusion layer [6]. Another commonly used diagnostic tool known as an oxygen gain experiment compares fuel cell performance using oxygen-depleted and oxygen-rich cathode fuel streams to evaluate oxygen transport characteristics. The most common fuel streams used include pure oxygen and air, however various other oxygen concentrations may also prove useful in this type of analysis. The oxygen gain is the resulting difference in cell potential for a fuel cell operating at a given current density due to reduced oxygen partial pressure and the blanketing effect of nitrogen [7]. This diagnostic tool is typically used to measure the oxygen gain and corresponding transport degradation as a function of time [8]. For example, an increasing oxygen gain indicates degrading oxygen mass transport properties in the cathode. While this application provides valuable time-dependent oxygen mass transport information, identifying where and why such degradation takes place would provide enhanced electrode structural design insight. This analysis employs a relatively simple model to identify where and why sources of mass transport resistance arise within a PEMFC cathode. Once the source of limited oxygen transport is located, its degradation behavior is characterized. Two limiting cases are treated in this analysis: (i) all mass transport degradation occurs external to the cathode catalyst layer and (ii) all mass transport degradation occurs internally within the cathode catalyst layer. The purpose of this work is to provide a fundamental diagnostic method to analyze PEMFC cathode performance using oxygen gain analysis. First, a relatively simple model for the cathode potential is presented that accounts for activity, mass transport, and ohmic losses both internal and external to the catalyst layer. The model then serves as a basis for the oxygen gain diagnostic analysis demonstrated in the results section. The results of this diagnostic analysis provide cell design insight for improving the oxygen mass transport properties of a given PEMFC cathode. Numerous studies for improving oxygen mass transport properties in the catalyst layer and gas-diffusion medium already exist and will not be discussed in this work [9e17].

Inlet

Fig. 1 e A schematic of the cathode used in the model development.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 3 7 3 e3 8 2

  2  d cðxÞ ai0 aF  exp   V  Uq cðxÞ ¼ 0 4Fcr D dx RT

(5)

Making the governing equations dimensionless leads to the following definition of the Thiele modulus: f2 ¼

   ai0 L2 aF  exp  V  Uq 4Fcr D RT

(6)

An arbitrary reference potential, Vr (a convenient value is 0.9 V), may be used to simplify the definition. The Thiele modulus at any other potential is simply:   aF f ¼ fr exp  ðV  Vr Þ 2RT

(7)

sffiffiffiffiffiffiffiffiffiffiffiffiffi    ai0 L2 aF  exp  Vr  Uq fr ¼ 4Fcr D 2RT

(8)

At this point, it proves useful to define another dimensionless parameter, the internal effectiveness factor, h:



L RU z 2k

tanh f f

(10)

When resistance to mass transport within the catalyst layer is severe (f is large): 1 hz ðmass transport limitedÞ f

(11)

When the resistance to mass transport with the catalyst layer is small: hz1 

f2 ðkinetically limitedÞ 3

(12)

Therefore, the cathode potential can be approximately represented by: V ¼ Uq þ

  RT RT I  IRU lnðai0 LÞ  ln aF aF hPO2

(13)

where a reference oxygen partial pressure of 1 bar is assumed and RU is the ohmic resistance of the ionomer within the catalyst layer (which is assumed to be independent of current density). This is an implicit equation for the cathode potential because the effectiveness factor depends upon the potential. The equation is approximate because it decouples the effects of oxygen diffusion and ionic resistance, which are actually intertwined inside the catalyst layer. It is exact if the ohmic

(14)

where k is the conductivity of the ionomer in the catalyst layer. The quantity ai0L may be conveniently fit to the potential intercept of experimental data. The partial pressure of oxygen is evaluated at the interface between the catalyst layer and the gas-diffusion substrate, and may be related to the bulk pressure by: (15)

where P is the bulk gas pressure, y is the mole fraction of oxygen, I*y is the limiting current, u is the oxygen utilization, and f is a parameter accounting for the degree of mixing in the flow field. We note that I*y is the limiting current for oxygen

actual overall rate of reaction rate of reaction if entire interior surface were exposed to surface conditions

The magnitude of the effectiveness factor (ranging from 0 to 1 for isothermal conditions) indicates the relative importance of diffusion and kinetic limitations, and can also be thought of as a measure of how far the reactant penetrates the catalyst layer. The effectiveness factor is found by solving the governing differential equation in dimensionless form. For this case, the effectiveness factor becomes: h¼

resistance can be neglected. If oxygen diffusion limitations and ohmic resistance are modest, then the reaction will be uniformly distributed throughout the depth of the electrode and:

  I PO2 ¼ Py 1   ð1  fuÞ Iy

where

375

(9)

transport in the gas-diffusion medium for the particular composition and mole fraction specified. I*, then, is a measure of the limiting current scaled by the composition of the oxidant stream, and is related to the effective diffusion coefficient and thickness of the backing layer. I* should be nearly independent of total pressure if the limiting current is determined by molecular diffusion in the gas phase. The factor f relates the inlet partial pressure of oxygen on the cathode to the average value, averaged over the entire cathode flow channel. Some useful values for f are 0.5 for a linear average between inlet and exit partial pressures, and 1.0 for a continuously stirred tank reactor (perfect mixing), in which the average partial pressure is equal to the exit partial pressure. This factor could vary slightly with large changes in flowrate as mixing is promoted, but is primarily determined by the arrangement of flow channels. The limiting current is assumed to be proportional to the mole fraction of oxygen, consistent with the gas-phase mass transfer limitations as the cause for the limiting current. The term with the second brackets is approximate. Ideally, the polarization equation should be applied locally as a function of gas concentration. Because of this uncertainty, it is best to perform this analysis at low oxygen utilizations, that is, under conditions with high oxygen stoichiometry such that the entire cathode surface is exposed to roughly the same oxygen partial pressure. For the sake of simplicity, utilization effects are neglected in this work. These effects may be important at higher utilizations than are considered here. One should be able to conduct experiments at high stoichiometric ratios, equivalent to low utilizations, using subscale test hardware reproducing the local humidifcation and temperature conditions that exist in particular regions of an overall full-sized cell.

376

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 3 7 3 e3 8 2

Combining Eqs. (13) and (15) yields an adequate description of the PEMFC cathode potential, provided the ohmic resistance of the solid phase is small:   RT RT I RT lnðai0 LÞ  ln  IRU þ lnðhÞ aF aF Py aF   RT I RT þ lnð1  fuÞ þ ln 1   aF Iy aF

V ¼ Uq þ

(16)

In this equation, the first four terms on the right hand side are independent of the specific oxygen mass transport properties external or internal to the catalyst layer. The fifth term depends on transport properties within the catalyst layer, and the last two terms depend on transport characteristics external to the catalyst layer. Low utilizations make the last term essentially negligible. Reinforcing the model assumptions, the separation of mass transfer and ohmic effects within the catalyst layer is inexact, but it is a useful approximation. Similarly, the treatment of the utilization effect is only approximate. Ideally, the polarization equation should be described as a function of the local oxygen and partial pressure instead of the average value as is implied by Eq. (16). When mass transport within the catalyst layer is severe, as described by Eq. (11), the cathode potential becomes:     RT ai0 L RT I  2 ln  2IRU V ¼ 2Uq  Vr þ 2 ln aF fr aF Py   RT I RT þ 2 lnð1  fuÞ þ 2 ln 1   aF Iy aF

ð17Þ

This corresponds to the well-known double Tafel slope that occurs when mass transport within the catalyst layer is limiting. The ohmic resistance doubles as the current shifts toward the interface between the catalyst layer and gasdiffusion medium.

2.2.

Oxygen gain

As previously mentioned, the oxygen gain is used to assess mass transport losses in fuel cells. From Eq. (16), the oxygen gain is: ! "     hO2 RT yO2 I þ ln þ ln 1   ln yair hair aF I yO2   #  I 1  fO2 uO2 þ ln  ln 1   1  fair uair I yair

DV ¼ VO2  Vair ¼

ð18Þ

assuming that the kinetic constants and ohmic resistances are the same for oxygen and air. Thus, to a reasonably good approximation, the oxygen gain should be insensitive to changes in electrode activity and internal resistance. yO2 and yair correspond to the oxygen ratios for oxygen-rich and oxygen-depleted fuel streams respectively. The first term amounts to 45 mV at 65  C, a ¼ 1, yO2 ¼ 1, and yair ¼ 0.21. Interestingly, oxygen gains lower than 45 mV are often recorded at potentials above 0.8 V where oxides begin to form on platinum, where kinetic parameters are therefore not necessarily constant. Again, the last term is essentially negligible by operating at low oxygen utilizations.

2.3.

Limitations of analysis

While the analytical techniques presented here are very helpful for identifying the nature of mass-transport limitations, it should be noted that the solutions developed here are not universally applicable. If, for instance, ohmic limitations within the catalyst layer invalidate the assumption of a uniform solution-phase potential across the thickness of the catalyst layer, pulling more current will necessarily distort the polarization of the catalyst layer further. To ensure that results are valid, one must perform oxygen gain analysis at suitably low currents such that potential drop through the thickness of the catalyst can be neglected. This can be accomplished by performing experiments and accompanying analysis at lower oxygen partial pressures such that ohmic polarization is minimized under conditions where masstransport polarization is significant. One can determine the appropriate conditions for identifying and isolating the nature of mass-transport limitations by running the tests as described below; if the results reveal a deviation from the derived form of the oxygen gain at a particular value of the current density for multiple oxygen pressures, the catalyst layer is likely ohmically limited, and the test can be re-run with an oxidant stream at an oxygen partial pressure that is sufficiently low so as to induce the mass-transport limiting behavior without ohmic complications.

3.

Results and discussion

3.1.

Identifying where mass transport is limited

Polarization (IeV) curves measured at different oxygen concentrations may be used to determine the dominant location of mass transport losses in the cathode at a given point in time. During these experiments, the current is varied slowly enough so that steady-state conditions exist, but the overall experiment is run quickly enough that oxygen transport parameters such as I* and D remain fixed over the course of the experiment. Gas-phase and liquid-phase compositions and pressure profiles will take a finite period of time to redistribute after the current is changed, but we expect that the time constants for concentration, potential, and pressure profiles in the cell to react to a change in current are much shorter than the time constants for the degradation of key mass transport phenomena. For instance, transients after a step change in currents tend to decay away after several hundred seconds [19]; fuel cells are designed to last for thousands of hours, so data for a typical polarization curve with ten discrete data points reporting stabilized performance should be taken over the course of roughly 30 min to 1 h, a period over which we should observe negligible changes in kinetic and transport properties. For a fuel cell where oxygen mass transport limitations external to the catalyst layer dominate, the relevant equations for the cathode potential and resulting oxygen gain become

V ¼ Uq þ

    RT RT I RT I lnðai0 LÞ  ln  IRU þ ln 1   aF aF Py aF Iy

(19)

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 3 7 3 e3 8 2

DV ¼

  RT yO2 =yair  I=I yair ln 1  I=I yair aF

(20)

since internal effects are assumed to be negligible. Fig. 2 demonstrates typical behavior for a PEMFC cathode dominated by external oxygen mass transport limitations. Using an oxygen-depleted oxidant stream produces a much lower value of the limiting current compared to an oxygen-rich stream. As the oxygen-depleted performance reaches its limiting current value, the oxygen gain increases without bound. In most experimental configurations in which cell current is controlled through a resistive load, one would only observe the increase in oxygen gain up to the point when the potential of the oxygen-depleted cell reaches 0 V, at which point, the oxygen gain would simply be the potential of the oxygen-rich cell, as DV ¼ VO2  Vair ¼ VO2  0. In an experimental configuration in which the cell potential is controlled explicitly, or in which current can be forced through the cell (both of which are easily simulated), the potential of the oxygen-poor cell could actually be forced to a negative potential, thereby ensuring that the oxygen gain could continue to increase as

a

1.2

0.20 Oxygen Air Oxygen Gain

1.0

0.10

Oxygen gain / V

Cathode potential / V

0.6

0.4 0.05

0.0

0.00 0

1

I*yair

2

3

4

5

I*yO2

-2

Current density / A cm

1.2 Air Half Air Oxygen Gain

1.0

0.15

0.8 0.10 0.6

Ox yg en g a i n / V

Cathode potential / V

V ¼ Uq þ

  RT RT I RT lnðai0 LÞ  ln þ lnðhÞ  IRU aF aF Py aF

    tanh fO2 RT RT yO2 DV ¼ 2 ln þ 2 ln tanh fair yair aF aF

(21)

(22)

since external effects are assumed to be negligible. Unlike Eqs. (19) and (20), Eqs. (21) and (22) are implicit equations for the cathode potential and oxygen gain because the effectiveness factor, h, and Thiele modulus, f, depend upon the potential. fr, described by Eq. (8), is a useful parameter for characterizing internal mass transport properties because it is independent of cathode potential and contains relevant transport terms such as the oxygen diffusion coefficient, D. Fig. 3 demonstrates typical behavior for a PEMFC cathode dominated by internal oxygen mass transport limitations. As the oxygendepleted performance diminishes, the oxygen gain reaches a value that is double its initial value.

Characterizing degradation behavior

0.8

0.2

b

the oxygen-poor cell potential would continue to decrease much more sharply as the current asymptotically approaches the limiting current of the gas-diffusion medium. For a fuel cell where oxygen mass transport limitations within the catalyst layer dominate, the relevant equations for the cathode potential and oxygen gain become

3.2.

0.15

377

0.4 0.05 0.2

0.0 0.0

0.2

0.4

I*yair

0.6

0.8

1.0

I*yO2

0.00

-2

Current density / A cm

Fig. 2 e Typical polarization curves for external oxygen mass transport limitations. T [ 65  C, I* [ 5 A/cm2, and RU [ 0.1 U (a) yO2 [1, yair [ 0.21 (b) yO2 [0:21, yair [ 0.105 Note that the current scale is not the same in upper and lower graphs.

While the previous results and discussion can aid in locating where oxygen mass transport is limiting at a given point in time, it does not characterize how oxygen transport degradation might evolve over time. By way of example, if the effective diffusion coefficient in the catalyst layer, D, or the limiting current in the gas-diffusion medium I* degrades over time, one will observe poorer performance after that degradation has occurred; either case would result in greater mass transport resistance and lowered performance, but the influence of these degraded properties on the overall performance curves would be different for oxidant streams with different partial pressure of O2. Successive polarization curves taken on different oxygen partial pressures at various time intervals can be used to determine how specific mass transport properties within the catalyst layer and external to the catalyst layer degrade. Simply comparing performance curves at fixed specified pressures might not provide sufficient information to discern the nature of the degradation, but oxygen gain can highlight the nature of the degraded performance. The plots and analysis provided here can prove useful for characterizing the extent and location of oxygen mass transport degradation over time. As shown above, when a fuel cell is limited by external mass transport limitations, the oxygen gain increases without bound due to lower limiting currents with lower oxygen concentrations in the flow channel. If external oxygen mass transport resistances increase with time, then this will deliver lower currents with time, thereby decreasing the transport parameter I*. Fig. 4 illustrates the characteristic oxygen gain behavior for external oxygen mass transport degradation. As the transport parameter I* decreases, cathode performance diminishes and the oxygen gain increases without bound at

378

0.20

0.10

1.2

0.15

0.08

0.8 0.06 0.6 0.04

Oxygen gain / V

Cathode potential / V

1.0

Oxygen gain / V

a

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 3 7 3 e3 8 2

0.10

2

I* = 1 A/cm

0.05

2

I* = 5 A/cm

2

I* = 10 A/cm

0.4

2

I* = 15 A/cm 0.00

0.02

Oxygen Air Oxygen Gain

0.2

0

1.0

1.5

2.0

Current density / A cm 1.2

0.05

1.0

0.04

0.8 0.03 0.6 0.02

Oxygen gain / V

Cathode potential / V

4

Fig. 4 e Oxygen gain behavior for degrading external oxygen mass transport limitations. T [ 65  C, RU [ 0.1 U, yO2 [1, and yair [ 0.21.

-2

b

3 -2

0.00 0.5

2 Current density / A cm

0.0 0.0

1

0.4

Air Half Air Oxygen Gain

0.2

0.0

0.01

0.00 0.0

0.5

1.0

1.5

2.0

-2

Current density / A cm

value at progressively lower current densities. Here we see several full expressions of oxygen gain versus current density; the circles show differences in oxygen gain at fixed current density and how those differences will change: in this case, the oxygen gain tends toward a limiting value at higher values of the current density, but larger differences in oxygen gain at different times will be revealed at lower current densities. The previous polarization curves demonstrate how to locate the dominant source of oxygen mass transport resistance within a PEMFC cathode at a given time and how to characterize its degradation over time by monitoring the resulting behavior of the oxygen gain. The location of severe oxygen mass transport resistance is best identified by comparing the limiting values of the oxygen gain. A PEMFC cathode where external oxygen transport resistance dominates produces oxygen gain values that increase without bound while a cathode with severe internal oxygen transport resistance produces oxygen gain values less than or equal to

Fig. 3 e Typical polarization curves for internal oxygen mass transport limitations. T [ 65  C, fr [ 1.00, and RU [ 0.1 U (a) yO2 [1, yair [ 0.21 (b) yO2 [0:21, yair [ 0.105.

0.10 0.09

φr = 0.1 φr = 0.5 φr = 1.0 φr = 2.0

progressively lower current densities. The Figure shows entire performance curves for different values of the transport parameter I*; the circles on the graph illustrate how performance data at fixed current densities will vary as that single parameter degrades with time: specifically, higher currents will exacerbate the difference in oxygen gain as I* degrades. When a fuel cell is limited by internal mass transport limitations, this will be revealed by an increase in the value of the transport parameter fr which affects the oxygen gain behavior in a different qualitative and quantitative fashion than degradation in I*. Fig. 5 illustrates the characteristic oxygen gain behavior for internal oxygen mass transport degradation. As the transport parameter fr increases, cathode performance diminishes and the oxygen gain increases to double its initial

Oxygen gain / V

0.08 0.07 0.06 0.05 0.04 0.03 0.0

0.5

1.0

1.5

2.0

2.5

3.0

-2

Current density / A cm

Fig. 5 e Oxygen gain behavior for degrading internal mass transport limitations. T [ 65  C, RU [ 0.1 U, yO2 [1, and yair [ 0.21.

379

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 3 7 3 e3 8 2

limDVI=I yair /0

  RT yO2 ðkinetically limitedÞ ¼ ln yair aF

limDVI=I yair /1 ¼ Nðmass transfer limitedÞ

1.0

Oxygen gain / V

Cathode potential / V

0.20

0.8 0.15 0.7 0.10 0.6 0.05

0.5

0.4

0.00 10

8

6

I/yair

4

2

I/yO2

0

-2

Limiting current / A cm

Fig. 6 e Cathode potential and oxygen gain measured at fixed current density with external mass transfer effects dominating the cell performance. T [ 65  C, RU [ 0.1 U, I [ 1 A/cm2, yO2 [1, and yair [ 0.21.

When the cell performance is dominated by external oxygentransport limitations, then degradation of the GDL has a major impact on the cell performance, since the GDL is the “valve” that regulates the amount of oxygen that the entire catalyst layer receives. Fig. 7 demonstrates how the degradation of internal mass transport parameters affects cathode performance and oxygen gain behavior. At (initially) small values of fr, the oxygen gain increases rapidly from its initial value. This behavior is due to the fact that the ORR is only occurring near the interface between the catalyst layer and gas-diffusion medium. At larger values of fr, the oxygen gain levels off to twice its initial value. The limiting values of the oxygen gain are limDVfr /0 ¼

  RT yO2 ðkinetically limitedÞ ln yair aF

(25)

  RT yO2 ðmass transport limitedÞ limDVfr /N ¼ 2 ln yair aF

(26)

1.0

0.10

0.09

0.8

0.07 0.4 0.06 0.2

(24)

0.0

Oxygen Air Oxygen Gain

0.05

0.04 0.0

0.5

1.0

1.5

2.0

2.5

3.0

φr

Fig. 7 e Cathode potential and oxygen gain measured at fixed current density with internal mass transfer effects dominating the cell performance. T [ 65  C, RU [ 0.1 U, I [ 0.6 A/cm2, yO2 [1, and yair [ 0.21.

O x y g e n g a in / V

0.08 0.6

(23)

As the current density is increased or external degradation ensues, the oxygen gain increases and diverges to infinity as the current density approaches the value of the limiting current, I*yair. This behavior is due to the fact that oxygen is no longer able to reach the catalyst layer for the ORR to occur.

0.25 Air Oxygen Gain Oxygen

0.9

Cathode potential / V

double the initial value. This analysis assumes that one location of oxygen mass transport resistance is dominant and that other sources are negligible. These are the two limiting cases for the location of oxygen-transport location; both internal and external mass transport limitations can also occur simultaneously. Furthermore, if transport properties change or degrade over time, a cell may start with internal transport dominating the performance, only for external transport limitations to become increasingly important until they become dominant, or vice versa. From Figs. 4 and 5, it can be shown that comparing the oxygen gain at two different fixed values of the current density as a function of time will provide insight as to where oxygen-transport degradation is taking place. At a given state of the cathode’s mass transport properties, each fixed current density will produce a value for the oxygen gain. As the system is allowed to degrade and the cathode is again held at the same two fixed values of the current density, different values of the oxygen gain will result. Comparing these values of the oxygen gain at their respective fixed current densities allows for the differentiation between internal and external oxygen mass transport degradation. For external mass transport degradation, the difference between oxygen gain values will increase at the higher current density. However, for internal mass transport degradation, the difference between oxygen gain values will approach the same value at the higher current density. These two different limiting cases result from the cathode performance and oxygen gain behavior being dominated by limiting mass transport parameter I* or fr. Subjecting the cathode to a fixed current over an extended period of time also allows for the characterization of mass transport degradation. A longer time scale ensures that the most prevalent source of transport resistance is effectively identified and characterized while mitigating the lesser effects from other evolving mass transport conditions. As the cathode is held at a fixed current, its oxygen mass transport capabilities will degrade. Over sufficiently long time scales, cathode performance and oxygen gain behavior can then be related to the limiting mass transport parameter I* or fr. Fig. 6 illustrates how the degradation of external mass transport properties affects cathode performance and oxygen gain behavior. At (initially) large values of I*, the oxygen gain does not vary significantly. However, as I* becomes sufficiently small, severe mass transport resistance causes the oxygen gain to increase dramatically. From this graph, one can discern the value of the limiting current I*yair, as the value beyond which the cell exposed to air cannot deliver additional current, regardless of the degree of polarization. The limiting values of the oxygen gain are:

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 3 7 3 e3 8 2

As shown in the previous analysis, limiting values of the oxygen gain indicate where oxygen mass transport limitations are dominant within a PEMFC cathode. Externally limited mass transport conditions produce limiting values of the oxygen gain that increase without bound while internally limited mass transport conditions produce limiting oxygen gain values that are double their initial values. Both polarization curves taken at a point in time and comparisons at fixed current densities over time illustrate the same limiting behavior for the oxygen gain. Polarization curves taken at one point in time provide a means for determining the location where one source of oxygen mass transport limitation is clearly dominant. Fixed-current comparisons provide a means for characterizing limiting cases of oxygen gain behavior over longer time scales so that the most prominent source of oxygen mass-transport resistance degradation can be identified. Finally, normalizing polarization curves like Figs. 2 and 3 to a reference cathode potential and oxygen gain will produce a dimensionless plot that effectively distinguishes the differing oxygen gain behaviors between the two limiting oxygen gain mass transport cases. Such a plot was created by comparing both external and internal mass transport limiting cases to a base case. The base case was chosen to be the internal masstransfer-free case with negligible external mass transport resistance (kinetic control, fr ¼ 0) so that dimensionless oxygen gain vs. dimensionless overpotential is expressed as: DV V  Uq vs:  f ¼0 f ¼0 r DV V  Uq r where DVfr ¼0 ¼ limDVfr /0 ¼

  RT yO2 ln yair aF

 f ¼0 RT RT Iref Vair  Uq r ¼ lnðaio LÞ  ln Pyair aF aF

(27) !  RU Iref

(28)

Iref was chosen to be 1 A/cm2, which is below the (arbitrarily) specified limiting current density, I* ¼ 5 A/cm2 and I*yair ¼ 1.05 A/cm2. Vair, VO2 , and DV vary with respect to I as shown in Figs. 2 and 3. Fig. 8 shows how the dimensionless oxygen gain varies with dimensionless overpotential. The oxygen gain for the internally limited case only ranges from 1 to 2, while the oxygen gain for the externally limited case begins at a value of 1 and increases without bound. Plots such as this prove effective for differentiating between internal and external oxygen mass transport effects by examining the limiting behavior. The most obvious difference is that when internal oxygen mass transport degradation dominates the system, the oxygen gain will level off at approximately twice its initial value. However, when external oxygen mass transport degradation dominates the system, the oxygen gain increases without bound. Therefore, at relatively large oxygen gains, this dramatic difference provides a simple and straightforward means for differentiating between these two limiting cases the location of these oxygen mass-transfer limitations. The preceding conclusions refer to the two extreme limiting cases treated in this work: (i) the oxygen transport is dominated by, or the majority of the degradation takes place

3.0

2.5

Dimensionless oxygen gain

380

External Internal

2.0

1.5

1.0

0.5 0.2

0.4

0.6

0.8

1.0

1.2

1.4

Dimensionless air potential

Fig. 8 e Dimensionless oxygen gain vs. dimensionless air potential. T [ 65  C, RU [ 0.1 U, I* [ 5 A/cm2, fr [ 1.00, yO2 [1, and yair [ 0.21.

within the catalyst layer and (ii) the oxygen transport is dominated by, or the majority of the degradation takes place outside the catalyst layer. In most PEMFC systems, it is likely that varying degrees of mass transport exists or that degradation is occurring in both locations. However, the results for the two extreme limiting cases may be used to identify the location of the most prominent sources.. The doubling of the oxygen gain refers to twice the internal mass-transport-free value where fr ¼ 0. Thus, the polarizations due to the oxygen-reduction kinetics and external masstransport resistance should both double. If the terminal oxygen gain is less than double its initial value, then it is likely that the internal mass-transport resistance also contributed to the initial polarization of the cell because fr > 0. Conversely, if the terminal oxygen gain is more than double the initial oxygen gain, then the external mass transfer resistance likely increased with time over the course of the experiment, namely, that I* decreased with time. Since external and internal degradation shift the terminal value of the oxygen gain in opposite directions, it proves useful to distinguish which effect is most dominant. Fig. 6 provides such a means for differentiating between these two sources of transport losses. Fig. 6 shows that when external mass transfer resistance dominates, the oxygen gain varies greatly with current density. Thus, the oxygen gain would vary considerably with current density when the external case dominates. However, the oxygen gain would vary diminutively with current density when the internal case dominates. Of course, the full model represented in Fig. 8 could also be used to gain a sense of the degradation’s origin. When both sources of oxygen transport resistance are present, the initial slope in a plot like Fig. 8 would remain unchanged, but the regime of appreciable oxygen gain increase and the terminal value of the oxygen gain would lie somewhere between the two extreme cases depicted. Their exact locations with respect to the extreme cases would provide insight as to which location of the degradation is most prominent.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 3 7 3 e3 8 2

4.

Conclusions

A model for PEMFC cathode potential and oxygen gain was developed and two limiting cases were analyzed where all oxygen mass-transport limitations are located only (i) internal to the catalyst layer and (ii) external to the catalyst layer in the gas-diffusion medium. The resulting analysis shows how to distinguish between these two limiting cases and how to characterize resulting degradation behavior. Limiting values of the oxygen gain can indicate where the dominant source of oxygen mass-transport resistance resides. For catalyst layer mass-transport resistance alone, oxygen gain values are limited to a finite range of values, with the maximum value being only double that of the initial masstransport-free value. For external mass-transport resistance alone, oxygen gain values are not limited to a finite range of values and the oxygen gain is strongly dependent upon limiting current density. In this way, comparing the value of the oxygen gain at very low current densities, when all masstransport losses should be essentially negligible, to the values at significantly higher current densities can easily elucidate whether attention should be paid to enhancement of the catalyst layer or the gas-diffusion medium to boost cathode performance. Both measurements and comparisons at a fixed point in time, as well as changes with time, produce the same limiting behavior for the oxygen gain. Polarization curves taken at different oxygen concentrations enable one to locate the dominant source of oxygen mass-transport resistance within a PEMFC cathode at a given time and subsequent curves may be used to characterize mass-transport degradation. Comparing cell performances measured at a fixed current over an extended period of time also allows for the characterization of mass-transport degradation and the longer time scale ensures that the most prevalent source of oxygen-transport resistance is effectively identified and characterized while mitigating the lesser effects from other evolving mass-transport conditions. Comparison of oxygen gain data taken at the same fixed current density as masstransport capabilities degrade allows the experimenter to delineate between internal and external resistances. The oxygen gain at sufficiently high current densities that the gain value is double that of the low-current case should not show further change if the performance is limited by catalyst-layer diffusion; the oxygen gain at higher current densities should continue to increase in magnitude if the performance is externally limited. Finally, a dimensionless plot (such as Fig. 8)allows for direct comparison of oxygen gain behavior for both limiting cases. The behavior in these limiting cases can serve as a benchmark for analyzing PEMFC cathodes with varying degrees of both internal and external oxygen mass-transport resistance.

Nomenclature List of symbols a catalyst area per unit volume of the electrode, cm1 c molar concentration of oxygen in the catalyst layer, mol/cm3

cL cr D F f in i0 I I* Iref L PO2 R RU T Uq u V Vr DV x y

381

molar concentration of oxygen at the catalyst layergas diffusion layer interface, mol/cm3 reference molar oxygen concentration, mol/cm3 diffusion coefficient of oxygen, cm2/s Faraday’s constant 96487, C/eq flow field mixing parameter local current density, A/cm2 exchange current density, A/cm2 current density, A/cm2 limiting current density, A/cm2 reference current density, A/cm2 catalyst layer thickness, cm partial pressure of oxygen, atm ideal gas constant, J K1 mol1 ohmic resistance of the ionomer in the catalyst layer, ohm absolute temperature, K standard cell potential, V oxygen utilization cathode potential, V reference cathode potential, V oxygen gain, V catalyst layer coordinate, cm mole fraction of oxygen

Greek symbols a cathodic charge transfer coefficient h internal effectiveness factor f Thiele modulus reference Thiele modulus fr

references

[1] Perry ML, Newman J, Cairns EJ. Mass transport in gasdiffusion electrodes: a diagnostic tool for fuel-cell cathodes. J Electrochem Soc 1998;145(1):5e15. [2] Springer TE, Wilson MS, Gottesfeld S. Modeling and experimental diagnostics in polymer electrolyte fuel cells. J Electrochem Soc 1993;140:3513e26. [3] Nonoyama N, Okazaki S, Weber AZ, Ikogi Y, Yoshida T. Analysis of oxygen-transport diffusion resistance in protonexchange-membrane fuel cells. J Electrochem Soc 2011; 158(4):B416e23. [4] Wu J, Zi X, Wang H, Blanco J, Martin JJ, Zhang J. Diagnostic tools in PEM fuel cell research: part I electrochemical techniques. Int J Hydrogen Energy 2008;33:1735e46. [5] Nakamura S, Nishikawa H, Aoki T, Ogami Y. The diffusion overpotential increase and appearance of overlapping arcs on the Nyquist plots in the low humidity temperature test conditions of polymer electrolyte fuel cell. J Power Sources 2009;186:278e85. [6] Bultel Y, Wiezell K, Jaouen F, Ozil P, Lindbergh G. Investigation of mass transport in gas diffusion layer at the air cathode of a PEMFC. Electrochim Acta 2005;51:474e88. [7] Prasanna M, Ha HY, Cho EA, Hong SA, Oh IH. Investigation of oxygen gain in polymer electrolyte fuel cells. J Power Sources 2004;137:1e8. [8] Murahashi T, Kobayashi H, Nishiyama E. Combined measurement of PEMFC performance decay and water droplet distribution under low humidity and high CO. J Power Sources 2008;175:98e105.

382

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 3 7 3 e3 8 2

[9] Shinozaki K, Haruhiko Y, Morimoto Y. Relative humidity dependence of Pt utilization in polymer electrolyte fuel cell electrodes: effect of electrode thickness, ionomer-tocarbon ratio, ionomer equivalent weight, and carbon support. J Electrochem Soc 2011;1585:B467e75. [10] Suzuki A, Sen U, Hattori T, Miura R, Nagumo T, Tsuboi H, et al. Ionomer content in the catalyst layer of polymer electrolyte membrane (PEMFC): effects on diffusion and performance. Int J Hydrogen Energy 2011;36:2221e9. [11] Kim KH, Lee KY, Cho E, Lee SY, Lim TH, Yoon SP, et al. The effects of Nafion ionomer content in PEMFC MEAs prepared by a catalyst-coated membrane (CCM) spraying method. Int J Hydrogen Energy 2010;35:2119e26. [12] Yoon YG, Park GG, Yang TH, Han JN, Lee WY, Kim CS. Effect of pore structure of catalyst layer in PEMFC on its performance. Int J Hydrogen Energy 2003;28:657e62. [13] Seo A, Lee J, Han K, Kim H. Performance and stability of Ptbased ternary alloy catalysts for PEMFC. Electrochim Acta 2006;52:1603e11.

[14] Fernandes A, Paganin V, Ticianelli E. Degradation study of Ptbased alloy catalysts for the oxygen reduction reaction in proton exchange membrane fuel cells. J Electroanal Chem 2010;648:156e62. [15] Chen G, Zhang H, Ma H, Zhong H. Electrochemical durability of gas diffusion layer under simulated proton exchange membrane fuel cell conditions. Int J Hydrogen Energy 2009; 34:8185e92. [16] Han M, Xu JH, Chan SH, Jiang SP. Characterization of gas diffusion layers for PEMFC. Electrochim Acta 2008;53:5361e7. [17] Chen J, Matsuura T, Hori M. Novel gas diffusion layer with water management function for PEMFC. J Power Sources 2004;131:155e61. [18] Fogler HS. Elements of chemical reaction engineering. 2nd ed. Englewood Cliffs, NJ: Prentice Hall; 1992. p. 607e635. [19] Olapade PO, Meyers JP, Mukundan R, Davey JR, Borup RL. Modeling the dynamic behavior of proton-exchange membrane fuel cells. J Electrochem Soc 2011;158: B536e49.