Calculation of reversible electrode heats in the proton exchange membrane fuel cell from calorimetric measurements

Calculation of reversible electrode heats in the proton exchange membrane fuel cell from calorimetric measurements
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  See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/232363892 Calculation of reversible electrode heats in theproton exchange membrane fuel cell fromcalorimetric measurements  ARTICLE   in  ELECTROCHIMICA ACTA · MARCH 2011 Impact Factor: 4.5 · DOI: 10.1016/j.electacta.2011.01.034 CITATIONS 11 READS 74 5 AUTHORS , INCLUDING:O.s. BurheimSør-Trøndelag University College 20   PUBLICATIONS   254   CITATIONS   SEE PROFILE Signe KjelstrupNorwegian University of Science and Techn… 319   PUBLICATIONS   3,738   CITATIONS   SEE PROFILE J.G. PharoahQueen's University 90   PUBLICATIONS   1,212   CITATIONS   SEE PROFILE Preben J. S. VieInstitute for Energy Technology 22   PUBLICATIONS   450   CITATIONS   SEE PROFILE All in-text references underlined in blue are linked to publications on ResearchGate,letting you access and read them immediately.Available from: Signe KjelstrupRetrieved on: 05 February 2016  This article appeared in a journal published by Elsevier. The attachedcopy is furnished to the author for internal non-commercial researchand education use, including for instruction at the authors institutionand sharing with colleagues.Other uses, including reproduction and distribution, or selling orlicensing copies, or posting to personal, institutional or third partywebsites are prohibited.In most cases authors are permitted to post their version of thearticle (e.g. in Word or Tex form) to their personal website orinstitutional repository. Authors requiring further informationregarding Elsevier’s archiving and manuscript policies areencouraged to visit:http://www.elsevier.com/copyright  Author's personal copy Electrochimica Acta 56 (2011) 3248–3257 Contents lists available at ScienceDirect ElectrochimicaActa  journal homepage: www.elsevier.com/locate/electacta Calculation of reversible electrode heats in the proton exchange membranefuel cell from calorimetric measurements Odne Burheim, Signe Kjelstrup ∗ , J.G. Pharoah, Preben J.S. Vie, Steffen Møller-Holst Department of Chemistry, Norwegian University of Science and Technology - NTNU, N-7491 Trondheim, Norway a r t i c l e i n f o  Article history: Received 29 October 2010Received in revised form 7 January 2011Accepted 8 January 2011 Available online 22 January 2011 Keywords: Thermal effectsReaction entropyHeat sourcesPeltier heatsPEM fuel cellsCalorimeter a b s t r a c t A calorimeter was used to measure the heat production in polymer electrolyte membrane (PEM) fuelcells operated on hydrogen and oxygen at 50 ◦ C and 1bar. Two cells were examined, one using a 35  mthick Nafion membrane and a catalyst loading of 0.6/0.4mgPtcm − 2 , for the cathode and anode layer,respectively, the other using a 180  m thick Nafion membrane and loading of 0.4/0.4mgPtcm − 2 . Thecellsinvestigatedthushaddifferentmembranesandcatalystlayers,butidenticalporoustransportlayersand micro-porous layers. The calorimeter is unique in that it provides the heat fluxes out of the cell,separately for the anode and the cathode sides. The corresponding cell potential differences, ohmic cellresistance and current densities are also reported. The heat fluxes through the current collector plateswere decomposed by a thermal model to give the contributions from the ohmic and the Tafel heats tothe total heat fluxes. Thus, the contributions from the reversible heat (the Peltier heats) to the currentcollectors were determined. The analysis suggests that the Peltier heat of the anode of these fuel cellmaterials is small, and that it is the cathode reaction which generates the main fraction of the totalheat in a PEM fuel cell. The entropy change of the anode reaction appears to be close to zero, while thecorresponding value for the cathode is near − 80JK − 1 mol − 1 . © 2011 Elsevier Ltd. All rights reserved. 1. Introduction Theenergythatisdissipatedasheatinfuelcellsisinterestingforseveral reasons. It provides key information for design of auxiliarysystem components; in particular the cooling system. Increasedknowledge about the dissipated energy can also help explain itssrcin [1], thereby enabling efforts to mitigate and minimize theselosses.Theseissuesarenowreceivingincreasedattention[2,3],andmotivatedtheconstructionofcalorimetersandthemeasurementsof the thermal signature of low temperature proton exchangemembrane (PEM) fuel cells [4,5]. In the present work the aim isto use the calorimeter to determine the asymmetry in the heatproduction, and the srcins of the reversible heat contributions.The total reversible heat production corresponds to the reactionentropy. The local contributions are known as the Peltier heats of the electrodes, as described by non-equilibrium thermodynamics[6,7].The long term motivation of this work is to facilitate the calcu-lation of not only the temperature profile across the cell, but alsothe electric potential profile. This requires information about massdiffusivities of reactants and products, thermal conductivities andohmic resistances of the various materials, interfacial resistances ∗ Corresponding author. E-mail address:  signe.kjelstrup@chem.ntnu.no (S. Kjelstrup). between cell layers and, finally, the Peltier heats of the individualelectrodes. This work should be seen as an effort to obtain someoftherequireddataandtherebyenhancetheunderstandingoftheprocesses taking place in the PEM fuel cell.The srcin of the single electrode reaction entropy for PEMfuel cells is discussed in several studies [8–15] but no directmeasurements are reported for a PEM fuel cell. The first anal-ysis of this thermodynamic entity in fuel cells was made by Jacobsen et al. [16] studying molten carbonate cell electrodesand later by Kjelstrup et al. [17], studying the oxygen electrodewith solid oxide electrolyte. The magnitude of the total reactionentropy for a hydrogen/oxygen fuel cell producing liquid wateris well known ( − 82JK − 1 mol − 1 at standard conditions). The sin-gle electrode reversible heat is given by the electrode temperaturemultipliedbythedifferenceintheentropyenteringandleavingtheelectrode; see [6] for a derivation. The Peltier heats can give rise toa local increase or decrease in the anode and cathode electrodetemperaturesandcontributetothermalgradients[1],see[6,7]and referencesthereinformoreexamples.Inthispaperwereportmea-surements that give further insight into the local entropy changesin PEM fuel cells.The outline of the paper is as follows. We present the thermo-dynamic basis for the energy dissipation assessment in Section 2.The apparatus description and the procedures to measure the heatfluxes and to deconvolute the experiments are provided in Section3. The results are presented and discussed in Section 4. 0013-4686/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2011.01.034  Author's personal copy O. Burheim et al. / Electrochimica Acta 56 (2011) 3248–3257  3249 2. Thermodynamic basis The efficient energy conversion taking place in fuel cells is to asubstantial degree dictated by the thermodynamics. The conven-tionalmodellingapproachtakenintheliteratureistoconsideronlytheworkfromafuelcell,whileignoring,ortreatingtheenergydis-sipated as heat in an ad hoc manner. In some situations, empiricalrelationships are used, rather than fundamental equations basedon thermodynamic properties. This limits the possibility to assessthe sources of dissipation and the ability to further improve effi-ciency and system performance. In this section the PEM fuel cellreactions are initially revisited, followed by a recapitulation of thethermodynamicrelationshipsofthecell.Finally,thereversibleheatcontributions, and in particular the Peltier heats of the individualelectrodes and how these may be determined, are described.  2.1. The fuel cell reaction The electrochemical reaction in the PEM fuel cell is well known(Eqs. (1)–(3)). At the operating conditions in question (50 ◦ C andreacting gases saturated with water vapour at 1bar) hydrogen andoxygenisconsumedandliquidwaterisformed.Inaddition,thereiselectro-osmotic transport of water from the anode to the cathodeside corresponding to the transference number (electro-osmoticdrag coefficient)  t  w , leading to an additional term in Eqs. (1)–(3).Thisisrelatedtothehydratedprotonstransportedacrossthemem-brane.Whilethistermislessimportantfortheelectricwork,itmaybe significant for the local heat production. The cathode reactionreads:14O 2(g) + H + + e + t  w H 2 O (l) ⇄  12  + t  w   H 2 O (l)  (1)We assume that this half reaction dominates at the chosenexperimental conditions. The anode half cell reaction is:12H 2(g) + t  w H  2 O (l) ⇄ H + + e + t  w H  2 O (l)  (2)The overall cell reaction is thus12H 2 + 14O 2 + t  w H 2 O ( l ) ⇄  12  + t  w  H 2 O (l)  (3)  2.2. Overall analysis of work and heat in the fuel cell The fuel cell is an open system, which exchanges heat, massand work with the surroundings. The first law of thermodynamicsunder reversible conditions reads: U   = TS −  pV   − nFE  rev  (4)and for a given pressure,  p , and temperature,  T  , we have G = H  − TS =− nFE  rev  (5)where  U  ,  S  ,  V  ,  G and  H  arethechangesininternalenergy,entropy, volume, Gibbs energy and enthalpy, respectively. The gaspressure,  p , and the temperature of the fuel cell,  T  , are those of thefuelcellsurroundings,i.e.gaschannelandthecurrentcollectorplates.Theelectricpotentialmeasuredunderreversibleconditionsis E  rev , F  isFaraday’sconstantand n isthenumberofmolesofelec-trons transferred in the cell reaction (Eq. (3)), here  n = 1.  The ratio  H/F= − E  tn  is called the thermo-neutral potential.Under reversible conditions, heat added to the cell defines itsentropy change. In this fuel cell,  S   is negative and relatively large(water is formed in the liquid state and gas molecules are con-sumed, cf. Eq. (3)). Therefore, a large positive heat is delivered tothe surroundings, in this study constituted by the calorimeter. Thetheoretical value of   E  rev  is 1.23V at  T  =298K when water is in theliquid state and the reactant gases are at 1bar [18]. The negative Fig. 1.  Thermodynamic properties (to the left) and the corresponding cell poten-tialsandpotentiallossesoccurringinthefuelcell(totheright).Thethermo-neutralpotential (right),  E  tn , is represented by the negative reaction enthalpy (left), −  H  .Partofthisenergyisneededtocompensatefortheentropychangeatagiventemper-ature, − T   S  ,leavinguswiththemaximumavailablework, −  G (left),representedbythereversiblepotential, E  rev .Atnon-reversibleconditions,thecellpotential, E  cell ,isequaltothereversiblepotentialminustheohmicpotentiallosses, Rj ,andtheTafelpotential losses,   . reaction entropy contributes  − 0.25V and  E  tn = −  H/nF= 1.48V at T  =298K (see Eq. (9)). Accordingly, even at low current densitiesthe relative heat production in the cell is substantial.At non-reversible conditions, when there is a net electric cur-rentflowingthroughthecell,theentropyproductionofthesystemplus near surroundings is no longer zero. There is now more heatdelivered to the calorimeter than that equivalent to − T   S  . This isreflectedinthepolarizationcurveofthecell,wherethecellpoten-tial E  cell isplottedasafunctionofcurrentdensity  j .Thecellpotentialis E  cell  = E  rev −  − Rj  (6)The two last terms on the right hand side give the part of the potential electrical work,  E  rev , that is now dissipated as heat.The symbol    represents the sum of the electrode overpotentialswhich is dominated by the cathode [19]. The overpotential can bedescribed by the Butler–Volmer or Tafel equation. The last termis the ohmic potential loss, with  R  as the total resistance, and  j  asthe current density, measured here per geometric cross-sectionalcellarea.Inthisstudy,experimentalconditionsareusedthatmini-mizemasstransfer-limitationsintheelectrodes,meaningthat  toa good approximation is equal to the reaction overpotential of thecathodeTherelationsbetweenthesewellknownthermodynamicprop-erties and the electrochemical entities are illustrated in Fig. 1.By multiplying Eq. (6) by the current density and introducingEq. (5) solved for  E  rev , the specific cell power is obtained: P   = E  cell  j = TS − H nF  j − j − Rj 2 (7)We can now identify the heat delivered to the calorimeter perunit of time and area; Q  FC   =− TSnF  j + j + Rj 2 (8)Thefirsttermrepresentsthereversiblecontributionandthetwolast terms are irreversible energy dissipation terms. P  FC   + Q  FC   =− H nF  j = E  tn  j  (9)The thermoneutral power of the cell is the hypothetical powercorresponding to the reaction enthalpy.  Author's personal copy 3250  O. Burheim et al. / Electrochimica Acta 56 (2011) 3248–3257  Fig.2.  The upper sketch depicts a cross section of the calorimeter carrying the fuel cell, the lower sketch depicts the model geometry (also shown inFig. 3) while the middleismeanttoillustrateandlinktheupperandlowersketchestogether.Potentialdifferences, E  1  and E  2 ,andthefuelcellpotential, E  cell ,werecontinuouslymeasured,alongwiththe four temperatures,  T   j,i .  A  denotes anode,  C   denotes cathode,  i  means inside and  o  means outside. The two inner temperatures controlled the individual electric heaters atthe two electrodes. Gases were fed to the cell through the sides (see arrows), and left the cell along the central axis, after passing the gas flow channels.  2.3. The reversible heat of the fuel cell electrodes According to non-equilibrium thermodynamics, the entropy of thecellreactioniscomposedofthePeltierheatsofthecathode,  C ,minusthatoftheanode,  A  [6]whenthetemperatureinthecellisuniform: TS =   A −  C   (10)Thereactionentropyisnegativeforthereactionconsideredhere(Eq. (3), Section 2.1). The Peltier heats can be positive or negative. Each Peltier heat results from a reversible entropy balance of theelectrode, see [6,7], as the heat added to the electrode in order to keep its temperature unaltered. In the present case, we obtain forthe anode and cathode reactions (2) and (1) per mole electronstransferred, respectively:   A T   =− 12 S H 2  + S ∗ H +  − t  w S w  (11)  C T   = 14 S O 2  − 12 S w + S ∗ H +  − t  w S w  (12)Intheseequations S  i denotesthepartialmolarentropyofspecies i  associated with the electrode reactions.There is reversible heat transported into the membrane on theanode side with the proton (the transported entropy  S ∗ H + ). At theanodeside,thesimultaneoustransportofwaterintothemembraneliberates heat corresponding to  t  w S  w . Removal of reactant hydro-gengasliberatesasimilarheatterm.Fromtheexpression(Eq.(11)),it seems likely that the Peltier heat of the anode is small or nega-tivebecausethewaterandhydrogenentropiesarelarge.Thewatertransferencenumber(electro-osmoticdragcoefficient) t  w  isafunc-tionofthemembranestate,itswatercontentandtemperature,andisthusdifficulttoquantify.Alsothewaterentropyinthemembraneis not known. It is thus difficult to predict the sign of the PEM fuelcell Peltier heats based solely on Eqs. (11), (12) and tabulated data. 3. Experimental The calorimeter and auxiliaries used in this study are describedin Section 3.1. In Section 3.2, the procedure to measure the elec- tric work and heat fluxes through the anode and cathode currentcollectors is assessed. The procedure to deconvolute the measure-ments into the Peltier heats of the electrodes, i.e., the location of the reversible heat production, is presented in Section 3.3.  3.1. Apparatus The calorimeter was designed to measure the heat productionin a PEM fuel cell and is thoroughly described in [5]. The calorime-ter, illustrated in the upper part of  Fig. 2, is additionally equippedto measure the cell potential and the total cell electric resistance.Thecalorimeterwasconstructedasacylinderwithinsulatedwalls(including an additional layer of expanded polyester, not depictedin Fig. 2 for improved readability); such that heat is transportedin the axial directions. A special feature of this calorimeter is thecapability of separately measuring the heats leaving through theanode and the cathode current collectors.The calorimeter, by design, maintains a constant temper-ature gradient between the current collectors and the outer
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