Positioning The Reference Electrode In Proton Exchange Membrane Fuel.pdf

Electrochimica Acta 49 (2004) 923–935

Positioning the reference electrode in proton exchange membrane fuel cells: calculations of primary and secondary current distribution Zhenyu Liu a , J.S. Wainright a , Weiwei Huang b , R.F. Savinell a,∗ a

Department of Chemical Engineering, E.B. Yeager Center for Electrochemical Sciences, Case Western Reserve University, Cleveland, OH 44106, USA b Eveready Battery Company Inc., Cleveland, OH 44101, USA Received 19 June 2003; received in revised form 19 September 2003; accepted 4 October 2003

Abstract The primary and secondary current distribution study indicates the geometry of a thin electrolyte in a proton exchange membrane (PEM) fuel cell has a direct relation to the measured electrode polarization, thus making the positioning of the reference electrode and ohmic compensation critical. The different kinetic overpotentials on the electrodes can also affect the potential distribution and therefore affect the measurement accuracy. The measurement error can be significant for the fuel cell system with different kinetic overpotentials and with electrode misalignment. The measurement error for both hydrogen and direct methanol fuel cells (DMFC) has been analyzed over the current density region with no mass transfer effects. By using two reference electrodes, the measurement error can be substantially decreased for both anode and cathode measurement in a direct methanol fuel cell, and for the cathode measurement in a hydrogen/air fuel cell. © 2003 Elsevier Ltd. All rights reserved. Keywords: Reference electrode; Overpotentials; IR-correction; PEM; Electrode measurement errors

1. Introduction Proton exchange membrane (PEM) fuel cells are promising energy conversion devices because of their high efficiency and because they can be environmental friendly. In PEM fuel cell studies, a reference electrode is sometimes used in an attempt to measure and monitor the polarization of both anode and cathode independently. Since the current and potential distribution in a PEM fuel cell system is usually non-uniform, ohmic drop is also non-uniform. Such measurement then could be significantly inaccurate. Newman [1] simulated the current distribution on a rotating disk electrode below limiting current, and showed that the ohmic potential drop is non-uniform along the disk. Therefore, significant error could be introduced in determining kinetics parameters unless special corrections are applied. Depending on the position of the reference electrode, such error can reach as high as 300% [2]. It was suggested that the reference electrode should be put far from disk and compensated for the introduced large ohmic drop. West and ∗ Corresponding author. Tel.: +1-216-368-4436; fax: +1-216-368-6939. E-mail address: [email protected] (R.F. Savinell).

0013-4686/$ – see front matter © 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2003.10.004

Newman [3,4] reported analysis on correcting the kinetic measurements taken from a disk electrode and a channel flow cell. In research on solid oxide fuel cell (SOFC), Nagata et al. [5] showed experimentally the effect of the reference electrode position on the overpotential measurement for a single solid oxide fuel cell with yttria-stabalized zirconia (YSZ) electrolyte. The platinum reference electrode was placed at different positions, and the overpotential measured varied with the reference electrode position. Winkle et al. [6] simulated the measurement error for several three-electrode configurations. They used effective resistances to describe a single SOFC, and calculated the charge transfer resistance from the impedance equivalent circuit to evaluate the measurement error. Their studies showed that the misalignment of the electrodes could create large errors in overpotential measurements. A pellet-like geometry was shown to give the best reliability. However, their studies did not assess the effect of different kinetic effects on working and counter electrodes and the overall effect of electrode alignments and electrodes kinetics. Adler et al. [7] compared the effect of slightly misaligned electrodes on a thick electrolyte and on a thin electrolyte. Their study indicated that since thin electrolyte is more

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sensitive to misalignment of the two electrodes, it usually can create larger error as compared to a thick electrolyte. Kato et al. [8] investigated the influence of electrode placements on interfacial impedance measurement using three electrodes. Chan et al. [9] investigated a single anode-support fuel cell, and the possible error in overpotential measurement. They concluded that the difference in size between working and counter electrodes could introduce significant errors. For polymer electrolyte fuel cells and most solid electrolyte fuel cells, the current distribution is often uniform within the two opposite electrodes and away from the edges, and is usually non-uniform near the edges. The reference electrode has to be positioned outside the region between the anode and the cathode and one then must compensate the ohmic loss between reference electrode and measured electrode. Generally, the current interruption method [10] or impedance spectroscopy can be used to compensate/correct the ohmic loss, if such ohmic loss is determinable by a proper location of the reference electrode. Therefore, an accurate measurement requires both the potential and the current distributions to be predictable, i.e. for example in the case of aligned working and counter electrodes. For misaligned electrodes with non-uniform current distribution, proper ohmic compensation may not be readily obtained. One of the remedies for solid oxide fuel cell measurement includes using a thicker electrolyte so that slight electrode misalignment can be neglected. The use of thick electrolyte however may not be an acceptable solution for PEM fuel cell, because membrane thickness impacts the electrode performance due to gas cross-over and water balance effects. As a result, the single electrode potential measurement in a PEM fuel cell is more difficult because the electrode misalignments are difficult to eliminate in MEA (membrane electrode assembly) manufacturing. In this study, we simulate the effect of reference electrode placement, electrode asymmetries, and the reaction kinetics on single-electrode potential measurements in a PEM

fuel cell, and give suggestions on reference electrode positioning and measurement methodology to minimize errors. We applied our analysis to a typical hydrogen PEM fuel cell (HFC) and to a direct methanol fuel cell (DMFC) with possible and reasonable electrode misalignments, and report on a measurement error analysis for each of the cases.

2. Theory and model A schematic of a fuel cell is shown in Fig. 1. Outside the double layer and within the electrolyte phase, the current and potential distributions can be estimated by solving the Laplace equation since there are no ion concentration gradients in the ion conducting domain of the PEM fuel cell: ∇ 2Φ = 0

(1)

For insulator type boundary, i.e. at membrane surface not in contact with an electrode, and for the line of symmetry within the ion conducting domain, the potential gradient is zero, or ∂Φ =0 ∂n

(2)

where n is the normal dimension from an insulating boundary surface, or across the plane of symmetry. The general boundary condition at the electrode surfaces can be written as: η = E − Φelectrolyte surface

(3)

where E is the potential of the electrode, and η the current dependent overpotential. Eq. (3) is valid only when the reference electrode and the working electrode are of same kind. Otherwise, an equilibrium potential difference must be included [11]. For the primary current distribution, η = 0, therefore Φ = E, over a highly conductive electrode, which is constant.

Fig. 1. (a) Schematic of the MEA of a PEM fuel cell structure, dimensions are in Table 1. (b) Typical mesh structure (local).

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For the secondary current distribution, the kinetic overpotential can be simplified by linear approximation for ηs ≤ 25 mV, or a Tafel approximation for ηs ≥ 120 mV. The Wagner number of the electrode, which is the ratio of the electrode kinetic resistance to the ohmic resistance, was used to determine the effect of kinetic resistance of the electrode under secondary current distribution situations. By noting that the current density, i, is related to potential gradient according to Ohm’s law for uniform ion concentration domain with conductivity κ, i = −κ∇Φ

(4)

then the linear boundary condition can be written as,
 ∂Φ RTκ − Φ=E−η=E− (αa + αc )Fbi0 ∂N b

(5)

The quantity RTκ/(αa + αc )Fbi0 is the Wagner number for linear approximation and N is a dimensionless direction normal to the electrode surface, e.g. y/b, where b is the membrane thickness, and αa + αc is often equal to number of electrons involved in the reaction. For Tafel approximation, Φ=E−η

(6)

As overpotential η is a function of current density i, linearized by Taylor expansion about the average current density and organized as: η=

RT RT RT ln i0c − ln iavg + αc F αc F αc F +

η=

RT κ ∂Φ αc Fiavg b ∂N

for cathodic current

RT RT RT ln iavg − ln i0a − αa F αa F αa F
 RT κ ∂Φ for anodic current + αa Fiavg b ∂N

(7)

(8)

where iavg is the average current density on the electrode surface, i0a and i0c are the exchange current densities, and αa and αc are the transfer coefficients for the anodic and cathodic reactions, respectively. The quantity RTκ/αc(a) Fbiavg is the Wagner number of the electrode for the Tafel approximation. To generalize our calculations, the Wagner number is used to quantify geometric, kinetics, and ohmic effects. The dimensionless geometric parameter r, is the ratio of the amount of electrodes misalignment relative to the thickness of the electrolyte. It is safe to assume that any small electrodes misalignment does not affect the cell performance because unless deliberately designed, the misalignment is usually much smaller as compared to the electrode size. The simulation was performed by finite volume method, using a commercial software package: CFDACE+ (CFDRC Corporation).

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3. Results and discussion We start by examining the case of exactly aligned electrodes. Then, one electrode is gradually extended, until it obviously oversizes the other electrode. If one assumes both electrodes are reversible and thus under primary current distribution, e.g. for a hydrogen pump cell, the cell geometry should be the only factor that affects the placement of reference electrode. Under secondary current distribution, a combination of cell geometry, kinetics, and ohmic resistance of the electrolyte determine the proper position of the reference electrode. We examine these factors on determining the correct position of the reference electrode and proper way of ohmic compensation for accurate potential measurements. 3.1. Primary current distribution Fig. 2 shows the numerical solution for potential and current distribution of the exactly aligned electrodes geometry. The coordinate x starts from the electrode edge (the shorter electrode edge if misalignment exists) with the negative direction toward the line of symmetry or to a position where the current density is uniform in x direction. The quantity iavg is the average current density over the electrode. The dimensionless primary current distribution in Fig. 2 shows a highly non uniform region near the electrodes’ edge due to the effect of ohmic drop. Away from the edge the current density is uniform because the ohmic resistance between the two electrodes is uniform. Fig. 2 also shows the corresponding potential profile. In the region between the electrodes but away from the edge, the potential varies linearly with position across the electrolyte from anode to cathode. However, near the electrodes edge, potential distributions are strongly nonlinear. When outside the electrodes gap, and in a region beyond the electrode edge about 1.5b, the potential becomes uniform at all points across and along the membrane. This region of uniform potential will be referred to as the region of constant potential (RCP). In the case of a primary current distribution with aligned electrodes, the potential at RCP is exactly equal to the potential at the middle plane between the electrodes, and the potential profile within the electrolyte is symmetrical about this centerline. Also, the current distributions at each electrode are the same. When a reference electrode is positioned within the RCP, on either side of the membrane, the measured potential includes one half of the total ohmic drop across the membrane. Consequently, by knowing the IR-drop across the electrolyte gap, one can easily correct the measured values of potential with respect to the reference to obtain the single-electrode potential. When electrodes are not exactly aligned with each other, the current distribution on each electrode will not be the same, and the potential profile within the electrolyte will not be symmetrical about the midpoint between the electrodes. Fig. 3 shows the current distribution and potential profile of a series of non-aligned geometries for values of r from 0.2 to 2. As with the case of exactly aligned electrodes, the potential

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Fig. 2. The current and potential distribution of the aligned electrodes geometry under primary current distribution.

distribution within the electrolyte of non-aligned geometries is still uniform at positions far from the electrodes’ edges, i.e. within the RCP, which is always 1.5b beyond the edge of the larger electrode. However, the IR-correction for each single-electrode potential with respect to the reference is no longer equal to one-half of the potential drop across the electrode gap. In fact, the IR-correction will be always less for the larger electrode than for the smaller electrode. Therefore, if one still uses half of the total ohmic drop across the membrane to correct the single electrode potential measurement, the oversized electrode will be underestimated and the smaller electrode will be overestimated. Fig. 3a shows the case for small misalignment, i.e. r = 0.2. For this case, the current distributions on both electrodes are nearly the same even near the edges. The potential profile indicates that the potential within the RCP deviates slightly from that of the midpoint between the electrodes. Depending on the required accuracy, such deviations often can be neglected. This criteria is often easy to achieve for SOFC since relatively thicker electrolytes in experimental test cells can be employed to minimize the measurement error. Fig. 3d and e show the cases where one electrode is larger than the other electrode (r ≥ 1.5). The current density on the oversized part of the electrode decreases substantially moving towards the edge with only a very small edge effect. The potential distribution shows that the potential within the RCP is overwhelmingly controlled by the value at the larger electrode. This means that the potential measured between reference electrode and the larger electrode represents the true value of potential near the larger electrode surface. Also, the potential measured between the reference electrode and

the smaller electrode contains the total IR-drop across the membrane. Therefore, it is possible and easy to obtain accurate single electrode potentials relative to a reference placed within the RCP when r ≥ 1.5. Obviously, there is a transition between the two extreme cases discussed above at intermediate values of r, i.e. 0.2 < r < 1.5. The current distributions of Fig. 3b and c clearly show how the current density changes near the edge of the larger electrode, while little change occurs at the smaller electrode. This, of course, is due to the non uniform ohmic drop within the electrolyte near the oversized electrode. The amount of alignment error may be expected in laboratory fabricated MEAs of PEM fuel cells. One interesting point here is if the electrodes are identical in size but misaligned, averaging the measurement of the single electrode potential with respect to two reference electrodes on both sides along the misaligned direction may minimize the measurement error. More will be discussed on this later for realistic cells. In summary for the primary current distribution, the reference electrode should be positioned within the RCP, which is located at least 1.5 times the electrolyte thickness beyond the edge of the larger electrode. For aligned or slight misaligned (r ≤ 0.2) systems, the measured potential should be corrected by one-half of the total ohmic drop across the membrane. For obvious misaligned cell configuration (r ≥ 1.5), the potential measured of the oversized electrode does not need an ohmic correction, and the potential measured of the smaller electrode should be corrected by an amount of the total ohmic drop between the electrodes gap. In the cases where r varies from 0.2 to 1.5, the correction is difficult

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due to non-uniform ohmic drop. Significant errors may exist with the three-electrode measurement.

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3.2. Secondary current distribution

kinetic resistances of anode and cathode are different, and often the kinetic differences are substantial. Therefore, kinetic resistance effects must be included when investigating the geometrical effects of misaligned electrodes.

Similar to the case of primary current distribution, when both electrodes have the same kinetic parameters, such as in a hydrogen pump cell, geometry is the only factor that affects the current and potential distributions. However, for a PEM fuel cell as with perhaps most electrochemical systems, the

3.2.1. Kinetic resistance effect Fig. 4 is a numerical simulation of the potential distribution for the case of aligned electrodes with equal kinetic resistance. The secondary current distribution (not shown) is more uniform than under primary current distribution, but

Fig. 3. The potential profile and current distribution for non-alignment electrodes geometry (primary current distribution).

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Fig. 3. (Continued ).

the level of uniformity depends on the Wagner number of that electrode. The kinetics has strong effect at the edge of the electrode, but the potential distribution at the edge is still very non-uniform. As with the primary case, the potential distribution for aligned electrodes is symmetrical about the midpoint between the electrodes. Also, the current distributions at each electrode are similar. When a reference electrode is positioned within the RCP, on either side of the membrane, the measured potential includes a potential drop equal to one half of the total ohmic drop across the membrane. Consequently, by knowing the IR-drop across

the electrolyte gap, one can easily correct the measured values to obtain the single-electrode potential, including the overpotential. Fig. 5 shows the potential distribution of the case for aligned electrodes, but with different kinetic resistance at each electrode. The kinetic resistance at anode is smaller than ohmic resistance (Wa (anode) = 0.1), while the kinetic resistance of cathode is much larger than ohmic resistance (Wa (cathode) =100). The current distribution on the cathode is uniform, but the current distribution on the anode is more like the primary distribution. Notice that the kinetics

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Fig. 3. (Continued ).

Fig. 4. Aligned electrodes with equal kinetic effect on both electrode.

of the cathode also has a small effect on the anode current distribution. The potential profile clearly indicates that the potential within the RCP is close to the value of the anode, which has a much smaller kinetic resistance. The potential

measured of each electrode includes an ohmic drop, but the ohmic correction for the anode is smaller than that for the cathode. Yet the exact amount of ohmic drop correction for each electrode is difficult to determine.

Fig. 5. The potential profile and current distribution for symmetric electrodes geometry under secondary current distribution (Wa (anode) = 0.1, Wa (cathode) = 100).

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3.2.2. Geometric and kinetic resistance effect Evaluating the combination of the geometric effect and the kinetic resistance effect, we examine the geometric parameter r at 0.5, 1.0 and 1.5. For each geometric case, different kinetic resistances are applied by setting different value of the Wagner number on each electrode. It turns out that the potential of the RCP is strongly affected by the oversized electrode. The potential profile is determined by the kinetic resistances on both electrodes, and the geometric factor r. Generally, if the oversized electrode has smaller kinetic resistance, depending on the value of r, the ohmic drop between the reference electrode and the oversized electrode is smaller than half of the total ohmic drop across the membrane.

We simulated the cases where r varies from 0.5 to 1.5, the Wa of anode is 0.1 and 1.0, and the Wa of cathode is 10 or 100. For each value of r, either oversized anode or oversized cathode is simulated. The results show that the potential profiles for equivalent geometries are quite similar in spite of difference in cathodic kinetics. The potential profiles for the geometry of r = 1.0 are shown in Fig. 6. When the Wa of anode is 0.1, and the Wa of cathode is either 10 or 100, then for anode oversized cases, the ohmic drop between the region of RCP and the anode is quite close to zero. The measurement accuracy is expected to be high when r is large (1.0–1.5 and larger), with the ohmic correction for oversized anode being nearly zero, and the ohmic correction for the cathode being equal to the total ohmic drop across the

Fig. 6. Potential distributions for Wa anode = 0.1, 1.0 Wa cathode = 10 or 100 with geometric parameter r = 1.0.

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membrane. For the same geometric cases with the Wa of the anode is 1.0, the potential profiles for the oversized anode cases are similar, but the actual error based on the same ohmic correction will be larger. Fig. 6 also shows that the potential profiles are quite different for an oversized anode verses an oversized cathode. Clearly, it is more accurate to assume no ohmic drop between the oversized cathode and the reference electrode than to assume a correction of half of the total ohmic drop across the membrane. However, the measurement error can still be significantly large. In all cases, when assuming no ohmic drop between the oversized electrode and the reference electrode, a certain but unknown error has been introduced. In summary, for the secondary current distribution, even with no electrodes misalignment, the different kinetic resistance on each electrode can affect the accuracy of potential measurement. It shifts the value of potential within the RCP close to that of the electrode with smaller kinetic resistance. Depending on the kinetics, correcting ohmic drop between the reference electrode and the measured electrode using half of the ohmic drop across the membrane may be acceptable. Once the cell geometric factor is introduced, accurate measurement can be achieved if one of the electrodes has small kinetic resistances, i.e. close to the primary current distribution. Otherwise, an error is certainly introduced and its magnitude depends on the electrode oversize and magnitude of kinetic resistance. 3.3. Measurement error for real systems A real fuel cell system is more complicated because the kinetic resistance at the anode and the cathode are usually not equal to each other. Hydrogen oxidation reaction is fast, while both the methanol oxidation reaction and the oxygen reduction reaction are slow. Considering the combination with the possible electrode misalignments, it is necessary to simulate the typical fuel cell systems, and to assess the possible measurement errors associated with electrode potential measurement. We simulate both a hydrogen PEM fuel cell and a direct methanol fuel cell within a current density range in which mass transfer effects can be neglected. The first step is to fit experimental data of both HFC and DMFC to a kinetic model by adjusting the exchange current densities of both anode and cathode reactions. Other parameters such as transfer coefficients are taken from the Tafel slopes found in literature. The simulation accuracy is checked by comparing the calculated cell current with the experimental cell current for each potential at which the mass transfer effect can be neglected. The measured overpotential can be obtained based on the position of the reference electrode (within the RCP region) and making ohmic compensation. Meanwhile, the true overpotential for both anode and cathode at different current densities can be calculated using the simulation parameters. Therefore the measurement error for different cell geometries and different ohmic compensation can be obtained. The simulations are run on different

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Table 1 The parameters for fuel cell simulation Parameter

H2 /air fuel cell

DFMC

Electrode size (cm × cm) Membrane thickness (␮m) Membrane conductivity (s/cm) HOR exchange current density (superficial) (mA/cm2 ) ORR exchange current density (superficial) (mA/cm2 ) MOR exchange current density (superficial) (mA/cm2 ) HOR transfer number ORR transfer number MOR transfer number Operation temperature (◦ C)

1×1 175 (NafionTM ) 0.1 190

–

6.5e-4

1.35e-2

–

0.33

αa + αc = 1.0 αc = 1.0 [14] – 80

– αa = 0.7 [13] 110

geometries of electrode misalignments where r varies from 0 to 1.5. 3.3.1. Hydrogen PEM fuel cell The hydrogen PEM fuel cell experimental data (H2 /air fuel cell, NafionTM 117, 10 wt.% Pt/C, operating temperature 80 ◦ C) was taken from the work of Tacianelli et al. [12]. Table 1 lists the estimated parameters for the simulation. The polarization curves in Fig. 7 indicate the simulation results fits the experiment data very well in the region where mass transfer effect can be neglected (cell potential >0.4 V). Fig. 8a plots the overpotential measurement error (%) for aligned electrodes. The ohmic compensation assumes the potential correction is half of the total ohmic drop across the membrane. Thus, the measurement error is the deviation of the assumed ohmic compensation from the true ohmic drop between reference electrode and the measured electrode relative to the true overpotential. Since the anode overpotential is smaller, the error for anode will be larger when written as a percentage. At low current density, the anode overpotential measurement gives a negative error, and cathode overpotential gives a positive error. In other words, the anode overpotential is underestimated, and the cathode overpotential is overestimated. At low current density, the Wagner number of the anode is smaller than that of the cathode. For this specific set of experimental data, the Wa of anode is 0.9, and the Wa of cathode is 7.9 at cell potential of 0.9 V and 1.2 at 0.8 V. As discussed above, the value of RCP should be close to that of the anode side of membrane and hence introduces the above measurement error. At high current density however, the Wa of cathode becomes smaller than that of anode. e.g. Wa of cathode is 0.43 at 0.7 V cell potential and 0.20 at 0.5 V cell potential. Thus, an overestimated anode overpotential and underestimated cathode overpotential are expected. Only when the Wagner number of the anode equals that of the cathode, then the measurement error for anode and cathode are both zero. In simulation this occurs at about 200 mA/cm2 current density. Fig. 8b shows the measurement error (%) for unaligned electrodes for which r = 0.5. The ohmic correction again

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1

potential / V

0.9 0.8

experiment

0.7

simulation

0.6 0.5 0.4 0.3 0.2 0.1 0 0

200

400

600

800

1000

1200

current density / mAcm-2 Fig. 7. Comparison of the simulation results and experiment data for hydrogen fuel cell as per the description in the text.

assumes the potential difference between the reference electrode and either anode or cathode is half of the total ohmic drop across the membrane. It turns out that with this method of ohmic correction, when one electrode is oversized relative to the other, the overpotential on the oversized electrode will be underestimated, and the other electrode will be overestimated. Since the anode has a smaller overpotential, the error for anode is therefore large as a percentage. The simulation shows the error is over 30%. The small error for cathode is due to relatively large overpotential, yet it still over 20% at high current density. The measurement of cathode overpotential at low current density however, has a small error of about 3%. Another way to make an ohmic compensation is to assume no ohmic drop between the reference electrode and the oversized electrode, and a compensation of total ohmic drop across the membrane is included in the potential measurement of the other electrode. Fig. 8c shows the measurement error (%) based on this method of ohmic compensation. Compared to the ohmic compensation method used in Fig. 8b, the method used in Fig. 8c gives smaller measurement errors (%) at most current densities. For example, at 0.8 V cell potential (∼150 mA/cm2 ), the cathode measurement error (%) is less than 1%. Even at high current density, the measurement error (%) is still small, less than 7% at 0.5 V cell potential (∼800 mA/cm2 ). Anode measurement error (%) is also smaller for this method of ohmic compensation. The maximum error (%) is less than 20% at high current density, and is less than 7% at low current density. 3.3.2. Direct methanol fuel cell The example experimental data of direct methanol fuel cell was taken from the work done by Baldauf et al. [15]. The cell was operated at 110 ◦ C and 3 bar abs., anode catalyst has 2 mg PtRu/cm2 , and a NafionTM 117 membrane was

used. The simulation parameters are listed in Table 1. In simulating the DMFC, the methanol cross-over, which in fact influences the apparent cathode kinetic resistance, was neglected. Fig. 9 compares the polarization curves based on experimental data and the simulation results. The simulation fits the experimental data well in the region where mass transfer effect can be neglected (output potential >0.4 V). The DMFC differs from HFC in that both anode and cathode are in the Tafel region, and the Wagner number ratio between anode and cathode is constant as the average current is changed. Both electrodes show a typical secondary current distribution or nearly a primary current distribution at high current density. Consequently, the measurement errors are different as compared to hydrogen fuel cell. Fig. 10a plots the overpotential measurement error (%) for aligned electrodes. The ohmic compensation assumes correcting the anode and cathode potential by an ohmic value equal to half of the total ohmic drop across the membrane. The measurement error (%) for both anode and cathode are very small, not more than 0.2%. Compared to hydrogen oxidation, methanol oxidation is slow and has an overpotential comparable to the cathode. For example, the Wagner numbers of anode and cathode are 13.2 and 9.2, respectively at 0.7 V cell potential, and 0.45 and 0.31, respectively at 0.4 V cell potential. Obviously with aligned electrodes, to correct the single electrode potential measurement with half ohmic drop across the membrane is suitable and gives high accuracy. Fig. 10b plots the measurement error (%) for unaligned electrodes when r = 0.5. The ohmic compensation assumes that the potential difference between the reference electrode and either anode or cathode is corrected by half of the total ohmic drop across the membrane. It turns out that the overpotential at the oversized electrode is underestimated and the overpotential at the other electrode is overestimated. The error (%) increase as current density becomes large.

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1

3

0.9

2

0.8

experiment

0.7 potential / V

measurement error / %

1 0 -1 cathode

-2

simulation

0.6 0.5 0.4 0.3

anode

0.2

-3

0.1 -4

0

200

(a)

400

600

800

1000

current density / mAcm-2

60 measurement error / %

A(c,o)

C(a,o)

0 C(c,o)

-20 A(a,o)

200

(b)

measurement error / %

25 15

A(c,o)

0

200

800

1000

3.4. Minimizing fuel cell measurement errors

C(c,o)

-15

600

1000

C(a,o)

-5

(c)

800

A(a,o)

5

-25

400 600 current density / mAcm-2

cathode (anode oversize) anode (anode oversize) cathode (cathode oversize) anode (cathode oversize)

35

400

tance, and the current distribution is typically secondary, and at high current density, the kinetic resistance is relatively small compared to the ohmic resistance, thus the current distribution approaches primary. The error becomes large as the current density increases because when the current distribution approaches the primary distribution, the geometric factor becomes dominant. For the DMFC system in this study, the measurement error for either electrode is as high as nearly 10%.

20

-60 0

200

Fig. 9. Comparison of the simulation results and experiment data for direct methanol fuel cell as per the description in the text.

40

-40

0

current density / mAcm-2

cathode (anode oversize) anode (anode oversize) cathode ( cathode oversize) anode ( cathode oversize)

80

0

400 600 current density / mAcm-2

800

1000

Fig. 8. (a) The measurement error for aligned electrodes in a H2 /air fuel cell, ohmic compensation: the potential difference between reference electrode and either anode or cathode is corrected by half of the IR across the membrane. The small overpotential measurement error is due to different kinetics on anode and cathode. (b) The measurement error for unaligned electrodes, r = 0.5 in a H2 /air fuel cell. Ohmic compensation: assume the potential difference between reference electrode and either anode or cathode is corrected by half of the IR across the membrane. (c) The measurement error for unaligned electrodes, r = 0.5 in a H2 /air fuel cell. Ohmic compensation: assume the potential difference between reference electrode and the oversized electrode includes no IR across the membrane.

Since the kinetic effects on anode and cathode are similar, the measurement error for anode and cathode is nearly symmetric about the x-axis. At low current density, the kinetic resistance is relative large compared to the ohmic resis-

Electrode misalignment is common in a laboratory fuel cell. The misalignment can be just in one direction or in both x and y direction, as shown in Fig. 11. Unfortunately, since the membrane is so thin, only a small amount of misalignment could have a significant effect on measurement accuracy. However, if the electrodes are identical in size, it is possible to assess the error due to misalignment and choose a proper ohmic compensation methodology. In the fuel cell measurement, the potential measurement could be made with two reference electrodes, with one positioned at point a and the other at point a in Fig. 11, or one at point b and the other at point b . In either case, all points are located within the RCP. If the misalignment exists in only one direction, i.e. x direction as shown in Fig. 11a, then the reference electrodes positioned at b and b along the y-direction will give the same value when measured against the anode (or the cathode). If the reference electrodes are placed at points a–a in Fig. 11a, or either points a–a or points b–b in Fig. 11b, the single electrode potential values measured against these different reference electrodes should be different. Here, we take the cathode potential measurement in an HFC as an example. Let Ec be the true potential of the cathode with respect to a reference electrode, Eˆ c/o to be the measured potential against a reference electrode positioned in the RCP near the oversized cathode, and Eˆ c/u to be the measured potential against a reference electrode positioned in the RCP

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measurement error / %

0.1 0.05

cathode anode

0 -0.05 -0.1 -0.15 -0.2 0

100

200

300

400

500

600

700

current density/ mAcm-2

(a) 25

cathode (anode oversize) anode (anode oversize)

20

cathode (cathode oversize) anode (cathode oversize)

measurement error / %

15 10 A(c,o)

5

C(a,o)

0 C(c,o)

-5

A(a,o)

-10 -15

0

100

200

(b)

300 400 500 current density / mAcm-2

600

700

Fig. 10. (a) The measurement error for aligned electrodes in a DMFC, ohmic compensation: the potential difference between reference electrode and either anode or cathode is corrected by half of the IR across the membrane. The measurement has high accuracy. (b) The measurement error for unaligned electrodes in a DMFC, r = 0.5. Ohmic compensation: assume the potential difference between reference electrode and either anode or cathode is corrected by half of the IR across the membrane.

near the oversized anode, Then we have: ˆ c/o − IRc/o Ec + δIR0 = E

(9)

ˆ c/u − IRc/u Ec + δIRu = E

(10)

b’

y x

a

(a)

b

ˆ c/u + E ˆ c/o ) − 1 IR Ec + 21 (δIRu + δIRo ) = 21 (E 2

b’

y

a’

x

a

(b)

where δIRo and δIRu are the unknown absolute errors introduced by the method of ohmic compensation. IRc/o and IRc/u are known corrected ohmic drop. The left-hand side of Eqs. (9) and (10) are the ohmic corrected measured potentials. For either method of compensation discussed in this paper, the sum of IRc/o and IRc/u is the IR across the membrane. Therefore,

a’

b

Fig. 11. The common misalignment in laboratory fuel cell MEA assembly: (a) misalignment exist in one direction and (b) misalignment exist in two direction.

(11)

Since δIRo and δIRu are of opposite signs, and often of different magnitudes, it is clear that the averaged potential is more accurate than the potential of a single measurement. Same result can be obtained for measuring and correcting the anode potential. One advantage of using the two-reference averaging method is that it neglects the detail misalignment and is independent of the ohmic compensation method. In Fig. 8b and c, comparing the oversized anode case and oversized cathode case, it can be found that the error is

Z. Liu et al. / Electrochimica Acta 49 (2004) 923–935

935

symmetric about the x-axis. That is, δIRo and δIRu are of opposite sign, but close in absolute value. Hence the measurement error can be substantially minimized by Eq. (11). In the case where there is a large misalignment, this method can increase the measurement accuracy, however, the error is still larger when compared to the case of a small misalignment. For the DMFC, the method of averaging measurement against two reference electrodes gives even more accurate potentials because of slow kinetics on both electrodes. The measurement error can be substantially minimized for both electrodes within a range of all the reasonable misalignment.

error for single electrode potential can be greater than 60% even with an appropriate ohmic compensation. However, for the PEM fuel cells with identically sized electrodes, two reference electrodes can be used to minimize measurement errors. The advantage of this method was shown for a HFC and a DMFC.

4. Conclusion

References

The simulations performed here show that the current and potential distributions are strongly affected by the electrode alignment and electrode kinetics. These parameters can be well described by using an oversize ratio r for misalignment and Wagner number for electrodes kinetic resistance. This study leads to the following conclusions. Under primary current distribution, the effect of large cell misalignment (i.e. r = 1.5) can be eliminated by positioning the reference electrode within the region of RCP and by not making any ohmic correction to the potential of the oversized electrode. Under secondary current distribution, the measurement accuracy is more difficult to assess, especially if there are widely different kinetic resistances at each electrode, together with the electrodes misalignment. Measurement error analysis on a hydrogen/air fuel cell and a direct methanol fuel cell indicate that the single potential measurement error cannot be completely eliminated over a typical range of current densities. The measurement

Acknowledgements This work was supported by Energizer/Yeager Center Fellowship Program.

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