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0013-4651/2004/151共5兲/A756/7/$7.00 © The Electrochemical Society, Inc.

The AirÕPlatinumÕNafion Triple-Phase Boundary: Characteristics, Scaling, and Implications for Fuel Cells Ryan O’Hayrea,*,z and Fritz B. Prinza,b a

Department of Materials Science and Engineering, bDepartment of Mechanical Engineering, Stanford University, Stanford, California 94305-303, USA

This contribution examines the heterogeneous kinetics of the oxygen reduction reaction 共ORR兲 at the Pt/Nafion/air triple-phase boundary 共TPB兲. This system is of particular interest for low-temperature polymer electrolyte membrane fuel cell applications. A focused ion beam system is used to prototype geometrically simple platinum microstructures directly on Nafion electrolyte membranes. By varying the size and shape of the platinum structures, the role and properties of the TPB are elucidated. Currentvoltage and electrochemical impedance spectroscopy measurements reveal that the ORR kinetics scale with TPB length. A faradaic resistance per unit TPB length of 6 ⫻ 109 ⍀ ␮m is extracted under short-circuit conditions at room temperature. Although this value is determined from microscopic measurements of geometrically simple platinum structures, it is successfully applied to predict the bulk performance of large-area sputtered platinum catalyst fuel cells. © 2004 The Electrochemical Society. 关DOI: 10.1149/1.1701868兴 All rights reserved. Manuscript submitted August 8, 2003; revised manuscript received November 5, 2003. Available electronically April 14, 2004.

The electrochemical behavior of systems governed by heterogeneous electrocatalysis depends strongly on the nature, size, scaling, and properties of the particular favored sites where the reaction occurs. For example, in fuel cell systems, the oxygen reduction reaction 共ORR兲 can only occur at confined spatial regions, called triplephase boundaries 共TPBs兲, where the electrolyte, gas, and electrically connected catalyst particles contact. Therefore, the overall electrochemical behavior of such a system is determined by an intimate convolution of fundamental materials’ properties and microstructure geometry. It is often difficult or impossible to deconvolute these factors; however, an independent understanding of both the geometric effects 共e.g., size, extent, and scaling of heterogeneous reaction sites兲 and the chemical effects 共activity, electric field, temperature, and pressure dependence兲 is necessary to yield predictive capabilities. Such an understanding has ramifications for diverse fields, including chemical and electrochemical catalysis, fuel cells, batteries, sensors, and corrosion research. This paper addresses the heterogeneous kinetics of the ORR at the Nafion-electrolyte/Pt-electrocatalyst interface. The Pt/Nafion interface is especially interesting for electrolysis and fuel cell applications. Most polymer electrolyte membrane fuel cells 共PEMFCs兲 employ Pt electrocatalysts and Nafion or Nafion-like polymer electrolytes. Due primarily to the low operating temperature of PEMFCs, the kinetics of the ORR often dictate the electrochemical performance.1 It is widely held that the ORR kinetics are governed by the amount of TPB available for the reaction to occur. Thus, detailed information about the nature, scaling, and properties of the TPB in polymer fuel cells is required. The structure of the catalyst in a state-of-the-art PEMFC is complex, consisting of a porous, heterogeneous mixture of conductive carbon powders and platinum particles, often mixed with a solid polymer electrolyte binder. Due to this complexity, the true amount of TPB in a PEMFC is difficult, if not impossible, to determine. Thus, the relationship between catalyst microstructure 共i.e., TPB geometry兲 and fuel cell performance is still unclear. Previous investigations of the Pt/Nafion interface yielded a partial insight but wrestled with the challenges of measuring an all solid-state system. Early studies characterized the Pt/Nafion interface in the presence of free liquid electrolytes.2,3 Later efforts used Pt microelectrode probes to extract area-related kinetic parameters for the ORR at solid-state Pt/Nafion interfaces.4-6 Unfortunately, due to the fixed size and geometry of the Pt probes, these studies could not examine heterogeneous TPB properties. Although these earlier microelectrode studies did not examine

* Electrochemical Society Active Member. z

E-mail: [email protected]

TPB properties, microelectrode techniques can prove especially effective for studies of this nature as well. By constructing reproducible, geometrically simple, well-defined electrocatalyst structures of various sizes, the relationship between electrocatalyst geometry and electrochemical behavior can be clearly delineated. Furthermore, microelectrodes alleviate complications arising from ohmic and mass-transport limitations. Mass transport at microelectrode surfaces is considerably enhanced due to nonplanar diffusion; furthermore, when the dimensions of the microelectrode are smaller than the dimensions of the electrolyte, the ohmic electrolyte resistance scales with 1/r 共where r is the microelectrode radius兲. Therefore, quiescent systems can be studied over larger current ranges before encountering ohmic or mass-transport limitations.6-8 Additionally, because electrode capacitance scales with 1/r 2 , the reduction of microelectrode dimensions also improves the ratio of faradaic vs. capacitive currents and provides access to smaller resistancecapacitance product/time constants, permitting the study of previously inaccessible phenomena.9 In this contribution, we investigate geometrically simple Pt-catalyst microstructures that are directly written on Nafion electrolytes using a focused ion beam 共FIB兲 system. By varying the size and shape of these Pt-catalyst features, we gain insight into the nature and behavior of the heterogeneous electrocatalytic reaction. These Pt-catalyst features are directly patterned on the Nafion electrolyte surface, thus mirroring as closely as possible the true Pt/ Nafion interface in a real PEMFC. Although solid oxide fuel cell studies can use lithographically patterned microelectrodes to investigate heterogeneous kinetics,10-14 these procedures are not applicable to polymer membranes, because the processes and chemicals used are incompatible with or irreversibly harm polymer electrolytes. Alternative techniques, such as catalyst patterning on support substrates followed by either Nafion spin coating or postbonding to Nafion membranes, do not accurately reflect the true nature of the Pt/Nafion interface in fuel cells. Thus, the use of the FIB to directwrite Pt-structures on Nafion is a key enabling technology in these studies. The FIB deposits the catalyst features in intimate contact with the electrolyte, providing an interface contact that is independent of external forces. This direct-write prototyping therefore circumvents the electrode/electrolyte contact issues inherent to external probe studies. Additionally, by avoiding the need for an aqueous electrolyte environment, we ensure that these results are inherently applicable to real-world PEMFC devices. Furthermore, as the FIB facilitates rapid prototyping of a wide variety of electrocatalyst geometries, we can investigate scaling effects previously inaccessible by other techniques.

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Figure 1. Depiction of the experimental setup. The electrochemical properties of FIB-patterned Pt particles on Nafion are probed in air vs. a large-area hydrogen reference/counter electrode.

Experimental Experimental configuration.—The experimental setup is depicted in Fig. 1. Commercially available ‘‘half-cell’’ fuel cell membrane electrode assemblies 共MEAs兲 were obtained from BCS Technologies Inc. These half-cell MEAs employed a Nafion 115 electrolyte membrane, on one side of which was hot-pressed a 0.5 cm2 carbon cloth catalyst-electrode structure. This large-area electrode served as the reversible reference and counter electrode. The other side of the MEA was left purposely bare. The Pt-catalyst electrode structures under investigation were then patterned on this bare electrolyte surface. The half-cell MEAs were either mounted on a reusable copper flow-structure electrode block with vacuum groove sealing, or permanently laminated to a copper-plated printed circuit board flowstructure electrode. Copper has been suggested to cause irreversible performance degradation in Nafion. In this study, the copper flow blocks were used to collect current from the MEA anodes but were not in direct contact with the Nafion electrolyte. A carbon-cloth diffusion layer protected the electrolyte and anode catalyst layer

from the copper flow blocks. Furthermore, dry hydrogen gas was used in the anode, and the amount of water produced at the cathode microelectrode structures was minimal; therefore copper dissolution is not expected to have occurred. Dry hydrogen gas was introduced through the flow structure to the sealed anode compartment, where it was delivered to the large-area counter/reference electrode. The Ptstructures on the bare electrolyte top surface were exposed to ambient air. No attempt was made to control the ambient air humidity, which typically ranged from 30-60%. A Gamry PC4/750 potentiostat-impedance system was used for all electrochemical measurements. Tests were conducted at room temperature and atmospheric pressure; H2 flow rate at the anode was regulated to 5 standard cubic centimeters per minute. The electrochemical properties of these Pt-structures were probed using either gold-coated tungsten needles in a micromanipulator under an optical microscope, or an atomic force microscope 共AFM兲 with a conductive doped-diamond coated tip, where electrochemical measurements could be obtained directly through the con-

Figure 2. Results of a computer simulation for 30 keV Ga⫹ ion bombardment of a CF2 Teflon-like material. The left graph shows the ion penetration depth distribution. The right graph shows a collision-events histogram vs. depth. The simulation approximates the FIB-induced surface damage in Nafion.

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ductive AFM tip. Further elaboration on the use of the AFM as a localized electrochemical probe is planned for a future publication. FIB microelectrode fabrication.—The platinum catalyst structures were directly written on the topside Nafion electrolyte surface using an FEI Strata Dual-Beam 235 FIB. The FIB was equipped with a platinum gas injection system needle to allow ion-beam assisted deposition of platinum. The platinum was deposited from a metallorganic precursor source, and the resulting features were not pure, but incorporated significant amounts of carbon. An energy dispersive X-ray analysis study of the FIB-deposited platinum showed it to be approximately 30 atom % Pt and 70 atom % C 共87 wt % Pt, 13 wt % C兲 with trace Ga, O, and F impurities. The bulk resistivity of the FIB Pt, acquired from thin-film resistance measurements, was around .001 ⍀ cm. Although considerably more resistive than pure metal, the FIB-deposited Pt still manifested more than sufficient conductivity. Thus, the resistance contributions from the FIB-deposited Pt-electrodes could be assumed negligible in comparison to the faradaic and electrolyte resistances measured in the experiments. During FIB deposition of Pt, the Nafion surface was unavoidably bombarded with 30 keV Ga⫹ ions. Trace Ga impurities were detected both in the Nafion electrolyte and in the deposited Pt. A simple simulation 共public domain freeware, www.srim.org兲 was run for a CF2 Teflon-like material to simulate the ion bombardment effects in Nafion. As shown in Fig. 2, the simulation suggests that the ion damage should be limited to the top 50 nm of the Nafion membrane. 共The collision events figure indicates that matrix-atom knockout 共vacancies produced兲 decays to zero within 50 nm of the surface.兲 It is unknown if this ion damage affects the electrochemical behavior of the Pt/Nafion structures. The computer numerical controlled direct-write capabilities of the FIB tool enabled rapid creation of a wide-ranging set of simple platinum catalyst features for investigation. Most of the platinum features investigated were simple circular electrodes 共see Fig. 3a兲, ranging in size over three orders of magnitude from several hundred micrometers down to several hundred nanometers; however, other platinum catalyst features such as rectangles and grids were also explored. The difficulties of measuring the ultrahigh impedances associated with the smallest microelectrodes (r ⬍ 10 ␮m兲 were overcome by using microelectrode arrays 共see Fig. 3b兲. Thus all reported data for r microelectrodes ⬍ 10 ␮m come from electrically connected microelectrode arrays. Array spacing rules (d separation ⫽ 5r microelectrode) were applied to minimize interaction effects. The array electrodes were connected with fine platinum wires, also patterned in the FIB. To confirm the trends of the FIB-patterned microelectrodes, macroscopic Pt-electrodes from 0.1 to 1 cm2 in area were also prepared using traditional shadow mask sputtering. All platinum catalyst features had a nominal deposited thickness of 2 ␮m. Microelectrode impedance measurements.—The Pt catalyst structures are deposited 2 ␮m thick to eliminate oxygen diffusion and reaction through the bulk electrode area. It is assumed that the catalyst deposits are conformal and defect/pinhole free. Thus, the bulk of the electrode area cannot participate in the ORR process. Instead, only the perimeter participates as an active TPB for the faradaic reaction. Furthermore, we assume that the micromanipulator tip/Pt contact impedance is negligible compared to the measured faradaic and electrolyte impedances of the system. We assume that the catalyst properties of the FIB-deposited Pt are not significantly influenced by the presence of carbon 共other than as a diluent兲. We assume that the ORR exhibits Tafel behavior, where the faradaic current, i f , produced by the reaction is exponentially dependent on the overpotential, ␩ ⫽ E 0 ⫺ E cell , applied to the cell if ⫽ Ae

B␩/RT

关1兴

Here A and B are constants, i f is the faradaic current, R is the gas constant, and T is the temperature in Kelvins. We neglect diffusion in our microelectrode system 共i.e., Nernstian concentration losses are zero; in other words, the surface concentration C s

Figure 3. 共a兲 Electron micrograph of a series of Pt-microelectrodes directly patterned via FIB on the surface of a Nafion membrane half-cell MEA. 共b兲 Higher magnification electron micrograph of a portion of an FIB-patterned array of 1 ␮m radius Pt-microelectrodes. After array patterning is complete, the electrodes are electrically interconnected with a series of FIB-deposited Pt wires 共not shown兲.

⫽ the bulk concentration, C b). We also neglect the anode processes, because the anode is highly reversible and much larger than the cathode microelectrode. Under these assumptions, the total current/voltage relationship is i ⫽ AeB共E0 ⫺共 Ecell⫹iRe兲兲/RT ⫹ Cdl

dE共t兲 dt

关2兴

where R e is the ohmic electrolyte resistance arising from the flow of solvated protons in the electrolyte and C dl is the double-layer capacitance at the electrolyte/electrocatalyst interface. Electrochemical impedance spectroscopy 共EIS兲 can be used to experimentally determine the relevant parameters in this relation, providing a route to characterize the electrochemical properties of the microelectrode. During an impedance measurement, a sinusoidal voltage excitation, E exc , of angular frequency w, is superimposed on the fixed dc cell voltage E共t) ⫽ Ecell ⫹ Eexce jwt

关3兴

The resulting current response is i共t) ⫽ AeB共E0 ⫺共 Ecell⫹Eexce

jwt⫹i共t兲R 兲兲/RT e

⫹ jwCdlEexce jwt

关4兴

Finally, the impedance, Z, can be calculated Z⫽

E共t兲 1 ⫽ Re ⫹ i共t) 1 ⫹ jwCdl Rf

关5兴

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Figure 4. EIS Nyquist plot for a 100 ␮m radius Pt-microelectrode. 共䊉兲 Experimental data, 共 兲 model fit based on Eq. 5 in the text, using a 兲 model fit using a constant-phase element, pure capacitor, C dl , and 共 ␾ CPE .

where R f is identified as the faradaic resistance and is equal to 1 关6兴 Rf ⫽ AB B␩/RT e RT The measured spectra from experimental microelectrodes were fit to this model impedance equation using a complex nonlinear leastsquares method. To improve the fit, a constant-phase element, ␾ CPE was used in place of the pure capacitor C dl . An example of the model fit to a 100 ␮m radius microelectrode is shown in Fig. 4. Using this procedure, values for the electrolyte resistance, R e , the faradaic resistance R f , and the double-layer capacitance, C dl , for all the microelectrodes were obtained. At each microelectrode radius, three impedance measurements were generally taken on each of three to four identically sized microelectrodes. The R e and R f data vs. microelectrode diameter presented in this study represent the mean values from this measurement procedure. All impedance data in this study were acquired under shortcircuit conditions, so that the potential between the anode and cathode was zero 共maximum overpotential兲. Measurement under short circuit provided an easily obtainable and reproducible point of comparison for all samples. Furthermore, it provided the best possible signal-to-noise ratio, because the electrochemical reaction proceeds at its maximum rate 共highest current兲 at short circuit. Results and Discussion Microelectrode micro fuel cells.—The microscale platinum features pictured in Fig. 3 are fully functioning fuel cells. Truly micro fuel cells, they may be some of the world’s smallest PEMFCs ever evaluated. Figure 5a shows the absolute current-voltage 共I-V兲 curves for three different circular fuel cells with radii varying from 10 to 40 ␮m. The absolute performance of these tiny fuel cells is insignificant; note the small values for the current. Not surprisingly, the larger the fuel cell, the greater absolute current it delivers. Figure 5b reports the results from the same three circular Pt-structures, but now normalized by area; on an area-normalized basis these results argue that smaller fuel cells are better. Intriguingly, the I-V curves of the three fuel cells are roughly comparable if they are scaled relative to their circumferences, rather than their areas, as shown in Fig. 5c. Microelectrode impedance results.—To understand this scaling phenomenon, it is necessary to consider the fundamental electrochemical characteristics of the Pt-catalyst structures. As discussed in the experimental section, a systematic impedance study allows us to separate the contributions of electrolyte resistance (R e) and faradaic impedance (R f) of the ORR. The results of this study are given in Fig. 6a and b. As Fig. 6a reveals, R e for the Pt-electrode structures is

Figure 5. I-V curves for a series of Pt-microelectrodes operating as hydrogen-air fuel cells. 共Heavy line兲 40 ␮m radius microelectrode, 共medium line兲 30 ␮m radius microelectrode, and 共thin line兲 10 ␮m radius microelectrode. 共a兲 Absolute current vs. voltage, 共b兲 current density vs. voltage, and 共c兲 perimeter normalized current density vs. voltage.

proportional to r ⫺2 for large-area electrodes and proportional to r ⫺1 for small-area electrodes. For small electrodes 共when the electrode size, r, is much smaller than the electrolyte thickness, t兲, the measured electrolyte resistance, R e , is shown to be inversely proportional to the electrode radius15 ␳ Re ⫽ , rⰆt 关7兴 4r

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Figure 6. 共a兲 Electrolyte impedance (R e) vs. Pt-microelectrode radius. 共⽧兲 Experimental data from FIB-patterned Pt-microelectrodes, 共䊏兲 experimental data from large-area shadow mask sputtered Pt electrodes, 共 兲 and model fit based on finite element simulation. Solid lines and equations show slope ⬇⫺1 for (r ⬍ 100 ␮m兲, slope ⬇⫺2 for (r ⬎ 100 ␮m兲 共b兲 Faradic impedance (R f) vs. electrode radius. 共⽧兲 Experimental data from FIBpatterned Pt-microelectrodes. Dashed lines and equations show slope ⬇⫺1 for (r ⬍ 40 ␮m兲, slope ⬇⫺2 for (r ⬎ 40 ␮m兲.

whereas for r Ⰷ t, the resistance is inversely proportional to the electrode area Re ⫽

␳ *t ␲r2

,

rⰇt

关8兴

Thus, Fig. 6a relates a purely geometrical effect caused by the transition from an area-related electrolyte resistance for r Ⰷ t to a point contact-dominated spreading resistance for r Ⰶ t. This transition is recovered in the results of a simple finite element simulation 共Fig. 7兲. Note that the trend in the microelectrode data matches up nicely with the data for the shadow mask Pt-macroelectrodes. This gives some assurance that the FIB Ga⫹ bombardment during microelectrode patterning has not significantly affected the properties of the Nafion membrane. The Nafion properties can be extracted by fitting the data to the simple finite element simulation, as shown by the dotted line in Fig. 6a. A parametric best fit of the finite element simulation to the experimental data is obtained for simulation values of Nafion thickness t ⫽ 90 ␮m and Nafion resistivity ␳ ⫽ 3000 ⍀ cm. 共Nominal reference values for dry Nafion 115 are t ⫽ 125 ␮m, ␳ ⫽ 10-100 ⍀ cm.16-18兲 The electrolyte in our experiments is subjected to a desiccating high-vacuum environment prior to electrochemical measurement, so it is not surprising that our experimentally fit resistivity values are high. Perhaps more surprising are the results in Fig. 6b, which show that R f is also roughly proportional to r ⫺2 for large electrodes and

Figure 7. Field simulation results from the finite element model showing the transition from spreading resistance dominance for r Ⰶ t to a uniform-field area-based resistance for r Ⰷ t.

proportional to r ⫺1 for small electrodes. Note first that the faradaic impedance is several orders of magnitude larger than the electrolyte impedance. This indicates that R f for the ORR dominates the electrochemical behavior of these circular micro fuel cells. 共The losses from R e are negligible in comparison.兲 For electrodes smaller than about 40 ␮m, we see a direct relation between Pt-microelectrode circumference and Rf. This expected result indicates that the ORR kinetics are scaling with the length of the TPB. As hypothesized earlier, the 2 ␮m thickness of the catalyst structures prevents the bulk of the electrode area from participating in the ORR process. Instead, only the perimeter participates as an active TPB for the faradaic reaction. Interestingly, for microelectrodes larger than 40 ␮m, the ORR kinetics no longer scale with a circumferential-based TPB length. The roughly r ⫺2 dependence for the larger Pt-electrodes is believed to arise from a cracking process due to the dimensional instability of the Nafion electrolyte. Electron microscope analysis of Pt-microelectrodes performed after the testing confirms that cracking typically occurs for electrodes larger than about 40 ␮m. 共See Fig. 8.兲 The cracking is believed to be due to the expansion of the Nafion electrolyte upon removal from the vacuum environment and exposure to ambient humidity. This areadistributed cracking introduces additional TPB sites in the larger electrode structures, which should scale roughly proportional to electrode area. For Pt-electrodes smaller than 30 ␮m, no cracking is observed. Thus, for these small, unblemished electrodes, it is possible to extract a faradaic resistance per unit TPB length (R TPB). R TPB is calculated as RTPB ⫽ 2␲r* Rf

关9兴

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From the data in Fig. 6b, R TPB can be estimated at roughly R TPB ⫽ 6 ⫻ 109 ⍀ ␮m.

Figure 8. 共a兲 A typical 10 ␮m radius FIB-patterned Pt-microelectrode imaged after testing under ambient conditions. Despite the vacuum-ambientvacuum cycling, the microelectrode remains intact. 共b兲 A typical 40 ␮m radius FIB-patterned Pt-microelectrode imaged after testing under ambient conditions. After the vacuum-ambient-vacuum cycling, the microelectrode exhibits cracking.

TPB scaling.—As noted earlier, the faradaic impedance dominates the electrochemical behavior of these micrometer-sized catalyst structures (R f Ⰷ R e). Thus, catalyst structures with an increased TPB length per unit area should show proportionally improved electrocatalytic performance. In Fig. 9, a uniform 40 ⫻ 40 ␮m square electrode is compared to a sectioned 40 ⫻ 40 ␮m square electrode. The two electrodes have the same total Pt area, but the sectioned electrode has a 5 times greater TPB length. 共Each interior section contributes two lengths of TPB.兲 As the impedance spectra for the two structures clearly show, the faradaic resistance of the sectioned electrode is about one-fifth that of the uniform electrode. Not only do the faradaic impedances for the two structures scale qualitatively as predicted, but the absolute quantitative values for the two structures scale almost exactly as predicted using the previously determined faradaic resistance per unit TPB length,

Figure 9. EIS Nyquist spectra and corresponding micrographs for two FIB-patterned ‘‘artificial Pt-catalyst microstructures’’ showing the direct relation between faradaic impedance and TPB length. 共a兲 40 ␮m square Pt-catalyst structure sectioned into 25 separate 8 ⫻ 8 ␮m squares. Electrical contact between the 25 sections is ensured by the Pt interconnect wires. The sectioned structure shows a faradaic impedance of around 8 M⍀. 共b兲 Undivided 40 ␮m square Pt-catalyst structure. This undivided electrode shows a faradaic impedance of around 40 M⍀. The two electrodes are imaged at a 53° angle; thus, because of foreshortening, they do not appear square.

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Table I. Estimated impedances of large-area sputtered platinum fuel cells „based on measured crack densities using the TPB assumption… compared to the actual experimentally measured values.

Pt thickness 共nm兲 100 30 15

Crack density from micrographs of Ref. 20 共␮m/␮m2兲 0.02 0.04 0.5

TPB length 共␮m/␮m2兲

Expected R A from TPB assumption 共⍀ cm2兲

Measured RA 共⍀ cm2兲

0.04 0.08 1

1560 780 60

1000-1400 500-600 20-40

R TPB ⫽ 6 ⫻ 109 ⍀ ␮m. This result grants at least some confidence that the TPB properties derived from the circular microelectrodes can be used for other geometries. Application to sputtered fuel cells.—The heterogeneous kinetic properties of the Pt/Nafion TPBs derived in this study are only truly useful if they can be applied to more complex systems. Significantly, these findings, although based on geometrically simple micrometersized Pt-catalyst structures, can be successfully applied to large-area complex Pt-catalyst microstructures. In an earlier work,19 we examined the bulk performance of large-area 共5 cm2兲 sputtered thin-film Pt-Nafion fuel cells. In these fuel cells, the Pt-catalyst layer was directly sputtered on the Nafion membrane surface. After sputtering, the thin Pt films would show significant cracking. Measurements indicated a relationship between fuel cell performance and sputtered Pt-film microstructure. Specifically, the performance of the sputtered thin-film fuel cells strongly depended on the crack density of the sputtered catalyst layer. Densely cracked films exhibited high performance, and sparsely cracked films showed poor performance. It was hypothesized that the kinetic performance was related to the crack microstructure, with the crack networks acting as the dominant TPBs for the fuel cell reaction. Based on the present microelectrode work, we now posses a quantitative metric for the faradaic resistance of Pt/Nafion TPBs that can be applied to these complex fuel cell microstructures. Revisiting previously published micrographs of the sputtered thin-film Pt fuel cells from Ref. 19, we can identify the cracks as TPB sites and thus calculate a TPB density (␳ TPB ⫽ TPB length per unit area). From this TPB density, we can extract an anticipated area-specific faradaic resistance (R A) for the sputtered platinum fuel cells RTPB RA ⫽ 关10兴 ␳ TPB Three micrographs were published for three different sputtered platinum fuel cells 共15 nm Pt, 30 nm Pt, and 100 nm Pt, respectively兲. Therefore, three R A values could be computed. Table I compares these R A values derived from Eq. 10 to the actual experimentally measured values obtained from bulk impedance measurements of the three fuel cells. The close agreement between the two sets of values supports the initial hypothesis that the cracks in the Ptsputtered thin films act as the dominant TPBs for the ORR. The agreement also suggests that TPB properties determined from geometrically simple Pt-microelectrodes can be successfully applied to more complex, bulk microstructures. Conclusions Having determined a quantitative value for the resistance per Pt/Nafion TPB length, we can also infer TPB density requirements for a high-performance PEMFC. For most fuel cell requirements, a cathodic ORR resistance of around 0.15 ⍀ cm2 is acceptable.20 This implies a TPB density on the order of 106 cm/cm2. Assuming planepacked spherical platinum particles, each of which contributes an average TPB on the order of its projected circumferential length, we suggest that an average catalyst particle size smaller than 30 nm is necessary to achieve the required ORR resistance.

While this study has observed perimeter based scaling of the ORR kinetics, previous microelectrode studies have extracted arearelated ORR kinetics.21 Comparison of area related ORR kinetics with the perimeter based ORR kinetics observed in this study requires careful analysis. Physically, knietic scaling should depend on the relative rates of oxygen reaction and oxygen transport at the Pt/Nafion interface. Converting between the two kinetic results therefore requires a model incorporating coupled reaction and diffusion processes. A main outcome of this model would be an effective TPB width term, which seeks to bridge the results of area related and perimeter related ORR kinetics. The assignment of an effective TPB width makes physical sense, by acknowledging that the TPB is not singular but must extend over a finite region of space. We can associate this width with the diffuseness of the reaction zone. Additionally, this effective width would be a measure of the roughness of the TPB; compared to a smooth Pt surface, a rough surface will present a greater number of potential reaction sites per unit dimension. Development of a coupled reaction/diffusion model to understand the nature, scaling and effective width of the triple phase boundary is currently ongoing and intended for future publicaiton.

Acknowledgments The authors warmly thank the members of the Rapid Prototyping Laboratory and especially the fuel cell team for their support and lively discussions. In particular, we recognize Minhwan Lee for his helpful insights and assistance with the study. Special thanks are also deserved for Jeremy Cheng, who provided the ion implantation simulations, and Eric Tao for the FIB platinum characterization data. This work was supported under a Stanford Graduate Fellowship. The U.S. Department of the Navy provided funding for a portion of the FIB unit 共contract no. N00014-02-1-0220-P00003兲. The Stanford Global Climate Energy Project also provided funding for this research. Stanford University assisted in meeting the publication costs for this article.

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