Fractal Analysis of Gas Diffusion Layer in PEM Fuel Cells

Vol 21 No IJoumal of Wuhan University of Technology-Mater. Sci.EdMarch 2006fractal Analysis of Gas Diffusion Layer in PEM Fuel CellsSHI Ying" XIAO Jinsheng PAN Mu YUAN Runzhang(1. State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, wuhan University of TechnologyWuhan 430070, China; 2. School of Automation, Wuhan University of Technology, Wuhan 430070,China3. School of Automotive Engineering, Wuhan University of Technology, Wuhan 430070, ChiAbstract: The aim of this study is to show how fractal analysis can be effectiely used to characterize thetexture of porous solids. The materials under study were carbon papers, the backing material of the gas diffulayer( GDL) in Proton Exchange Membrane Fuel Cell( PEMFC). The fractal dimensions were calculatedanalyzing data from mercury porosimetry. The polytetrafluoroethylene( PTFE)treated carbon paper shous a sig-nificantly high fractal dimension ualue than pure sample, and the high fractal dimension signifies that the physicalcomplexity of the pore surface is enhanced, The fractal dimension can be used as a walid parameter to monitor theextural evolution of the samples as the treatment progresses, as this behaves in a similar way to other textural parameters. The use of fractal analysis in conjunction with the results of classical characterization methods leads to abetter understanding of textural modifications in the processing of materialsKey words: PEMFC; gas diffusion layer; fractal dimension mercury porosimetry1 Introductioninformation that may be added to the results of traditionaldeterminations. The aim of the present study is threefoldFirst, it will show that the gDl has a fractal characterisThe gas diffuse layer(GDL) is one of the most im- tic. Second, fractal techniques can enhance the underportant components in PEM fuel cells( PEMFC).TheGDL can make reactant gases be dispersed uniformly onstanding of textural modifications undergone by carbonelectrode surface, and provide electron channels and per as a consequence of PtFe treatment. Third, the fracdrain channels. Meanwhile, the GDL supports the cata- tal dimension is a useful parameter to monitor the texturalevolution during the PTFE treatmentFor these reasons, the structure and material parameters 2 Pore Distribution Measurement ofof the GDl influence the overall performance of the PEM-GDLFC significantly. In order to obtain a suitable end product, the textural properties of carbon paper, backing ma-terial of the GDL, are very important, and it is desirable 2.1 Preparation of the GDL sampleto know as much as possible about their textural featuresSince carbon papers have a homogeneous porous laThe surface area, porosity and pore size distribution are, mella structure, as well as excellent conductance, chemiamong others, useful parameters in achieving this goal, cal stability, and thermal stability as graphite, they areand are traditionally used to characterize the texture of po- widely used as GDl material in the PEMFC electroderous solids. In recent years, a new approach to the study For the same reasons, carbon papers are also used asof porous structures and surfaces, fractal analysis, is in- backing materials of the GDL in our present research.Thecreasingly used. This method has its origin in fractal theo- carbon papers that are most widely used in China are fromry, which was formally introduced in the mid-1970sJapanese TORAY Inc, German SGL technique IncThe fractal approach relies on the concept of self-similari- Canadian Ballard Inc. or E-Tek Inc. The TGP-H-060ty and is an altemative way to characterize complex georcarbon papers used in our experiments are from Japaneseetries such as the surface area or pore structure of mate- TORAY Inc. The thickness of the carbon papers is 0. 19rials(2-53. The fractal analysis of data collected from mer- mm. PTFE emulsion( Du Pont )was diluted to makeury porosimetric analysis furmishes us with extra textural aqueous solutions. The carbon papers were dipped entirely in the PTFE solutions and dried at room temperatureReceived: March 24, 2004; Accepted June 23, 2005)After then, the samples were heat-treated in air. The ac-SHI Ying(11): Lecturer: PhD Candidate: E-mail: a- laly@ tive carbon powder(Vulcan XC72)was mixed with PTFE* Corresponding Author: XIAO Jinsheng(肖金生):PhD;Pof.;Eemulsion in the solvent of water and ethanol then soni.mail, whut. edu. en中国煤化工 e was obtained.TheFunded byundation of Hubeixture. This coating2003ABA088)and the Special Scientific Research Foundation for laverCNMHGCollege Doctor Subjects from Ministry of Education of China(N20030497012)2.2 Testing methodVol 21 No. 1SHI Ying et al: Fractal Analysis of Gas Diffusion Layer in PEM Fuel CellsThe USA Quantachrome PoreMaster 33, which can try)is an important and widely used technique for thedistinguish the size to 7 nm, was used to measure the pore analysis of the pore structure of a variety of porous materi-size. In order to compare the change of pore size and pore als. It is based on the gradual intrusion of mercury into ardistribution between the pure carbon paper and the carbon evacuated pore system as an extemal pressure is applied;paper treated by PTFE, we chose the TGP-H-060 carbon increasing pressure makes smaller pores accessible to merpaper and the carbon paper with PTFE, respectively. Af- cury. The amount of mercury uptake is a function of prester fully dried for 2 h at 120 C, the samples weight was sure so that one can estimate the pore size distribution31.7954 g and 33. 7781 g, respectively, including the The amount of mercury uptake( calculate with mercurytest tube. And their pore sizes vary from 0. 2 um to 30 saturation)us pressure of carbon fiber paper is shown inFig 1, and the relationship of pore size us pore volume2. 3 Testing resultpercent is shown in Fig. 2Mercury intrusion porosimetry (or mercury porosime-020.1言004已003202530Pressure/MPaFig1 Relation between the amount of mercury uptake and the pressure drop datr ated with PTFE(a)Sample: TGP-H-060 carbon paperb)Sample 2: TGP-H-060 carbon paper tiPore diameter/um(a)Sample 1: TGP-H-060 carbon paper(b)Sample 2: TGP-H-060 carbon paper treated with PTFEFig2 Relation between the pore size and the pore volume percentFig2 shows that the pore sizes of sample I mainlyrange from I um to 3 um, and those of sample 2 varyN(L≥λ=)=around I um. After PTFE treatment, the pore sizes ofThe first derivative of Eq (1)with respect to a canTGP-H-060 carbon paper decreasebe written as3 Fractal Characteristic Analysis for-dN= Da%a a-(D2+1)the GDLThe pore number between sizes ofλand+dλisgiven by Eq (3),-dN >0. Eq (3)is divided by Eq(2),and thusThe relationship between the cumulative number NdN(for example, the number of pore)of the fractal objectN(L≥m)=DAax9d=f()dand pore size distribution has a fractal characteristic and(4)can be written ashere(a)= da%-"*is the probability densityN(L≥A)=(1) function of pore size distribution, which should satisfy thewhere A and Amax are the pore size and the maximum poresize, respectively, as far as porous media are concemed中国煤化工)dx=1(5)D, is the fractal dimension. Eq. (1)shows the relationship between the number N of pores that pore size greaterCNMHGcates that the tenablethan a andλcondition of Eq (5)must bFrom Eg. (1), the total pore number can bebe esti(6)mated byJoumal of Wuhan University of Technology-Mater.SciEdMarch 2006Eq (6)can be used as a preliminary judgment ifistence,so porous media can not be analyzed by fractal mension D is shown as follows +=dve p dporous media can be analyzed by fractal theory. If eq(6)does not work, then Eq (5)does not come into exThe dependence of pore volume Vp(r)on fractal ditheory. In fact, as long as Amin /A ma 10-, Eq. (6)apdv2.0proximately works, porous media can be studied using(9)fractal theory and methodEq (7)and Eq (8)are taken into Eg (sData obtained from Mercury- intrusion porosimetry indicate that for sample 1, amin/A max =0. 04897/7. 4120.0607<10; and for sample2,λm/A-=0.01487/dP(10)7.139≈0.002083<10The fractal dimension is obtained by taking logarithmprmarily judge that the pore of Eq (10)structure of the GDL can be studied by fractal theoryNext, we will compute the fractal dimension of pore sur-p)=(D-4)hP+C(1)face and use fractal techniques to see the textural modifiHence, D values can be derived from the slope of Incations of carbon paper after PTFE treatmentdv/dP versus InP plots. Smooth surfaces(D=2)wouldpresent slopes close to-2, whereas rougher surfaces(for4 Calculation of Fractal Dimensionwhich D approaches 3)would present slopes approachingcal mercury porosimetry curves re-The pore volume V, of carbon paper and other po- veals that constant slopes in the appropriate range are of.rous media can be obtained by mercury porosimetry. The ten encountered at pressure regions which coincide withoperation of all mercury porosimeter is based upon thethe filling or emptying of pores of distinct sizewill al principle that a nonreactive, non-wetting liquid each step of a cumulative intrusion or extrusion volumeot penetrate into fine pores until sufficient pressure versus pressure plot can yield a unique D value that chanis applied to force its entry. The relationship between the acterizes the particular range and type of pores being filledapplied pressure P(r)and diameter r of the cylinderical or emptied in given pressure ranges. Once pores of a dis-pore into which mercury will intrude is given by the tinct size become filled or emptied, the mercury volumeceases to change significantly and d/dP decreasesP(7) thereby complicating fractal calculations in the transitionwhere o is the surface tension of ,mercury, 0.48N.m": regions between pore ranges of materials with multimodal0 is the contact angle of mercury and the pore wall, usu- pore size distributionsally taken asThe data obtained from mercury porosimetry of twoOn trial, the amount of mercury uptake ve at the carbon papers are processed by Eq (11), the results areapplied pressure is the cumulative pore volume corre-shown in Fig 3 and Fig 4, respectivelyponding to the pore radius size bigger than r. We obtainFig 3 Fractal dimension analyses of theFig 4 Fractal dimension analyses of the TGP-H-060TGP-H-060 carbon papercarbon-fiber paper treated with PTFEwith PTFE, the fractal dimension D is 2. 9595. the cor-5 Results and Discussionrelation coefficient is 0.9925, F=600. 47> Foor(1, 9)10. 56, the regressive characteristic is also veryLinear regression is taken after processing thestronaimental data, the results are shown as followsa)The fractal dimension D of the TGP-H-060 car中国煤化工ig4tat, in doubleP have a very goodbon-fiber paper is 2. 3382, the correlation coefficient is lineaCNMHGion character is very0.9836, and F=149.36>Foor(1, 5)=16.26, the obvious. It means that pore structures and surfaces of twogressive characteristic is very strongporosity media have a fractal characteristicb)For the TGP-H-060 carbon-fiber paper treatedIn the three-dimension space, values of the fractalVol 21 No ISHI Ying et al: Fractal Analysis of Gas Diffusion Layer in PEM Fuel Cellsdimension d should belong to the interval[ 2, 3 ]. The re- ty of the pore surface, at the range of sizes reached bysults above, 2. 3382 and 2. 9595, are reasonable. Areas mercury, is enhanced. Observation of two samples showsexposed by perfectly flat surfaces can be calculated as a the same difference between treated and untreated sam-function of a characteristic dimension, eg 4R" for a ples. The fractal dimension of pore system can be used asnonporous sphere with a radius R. Any surface roughness a descriptor of the GDL pore surface and structure. Thisor porosity will increase the spheres surface area up to parameter, D, is not intended to replace the use of pn extreme point in which the sphere would be so porous size distribution, a very useful tool to describe GDl porethat its entire volume could be occupied by pore walls. At system; however, in some cases, the fractal dimensionthis hypothetical point, the surface area would be propor- allows a more evident differentiation between treated andtional to the volume of the sphere, i e 4/3R. Areas ex- untreated carbon papers and providing a very valuable exposed by real solids, following fractal arguments, are pro- tra informationportional to R, with their fractal dimension D ranging be-tween 2 for flat surfaces and about 3 for extremely rough ReferencessurfacesThe fractal dimension D of a solid is a parameter [1] Mandelbrot B B. The Fractal Geometry of Nature. San Franthat characterizes the degree of roughness of its surface orcisco: Freeman. 1982complexity of porous structure. The increase[2 YANG Zhiyuan, ZHOU Anning. Fractal Characteristics and Frac-fractal dimension with PtFE treatment is the general trendtal Dimension Measurement on Boken Surfaces of AlminumElectric Porcelain. Journal of Wuhan University of Technologyobserved. The practical consequence is that PTFE treatMater. Sci. Ed, 205, 20(1): 37-41ment tends to make rougher the surface measured by mer-[3]LIUing, BIcury porosimetry. An increase in the fractal dimensionof Hamiltonian for a Quantum Fractal Network. Journal ofsignifies that the physical complexity of the surface, inWuhan University of Technology- Mater. Sci. Ed, 2000, 15the range of sizes reached by mercury, is enhanced. This(3):3340offers the possibility of seeing how the treatment modifies [4 Thompson A H, Katz A J, Krohn C E. The Microgeometry andtexture of the materials. The evolution of the fractalransport Properties of Sandstones. Aduances in Physicsdimensions of different pore1987,36(5):625-694progresses can help to better understand the phend[5] Tyler S W, Wheatcraft S W. Fractal Process in Soil Water Retention. Water Resoure Res., 1990, 26: 1047-1054underlying textural modifications[6 Feder J Fractals. New York: Plenum Press, 1988[7] Sahimi M. Flow and Transport in Porous Media and Fractured6 ConclusionsRocks. Germany: VCH Verlagsgesellshaft mbH, 1995[8 Yu BM, Li J H. Some Fractal Characters of Porous MediaIn this work, it has been demonstrated that the poreFcas,2001,9(3):365-372system of the GDL material, carbon paper, is fractal. TH[9 Lowell S, Shields J E. Ponder Suface Area and Porosity, 3rdfractal dimension can be calculated by analyzing data fromed. Chapman and Hall, New York, 1991[ 10] Wei Chengfumercury porosimetry. The PTFE treated carbon paperMaterials Science& Engineering, 1995, 13(3): 35-40(in Chinese)shows a significantly high D value than pure sample. Thehigh fractal dimension signifies that the physical complexi中国煤化工CNMHG