Analysis of the Key Parameters in the Cold Start of Polymer Electrolyte Fuel Cells

Transcription

1 Analysis of the Key Parameters in the Cold Start of Polymer Eletrolyte Fuel Cells Yun Wang*,z Journal of The Eletrohemial Soiety, B1041-B /2007/15410/B1041/8/$20.00 The Eletrohemial Soiety Renewable Energy Resoures Lab and National Fuel Cell Researh Center, Department of Mehanial and Aerospae Engineering, The University of California, Irvine, Irvine, California 92612, USA B1041 This paper investigates the heat/mass transfer and eletrohemial kinetis in the athode atalyst layer of polymer eletrolyte fuel ells PEFCs during old start below the freezing temperature. A number of key parameters that govern the old-start operations, suh as time onstants and the Damköhler number, are defined and their impats are explored. A lumped parameter model for ell temperature and ie formation is developed and one-dimensional analysis is performed on the reatant transport in the atalyst layer. We found that a dimensionless parameter, defined as ratio of the time onstant of ell warmup to that of ie-volume growth, is important for self-startup of fuel ells in subzero onditions, and a high value of tortuosity has profound impat on reatant starvation during old start. In addition, the redution in the eletrohemial ative surfae of the atalyst layer due to the ie overage is found to be a major mehanism leading to ell voltage loss during old start The Eletrohemial Soiety. DI: / All rights reserved. Manusript submitted April 6, 2007; revised manusript reeived June 4, Available eletronially August 16, * Eletrohemial Soiety Ative Member. z yunw@ui.edu Cold-start subzero startup apability of polymer eletrolyte fuel ells PEFCs is of paramount importane for PEFC automobile appliations. During startup in subzero environments, produed water in the eletrodes may freeze instantaneously at the reation sites, overing and hene reduing the eletrohemial ative surfae as well as plugging the open pores of reatant passage. To ensure a suessful startup below the freezing point, the fuel ell needs to be heated, by either external heat soure or self-heating, to at least 0 C before the solid water in the atalyst layer auses severe reatant starvation and onsiderable reative area redution and a onsequent substantial voltage loss. In automobile appliations, suh a startup must be short less than minutes in order to ompete with the traditional internal ombustion engines. Though muh researh has been arried out to haraterize the steady-state operation and the transient operation 0 C, 1 the physis during old-start operation is poorly understood despite its importane in fuel ell deployment. ne of the first studies on old start was onduted by Hishinuma et al., 2 MDonald et al., 3 and Cho et al. 4 Hishinuma et al. 2 studied the performane of a single ell under a variety of operating onditions during old start from 25 to 3 C. They found that the performane of a PEFC dereases due to ie formation on the reative area of the athode and heat generated by fuel ells might be enough to warm up the ell from old start at 5 C and make self-starting possible. They also indiated that it is neessary to heat the ell with external soures in order to make a startup below 5 C. MDonald et al. 3 onduted an experimental study to investigate the physial hanges in fuel ell membranes arising from freeze/thaw yling. They onsidered hundreds of temperature yles between 80 and 40 C over months. Cho et al. 4 arried out a study on ell degradation related to the thermal yle. They ran fuel ells at 80 C, stopped, ooled to a subzero ondition, and reheated to 80 C for another thermal yle. They found that the observed degradation was attributed to freezing of water that was produed during operation and remained in the PEFC after the operation. By using the gas-purging method, they suessfully redued the degradation rate. Reently, szipok et al. 5 onduted isothermal potentiostati old start measurements of fuel ells under various operating onditions and found that water freezes in the porous strutures of the athode eletrode, the miroporous layer, and the gas diffusion layer GDL. They also arried out statisti evaluation of the experiments, whih indiated that dryer membranes and high air-flow rates are benefiial for high harge-transfer rates. Yana et al. 6 investigated the effet of subfreezing temperatures on ell performane and omponents. They showed that fuel ells were able to start at 5 C after being prepurged and insulated, and with the higher air stoihiometry and higher feed gas temperature at 10 C, it was possible to make a startup at low urrent densities 0.1 A/m 2. They also found delamination of the atalyst layer from both the membrane and GDL during old-start operations. The modeling work of old start was attempted by He and Menh 7 and Mao and Wang. 8 He et al. 7 presented a 1D transient model to desribe the water migration and ie-lens formation proess. They found that the Nafion thikness and initial water ontent might have a diret effet on the potential damage to delamination between the Nafion and atalyst layer. The multidimension model of Mao and Wang 8 was built upon the transient model of Wang and Wang, 9,10 by inorporating the mehanisms of ie formation. They explored the effets of startup urrent density and membrane thikness on ell performane during old start. In addition to the ell performane during old start, Saito et al. 11 and Cappadonia et al. 12 onduted a study with fous on the membrane at low temperatures. Saito et al. 11 investigated the temperature dependene of the ion and water transport in several types of membranes. They found that a portion of water is frozen around 20 C, but nonfreezing water remains and is able to transport in the membrane. Cappadonia et al. 12 employed impedane spetrosopy to study the ondutane of Nafion membranes as a funtion of temperature. They measured the ondutane of Nafion membranes in a wide range of temperatures down to the subzero regime. Despite the efforts in previous studies, the following aspets of fundamental researh are still highly needed for old start. ne is to eluidate the eletrohemial and transport mehanisms during old start; the other is to investigate the key physial parameters that haraterize the PEFC old start and the mehanisms that govern the voltage loss. In this paper, haraterization of heat and water transport in fuel ells is presented for development of a lumped parameter thermal/water model. Analysis of the key parameters suh as time sales is onduted and physis of oxygen transport and overpotential behaviors in the atalyst layer are investigated. Modeling and Theoretial Analysis Charaterization of Heat Transfer. Figure 1 shematially shows the omponents of a PEFC in one dimension. To investigate the spatial variation of temperature in a fuel ell at old start, we follow the heat-analysis approah outlined in Ref. 13 and 14 and haraterize the heat soures during old start to two ategories: the heat produed only in the atalyst layer and that in most parts of fuel ells. The primary thermal soure in the seond ategory is the ohmi heat i 2 e / eff + i 2 s / eff and is fairly small at low urrent densities. Considering a typial resistane of 100 m m 2, the ratio of ohmi heat release to the power density I V ell is less than 2%

2 B1042 Journal of The Eletrohemial Soiety, B1041-B Figure 1. Color online Shemati of PEFC in one dimension. at urrent density of 0.1 A/m 2. Two major soures in the first ategory are the reation heat j + TdU o /dt and latent heat of phase hange h sg ṁ sg. These heating mehanisms primarily take plae at the reation surfae within the atalyst layer. Negleting the ohmi heat, the variation of temperate aross the atalyst layer an be estimated by employing the total heat release, S T T CL CL 2 S T eff k CL = CLIE Vell o eff k CL where E o is defined as h /2F and represents the eletromotive fore EMF that all the energy from hydrogen/oxygen, the alorifi value, heating value, or enthalpy of formation, were transformed into eletrial energy with the ie as the reation produt. 15 The value of E o also onsiders the latent heats of fusion and ondensation as well as the sensible heat. E o = 1.25 and 1.48 V for low-heat value LHV and high-heat value HHV, 15 respetively, while E o 1.53 V during old start. Typially, the effetive ondutivity, k eff, is around 3.0 W/m K, leading to T CL K at 0.1 A/m 2. Similarly, T GDL and T BP are both 0.05 K. Therefore, temperature an be assumed uniform in a fuel ell during old start. The ell temperature an then be obtained through onservation of thermal energy t IE o VellA m + Q gasflow + Q oolant Q lossdt 0 T = + T o m m Cp m + m CL Cp CL + m GDL Cp GDL + m BP Cp BP 2 where T o is the initial temperature. Considering the ase of selfheating and no heat loss, the time onstant of ell warmup to the freezing temperature an be estimated by 1 Charaterization of water transport. Water gained in the athode atalyst layer an be expressed as CLS w dv =CLS prod dv +CLS ED dv G MEM ds G GDL ds /MEM CL /GDL CL 5 where S prod = j /2F, S ED = n d /Fi = n d j /F, and j is transfer urrent density at the reation site. Note that the eletro-osmati drag ED, n d, may be a funtion of water ontent. For analysis purposes, we use a onstant value of n d. G MEM represents the amount of water flux bak to the membrane, either hydrating the eletrolyte or ompensating for water loss in the anode. At steady state, a oeffiient is used to indiate water transfer between the anode and athode. Here, we still use this term to show the net water gain in the athode in addition to the water prodution during old start. Note that the oeffiient here ombines the effets of the water exhange between the two sides as well as the water absorbed/released by the ionomer membrane. In addition, an vary with time. For analysis purposes, we use a onstant value or the time average of. Assuming no spatial variations, i.e., / CL dv = V CL, the first three terms at the right side of Eq. 5 an be expressed as 1 +2 j 2F V CL = 1 +2 I 2F A m 6 The water flux aross the interfae between the atalyst layer and GDL is alulated by G GDL = D w,eff C w + uc w GDL CL. For 0 T,1 E o Velldt = m mcp m + m CL Cp CL + m GDL Cp GDL + m BP Cp BP T o A m I 3 Typially, the value of m BP Cp BP is muh larger than the summation of the others. Negleting other parts and assuming a onstant heat generation, one obtains T,1 = BPCp BP BP IE o Vell T o where the effetive length of bipolar plates, BP, is defined as m BP /A m BP. Typially, BP Cp BP is 1600 kj/k m 3, BP is 0.02 m, and I is 0.1 A/m 2, yielding T,1 100 s for old start at 30 C. Considering m GDL Cp GDL /m BP Cp BP 0.03, it takes about a few seonds 3s to solely heat the GDLs to the freezing point. The geometrial physial and operating parameters are shown in Table I. 4 the traditional design of PEFC flow fields, diffusion dominates reatant transport in the GDL, 16 while for the interdigitated flow field 17 or the one in Ref. 18, onvetion an be the dominant mehanism in the GDLs. Assuming no ie or liquid water formation in the GDL, onservation of water in the athode hannel and GDL yields G GDLds = uc w ds + uc w ds /GDL CL /outlet /inlet = IA m F w C,out 4C 2,in C,in w where C is the average value, defined by /ucds// inlet uds. If this flux term is larger than the water gained in the athode in Eq. 6, no 7

3 Journal of The Eletrohemial Soiety, B1041-B B1043 Table I. Geometrial, physial, and operating parameters. Quantity Value Gas hannel depth/width 0.5/1.0 and 1.0 mm and shoulder width Catalyst layer/gdl/bp thikness, 0.01/0.2/2.0 mm CL / GDL / BP Porosity of GDLs/atalyst layers, 0.6/0.5 GDL / CL Volume fration of ionomer 0.23 in atalyst layers, m Ativation energy for oxygen redution J/mol 14 reation, E a Thermal ondutivity 3.0/3.0/20.0 W/mK of atalyst layer/gdl/bp, k eff eff eff8,13 CL /k GDL /k BP Speifi heat of atalyst layer/gdl/membrane/bp, CL p / GDL m14 p / p ie forms in the athode. Here, a dimensionless parameter of 1, an be defined as 1, = IA m F w C,out C,in w 4C 2,in 1 +2 I 2F A m = w C,out C,in w C,in 1, represents the ratio of the water removal rate by the athode stream to the one gained by the athode atalyst layer. If 1, is less than one, there is a water aumulation in either the solid or ionomer phase in the athode. A similar definition an also be made in the anode. Note that 1, may be a funtion of time during transients and at steady state 1, must be equal to 1. Under old start or lowhumidity operations, water is totally taken away by the gas flow assuming no liquid/solid water in the stream. Therefore, it is espeially of interest to only onsider the gas flow in the hannel 1,,g = sat RH,out C out 21 +2C,in RH,in C sat in It an be seen that 1,,g reahes its maximum value at RH,out =1. Note that the temperatures at outlet and inlet are usually different e.g., see Ref. 19. Here we only onsider the ases with the same temperature at the inlet and outlet. The saturated onentration, C sat T, an be alulated through the six-degree polynomial funtion proposed by Rasmussen, 20 whih is aurate relative error from 50 to 50 C. Figure 2 shows the plot of maximum 1,,g at different temperatures and pressures related to C 2,in.Inthe subzero startup, the value of 1,,g is mostly very small 2%. Here, for analysis purposes, we neglet the water taken away by the gas flow in the following disussion. In the atalyst layer below the freezing temperature, water moleules exist in gas, solid, and ionomer phases. The ionomer, typially Nafion, an hold muh water as indiated by Ref. 9, whih demonstrated that the amount of water in the membrane an be hundreds of times more than that in the gaseous phase of hannel streams. Therefore, we an neglet the small amount of water in the 2 709/709/500 J/kg K Density of ie/dry membrane, 917/1980 kg/m 3 18 ie / m 2 diffusivity in athode gas m 2 /s at standard ondition, D 2 18 M,0 Net water transport per proton, Transfer oeffiient, 1.0 Exhange urrent density A/m 3 8,18 reation surfae area, a 0 i 0 RH of the fuel ell at initial state 50% EW 8, Latent heat of ie fusion, h fusion J/kg 8 9 Figure 2. Funtional dependene of 1,,g on stoihiometri ratios and pressures. gaseous phase in the atalyst layer. The old start has two stages of operations before reahing the freezing point. ne involves only membrane hydration in the atalyst layer; the other also inludes the ie formation in the void spae. The third stage starts when the fuel ell reahes 0 C, in whih the residual ie in the atalyst layer melts. Assuming thermodynami equilibrium between the gas and ionomer phases as well as between the ie and gas phases prevail due to the large phase interfaial area present within the porous atalyst layer, no solid water is produed at the first stage as the atalyst layer is partially hydrated, and the time onstant, ie,1, for this stage an be alulated by ie,1 14 S 0 w m dt m EW =0 d 10 where m is the volume fration of the ionomer in the atalyst layer. Considering a onstant S w, ie,1 an be rewritten as ie,1 = m CL m EW I 2F = 2F m m CL 14 0 EW1 +2I 11 Given the typial values of parameters for PEFCs, ie,1 is 10 s at 0.1 A/m 2. Assuming no liquid water at superooled state forms, solid water is produed at t ie,1 and the ie volume fration in the void spae, s ie, an be expressed as Mw s ie t = S w tdt CL ie ie,1 14 t t m m EW d 12 For a onstant S w, negleting the ionomer absorption in Eq. 12 due to no liquid water present yields s ie t = 1+2Mw I t ie,1 = t ie,1 t = k 2F CL ie CL ie,2 ie,2 ie,1 t ie,2 13 where the time onstant for the seond stage, ie,2, and ratio of the two time onstants, k, are defined as

4 B1044 Journal of The Eletrohemial Soiety, B1041-B ie,2 = 2F CL ie CL 1 +2M w I and k = ie,1 = m m 14 0 M w ie,2 ie CL EW 14 k is determined by the geometrial and material properties as well as initial membrane ondition. Combining the two time onstants yields sie = ie,1 + ie,2 = 2F CL 1 +2I m m 14 0 EW + CL ie M w 15 This time onstant sie represents the time period for solid water to oupy the void spae i.e., s ie =1. Assuming the ell shuts down at s ie =1this might not hold true when tortuosity of the atalyst layer is suffiiently large; in that ase, sie an be defined as the time period for ie-volume fration reahing the ritial value, T,1 sie leads to failure of the startup due to the ie plug, while for T,1 sie, the fuel ell is able to start up from a subzero environment. Therefore, one an further define a dimensionless parameter of 2 as 2 = T,1 16 sie The PEFC is able to make a startup from subzero onditions upon 2 1 and 2 is independent of urrent densities. ne the ell temperature reahes 0 C, it starts dereasing due to fusion of the residual ie in the atalyst layer, and therefore there exists a maximum value of ie-volume fration whih an be alulated by s max ie = T,1 k 17 ie,2 To estimate the time onstant of the ie fusion at 0 C, we an follow the approah of Eq. 3 and obtain T,2 by solving T,1 T,1 + T,2 max IE o Velldt = ieh fusion CL CLs ie = ie h fusion CL CL T,1 k ie,2 18 Here E o is defined for the ondition with liquid water at 0 C as produt approximately an use the EMF value of HHV for E. o Given the typial values of the parameters for PEFCs, s max ie =1 yields T,2 2.0 s at 0.1 A/m 2, whih is fairly fast. We an then obtain s ie through the following equation t IE o Velldt s ie = s max T,1 ie ie h fusion CL CL T,1 t T,1 + T,2 19 Considering a onstant rate of heat generation, we an simplify the expression as max s ie = s T,2 + T,1 t ie = T,2 T,1 k ie,2 T,2 + T,1 t T,2 T,1 t T,1 + T,2 20 f ourse s ie =0 t T,1 + T,2 21 In addition, there oexist solid and liquid waters during T,1 t T,1 + T,2.Att T,1 + T,2, there is purely liquid water in the atalyst layer whih may be able to transport to the GDL due to apillary ation. Disussions of liquid-water transport are beyond the sope of this paper. Analysis of ell voltage loss. The solid water may over the atalyst partiles, therefore reduing the eletrohemial ative surfae. The eletrohemial kinetis is generally desribed by the Butler Volmer equation j = ai o,t exp F F a RT exp 22 RT where i o,t is the exhange urrent density, determined by the atalyst eletrohemial kinetis, and a is the surfae-to-volume ratio, desribing the roughness of the porous eletrodes. We follow the approah of the liquid-water impat on reation surfae and use the following empirial formula to aount for the ie effet a = 1 s ie aa 0 23 The oeffiient, a, is determined by the morphology of the solid water formed in the atalyst layer. In PEFCs, the sluggish kinetis of oxygen redution reation RR results in a high athode overpotential. Thus, the Butler Volmer equation an be well approximated by Tafel kinetis, i.e. C 2 F j = ai 0,T C,refexp 2 RT 24 where the surfae overpotential is defined as = s e U o 25 where s and e are eletroni and eletrolyte phase potentials, respetively, and the equilibrium potential, U o, is a funtion of temperature U o = T In addition, temperature affets the RR reation rate and the exhange urrent density, i 0,T, whih an be expressed in Arrhenius form as follows i 0,T = i 0 exp E a R 1 T where E a denotes the ativation energy for RR at the Pt/Nafion eletrode as provided by Parthasarathy et al. 21 In transients, the output urrent density onsists of the faradai urrent of eletrohemial reations and the one from the doublelayer harging or disharging I = j l + I db 28 The double layer ours in a thin layer of the order of nanometers adjaent to the reation interfae and ats as a apaitor during the transiene. Similar to porous eletrodes of batteries, the double layer in the atalyst layer of a PEFC an be regarded as being in parallel to a harge-transfer-reation resistor. The time onstant of the double-layer harging/disharging was less than 1 ms. 9 The ontribution from the double-layer harging/disharging an be estimated through the following equation V ell I db ac db CL 29 t Typially, the apaity C db is around 20 F/m 2 and speifi area, a, is about 10 3 /m, and V ell of 0.5 V and t of 100 s lead to I db of 0.01 A/m 2. The effet of double layer is small, 10% of typial operating urrent during old start. For analysis purpose, we ignore the double-layer effet in this paper. The solid water also hampers the transport of oxygen to reation sites. The oxygen equation in one dimension an be expressed as C 2 t + uc 2 x = xd C2 2,eff + S 2 x 30 Two types of diffusive transport are onsidered here. ne is the moleular or Fikian diffusion, whih takes plae when the mean free length of moleules is relatively large ompared with the pore

5 Journal of The Eletrohemial Soiety, B1041-B B1045 size. Under this irumstane, the moleules ollide with eah other during their passage through the pores, and hene the moleules move dependently of eah other. In GDLs, moleular diffusion ours and the oeffiient is a funtion of temperature and pressure as desribed by D 2 M = D 2 M, /2 P T 1 31 The other is the Knudsen diffusion, whih ours in situations in whih gas moleules ollide more frequently with pore walls than with other gas moleules. This type of diffusion is enountered when the mean free path of gas moleules is of the order of the pore harateristi length sale. In the atalyst layer, the mean radius of the miropores 22 and the mean free path of the oxygen moleule moleule = 8RT/ 2D 2 NaP are both a 0.1 m; therefore the Knudsen diffusion is an important mehanism of oxygen transport in the atalyst layer. The Knudsen diffusion oeffiient in a long straight pore an be alulated through the kineti theory of gases D K 2 = 2r pore 3 8RT M 2 32 The value of D 2 K is around m 2 /s at r pore = 0.1 m. Note that this value is omparable to the moleular one. To ombine the two mehanisms, the harmoni mean is taken to alulate the average diffusivity. In addition, as the ie-volume fration inreases, the Knudsen diffusion beomes the dominant mehanism due to the dereasing pore radius. For analysis proposes, we denote the average diffusion oeffiient in the atalyst layer as D 2 K to distinguish from the one in GDLs where the moleular diffusion dominates. To aount for the porosity and tortuosity fator,, of a porous media, the effetive gas diffusion oeffiient is given by D 2,eff = D 2 = d,0d 2 33 where the Bruggeman fator, d,0, is onstant, indiative of tortuosity of a porous medium. Note that the last term in Eq. 33 is also referred to as Bruggeman relation. In most of the previous work, the Bruggeman fator, d,0, is set to be a onstant of 1.5. Wang et al. 23 indiated that the values of this fator for arbon paper and arbon loth are different due to the differene in their pore struture. In the presene of ie, the solid water attahes on the surfae of the wall, narrowing the pore as well as hanging the morphology of the solid matrix. To aount for the effet of ie on diffusion, we follow the modeling approah in liquid-water transport and modify the oeffiient as D 2,eff = 1 s ie dd 2 34 Note that tortuosity fator, d, also aounts for the effet of poresize hange on the Knudsen diffusion see Eq. 32 andmaybea funtion of the ie volume depending on morphology of the ie rystals. Given no ie formation in the GDL, the time onstant of the oxygen diffusion aross the GDL an be estimated as diff = 2 GDL D 2,eff 35 GDL The value of diff is s for typial GDLs, whih is fairly short. Therefore, the transient term of Eq. 30 an be negleted for oxygen transport in GDLs. In addition, ignoring the onvetion term in GDLs, the maximum drop of oxygen onentration aross the GDL an be estimated by only onsidering the diffusive transport C 2 GDL = C 2 GDL C 2 CL = I 4F At the urrent density of 0.1 A/m mol/m 3. GDL D 2,eff M d,0 GDL 36 during old start, C 2 GDL In the atalyst layer, assuming diffusion is the dominant transport mehanism and reation rate is uniform, the oxygen profile an be obtained as C 2 = C 2 CL I 2 CL x x CL + CL 2 8F CL D 2 K CL 1 s ie d = C 2 1 x x 2 CL CL +1 CL 1 Da d d,0 CL 1 s ie 37 d where the dimensionless parameter, Da, is alled the Damköhler number defined as Da = I CL 8F C 2 CL D 2 K = Reation rate 38 d,0 Mass-transport rate Current density of 0.1 A/m 2, P of 1.0 atm, and T of 30 C yield Da Note that several key parameters, suh as operating pressure, stoihiometri ratio, urrent density, and atalyst layer thikness, are lumped in Da. It is of interest to evaluate the oxygen onentration drop aross the atalyst layer C 2 GDL = C 2 CL C 2 MEM = Da C 2 CL d d,0 CL 1 s ie d 39 whih is small 0.5 mol/m 3 at 0.1 A/m 2, d,0 = d = 1.5, and s ie Therefore, the solution of Eq. 37 is valid at s ie up to 98%. When s ie reahes a level that auses serious starvation therefore j is no longer uniform and the transient term annot be negleted, the solution, Eq. 37, an be invalid. In that ase, the oxygen profile an be obtained by oupling Eq. 24 and 30. Substituting Eq. 37 into Eq. 24 yields s ie,x = RT F ln IC 2,ref a 0 i ref 0, CL C 2 1 s ie a1 CL 1 x x 2 1 CL CL +1 Da d d,0 CL 1 s ie 40 d Therefore, a dimensionless funtion an be defined as 1 x x 2 CL s ie,x =ln1 s ie CL +1 a1 Da d d,0 CL 1 s ie d 41 It an be seen that impats of the solid water are solely ontained in the funtion. The funtion onsists of two parts: one is from the redution of eletrohemial ative surfae due to solid water overage, and the other is oxygen starvation. Then Eq. 40 an be written as s ie,x = RT F ln IC 2,ref a 0 i ref 0, CL C 2 CL + RT F s ie,x =,o + 42 where,o = RT F ln IC 2,ref a 0 i ref 0, CL C 2 CL and = RT F s ie,x 43,o denotes the overpotential at the interfae between the athode atalyst layer and GDL when no ie is present. The overpotential hange due to ie presene an be further expressed as s ie,x =,1 +,2 44 where

6 B1046 Journal of The Eletrohemial Soiety, B1041-B Figure 4. Profiles of,1,,2 at the interfae between the membrane and athode atalyst layer and their ratio, 3,at 30 C, a = 1 and d = 1.5. Figure 3. xygen profiles in the athode atalyst layer at different ievolume frations and Da s.,1 = a RT F ln1 s ie,2 = RT F ln 1 Da 1 x x CL CL 2 +1 d d,0 CL 1 s ie d 45,1 and,2 represent the voltage losses due to the reative surfae redution and oxygen starvation, respetively. Therefore, a dimensionless parameter 3 an be defined as the ratio of these two 3 =,1 46,2 In addition, we an evaluate the voltage loss due to oxygen starvation by onsidering the loation at the interfae between the membrane and atalyst layer,2 s ie,x CL CL = RT F ln 1 Da d d,0 CL 1 s ie d 47 Another important fator is the sensitivities of,1 and,2 to s ie, defined as k,1 =,1 s ie and k,2 =,2 s ie 48 ne the athode overpotential is alulated, the ell voltage an be obtained through V ell = U o + a R I 49 Assuming no ie in the anode during old start, a an be negleted at low urrent density. The last term on the right side represents voltage loss due to ohmi resistane. It onsists of the ioni resistanes in the membrane and atalyst layers and eletroni one, as well as ontat resistane. R an be alulated through R = m m + acl 2 acl m k + Usually, R e is small and negligible. CL 2 CL m k + R e + R ontat 50 Results and Disussion Figure 3 shows the oxygen profiles in the atalyst layer at different levels of the ie-volume fration with a onstant value of tortuosity d,0 = d = 1.5 in the atalyst layer. The oxygen onentration undergoes a fairly small derease 0.5 mol/m 3 or 5% in the atalyst layer for the ie-volume fration up to 98% for Da = at 0.1 A/m 2. When the ie fration reahes 99%, the oxygen onentration inside the atalyst layer starts to derease by a onsiderable value 1mol/m 3.AstoDa = e.g., I = 1.0 A/m 2, the drop is small at the ie-volume fration up to 90%. In addition, the oxygen-onentration value at the interfae between the atalyst layer and GDL is smaller at the larger Da due to a higher urrent density onsidered for Da = The magnitude of the onentration drop within the GDL an be estimated through Eq. 36. Figure 4 presents the profiles of,1 and,2 as well as their ratio 3 at 30 C. The magnitude of,1 inreases steadily with ie-volume fration, while that of,2 is fairly small exept near s ie =1.,1 is several orders of magnitude larger than,2 in a large range of the ie-volume fration. At very high ie fration 95%,,2 starts to inrease dramatially. In addition, the trend of the parameter, 3, shows an inrease at first to about thousands, followed by a derease at the very end. Redution in the reative surfae due to ie overage is a major mehanism leading to the voltage loss during old start. Note that the above onlusions are based on a onstant tortuosity fator, d = 1.5. Figure 5 shows the,2 profiles at different tortuosities and Das. The value of Da has a small effet on the urve of,2 and it only slightly moves the starting point of oxygen starvation ahead, while the tortuosity of the atalyst layer has great impat on the voltage loss. Under the tortuosity of 4.0,,2 starts to dramatially inrease its magnitude around s ie = 0.8. Figure 6 displays the profiles of sensitivities of,1 and,2, i.e., k,1 and k,2, at different d and a. Here, we assume d and a are independent of s ie. It an be seen that both values inrease dramatially as s ie approahes unity, and k,2 is muh smaller than k,1 in most of the region exept s ie lose to 1. In addition, k,1 is Figure 5. Profiles of,2, at the interfae between the membrane and athode atalyst layer for different d and Da s.

7 Journal of The Eletrohemial Soiety, B1041-B B1047 Figure 6. Profiles of sensitivities,,1 and,2 at different d and a. Figure 8. Evolution of temperature, ie-volume fration, and ell voltage during old start from 15 C. linear with a, as shown in Eq. 45 and 48, while d is nonlinear with k,2 and has a profound impat on the value of the latter. Figure 7 shows the evolution of temperature, ie-volume fration, and ell voltage during old start from 30 C with the time onstants indiated in the plot. In this ase, 2 = T,1 s ie 1 and the ie-volume fration reahes unity before the ell temperature inreases to 0 C, therefore the startup fails. Due to a onstant urrent density of 0.1 A/m 2 onsidered, the ie-volume fration inreases almost linearly after the operation is beyond the time onstant of membrane hydration, ie,1. The ell temperature also displays a nearly linear inrease with time. As to the ell voltage, it first inreases due to inreasing temperature, whih benefits the reation kinetis and transport mehanisms. As the ie-volume fration further inreases, the ell-voltage hange is then dominated by the redution of eletrohemial ative surfae and oxygen starvation, leading to a fast drop in ell voltage. Figure 8 shows the startup of the fuel ell from 15 C. In this ase, 2 1, therefore the ell temperature inreases to 0 C before the ie-volume fration reahes unity. The temperature stays onstant at 0 C for a short while due to fusion of the residual ie. Simultaneously, the ie-volume fration dereases with time, resulting in the voltage inreases. However, this model does not aount for liquid-water effet, whih may have a profound effet on atalyst-layer performane; therefore the slight inrease in ell voltage during the fusion proess is drawn by a dashed line. The fuel ell used in Ref. 2 needs external heating soures in order to make a startup below 5 C. From the previous analysis and Fig. 7 and 8, it an be seen that 2 is the key parameter that determines if fuel ells are able to start suessfully. The fuel ell in Ref. 2 has a deeper gas hannel 1 mm, whih may lead to a larger value of the effetive length of bipolar plates BP and hene T,1 see Eq. 4. Conlusion This paper investigated the eletrohemial and transport phenomena in the athode atalyst layer of fuel ells during startup from subzero environments. We found that the spatial variation of temperature in a fuel ell is small and negligible under low urrent densities during old start, and thereby a lumped parameter thermal model was developed for PEFCs. In addition, one-dimensional analysis indiated that the onentration drop of oxygen within the atalyst layer is fairly small when the ie-volume fration and tortuosity of the atalyst layer are at moderate levels. A high value of tortuosity has a profound impat on reatant starvation in the atalyst layer during old-start. In addition, we defined a number of key parameters that govern the old-start operations and investigated their impats on ell performane. These parameters are extremely important for ell designs and ontrols for PEFC old start. Finally, we found that redution in the eletrohemial ative surfae of the atalyst may be a major mehanism leading to the ell voltage loss during old start. Aknowledgments Partial support of this work by the UC Irvine Aademi Senate Counil on Researh, Computing and Library Resoures CRCLR is gratefully aknowledged. The University of California, Irvine assisted in meeting the publiation osts of this artile. List of Symbols Figure 7. Evolution of temperature, ie-volume fration, and ell voltage during old start from 30 C. A m eletrode area, m 2 a water ativity; effetive atalyst area per unit volume, m 2 /m 3 a o atalyst surfae area per unit volume, m 2 /m 3 BP bipolar plate C apaitane of double layer, mf/m 2 ; molar onentration of speies k, mol/m 3 C p speifi heat, J/kg K

8 B1048 Journal of The Eletrohemial Soiety, B1041-B Greek D speies diffusivity, m 2 /s; diameter of moleule, m EW equivalent weight of dry membrane, kg/mol F Faraday s onstant, 96,487 C/equivalent I urrent density, A/m 2 i superfiial urrent density, A/m 2 j transfer urrent density, A/m 3 k thermal ondutivity, W/m K; sensitivity of overpotential, V K Knudsen diffusion M moleular weight, kg/mol; moleular diffusion Na Avogadro s number n the diretion normal to the surfae n d eletro-osmoti oeffiient, H 2 /H + P pressure, Pa Q rate of heat transfer r radius, m R universal gas onstant, J/mol K; ohmi resistane, m m 2 RH relative humidity S soure term s ie ie volume fration ds differential element of surfae area t time, s T temperature, K U o equilibrium potential, V u veloity vetor, m/s V volume, m 3 transfer oeffiient; net water flux per proton flux dimensionless parameter density, kg/m 3 phase potential, V proton ondutivity, S/m stoihiometri flow ratio membrane water ontent porosity surfae overpotential, V tortuosity; time onstant, s thikness, m Supersripts and subsripts CL d athode atalyst layer diffusion db e eff g GDL m o ref s sat sg w double layer eletrolyte effetive value gas phase gas diffusion layer membrane phase referene value; initial value referene value solid saturate value phase hange between ie and water vapor water Referenes 1. C. Y. Wang, Chem. Rev. (Washington, D.C.), 104, Y. Hishinuma, T. Chikahisa, F. Kagami, and T. gawa, JSME Int. J., Ser. B, 47, R. C. MDonald, C. K. Mittelsteadt, and E. L. Thompson, Fuel Cells, 4, E. Cho, J. J. Ko, H. Y. Ha, S. A. Hong, K. Y. Lee, T. W. Lim, and I. H. h, J. Eletrohem. So., 151, A M. szipok, D. Riemann, U. Kronenwett, M. Kreideweis, and M. Zedda, J. Power Soures, 145, Q. Yana, H. Toghianib, Y.-W. Leea, K. Liangb and H. Causey, J. Power Soures, 160, S. He and M. M. Menh, J. Eletrohem. So., 153, A L. Mao and C. Y. Wang, J. Eletrohem. So., 154, B Y. Wang and C. Y. Wang, Eletrohim. Ata, 50, Y. Wang and C. Y. Wang, Eletrohim. Ata, 51, M. Saito, K. Hayamizu, and T. kada, J. Phys. Chem. B, 109, M. Cappadonia, J. W. Erning, S. M. S. Niaki, and U. Stimming, Solid State Ionis, 77, Y. Wang and C. Y. Wang, J. Eletrohem. So., 153, A Y. Wang and C. Y. Wang, J. Eletrohem. So., 154, B J. Larminie and A. Diks, Fuel Cell Systems Explained, 2nd ed., John Wiley & Sons, New York Y. Wang and C. Y. Wang, J. Eletrohem. So., 152, A J. S. Yi and T. V. Nguyen, J. Eletrohem. So., 146, Y. Wang and C. Y. Wang, J. Power Soures, 147, Y. Wang and C. Y. Wang, J. Power Soures, 153, L. A. Rasmussen, J. Appl. Meteorol., 17, A. Parthasarathy, S. Srinivasan, and A. J. Appleby, J. Eletrohem. So., 139, M. C. Tuker, M. dgaard, P. B. Lund, S. Yde-Andersen, and J.. Thomas, J. Eletrohem. So., 152, A Y. Wang, C. Y. Wang, and K. S. Chen, Eletrohim. Ata, 52,