Loughborough University Institutional Repository A generi eletrial iruit for performane analysis of the fuel ell athode atalyst layer through eletrohemial impedane spetrosopy This item was submitted to Loughborough University's Institutional Repository by the/an author. itation: RUZ-MANZ,. and HEN, R., 013. A generi eletrial iruit for performane analysis of the fuel ell athode atalyst layer through eletrohemial impedane spetrosopy. Journal of Eletroanalytial hemistry, 694, pp.45-55. Metadata Reord: https://dspae.lboro.a.uk/134/15609 Version: ubmitted for publiation ublisher: Elsevier Rights: This work is made available aording to the onditions of the reative ommons Attribution-Nonommerial-NoDerivatives 4.0 International ( BY-N-ND 4.0) liene. Full details of this liene are available at: https://reativeommons.org/lienses/by-n-nd/4.0/ lease ite the published version.
A Generi Eletrial iruit for erformane Analysis of the Fuel ell athode atalyst Layer through Eletrohemial Impedane petrosopy amuel ruz-manzo and Rui hen Department of Aeronautial and Automotive Engineering, Loughborough University, UK orrespondene author s urrent ontat information: rofessor Rui hen Department of Aeronautial and Automotive Engineering Loughborough University Loughborough, Leiestershire, LE11 3TU, UK Tel: +44(0)1509-755 Fax: +44(0)1509-775 e-mail: R.hen@lboro.a.uk
Abstrat In this study, a generi eletrial iruit is presented to haraterise the frequeny response of the olymer Eletrolyte Fuel ell (EF) athode atalyst Layer (L) at different urrent densities. The new eletrial iruit is derived from fundamental eletrohemial and diffusion theory. It onsists of a transmission line in ombination with distributed arburg elements. The validation of this study is divided into a theoretial validation and an experimental validation. In the theoretial validation the impedane response of the L generated from three different iruits reported in the literature was ompared with the simulated data from the generi eletrial iruit. In the experimental validation, Eletrohemial Impedane petrosopy (EI) measurements were arried out in an H /air EF and through a three-eletrode onfiguration in the measurement system and were ompared with the simulated data from the generi iruit. The results show that the generi iruit is able to aurately reprodue the measured data of the L at different urrent densities and is able to represent the eletrohemial and diffusion mehanisms of the L in the frequeny domain. It is possible to generate a deeper understanding of how and where the hemial energy that is released from the redox reation is being dissipated and retained within the real physial system. Keywords: Eletrohemial Impedane petrosopy, athode atalyst Layer, Equivalent iruit, Impedane Model, Eletrohemial Mehanisms. 1. Introdution Eletrohemial Impedane petrosopy (EI) is an experimental tehnique to measure the opposition to the flow of an Alternating urrent (A) within an eletrohemial system whih ontains elements that dissipate energy and store energy. The opposition to the A load, or impedane, an be measured over a range of frequenies, thereby revealing the frequeny response of the system. ne key advantage of the EI tehnique is that it is non-invasive and an be applied insitu. Another advantage is that the frequeny response tests are simple to arry out and an be easily tuned for greater aurately by using readily-available sinusoidal generators and preise measuring equipment. Frequeny response is often represented in a omplex-impedane-plane or Nyquist format.
The data are presented as a lous of points, where eah data orresponds to a different measurement frequeny. omplex-impedane-plane plots are very popular beause the lous of the points yields an insight into the possible mehanisms of governing phenomena. The frequeny response of a olymer Eletrolyte Fuel ell (EF) that results from EI is in essene haraterised by energy dissipating and energy storing elements of the ell. It an be represented by an equivalent eletrial iruit model that is omposed of resistors and apaitors respetively. By understanding the arrangement and magnitude of the resistive and apaitive elements in the equivalent iruit, it is possible to generate a deeper understanding of how and where the hemial energy that is released from the redox reation is being dissipated and retained within the real physial system. Different arrangements of eletrial iruits from simple omponents [1,,3,4] to more ompliated transmission line representations [5,6,7,8,9,10] have been reported in the literature to model and haraterise different proesses in a EF. Eah equivalent eletrial iruit an represent a speifi physial proess ourring in a EF. However the iruits are limited to a ertain range of operating urrents. The interpretation of the eletrohemial mehanisms whih are truly ourring in the EF using EI will only be possible through a generi but robust equivalent iruit design whih is derived from fundamental eletrohemial and diffusion theory. In this study, a generi equivalent eletrial iruit whih is apable of haraterising the impedane response of the athode atalyst Layer (L) operated at any urrent of the polarisation urve has been developed. This new equivalent iruit is derived from fundamental eletrohemial and diffusion theory. However, this new iruit has limitations in reproduing EI measurements in the positive imaginary part of the ompleximpedane-plane at low frequenies, whih normally aounted for poisoning or adsorbed speies in the atalyst Layer (L).. Available Equivalent iruits and Limitations The use of equivalent eletrial iruits with the experimental EI tehnique is a well-established methodology to haraterise proesses in the EF. Equivalent eletrial iruits to interpret the mehanisms related to the impedane response of an eletrohemial system have been used for over
thirty years [11]. An eletrial iruit an represent an idential impedane response to that obtained from the eletrohemial system studied. Eah eletrial omponent in the eletrial iruit desribes a physial proess that takes plae in the eletrohemial system. The most ommon eletrial omponents to represent the impedane response in an eletrohemial system are as follow: Resistor, this omponent represents energy losses, eletroni and ioni ondutane in solid and aqueous medium. This element does not depend upon the frequeny range applied. Indutane, this omponent relates a magneti field generated in eletrial ondutors of the measurement system and in the eletrodes of an eletrohemial system studied. apaitane, this omponent reflets the aumulation of eletrostati energy between two dissimilar materials. arburg, this element represents the opposition for diffusion of a hemial speie in a finite or semi-infinite planar medium in the frequeny domain. onstant hase Element (E), this element reflets the exponential distribution of time-onstants in an eletrode-eletrolyte interfae. Different arrangements of the eletrial omponents have been reported in the literature to model and haraterise other phenomenologial proesses in the EF. For instane, an eletrial iruit proposed by agner [1] represents the EF during normal operation and during poisoning in the anode eletrode. iureanu [1] proposed an eletrial iruit to study the performane of the anode eletrode of an H /H fed Fuel ell, this iruit also models the effet of poisoning and adsorbed speies in the L. Randles iruit. The equivalent iruit for EF impedane generated from EI analysis has typially been reported [3,13] to be based on Randles iruits whih are onneted in series with a resistane. Eah Randles iruit orresponds to an eletrode (anode or athode) while the resistane orresponds mainly to the polymer eletrolyte membrane (EM). In the ase of the eletrode, the
eletrial omponents of Randles iruit reflet; (i) a double-layer apaitane for the interfae between the dissimilar materials, i.e., the nafion/arbon interfae, and; (ii) a parallel resistane to harge transfer aross the same interfae, as shown in Fig.1a. The Randles iruit does not take into aount the ioni resistane in the L eletrolyte and reatant transport limitations; therefore it an only be applied at low urrents. Randles iruit with arburg element. At high urrents, the produt water formed in the L an begin to saturate the tortuous pathways of the porous network, whih then ats as a resistane to the mass transport of oxygen from the interfae with the Gas Diffusion Layer (GDL) to the atalyst sites in the L. A arburg element whih desribes resistane of diffusion of hemial speies through a finite diffusion medium at the frequeny domain and derived from Fik s seond law and Faraday s Law has been broadly used together with the Randles iruit onfiguration to aount for oxygen transport limitations at high urrents in EI measurements [,4] as shown in Fig. 1b. This onfiguration does not take into aount the ioni resistane in the L eletrolyte. Transmission line iruit (no oxygen transport limitations). Eikerling and Kornyshev [5] proposed an eletrial iruit using a transmission line to represent the impedane and to haraterise the porous L of EF s. This equivalent iruit onsists of an upper rail to aount for the ioni ondution, and a lower rail to represents the eletron aess in the L. In the upper rail distributed resistanes to aount for the ioni resistane in the L eletrolyte are onsidered. Usually the distributed eletron resistanes are negleted to simplify the mathematial analysis beause the resistane to ion transfer in the eletrolyte of the L is muh greater than the resistane to the eletron transfer in the arbon of the L by several orders of magnitude. Between the upper rail and lower rail parallel distributed resistanes and apaitanes to aount for the harge transfer proess and the apaitane effet between the nafion/arbon interfae are onsidered. These three elements are then repeated a finite number of times as shown in Fig. 1. The transmission line iruit reported by Eikerling and Kornyshev to haraterise the L operated at high urrents annot be used beause it does not aount for oxygen transport limitations in the L. At low urrents, this phenomenon does not our
beause the rate of water prodution is low and so does not appear as an equivalent eletrial omponent in the transmission line. 3. Fundamentals of L The atalyst layer is ommonly formed by a omposite struture of a matrix of arbon grains providing the eletron ondutivity, t supported on arbon as the atalyst, Teflon (TFE) as a binder stabilizing the arbon matrix and as a hydrophobizing agent, and eletrolyte network of perfluorosulfonate ionomer (FI) soaked with water. The arbon partiles typially support noble metal or noble metal alloy deposits (i.e., platinum t, platinum-ruthenium tru) with sizes in the range of -5 nm on its surfae to drive the eletrohemial reations forward at the operating temperatures of the EF. In addition, the atalyst layer ontains a dispersion of polymer eletrolyte to ensure ontinuity for ion ondution via the EM. The resulting matrix struture is porous in nature and haraterised by tortuous pathways for reatant transport. The matrix of arbon grains forms agglomerate strutures. The agglomerated struture of the atalyst layer presents a bi-funtional pore distribution. rimary pores are alled to the pores existing inside the agglomerates between the t/ partiles. It has been proposed that the moleules of the polymer eletrolyte do not penetrate into the t/ partiles [14]. Instead these moleules form a pathway of ion ondution attahed to the surfae of the agglomerated struture. eondary pores onstitute the void spaes between agglomerates. 3.1 xygen diffusion in the L There are three modes of transport of oxygen in the L whih an have an effet on mass transport limitations: gas-diffusion in the eletrode-pore, dissolved oxygen diffusion in the liquid water surrounding the agglomerate, and dissolved oxygen in the ionomer phase []. The finite diffusion distane for oxygen to reah the reation sites in the L forms a ompliated network of multi-phase parallel and serial paths [15].
The finite diffusion distane ould hange in dimension for different L omposition (e.g. nafion loading, porosity, tortuosity) and at different fuel ell operating onditions (urrent density, temperature, relative humidity, et.) [16]. The study of mass transport in the L is very omplex; the literature has treated it with some simplifiations and approximations [17]. 3. L erformane In the literature [18] the performane of the L has been desribed by the following system of equations: harge onservation: dl η j + = t x j o * η sinh b (1) Eq. 1 represents the urrent density j aross the thikness x of the L that an take in the harge transfer due to the oxygen redution reation (RR) or ontribute to the harge in the apaitive effet between the dissimilar materials, i.e., the nafion-arbon interfae; where j o represents the exhange urrent density, b is the Tafel slope, represents the loal oxygen onentration in the L, * is the equilibrium oxygen onentration, η is the L overpotential and is the double dl layer apaitane. hm s Law: η j = σ () x Eq. represents the potential in the eletrolyte network of the L where σ is the ondutivity of ions in the eletrolyti phase of the L. Mass onservation: t D x jo = zf * η sinh b (3)
Eq. 3 represents the oxygen transport through the L thikness x during the RR where D is the effetive oxygen diffusion, z the number of eletrons onsumed during the RR and F is the Faraday onstant. In the reent work of Kulykovsky [18] the above equations (Eqs. 1, and 3) were ombined to define the impedane response of the L. This resulted in ompliated mathematial equations, whih an only be solved numerially using mathematial software, and only approximate analytial solutions were reported. The author onluded that due to the thin L in EFs oxygen transport is usually good, therefore the resulting equation in the frequeny domain from the ombination of Eqs. 1, and 3 ould be simplified and used for fitting experimental EI; however no attempt was made to validate the resulting L impedane model with real-world EI measurements. It is worth mentioning that oxygen transport limitations in the L of EFs should not be onsidered as negligible beause it is suspeted that the L beomes flooded before the GDL beause water is generated in the L and transported into the GDL, and has a lower porosity and smaller pore size, and tends to have higher flooding levels than the GDL [19]. Eq. 3 does not aount for the oxygen diffusion on every single phase of the L material whih an have an effet on mass transport limitations. As mentioned previously the finite diffusion distane for oxygen to reah the atalyst sites forms a ompliated network of multi-phase parallel and serial paths and ould hange at different EF operation. A modelling approah to onsider oxygen transport through the L thikness as part of a multi-speies mixture using mass transport theory with onentrated solution theory [0] ould give a detailed haraterisation of the loal oxygen onentration through the thikness x of the L during the RR. Nevertheless the validation and appliation of the resulting equations with real-world EI measurements ould beome a hallenge. 4. Development of a Generi Equivalent iruit for L Analysis As reported by Brett et al. [1], the problem when hoosing an equivalent eletrial iruit is that must suit the bulk EI results when atually different parts in the EF frequeny response may be fit
to the equivalent iruit with very different parameters or may require a different equivalent iruit altogether. An improved generi iruit design whih is apable of interoperating variations in EF impedane harateristis is needed. The solution of the system of differential equations defining the physis of the L (Eq. 1, Eq., Eq. 3) an be simplified to simulate the L impedane response by transforming them in the frequeny domain and addressing onsiderations based on the theory of EI. 4.1 Modelling onsiderations based on EI The use of a low amplitude perturbation in the EI tehnique allows the use of a linear model to interpret the impedane response of the L from EI. EI measurements are arried out in EFs operated at steady state; therefore it is possible to relate the urrent density from Faraday s Law (oxygen onsumed in the RR) with diffusion flux from Fik s Law. EI only measures bulk parameters in the total L thikness and reflets a total mass transport resistane and a total finite diffusion distane for the three modes of oxygen transport in the L. In the mathematial treatment of this study, the finite diffusion distane y for oxygen to diffuse through the L will be onsidered to be independent from the thikness x of the L, as shown in Fig., to simulate the L impedane response. The hange in oxygen onentration in the L during the RR and represented in EI measurements will be onsidered from the L-GDL interfae *' at y=0 to the L-EM interfae ' at y=δ, as shown in Fig.. Even though this mathematial treatment results in an over-simplifiation of the oxygen diffusion in the total L this will simplify the mathematial analysis, and therefore the resulting model will present parameters ommonly known in the eletrohemial area suh as the arburg impedane [4] whih allows the haraterisation of the low frequeny semiirle of EI measurements aounted to oxygen transport limitations.
4. L erformane in the Frequeny Domain A new system of equations in the frequeny domain an be defined based on the modelling onsiderations addressed in setion 4.1 and EI theory as suh: harge onservation equation at frequeny domain. onsidering trigonometri identities in Eq. 1 yields: j = j x o * η η exp exp b b dl η t (4) Eq. 4 expresses the harge distribution in the L thikness x onsidering boundary onditions as L-EM interfae at x=0 and GDL-L at x=1 [18]. The mathematial treatment in this study will onsider the boundary onditions shown in Fig. as: GDL-L at x=0 and L-EM at x=1, therefore a hange in sign (positive) has to be onsidered on the right-hand side of Eq. 4. The first exponent on the right-hand side of Eq. 4 represents the RR and the seond exponent represents the reverse reation of the RR. Also when the overpotential η inreases during L operation the ontribution of the seond exponent beomes small, and therefore it an be negleted, as suh: j = x j o * η exp + b dl η t (5) EI tehnique allows the use of a linear equation to simulate impedane spetra. A linear model an be derived using the Taylor series expansion to Eq. 5, (Appendix A) as suh: j = x * η + R dl η t (6) where R represents the harge transfer resistane during the RR and is defined as R = b / j0 exp( η / b), η represents the ativation overpotential in L and represents the loal oxygen onentration in the L. This loal onentration will depend on the diffusion of oxygen through the multiphase parallel and serial paths in the L. To simplify the mathematial treatment, the ratio between oxygen onentration at the L-EM interfae and L-GDL interfae ' * defined in previous setion 4.1 is taking into aount in Eq. 6. This ratio between oxygen onentrations is onsidered from the fat that EI tehnique only measures the hange in oxygen /
onentration in the total L thikness. This mathematial treatment will allow the derivation of the arburg Impedane whih has been broadly used in the EI area [,4] to haraterise oxygen transport limitations during EF operation. The eletrohemial reation in the EF results in an inhomogeneous distribution of harge in the L. To orret for this inhomogeneity, a onstant phase element (E), Ys with s = iω, whih is defined in the frequeny domain has to be used in the Laplae transform s of Eq. 6 to replae the apaitor [], as suh: dl j ' = * x η R + Ys η (7) where s = iω is the frequeny domain defined from Laplae domain, ω is the angular frequeny, i is the imaginary omponent, ' is the oxygen onentration at the L-EM interfae, * is the equilibrium oxygen onentration at the GDL-L interfae in the frequeny domain, Y represents a parameter related to E, supersript represents a parameter to orret the inhomogeneity in the distribution of harge, x represents the thikness (dimensionless) of the L from x=0 L-GDL interfae to x=1 L-EM interfae. xygen Transport during the RR at frequeny domain. The onentration profile of hemial speies during a simple eletron-transfer reation x + e Re an be derived from the general theory of ontrolled-urrent methods [3]. This theory solves Fik s eond Law of diffusion and relates its solution with the flux of hemial speies and Faraday s Law to aount for the hange in onentration of hemial speies during an eletrohemial reation at a fixed urrent. The same proedure will be taken into aount for the derivation of the hange of oxygen onentration during the RR in the L. K The first term on the right-hand side of Eq. 7 represents the urrent at whih oxygen is onsumed during the RR in the frequeny domain: ' j1 η 1 = * x (8) R
From Faraday s Law it is possible to establish that the urrent density in the frequeny domain is proportional to the harge transferred and the onsumption of reatant: j 1 = zfv (9) x where z is the number of eletrons onsumed during the RR and F is the Faraday onstant. From Fik s First Law it is possible to establish that the flux of reatant is proportional to onentration gradient: v = D y ( y, s) (10) y=δ where D is the effetive diffusion oeffiient of oxygen and y is the finite distane for oxygen to diffuse in the L, as shown in Fig.. In steady state the urrent density at whih the oxygen is onsumed in the RR from Faraday s Law is equal to the diffusion flux from Fik s First Law [16]. ombining Eqs. 8, 9 and 10 yields: ( y s) ' η 1, = D * zfr y y= δ (11) EI measurements are arried out in EFs operated at steady state. At steady state the oxygen onentration is independent of time; hene the Fik s eond Law an be expressed in Laplae domain s, as suh: D y ( y, s) = s * ( y, s) (1) Eq. 1 represents the Fik s eond Law in the Laplae domain onsidering the initial ondition at * t=0 as ( y ) =, The solution of Eq. 1 through the method of undetermined oeffiients for a, 0 nonhomogeneous linear differential equation and onsidering boundary onditions from L-GDL * ' interfae ( 0, s) = to L-EM interfae ( δ, s) =, as shown in Fig., yields: * ( y, s) = * ' [ ] exp( λ1 y) exp( λ δ ) exp( λ δ ) 1 + ' * [ ] exp( λ y) exp( λ δ ) exp( λ δ ) 1 (13) where λ 1, = ± s / D. The ratio between oxygen onentration at the L-EM interfae and L- GDL interfae ' * / an be expressed as a funtion of mass transport resistane in the frequeny
domain and harge transfer resistane. Differentiating Eq. 13 with respet to y and substituting it into 1 = * * Eq. 11 and onsidering trigonometri identities, the Laplae form η ( s ) n1/ s and = s, and / replaing η by η RT / zf whih represents a linearized relation of the overpotential [3], where R 1 1 = is the ideal gas onstant and T is the operating temperature, yields : ' * R = R + Z (14) where ( st ) ( st ) 0. 5 0.5 tanh Z = R (15) is known as the arburg Impedane [,4] and represents the mass transport resistane in the frequeny domain and simulates the low frequeny semiirle in EI measurements of EFs, with R RTδ = (16) z F D * defined as resistane for the diffusion proess and δ T = (17) D defined as the time onstant to diffuse oxygen through the L. hmi Law at frequeny domain. The ion ondution in the L depends upon the eletrolyti dispersion and the state of hydration within the L. It is assumed that the resistane to the eletron flow in the eletrode network is smaller than the ioni resistane in the eletrolyte network. Therefore, eletroni ohmi loss in L an be regarded as being negligible [6,8,9]. The potential in the eletrolyte network an be expressed by hms law: η x ( s ) = R j (18) where R is the resistane to the flow of ions in the eletrolyti phase of the L.
4.3 urrent Density in Frequeny Domain ubstituting Eq. 14 into Eq. 7 yields: j x η = R + Z + Ys η (19) If Eq. 19 is substituted into Eq. 18 and onsidering the ativation overpotential η in R as a onstant due to R /R <<1 [6], (Appendix B), yields: j x R j = R p + Z + Ys j (0) Eq. 0 is a nd order homogeneous equation and represents the urrent distribution through the thikness of the L in the frequeny domain taking into aount mass transport resistane, eletrode kinetis, harge apaitane and ioni resistane in the L. Its solution an be obtained by applying the method of the nth-order homogeneous equation with onstant oeffiients: j 1 Aexp( γ x) + B exp( γ x) = (1) where 1 γ = ± Rp + Ys represents the distint roots of the harateristi equation 1, R + Z represented. Evaluating boundary onditions in Eq. 1, at the GDL-L x = 0 and j = 0, while at the L- EM interfae x = 1 and j = j urrent density in the frequeny domain, j j ( γ1x) ( γ ) 1 m, where j m represents the urrent density of the ell, gives the sinh = () m sinh 4.4 verpotential in Frequeny Domain The overpotential in the frequeny domain an be obtained by arranging Eq. 7 as: R + Z j ( ) η s = (3) 1+ Ys ( R + Z ) x
Differentiating Eq. with respet to x and substituting into Eq. 3 gives the overpotential in the frequeny domain η [ R + Z ] jm γ 1 osh( γ 1x) 1+ Ys [ R + Z ] sinh γ = (4) { } ( ) 1 4.5 Impedane Model of L The impedane of the L is defined as the ratio between the overpotential, Eq. 4, and the urrent, Eq. at frequeny domain with s = iω. Z L η = j ( iω) ( iω) = [ R + Z ] γ 1 oth( γ 1 ) 1+ Y ( iω) [ R + Z ] (5) ith 1 ( ) γ = 1 Rp R + Z + Y iω Eq. 5 represents the opposition to the flow of an alternating urrent A within the L whih ontains physial proesses that dissipate energy and store energy. The opposition to the A load, or impedane, an be measured over a range of frequenies, thereby revealing the frequeny response of the L. By understanding the magnitude of the eletrohemial and oxygen transport mehanisms represented in Eq. 5, it is possible to generate a deeper understanding of how and where the hemial energy that is released from the redox reation is being dissipated and retained within the L. For the speifi ase where Z is onsidered to be negligible either due to a high diffusion oeffiient or high equilibrium oxygen onentration, Eq. 5 will represent the impedane response of the L with equilibrium boundary onditions in terms of oxygen onentration. These onditions an our for low urrent operation and as suh, Eq. 5 redues to the equation representing a transmission line equivalent iruit as reported by Makharia et al. [6]. The solution of Eq. 5 over a range of frequenies will ontain real and imaginary omponents, whih an be presented on a Nyquist plot. Eq. 5 an be represented through the impedane of the eletrial iruit shown in Fig. 3. The four elements represented in Fig. 3 are repeated k N a finite number of times, where k represents a olletion of arbon-supported atalyti agglomerates oated by a thin layer of polymer eletrolyte. Eq. 5 represents the impedane of the generi iruit onsidering k N parameters.
5. Model Validation In this study the validation of the impedane spetrum generated from the generi iruit (Eq. 5) is divided into a theoretial validation and an experimental validation. In the theoretial validation the impedane spetrum generated from the generi eletrial iruit proposed in this study is validated against the L impedane response generated from three different eletrial iruits ommonly used in the literature. In the experimental validation the impedane spetrum generated from the generi iruit is ompared with measured impedane data of an H /air EF operated at 8mA/m and 0.1 A/m. 5.1 Theoretial validation Equivalent iruits negleting oxygen transport limitations. The impedane response of a H /air EF was investigated by iureanu and Roberge [3]. The authors used a Randles eletrial iruit as shown in Fig. 1a to haraterise the L impedane response at low urrents. This eletrial iruit aounts just for the harge transfer resistane during the RR and does not aount for ioni resistane in the L eletrolyte and oxygen transport limitations. The parameters from the Randles iruit as reported by iureanu suh as harge transfer resistane R =0.4148 Ω.m, and E derived from the apaitane =0.3950 F/m were substituted into Eq. 5. The ioni resistane R was onsidered with a small order of magnitude 10-9 to be regarded as being negligible. The arburg impedane Z was onsidered as being negligible Z = 0 in Eq. 5. These two elements do not appear in the Randles onfiguration. The results in Fig. 4a show a good agreement between simulated spetrum using Eq. 5 and the measured data from the Randles iruit. Makharia et al. [6] estimated the ioni resistane in the L for a 5 m EF (H - ) operated at low urrent with MEA 0.8 and 0.4 Nafion/arbon (N/) ratio through impedane measurements. The ioni resistane R =0.103Ω.m, harge transfer resistane R =0.783Ω.m and apaitane =0mF.m - of the L were estimated by fitting the experimental EF spetrum to the equivalent eletrial iruit type transmission line as shown in Fig. 1 using Zview software (Transmission Line-
pen iruit Terminus, DX-Type 6, ribner Assoiates, In., version.3). This eletrial iruit does not aount for oxygen transport limitations in the L. The parameters of the transmission line were substituted into Eq. 5 to simulate the experimental impedane spetrum with no mass transport effet Z = 0 as reported by Makharia et al. and as shown in Fig.4b. A 45 o region representing the ioni resistane in the L at high frequeny is presented and has been estimated by projeting the 45 o region onto the real part Z and alulated as R / 3. The diameter of the semiirle is related to the harge transfer resistane during the RR. Equivalent iruit onsidering oxygen transport limitations. The parameters of the Randles iruit and arburg element to haraterise the impedane response of L operated at high urrents were reported by Fouquet et al. [4]. This eletrial iruit does not aount for the ioni resistane in the L eletrolyte. This eletrial iruit an fit the low frequeny semiirle in the impedane spetrum whih normally aounted for mass transport limitations beause of the shortage of the oxygen supplied during fuel ell operation. The harge transfer resistane R =0.008Ω, E with Y =1.109 /Ω, and arburg element with R =0.0034Ω, T =0.087se were substituted in Eq. 5. The ioni resistane R was onsidered with a small order of magnitude 10-9 in Eq. 5 to be regarded as being negligible. The results show a good agreement between simulated spetrum using Eq. 5 and the generate data from the Randles-arburg iruit, as shown in Fig. 5. The diameter of the semiirle at high frequenies is related to the harge transfer resistane during RR. The semiirle at low frequenies is related to gas phase oxygen transport limitations in the L-GDL interfae. 5. Experimental validation Experimental. A 5 m ommerially-available fuel ell and test rig aquired from Balti Fuel ells were used for the experimental tests. The MEA onsisted of a atalyst oated membrane Duont Nafion-115 with a platinum loading of 0.4mg/m and arbon blak for the eletrodes. The thikness of the L is 1µm. The ontat pressure on the ative ell area was adjusted through a pneumati air ylinder from the Balti Fuel ell ompression unit. The ontat pressure on the ative area was fixed
to 1.4 N/mm. The operational temperature was 50 o and the bak gas pressure was held to 0.9 bar(g) for both the anode and athode. Flow rates were held onstant during all the experiments, hydrogen to the anode was supplied at a stoihiometry of and air to the athode supplied at a stoihiometry of.5. The EF was operated with 98% hydrogen relative humidity (RH) in the anode and 55% RH in the athode. EI measurements were arried out through a olartron 180 eletrohemial interfae and a olartron 180 frequeny response analyser as shown in Fig. 6. EI measurements were arried out at two different urrent densities 0.008 and 0.1 A/m. The frequeny san was performed from 0 khz down to 0.1 Hz, with an alternating voltage signal and 10 mv amplitude. To separate the impedane spetrum of the athode from the impedane spetrum of the ell, a referene eletrode made of a platinum wire was inserted suh that it was in diret ontat with the membrane of the athode side. Under suh onditions, the signals are measured between the working eletrode (E) and the referene eletrode (RE), and the urrent indued is olleted by the ounter eletrode (E). Measured athode Impedane Response. In these experimental results the use of a referene eletrode in the measurement system ensures that the data aounting for the proesses in the athode are aptured for analysis and interpretation. The resulting impedane is ommonly shown in a omplex plane and represents the eletrohemial and diffusion mehanisms of the EF in the frequeny domain. Fig. 7 shows the measured impedane response of the athode obtained through a three-eletrode onfiguration in the measurement system. The diameter of the spetrum dereases with inreasing urrent density from 0.008 A/m to 0.1 A/m. At 0.008 A/m the kinetis of the RR dominates the athode performane and the impedane spetrum mainly represents the harge transfer effet during the RR. At 0.1 A/m the diameter of the spetrum dereases due to an inrease in the driving fore for the interfaial oxygen redution proess [4]. At urrent density of 0.1 A/m the presene of an overlapped seond semiirle at low frequenies demonstrates that oxygen transport limitations beomes a limiting fator in the EF performane [3,4], as shown in Fig. 7a. xygen transport limitations are mainly attributed to high water onentration during the RR whih ats as a resistane for oxygen to permeate through the GDL and L. The hypothesis
that there is an inrease in water onentration in these EI results is supported by the fat that at 0.1 A/m there is a derease in ohmi resistane in the EM. This effet is shown in Fig. 7b where the impedane spetra interept the real omponent Z in the omplex plot [3] at high frequenies. The measured data with positive imaginary omponents at high frequenies as shown in Fig. 7b are related to the indutane of the eletrial ables of the measurement system [5]. Validation at 8 ma/m. The produt of water formed in the L an begin to saturate the tortuous pathways of the porous network, whih then ats as a resistane to the mass transport of oxygen from the interfae with GDL to the atalyst sites in the L. At low urrents, this phenomenon does not our beause the rate of water prodution is low; therefore the mass transport resistane (arburg impedane) is onsidered as being negligible Z = 0 in Eq. 5, and the generi iruit shown in Fig. 3 aounted to the L takes the form as the iruit reported by Eikerling and Kornyshev [5] as shown in Fig. 1. The generi iruit that represents the L with Z = 0 is onneted in series with an indutor element and a resistor as shown in Fig. 8 to simulate the athode impedane response negleting oxygen transport limitations and obtained through a three-eletrode onfiguration in the measurement system. Therefore the impedane response of the athode negleting oxygen transport limitations and obtained from a three eletrode onfiguration an be represented as: Z athode = L ( iω) oth( γ 1 ) ( iω) R Rγ + Re + 1 (6) 1+ Y where L represents the indutane in the eletrial ables of the measurement system, R e represents the total ohmi resistane to flow eletrons and ions in the bipolar plate, GDL and EM and the third term on the right-hand side represents the L impedane (Eq. 5) negleting oxygen transport limitations Z = 0. The iruit shown in Fig. 8 was fitted to the measured impedane response at 8mA/m using Zview software (Transmission Line-pen iruit Terminus, DX-type 6, ribner Assoiates, In., version 3.0). The parameters of the transmission line extrated from the measured data are shown in Table I. The parameters from Table I were substituted into Eq. 6 to simulate the athode impedane response at 8mA/m. Figure 9 shows that with the parameters given in Table I,
the theoretial model is apable of simulating the frequeny response of the athode impedane. The results show a good agreement between the measured and simulated data in the omplex plot with an exeption at the highest frequenies (EI measurements with positive imaginary omponents Z ), as shown in Fig. 9. EI measurements with positive imaginary omponents at the high frequeny end of the spetrum have been mainly attributed to the indutane of the eletrial ables of the measurement system [5]. In a previous study [6] it was demonstrated that the property of ausality in the Kramers-Kroning mathematial relations for EI measurements is violated by the external indutane of the measurement ables. Also it was demonstrated that the indutane of the measurement system deforms the high frequeny region of the impedane spetrum and as a result it is possible to draw an inorret onlusion about the eletrohemial mehanisms at high frequenies by visual inspetion, e.g. ohmi resistane. Therefore it is possible to onlude that the measured data with positive imaginary omponents do not represent the physis and hemistry of the athode. A 45 region at high frequenies is shown in Fig. 9b. This has been assoiated with the ioni resistane R in the L eletrolyte [6,7]. The semiirle of the spetrum is related to the harge transfer resistane R during the RR and harge apaitane between dissimilar materials, i.e. nafion-arbon interfae. Validation at 0.1 A/m. At high urrents, the produt water formed in the L an begin to saturate the tortuous pathways of the porous network, whih then ats as a resistane to the mass transport of oxygen from the interfae with the GDL to the atalyst sites in the L. Under suh onditions the eletrial iruit shown in Fig. 3 is onneted in series with an indutor element and a resistor as shown in Fig. 10 to simulate the athode impedane response onsidering oxygen transport limitations and obtained through a three-eletrode onfiguration in the measurement system. The impedane response of the athode onsidering oxygen transport limitations and obtained from a three eletrode onfiguration an be represented as: Z athode = L ( iω) + R + e [ R + Z ] γ oth( γ 1 ) 1+ Y ( iω) [ R + Z ] 1 (7) where the third term represents the impedane equation of the L derived in setion 4.5 (Eq. 5). ome ommerial software (Zview, ZMAN, et.) fit experimental impedane data by using nonlinear
regression strategies suh as Levenberg-Marquardt, Gauss-Newton Method, et., and with the use of available equivalent eletrial iruits (Fig 1a-). However this tehnique strongly requires some parameters of the eletrial iruit to be defined as initial values in order to ahieve the best-fit. The simulated data from the iruit shown in Fig. 10 were ompared with the athode measured data at 0.1 A/m using a graphial user interfae (GUI) developed in Matlab, as shown in Fig. 11. The GUI allows the fitting of the parameters from Eq. 7 to ahieve a good agreement between the experimental and simulated data. The least-squares fitting method was used in order to find the best fit between the model and the measured data. A good quality fit is obtained when the sum of the deviations squared (least-square error) between the simulated and measured impedane data as a minimum value, for example <0.1. The GUI developed for EI analysis relies on the mathematial model of this study whih is based on fundamental eletrode and diffusion theory. The eletrohemial and diffusion parameters defined in the model are related to one another in whih ounterating interdependenies are aounted for, for instane, by hanging the ioni resistane at high frequeny, the values of the impedane spetrum at low frequeny will be hanged. Eq. 7 was fitted to the measured data at 0.1 A/m and the results are shown in Table II. The measured data with positive imaginary omponents are mainly attributed to the indutane of the measurement system as disussed in a previous study [6]. In the EI results shown in Fig. 1b a 45 region an be notieable in the high frequeny region of the spetrum. This linear region has been assoiated with the ioni resistane in the L eletrolyte [6,7]. The impedane results of Fig. 1 reflet the overlapping of two semiirles. ne at high-medium frequenies is related to the harge transfer resistane during the RR, and the other at low frequenies is related to gas phase oxygen transport limitations in the L-GDL interfae [7]. It has been proposed [15] that improving one property of the L an adversely affet another. For instane, by inreasing the amount of the eletrolyte between the agglomerates, the ioni ondutivity an be enhaned but also loses void spaes for reatant transport. This effet ould also be refleted in the impedane response of the L at high and low frequenies.
6. Disussion The eletrohemial and diffusion mehanisms in the L hange during fuel ell operation. The use of equivalent eletrial iruits with the experimental EI tehnique is a well-established methodology to haraterise proesses in the L. However the iruits reported in the literature are limited to a ertain range of operating urrent densities and do not represent the eletrohemial and diffusion proesses whih are truly ourring in the L. For example the ioni resistane in the L has been ommonly estimated in EI measurements using the transmission line iruit during L operation at low urrents. However the ioni resistane in the L is also dependent on the hydrated state and water onentration of the L at high urrents. If the ioni resistane in the L eletrolyte (straight line in the L spetrum at high frequeny) is redued by inreasing Nafion loading and water onentration, an inrease in oxygen transport limitations (low frequeny semiirle in the L spetrum) is expeted. This study has demonstrated that the eletrohemial and diffusion mehanisms of the L in the frequeny domain an be simulated through a newlydeveloped equivalent iruit. This eletrial iruit was derived from fundamental eletrohemistry and diffusion theories. This new iruit has limitations in reproduing EI measurements in the positive imaginary part of the omplex-impedane-plane at low frequenies, whih normally aounted for poisoning or adsorbed speies in the L. This is the aim of a future work. 7. onlusions A generi eletrial iruit based on fundamental eletrode and diffusion theory has been developed to haraterise the impedane response of the L at different urrent densities. The urrent study begins by defining the equations of the L performane in the frequeny domain from EI suh as harge onservation, oxygen onentration during the RR and potential in the L eletrolyte network. Modelling onsiderations based on EI theory were taking into aount to simplify the mathematial treatment in this study. EI reflets only bulk measurements on the total L thikness, therefore the finite diffusion distane and surfae onentration of oxygen in the L are onsidered to be independent from the thikness of the L. This approah simplifies the mathematial treatment to predit the impedane response of the L, and as result it an be suessfully validated against
real-world EI measurements. The resulting theoretial model is validated against the impedane response generated from three eletrial iruits reported in the literature. Also the theoretial model is validated against the measured EI response of an H /air EF. The results show that the model an predit the impedane response of the L at different urrent densities of the polarisation urve. The model has established a wider sope to relate the measured eletrohemial impedane data to the fundamental theory of EFs. Aknowledgments The authors thank the Mexian National ounil for iene and Tehnology (NAYT) for the sponsorship of the h.d researh study of. ruz-manzo (grant no. 183195). Appendix A olution of Linear Equations approximated by the Taylor eries Expansion d dt η = f ( η, j) (A-1) Expanding the seond term of Eq. A-1 whih ontains the nonlinear term in Taylor series up to its first derivative form, gives: f ( η, j) f ( η, j ) + ( η η ) + ( j j ) (A-) f η n, j f j η, j Given that the expansion is arried out around a steady state ( η, ), Eq. (A-1) an be expressed as d η f ( η, j ) = 0. (A-3) dt = ine η is a onstant, the left side of Eq. (A-1]) an be expressed as dη dt d( η η ) dη = = (A-4) dt dt j where η = η η represents the deviation of variable η in the steady state η. The linear equation an be defined as: dη dt f f = + (A-5) η η, j η j η, j j
Appendix B harge transfer resistane R = b / j0 exp( η / b) overpotential in the eletrolyte dη = R j dx R R dη j0 exp( η / b = eparating variables R bj exp( η / b) dη = dx dx bj R j ) Integrating with limits at x=0 L-GDL interfae η =η 0, and at x=1 L-EM interfae η =η 1. 0 η 1 R bj b exp( η / b) dη = dx yields R j η 0 1 0 0 R j exp( η / b) = exp( η / b) 0 for j > j 1 0 R j 0 if R / R 1 therefore η η 0 1 but if R /R << 1 therefore the variation is small η η and 0 η an be onsidered onstant along x. 1 List of ymbols b tafel slope, mv loal oxygen onentration through the L, 3 mol / m ' oxygen onentration at the L-EM interfae, 3 mol / m * oxygen onentration at the GDL-L interfae, 3 mol / m dl apaitane between dissimilar materials, F / m D effetive diffusion oeffiient, m / seg i F j o faraday onstant, 96485 /mol imaginary omponent in impedane exhange urrent density, A / m j m maximum rate of ion transfer, A / m j urrent distribution in atalyst layer, A / m L R indutane of the measurement ables, H parameter related to E (onstant phase element) ideal gas onstant, 8314.3 Joule/mol.K
R harge transfer resistane, Ω.m R e total ohmi resistane, EM, GDL, late, Ω.m R M mass transfer resistane, Ω.m R R s T T t ioni resistane in athode atalyst layer, resistane for the diffusion proess, laplae domain temperature, K Ω.m time onstant for the diffusion proess, seg time, seg Ω.m v flux of the oxygen through the L, mol. m s ω angular frequeny, rad/se x distane along the atalyst layer, 0 x 1 Y parameter related to E (onstant phase element), / Ω. m Z L impedane of athode atalyst layer, Z arburg impedane, Ω.m Ω.m z ' Z '' Z eletrons onsumed real part of impedane imaginary part of impedane Greek σ δ η ioni ondutivity in the L finite diffusion distane of oxygen transport from L-GDL to L-EM interfae, m overpotential in the L, V η Linearised overpotential in atalyst layer, V η steady state overpotential, V
Figure aptions Figure 1 a) Randles iruit for low urrent operation, b) Randles-arburg iruit for high urrent operation, ) Transmission line iruit for low urrent operation Figure xygen transport in the L Figure 3 Generi iruit for the L haraterisation
Figure 4 omparison between iruits onsidering no oxygen transport limitations ( ) and Generi iruit (-), a) Randles, b) Transmission line Figure 5 omparison between Randles-arburg iruit ( ) and Generi iruit (-) Figure 6 Experimental et-up Figure 7 Measured athode Impedane Response, b) high frequeny region
Figure 8 Generi iruit aounting for the athode negleting mass transport limitations Figure 9 omparison between simulated (-) and measured ( ) data at 0.008 A/m, b) high frequeny region Figure 10 Generi iruit aounting for the athode onsidering oxygen transport limitations
Figure 11 Graphial User Interfae for EI validation Figure 1 omparison between simulated (-) and measured ( ) data at 0.1 A/m, b) high frequeny region
Referenes [1] N. agner, E. Gülzow, J. ower oures 17 (004) 341-347. [] D. Malevih, E. Halliop, B. A. eppley, J. G. haroah, K. Karan, J. Eletrohem. o. 156 (009) B16-B4. [3] M. iureanu, R. Roberge, J. hys. hem. B 105 (001) 3531-3539. [4] N. Fouquet,. Doulet,. Nouillant, G. Dauphin-Tanguy, B. uld-bouamama, J. ower oures 159 (006) 905-913. [5] M. Eikerling, A. A. Kornyshev, J. Eletroanal. hem. 475 (1999) 107-13. [6] R. Makharia, M. F. Mathias, D. R. Baker, J. Eletrohem. o. 15 (005) A970-A977. [7] M.. Lefebvre, R. B. Martin,. G. ikup, Eletrohem. olid-tate Lett. (1999) 59-61. [8] T. uzuki, H. Murata, T. Hatanaka, Y. Morimoto, R&D Review of Toyota, Toyota entral R&D Labs, In. 39 ( 003) 33-38. [9] J. Hou,. ong, H. Yu, Y. Fu, L. Hao, Z. hao, B. Yi, J. ower oures 176 (008) 118-11. [10] G. Li,. G. ikup, J. Eletrohem. o. 150 (003) 745-75. [11] N. A. Hampson,. A. G. R. Karunathilaka, R. Leek, J. of Appl. Eletrohem. 10 (1980) 3-11. [1] M. iureanu, H. ang, J. New Mat. Eletrohem. ystems 3 (000) 107-119. [13] N. agner, J. Appl. Eletrohem. 3 (00) 859-863. [14] K. Malek, M. Eikerling, Q. ang, T. Navessin, Z. Liu, J. hys. hem. 111 (007) 1367-13634. [15] M. Eikerling, A. A. Kornyshev, J. Eletroanal hem. 453 (1998) 89-106 [16] J. Zhang, EM Fuel ell Eletroatalysts and atalysts Layers, pringer, London, 008. [17]. Berger, Handbook of Fuel ell Tehnology, rentie-hall, In. / Englewood liffs, N.J., New York, 1968. [18] A.A.Kulikovsky, J. Eletroanal. hem, 669 (01) 8-34. [19] G. Lin,. He, T. V. Nguyen, J. Eletrohem. o. 151 (004) A1999-A006. [0]. Rama, R. hen, AME J. Fuel ell i. Tehnol. 7 (010) 051007 05103. [1] D. J. L. Brett,. Atkins, N.. Brando, V. Vesovi, N. Vasileiadis, A. Kuernaka, Eletrohem. olid-tate Lett. 6 (003) A63-A66. []. H. Hsu and F. Mansfeld, orrosion 57 (001) 747-748. [3] A. J. Bard, and L. R Faulkner, Eletrohemial Methods, John iley & ons, In., New York, (001). [4] V. A. aganin,. L. F. liveira, E. A. Tiianelli, T. E. pringer and E. R. Gonzalez, Eletrohim. Ata 43, (1998) 3761-3766. [5]. Mérida, D. A. Harrington, J. M. Le anut, G. MLean, J. ower oures 161 (006) 64-74. [6]. ruz-manzo, R. hen and. Rama, J. Fuel ell iene Tehnology, 9 (01) 05100 [7]. ruz-manzo, R. hen and. Rama, Int. J. Hydrogen Energy (01) http://dx.doi.org/10.1016/j.ijhydene.01.08.141