hydrogen peroxide formation in the cathode

Transcription

1 Loughborough Unversty Insttutonal epostory An mpedane model for analy of EIS of polymer eletrolyte fuel ells under hydrogen peroxde formaton n the athode Ths tem was submtted to Loughborough Unverstys Insttutonal epostory by the/an author. Ctaton: CU-MAN S. CEN. and GEEND P.S. 05. An mpedane model for analy of EIS of polymer eletrolyte fuel ells under hydrogen peroxde formaton n the athode. Journal of Eletroanalytal Chemstry 745 pp Metadata eord: Verson: Aepted for publaton Publsher: Elsever B.V. ghts: Ths work s made avalable aordng to the ondtons of the Creatve Commons Attrbuton-NonCommeral-NoDervatves 4.0 Internatonal (CC BY-NC-ND 4.0 lene. Full detals of ths lene are avalable at: Please te the publshed verson.

2 An Impedane Model for Analy of EIS of Polymer Eletrolyte Fuel Cells under ydrogen Peroxde Formaton n the Cathode Samuel Cruz-Manzo* u Chen and Paul Greenwood Department of Aeronautal and Automotve Engneerng Loughborough Unversty Leestershre LE 3TU Unted Kngdom *E-mal: s.ruz-manzo@hotmal.om Abstrat In ths study an mpedane model based on eletrohemal theory onsderng hydrogen peroxde formaton durng a two-step oxygen reduton reaton ( n polymer eletrolyte fuel ells (PEFCs has been developed. To valdate the theoretal treatment eletrohemal mpedane spetrosopy (EIS measurements were arred out n an open-athode 6 m /ar PEFC stak. The results show that ndutve loops at low frequenes of the mpedane spetra are attrbuted to mehansms related to hydrogen peroxde formaton durng. The results also demonstrate that the mehansms durng onsumpton of hydrogen peroxde to form water (seond-step n an be the domnatng proe for loes n the PEFC ompared to the mehansms durng oxygen onsumpton to form hydrogen peroxde (frst-step n. xygen transport lmtatons an be a result of hydrogen peroxde adsorbed onto the surfae of the eletrode whh redues the number of atve stes n the athode atalyst layer for oxygen to reat. Ths study ould support results from other ermental tehnques to dentfy hydrogen peroxde formaton durng the that lmt the performane of PEFCs. Key words: EIS hydrogen peroxde PEFC two-step oxygen reaton mpedane model. Introduton Eletrohemal mpedane spetrosopy (EIS s a powerful ermental tehnque that an be appled n-stu for dagno of polymer eletrolyte fuel ell (PEFC performane. The mpedane response resultng from EIS represents the eletrohemal mehansms of the PEFC n the frequeny doman. It an be shown n a Nyqust plot showng real and magnary omponents the magntude and phase of the mpedane as a funton of frequeny an also be plotted n a Bode plot. The use of eletral equvalent ruts wth the ermental EIS tehnque s a well-establshed methodology to haraterse proees n the PEFC. An eletral equvalent rut an represent an dental mpedane response to that obtaned from the PEFC studed. Eah eletral

3 omponent n the eletral equvalent rut an desrbe a physal proe that takes plae n the PEFC. In the authors prevous study [] an eletral equvalent rut based on eletrohemal theory was developed to smulate and haraterse the frequeny response of the PEFC at any urrent of the polarsaton urve. owever the eletral rut had lmtatons n reprodung EIS measurements wth postve magnary omponents at low frequenes. EIS measurements wth postve magnary omponents at low frequenes are known as an ndutve loop and have been reported n EIS measurements of PEFCs [3]. Makhara et al. [3] suggested that the poble reasons for ths ndutve effet at low frequenes are the sde reaton and ntermedates nvolved n fuel ell reatons. oy et al. [4] developed mpedane models to aount for the reaton mehansms that may be responsble for the ndutve response at low frequenes; the models propose the formaton of hydrogen peroxde and platnum doluton durng the oxygen reduton reaton (. It has been reported [5] that roover of hydrogen to the athode faltates the reaton of oxygen and hydrogen at the athode generatng hydroxyl and hydroperoxyl radals whh reat further to produe hydrogen peroxde at the athode. The hypothe that hydrogen peroxde may be formed at the athode of a fuel ell s supported by the results of Inaba et al. [6]. In ths study an mpedane model onsderng fundamental eletrode theory and onsderng hydrogen peroxde formaton n a two-step has been developed. Modellng onsderatons based on EIS theory were taken nto aount to smplfy the mathematal treatment the hgh frequeny regon related to on dffuson mehansms n porous eletrodes found n the prevous study [] were not onsdered here. The fous of the urrent study s at the low frequeny range where the mehansms relatng to hydrogen peroxde formaton durng the oxygen reduton are represented. The mpedane model onsderng formaton of hydrogen peroxde durng a two-step was valdated aganst EIS measurements arred out n an openathode 6 m PEFC stak.. Eletrohemal mehansms of hydrogen peroxde formaton durng The two-step whh yelds the formaton of hydrogen peroxde ( and the formaton of water ( has been reported n the lterature [47] as: k e ( k e ( The urrent denstes orrespondng to reatons ( and ( have been reported n the lterature [8] as: ( ( b V nfk 3/ (3

4 ( b V nfk 3/ (4 where F s the Faraday onstant k s the rate onstant whh depends on the global order of reaton s the onentraton at the eletrode surfae n s the number of eletrons onsumed durng the reaton fratonal surfae overage of hydrogen peroxde b s the apparent Tafel slope and V s the eletrode potental. The followng aumptons are onsdered to faltate the mathematal treatment: s the. Ths study gnores hydrogen peroxde dffuson n the CCL durng EIS measurements as a frst approxmaton. Inaba et al. [6] reported that when Pt/C atalysts are hghly agglomerated the moleules easly dffuse to nearby Pt/C partles where they are transformed to water. To aount for hydrogen peroxde dffuson durng EIS measurements the effet of partle sze nteratons between Pt partles and the substrate arbon on Pt/C agglomeraton should be studed and onsdered n the modellng work. Ths wll be addreed n future work.. Sethuraman et al. [9] reported that the rate of hydrogen peroxde formaton durng the s nreased wth nreasng proton onentraton. Proton onentraton n the CCL s a funton of the amount of onomer or eletrolyte n the maropore spaes between agglomerates [0]. In ths study t has been onsdered that there s no effet to the opposton of flow of protons n the CCL on hydrogen peroxde formaton. Proton retane n the CCL s negleted. Ths smplfed the mathematal treatment by onsderng that the onentraton of protons aro the CCL s onstant from the CCL- PEM nterfae to the Pt/C atalyst agglomerates. 3. There are three modes of transport of oxygen n the CCL whh an have an effet on ma transport lmtatons: gas-dffuson n the eletrode-pore dolved oxygen dffuson n the lqud water surroundng the agglomerate and dolved oxygen n the onomer phase []. The fnte dffuson dstane for oxygen to reah the reaton stes n the CCL forms a omplated network of mult-phase parallel and seral paths. EIS only measures bulk parameters n the total CCL thkne and reflets a total ma transport retane and a total fnte dffuson dstane for the three modes of oxygen transport n the CCL therefore dffuson of oxygen n the CCL wll be onsdered from the gas dffuson layer (GDL-CCL nterfae to the CCL-PEM nterfae. Ths wll smplfy the mathematal analy and therefore the resultng model wll present parameters ommonly known n the

5 eletrohemal area suh as the arburg mpedane [] whh allows the haratersaton of oxygen transport lmtatons durng EIS measurements. Takng nto aount the frst and seond aumptons prevously defned Eqs. 3 and 4 an be defned as: ( ( b V 3 / nfk (5 ( b V 3/ nfk eq (6 where eq represents the onentraton at equlbrum ondtons as t s aumed that surfae onentraton of protons and hydrogen peroxde s onstant. The rate at whh the transfer of harge ours at equlbrum ondtons s known as the exhange urrent. The exhange urrent denstes n a two-step eletron transfer reaton are desrbed n Appendx A. The exhange urrent denstes for reatons ( and ( at equlbrum ondtons wth ( ( b V 3/ nfk an be defned as: V V eq 0 (7 ( b V 0 nfk (8 3/ where 0 represents the exhange urrent densty s the fratonal surfae overage of hydrogen peroxde under equlbrum ondtons and V eq s the equlbrum potental. Multplyng both terms of Eq. 5 by ( ( b V ( b V eq ( ( and substtutng Eqs. 7 and 8 yelds: [ b ( V V ] 0 and smlarly Eq. 6 by (9 [ b ( V V ] 0 (0 Aumng that the formaton of hydrogen peroxde s governed by the Langmur sothermal t s poble to defne the total urrent and the varaton rate of as [3]: (

6 F d β ( dt where β s the maxmum surfae overage by hydrogen peroxde. Substtutng Eqs. 9 and 0 nto Eqs. and yelds: ( ( [ b ( V V ] [ b ( V V ] 0 (3 F d 0 ( ( [ b ( V V ] [ b ( V V ] b 0 0 (4 eq dt. a mpedane response If a small a perturbaton s appled to the workng eletrode the EIS tehnque allows the use of a lnear equaton to smulate mpedane spetra. A lnear model an be derved usng the Taylor seres anson as reed below: V V (5 To faltate the mathematal treatment the small dsturbane of oxygen from the a perturbaton s not onsdered n Eq. 5. Based on ermental EIS measurements n whh physal parameters are measured aro the entre CCL the hange n oxygen onentraton durng the wll be onsdered from the PEM- CCL nterfae to the CCL-GDL nterfae. The term that defnes the hange of oxygen onentraton from the GDL-CCL nterfae to the PEM-CCL nterfae at the frequeny doman has already been developed n the authors prevous study [] and wll be onsdered n the next seton. It wll be poble to norporate the arburg Impedane whh has been broadly used n the analy of oxygen transport lmtatons n ermental EIS measurements of PEFCs nto the mathematal treatment. The omplex value of an be related to V f Eq. s lnearzed by the followng equaton [4]: Fβ jω V V (6 where ω s the angular frequeny and j s the magnary omponent.

7 Applyng Eqs. 3 and 4 nto Eqs. 5 and 6 and onsderng the oxygen onentraton at the PEM-CCL nterfae yelds: 0 b Fb ( ( 0 b jω ( b η 0 ( b η ( ( b V 0 ( b η ( b η b 0 V ( 0 ( 0 ( b η ( b η (7 0 ( b η ( b η where the subsrpt represents the steady-state η V s the overpotental at steady-state oxygen onentraton at the CCL-PEM nterfae and V (8 s the s the onentraton at the GDL-CCL nterfae. The eletrode surfae overage of hydrogen peroxde at steady-state an be alulated from Eq. 4 onsderng d / dt 0 and 0 ( ( b η eq 0 0 ( ( b ( η b η (9 The eletrode surfae overage of hydrogen peroxde at steady-state represented n Eq. 9 an be reed n terms of steady-state urrents ; ths an be demonstrated n Appendx B. Epelbon and Keddam [5] defned the overage oeffent of adsorbed ntermedate spees at steady-state n a two-step reaton as the rato between the partal urrent of the frst reaton and the sum of the urrent of the frst and seond reatons. The hange n oxygen onentraton aro the CCL resultng from the small a dsturbane of the surfae overage of hydrogen peroxde formaton n the frequeny doman s onsdered neglgble. Therefore the rato of oxygen onentraton between the CCL-PEM and GDL-CCL nterfaes / eq whh are multpled by n Eqs. 7 and 8 (thrd term on the rght hand sde s onsdered to be steady-state. Under suh onsderatons t s poble to defne Eqs. 7 and 8 n terms of harge transfer retanes and steady-state urrents: V [ ] (0

8 Fβ jω V [ ] ( where represents the harge transfer retane: 0 b ( b η ( b 0 ( b η (3 and represents the steady-state urrent: 0 0 ( ( b η ( b η (45. xygen transport lmtatons The oxygen onentraton at the eletrode surfae depends on the dffuson of oxygen through the multphase va parallel and seral paths n the CCL [6]. In the authors prevous study [] the rato between oxygen onentratons at the CCL-PEM and CCL-GDL nterfaes n the frequeny doman was derved to haraterse oxygen transport lmtatons n the mpedane response of PEFCs. Ths rato between oxygen onentratons s onsdered as the EIS tehnque measures the hange n oxygen onentraton n the total CCL. Ths also allows the dervaton of the arburg Impedane whh has been broadly used n the EIS area [] to haraterse oxygen transport lmtatons n the frequeny doman durng PEFC operaton. The rato of oxygen onentraton at the PEM-CCL and GDL-CCL nterfae at the frequeny doman s reed as []: (6 where and s the harge transfer retane for the oxygen reduton whh an be represented through Eq. ( jωt ( jωt tanh (7 s known as the arburg Impedane [] and haraterses oxygen transport lmtatons n EIS measurements of PEFCs wth Tδ (8 z F D *

9 defned as the retane of the dffuson proe and D T δ (9 defned as the tme onstant to dffuse oxygen through the CCL. 3. Eletrohemal Impedane of the PEFC under ydrogen Peroxde Formaton Substtutng Eq. 6 nto Eqs. 0 and gves: [ ] V (30 [ ] V j F ω β (3 Arrangng Eq. 3 for yelds: ( ( V j F ω β (3 Substtutng Eq. 3 nto Eq. 30 yelds: ( ( ( ( V j F ω β (33 The CCL s formed by a double layer struture of the nterfae between dmlar materals.e. the eletrodeeletrolyte nterfae. The eletrode represents the eletron-ondutng network of arbon-supported platnum agglomerates whle the eletrolyte represents the on-ondutng dsperson of Nafon. At ths nterfae an eletr feld s present and has a determnant role n the harge dstrbuton wthn the reatants as well as n the poston and orentaton of the reatant to form the desred produts. Ths double layer an behave lke a apator that s n parallel wth the eletrode reatons; the urrent pang from the eletrode to the eletrolyte an ether take part n the harge transfer reatons or ontrbute to the harge n the apatve effet. The eletrohemal reaton n the eletrode results n an nhomogeneous dstrbuton of harge n the atalyst layer. As a result a non-deal apator (Constant Phase Element [7] defned n the frequeny doman jω has to be onsdered n the theoretal treatment n order to orret for ths nhomogenety:

10 ( ( ( ( ( V j Y V j F P ω ω β (34 where Y represents a parameter related to apatane and supersrpt P represents a parameter to orret the nhomogenety n the dstrbuton of harge. Eq. 34 an be rearranged to re the eletral urrent that enters a rut omposed of retve and apatve elements as shown n Fg. gvng: ( V j Y A P ω φ (35 where ( φ ω τ φ j A F β τ ( ( s I φ and ( ( s I haraterse ndutve loops at low frequenes n the mpedane response of PEFCs. earrangng Eq. 35 yelds the eletrohemal mpedane of the athode aountng for hydrogen peroxde formaton durng the : ( P j Y A ω φ (36 The hydrogen oxdaton reaton ( mehansms ourrng at the anode have been proposed by Malevh et al. [] to be represented as an eletral rut omposed of a retor (harge transfer retane n parallel wth a apator (representng the double layer apatane. takng plae n the anode s a faster and a le omplated reaton sequene than the n the athode and an be represented at the frequeny doman as: aca j a a ω (37 f no ontamnants suh as C are present where a s harge transfer retane and Ca s apatane.

11 The opposton of ons flowng through the PEM and eletrons flowng through the bpolar plate and GDL an be represented by retanes onneted n seres. The overall proe an be represented wth a total retane ohm that aounts for the dfferent retanes n the layers of the PEFC. Therefore the mpedane of the PEFC nludng anode athode and PEM an be represented through the followng equaton: PEFC ohm a (38 where ohm represents the ohm retane of the PEM bpolar plates GDL the seond term on the rght hand sde represents Eq. 37 and the thrd term represents the athode mpedane (Eq. 36. Eq. 38 an be represented through the equvalent eletral rut shown n Fg. For the spef ase when the harge transfer retane related to hydrogen peroxde reaton durng the seond-step s smaller than the sum of harge transfer retane and ma transport retane durng the frst-step ; n Eq. 35 beomes negatve and a apatve loop at the low φ frequeny end of the spetrum s predted nstead of an ndutve loop as shown n Fg Expermental A ommeral pen-cathode 4-ell stak wth a 6 m atve area was used for the ermental tests. The membrane eletrode aembles (MEAs were made of Nafon wth platnum loadngs of 0.4mg/m and arbon blak for the eletrodes. The GDLs were made of arbon felt wth 00 µm wdth. The 4-ell stak onts of open athodes wth two 5V DC fans for oxdant supply (as ar and oolng. The stak onts of bpolar plates made of FU4369 T materal wth a thkne of 5 mm. gh purty hydrogen ( % was used durng the tests to redue fuel mpurtes whh an lmt the performane of the PEFC. pen-cathode fuel ells are ommonly operated wth a dead-ended hydrogen outlet; however under suh a onfguraton a nonsteady response s eted at medum and hgh urrents due to buld-up of water. In ths study the fuel ell stak was run n a through flow mode at the anode. The flow rate of hydrogen n the anode was kept onstant durng the erments wth a stohometry of. The hydrogen suppled was dry. The PEFC stak was operated at an ambent temperature of C and the hydrogen bak preure was held at 0.4 bar(g. A polarsaton urve was reorded pror to mpedane measurements as shown n Fg. 4.

12 EIS measurements were arred out through a #06 onateh frequeny response analyser (FA. EIS measurements were arred out at three dfferent urrent denstes and A/m of the polarsaton urve as shown n Fg. 4. The PEFC stak was run over 60 mnutes at the requred urrent wth no varaton n the voltage to ensure a steady state for EIS measurements. EIS measurements for urrent denstes < 0.875A/m were not poble as the low AC ampltude supermposed onto the DC urrent made t dffult for the FA to dstngush between nose and response. At hgh urrent denstes > A/m the fuel ell stak was not steady for a long perod of tme due to the hgh water onentraton produed by the. The frequeny san was performed from 0 kz down to 0. z wth a 5% AC ampltude of the DC urrent. It has been ommonly onsdered that the oxygen n the fuel ell an be eletrohemally redued dretly to water wthout the formaton of ntermedate spees. The hypothe that a -step s present durng fuel ell operaton s supported by the results from Inaba et al. [6]. The authors revealed that hydrogen peroxde an be formed by a two-eletron reduton pathway and exsts on Pt partles supported on arbon. After hydrogen peroxde s desorbed from the Pt surfae and dffuses away to the bulk of the soluton. If Pt/C atalysts are hghly agglomerated the moleules easly dffuse to nearby Pt/C partles where they are transformed to water by further two-eletron reduton (seres four-eletron reduton or -step. 5. Expermental Valdaton and esults EIS measurements are ommonly analysed by fttng an mpedane model wth ermental data. An nrease n the number of parameters n an equaton that represents the PEFC mpedane response may lead to nreased error n the resultng ftted values wth ermental EIS. A andles rut as reported by Malevh et al. [] was frst ftted to the measured EIS spetra usng Vew.9 software (Srbner Aoates In as shown n Fg. 5. The andles rut was ftted to the EIS measurements through a omplex nonlnear regreon method (Levenberg-Marquardt. Ths allowed the estmaton of Y P ohm and the parameters related to a n Eq. 38. Notng that the andles rut shown n Fg. 5a represents the eletral rut shown n Fg. wthout the parameters. and A φ whh are related to hydrogen peroxde reaton mehansms durng the

13 φ n Eq. 38 s a frequeny dependent parameter therefore t annot be reed as a retor n a ommeral software (e.g. vew. The parameters τ and the ones related to φ from Eq. 38 were estmated usng a Graph User Interfae (GUI developed n Matlab. The use of the GUI for EIS analy has already been demonstrated n the authors prevous study [8]. The parameters τ and from φ were ftted to the EIS measurements usng the GUI to reprodue the ndutve loop at low frequenes as shown n Fg. 6. The GUI allows the fttng of the parameters from Eq. 38 to aheve a good agreement between the ermental and smulated data. The parameter was realulated to aount for the harge transfer retane of oxygen onsumpton durng a two-step. The least squares fttng method was used n order to fnd the best-ft between the model and the measured data. A good qualty ft s obtaned when the sum of the devatons squared (least square error between the smulated and measured mpedane data has a mnmum value for nstane <0.. The parameters of Eq. 38 extrated from the measured EIS data are shown n Table I. Fgure 6 shows that wth the parameters gven n Table I the theoretal model s apable of smulatng the mpedane response of the PEFC stak. The results show good agreement between the measured and smulated data n the Nyqust plot. oy et al. [4] developed an mpedane model to aount for formaton of hydrogen peroxde durng the. The model was ompared wth ermental results and the results show that hydrogen peroxde formaton mehansms ould aount for the ermentally observed low-frequeny ndutve loops n EIS measurements. The omparson between smulated and measured data n the urrent study shows a better agreement than the omparson between smulated and measured data reported by oy et al. [4]. ne of the reasons of fndng a better agreement n ths study s the fat that a onstant phase element whh aounts for nonhomogeneous harge dstrbuton n the atalyst layer was onsdered n the modellng approah. Dfferent to the modellng approah by oy et al. [4] where an deal apator whh represents homogenous harge dstrbuton n the atalyst layer was onsdered. Fg. 6 shows that the dameter of the spetrum dereases from a urrent densty of m to 0.35 A/m and nreases from a urrent densty of 0.35 A/m to A/m. Smlar results were reported by Yuan et al. [9] when EIS measurements were arred out n a 500 sx-ell PEFC stak. Ther results showed that the mpedane spetrum dereased wth nreasng urrent up to 80 amperes and beyond 80 amperes the mpedane spetrum nreased agan. Pagann et al. [0] reported that when the knets of the domnates the ell performane suh as n the low urrent densty range of the polarsaton urve the mpedane spetrum manly

14 represents the harge transfer effet durng the and ts dameter dereases wth nreasng urrent densty. At hgh urrents the nrease n dameter of the spetra wth nreasng urrent densty an be attrbuted to an nrease n oxygen transport lmtatons [9]. ne of the dsadvantages of the EIS tehnque s that multple energy ontrolled proees durng the eletrohemal reaton an be masked n the mpedane plot. The harge transfer retanes related to oxygen reduton and hydrogen peroxde reaton derease when urrent densty s nreased from m to 0.35 A/m as shown n Tab.. The oxygen harge transfer retane s smaller than the hydrogen peroxde harge transfer retane. Tafel slopes related to a two-step wth hydrogen peroxde formaton have been reported n the lterature. The apparent Tafel slope related to oxygen onsumpton to form hydrogen peroxde has been reported to be greater than the apparent Tafel slope related to the hydrogen peroxde onsumpton to form water [4]. A hgh value of apparent Tafel slope (V - dereases the value of the harge transfer retane. Tab. shows that the harge transfer retane of hydrogen peroxde reaton nreases wth nreasng urrent densty from 0.35 A/m to A/m. Ths nrease an be a result due to the fat that Eq. 38 does not take nto aount the varaton of hydrogen peroxde onentraton at the reaton stes. In ths study the surfae onentraton of hydrogen peroxde was onsdered onstant to faltate the mathematal treatment. The nrease of hydrogen peroxde harge transfer retane an be related to a hange of the value of b Tafel slope wth nreasng urrent densty when dffuson effet s present. Further work s requred to develop an analytal reon that onsders dffuson of hydrogen peroxde n EIS measurements as a funton of ell potental. A further valdaton of the mathematal model aganst the modulus and phase angle of the frequeny response of the measured data was arred out. Fgs. 7 8 show the omparson between measured and smulated data n Bode format. Fg. 7 shows that the model s able to reprodue the Bode modulus for all the frequenes. Fg. 8 shows a dsrepany n the phase angle between measured and smulated data at the hghest frequenes ( > 5 kz. razem and Trbollet [] reported n ther study that the Bode modulus and real part omponent of the mpedane plots are relatvely nsenstve to the qualty of the ft of a model to mpedane data. The magnary omponent of the mpedane and Bode phase angle plots are modestly senstve to ft qualty. The on retane n the CCL has been represented n EIS measurements [3] as a 45 o regon at hgh frequenes. At hgh frequenes (Fg. 6 t s learly shown that the 45 straght lne represents the on retane of the atalyst layer. The dsrepany between the measured data and smulated data n phase angle at hgh frequenes

15 (5-0 kz shown n Fg. 8 an be related to the fat that the on retane n the CCL was not onsdered n Eq. 38. A property from EIS measurements s that as the frequeny reahes a value of zero the operatng ondtons of the fuel ell must onverge to steady state ondtons [3]. Ths means that a retve value (no frequeny dependene for the mpedane response s eted as the frequeny reahes zero. Ths retve value s named polarsaton retane and s related to the slope of the E-I (polarsaton urve [4]. oy et al. [4] reported that the presene of sde reatons (e.g. hydrogen peroxde formaton has lttle nfluene on polarsaton urves as these reatons take plae a low rate ompared to and. Also the authors onluded that EIS measurements are more senstve than polarsaton urves wth the sde reatons present. A further study for EIS measurements n a PEFC wth low rate of sde reatons (no ndutve loop and ndung sde reatons (ndutve loop should be arred out. Ths s to study the relaton between polarsaton retane and the mpedane response at frequenes near 0 z for both ondtons. 6. Dsuon The eletral urrent durng a smple eletron-transfer takes part n the harge transfer and smultaneously takes part n the onsumpton of oxygen durng the. Ths proe an be represented through the andles rut where the farada mpedane onts of the harge transfer retane onneted n seres wth the ma transport retane (arburg element []. Durng a two-step eletron transfer the sum of the reatons hydrogen peroxde formaton and water formaton n the two-step yelds the reaton aountng for formaton of water wthout any ntermedates. The resultng eletral rut that aounts for formaton of hydrogen peroxde durng the an be represented through a parallel eletr rut onfguraton between the two-step mehansms as shown n Fg.. In the study of oy et al. [4] eletral ruts were developed to aount for adsorbed spees durng a two-step n whh the mpedane related to the frst step of the s n parallel wth the mpedane related to the seond step of the. agner and Gülzow [5] reported an eletral rut onfguraton to aount for a PEFC durng posonng of the anode wth C n whh the anode harge transfer retane s onneted n parallel wth a relaxaton mpedane desrbng the surfae relaxaton of the eletrode-eletrolyte nterfae. Ther study reported ndutve loops at low frequenes related to C posonng n PEFC eletrodes. gh purty hydrogen ( % was used durng these ermental tests therefore the nfluene of C on EIS measurements an be ruled out n ths work.

16 The harge transfer retane for anode a was one order of magntude le than the harge transfer retanes and related to as shown n Table. Ths demonstrates that the takng plae n the anode s a faster and a le omplated reaton sequene than the n the athode. Commonly t has been aumed durng the analy of EIS measurements that there s no ontrbuton of the anode mpedane to the ell mpedane []. owever t s hghly reommended to onsder the anode mpedane durng the fttng proe of EIS measurements f a referene eletrode s not used wthn the ermental system. Ths would avod unertanly n the resultng data. The value of harge transfer retane ourrng durng the frst step n the (oxygen onsumpton was smaller than the value of the harge transfer retane durng the seond step n the (hydrogen peroxde onsumpton. ydrogen roover from anode to athode has been reported as the mehansm responsble for the formaton of hydrogen peroxde [4]. The model predted that when the harge transfer retane related to hydrogen peroxde reaton the harge transfer retane and ma transport retane durng the seond-step s greater than the sum of durng the frst-step an ndutve loop an be seen at low frequenes of the mpedane spetrum. Ths relaton > was valdated wth ermental measurements as shown n Tab and therefore demonstrates that the knet mehansms durng onsumpton of hydrogen peroxde to form water an be the domnatng proe for loes n the PEFC ompared wth the mehansms durng oxygen reduton. ne of the dsadvantages of the EIS tehnque s that the tme onstants related to the dfferent eletrohemal proees are overlapped n the omplex-mpedane plot [6]. The nrease n oxygen onentraton lmtatons durng the frst step of the an be a result of the ntermedate spees adsorbed onto the eletrode surfae whh redue the number of atve stes n the CCL for oxygen to reat. From Table I t an be demonstrated that the tme onstant proe τ whh relates to the reaton of hydrogen peroxde durng the seond step of the s greater than the tme onstant for oxygen to dffuse through the CCL T. Ths an be demonstrated n the EIS omplex plot where the ndutve loop related to hydrogen peroxde formaton mehansms are present at the lowest frequenes. The proe responsble for the ndutve haratersts at low frequenes has been attrbuted to hydrogen roover through the PEM [5] to form hydrogen peroxde at the athode. ydrogen roover from anode to

17 athode through onventonal graphte for bpolar plates due to ther porous nature ould also be a responsble proe for hydrogen peroxde formaton and ndutve loops n EIS measurements. Fg. 6 shows a slght dfferene n the shape of the ndutve loop from ermental data ompared to the smulated data. Ths dfferene ould reveal that durng fuel ell operaton not only hydrogen peroxde formaton s present but also other eletrohemal mehansms that an ause fuel ell degradaton. It has been proposed [4] that platnum doluton ould also be represented as an ndutve loop at low frequenes. Therefore the results shown n Fg. 6 an lead to the development of a future mpedane model whh ombnes hydrogen peroxde formaton wth platnum doluton. 7. Conlusons An mpedane model based on hydrogen peroxde formaton durng the has been developed to haraterse EIS measurements of PEFCs featurng ndutve loops at low frequenes. The urrent study begns by defnng the eletrohemal equatons representng the rate of harge transfer durng hydrogen peroxde formaton n a two-step. Modellng onsderatons based on EIS theory were taken nto aount to smplfy the mathematal treatment. The equatons defnng the eletrohemal mehansms durng the two-step were transformed from the tme doman to the frequeny doman to smulate the frequeny response of the PEFC and thus the low frequeny ndutve loop. The theoretal treatment s valdated aganst the measured EIS response of an open-athode PEFC stak. The results show that the model an predt the ermental mpedane response presentng an ndutve loop at low frequenes attrbuted to mehansms of hydrogen peroxde reaton. The results also show that eletrohemal mehansms related to the reaton of hydrogen peroxde durng the an lmt the PEFC performane. Ths study ould ast wth other ermental studes to dentfy hydrogen peroxde formaton durng the whh lmt the performane of PEFCs. Aknowledgements The authors thank the Mexan Natonal Counl for Sene and Tehnology (CNACYT for the sponsorshp of the Ph.D researh study of S. Cruz-Manzo (Grant No Appendx A Dard et al. [3] desrbed some examples of the mehansms represented by a two-step eletron transfer reaton wth an adsorbed ntermedate spees suh as athod produton of hydrogen:

18 e (A ads ads e (A eatons A and A an be represented as: K rea tan t e adsorbate (A3 Kr ( rea tant adsorbate e produt K (A4 K r The net urrent for reatons (A3 and (A4 an be reed as: { K o θ K ( θ } FΓ (A5 r { K o ( θ K θ } FΓ (A6 r wth K k ( α FE T and K k ( α FE T oj oj oj / j rj rj rj / where F s the Faraday onstant Γ s the number of eletrosorpton stes per unt area of eletrode surfae and θ s the overage of the eletrode surfae by the adsorbate. The onentraton of the hemal spees s onsdered onstant and s ntrodued nto the rate onstants. At equlbrum ondtons 0 the exhange urrent denstes are defned as: * o eq * r ( q eq 0 FΓK q FΓK (A7 * o * ( qeq F Krq eq 0 FΓK Γ (A8 wth K * k ( α FE T and K k ( α FE T * oj oj oj eq / j rj rj rj eq / Appendx B The steady-state value s alulated from Eq. 4 wth d / dt 0 and gvng: ( ( 0 η 0 ( b η ( b 0 (B Arrangng Eq. B for gves: 0 ( ( b η 0 0 ( ( b η ( b η (B The total urrent for reatons ( and ( n steady-state onsderng Eq. 3 and an be reed as:

19 ( ( (B3 0 ( b η ( b η 0 Substtutng Eq. B nto Eq. B3 yelds: 0 ( 0 ( ( b η 0 ( b η ( b η 0 ( b η (B4 Eqs. (B and (B4 an be reed n terms of steady-state urrents: (B5 (B6 wth 0 0 ( ( b η ( b η Epelbon and Keddam [5] reported a smlar relaton for the total urrent and fratonal surfae overage of hydrogen peroxde at steady-state. Lst of Symbols b apparent tafel slope V Ca double layer apatane n anode F/m oxygen onentraton at the eletrode surfae mol/m 3 eq oxygen onentraton at equlbrum mol/m 3 oxygen onentraton at the CCL-PEM nterfae mol/m 3 * oxygen onentraton at equlbrum ondtons mol/m 3 D F j effetve dffuson oeffent m /se faraday onstant C/mol magnary omponent n mpedane urrent densty A/m 0 exhange urrent densty A/m steady-state urrent densty A/m

20 k P devaton of varable n the steady-state. A/m rate onstant of reaton parameter related to apatane (onstant phase element a harge transfer retane durng Ω.m harge transfer retane Ω.m ohm total ohm retane PEM GDL Plate Ω.m retane for the dffuson proe Ω.m s T t ω laplae doman tme onstant for the dffuson proe se tme se angular frequeny rad/se Y parameter related to apatane ( a mpedane of anode Ω.m mpedane of athode Ω.m mpedane of PEFC Ω.m PEFC arburg mpedane Ω.m se P / Ω. m real part of mpedane magnary part of mpedane Greek β maxmum surfae overage by hydrogen peroxde mol / m fratonal surfae overage of hydrogen peroxde dmensonle fratonal surfae overage of hydrogen peroxde at equlbrum ondtons dmensonle surfae overage at steady-state dmensonle devaton of varable n the steady-state dmensonle δ η fnte dffuson dstane of oxygen transport from CCL-GDL to CCL-PEM nterfae m overpotental n the CCL V

21 η devaton of varable η n the steady-state η V η steady-state overpotental V eferenes [] S. Cruz-Manzo and. Chen J. Eletroanal. Chem (03. [] N. V. Dale M. D. Mann. Salehfar A. M. Dhrde and T. an ASME J. Fuel Cell 7 ( /-0300/0 [3]. Makhara M. F. Mathas and D.. Baker J. Eletrohem. So. 5 A970 (005. [4] S. K. oy M. E. razem and B. Trbollet J. Eletrohem. So. 54 B378 (007. [5] J. Xe D. L. ood III K. L. More P. Atanaov and. L. Borup J. Eletrohem. So. 5 A0 (005. [6] M. Inaba. Yamada J. Tokunaga and A. Tasaka Eletrohem. Sold-State Lett. 7 A474 (004. [7] A. Damjanov and V. Brus Eletrohm. Ata 65 (967. [8] S. K. oy and M. E. razem ECS Trans. 3( 03 (006. [9] Vjay A. Sethuraman John. edner Andrew T. aug Sathya Motupally and Lesa V. Protsalo J. Eletrohem. So. 55 (008 B50-B57 [0] M. Ekerlng A.A. Kornyshev J. Eletroanal. Chem. 453 ( [] D. Malevh E. allop B. A. Peppley J. G. Pharoah K. Karan J. Eletrohem. So. 56 (009 B6-B4. [] N. Fouquet C. Doulet C. Noullant G. Dauphn-Tanguy B. uld-bouamama J. Power Soures 59 ( [3] J.-P. Dard B. Le Gorre and C. Montella J. Eletroanal. Chem (99. [4] I. Epelbon M. Keddam and J. C. Lestrade Faraday Dsu. Chem. So (973. [5] I. Epelbon and M. Keddam J. Eletrohem. So (970. [6] Ekerlng M. and Kornyshev A. A. J Eletroanal. Chem. 475 (999 pp [7] C.. su and F. Mansfeld Corroson 57 ( [8] S. Cruz-Manzo and. Chen J. Eletrohem. So. 60 (03 F09- F5 [9] Yuan X. Sun J. C. Blano S. ang. hang J. and lknson D. P. J. Power Soures 6 (006 pp [0] Pagann V. A. lvera C. L. F. Tanell E. A. Sprnger T. E. and Gonzalez E.. Eletrohm. Ata 43 ( [] razem M. and Trbollet B. Eletrohemal Impedane Spetrosopy ley New Jersey (008. [] S. Cruz-Manzo. Chen and P. ama Journal of Fuel Cell Sene and Tehnology 9 ( [3] G. Maranzana J. Manka. Lottn J. Dllet A. Lambra A. Thomas and S.Dderjean Eletrohm. Ata 83 ( [4] N. agner J. of Appl. Eletrohem. 3 ( [5] N. agner and E. Gülzow J. Power Soures 7 34 (004. [6] S.Cruz-Manzo. Chen and P. ama Int. J. ydrogen Energy 38 (

22 Fgures Fgure. Eletral rut representng eletrohemal mehansms n the reaton wth hydrogen peroxde formaton Fgure. Eletral rut representng the PEFC Fgure 3. Effet of harge transfer retane of hydrogen peroxde reaton on mpedane spetrum a > b <

23 Fgure 4 Polarsaton urve for open-athode stak Fg. 5 Comparson between ermental and smulated data a andles rut b fttng result Fgure 6. Comparson between ermental and smulated data from Eq. 38

24 Fgure 7. Comparson n Bode format (modulus between measured and smulated data Fgure 8. Comparson n Bode format (phase between measured and smulated data