Research Article Experimental Investigation of a Direct ...downloads.hindawi.com/journals/jchem/2014/371616.pdf · Research Article Experimental Investigation of a Direct Methanol

Research ArticleExperimental Investigation of a Direct Methanol Fuel Cell withHilbert Fractal Current Collectors

Jing-Yi Chang1 Yean-Der Kuan2 and Shi-Min Lee3

1 Ho Tai Development Co LTD 12F No 143 Fuxing N Road Taipei 105 Taiwan2National Chin-Yi University of Technology No 35 Lane 215 Section 1 Chung-Shan Road Taiping District Taichung 411 Taiwan3 Tamkang University No 151 Ying-Chuan Road Tamsui District New Taipei City 251 Taiwan

Correspondence should be addressed to Yean-Der Kuan ydkuanncutedutw

Received 21 February 2014 Revised 29 April 2014 Accepted 29 April 2014 Published 20 May 2014

Academic Editor Lin Liu

Copyright copy 2014 Jing-Yi Chang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The Hilbert curve is a continuous type of fractal space-filling curve This fractal curve visits every point in a square grid with a sizeof 2 times 2 4 times 4 or any other power of twoThis paper presents Hilbert fractal curve application to direct methanol fuel cell (DMFC)current collectorsThe current collectors are carved following first second and third order Hilbert fractal curvesThese curves givethe current collectors different free open ratios and opening perimeters We conducted an experimental investigation into DMFCperformance as a function of the free open ratio and opening perimeter on the bipolar plates Nyquist plots of the bipolar platesare made and compared using electrochemical impedance spectroscopy (EIS) experiments to understand the phenomena in depthThe results obtained in this paper could be a good reference for future current collector design

1 Introduction

A fuel cell is an energy generator that converts chemicalenergy stored in the fuel directly into electrical energy using aseries of electrochemical reactions without anymoving partsThe fuel cell system is therefore simple and ideally noiselessCompared with a traditional combustion engine the fuel cellhas the main advantages that it is clean efficient quiet andsimple with a power and capacity ratio that can be scaled[1] The direct methanol fuel cell (DMFC) is a prominentpotential substitute power source for portable applicationsThe advantages of the DMFC are operating at near roomtemperature usingmethanol without a bulk transformer andusing convenient combination liquid fuel storage and refuel-ing system The DMFC is therefore suitable for miniaturedesigns and can be easily carried [2 3]

A DMFC usually operates near room temperature Theanode cathode and overall reactions are

Anode CH3OH +H

2O 997888rarr 6eminus + 6H+ + CO

2(1)

Cathode 32O2+ 6eminus + 6H+ 997888rarr 3H

2O (2)

Overall CH3OH + 32O2997888rarr 2H

2O + CO

2 (3)

The anode reactants are methanol and water The oxida-tion reaction occurs at the anode which converts the reac-tants into hydrogen protons electrons and carbon dioxideThe hydrogen protons are transported from the anode tothe cathode through a polymer electrolyte membrane Theelectrons released at the anode are conducted through anexternal circuit to the cathodeThe reduction reaction occursat the cathode to change protons electrons and oxygen intowater [4]

In a typical DMFC fuel cell the bipolar plate is the unitthat carries electrons away from the anode to be receivedat the cathode distributes the fuel and oxidant within thecell separates the individual cells in the stack and assistsin water and thermal management The bipolar plate mate-rials should have high electrical and thermal conductivitygood corrosion resistance sufficient compressive strength

Hindawi Publishing CorporationJournal of ChemistryVolume 2014 Article ID 371616 7 pageshttpdxdoiorg1011552014371616

2 Journal of Chemistry

and low density characteristics such that the fuel cell willexhibit high performance and maintain stable operations[5ndash7]

A DMFC is conventionally stacked in the vertical direc-tion with each bipolar plate serving as the anode in onecell and cathode in the next cell (resulting in multiple cellsconnected in series) The flow channels inside the bipolarplates are grooved to distribute fuel and collect the electricalcharge PEMFCDMFC planar interconnection designs haverecently been presented in which the architecture alternatesbetween vertical stacking and planar connection in seriesThis configuration produces better volumetric packagingthan the vertical stack thus giving better design flexibilityfor portable applications [8] In planar type DMFCs suchas the planar printed-circuit-board fuel cell module there isno bipolar plate in the structure Instead of bipolar platesthis fuel cell has separate current collector componentswith openings to collect electrons as well as flow boards todistribute fuel among the cells

Fuel cell performance can be represented by a polariza-tion curve that is the cell potential versus current densitycurve which reflects the fuel cell activation loss in the lowcurrent density range the ohmic losses in the intermediatecurrent density range and the concentration loss in thehigh current density range The fuel cell polarization curveis determined by measuring the open circuit potential andmaking the voltage or current measurements at prescribedpotential or current intervals [8]

Fractal geometry ismathematically defined in ldquoHausdorffdimensionsrdquo a set of nonintegers according to the theoryproposed byMandelbrot [9] Fractal theory describes certainphenomena that are difficult to describe in terms of very finevariations using convectional methods The main character-istics of a fractal pattern are self-similarity subdivisibilityand a recursive nature Fractal patterns have been applied inmany engineering fields such as describing the variations inentropy and heat transfer [10] electronic cooling applications[11] heat sink fins (by Lee et al [12]) and the automaticpolishing path [13]

The first application of fractal theory to the fuel cell waspresented by Tuber et al [14] who applied the ldquoFracThermrdquotheory in PEMDMFC flow designs for bipolar plates Theirfractal flow boards were designed as biological fluid channelswith a multibranched structure with smooth flow pathsBased on a performance comparison of the fractal serpen-tine and parallel flow fields the cell with a serpentine flowchannel yields better cell performance but has a much greaterpressure drop across the channel Both themultiple-branchedfractal and parallel flow fields create a lower pressure dropwith similar performance Chang et al [15] proposed a typeof current collector with a Siepinski carpet fractal geometryTheir current collector design included first and secondSiepinski carpet fractal hole arrangements and was comparedagainst the standard hole arrangement The results showedthat the open ratio and perimeter length of the holes are twoimportant factors that affect the performance A longer totalhole perimeter resulted in better cell performance while ashorter total perimeter length and free open hole ratio led

to poor cell performance Therefore a longer total perimeterlength under the same free open ratio is recommended LaterKuan et al [16] presented a DMFC with Hilbert curve fractalcurrent collectors They concluded that current collectorswith a more uniform opening distribution and higher totalopening perimeter length could reduce the anode flow rateeffect A higher total free open ratio and total openingperimeter length in the current collectors could increase thecell performance In the previous paper only polarizationcurvesweremeasured to discuss the cell performancewith nofurther quantitative analysis to explore the impedance behav-ior caused by the electric charge migration under electro-chemical reactions The current collectors in this work weredesigned using the Hilbert curve one of the continuous typefractal geometries Experiments to measure the polarizationcurves and Nyquist plots using electrochemical impedancespectroscopy (EIS) were also carried out as part of thisstudy

2 Current Collectors with a HilbertCurve Geometry

The Hilbert curve fractal is a continuous space-filling curvethat fills a square and is typically defined as the limit of asequence of iteratively defined curves that have only shortvertical and horizontal jumps between the points in a squaregridwith a size of 2times2 4times4 8times8 16times16 or any other power of2The curves donot have self-intersections or touching pointsat any stage [17 18]

A DMFC with first second and third Hilbert curvecurrent collectors and a standard circular hole arrangement isstudied To simplify the experiments and ensure cell stabilitya DMFC with stainless steel 316L (SS316L) current collectorswas used because SS316L has the advantage of being easy tomachine and lower cost and demonstrates good mechanicalproperties [19 20]TheMEA reactive area is 35mm times 35mmand the size of each current collector is 95mm times 95mm times2mm

Figure 1 shows a Hilbert curve fractal current collectorThe geometric information on the current collectors is shownin Table 1 The widths of the HFCC1 HFCC2 and HFCC3Hilbert curves were 22mm 22mm and 11mm respec-tively The total perimeter lengths of the current collectorwith SRCC HFCC1 HFCC2 and HFCC3 openings were61412mm 26690mm 55565mm and 111782mm respec-tively The total free open areas in the current collectorswith the SRCC HFCC1 HFCC2 and HFCC3 openingswere 6125mm2 28875mm2 60637mm2 and 61359mm2respectively The free open ratios in the current collectorwith the SRCC HFCC1 HFCC2 and HFCC3 openings were5000 2350 4940 and 5000 respectively Howeverfurther increasing the free open ratio that is making higherHilbert fractal current order the carved paths of the currentcollectors become extremely narrow making the machiningdifficult This paper therefore does not discuss fourth orhigher fractal order current collectors

Journal of Chemistry 3

655 220

220

220

9500

9500

11000

Unit (mm)

(a) HFCC1

9500

9500

11000

220

220

220

220

218

Unit (mm)

(b) HFCC2

9500

9500

11000

110

110

110

110

110

109

Unit (mm)

(c) HFCC3

9500

9500

11000

088

088

R199

Unit (mm)

(d) SRCC

Figure 1 Hilbert curve fractal current collectors

3 Experimental Setup

A single cell DMFC test fixture was used in this study alongwith the following components an anode flow board gasketanode current collector gasketMEA gasket cathode currentcollector gasket and cathode airflow board The anode andcathode flow boards were made of acrylic Both the anodeand cathode current collectors were made of SS316L Toprevent liquid fuel and air leakage a gasket was placedbetween each of the components The membrane electrodeassembly (MEA) was sandwiched between the SS316L plates(Nafion 117 was used as the electrolyte) and a 4mg cmminus2 Pt-Ru catalyst was loaded onto the anode and a 4mg cmminus2 Ptwas loaded onto the cathode The active single cell size inthe experimental DMFC was 35mm times 35mm The completesingle DMFC test fixture assembly is shown in Figure 2

Figure 3 shows a schematic diagram of the experimentalsetup The anode methanol solution was preheated usinga temperature controlled water bath that was fed using asquirm pump The cathode airflow was driven by an airpump and the flow rate was controlled using an airflowregulator The DMFC was connected to an electrochemicalimpedance spectroscopic instrument to make the relatedmeasurements Figure 4 includes a schematic drawing of thephysical picture a circuit diagram and a Nyquist plot for asimple DMFC impedance model The symbols are definedas follows 119877

Ω ohmic resistance 119877

119891A anode Faradaic resis-tance 119862dlA anode double-layer capacitance 119877

119891C cathodeFaradaic resistance 119862dlC cathode double-layer capacitance120596 radial frequency and 119885

119882 Warburg impedance element

Two semicircles are shown in the Nyquist plot The first loopcorresponds to the anode activation kinetics and the second


Table 1 Geometric information on current collectors

Factors GeometrySRCC HFCC1 HFCC2 HFCC3

Total length of the Hilbert curve path (mm) None 13125 27562 55781Width of the Hilbert curve path (mm) None 220 220 110Total perimeter opening length (mm) 61412 26690 55565 111782Total free open area (mm2) 61250 28875 60637 61359Total active MEA area (mm) 1225 1225 1225 1225Free open ratio () 5000 2350 4940 5000

Figure 2 Single cell DMFC assembly

loop corresponds to the cathode activation kinetics At highfrequencies the real-axis intercept corresponds to the ohmicresistance The diameter of the first loop gives 119877

119891A and thediameter of the second loop gives119877

119891C At low frequencies thediagonal line is due to mass transport which is enabled by theinfinite Warburg impedance The impedance response char-acterization depends on the operating voltageThe activationkinetics dominate and the Faradaic resistance (119877

119891) is large

for high voltages The activation loops decrease due to thedecreasing value of 119877

119891at the intermediate operating voltage

range The activation loops would continue to decrease butthe diagonal Warburg response might occur at low frequen-cies because of the mass transport effect in the low operatingvoltage range [10] This paper only discusses the character-ization at high and intermediate operating voltage rangesThe low operating voltage range is not covered because aDMFC should generally operate above the concentrationpolarization range

4 Results and Discussion

In all of these experiments the environmental conditionswerekept at room temperature and humidity (sim60 RH) Theanode was supplied with a 55∘C and 2MMeOHDI water-methanol solution In our previous study the results indicatedthat the performances are close under different DMFC anodeflow rates with standard circular hole current collectorsTherefore this study maintained the anode flow rate at 15ccminminus1 and cathode airflow rate of 1000ccminminus1 throughoutthe study [16]

Figure 5 shows a comparison of the polarization curvesfor the DMFC at a 15ccminminus1 anode flow rate The DMFCwith HFCC3 showed the best cell performance the DMFCwith HFCC2 showed the second best performance theDMFC with SRCC showed the third best cell performanceand the HFCC1 had the worst cell performance

Figure 6 is a comparison of the Nyquist plots obtainedusing the EIS measurements at 05 V for the DMFCs withdifferent current collectors The DMFC with HFCC1 showedthe largest cell impedance response which leads to the worstcell performance The DMFC with SRCC showed the secondlargest cell impedance response The DMFC with HFCC2showed the third largest cell impedance response and theDMFC with HFCC3 showed the lowest impedance response

Figure 7 shows a comparison of the Nyquist plotsobtained by the EIS measurements at 04V for the DMFCswith different current collectors The DMFC with HFCC1showed a significantly larger impedance response than theothers which leads to the worst cell performanceTheDMFCwith SRCC showed the second largest impedance responsebut it was still much lower than the DMFC with HFCC1The DMFC with HFCC2 showed the third largest impedanceresponse and the DMFC with HFCC3 showed the lowestimpedance response

The DMFC current collectors with a low free open ratioand short total perimeter opening length such as HFCC1showed significant large cell impedance thus resulting in theworst cell performanceWhen a high free open ratio and longtotal perimeter opening length were used the significant cellimpedance dropped at 04V (ie the ohmic impedance wasobviously reduced) and the cell impedance showed a drop at05 V (ie the activation impedance was reduced but not asmuch as the change at 04V)

The experimental results do not show the long tails upas in Figure 5 for the EIS measurements in Figures 6 and 7At the low AC frequency range if the electrode receives anapplied voltage the reaction time becomes longer and thereactants at the electrode surfaces react completely leadingto insufficient fuel The mass polarization effect might thenbecome significantly prominent causing the long tails up asshown in Figure 5 However this phenomenon did not occurin the experiments such that there were no long tails up inFigures 5 and 7

The total free open ratio is almost the same for the DMFCcurrent collectors with HFCC2 HFCC3 and SRCC TheHFCC3 has a significantly longer total perimeter opening


Ano

de

Cath

ode

Fuel cell

Liquid pump

Methanol solution tank

Temperature controlled water

bath

Air pump

Air in

Airflow regulator

Air outMethanol vent

Electrochemical impedance

spectroscopyPC

Figure 3 Experimental setup

RΩ

RΩ

minusZ998400998400

minusZ998400

Decreasing 120596

ZW

ZW

CdlA CdlC

RfA

RfA

RfC

RfC

Figure 4 Schematic drawing of Nyquist plot and circuit diagramfor a simple fuel cell impedance model

length The HFCC2 and SRCC have the close total perimeterlength of opening but the SRCC is slightly longer thanHFCC2 Through a comparison of the DMFC HFCC2 andSRCC we found that the HFCC2 showed slightly lower cellimpedance than the SRCC at 05 V that is the activationimpedance was slightly lower In addition the HFCC2 hadlower cell impedance than the SRCCat 04V that is the ohm-ic impedance was obviously lowerTherefore at the close freeopen ratio and total perimeter opening length the DMFCwith continuous openings reduced the ohmic impedancewith slightly smaller activation impedance than the unit withthe separate openings Thus the DMFC with the continuousopening performed better Under the same free open ratiothe current collector with HFCC3 has a much longer totalperimeter opening length Through a com-parison of the

0510152025303540

00

02

04

06

08

10

0 20 40 60 80 100 120 140 160

Volta

ge (V

)

Current density (mAcm2)

Pow

er d

ensit

y (m

Wc

m2)

SRCC (I V curve)

HFCC1 (I V curve)

HFCC2 (I V curve)

HFCC3 (I V curve)SRCC (I P curve)

HFCC1 (I P curve)

HFCC2 (I P curve)

HFCC3 (I P curve)

Figure 5 Performance comparison of the DMFC with differentcurrent collectors

DMFC with the HFCC3 and HFCC2 the HFCC3 had lowercell impedance values at both 05 V and 04V Thereforecontinuously increasing the total perimeter opening lengthwould reduce both the activation and ohmic impedance andresult in better cell performance

According to the experimental results the DMFC withHFCC1 shows the lowest cell performance and highestimpedance The HFCC1 geometrical design has the smallesttotal free opening ratio and the shortest total perimeteropening length At the 05 V and 04DC load there is largerelectric charge resistance during the DMFC electrochemicalreaction process thus increasing the internal resistanceTherefore the DMFC shows lower cell performance andhigher resistance The total free opening ratio of HFCC3HFCC2 and SRCC is designed about 50 the HFCC3 has


000

005

010

015

020

000 010 020 030 040 050minus010

minus005

SRCC 05VHFCC1 05V

HFCC2 05VHFCC3 05V

Zre (Ohms)

Zim

(Ohm

s)

Figure 6 Comparison of the Nyquist plots at 05 V for the DMFCwith different current collectors

the longest total perimeter opening length SRCC has thesecond longest andHFCC2 has the shortestThe polarizationmeasurements show that the DMFCwith the HFCC3 currentcollectors has the highest cell performance with the HFCC1having the second and with the SRCC having the lowestThe EIS experiments show that the DMFC with the HFCC3current collectors has the lowest impedance with HFCC2the second and with SRCC the highest The main reason theDMFC with HFCC2 currents has higher cell performanceand lower impedance is because the HFCC2 is a continuoustype of geometry which could help supply the fuel anddrain the production more smoothly In addition the freeopening distribution for theHFCC2 couldmake the reactantsat both the anode and cathode more uniformly distributedinto the diffusion layers allowing the reactants to drain outmore smoothly As the HFCC2 geometry is more uniformlyand systematically divided it provides longer total currentcollector perimeter opening length than SRCC under thesame reaction area The electric charge distribution is thendistributedmore uniformly and the inner resistance reducedAs the HFCC3 has the longest total perimeter opening lengthunder the approximately same total free opening ratio theDMFC with HFCC3 current collectors shows the highest cellperformance and lowest cell resistance

5 Conclusions

This paper investigated a DMFC design with Hilbert curvefractal openings The DMFC with HFCC1 which had thesmallest free area ratio and the shortest total perimeteropening length had the worst cell performance and thelargest impedance at both 04V and 05 V Increasing boththe free area ratio and total perimeter opening length couldsignificantly reduce the impedance at 04V that is ohmicimpedance and also reduce the impedance at 05 V (acti-vation impedance) although this effect is expected to besmaller than at 04 V Under the same free open ratio andtotal perimeter opening length the DMFC with continuousopenings could help to reduce the ohmic impedance with

000

002

004

006

008

010

000 010 020 030 040minus004

minus002

SRCC 04VHFCC1 04V

HFCC2 04VHFCC3 04V

Zre (Ohms)

Zim

(Ohm

s)


slightly less activation impedance A further increase inthe total perimeter opening length such as in the caseof the DMFC with HFCC3 (which contains the longesttotal perimeter opening length and free open ratio) couldcontinuously reduce the activation and ohmic impedancesleading to better cell performance

Conflict of Interests

The authors declare no conflict of interests

Acknowledgment

The authors would like to acknowledge financial supportfrom the National Science Council of Taiwan (NSC-2221-E-167-030 and NSC 101-2628-E-167-001-MY3)

References

[1] R OrsquoHayre S W Cha W Colella and F B Prinz Fuel CellFundamentals John Wiley amp Sons Hoboken NJ USA 2006

[2] J Larminie and A Dicks Fuel Cell Systems Explained JohnWiley amp Sons Chichester UK 2nd edition 2003

[3] G Apanel and E Johnson ldquoDirectmethanol fuel cellsmdashready togo commercialrdquo Fuel Cells Bulletin vol 2004 no 11 pp 12ndash172004

[4] JH Hirschenhofer DB Stauffer RR Engleman and MGKlett Fuel Cell Handbook EampG Services Parson Inc ScienceApplications International Corporation Morgantown WVaUSA 5th edition 2000

[5] T Schultz S Zhou and K Sundmacher ldquoCurrent status of andrecent developments in the direct methanol fuel cellrdquo ChemicalEngineering amp Technology vol 24 no 12 pp 1223ndash1233 2001

[6] H Tsuchiya and O Kobayashi ldquoMass production cost of PEMfuel cell by learning curverdquo International Journal of HydrogenEnergy vol 29 no 10 pp 985ndash990 2004


[7] A Hermann T Chaudhuri and P Spagnol ldquoBipolar plates forPEM fuel cells a reviewrdquo International Journal of HydrogenEnergy vol 30 no 12 pp 1297ndash1302 2005

[8] F BarbirPEMFuel Cells Elsevier BurlingtonMass USA 2005[9] B B Mandelbrot The Fractal Geometry of Nature W F

Freeman San Francisco Calif USA 1982[10] D J Lee and W W Lin ldquoSecond law analysis on fractal-like fin

under crossflowrdquo AIChE Journal vol 41 no 10 pp 2314ndash23171995

[11] G Ledezma A Bejan and M Errera ldquoContractual tree net-works for heat transferrdquo Journal of Applied Physics vol 82 pp89ndash100 1997

[12] S Lee Y Wang and C Chen ldquoThermal performance ofnovel fractal heat sink finsrdquo Journal of the Chinese Society ofMechanical Engineers vol 25 pp 547ndash556 2004

[13] C A Chen Y Juang and W Lin ldquoGeneration of fractaltoolpaths for irregular shapes of surface finishing areasrdquo Journalof Materials Processing Technology vol 127 no 2 pp 146ndash1502002

[14] K Tuber A Oedegaard M Hermann and C Hebling ldquoInves-tigation of fractal flow-fields in portable proton exchangemembrane and direct methanol fuel cellsrdquo Journal of PowerSources vol 131 no 1-2 pp 175ndash181 2004

[15] J Chang Y Kuan S Lee and S Lee ldquoCharacterization of aliquid feed direct methanol fuel cell with Sierpinski carpetsfractal current collectorsrdquo Journal of Power Sources vol 184 no1 pp 180ndash190 2008

[16] Y Kuan J Chang S Lee and S Lee ldquoCharacterization of adirect methanol fuel cell using Hilbert curve fractal currentcollectorsrdquo Journal of Power Sources vol 187 no 1 pp 112ndash1222009

[17] R Crownover Introduction to Fractals and Chaos Jones andBartlett Publishers Boston Mass USA 1995

[18] H Peitgen H Jurgens and D Saupe Chaos and Fractals NewFrontiers of Science Springer New York NY USA 1992

[19] R C Makkus A Janssen F A de Bruijn and R MallantldquoStainless steel for cost-competitive bipolar plates in PEMFCsrdquoFuel Cells Bulletin vol 3 no 17 pp 5ndash9 2000

[20] J Wind R Spah W Kaiser and G Bohm ldquoMetallic bipolarplates for PEM fuel cellsrdquo Journal of Power Sources vol 105 no2 pp 256ndash260 2002

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Analytical ChemistryInternational Journal of


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Organic Chemistry International

ElectrochemistryInternational Journal of



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and low density characteristics such that the fuel cell willexhibit high performance and maintain stable operations[5ndash7]

A DMFC is conventionally stacked in the vertical direc-tion with each bipolar plate serving as the anode in onecell and cathode in the next cell (resulting in multiple cellsconnected in series) The flow channels inside the bipolarplates are grooved to distribute fuel and collect the electricalcharge PEMFCDMFC planar interconnection designs haverecently been presented in which the architecture alternatesbetween vertical stacking and planar connection in seriesThis configuration produces better volumetric packagingthan the vertical stack thus giving better design flexibilityfor portable applications [8] In planar type DMFCs suchas the planar printed-circuit-board fuel cell module there isno bipolar plate in the structure Instead of bipolar platesthis fuel cell has separate current collector componentswith openings to collect electrons as well as flow boards todistribute fuel among the cells

Fuel cell performance can be represented by a polariza-tion curve that is the cell potential versus current densitycurve which reflects the fuel cell activation loss in the lowcurrent density range the ohmic losses in the intermediatecurrent density range and the concentration loss in thehigh current density range The fuel cell polarization curveis determined by measuring the open circuit potential andmaking the voltage or current measurements at prescribedpotential or current intervals [8]

Fractal geometry ismathematically defined in ldquoHausdorffdimensionsrdquo a set of nonintegers according to the theoryproposed byMandelbrot [9] Fractal theory describes certainphenomena that are difficult to describe in terms of very finevariations using convectional methods The main character-istics of a fractal pattern are self-similarity subdivisibilityand a recursive nature Fractal patterns have been applied inmany engineering fields such as describing the variations inentropy and heat transfer [10] electronic cooling applications[11] heat sink fins (by Lee et al [12]) and the automaticpolishing path [13]

The first application of fractal theory to the fuel cell waspresented by Tuber et al [14] who applied the ldquoFracThermrdquotheory in PEMDMFC flow designs for bipolar plates Theirfractal flow boards were designed as biological fluid channelswith a multibranched structure with smooth flow pathsBased on a performance comparison of the fractal serpen-tine and parallel flow fields the cell with a serpentine flowchannel yields better cell performance but has a much greaterpressure drop across the channel Both themultiple-branchedfractal and parallel flow fields create a lower pressure dropwith similar performance Chang et al [15] proposed a typeof current collector with a Siepinski carpet fractal geometryTheir current collector design included first and secondSiepinski carpet fractal hole arrangements and was comparedagainst the standard hole arrangement The results showedthat the open ratio and perimeter length of the holes are twoimportant factors that affect the performance A longer totalhole perimeter resulted in better cell performance while ashorter total perimeter length and free open hole ratio led

to poor cell performance Therefore a longer total perimeterlength under the same free open ratio is recommended LaterKuan et al [16] presented a DMFC with Hilbert curve fractalcurrent collectors They concluded that current collectorswith a more uniform opening distribution and higher totalopening perimeter length could reduce the anode flow rateeffect A higher total free open ratio and total openingperimeter length in the current collectors could increase thecell performance In the previous paper only polarizationcurvesweremeasured to discuss the cell performancewith nofurther quantitative analysis to explore the impedance behav-ior caused by the electric charge migration under electro-chemical reactions The current collectors in this work weredesigned using the Hilbert curve one of the continuous typefractal geometries Experiments to measure the polarizationcurves and Nyquist plots using electrochemical impedancespectroscopy (EIS) were also carried out as part of thisstudy

2 Current Collectors with a HilbertCurve Geometry

The Hilbert curve fractal is a continuous space-filling curvethat fills a square and is typically defined as the limit of asequence of iteratively defined curves that have only shortvertical and horizontal jumps between the points in a squaregridwith a size of 2times2 4times4 8times8 16times16 or any other power of2The curves donot have self-intersections or touching pointsat any stage [17 18]

A DMFC with first second and third Hilbert curvecurrent collectors and a standard circular hole arrangement isstudied To simplify the experiments and ensure cell stabilitya DMFC with stainless steel 316L (SS316L) current collectorswas used because SS316L has the advantage of being easy tomachine and lower cost and demonstrates good mechanicalproperties [19 20]TheMEA reactive area is 35mm times 35mmand the size of each current collector is 95mm times 95mm times2mm

Figure 1 shows a Hilbert curve fractal current collectorThe geometric information on the current collectors is shownin Table 1 The widths of the HFCC1 HFCC2 and HFCC3Hilbert curves were 22mm 22mm and 11mm respec-tively The total perimeter lengths of the current collectorwith SRCC HFCC1 HFCC2 and HFCC3 openings were61412mm 26690mm 55565mm and 111782mm respec-tively The total free open areas in the current collectorswith the SRCC HFCC1 HFCC2 and HFCC3 openingswere 6125mm2 28875mm2 60637mm2 and 61359mm2respectively The free open ratios in the current collectorwith the SRCC HFCC1 HFCC2 and HFCC3 openings were5000 2350 4940 and 5000 respectively Howeverfurther increasing the free open ratio that is making higherHilbert fractal current order the carved paths of the currentcollectors become extremely narrow making the machiningdifficult This paper therefore does not discuss fourth orhigher fractal order current collectors


655 220

220

220

9500

9500

11000

Unit (mm)

(a) HFCC1

9500

9500

11000

220

220

220

220

218

Unit (mm)

(b) HFCC2

9500

9500

11000

110

110

110

110

110

109

Unit (mm)

(c) HFCC3

9500

9500

11000

088

088

R199

Unit (mm)

(d) SRCC


















119891) is large













Ano

de

Cath

ode

Fuel cell

Liquid pump



bath

Air pump

Air in

Airflow regulator



spectroscopyPC


RΩ

RΩ

minusZ998400998400

minusZ998400

Decreasing 120596

ZW

ZW

CdlA CdlC

RfA

RfA

RfC

RfC



0510152025303540

00

02

04

06

08

10

0 20 40 60 80 100 120 140 160

Volta

ge (V

)


Pow

er d

ensit

y (m

Wc

m2)

SRCC (I V curve)

HFCC1 (I V curve)

HFCC2 (I V curve)


HFCC1 (I P curve)

HFCC2 (I P curve)

HFCC3 (I P curve)





000

005

010

015

020

000 010 020 030 040 050minus010

minus005

SRCC 05VHFCC1 05V

HFCC2 05VHFCC3 05V

Zre (Ohms)

Zim

(Ohm

s)



5 Conclusions


000

002

004

006

008

010

000 010 020 030 040minus004

minus002

SRCC 04VHFCC1 04V

HFCC2 04VHFCC3 04V

Zre (Ohms)

Zim

(Ohm

s)





Acknowledgment


References































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


655 220

220

220

9500

9500

11000

Unit (mm)

(a) HFCC1

9500

9500

11000

220

220

220

220

218

Unit (mm)

(b) HFCC2

9500

9500

11000

110

110

110

110

110

109

Unit (mm)

(c) HFCC3

9500

9500

11000

088

088

R199

Unit (mm)

(d) SRCC


















119891) is large













Ano

de

Cath

ode

Fuel cell

Liquid pump



bath

Air pump

Air in

Airflow regulator



spectroscopyPC


RΩ

RΩ

minusZ998400998400

minusZ998400

Decreasing 120596

ZW

ZW

CdlA CdlC

RfA

RfA

RfC

RfC



0510152025303540

00

02

04

06

08

10

0 20 40 60 80 100 120 140 160

Volta

ge (V

)


Pow

er d

ensit

y (m

Wc

m2)

SRCC (I V curve)

HFCC1 (I V curve)

HFCC2 (I V curve)


HFCC1 (I P curve)

HFCC2 (I P curve)

HFCC3 (I P curve)





000

005

010

015

020

000 010 020 030 040 050minus010

minus005

SRCC 05VHFCC1 05V

HFCC2 05VHFCC3 05V

Zre (Ohms)

Zim

(Ohm

s)



5 Conclusions


000

002

004

006

008

010

000 010 020 030 040minus004

minus002

SRCC 04VHFCC1 04V

HFCC2 04VHFCC3 04V

Zre (Ohms)

Zim

(Ohm

s)





Acknowledgment


References































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of









119891) is large













Ano

de

Cath

ode

Fuel cell

Liquid pump



bath

Air pump

Air in

Airflow regulator



spectroscopyPC


RΩ

RΩ

minusZ998400998400

minusZ998400

Decreasing 120596

ZW

ZW

CdlA CdlC

RfA

RfA

RfC

RfC



0510152025303540

00

02

04

06

08

10

0 20 40 60 80 100 120 140 160

Volta

ge (V

)


Pow

er d

ensit

y (m

Wc

m2)

SRCC (I V curve)

HFCC1 (I V curve)

HFCC2 (I V curve)


HFCC1 (I P curve)

HFCC2 (I P curve)

HFCC3 (I P curve)





000

005

010

015

020

000 010 020 030 040 050minus010

minus005

SRCC 05VHFCC1 05V

HFCC2 05VHFCC3 05V

Zre (Ohms)

Zim

(Ohm

s)



5 Conclusions


000

002

004

006

008

010

000 010 020 030 040minus004

minus002

SRCC 04VHFCC1 04V

HFCC2 04VHFCC3 04V

Zre (Ohms)

Zim

(Ohm

s)





Acknowledgment


References































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


Ano

de

Cath

ode

Fuel cell

Liquid pump



bath

Air pump

Air in

Airflow regulator



spectroscopyPC


RΩ

RΩ

minusZ998400998400

minusZ998400

Decreasing 120596

ZW

ZW

CdlA CdlC

RfA

RfA

RfC

RfC



0510152025303540

00

02

04

06

08

10

0 20 40 60 80 100 120 140 160

Volta

ge (V

)


Pow

er d

ensit

y (m

Wc

m2)

SRCC (I V curve)

HFCC1 (I V curve)

HFCC2 (I V curve)


HFCC1 (I P curve)

HFCC2 (I P curve)

HFCC3 (I P curve)





000

005

010

015

020

000 010 020 030 040 050minus010

minus005

SRCC 05VHFCC1 05V

HFCC2 05VHFCC3 05V

Zre (Ohms)

Zim

(Ohm

s)



5 Conclusions


000

002

004

006

008

010

000 010 020 030 040minus004

minus002

SRCC 04VHFCC1 04V

HFCC2 04VHFCC3 04V

Zre (Ohms)

Zim

(Ohm

s)





Acknowledgment


References































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


000

005

010

015

020

000 010 020 030 040 050minus010

minus005

SRCC 05VHFCC1 05V

HFCC2 05VHFCC3 05V

Zre (Ohms)

Zim

(Ohm

s)



5 Conclusions


000

002

004

006

008

010

000 010 020 030 040minus004

minus002

SRCC 04VHFCC1 04V

HFCC2 04VHFCC3 04V

Zre (Ohms)

Zim

(Ohm

s)





Acknowledgment


References































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of










Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

Documents

Research Article Experimental Investigation of a Direct ...downloads.hindawi.com/journals/jchem/2014/371616.pdf · Research Article Experimental Investigation of a Direct Methanol