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Electrochemical sensors for detection of hydrogen in air: model of the non-Nernstian potentiometric response of platinum gas diffusion electrodes
Electrochimica Acta 50 (2005) 2943–2953
Electrochemical sensors for detection of hydrogen in air: model of the non-Nernstian potentiometric response of platinum gas diffusion electrodes S. Rosini, E. Siebert∗ Laboratoire d’Electrochimie et de Physico-chimie des Mat´eriaux et des Interfaces (UMR 5631 CNRS – INPG – UJF), Ecole Nationale Sup´erieure d’Electrochimie et d’Electrom´etallurgie de Grenoble, 1130 rue de la piscine, BP 75, 38402 Saint Martin d’H`eres cedex, France Received 3 March 2004; received in revised form 3 September 2004; accepted 21 November 2004 Available online 5 January 2005
Abstract The potentiometric response of three different platinum gas diffusion electrodes deposited on H3 PO4 doped polybenzimidazole (PBI) was investigated under humidified atmospheres that contained H2 or mixtures of H2 and O2 . Continuum modelling was used to analyse the response. It is shown that the non-Nernstian response under H2 H2 O N2 mixtures can be explained by a difference of water activity on both sides of the membrane. Under H2 O2 N2 mixtures, the oxygen mass transport parameters have a strong effect on the electrode sensitivity. © 2004 Elsevier Ltd. All rights reserved. Keywords: Hydrogen sensors; Mixed potential; Polybenzimidazole; Gas diffusion electrode; Oxygen reduction; Hydrogen oxidation
1. Introduction Potentiometric sensors have been proposed for the detection of hydrogen because they are easy to use [1–4]. These devices commonly use protonic conductors such as Nafion [5] or antimonic acid [4] at low temperature and zirconium acid phosphate based electrolyte at high temperature [6]. Recently, we have proposed the use of H3 PO4 doped polybenzimidazole (PBI) [7] because it exhibits excellent mechanical and thermal properties [8] and it shows a good protonic conductivity even in dry atmospheres [9]. Most of the potentiometric sensors use platinum as the sensing electrode. When exposed to a humid atmosphere containing H2 , this electrode deposited on Nafion exhibits a non-Nernstian open-circuit voltage [10]. In ambient air, the hydrogen sensor sensitivity (defined as the slope of the E versus log(P(H2 )) curve) is always higher than that given by the Nernst equation and the potential is influenced by electrode morphology [11]. In par∗
Corresponding author. Tel.: +33 476826573; fax: +33 476826670. E-mail address: [email protected] (E. Siebert).
0013-4686/$ – see front matter © 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2004.11.044
ticular, gas diffusion electrodes, typically used in PEM fuel cell technology, exhibit a sigmoidal response, which is well explained by the mixed potential model resulting from hydrogen oxidation (HOR) and oxygen reduction (ORR) [11]. According to this model: • For low hydrogen partial pressure, the sensor potential varies linearly with the logarithm of the hydrogen partial pressure and the sensitivity, deduced from the ORR Tafel slope, is of the order of 120 mV/decade. • For high hydrogen partial pressure, the sensor potential varies linearly with the logarithm of the hydrogen partial pressure and the sensitivity is in agreement with the Nernst equation (30 mV/decade at room temperature). • The abrupt change of potential between these two zones can be explained by mass transport limitations of both HOR and ORR reactions. The objective of this paper was to better understand the potentiometric response of a Pt gas diffusion electrode when it was exposed to H2 H2 O N2 and H2 O2 N2 atmospheres. In the first part of this paper, experimental data obtained on
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Table 1 Description of the gas diffusion electrodes Electrode (mg/cm2 )
Platinum loading NAFION (mg/cm2 ) Roughness factor Active layer (10−6 m) Diffusion layer (10−6 m)
ETEK
SORAPECH2
SORAPECO2
0.5 Unknown 5 10 250
0.2 1 80 5 250
0.35 0.8 150 5 250
gas diffusion electrodes containing different platinum loadings in the active layer and deposited on PBI-X H3 PO4 are presented. In parallel to the experimental work, a continuum model that took into account the electrode structure consisting of a uniform diffusion layer placed on an active layer was developed. In this model, current was calculated separately for both HOR and ORR and then recombined according to the mixed potential assumption. Finally, analysis of the experimental results and comparison with the theoretical model allowed us to determine the parameters influencing the sensor response.
2. Experimental PBI, purchased from Celanese, was dissolved in dimethyl acetamide (DMAc) by stirring for 24 h. The film was drawn from this solution on a glass plate and dried for 10 h at 80 ◦ C. The membrane was then washed in water and dried during 1 h in order to remove any trace of DMAc. The film was immersed in phosphoric acid solution (85 w/o) in order to obtain a protonic conduction and dried for 1 h at 80 ◦ C. X was defined as the ratio of phosphoric acid on the number of PBI monomer and was between 3 and 3.8 for all the membranes tested. Three diffusion gas electrodes were used in this work. Table 1 summarises some of their main features. The elec-
trode manufacturers provided the platinum and Nafion loadings. The roughness factor (γ), defined as the ratio between active and geometric surface area, was determined in phosphoric acid solution (1 M) by cyclic voltammetry as described in [12]. The low roughness factor observed for all the ETEK electrodes in comparison to the platinum loading can be easily explained by ageing of the electrodes [13]. Electrode membrane assemblies were prepared by hot pressing at 150 ◦ C and 150 kg/cm2 . Fig. 1 shows a typical SEM micrograph of the cross section of the electrode/membrane interface. The active layer (containing platinum particles) is white and the diffusion layer is dark, as seen in the figure. The contact between electrode and electrolyte is continuous. The micrograph was used to estimate the macroscopic thickness of the active and diffusion layers. The corresponding results are reported in Table 1. For all the tested electrodes, the diffusion layer thickness (δ) is of order of 250 × 10−6 m. The macroscopic thickness (L) of the active layer was 5 × 10−6 m for the SORAPEC electrodes and 10 × 10−6 m for those purchased from ETEK. The potentiometric response was tested in a three electrode cell as described elsewhere [14]. A schematic representation is given in Fig. 2. A platinum ring electrode was deposited by sputtering on the same side as the working electrode and served as the reference electrode. A Pt electrode was deposited on the opposite side of the electrolyte in order to act as counter electrode. The reference electrode was in contact with pure hydrogen and the counter electrode was in contact with ambient air. The sensor emf was recorded in N2 H2 and N2 O2 H2 mixtures. The different gases were mixed with three mass flowmeters (BROOKS) to obtain various partial pressures of hydrogen. The N2 O2 concentration was adjusted to correspond to air. This condition is referred to as dry air further in the text. A part of the gas mixture could be humidified by bubbling
Fig. 1. SEM micrograph of the PBI-X H3 PO4 /SORAPECO2 interface.
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der dry condition (RH = 0%), the behaviour of the platinum electrodes was reproducible. The emf obeys to the Nernst’s law in agreement with our previous results [7]. However, in wet atmospheres, the response was no longer Nernstian. The sensitivity is of the order of 30 mV/decade but the emf value at P(H2 ) equal to one is different from zero. The sensor response can thus be expressed as: E = E0 −
Fig. 2. Schematic representation of the electrochemical cell.
through water and recombined with dry gases to obtain an atmosphere with controlled relative humidity (RH). Open-circuit potential was recorded using a high impedance voltammeter (HP 34401A). Polarisation studies were performed using a Solarton 1287 electrochemical interface. ORR polarisation curves were measured under dry air for each type of electrode. HOR polarisation curves were plotted under various H2 N2 mixtures. All the measurements were performed at ambient temperature. All simulation of potentiometric response were made using Matlab software.
3. Experimental results 3.1. Open-circuit voltage in inert gas The potentiometric response of an ETEK electrode in H2 N2 mixtures for different RH is shown in Fig. 3(a). Un-
RT ln(P(H2 )) 2F
(1)
where E0 is dependent on the relative humidity in the gas mixture. Fig. 3(b) shows the variation of E0 as a function of RH for the three types of electrodes. We can see from the figure that the potential decreases with increasing relative humidity. This phenomenon has already been observed in potentiometric hydrogen sensors based on PBI-X H3 PO4 [11] and protonic NASICON (Hyceram) [15]. With PBI, Bouchet et al. [11] have shown that E0 for gas diffusion electrodes was a function of the acid content in the polymer membrane. On the contrary, with a platinum grid and a thin film, E0 was equal to zero indicating that the Nernst law was obeyed with this type of Pt electrodes. With Nafion, Jak et al. [5] have recently found a variation of the sensitivity as a function of the humidity present in gas mixtures in contrast to our results. They attribute this behaviour to the fact that, in Nafion, the proton conduction is influenced by water activity in the polymer and by a difference of water adsorption properties of the reference and working electrodes. 3.2. Open-circuit voltage in air The potentiometric response as a function of log(P(H2 )) in dry air for the three platinum electrodes is shown in Fig. 4. As expected from previous results [11], the opencircuit voltage does not obey to the Nersnt’s law. At high P(H2 ) (P(H2 ) > 0.14 bar), the potential varies linearly with the logarithm of P(H2 ) and the sensitivity is between 27 and 30 mV/decade. At low P(H2 ) (P(H2 ) < 0.08 bar), the potentiometric response varies linearly with the logarithm of P(H2 ) but the sensitivity is higher than that given by the Nernst
Fig. 3. (a) Open-circuit voltage of the ETEK electrode for various relative humidities. 䊉: RH = 0%, ♦: RH = 20%, +: RH = 50%, : RH = 100%. (b) E0 vs. RH for : ETEK, : SORAPECO2, *: SORAPEC H2.
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Fig. 4. (a) Open-circuit voltage as a function of log(P(H2 )) in dry air for the three electrodes. +: ETEK, : SORAPECH2, : SORAPECO2. (b) Evolution of the curve with the time. The curve () was recorded 24 h after the curve () for a SORAPECH2 electrode. The curve (♦) was recorded for a SORAPECO2 electrode at time t = 0.
equation. In this domain of P(H2 ), the sensitivity is typically of the order of 120 mV/decade. The transition between the two limiting regimes is marked by a strong potential jump (0.14 < P(H2 ) < 0.08 bar). The position of the potential step on the P(H2 ) axis is not the function of the platinum loading. The variation of the E versus log(P(H2 )) curve as a function of the time is shown in Fig. 3(b). Only the response at low P(H2 ) was found to vary from one day to another. This behaviour was observed for all the series of electrodes tested over an extended period of time. The potential in the low P(H2 ) domain was found to decrease systematically. However, the decrease was not reproducible and the discrepancy was of the order of 100 mV. Another interesting feature is that, at the beginning of the experiments, a sensitivity as high as 240 mV/decade can be obtained as illustrated on Fig. 4(b) for a SORAPECO2 electrode. This phenomenon progressively disappears during the measurement in air and the sensitivity finally reaches a classical value of 120 mV/decade. The influence of humidity on the open-circuit voltage output of the sensors has also been tested. As previously shown by Bouchet et al. [14], variation of RH does not modify the potentiometric response at high P(H2 ) and does not change the
position of the potential step. However, we observe a modification of the potentiometric response at low P(H2 ). This behaviour is illustrated in Fig. 5, where the potentiometric response obtained with a SORAPECO2 electrode for different RH in the gas mixture is shown. In the low P(H2 ) range, the potentiometric response can be identified with a straight line corresponding to the following equation: E = E0 − a log(P(H2 ))
(2)
Increasing RH does not change the sensitivity of the sensors which remains of the order of 120 mV/decade. However, an enhancement of E0 is observed. It is worth noting that when an enhanced slope is obtained in dry air, a decrease of electrode sensitivity is systematically observed when RH is increased. The same phenomenon was reported for a sensor based on Nafion as electrolyte [16]. 3.3. ORR and HOR polarisation curves The shape of the polarisation curves is identical to that usually reported in the literature for the ORR and HOR
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Fig. 5. Open-circuit voltage as a function of log(P(H2 )) in wet air (electrode SORAPECH2). : RH = 0%, : RH = 20%, : RH = 50%, 䊉 RH = 100%.
[11,17,18]. At low current densities, the ORR polarisation curve exhibited a Tafel line behaviour and a limiting current was observed at high cathodic overvoltage. Table 2 shows the slope of the Tafel line, the exchange current I0 and the limiting current Ilim for each type of electrode. I0 was determined by extrapolation of the straight line to the open-circuit voltage. The HOR polarisation curve exhibited a limiting current that varied linearly with P(H2 ). m(P(H2 )) is defined as the slope of the Ilim versus P(H2 ) curve. The values of m(P(H2 )) are indicated in Table 2. As shown in Table 2, the slope of the Tafel line is equal to 120 mV/decade. The exchange current of the ETEK electrode is the lowest, in agreement with the roughness factor determined in solution. It must be emphasised that the experimental error in determination of the exchange current may be important due to non-reproducibility of the open-circuit potential whose variation can reach 250 mV. Taking this into consideration, it is likely that the roughness factors determined in liquid medium are different from those in the solid state [19]. The ORR limiting currents slightly depend on the nature of the electrode and are around 23 mA (±4 mA). Similarly, m(P(H2 )) is almost the same irrespective of the platinum loading of the gas diffusion electrode. According to these results, it appears that the limiting currents for ORR and HOR are due to mass transport phenomena.
In order to better understand the origin of the enhancement of sensor sensitivity to 240 mV/decade, the ORR polarisation curve in dry air was recorded immediately after a potentiometric measurement thus giving a high sensitivity in the low hydrogen partial pressure range. The Tafel slope was also enhanced and equal to 240 mV/decade. So, we can conclude that the high sensitivity is related to a modification of the ORR kinetics. Fig. 6 gives the ORR polarisation curves obtained in dry air after a potentiometric measurement, as a function of time. The curve at time t = 0 had a Tafel slope of 120 mV/decade and a limiting current around 20 mA. The limiting current decreased with time and was reduced to 5 mA after 8 h. Concurrently the Tafel slope increased to a value of 240 mV/decade. As shown in Fig. 6, the original ORR polarisation curve could be recovered by exposing the sensors to humidified air (RH = 100%) for 5 h. It can therefore be concluded that the enhanced sensitivity can be related to a low water level in the electrode.
4. Theoretical analysis The theoretical treatment deals with the calculation of the open-circuit voltage of the Pt gas diffusion electrode either
Table 2 Kinetics parameters of ORR and HOR. I0 and Ilim are deduced from the ORR polarisation curves in dry air Electrode SORAPECO2 SORAPECH2 E-TEK
Open potential under air (mV)
I0 at open potential (A)
Ilim (mA)
m(P(H2 )) (mA/bar)
808 840 910
2.5 × 10−4
23 27 19
112 146 128
1.1 × 10−4 3.5 × 10−5
m(P(H2 )) is determined from HOR polarisation curves measured at various P(H2 ) and corresponds to the proportionality coefficient of the Ilim vs. P(H2 ) straight line.
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Fig. 6. ORR polarisation curves measured in dry air after a potentiometric measurement (ETEK electrode). (a) t = 0, (b) t = 1 h, (c) t = 7 h. Curve measured in wet air after (d) t = 3 h at RH = 50% and (e) t = 5 h at RH = 100%.
in inert gas (thermodynamic potential) or in air (mixed potential). 4.1. Open-circuit voltage in inert gas Under dry atmospheres, the open-circuit voltage is given by Nernst’s law as described by the following equation: E=−
1 [RT ln(P(H2 ))] 2F
(3)
Under humidified atmospheres, PBI may absorb water from the gas phase [14]. In particular, Glipa et al. have shown that the quantity of water inside PBI was a function of the acid content [20]. The difference of water activity between the reference (under 100% H2 ) and the working electrode may be responsible for a water flux across the polymer membrane. If both sides of the polymer membrane were exposed to the same RH, an equilibrium could be reached. Under this condi∗ (H O) tion, water activity inside PBI would be equal to aPBI 2 and the potential would be given by Eq. (3). The equilibrium between the gas phase and the Pt gas diffusion electrode containing Nafion takes into account the difference of water activity. This leads to the following equilibrium, as already proposed to explain Nafion transport properties [5]: H2 + 2mH2 O 2[(H+ )H2 Om ]act + 2 e−
(I)
where act stands for active layer of the Pt gas diffusion electrode. Contrary to Nafion, acid doped PBI transports proton without water since the drag number has been measured to be near zero [21]. As a consequence, the thermodynamic equilibrium at the Pt electrode/PBI interface is expressed as: + H+ PBI + mH2 OPBI [(H )H2 Om ]act
(II)
Combining (I) and (II) with the Nernst equation for the Pt reference electrode exposed to 100% H2 leads to the following
expression for the Pt gas diffusion electrode potential: E=
m 0 (µ (H2 O) − µ0gaz (H2 O)) F PBI RT aPBI (H2 O) 1 +m ln − [RT ln(P(H2 ))] (4) F P(H2 O) 2F
where µ0Y (X) is the normal chemical potential of X in Y and P(X) the partial pressure of X. Equilibrium between water in gas phase and water in PBI can be expressed as following: ∗ aPBI (H2 O) 0 0 µgaz (H2 O) − µPBI (H2 O) = RT ln (5) P(H2 O) This leads:
aPBI (H2 O) RT ln E=m ∗ (H O) F aPBI 2 Preference (H2 ) 1 RT ln + 2F Pwork (H2 )
(6)
∗ (H O) is the water activity in PBI at equilibrium. where aPBI 2 Previous equation shows that the open-circuit potential under N2 H2 H2 O is related to m, the water transference number of Nafion as well as the water activity in the polymer membrane.
4.2. Open-circuit voltage in air Under air, hydrogen can react on the platinum electrode to produce H2 O. The potential under open-circuit condition is then deduced from: IO2 + IH2 = 0
(7)
where IO2 and IH2 are the current associated with ORR and HOR, respectively. This equation combined with the kinetics law of both ORR and HOR in a volumic electrode can be used to calculate the E versus log(P(H2 )) curve in air. Fig. 2 shows a schematic diagram of the gas diffusion electrode. The reacting gas goes first through the diffusion layer and then diffuses in the active layer where the reaction takes
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place. At each interface, it is possible to define a thermodynamic equilibrium and a thermodynamic constant according to: K1 =
a(X)diff a(X)gas
(8)
a(X)act a(X)diff
(9)
and K2 =
where a(X)Y is the activity of X in Y. This activity is either a concentration when Y is a solid phase or a partial pressure when Y is a gas phase. The assumptions of the model are as follows: • In the active layer, the ORR current density is given by the relation: O2 (x) 2.3 ab iO2 = −i0O2 ∗ act exp − (E − EO ) (10) 2 O2 act bO2 where O∗2 act
stands for the oxygen concentration in the active layer at equilibrium, O2 (x)act is the oxygen concentraab is the open-circuit potential tion at the abscise x and EO 2 in air. In Eq. (10), the reverse term of the kinetic law is neglected because ORR is low. • The HOR current density is given by the relationship: H2 (x)act 2.3 ab iH2 = i0H2 exp (E − E ) H2 H∗2 act b H2 2.3 ab − exp − ∗ (E − EH2 ) (11) bH2 where H∗2 act is the hydrogen concentration in the active layer at equilibrium, H2 (x)act is the hydrogen concentration ab is the open-circuit potential in air. at the abscise x and EH 2 ab is dependent on the relative As shown in section 0, EH 2 humidity in the gas mixture. • Mass transport limitations are only due to hydrogen and oxygen diffusion in the active layer and so the ohmic drop is neglected. Since the electrode operates under mixed potential conditions, the number of protons consumed by oxygen reduction is equivalent to the number of protons produced by hydrogen oxidation. Moreover, Ihonen et al. [22] have shown that mass transport limitations for oxygen reduction in a gas diffusion electrode are due to the diffusion of oxygen. • In the diffusion layer, the diffusion is expressed by Fick’s law. We only present the derivation for the HOR current since derivation of the ORR is identical. The current density can be calculated from mass balance for hydrogen in the active layer, which gives the differential equation [23]: DH2
∂2 H2 (x)act iH γ = 2 2 ∂x 2FL
(12)
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where DH2 is the hydrogen diffusion coefficient in the active layer and γ the roughness factor of the electrode. By defining Γ = H2 (x)act /H∗2 act and X = x − δ/L, Eq. (12) reduces to: ∂2 Γ − AΓ = −B ∂X2
(13)
ab )/b ) and where A = Lγ/2FDH2 H∗2 act i0H2 exp((E − EH H2 2 0 ab ∗ ∗ B = Lγ/2FDH2 H2 act iH2 exp(−(E − EH2 )/bH2 ) This equation is solved analytically with the boundary conditions:
∂Γ =0 ∂X DH2
at X = 1
(14)
∂H2 (x = l1 ) ∂x active layer
= D
∂H2 (x = l1 ) ∂x diffusion layer
at X = 0
(15)
where D is the hydrogen diffusion coefficient in the diffusion layer. This equation results from the flux continuity at the active layer/diffusion layer interface. In the diffusion layer, mass transport obeys to Fick’s law. We obtain the equation: D
∂2 H2 (x)diff =0 ∂x2
(16)
The boundary condition at x = δ (or at X = 0) is given by Eq. (15) and at x = 0, it is given by H2 (x = 0) = K1 P(H∗2 ). Combining (13), (14), (15) and (16), we can calculate the nondimensional hydrogen concentration Γ (X). This leads: √ √ B B e− A(X−1) + e A(X−1) √ Γ (X) = + 1 − A A cosh( A) + (DH2 δK2 /DL) √ √ × A sinh( A)
(17) The current for HOR is then obtained by using the following relationship: IH2 =
γi0H2 L
1
∗
(eπ0 Γ (X) − eπ0 )L dX
(18)
0
ab )/b ab ∗ ∗ where π0 = (E − EH H2 and π0 = (E − EH2 )/bH2 2 This leads to the expression: ∗
IH2 = γi0H2 Ag[eπ0 − eπ0 ] ×√
1 √ A/ tanh( A) + (DH2 δK2 /DL)A
(19)
where Ag is the geometric surface area. The ORR current is expressed by an equation similar to Eq. (18) in which the reverse term is neglected. Three asymptotic cases may be distinguished:
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Table 3 Parameters used for simulation of the E vs. log(P(H2 )) curves in dry air Parameters
Value
Geometrical electrode parameters Length of active layer (L) (10−4 cm) Length of diffusion layer (δ) (10−4 cm) Roughness factor (γ) Geometric area (Ag) (cm2 )
1 0.1 100 0.5
ORR Exchange current density (i0O2 ) (A cm2 ) Tafel slope (bO2 ) (mV) ab Open potential under air (EO ) (mV) 2 Diffusion coefficient in active layer (DO2 ) (cm2 /s) Diffusion coefficient in diffusion layer (D2 ) (cm2 /s)
4 × 10−7 120 860 2.5 × 10−6 2.5 × 10−6
[17,18,31] [17,18]
HOR Exchange current density (i0H2 ) (A/cm2 ) ∗ = b ) (mV) Tafel slope (bH H2 2 ab Open potential (EH ) 2 Diffusion coefficient in active layer (DH2 ) (cm2 /s) Diffusion coefficient in diffusion layer (D) (cm2 /s)
1 × 10−2 30 Nernst 2.5 × 10−6 7.6 × 10−6
[17,18,24] [17]
Thermodynamic constant for hydrogen and oxygen separation K1 , K2
1 × 10−6
[22,31]
• At low polarisation, √ i.e. when reaction is controlled by kinetics, the value of A is low. Eq. (19) can be simplified to: ∗
IH2 = γi0H2 Ag[eπ0 − eπ0 ]
(20)
• At high polarisation, Eq. (19) tends to a limiting current expressed by: IH2
lim
=
2F AgDK1 P(H2 ) δ
(21)
• for δ equal to zero (i.e. no diffusion layer), then Eq. (19) is similar to that obtained in the literature [24]. In particular, at high polarisation the current tends to: IH2 = Ag
DH2 H2∗act √ A L
(22)
The open-circuit potential for the Pt gas electrode was simulated according to Eq. (7) by numerical minimisation of the
Ref.
[25,31] [25,30]
[26] [26]
difference between ORR and HOR currents. For each oxygen/hydrogen partial pressure point, a simplex method was used to calculate the open-circuit potential. Parameters used for the simulation are given in Table 3. They were chosen in order to fulfil the following requirements: • Diffusion occurred through a polymer or liquid layer. The low values of limiting currents obtained experimentally allowed us to exclude gas phase diffusion. • The position of the abrupt change in potential on the E versus log(P(H2 )) curve should be in agreement with the experimental value. • Current densities for both reactions and mass transport parameters should be in agreement with literature data [25,26]. Fig. 7 shows the simulated E versus log(P(H2 )) curves for various roughness factors. The roughness factor has no clear influence of the potential jump position but it clearly
Fig. 7. Simulated E vs. log(P(H2 )) curves in dry air for various electrode roughness factors (gamma). (DO2 = 5 × 10−5 cm2 /s.)
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Fig. 8. Simulated E vs. log(P(H2 )) curves in dry air for various oxygen diffusion coefficients in the active layer.
influences the amplitude of the potential jump. From the figure, we clearly see that the limit of sensitivity (defined as the limit at low hydrogen partial pressure of the linear regime with a slope of 120 mV/decade) is dependent on the electrode roughness factor, in agreement with previous observations by Bouchet et al. [27] and as proposed by Opekar et al. [28,29]. Figs. 8 and 9 illustrate the influence of the oxygen mass transport parameters in the active layer. As expected, in the high P(H2 ) range the potentiometric response of the sensor is the same irrespective of the values of the oxygen mass transport parameters DO2 and L. In the P(H2 ) range between 10−3 and 10−1 bar, the theoretical sensitivity of the sensor is strongly dependant on DO2 . Fig. 8 shows that decreasing the oxygen diffusion coefficient from 5 × 10−5 to 1 × 10−7 cm2 /s changes the sensitivity from 120 to 240 mV/decade. This effect can be related to a change of the asymptotic behaviour of ORR from Eqs. (20)–(22). We observe also a decrease in the abruptness of the potential change and a broadening of the region where the potential change takes place. The results in Fig. 9 show that the effect of the active layer length is similar to that of the oxygen diffusion coefficient in the active layer. As expected, the effect of mass transport limitation is observed for high values of L and it corresponds to a Tafel slope close to 240 mV/decade.
5. Discussion The experimental results and the theoretical model presented above suggest that the E versus log(P(H2 )) curve for the platinum gas diffusion electrode in inert gas exhibits a Nernstian slope (i.e. 30 mV/decade at 25 ◦ C) and that E0 (corresponding to the emf for P(H2 ) = 1 bar) depends on the relative humidity in the measuring atmosphere. The proposed model indicates that E0 may result from the shift from equilibrium of the water activity in PBI. As a consequence, we expect that this shift should increase as the relative humidity increases. In agreement with the prediction of the model, our experimental results have shown that E0 shifted from 0 to more negative values as RH was increased from 0 to 100%. The good agreement between the shape of the E versus log(P(H2 )) curve under dry air observed experimentally and calculated from our model confirms that the mixed potential model can be used to describe the sensor behaviour in air. Moreover, from our theoretical model, it appears that the oxygen mass transport parameters in the active layer (DO2 , L) are crucial in determining the sensitivity of the Pt gas diffusion electrode in the medium P(H2 ) region. Recently, a proposal based on both experimental [22] and theoretical [30,31] arguments suggests that the water activity inside a gas diffusion electrode greatly influences the oxygen mass transport parameters. Therefore, we suggest that the difference in
Fig. 9. Simulated E vs. log(P(H2 )) curves in dry air for various active layer lengths. The thickness is in microns.
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Fig. 10. E vs. log(P(H2 )) curve in dry air obtained experimentally from potentiometric measurements () and from the ORR and HOR polarisation curves (䊉). The E vs. log(P(H2 )) curve in dry air simulated from the polarisation curve is also shown (dashed line) along with a curve showing the effect of the increasing the oxygen diffusion coefficient in the active layer (continuous line).
humidity may be responsible for differences between sensors responses observed experimentally. The fitting of the E versus log(P(H2 )) curve given in Fig. 10 illustrates this point. In this figure, the experimental E versus log(P(H2 )) data as well as the E versus log(P(H2 )) curve deduced from the plot of the ORR and HOR polarisation curves are presented. Comparison between both sets of experimental data shows that a good agreement for both low and high P(H2 ) is obtained. However, the curve deduced from the polarisation measurement deviates from the experimental curve in the medium P(H2 ) range. In order to explain this shift, we propose that the mass transport parameters are different during the polarisation and the mixed potential measurements. Using our theoretical model, we have fitted the ORR polarisation curve and used the fitted values of identified parameters to reconstruct the emf curve. As previously mentioned, the mass rate transfer of hydrogen was chosen in order to have an abrupt change of potential for a H2 /O2 ratio equal to 0.61. A discrepancy was observed between the model and experimental data in the medium P(H2 ) range with a potential shift towards more positive value under mixed potential conditions. In agreement with the simulation shown in Fig. 9, increasing the value of the oxygen diffusion coefficient in the active layer allowed us to decrease the discrepancy between experimental and calculated curves. The production of water under mixed potential measurement conditions could then explain why mass transport parameters are higher during potentiometric measurements. We also propose that the sensitivity enhancement observed for some sensors can also attributed to the same phenomenon. We have seen (from our theoretical model) that, when the oxygen diffusion coefficient in the active layer decreases, electrode potential in the low P(H2 ) domain varies linearly with log(P(H2 )) but that the sensitivity progressively increases from 120 to 240 mV/decade. Thus, we proposed to attribute the enhancement of sensor sensitivity observed at the beginning of the experiments to a small value of DO2 due to a low level of water in the Pt gas diffusion electrode. This phenomenon can disappear during mixed poten-
tial measurements, as observed experimentally, since water is produced. From a practical point of view, the great discrepancy between the E versus log(P(H2 )) curves tends to exclude the use of a platinum gas diffusion electrode as sensitive electrode for hydrogen gas sensors. Nevertheless, the reproducibility of the position of the abrupt potential change can be used to indicate a transition between high and low hydrogen partial pressure. For future work, it would be interesting to adjust the gas mass transport parameters in the diffusion layer in order to modify this position and thus obtain a system with a series of sensors that could sequentially analyse hydrogen partial pressure.
6. Conclusion In this work, we have studied the potentiometric response of different gas diffusion electrodes to hydrogen in inert gas and in air with various relative humidities. In dry inert atmospheres, all tested electrodes showed a Nernstian response with a sensitivity close to 30 mV per decade. In wet atmospheres, the sensitivity remained close to 30 mV/decade but an additional potential, E0 , which was a function of the relative humidity in the measuring atmosphere was observed. We attributed this phenomenon to a modification of water activity between both sides of the sensor. A thermodynamical expression taking into account the difference of water activity was proposed. For all the tested electrodes, the potentiometric response in air was explained by a mixed potential model and could be reconstructed from the polarisation curves obtained separately in air and in hydrogen–nitrogen gas mixtures. The influence of the oxygen mass transport parameters in the active layer was demonstrated both theoretically and experimentally. The enhancement of sensitivity from 120 to 240 mV/decade was attributed to the variation of the water content inside the electrode leading to a modification of the oxygen diffusion coefficient in the active layer.
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Acknowledgement The authors thank J. Deseure for his help in the simulation studies and for his help with the software.
References [1] N. Miura, N. Yamazoe, Proton Conductors-solids Membrane and Gels – Materials and Device, Cambridge University Press, 1992, pp. 527–536. [2] N. Miura, G. Lu, N. Yamazoe, Solid State Ionics 136 (2000) 533. [3] F. Opekar, K. Stulik, Anal. Chim. Acta 358 (1999) 151. [4] V.G. Ponomareva, G.V. Lavrova, E.F. Hairetdinov, Sensors Actuat. B 40 (1997) 95. [5] M.J.G. Jak, S. Raz, L.N. van Rij, J. Schoonman, I. Riess, Solid State Ionics 143 (2001) 205. [6] G. Lu, M. Norio, N. Yamazoe, Sensors Actuat. B 35 (1996) 130. [7] R. Bouchet, E. Siebert, G. Vitter, J. Electrochem. Soc 144 (1997) L95. [8] Handbook of Chemistry and Physics, 58th ed., CRC press. [9] R. Bouchet, E. Siebert, Solid State Ionics 118 (1999) 287. [10] F. Opekar, J. Langmaier, Z. Samec, J. Electroanal. Chem. 379 (1994) 301. [11] R. Bouchet, E. Siebert, G. Vitter, J. Electrochem. Soc. 147 (2000) 3548. [12] M.J. Weaver, S.C. Chang, L.W.H. Leung, X. Jiang, J. Electroanal. Chem. 327 (1992) 247. [13] H. Olender, W.E. O’Grady, H.S. Isaacs, S. Srinisivan, J. Appl. Electrochem. 12 (1982) 135.
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[14] R. Bouchet, E. Siebert, G. Vitter, J. Electrochem. Soc. 147 (2000) 3125. [15] S.F. Chehab, J.D. Canaday, A.K. Kuriakose, T.A. Wheat, A. Ahmad, Solid State Ionics 45 (1991) 299. [16] P. Hrncirova, F. Opekar, Sensors Actuat. B 81 (2002) 329. [17] O. Antoine, I.N.P. Grenoble Thesis, 1997. [18] O. Antoine, Y. Bultel, R. Durand, P. Ozil, Electrochim. Acta 43 (1998) 3681. [19] H. Olender, W.E. O’Ggrady, H.S. Isaacs, S. Srinisivan, J. Appl. Electrochem. 12 (1982) 135. [20] X. Glipa, B. Bonnet, B. Mula, D.J. Jones, J. Rozi`eres, J. Mater. Chem. 9 (1999) 3045. [21] D. Weng, J.S. Wainright, U. Landau, R.F. Savinell, J. Electrochem. Soc. 143 (1996) 1260. [22] J. Ihonen, F. Jaouen, G. Lindbergh, A. Lundblad, G. Sundholm, J. Electrochem. Soc. 149 (2002) A448. [23] F. Gloaguen, F. Andolfatto, R. Durand, P. Ozil, J. Appl. Electrochem. 24 (1994) 863. [24] Y. Bultel, I.N.P. Grenoble Thesis, 1997. [25] V. Basura, P.D. Beatti, S. Holdcroft, J. Electroanal. Chem. 458 (1998) 1. [26] J. Maruyma, M. Inaba, K. Katura, Z. Ogumi, Z-I. Takahara, J. Electroanal. Chem. 447 (1998) 201. [27] R. Bouchet, I.N.P. Grenoble Thesis, 1998. [28] F. Opekar, J. Langmaier, Z. Samec, J. Electroanal. Chem. 379 (1994) 301. [29] Z. Samec, F. Opekar, J.E.F. Crinjs, Electroanalysis 7 (1995) 1054. [30] M.L. Perry, J. Newman, E.J. Cairn, J. Electrochem. Soc. 145 (1998) 5. [31] F. Jaouen, G. Lindbergh, G. Sundholm, J. Electrochem. Soc. 149 (2002) A437.
Electrochemical sensors for detection of hydrogen in air: model of the non-Nernstian potentiometric response of platinum gas diffusion electrodes S. Rosini, E. Siebert∗ Laboratoire d’Electrochimie et de Physico-chimie des Mat´eriaux et des Interfaces (UMR 5631 CNRS – INPG – UJF), Ecole Nationale Sup´erieure d’Electrochimie et d’Electrom´etallurgie de Grenoble, 1130 rue de la piscine, BP 75, 38402 Saint Martin d’H`eres cedex, France Received 3 March 2004; received in revised form 3 September 2004; accepted 21 November 2004 Available online 5 January 2005
Abstract The potentiometric response of three different platinum gas diffusion electrodes deposited on H3 PO4 doped polybenzimidazole (PBI) was investigated under humidified atmospheres that contained H2 or mixtures of H2 and O2 . Continuum modelling was used to analyse the response. It is shown that the non-Nernstian response under H2 H2 O N2 mixtures can be explained by a difference of water activity on both sides of the membrane. Under H2 O2 N2 mixtures, the oxygen mass transport parameters have a strong effect on the electrode sensitivity. © 2004 Elsevier Ltd. All rights reserved. Keywords: Hydrogen sensors; Mixed potential; Polybenzimidazole; Gas diffusion electrode; Oxygen reduction; Hydrogen oxidation
1. Introduction Potentiometric sensors have been proposed for the detection of hydrogen because they are easy to use [1–4]. These devices commonly use protonic conductors such as Nafion [5] or antimonic acid [4] at low temperature and zirconium acid phosphate based electrolyte at high temperature [6]. Recently, we have proposed the use of H3 PO4 doped polybenzimidazole (PBI) [7] because it exhibits excellent mechanical and thermal properties [8] and it shows a good protonic conductivity even in dry atmospheres [9]. Most of the potentiometric sensors use platinum as the sensing electrode. When exposed to a humid atmosphere containing H2 , this electrode deposited on Nafion exhibits a non-Nernstian open-circuit voltage [10]. In ambient air, the hydrogen sensor sensitivity (defined as the slope of the E versus log(P(H2 )) curve) is always higher than that given by the Nernst equation and the potential is influenced by electrode morphology [11]. In par∗
Corresponding author. Tel.: +33 476826573; fax: +33 476826670. E-mail address: [email protected] (E. Siebert).
0013-4686/$ – see front matter © 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2004.11.044
ticular, gas diffusion electrodes, typically used in PEM fuel cell technology, exhibit a sigmoidal response, which is well explained by the mixed potential model resulting from hydrogen oxidation (HOR) and oxygen reduction (ORR) [11]. According to this model: • For low hydrogen partial pressure, the sensor potential varies linearly with the logarithm of the hydrogen partial pressure and the sensitivity, deduced from the ORR Tafel slope, is of the order of 120 mV/decade. • For high hydrogen partial pressure, the sensor potential varies linearly with the logarithm of the hydrogen partial pressure and the sensitivity is in agreement with the Nernst equation (30 mV/decade at room temperature). • The abrupt change of potential between these two zones can be explained by mass transport limitations of both HOR and ORR reactions. The objective of this paper was to better understand the potentiometric response of a Pt gas diffusion electrode when it was exposed to H2 H2 O N2 and H2 O2 N2 atmospheres. In the first part of this paper, experimental data obtained on
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Table 1 Description of the gas diffusion electrodes Electrode (mg/cm2 )
Platinum loading NAFION (mg/cm2 ) Roughness factor Active layer (10−6 m) Diffusion layer (10−6 m)
ETEK
SORAPECH2
SORAPECO2
0.5 Unknown 5 10 250
0.2 1 80 5 250
0.35 0.8 150 5 250
gas diffusion electrodes containing different platinum loadings in the active layer and deposited on PBI-X H3 PO4 are presented. In parallel to the experimental work, a continuum model that took into account the electrode structure consisting of a uniform diffusion layer placed on an active layer was developed. In this model, current was calculated separately for both HOR and ORR and then recombined according to the mixed potential assumption. Finally, analysis of the experimental results and comparison with the theoretical model allowed us to determine the parameters influencing the sensor response.
2. Experimental PBI, purchased from Celanese, was dissolved in dimethyl acetamide (DMAc) by stirring for 24 h. The film was drawn from this solution on a glass plate and dried for 10 h at 80 ◦ C. The membrane was then washed in water and dried during 1 h in order to remove any trace of DMAc. The film was immersed in phosphoric acid solution (85 w/o) in order to obtain a protonic conduction and dried for 1 h at 80 ◦ C. X was defined as the ratio of phosphoric acid on the number of PBI monomer and was between 3 and 3.8 for all the membranes tested. Three diffusion gas electrodes were used in this work. Table 1 summarises some of their main features. The elec-
trode manufacturers provided the platinum and Nafion loadings. The roughness factor (γ), defined as the ratio between active and geometric surface area, was determined in phosphoric acid solution (1 M) by cyclic voltammetry as described in [12]. The low roughness factor observed for all the ETEK electrodes in comparison to the platinum loading can be easily explained by ageing of the electrodes [13]. Electrode membrane assemblies were prepared by hot pressing at 150 ◦ C and 150 kg/cm2 . Fig. 1 shows a typical SEM micrograph of the cross section of the electrode/membrane interface. The active layer (containing platinum particles) is white and the diffusion layer is dark, as seen in the figure. The contact between electrode and electrolyte is continuous. The micrograph was used to estimate the macroscopic thickness of the active and diffusion layers. The corresponding results are reported in Table 1. For all the tested electrodes, the diffusion layer thickness (δ) is of order of 250 × 10−6 m. The macroscopic thickness (L) of the active layer was 5 × 10−6 m for the SORAPEC electrodes and 10 × 10−6 m for those purchased from ETEK. The potentiometric response was tested in a three electrode cell as described elsewhere [14]. A schematic representation is given in Fig. 2. A platinum ring electrode was deposited by sputtering on the same side as the working electrode and served as the reference electrode. A Pt electrode was deposited on the opposite side of the electrolyte in order to act as counter electrode. The reference electrode was in contact with pure hydrogen and the counter electrode was in contact with ambient air. The sensor emf was recorded in N2 H2 and N2 O2 H2 mixtures. The different gases were mixed with three mass flowmeters (BROOKS) to obtain various partial pressures of hydrogen. The N2 O2 concentration was adjusted to correspond to air. This condition is referred to as dry air further in the text. A part of the gas mixture could be humidified by bubbling
Fig. 1. SEM micrograph of the PBI-X H3 PO4 /SORAPECO2 interface.
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der dry condition (RH = 0%), the behaviour of the platinum electrodes was reproducible. The emf obeys to the Nernst’s law in agreement with our previous results [7]. However, in wet atmospheres, the response was no longer Nernstian. The sensitivity is of the order of 30 mV/decade but the emf value at P(H2 ) equal to one is different from zero. The sensor response can thus be expressed as: E = E0 −
Fig. 2. Schematic representation of the electrochemical cell.
through water and recombined with dry gases to obtain an atmosphere with controlled relative humidity (RH). Open-circuit potential was recorded using a high impedance voltammeter (HP 34401A). Polarisation studies were performed using a Solarton 1287 electrochemical interface. ORR polarisation curves were measured under dry air for each type of electrode. HOR polarisation curves were plotted under various H2 N2 mixtures. All the measurements were performed at ambient temperature. All simulation of potentiometric response were made using Matlab software.
3. Experimental results 3.1. Open-circuit voltage in inert gas The potentiometric response of an ETEK electrode in H2 N2 mixtures for different RH is shown in Fig. 3(a). Un-
RT ln(P(H2 )) 2F
(1)
where E0 is dependent on the relative humidity in the gas mixture. Fig. 3(b) shows the variation of E0 as a function of RH for the three types of electrodes. We can see from the figure that the potential decreases with increasing relative humidity. This phenomenon has already been observed in potentiometric hydrogen sensors based on PBI-X H3 PO4 [11] and protonic NASICON (Hyceram) [15]. With PBI, Bouchet et al. [11] have shown that E0 for gas diffusion electrodes was a function of the acid content in the polymer membrane. On the contrary, with a platinum grid and a thin film, E0 was equal to zero indicating that the Nernst law was obeyed with this type of Pt electrodes. With Nafion, Jak et al. [5] have recently found a variation of the sensitivity as a function of the humidity present in gas mixtures in contrast to our results. They attribute this behaviour to the fact that, in Nafion, the proton conduction is influenced by water activity in the polymer and by a difference of water adsorption properties of the reference and working electrodes. 3.2. Open-circuit voltage in air The potentiometric response as a function of log(P(H2 )) in dry air for the three platinum electrodes is shown in Fig. 4. As expected from previous results [11], the opencircuit voltage does not obey to the Nersnt’s law. At high P(H2 ) (P(H2 ) > 0.14 bar), the potential varies linearly with the logarithm of P(H2 ) and the sensitivity is between 27 and 30 mV/decade. At low P(H2 ) (P(H2 ) < 0.08 bar), the potentiometric response varies linearly with the logarithm of P(H2 ) but the sensitivity is higher than that given by the Nernst
Fig. 3. (a) Open-circuit voltage of the ETEK electrode for various relative humidities. 䊉: RH = 0%, ♦: RH = 20%, +: RH = 50%, : RH = 100%. (b) E0 vs. RH for : ETEK, : SORAPECO2, *: SORAPEC H2.
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Fig. 4. (a) Open-circuit voltage as a function of log(P(H2 )) in dry air for the three electrodes. +: ETEK, : SORAPECH2, : SORAPECO2. (b) Evolution of the curve with the time. The curve () was recorded 24 h after the curve () for a SORAPECH2 electrode. The curve (♦) was recorded for a SORAPECO2 electrode at time t = 0.
equation. In this domain of P(H2 ), the sensitivity is typically of the order of 120 mV/decade. The transition between the two limiting regimes is marked by a strong potential jump (0.14 < P(H2 ) < 0.08 bar). The position of the potential step on the P(H2 ) axis is not the function of the platinum loading. The variation of the E versus log(P(H2 )) curve as a function of the time is shown in Fig. 3(b). Only the response at low P(H2 ) was found to vary from one day to another. This behaviour was observed for all the series of electrodes tested over an extended period of time. The potential in the low P(H2 ) domain was found to decrease systematically. However, the decrease was not reproducible and the discrepancy was of the order of 100 mV. Another interesting feature is that, at the beginning of the experiments, a sensitivity as high as 240 mV/decade can be obtained as illustrated on Fig. 4(b) for a SORAPECO2 electrode. This phenomenon progressively disappears during the measurement in air and the sensitivity finally reaches a classical value of 120 mV/decade. The influence of humidity on the open-circuit voltage output of the sensors has also been tested. As previously shown by Bouchet et al. [14], variation of RH does not modify the potentiometric response at high P(H2 ) and does not change the
position of the potential step. However, we observe a modification of the potentiometric response at low P(H2 ). This behaviour is illustrated in Fig. 5, where the potentiometric response obtained with a SORAPECO2 electrode for different RH in the gas mixture is shown. In the low P(H2 ) range, the potentiometric response can be identified with a straight line corresponding to the following equation: E = E0 − a log(P(H2 ))
(2)
Increasing RH does not change the sensitivity of the sensors which remains of the order of 120 mV/decade. However, an enhancement of E0 is observed. It is worth noting that when an enhanced slope is obtained in dry air, a decrease of electrode sensitivity is systematically observed when RH is increased. The same phenomenon was reported for a sensor based on Nafion as electrolyte [16]. 3.3. ORR and HOR polarisation curves The shape of the polarisation curves is identical to that usually reported in the literature for the ORR and HOR
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Fig. 5. Open-circuit voltage as a function of log(P(H2 )) in wet air (electrode SORAPECH2). : RH = 0%, : RH = 20%, : RH = 50%, 䊉 RH = 100%.
[11,17,18]. At low current densities, the ORR polarisation curve exhibited a Tafel line behaviour and a limiting current was observed at high cathodic overvoltage. Table 2 shows the slope of the Tafel line, the exchange current I0 and the limiting current Ilim for each type of electrode. I0 was determined by extrapolation of the straight line to the open-circuit voltage. The HOR polarisation curve exhibited a limiting current that varied linearly with P(H2 ). m(P(H2 )) is defined as the slope of the Ilim versus P(H2 ) curve. The values of m(P(H2 )) are indicated in Table 2. As shown in Table 2, the slope of the Tafel line is equal to 120 mV/decade. The exchange current of the ETEK electrode is the lowest, in agreement with the roughness factor determined in solution. It must be emphasised that the experimental error in determination of the exchange current may be important due to non-reproducibility of the open-circuit potential whose variation can reach 250 mV. Taking this into consideration, it is likely that the roughness factors determined in liquid medium are different from those in the solid state [19]. The ORR limiting currents slightly depend on the nature of the electrode and are around 23 mA (±4 mA). Similarly, m(P(H2 )) is almost the same irrespective of the platinum loading of the gas diffusion electrode. According to these results, it appears that the limiting currents for ORR and HOR are due to mass transport phenomena.
In order to better understand the origin of the enhancement of sensor sensitivity to 240 mV/decade, the ORR polarisation curve in dry air was recorded immediately after a potentiometric measurement thus giving a high sensitivity in the low hydrogen partial pressure range. The Tafel slope was also enhanced and equal to 240 mV/decade. So, we can conclude that the high sensitivity is related to a modification of the ORR kinetics. Fig. 6 gives the ORR polarisation curves obtained in dry air after a potentiometric measurement, as a function of time. The curve at time t = 0 had a Tafel slope of 120 mV/decade and a limiting current around 20 mA. The limiting current decreased with time and was reduced to 5 mA after 8 h. Concurrently the Tafel slope increased to a value of 240 mV/decade. As shown in Fig. 6, the original ORR polarisation curve could be recovered by exposing the sensors to humidified air (RH = 100%) for 5 h. It can therefore be concluded that the enhanced sensitivity can be related to a low water level in the electrode.
4. Theoretical analysis The theoretical treatment deals with the calculation of the open-circuit voltage of the Pt gas diffusion electrode either
Table 2 Kinetics parameters of ORR and HOR. I0 and Ilim are deduced from the ORR polarisation curves in dry air Electrode SORAPECO2 SORAPECH2 E-TEK
Open potential under air (mV)
I0 at open potential (A)
Ilim (mA)
m(P(H2 )) (mA/bar)
808 840 910
2.5 × 10−4
23 27 19
112 146 128
1.1 × 10−4 3.5 × 10−5
m(P(H2 )) is determined from HOR polarisation curves measured at various P(H2 ) and corresponds to the proportionality coefficient of the Ilim vs. P(H2 ) straight line.
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Fig. 6. ORR polarisation curves measured in dry air after a potentiometric measurement (ETEK electrode). (a) t = 0, (b) t = 1 h, (c) t = 7 h. Curve measured in wet air after (d) t = 3 h at RH = 50% and (e) t = 5 h at RH = 100%.
in inert gas (thermodynamic potential) or in air (mixed potential). 4.1. Open-circuit voltage in inert gas Under dry atmospheres, the open-circuit voltage is given by Nernst’s law as described by the following equation: E=−
1 [RT ln(P(H2 ))] 2F
(3)
Under humidified atmospheres, PBI may absorb water from the gas phase [14]. In particular, Glipa et al. have shown that the quantity of water inside PBI was a function of the acid content [20]. The difference of water activity between the reference (under 100% H2 ) and the working electrode may be responsible for a water flux across the polymer membrane. If both sides of the polymer membrane were exposed to the same RH, an equilibrium could be reached. Under this condi∗ (H O) tion, water activity inside PBI would be equal to aPBI 2 and the potential would be given by Eq. (3). The equilibrium between the gas phase and the Pt gas diffusion electrode containing Nafion takes into account the difference of water activity. This leads to the following equilibrium, as already proposed to explain Nafion transport properties [5]: H2 + 2mH2 O 2[(H+ )H2 Om ]act + 2 e−
(I)
where act stands for active layer of the Pt gas diffusion electrode. Contrary to Nafion, acid doped PBI transports proton without water since the drag number has been measured to be near zero [21]. As a consequence, the thermodynamic equilibrium at the Pt electrode/PBI interface is expressed as: + H+ PBI + mH2 OPBI [(H )H2 Om ]act
(II)
Combining (I) and (II) with the Nernst equation for the Pt reference electrode exposed to 100% H2 leads to the following
expression for the Pt gas diffusion electrode potential: E=
m 0 (µ (H2 O) − µ0gaz (H2 O)) F PBI RT aPBI (H2 O) 1 +m ln − [RT ln(P(H2 ))] (4) F P(H2 O) 2F
where µ0Y (X) is the normal chemical potential of X in Y and P(X) the partial pressure of X. Equilibrium between water in gas phase and water in PBI can be expressed as following: ∗ aPBI (H2 O) 0 0 µgaz (H2 O) − µPBI (H2 O) = RT ln (5) P(H2 O) This leads:
aPBI (H2 O) RT ln E=m ∗ (H O) F aPBI 2 Preference (H2 ) 1 RT ln + 2F Pwork (H2 )
(6)
∗ (H O) is the water activity in PBI at equilibrium. where aPBI 2 Previous equation shows that the open-circuit potential under N2 H2 H2 O is related to m, the water transference number of Nafion as well as the water activity in the polymer membrane.
4.2. Open-circuit voltage in air Under air, hydrogen can react on the platinum electrode to produce H2 O. The potential under open-circuit condition is then deduced from: IO2 + IH2 = 0
(7)
where IO2 and IH2 are the current associated with ORR and HOR, respectively. This equation combined with the kinetics law of both ORR and HOR in a volumic electrode can be used to calculate the E versus log(P(H2 )) curve in air. Fig. 2 shows a schematic diagram of the gas diffusion electrode. The reacting gas goes first through the diffusion layer and then diffuses in the active layer where the reaction takes
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place. At each interface, it is possible to define a thermodynamic equilibrium and a thermodynamic constant according to: K1 =
a(X)diff a(X)gas
(8)
a(X)act a(X)diff
(9)
and K2 =
where a(X)Y is the activity of X in Y. This activity is either a concentration when Y is a solid phase or a partial pressure when Y is a gas phase. The assumptions of the model are as follows: • In the active layer, the ORR current density is given by the relation: O2 (x) 2.3 ab iO2 = −i0O2 ∗ act exp − (E − EO ) (10) 2 O2 act bO2 where O∗2 act
stands for the oxygen concentration in the active layer at equilibrium, O2 (x)act is the oxygen concentraab is the open-circuit potential tion at the abscise x and EO 2 in air. In Eq. (10), the reverse term of the kinetic law is neglected because ORR is low. • The HOR current density is given by the relationship: H2 (x)act 2.3 ab iH2 = i0H2 exp (E − E ) H2 H∗2 act b H2 2.3 ab − exp − ∗ (E − EH2 ) (11) bH2 where H∗2 act is the hydrogen concentration in the active layer at equilibrium, H2 (x)act is the hydrogen concentration ab is the open-circuit potential in air. at the abscise x and EH 2 ab is dependent on the relative As shown in section 0, EH 2 humidity in the gas mixture. • Mass transport limitations are only due to hydrogen and oxygen diffusion in the active layer and so the ohmic drop is neglected. Since the electrode operates under mixed potential conditions, the number of protons consumed by oxygen reduction is equivalent to the number of protons produced by hydrogen oxidation. Moreover, Ihonen et al. [22] have shown that mass transport limitations for oxygen reduction in a gas diffusion electrode are due to the diffusion of oxygen. • In the diffusion layer, the diffusion is expressed by Fick’s law. We only present the derivation for the HOR current since derivation of the ORR is identical. The current density can be calculated from mass balance for hydrogen in the active layer, which gives the differential equation [23]: DH2
∂2 H2 (x)act iH γ = 2 2 ∂x 2FL
(12)
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where DH2 is the hydrogen diffusion coefficient in the active layer and γ the roughness factor of the electrode. By defining Γ = H2 (x)act /H∗2 act and X = x − δ/L, Eq. (12) reduces to: ∂2 Γ − AΓ = −B ∂X2
(13)
ab )/b ) and where A = Lγ/2FDH2 H∗2 act i0H2 exp((E − EH H2 2 0 ab ∗ ∗ B = Lγ/2FDH2 H2 act iH2 exp(−(E − EH2 )/bH2 ) This equation is solved analytically with the boundary conditions:
∂Γ =0 ∂X DH2
at X = 1
(14)
∂H2 (x = l1 ) ∂x active layer
= D
∂H2 (x = l1 ) ∂x diffusion layer
at X = 0
(15)
where D is the hydrogen diffusion coefficient in the diffusion layer. This equation results from the flux continuity at the active layer/diffusion layer interface. In the diffusion layer, mass transport obeys to Fick’s law. We obtain the equation: D
∂2 H2 (x)diff =0 ∂x2
(16)
The boundary condition at x = δ (or at X = 0) is given by Eq. (15) and at x = 0, it is given by H2 (x = 0) = K1 P(H∗2 ). Combining (13), (14), (15) and (16), we can calculate the nondimensional hydrogen concentration Γ (X). This leads: √ √ B B e− A(X−1) + e A(X−1) √ Γ (X) = + 1 − A A cosh( A) + (DH2 δK2 /DL) √ √ × A sinh( A)
(17) The current for HOR is then obtained by using the following relationship: IH2 =
γi0H2 L
1
∗
(eπ0 Γ (X) − eπ0 )L dX
(18)
0
ab )/b ab ∗ ∗ where π0 = (E − EH H2 and π0 = (E − EH2 )/bH2 2 This leads to the expression: ∗
IH2 = γi0H2 Ag[eπ0 − eπ0 ] ×√
1 √ A/ tanh( A) + (DH2 δK2 /DL)A
(19)
where Ag is the geometric surface area. The ORR current is expressed by an equation similar to Eq. (18) in which the reverse term is neglected. Three asymptotic cases may be distinguished:
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Table 3 Parameters used for simulation of the E vs. log(P(H2 )) curves in dry air Parameters
Value
Geometrical electrode parameters Length of active layer (L) (10−4 cm) Length of diffusion layer (δ) (10−4 cm) Roughness factor (γ) Geometric area (Ag) (cm2 )
1 0.1 100 0.5
ORR Exchange current density (i0O2 ) (A cm2 ) Tafel slope (bO2 ) (mV) ab Open potential under air (EO ) (mV) 2 Diffusion coefficient in active layer (DO2 ) (cm2 /s) Diffusion coefficient in diffusion layer (D2 ) (cm2 /s)
4 × 10−7 120 860 2.5 × 10−6 2.5 × 10−6
[17,18,31] [17,18]
HOR Exchange current density (i0H2 ) (A/cm2 ) ∗ = b ) (mV) Tafel slope (bH H2 2 ab Open potential (EH ) 2 Diffusion coefficient in active layer (DH2 ) (cm2 /s) Diffusion coefficient in diffusion layer (D) (cm2 /s)
1 × 10−2 30 Nernst 2.5 × 10−6 7.6 × 10−6
[17,18,24] [17]
Thermodynamic constant for hydrogen and oxygen separation K1 , K2
1 × 10−6
[22,31]
• At low polarisation, √ i.e. when reaction is controlled by kinetics, the value of A is low. Eq. (19) can be simplified to: ∗
IH2 = γi0H2 Ag[eπ0 − eπ0 ]
(20)
• At high polarisation, Eq. (19) tends to a limiting current expressed by: IH2
lim
=
2F AgDK1 P(H2 ) δ
(21)
• for δ equal to zero (i.e. no diffusion layer), then Eq. (19) is similar to that obtained in the literature [24]. In particular, at high polarisation the current tends to: IH2 = Ag
DH2 H2∗act √ A L
(22)
The open-circuit potential for the Pt gas electrode was simulated according to Eq. (7) by numerical minimisation of the
Ref.
[25,31] [25,30]
[26] [26]
difference between ORR and HOR currents. For each oxygen/hydrogen partial pressure point, a simplex method was used to calculate the open-circuit potential. Parameters used for the simulation are given in Table 3. They were chosen in order to fulfil the following requirements: • Diffusion occurred through a polymer or liquid layer. The low values of limiting currents obtained experimentally allowed us to exclude gas phase diffusion. • The position of the abrupt change in potential on the E versus log(P(H2 )) curve should be in agreement with the experimental value. • Current densities for both reactions and mass transport parameters should be in agreement with literature data [25,26]. Fig. 7 shows the simulated E versus log(P(H2 )) curves for various roughness factors. The roughness factor has no clear influence of the potential jump position but it clearly
Fig. 7. Simulated E vs. log(P(H2 )) curves in dry air for various electrode roughness factors (gamma). (DO2 = 5 × 10−5 cm2 /s.)
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Fig. 8. Simulated E vs. log(P(H2 )) curves in dry air for various oxygen diffusion coefficients in the active layer.
influences the amplitude of the potential jump. From the figure, we clearly see that the limit of sensitivity (defined as the limit at low hydrogen partial pressure of the linear regime with a slope of 120 mV/decade) is dependent on the electrode roughness factor, in agreement with previous observations by Bouchet et al. [27] and as proposed by Opekar et al. [28,29]. Figs. 8 and 9 illustrate the influence of the oxygen mass transport parameters in the active layer. As expected, in the high P(H2 ) range the potentiometric response of the sensor is the same irrespective of the values of the oxygen mass transport parameters DO2 and L. In the P(H2 ) range between 10−3 and 10−1 bar, the theoretical sensitivity of the sensor is strongly dependant on DO2 . Fig. 8 shows that decreasing the oxygen diffusion coefficient from 5 × 10−5 to 1 × 10−7 cm2 /s changes the sensitivity from 120 to 240 mV/decade. This effect can be related to a change of the asymptotic behaviour of ORR from Eqs. (20)–(22). We observe also a decrease in the abruptness of the potential change and a broadening of the region where the potential change takes place. The results in Fig. 9 show that the effect of the active layer length is similar to that of the oxygen diffusion coefficient in the active layer. As expected, the effect of mass transport limitation is observed for high values of L and it corresponds to a Tafel slope close to 240 mV/decade.
5. Discussion The experimental results and the theoretical model presented above suggest that the E versus log(P(H2 )) curve for the platinum gas diffusion electrode in inert gas exhibits a Nernstian slope (i.e. 30 mV/decade at 25 ◦ C) and that E0 (corresponding to the emf for P(H2 ) = 1 bar) depends on the relative humidity in the measuring atmosphere. The proposed model indicates that E0 may result from the shift from equilibrium of the water activity in PBI. As a consequence, we expect that this shift should increase as the relative humidity increases. In agreement with the prediction of the model, our experimental results have shown that E0 shifted from 0 to more negative values as RH was increased from 0 to 100%. The good agreement between the shape of the E versus log(P(H2 )) curve under dry air observed experimentally and calculated from our model confirms that the mixed potential model can be used to describe the sensor behaviour in air. Moreover, from our theoretical model, it appears that the oxygen mass transport parameters in the active layer (DO2 , L) are crucial in determining the sensitivity of the Pt gas diffusion electrode in the medium P(H2 ) region. Recently, a proposal based on both experimental [22] and theoretical [30,31] arguments suggests that the water activity inside a gas diffusion electrode greatly influences the oxygen mass transport parameters. Therefore, we suggest that the difference in
Fig. 9. Simulated E vs. log(P(H2 )) curves in dry air for various active layer lengths. The thickness is in microns.
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Fig. 10. E vs. log(P(H2 )) curve in dry air obtained experimentally from potentiometric measurements () and from the ORR and HOR polarisation curves (䊉). The E vs. log(P(H2 )) curve in dry air simulated from the polarisation curve is also shown (dashed line) along with a curve showing the effect of the increasing the oxygen diffusion coefficient in the active layer (continuous line).
humidity may be responsible for differences between sensors responses observed experimentally. The fitting of the E versus log(P(H2 )) curve given in Fig. 10 illustrates this point. In this figure, the experimental E versus log(P(H2 )) data as well as the E versus log(P(H2 )) curve deduced from the plot of the ORR and HOR polarisation curves are presented. Comparison between both sets of experimental data shows that a good agreement for both low and high P(H2 ) is obtained. However, the curve deduced from the polarisation measurement deviates from the experimental curve in the medium P(H2 ) range. In order to explain this shift, we propose that the mass transport parameters are different during the polarisation and the mixed potential measurements. Using our theoretical model, we have fitted the ORR polarisation curve and used the fitted values of identified parameters to reconstruct the emf curve. As previously mentioned, the mass rate transfer of hydrogen was chosen in order to have an abrupt change of potential for a H2 /O2 ratio equal to 0.61. A discrepancy was observed between the model and experimental data in the medium P(H2 ) range with a potential shift towards more positive value under mixed potential conditions. In agreement with the simulation shown in Fig. 9, increasing the value of the oxygen diffusion coefficient in the active layer allowed us to decrease the discrepancy between experimental and calculated curves. The production of water under mixed potential measurement conditions could then explain why mass transport parameters are higher during potentiometric measurements. We also propose that the sensitivity enhancement observed for some sensors can also attributed to the same phenomenon. We have seen (from our theoretical model) that, when the oxygen diffusion coefficient in the active layer decreases, electrode potential in the low P(H2 ) domain varies linearly with log(P(H2 )) but that the sensitivity progressively increases from 120 to 240 mV/decade. Thus, we proposed to attribute the enhancement of sensor sensitivity observed at the beginning of the experiments to a small value of DO2 due to a low level of water in the Pt gas diffusion electrode. This phenomenon can disappear during mixed poten-
tial measurements, as observed experimentally, since water is produced. From a practical point of view, the great discrepancy between the E versus log(P(H2 )) curves tends to exclude the use of a platinum gas diffusion electrode as sensitive electrode for hydrogen gas sensors. Nevertheless, the reproducibility of the position of the abrupt potential change can be used to indicate a transition between high and low hydrogen partial pressure. For future work, it would be interesting to adjust the gas mass transport parameters in the diffusion layer in order to modify this position and thus obtain a system with a series of sensors that could sequentially analyse hydrogen partial pressure.
6. Conclusion In this work, we have studied the potentiometric response of different gas diffusion electrodes to hydrogen in inert gas and in air with various relative humidities. In dry inert atmospheres, all tested electrodes showed a Nernstian response with a sensitivity close to 30 mV per decade. In wet atmospheres, the sensitivity remained close to 30 mV/decade but an additional potential, E0 , which was a function of the relative humidity in the measuring atmosphere was observed. We attributed this phenomenon to a modification of water activity between both sides of the sensor. A thermodynamical expression taking into account the difference of water activity was proposed. For all the tested electrodes, the potentiometric response in air was explained by a mixed potential model and could be reconstructed from the polarisation curves obtained separately in air and in hydrogen–nitrogen gas mixtures. The influence of the oxygen mass transport parameters in the active layer was demonstrated both theoretically and experimentally. The enhancement of sensitivity from 120 to 240 mV/decade was attributed to the variation of the water content inside the electrode leading to a modification of the oxygen diffusion coefficient in the active layer.
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Acknowledgement The authors thank J. Deseure for his help in the simulation studies and for his help with the software.
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