The Seebeck coefficient and the Peltier effect in a polymer electrolyte membrane cell with two hydrogen electrodes

Electrochimica Acta 99 (2013) 166–175

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The Seebeck coefficient and the Peltier effect in a polymer electrolyte membrane cell with two hydrogen electrodes S. Kjelstrup a,b,∗ , P.J.S. Vie c , L. Akyalcin d , P. Zefaniya a , J.G. Pharoah e,f , O.S. Burheim a,g a

Department of Chemistry, Norwegian University of Science and Technology, N-7491 Trondheim, Norway Department of Process and Energy, Delft University of Technology, Leeghwaterstraat 44, 2628 CA Delft, The Netherlands c IFE - Institute for Energy Technology, Kjeller, N-2007 Lillestrøm, Norway d Department of Chemical Engineering, Anadolu University, Iki Eylul Campus, 26555 Eskisehir, Turkey e Queen’s-RMC Fuel Cell Research Centre, 945 Princess Street, 2nd floor, Kingston, ON K7L 5L9, Canada f Mechanical and Materials Engineering, Queen’s University, Kingston, ON K7L 3N6, Canada g Wetsus - Centre of Excellence for Sustainable Water Technology, Agora 1, 8900 CC Leeuwarden, The Netherlands b

a r t i c l e

i n f o

Article history: Received 8 November 2012 Received in revised form 5 March 2013 Accepted 9 March 2013 Available online 19 March 2013 Keywords: Seebeck coefficient Peltier heat Temperature profiles Hydrogen–hydrogen PEM cell Thermal effects

a b s t r a c t We report that the Seebeck coefficient of a Nafion membrane cell with hydrogen electrodes saturated with water vapour, at 1 bar hydrogen pressure and 340 K, is equal to 670 ± 50 ␮V/K, meaning that the entropy change of the anode reaction at reversible conditions (67 J/(K mol)) corresponds to a reversible heat release of 22 kJ/mol. The transported entropy of protons across the membrane at Soret equilibrium was estimated from this value to 1 ± 5 J/(K mol). The results were supported by the expected variation in the Seebeck coefficient with the hydrogen pressure. We report also the temperature difference of the electrodes, when passing electric current through the cell, and find that the anode is heated (a Peltier heat effect), giving qualitative support to the result for the Seebeck coefficient. The Seebeck and Peltier effects are related by non-equilibrium thermodynamics theory, and the Peltier heat of the cathode in the fuel cell is calculated for steady state conditions to 6 ± 2 kJ/mol at 340 K. The division of the reversible heat release between the anode and the cathode, can be expected to vary with the current density, as the magnitude of the current density can have a big impact on water transport and water concentration profile. © 2013 Elsevier Ltd. All rights reserved.

1. Introduction The heat production in fuel cells consists of a reversible part (the cell’s entropy change times the temperature) and an irreversible part (the energy dissipated as heat). The sum provides information that is important for design of auxiliary systems; in particular cooling systems. Knowledge of the dissipated energy can help locate causes of power losses in the cell [1]. This may give us a possibility to mitigate or reduce them. It is therefore important to understand both parts. The heat production in the polymer electrolyte fuel cell (PEMFC) has received increased attention among modellers the last ten years. This is well summarized by Bapat and Thynell [2], Ramousse

∗ Corresponding author at: Department of Chemistry, Norwegian University of Science and Technology, N-7491 Trondheim, Norway. Tel.: +47 735 50870; fax: +47 735 50877. E-mail addresses: [email protected], [email protected] (S. Kjelstrup). 0013-4686/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.electacta.2013.03.045

et al. [3], Das and Bansode [4] and Zhang and Kandlikar [5]. The single electrode reaction entropy, that is relevant for the reversible heat production at electrodes, is discussed [3,6–13]. We are not aware of any experimental results with hydrogen electrodes and the Nafion membrane as electrolyte, but values for the standard electrode where hydrogen is consumed has been reported [6,14]. The values differ widely, from −66.6 J/(K mol) (obtained from half cell potentials and assumptions of the single entropies) for a 1 molal acid solution [6], to −87.6 J/(K mol) from calorimetry at varying current densities at standard conditions [14]. For the alkaline fuel cell, a value near zero was obtained [7]. Using calorimetry on a disc-shaped fuel cell, we measured the heat flux out of the anode current collector separate from the flux out of the cathode current collector [15,16]. The heat flux on the anode side differed significantly from the heat flux on the cathode side in these experiments. It was concluded, that a small part of the reversible heat in the cell evolved at the anode at current densities of 0.2–0.8 A/cm2 . The aim of this work is to shed further light on these results, contributing to the understanding of thermal management in the PEM fuel cell.

S. Kjelstrup et al. / Electrochimica Acta 99 (2013) 166–175

0

a

PTL

sa

m

Membrane

sc

c

167

l

PTL

Fig. 1. A cross section of a the cell is illustrated, showing the five characteristic layers and the notation used throughout the paper.

We shall use a cell with two hydrogen electrodes and a polymer electrolyte membrane, the Nafion membrane. The hydrogen–hydrogen cell was used by Meland et al. [17,18] and Malevich et al. [19–21] for impedance studies. The hydrogen–hydrogen cell has also been used to elucidate proton transport [22] and water transport in the anode of the fuel cell [23]. The use of this cell, gives the best opportunity to study the reversible electrode heats in the anode of the PEMFC without disturbances from irreversible effects (i.e. oxygen reduction reaction kinetics). The advantage is that one can obtain directly the reversible hydrogen electrode heat effect from the experiments. The effect at the oxygen electrode can then be computed from knowledge of the hydrogen electrode and the overall entropy change in the cell. This shall be done here. The reversible heat produced by the hydrogen electrode, can be obtained from electromotive force (emf) measurements when the H2 (g)||H2 (g) polymer electrolyte cell is exposed to a temperature gradient (a Seebeck coefficient measurement), or by finding the local heat effect by applying an electric current (a Peltier experiment). We shall report theoretical and experimental studies of the Seebeck and Peltier coefficients. Such studies are documented in the literature of non-equilibrium thermodynamics, for an overview see e.g. [24]. Early theoretical and experimental analyses of these properties for fuel cells were carried out by Jacobsen et al. [25] for carbonate reversible electrodes and molten carbonate electrolyte, and by Kjelstrup et al. [26] for oxygen electrodes and yttrium stabilized zirconia electrolyte. The single electrode reversible heat, or the Peltier heat, is given by the electrode temperature multiplied by the difference in the entropy entering and leaving the electrode [27]. The Peltier heat can give rise to a local increase or decrease in the electrode temperature [28–31], and contributes therefore to thermal gradients, see [1,27,24,29] and references therein. The outline of the paper is as follows. We describe the system in Section 2, give the thermodynamic basis and the theory for the Seebeck and the Peltier effects in Section 3. The two experimental set-ups and the procedures are described in Section 4. The Seebeck coefficient measurements are first presented. We next report on the temperature profile between the electrodes when an electric current is passing the cell. The results are presented and discussed in Section 5. 2. The polymer electrolyte cell with hydrogen electrodes For the analysis of the experiments to be reported, we consider a cylindrical cell, with half cells mirror symmetric around the centre plane given by the polymer electrolyte membrane. There are five subsystems; the anode backing (a), the two catalyst layers (sa and sc), the membrane (m), and the cathode backing (c), but the two backings and the catalyst layers are identical. An illustration of the cell is given in Fig. 1. The figure labels the left and right electrode backings by (a) and (c). These backings consist of a Porous Transport

Fig. 2. Notation used for transport across interfaces. A position is indicated by two superscripts, say i, o, where the first symbol (i) denotes the layer (or phase) and the second denoted the nearest layer (o). A difference between two positions is indicated by two subscripts, say i, o, for , meaning that the difference should be taken between states o and i.

Layer (PTL) coated with a micro porous layer (MPL) of carbon (not indicated in the figure). The membrane (m) that separates the electrode compartments, is a Nafion membrane for transport of protons and water. The electrode regions are denoted sa and sc, respectively. Platinum wires are connected to the catalytic layers, and we measure the emf between two Cu-wires, attached to the Pt wires. The Pt–Cu contacts are at the temperature of the room. The positions of the current collector plates on the two sides are at positions 0 and 1 at the beginning and end of the graphite backings. We shall apply a potential difference between the current collectors and measure the corresponding electric current. With standard electrochemical notation, the cell is: (C,Pt)H2 (pa , T a )|H2 O(paw , T a )|m|H2 (pc , T c ), H2 O(pcw , T c )|(Pt,C) When current is passing the cell, water is carried along with the charge carriers, the protons. This is called electro-osmosis. When the sides of the membrane are kept at different temperatures, water can also be transported by thermal osmosis [32]. The water phase is continuous through the system. Both transport phenomena give contributions to the electric potential, as we shall see. These contributions to the cell potential are normally small, but thermal osmosis can give a significant contribution to the heat flux, as we shall see. We are therefore in need of a systematic description of these interacting phenomena. The theory connecting these effects is non-equilibrium thermodynamics. By using this systematic theory, one obeys the proper symmetry of effects and as well as criteria given by the second law. The expressions show how that the nature of the electrolyte has an impact on the single electrode heat. The analysis using non-equilibrium thermodynamics for heterogeneous systems was explained in detail, see Chapter 19 of Kjelstrup and Bedeaux [24], and we follow their procedure and notation. Symbols are further explained in Fig. 2. In this figure i and o denote separate phases, meaning a, m or c, while s is the electrode (catalyst) region (sa or sc), cf. Fig. 1. A position in the ophase next to the i-phase is given by superscript o, i. The difference between the value on the i-side and the o-side is given by i,o , etc. The membrane is a homogeneous phase, thanks to the presence of water. The backings a and c contain a porous graphite phase (for electron conduction), which we deal with separate from the gas filled, homogeneous pores. The electrode regions are course grained in this analysis, where they are considered as two-dimensional subsystems. This simplifies matter. The finer structure of these regions will be integrated

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out in a systematic manner following Gibbs prescription for excess variables, as explained e.g. by [24]. In this manner, the cell appears as a series of five layers. In the absence of global equilibrium, the chemical potential of water, the temperature and the electric potential, will jump across the electrode regions, while they vary continuously through the phases a, m and c. In the experiment, or during cell operation, the temperature can differ between the positions 0 and 1. The cell reaction includes electroosmosis, but not thermal osmosis, as this process is superimposed on the charge transfer, and can be written as: 1 1 m m H2 (a) + tw H2 O(a) → H2 (c) + tw H2 O(c) 2 2

2

3. Theory In non-equilibrium thermodynamics, the mass and energy balances are combined with Gibbs equation, to give the entropy balance and the entropy production for each layer in the cell. In the construction of the entropy production, we always use Gibbs definition of independent (excess) variables. The proper fluxes and driving forces of the layer are defined through the entropy production, see Ref. [24]. By regarding the electrode regions as twodimensional thermodynamic systems, we avoid the problem of deficient knowledge of surface properties. Furthermore, all intensive variables can be well defined as homogeneous phase values resolving Guggenheims’s problem [33]. The lengthy derivation of the entropy production can be found in the literature [24]. We present here the balance equations and the transport equations that can be derived from the entropy production (Section 3.2) [24]. From these we find the expressions for the Seebeck coefficient and Peltier effect in Sections 3.3 and 3.4. The expressions provide the theoretical basis for the experiments which are described in Section 4 and analyzed Section 5. 3.1. Balance equations Balance equations are written, assuming that the transport problem can be regarded as one-dimensional. This means that there is no leakage of heat, i.e. perpendicular to the x-direction of transport. 3.1.1. Mass balances At steady state, disappearance or production of hydrogen and movement of water can be related to the electric current: a JH 2

a,m c,m m Jw = Jw = Jw = tw

(1) j F

3.1.2. Energy balances Energy transport takes place in the x-direction due to charge and mass transfer. Near the electrocatalytic layer on the a-side, the energy flux is equal to: a,m a,m Ju = Jqa,m + JH2 HH + Jw Hw + ja,m

where the transference coefficient for water (electro-osmotic drag) m , can be connected with the number of water in the membrane, tw molecules transported by each proton through the membrane. This cell shall be studied (1) when the electric current density across the cell is negligible and a temperature difference is maintained (the Seebeck coefficient measurement) and (2) when power is applied to create an electric current (the Peltier effect measurement). The total pressure shall be kept the same on each side of the membrane, meaning that pa = pc = p. The total pressure is the sum of the hydrogen pressure and the pressure of the saturated water vapour. When the temperatures differ between the two sides, the water vapour pressures differ accordingly. We neglect the small impact of this difference on p. The thermodynamic equations that describe and link the two measurements are given below.

j c = JH = 2 2F

relations, we do not need to solve the diffusion equations for gases and water in the porous transport layers. We shall describe experiments when j = 0 (Seebeck coefficient measurements), expecting Eq. (2) to hold, such that we can take advantage of the relation m j/F. This situation can be realized with Soret equilibrium Jw = tw for water across the membrane, see Section 3.2.3.

(2)

The flux of a component is denoted Ji , j is the electric current denm was defined above. Using these sity, F is Faraday’s constant, and tw

(3)

where Hi is the partial molar enthalpy of i. In the membrane near the a-side, the energy flux is m,a Ju = Jqm,a + Jw Hw + jm,a

(4)

The corresponding flux in the membrane near the c-side is: m,c Ju = Jqm,c + Jw Hw + jm,c

(5)

For the porous transport layer (PTL) on the c-side, the energy flux is c,m c,m Ju = Jqc,m + JH2 HH + Jw Hw + jc,m 2

(6)

The equations describe how energy is transformed as enthalpy and mass flows through the layers. The electric potential is created with enthalpy of hydrogen and heat (entropy) available. We see from Eqs. (3)–(6) that  is not absolute, as it depends on the reference state of the enthalpy of hydrogen. For the total cell, the reference states disappear, however. In the steady state, Ju is constant through all layers and interfaces, and we can use the energy balance equations along with the transport equations to determine the potential differences that can develop across the interfaces and the membrane. We shall find  for each layer from the transport equations, see Section 3.2. The difference can be understood as a difference in electrochemical potential of electrons (in layers a and c) or protons (in layers sa, m and sc). The sum of the local potential differences gives the measured cell potential. At isothermal, isobaric conditions, the cell potential difference is zero. We shall keep isobaric conditions, and examine non-isothermal effects in this cell; which are useful in considerations of the fuel cell. 3.2. The sets of transport equations 3.2.1. The porous transport layers The entropy production in the electron conducting layers is due to transport of charge and heat. This leads to the following fluxforce relations: dT j + a F dx

(7)

d a dT =− − raj TF dx dx

(8)

Jqa = −a

where a is the thermal conductivity, ra the electric resistivity of the graphite or platinum, depending on the measurement, and a is the Peltier heat of the electronic conductor. a = TSe∗

(9) Se∗

Here T is the temperature and is the transported entropy of the electrons. The value of Se∗ in carbon is −2 J/K mol [34], while it is −1 J/K mol in Pt [27]. The thermal conductivity of the layer is that of graphite (when we apply a potential to the cell) and that of Pt (in the Seebeck coefficient measurement), cf. Section 4. Eqs. (1) and (2) give the steady mass transports in the pores of the layer.

S. Kjelstrup et al. / Electrochimica Acta 99 (2013) 166–175

3.2.2. The electrode region on the a-side The electrochemical reaction of the hydrogen electrode is simply: 1 H2 → H+ + e 2

(10)

The expression for the entropy production in the electrode region has contributions from a heat flux into and out of the layer, from water flux and electric current density across the layer, from hydrogen flux into the layer, and from the electrochemical reaction [24]. We are not able to measure the temperature of the surface with sufficient resolution, so we shall assume that the electrocatalytic layer is isothermal, Ta,m ≈ Tsa ≈ Tm,a . For reversible electrodes, with equilibrium for adsorption of hydrogen at the electrodes, the potential jump becomes: 1 a tm a,m  =  − w a,m w,T − r sa ısa j 2F H2 F

(11)

where the first term on the right-hand side is due to the chemical reaction, and the second term is due to electro-osmosis of water across the layer. The ohmic resistance of the layer is rsa . Any overpotential for the electrode reaction in Eq. (11) is also neglected. The heat flux into and out of the layer obtains contributions from the Peltier heats: a Jqa,m = −hsa q a,sa T + 

Jqm,a

=

−hsm q sa,m T

j F

j + F m

(13)

∗ m m m = T (SH+ − tw Sw )

(14)

m is the partial molar entropy of water in the membrane, Here Sw ∗ is the transported entropy of protons in the Nafion memand SH+ brane. The equations express a discontinuity in the heat flux across the boundary, when the Peltier heats differ on the two sides. The disappearance of hydrogen liberates heat at the junction. This will affect the energy balance, Eq. (3).

3.2.3. The membrane The entropy production in the membrane has contributions from the flux of heat, water and protons [24]. This leads to the following set of three coupled flux-force equations:



dT m j + q∗,m Jw − tw F dx



+ m

j F

m dT m d cw Dw q∗,m cw Dw w,T m j − + tw Jw = − 2 RT F dx dx RT

m

m tw

dw,T dT d =− − − rmj TF dx F dx dx

(15) (16) (17)

The transport properties are membrane-specific. The membrane thermal conductivity is m , the electric resistivity is rm , the diffusion m , the water concentration coefficient of water in the membrane is Dw *,m is cw , the water heat of transfer is q , while R is the gas constant. The water flux is normally zero in the start of an experiment, at t = 0. A steady state is developed at t =∞, as a constant electric current is applied to the cell. In the steady experiments, all mass and energy fluxes are constant. With the condition of Eq. (2) we then have that: Jw − tw

j q∗,m cw Dw =− F RT 2

 dT  dx

−

cw Dw dw,T =0 RT dx

(18)

leading to the condition for Soret equilibrium: dw,T q∗,m =− T dx

 dT  dx

This Soret equilibrium can be maintained during electro-osmosis, when Jw − tw j/F = 0, or when Jw = 0, j = 0. If there is equilibrium for water across the membrane, we can use the relation dT = SdT + d, and the equilibrium condition dw = 0 to indentify the gradient in w,T . By comparing to Eq. (19) we obtain: q∗,m = −TS m w

(20)

The heat flux across the membrane under these circumstances is Jqm = −m

 dT  dx

m

+ m

j F

(21)

and the electric potential gradient is found by introducing Eq. (19) into Eq. (17): 1 dT d = − (m − tw q∗,m ) − rmj T dx dx

(22)

By integrating the electric potential gradient across a membrane with thickness ım , using also Eq. (14), we obtain the membrane potential difference for Soret equilibrium: 1 ∗ (T m,c − T m,a ) − r m ım j m  = − SH+ F

(23)

In the absence of equilibrium for water, one cannot take advantage of Eqs. (19) and (20).

(12)

where a was defined in Eq. (9), hiq is thermal conductance of the layer s, i.

Jqm = −m

169

(19)

3.2.4. The electrode region and porous transport layers on the c-side From the symmetry of the cell, the electrode on the c-side has equations of the same form as on the a-side: m Jqm,c = −hsm q sc,m T +  c Jqc,m = −hsc q c,sc T + 

j F

j F

(24) (25)

where c , the Peltier heat of the right hand side, is equal to a . Hydrogen is produced in the electrochemical reaction, and the electric potential jump due to this production at constant temperature is m,c  = −

1 c tm  − w m,c w,T − r sc ısc j 2F H2 F

(26)

These equations apply when Tm,c ≈ Tsc ≈ Tc,m and there is no overpotential of the hydrogen electrode. For the porous transport layer on the c-side, we obtain equations similar to Eq. (8). 3.3. The Seebeck coefficient We are now in a position to find expressions for the Seebeck coefficient of the cell. The cell electromotive force (emf) is the sum of the contributions from all layers at j ≈ 0: a,c  = a  + a,m  + m  + m,c  + c 

(27)

The cell emf can be measured in a well defined way in two states. The initial state when the electrolyte is homogeneneous and dw,T = 0, will be given subscript t = 0. The steady state, when Eq. (19) applies is indicated with subscript t =∞. The Seebeck coefficient is the potential difference divided by the temperature difference between the electrodes. The electrodes are connected via graphite and current collectors to the external cell house. From the cell house, connections are made with Cu. The contacts at the cell house are at the same temperature, meaning that there is no thermoelectric contributions from the Cu–Pt contacts. The sum of the potential differences across the platinum wires is from Eqs. (8) and (9): ∗ ∗ (T sa − T 0 ) − Se,Pt (T 0 − T sc ) a  + c  = −Se,Pt

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With the Pt–Cu contact at the temperature T0 , the thermoelectric power contribution from the Pt conductor becomes a  + c  ∗ = Se,Pt (T sc − T sa ) With uniform water contents dw,T = 0, we obtain the membrane contribution from Eq. (17) with (14):





am,cm 

sa,sc T

= j≈0,t=0

1 F

1 2

∗ ∗ m − SH SH2 + Se,Pt + + tw Sw

 (28)

m − S a . By waiting until Soret equilibrium has been where Sw = Sw w established, we can use relation (20) with (22). The total thermoelectric potential becomes

  a,c sa,sc T

= j≈0,t=∞

 1 1 F

2

∗ ∗ SH2 + Se,Pt − SH +

 (29)

We see that we can expect a development in  with time. By waiting ∗ , untill Soret equilibrium is established, we can find the unkown SH + measuring the Seebeck coefficient, knowing the entropy of hydrogen. Eq. (30) predicts the variation in the Seebeck coefficient with the natural logarithm of the hydrogen pressure:

  a,c sa,sc T

= j≈0,t=∞

1 F

1  2

0 SH − R ln 2

pH2



p0

∗ ∗ + Se,Pt − SH +



The Peltier heat is defined as the heat adsorbed at a junction per mole charges passing, when positive current is passing from left to right. The Peltier effect is used to cool or heat. The heat changes, which follow directly from the Seebeck coefficient, can be substantial in electrochemical cells [11]. In a cell like the present, the entropy changes at the electrodes are equal in magnitude, but opposite in sign, leading to heating or cooling at the two electrodes, respectively, when current is passing. The equations that determine the temperature profile across the cell are therefore of interest. Consider again the state described m for t =∞, and Eqs. (3) and (4). For the left-hand side by FJ w /j = tw electrode region, we obtain:

2

HH2 − tw a,m Hw

+(a − m )

j F



aH − tw a,m w,T 2



− r sa ısa j2 =

sm − ha,s q a,sa T + hq a,sm T

(31)

j F

1 2

HH2 − tw a,m Hw

sm ∗ ∗ m m − hsa q a,sa T + hq a,sm T + T (Se,C − SH+ + tw Sw )

j F



(32)

where we have replaced the transported entropy of platinum with that of graphite. The terms on the left-hand side can be combined with the enthalpy terms on the right-hand side. We reshuffle and obtain sm sa sa 2 hsa q a,sa T − hq sa,m T = r ı j

+T

1 2

∗ ∗ m a − SH+ + tw Sw SH2 + Se,C

j F

(33)

The equation describes how the heat source or sink at the junction leads to conduction. We see how the Seebeck coefficient give information on the expression. In this experiments, one must use the transported entropy in graphite. A positive parenthesis (positive Seebeck-coefficient), means that the net flux out of the anode is large. For the right hand side electrode, we obtain in a similar manner;

1 2

∗ ∗ a − SH+ + tw Sw SH2 + Se,C

j F

(34)

A problem with these equations is that the thermal conductances of the surfaces are not known. Until such information is available, we need to use approximations. An approximative solution is shown below. 3.4.1. An approximative solution This experimental cell is set-up with temperature controls at the current collectors, setting T0 = T1 . The cell has a symmetry plane through the centre of the membrane. The temperatures in the electrode regions are also measured. The thermocouples have, however, an extension which is near the thickness of the catalytic layer. This makes it impossible to determine any temperature jump across the electrodes, prompting us to use the approximation, Tm,a = Tsa = Ta,m and Tm,c = Tsc = Tc,m . Consider first the contribution to the temperature profile across the cell from the Peltier heats. One electrode is heated, the other is cooled equally much. With the given approximations (constant boundary temperature and pressure, unidirectional transport, and constant thermal resistivities), the Peltier heat effects will eventually lead to a temperature rise on one electrode surface, and a corresponding drop on the other electrode surface. A negative temperature difference sa,sc T between the cathode and the anode surfaces, means from the symmetry of the problem that the cathode temperature is sa,sc T/2 below the controlled temperature, T0 . Vice versa, the anode is sa,sc T/2 above T0 . These differences will not depend on additional uniformly distributed heat sources like the Joule heat or the heat from the overpotential. In lack of information of surface temperatures and resistivities, we assume for the anode that a,sa T = − sa,m T =

j HH2 − Jw a,m Hw + Jqa,m − Jqm,a 2F

1

2

−T

3.4. The Peltier effect at steady state

j F

1

sa sa sa 2 hsm q m,sc T − hq sc,c T = −r ı j

where is the standard pressure (1 bar). By plotting the Seebeck coefficient versus ln pH2 /p0 , the results should give a slope equal to −R/2F. We shall see that this can indeed be found. Entropies are changing less than 1% for an increase in T of 10 K. In order to determine the Seebeck coefficient for the various conditions, one can therefore plot experimental values for a,c  versus sc,sa T and determine the slope. A positive Seebeck coefficient means that positive electric work is done in the external circuit, or that heat is transported inside the cell in the direction of the temperature gradient. To give numerical insight, consider a transported entropy of 2 J/K mol giving a Seebeck coefficient of 20 ␮V/K or a contribution of by 2 mV to the cell potential when the temperature difference between the electrodes is 100 K. This seems to be a small contribution. Most thermoelectric generators have Seebeck coefficients which are one order of magnitude larger [35,36]. With ionic conductors and gas electrodes, one can increase the value further.

=

j F

(30)

p0

ja,m  =

Using the definitions of a and m , we obtain

sa,sc T 2

sa,sc T 2

(35) (36)

and that the interfaces (a, sa) and (sa, m) have the resistance of the nearest phase for a thickness defined by the temperature difference has =

1 Ra

(37)

S. Kjelstrup et al. / Electrochimica Acta 99 (2013) 166–175

Fig. 3. Sketch of temperature profiles through a hydrogen–hydrogen cell using ˘ = −40 J/mol in Eq. (39). For other cell properties, see the text. The current density is near zero for the lower curve, while it is 1 A/cm2 for the upper curve.

hsm =

2 Rm



sa,sc T 1 2 + m = −2 Ra R j/F

−1  1 T

2

∗ ∗ m a − SH+ + tw Sw SH2 + Se,C



≡ Z˘

(39) (40)

The definition of Z follows in Eq. (41), while the rest of the expression is called ˘. The equations can be used to estimate the outcome of the type of experiments we are going to report. The thermal resistance of wet Nafion 115 is Rm = 5.8 ± 0.6 × 10−4 m2 K/W [37], while the value for wet ETEK ELAT PTL is Ra 3.2 ± 0.5 × 10−4 m2 K/W [38]. This gives

1 Ra

Fig. 4. A sketch of the cell, indicating the positioning of the thermocouples in the experiments. The electrode compartments were fed with hydrogen gas saturated with water at very low flow rates. The catalyst coated porous transport layers are identical on both sides of the membrane.

(38)

Eq. (33) gives then

Z=2

171

+

2 Rm

−1

= 3.0 ± 1.1 × 10−4 m2 K/W

(41)

Using this value for Z and ˘ = −40 J/mol, we find from Eq. (39) that the temperature difference between the electrodes is around half a degree for a 120 ␮m thick wet Nafion membrane sandwiched between two 300 ␮m thick dry E-TEK layers at 1 A/cm2 . The solution is illustrated in Fig. 3 in the presence (top curve) and absence (lower curve) of Joule heat. We see that the presence of Joule heat (electric current) does not alter the temperature difference between the extrema of the curves. The temperature difference between the two electrodes can be plotted versus the electric current density, to give information on ˘ and the Seebeck coefficient. Considering the assumptions used, the information is only qualitative. 4. Experimental 4.1. The Seebeck coefficient of the hydrogen concentration cell The cell used for Seebeck coefficient determinations was reported earlier [17,18,28]. In the experiment we encapsulated each half cell house with custom-made heating jackets, allowing a temperature difference across the cell membrane. Thermostated water was flowing through each jacket, maintaining a constant temperature inside the jacket and in the half cell and a fully humidified membrane. Two separate water baths were used for this purpose. Four temperatures were measured, in the two gas supply channels, and on each side of the membrane in the catalytic layer. Tiny channels were tailored into the jackets to allow insertion of thermocouples into the gas channels. K-type thermocouples (thickness <0.25 mm) were inserted between the catalytic layers

and the membrane. The positions of the thermocouples are illustrated in Fig. 4. The thermocouples were calibrated in ice-water, and gave a variation in the temperature of ±0.1 K. The cell compaction pressure was 9.3 bar. One to four Nafion 1110 membranes were compacted to one membrane in order to find conditions for a stable membrane temperature gradient. The membranes were sandwiched between two catalyst-coated porous transport layers (E-TEK ELAT coated with 0.8 mg/cm2 ), identical on the two sides of the membrane; the catalyst facing the membrane. The Pt wires were in contact with the catalytic layers. The cell potential was measured with Cu wires in contact with 0.3 mm thick Pt wires at room temperature. The hydrogen gas (99.999%) was humidified with distilled water in a bubble humidifier before entering the cell, see [28]. The temperature in the humidifier was controlled within 1 K. Cooling of the humidifier took time since the system depended on cooling from the surroundings, but ensured local equilibrium for water everywhere in the cell. A considerable amount of water was used in the humidifier in accordance with Vasu et al. [39]. The humidifier temperature was first adjusted to 5 K above the temperatures of the baths used to thermostat the cell. The gas entering the cell was therefore slightly supersaturated, and some liquid water would therefore be present in the gas channels and the PTLs. The gases flowed through the cell slowly (0.02–0.04 l/s), keeping open the path for hydrogen to the active sites. The feeding channels’ depth and width were 0.5 mm and 1.0 mm, respectively. Flow-controllers and needle valves were used to maintain constant gas flow into the cell. The experiment started by setting the same temperature in both water baths. Then a temperature gradient was imposed to the cell, keeping the average temperature of the cell constant. Stable cell conditions were obtained after 15–60 min, depending on the magnitude of the gradient. Every time a new temperature difference was set, the humidification temperature was also changed. Four or five different temperature differences were imposed, keeping the average temperatures the same, equal to 40 or 60 ± 1 ◦ C. An accurate determination of the temperature difference between the electrodes is essential for an accurate determination of the Seebeck coefficient. For the particular measurement conditions (j = 0 and Jw = 0), Fourier’s law relates the temperature differences via the fraction f: f =

sa,sc T Rm = tot R 0,1 T

(42)

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measurments in order to keep the electrode and thermocouples at the same position. 4.2. The thermal signature of an applied potential to the hydrogen concentration cell

Fig. 5. The measured cell potential, as,cs  and the temperatures from positions 1–4, as a function of time.

where Rm is the thermal resistance of three membranes, and Rtot is the total thermal resistance (the total membrane resistances plus the resistances of two porous layers and two interface contact resistances). Searching for good experimental conditions, we compared the measured f-ratio to the calculated one. With one, two, three and four Nafion 1110 membranes, we observed a systematic change. The measured values of f (number of membranes in parenthesis) were 0.54 ± 0.02 (1), 0.62 ± 0.01 (2), 0.74 ± 0.04 (3), and 0.80 ± 0.05 (4), respectively. These results did not depend significantly on the membrane compaction pressure. Using measured thermal resistances at 314 K [37,38], we calculated f = 0.65 ± 0.09 (1), 0.79 ± 0.11 (2) and f = 0.85 ± 0.12 (3), respectively, which gave qualitative support for the measured values. The deviation between the measured and calculated f-ratio decreases as the number of membranes increases. The Seebeck coefficient measurements were therefore carried out with 3 membranes. Uncertainties from the positioning in thermocouples and electrodes are then reasonable. The cell potential was 0 ± 200 ␮V before a temperature difference was imposed. Temperature differences above 60 K were avoided, in order not to perturb the cell too much, and avoid unwanted phenomena like clogging/evaporation of water. The potential relaxed to a steady state value within minutes, and the steady state could be maintained for hours, see Fig. 5. The figure shows a stable state evolving in about 30 min, which is kept for hours, and with temperatures at positions 1–4, all constant and easily be separated. We can therefore assume that there is equilibrium for water thoughout the system, and that the condition for Soret equilibrium q∗,m = −TS m w can be applied to Eq. (22). The Seebeck coefficient so determined, was in all cases positive, meaning that transfer of heat from right to left is used to generate the potential. Fig. 5 shows temperature measurements at positions 1–4 for an average cell temperature of 40 ◦ C. The temperature difference measured across the porous transport layers are then the same, as long as the thermostat on the high temperature side is below 60 ◦ C. Above this value, the temperature difference across the PTL on the hot side became smaller than that of the cold side. This can be explained by a temperature variation in the thermal conductivity of humidified PTL [40]. The temperatures recorded at the membrane surface determine the Seebeck coefficient. The corresponding measured cell potential is shown on the right hand side of Fig. 5. The first set of experiments were done with a hydrogen pressure of 1 bar. The next experiments were done with a mixture of hydrogen and helium, giving a partial pressure of hydrogen equal to 0.05, 0.25, 0.75 and 1 bar. The cell was not opened during these

The same cell was also used without the heating jackets and with a thinner membrane, Nafion 115, to study the heat production in the cell when electric current is passing. The temperature control of the cell was described by Vie [28]. The position of the thermocouples were again as shown in Fig. 4. The two thermocouples in the gas channels were used to control the cell temperature to 65 ◦ C, making T0,1 = 0. The temperature difference between two thermocouples was first determined in the absence of an applied electric potential to the cell, in order to calibrate the thermocouples, and set a reference for the next measurements. In a stirred water solution, the K-type thermocouples fluctuated less than 0.1 K (95% confidence interval). Also the temperature difference fluctuated less than this value. A similar difference was found with the thermocouples in position, and with zero applied potential. The thermocouples were insulated using a thin layer of cyclotene to avoid corrosion and the possible interference of the non-zero current. Temperatures were next measured close to each electrode as a function of current density, at hydrogen pressures of 1, 2 and 4.5 bar. The electric potential applied to the cell, 0,1 , and the corresponding current density was also recorded. The value sa,sc T = Tsc − Tsa was negative in all cases, making the electrode on the left hand side hotter than the other one, in agreement with expectations from theory. When an electric potential is applied to the cell, heat is transported from right to left. 4.3. Accuracy of measurements The formula of propagation of errors was used to calculate standard deviations of derived quantities: A2 =

n   ıA

ıxi

i=1

2 xi

(43)

where A is a function of several variables, i.e. A = f(x1 , x2 , . . ., xn ), and xi is the standard deviation of the variable xi . For instance, when one value is obtained from a regression in this paper and another value from a cited paper the error propagation is given by Eq. (43). 5. Results and discussion 5.1. The thermoelectric potential and the Seebeck coefficient The steady state potential is plotted as a function of the temperature difference between the electrodes, in a typical case with 340 K and 1 bar in Fig. 6. The intercept of the curve is zero within the error limits given, as it should be, and the slope gives the thermoelectric potential. Linear regression of 3 results like in Fig 6 for a membrane thickness of 3 Nafion membranes gave



as,cs 

m T



j≈0,t=∞

= 670 ± 50 ␮V/K

(44)

The measurements were done for steady, thermally stable states at j = 0. To obtain further evidence for this value, we plotted the Seebeck coefficient as a function of the logarithm of the dimensionless hydrogen pressure ln(pH2 /p0 ) according to the prediction of Eq. (30) (not shown). The average slope was −49 ± 32 ␮V/K, which includes the theoretical slope, −42 ␮V/K or −R/2F. In the steady

∆φ/ mV

S. Kjelstrup et al. / Electrochimica Acta 99 (2013) 166–175

173

A value for the parts of ˘/T was also calculated using the appropriate pressure in the following equation

15

15

10

10

5

5

0

0 0

5

10 ∆Tm / K 15

20

25

Fig. 6. The measured cell potential, as,cs , at average temperature 340 ◦ C and 1 bar hydrogen pressure, as a function of the measured temperature difference between the electrodes, m T.

state, when we can expect that dw = 0, we have according to Eq. (30) that 1 0 ∗ ∗ − SH S + Se,Pt + = 67 ± 5 J/(K mol) 2 H2

(45)

The standard value for hydrogen gas is 135 J/(K mol) at 340 K [41] ∗ and Se,Pt = −1 J/(K mol), giving ∗ SH + = 1 ± 5 J/(K mol)

(46)

The value of Eq. (45) can be used to find the reversible heat effect of the oxygen electrode in the polymer electrolyte fuel cell for the same state of water, see Section 5.3. 5.2. The thermal signature of the potential applied to the H2 ||H2 cell

as,cs T (3.0 ± 1.1) × 10−4 W/(m2 K) j/F

(47)

Table 1 Measured temperature differences between anode and cathode at steady state in the hydrogen hydrogen-cell for various constant pressures. The average cell temperature was 65 ◦ C. For computed properties, see text. p (bar)

cs,as T/(j/F) from Fig. 7 (K m2 s/mol)

1 2 4.5

−2.4 ± 1.0 −5.4 ± 1.0 −4.8 ± 0.8

˘ exp /T (J/mol K) −22 ± 9 −48 ± 9 −43 ± 6

˘ calc /T (J/mol K) −53 ± 10 −48 ± 10 −42 ± 10

1 2

0 − R ln SH 2

pH2 p0

∗ ∗ m a + Se,C − SH+ + tw Sw



(48)

We used the value for the steady state Seebeck coefficient cor0 + S ∗ − S ∗ ) = 66 ± 5 J/(mol K) and the rected for graphite, ( 12 SH H+ e,C 2 value for p. The transference coefficient for water is equal to 1.2 [24] when the membrane is in contact with water in the vapour phase on both sides, but the value is higher in the presence of water. Kjelstrup m Sa et al. [42] obtained 13.4 J/(K mol) for the combination S ∗ + − tw w H for a Nafion 115 membrane, using Ag|AgCl-electrodes. This value is used in an estimation of ˘ cal in the last column of Table, even if it suggests a very different value for the transported entropy than found here 1. The results from the two experiments compare well, when the assumptions used and the experimental inaccuracies are taken into account. The trend with increased pressure is not reproduced in the few data in Table 1. We explain the deviations by big uncertainties connected with the state of water in the membrane in the Peltier experiments. The equations show how the state of water will change the heat fluxes out of the cell to a large degree. Depending on whether or not Soret equilibrium is possible (this may depend on the current density used), the value of ˘/T is able to change significantly. Direct measurement of Peltier effects can thus be severely hampered by lack of control of the state of water. This means that half cell potentials calculated with certain electrolyte solutions do not give good predictions for membrane cells. Therefore, it is convenient that the reversible heat effect can be determined also from Seebeck coefficient determinations, which have a much better precision. This situation is not unknown in the literature, for references, see [24]. In a search for accurate values for transported entropies, Seebeck-measurements rather than Peltier, can be recommended. 5.3. Relevance for the polymer electrolyte fuel cell

The current densities arising from the applied potential, j, and the resulting temperature differences at steady state, as,cs T, are plotted for 1, 2 and 4.5 bar gas pressure, respectively, in Fig. 7. For the results shown, the polarization curve is linear (not shown), meaning that effects of overpotentials are negligible. The current densities were larger in the experiments at 1 bar, so these are less reliable for determination of Peltier effects. The scatter in the results for the temperature difference is large. This is not surprising, as it is difficult to reach the particular steady state for water described by Eq. (18). The scatter became worse at higher current densities, when the polarization curve (not shown) deviated from a straight line. These results were therefore not considered. The slopes as,cs T/j for the three experiments are given in Table 1. The results for as,cs T/(j/F) were used to find ˘ exp /T from Eq. (47), see column 3, Table 1. ˘ exp =

˘ cal = −T

We are now in a position to discuss the single electrode reversible heat change of the hydrogen and of the oxygen electrodes in the fuel cell. The entropy change of the whole polymer electrolyte fuel cell rection is equal to −85 J/(K mol) at 340 K. According to the Seebeck coefficient measured above at j ≈ 0, the entropy change at the anode is −66 ± 5 J/(K mol), when there is Soret equilibrium for water across the membrane. At 340 K this corresponds to a heat release 22 ± 2 kJ/mol. The oxygen electrode thus represents the remaining entropy change of −19 ± 5 J/K mol, or a heat release of 6 kJ/mol. The reversible heat release at the anode is then larger than that at the cathode. This is likely, considering that the change in number of molecules in the reaction is larger here, but as we have seen, there can also be a considerable transport of heat along with protons and water via the membrane. The considerations above apply only when there is Soret equilibrium for water in the membrane. Realistic operating conditions may lead to large deviation from this, as illustrated by beautiful experiments of Thomas et al. [29], and also by our inaccurate Peltier effect experiments and the observations of Burheim et al. [15]. Our determination of ˘ exp /T gave a lower value for the reversible heat effect. At 1 bar it was equal to 7.8 kJ/mol. Knowing the value of the Seebeck coefficient, one could interprete the discrepancy as a shift in the heat production towards the cathode when we move away from Soret equilibrium conditions. The observations of Burheim et al. [15] (small anode heat production) may be explained partly by this, even if their results also can be masked by a large cathode overpotential. It is nevertheless interesting that Vie and Kjelstrup [28]

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1 bar;

ΔTelec / K

0.75

0.75

∆ as,cs T / K = (0.24 ± 0.10) j - (0.01 ± 0.04)

0.5

0.5

0.25

0.25

0

0

-0.25

-0.25 0

0.2

0.4

-2

0.6

0.8

1

j / A cm

2 bar; 0.75

0.75

0.5

0.5

0.5

0.5

0.25

0.25

0.25

0.25

∆ as,cs T / K = (0.56 ± 0.10) j + (0.00 ± 0.04)

0

-0.25 0.00

0

0.20

0.40 0.60 j / A cm-2

0.80

-0.25 1.00

ΔTelec / K

Δas,csT / K

0.75

4.5 bar 0.75

∆ as,cs T / K = (0.50 ± 0.08) j - (0.02 ± 0.02)

0

0

-0.25

-0.25 0

0.2

0.4

-2

j / A cm

0.6

0.8

1

Fig. 7. The temperature difference T = Tsa − Tsc (circles) across the Nafion 115 membrane as a function of electric current density in the hydrogen electrode polymer electrolyte cell at 65 ◦ C. Experimental points are given for 1, 2 and 4.5 bar.

observed that the anode was slightly hotter than the cathode, at stationary state operation of a polymer fuel cell with ETEK-electrodes and one Nafion 115 membrane. This supports the present findings, but more work may be needed to clarify this further.

concentration profile. This may partially explain a discrepancy with earlier results [15].

6. Conclusions

The authors acknowledge the Norwegian Research Council for financial support under the RENERGI programme, grant no 164466/S30.

The Seebeck coefficient of the hydrogen–hydrogen cell, a symmetrical cell with two hydrogen electrodes, was experimentally determined to 670 ± 50 ␮V/K at 1 bar, supported by an expected variation in the value with the hydrogen pressure. The transported entropy of protons across the membrane was estimated to 1 ± 5 J/(K mol) for the steady state with a negligible net water flux across the membrane, and with Soret equilibrium for water in the membrane. Results from experimental studies of the Peltier effect gave qualitative support to the value. The results are useful for interpretation of local thermal effects in polymer electrolyte fuel cells. They enabled us to calculate the Peltier heat of the anode in a cell with Soret equilibrium for water equal to −22 ± 2.0 kJ/mol at 340 K. From this value and the total entropy change of the fuel cell, we find the Peltier heat of the cathode equal to −6 ±2.0 kJ/mol at 340 K and the same conditions. From the experimental results on Peltier effects a shift in the heat production towards the cathode can be expected during fuel cell operation, probably caused by an impact of the current density on the water

Acknowledgement

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