[12]sofc : Lscm-ysz Composite Anodes For Methane Oxidation
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Solid State Ionics 177 (2006) 149 – 157 www.elsevier.com/locate/ssi
(La0.75Sr0.25)(Cr0.5Mn0.5)O3/YSZ composite anodes for methane oxidation reaction in solid oxide fuel cells S.P. Jiang *, X.J. Chen, S.H. Chan, J.T. Kwok, K.A. Khor School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore Received 19 April 2005; received in revised form 10 August 2005; accepted 7 September 2005
Abstract The synthesis and performance of (La0.75Sr0.25)(Cr0.5Mn0.5)O3/Y2O3 – ZrO2 (LSCM/YSZ) composites are investigated as alternative anodes for the direct utilization of methane (i.e., natural gas) in solid oxide fuel cells. Addition of YSZ phase greatly improves the adhesion and reduces the electrode polarization resistance of the LSCM/YSZ composite anodes. LSCM/YSZ composite anodes show reasonably good performance for the methane oxidation reaction in wet CH4 and the best electrode performance was achieved for the composite with LSCM contents of 50 – 60 wt.% with polarization resistances of 2 – 3 V cm2 in 97% CH4/3% H2O at 850 -C. The electrode impedance for the methane oxidation in wet CH4 on the LSCM/YSZ composite anodes was characterized by three separable arcs and the electrode behavior could be explained based on the ALS model for the reaction on the MIEC electrode. The results indicate that electrocatalytic activity of the LSCM/YSZ composite anodes for the methane oxidation is likely limited by the oxygen vacancy diffusion in the substituted lanthanum chromite-based materials. D 2005 Elsevier B.V. All rights reserved. PACS: 84.60.D Keywords: Alternative anodes; LSCM/YSZ composite; Methane oxidation; Solid oxide fuel cells
1. Introduction It is well known that Ni/Y2O3 –ZrO2 (Ni/YSZ) cermet anodes of solid oxide fuel cells (SOFC) have excellent catalytic properties and stability for the H2 oxidation of hydrogen fuel at SOFC operation conditions [1,2]. However, Ni/YSZ-based anode suffers a number of drawbacks in systems where hydrocarbon fuel is used such as sulfur poisoning and carbon deposition [2]. Carbon deposition covers the active sites of the anode, resulting in the loss of the cell performance [3]. Under high carbon activity environment, Ni metal could be corroded by a process known as metal dusting [4]. As Ni is a good catalyst for hydrocarbon cracking reaction, Ni/YSZ cermet anodes can only be directly used in hydrocarbon fuels if excess steam is present to ensure the complete fuel reforming and to suppress the carbon deposition. High steam/ carbon ratio is not attractive for fuel cells as it lowers the electrical efficiency of the fuel cells by diluting the fuel. The
* Corresponding author. Fax: +65 6791 1859. E-mail address: [email protected] (S.P. Jiang). 0167-2738/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2005.09.010
endothermic nature of the steam reforming reaction can also cause local cooling and steep thermal gradients potentially capable of mechanically damaging the cell stack [5]. Thus, development of structurally stable anodes with high electrocatalytic activity for hydrocarbon fuel oxidation is vital for the natural gas fuel-based SOFC. Replacing Ni/YSZ cermet anodes by Ni-free oxides such as ceria, titanate and lanthanum chromite-based oxides has attracted a great attention recently. Doped LaCrO3-based materials have been extensively investigated as interconnect material in SOFC [6]. LaCrO3-based oxide such as (LaSr)CrO3 was shown to have very low activity towards carbon deposition [7]. Catalytic activity of LaCrO3 for methane oxidation can also be substantially enhanced by partial substitution at A- and Bsites. Sfeir et al. [8,9] studied the thermodynamic stability and the catalytic activity of (LaA)(CrB)O3 system (A= Ca, Sr and B = Mg, Mn, Fe, Co, Ni) as alternative anode materials under simulated SOFC operation conditions. Thermodynamically, Sr and Mn substitution maintains the stability of the perovskite while other substitutes destabilize the system. However, transition metal substituted LaCrO3 did not decompose easily under reducing conditions, indicating that the decomposition of
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the substituted LaCrO3 would be hindered kinetically. Ca and Sr substitution at the A-site improves the catalytic activity and for B-site substitution, Co and Mg show an inhibiting effect while Mn, Fe and Ni improve the activity. Recently, Tao and Irvine [10,11] reported promising results of La0.75Sr0.25Cr0.5Mn0.5O3 (LSCM) as anode for SOFC. LSCM is a p-type conductor with conductivity of ¨ 38 S cm 1 in air and 1.5 S cm 1 in 5% H2 at 900 -C. The electrode polarization resistance for the oxidation reactions in wet CH4 and H2 at 900 -C was 0.85 V cm2 and 0.26 V cm2, respectively. The performances are considered to be compatible to the Ni/YSZ cermet anodes. Addition of the ionic conducting phase such YSZ allows delocalization of the reaction in the entire electrode volume, increasing the reaction sites and enhancing the performance of the electrode. Thus, it would be interesting to investigate the performance of LSCM/YSZ composite anodes. In this report, the fabrication and performance of LSCM/YSZ composite anodes were investigated to assess their feasibility as alternative anodes for methane oxidation reactions for SOFC. The process and reaction mechanism of the CH4 oxidation reaction in wet CH4 (3% H2O) are discussed. 2. Experimental YSZ electrolyte substrates were prepared from 8 mol% yttria-stabilized zirconia (YSZ, Tosoh, Japan) powders by die pressing and sintered at 1550 -C for 4 h. The diameter and thickness of the YSZ electrolyte were ¨ 20 mm and ¨ 1 mm, respectively. The surface of YSZ discs was ground using sandpapers to increase the roughness of the surface and the contact between the electrode and the YSZ electrolyte. The composition of LSCM was chosen as La0.75Sr0.25 Cr0.5Mn0.5O3 (LSCM) [10,11]. LSCM was prepared from La2O3, SrCO3, Cr2O3 and MnCO3 (all from Aldrich) by solid-state reaction. La2O3 was heat-treated at 1000 -C to get rid of the moisture. The powders were mixed and ball-milled for 4 h with propanol. The mixture was then heated at 1200 -C for 20 h in air. LSCM/YSZ composites with various weight ratios were made by ball milling for 1 h. The mixture of LSCM and YSZ was again mixed thoroughly with addition of PG400 in mortar for another 30 min to form slurry. Carbon (5 wt.%) was added to the composite slurry as pore-former. LSCM and LSCM/YSZ composite electrodes were applied to the electrolyte disk by slurry painting. To study the sintering temperature, LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes were sintered at 1100, 1200 and 1300 -C in air, respectively, for 2 h. The thermal expansion coefficients of the LSCM and LSCM (50%)/YSZ (50%) composites were measured by a Perkin Helmer Dynamic Mechanical Analyzer. The samples were pressed into cylinder with a diameter of 10 mm and a length of 5 mm. After sintering at 1200 -C for 2 h, the diameter of the cylinders shrank to ¨ 8 mm. Temperature was raised from 30 -C to 900 -C with heating rate of 10 -C min 1. Data were recorded and thermal expansion coefficient (TEC) was calculated from the slope of the curve.
Platinum paste was painted onto the center of the other side of the electrolyte substrate as the counter electrode and the reference electrode was painted as a ring at the edge of the electrolyte substrate. Pt mesh was used as current collector for both anode and counter electrode. Different to the experimental settings reported by Tao and Irvine [11], no additional Pt or Au paste was applied to the coating surface of the anode. The distance between the counter and ring reference electrodes was ¨ 4 mm. Methane humidified at room temperature (97% CH4/ 3% H2O) was used as fuel and air was used as oxidant. The fuel flow rate was controlled at 100 sccm. Electrochemical impedance spectroscopy was carried out using a Solartron 1255 frequency response analyzer coupled to a Solartron 1287 electrochemical interface. The impedance spectra of the electrochemical cell were recorded at open circuit voltage (OCV) with amplitude of 10 mV over the frequency range 0.01 Hz to 1 MHz. The ohmic resistance of the electrolyte and the anode (R V) was estimated from the high frequency intercept of the impedance curves and the overall electrode polarization (interface) resistance (R E) was directly measured from the differences between the low and high frequency intercepts on the impedance curves. The impedance responses were analyzed using an equivalent circuit method. The measurement was carried out in the temperature range of 800 to 950 -C. Microstructure of the anodes after the performance testing was inspected by scanning electron microscopy (SEM, Leica 360, Germany). 3. Results and discussions 3.1. The phase and thermal expansion coefficient Fig. 1 is the X-ray diffraction (XRD) pattern of a LSCM powder sintered at 1200 -C. The patterns are identical to the La0.75Sr0.25Cr0.5Mn0.5O3 obtained at 1400 -C [11], indicating the formation of the perovskite phase of the LSCM powder. Fig. 2 shows the thermal expansion of pure LSCM and LSCM (50%)/YSZ (50%) composite. The linear thermal expansion coefficient (TEC) of LSCM is 9.2 10 6 K 1 in the
Fig. 1. XRD pattern of La0.75Sr0.25Cr0.5Mn0.5O3 (LSCM) powder sintered at 1200 -C for 20 h.
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Fig. 4. Impedance curves of the reaction on LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes sintered at different temperatures. The EIS was measured at 850 -C in wet CH4. Fig. 2. The TEC of La0.75Sr0.25Cr0.5Mn0.5O3 (LSCM) and LSCM (50%)/YSZ (50%) at high temperatures in air.
temperature range of 34 – 135 -C and 13.7 10 6 K 1 between 161 -C and 900 -C. There is a slope change at 135 –161 -C. The average TEC between 30 -C and 900 -C is 11.4 10 6 K 1, which is higher than 9.3 10 6 K 1 reported by Tao and Irvine [11] for the same oxide. Addition of YSZ phase reduces the thermal expansion of the composite. In the case of LSCM (50%)/YSZ (50%) composites, the TEC is 8.4 10 6 K 1 and 12.2 10 6 K 1 in the temperature range of 30– 243 -C and 291– 900 -C, respectively. The slope change occurred between 243 and 291 -C. The average TEC between 30 and 900 -C is 10.3 10 6 K 1, identical to that of the YSZ electrolyte. This indicates that matching of the TEC of the LSCM/YSZ composites with YSZ electrolyte can be achieved. 3.2. Open circuit potential (OCP) behavior The open circuit potential (OCP) of the LSCM (50 wt.%)/ YSZ (50 wt.%) composite anodes was recorded at different
Fig. 3. Open circuit potentials (OCP) of the LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes at different temperatures in wet CH4. The composite anodes were sintered at different temperatures. The solid lines are the theoretical OCP for the systems of 97% CH4/3% H2O and 97% H2/3% H2O fuels and air as oxidant.
temperatures in 97% CH4/3% H2O (wet CH4), as shown in Fig. 3. In the figure, the solid lines are the theoretical open circuit potentials based on the equilibrium of the 97% CH4/3% H2O fuel and air as oxidant (the theoretical calculation for H2O – CH4/air system is given in Appendix A). In comparison, the theoretical OCP and the measured OCP on a LSCM (50 wt.%)/ YSZ (50 wt.%) composite anode sintered at 1200 -C in 97% H2/3% H2O is also given in the figure. For the LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes in wet CH4, the OCP was typically in the range 0.91 to 0.93V at 850 -C and decreased slightly with the increase in the sintering temperature of the anodes. The OCP in wet CH4 decreases with the decrease in temperature and shows the same trend as the calculated OCP based on the thermodynamic equilibrium in the 97% CH4/3% H2O fuel. However, the theoretical OCP at 97% CH4/3% H2O is 1.246 V at 850 -C, much higher than that measured on the LSCM/YSZ composite anodes. The very low observed OCP as compared to the theoretical OCP is most likely due to the low conversion of methane on the substituted lanthanum chromites [8]. This is also supported by the observation that addition of small amount of Ni (¨ 5 wt.%)
Fig. 5. Electrode polarization resistance, R E, of the reaction on LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes as a function of anode sintering temperature. EIS was measured at open circuit in wet CH4 at different temperatures.
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(a) 1100°C
(b) 1200°C
(c) 1300°C
2 µm
Fig. 6. SEM micrographs of the surface of the LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes sintered at different temperatures after testing.
to the LSCM/YSZ composite anodes significantly increased the OCP values for the reaction in wet CH4. For example, for the reaction on a 5 wt.% Ni added LSCM (50 wt.%)/YSZ (50 wt.%) composite anode in wet CH4, the OCP increased to ¨ 1.19 V at 850 -C, which is much higher than ¨ 0.92 V observed on the same composite anodes without Ni addition at the same temperature. However, we found no significant improvement of the electrochemical performance of the Ni added LSCM/YSZ composite anodes for the methane oxidation reaction. In wet H2, as would be expected, the OCP for the H2 oxidation reaction on LSCM/YSZ composite anode increases with the decrease in temperature and is close to that calculated for the 97% H2/3% H2O system. This indicates that the lower OCP observed on LSCM/YSZ composite anodes in wet CH4 as compared to the calculated one is not due to the leakage of the system.
example, for the LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes sintered at 1100 -C, R V was 3.0– 3.5 V cm2 at 900 -C. When the sintering temperature increased to 1200 -C, R V at 900 -C decreased significantly to 1.3 –1.6 V cm2. Further increase in the anode sintering temperature only slightly increased the R V values to ¨ 2.0 V cm2. At 900 -C, the conductivity for the Tosoh YSZ powder was reported as 0.109 S cm 1 [12]. Thus, the ohmic contribution of the YSZ electrolyte with thickness of 1 mm would be 0.92 V cm2 at 900 -C. The higher resistance of the cell with the LSCM/YSZ composite anodes as compared to the electrolyte resistance indicates the ohmic resistance of the LSCM/YSZ composite is not negligible and this is probably due to the low conductivity of the LSCM material in reducing environment [11]. Nevertheless, the significant variation of the R V with the sintering temperature shows the cell resistance of LSCM/YSZ anode also depends on the anode sintering temperatures. Fig. 4 is the impedance curves of the methane oxidation reaction on LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes sintered at different temperatures. For the purpose of comparison, the high frequency intercept of the impedance responses was adjusted to zero. For the methane oxidation at 850 -C, the electrode polarization resistance was 11.5, 2.3 and 12.7 V cm2 for the LSCM/YSZ composite anodes sintered at 1100, 1200 and 1300 -C, respectively. Clearly, the composite anode sintered at 1200 -C has the lowest electrode polarization resistance (R E). It is interesting to note that the sintering temperature has significant effect on the impedance responses at low frequencies. This is also the case for the electrode polarization resistance measured at other temperatures. Minimum R E was obtained for the composite anodes sintered at 1200 -C, as shown in Fig. 5. The electrode performance for the LSCM/YSZ composite anode in the present study is lower than that reported for the graded LSCM anodes (R E is ¨ 0.8 V cm2 in wet CH4 at 900 -C [11]). This is probably due to the fact that we did not use Pt or Au paste on the anode coating and have not attempted to optimize the electrode structure and structure of the composite anodes using functional graded electrode approaches. As shown recently, the resistance and polarization performance of the fuel cell depends significantly on the contact area between the electrode coating and the current collector and the mechanical
3.3. Effect of composite anode sintering temperature The electrolyte and electrode ohmic resistance, R V, varied significantly with the anode sintering temperatures. For
Fig. 7. Impedance curves of the LSCM (30 wt.%)/YSZ (70 wt.%), LSCM (50 wt.%)/YSZ (50 wt.%) and LSCM (70 wt.%)/YSZ (30 wt.%) composite anodes in wet CH4 at 900 -C.
S.P. Jiang et al. / Solid State Ionics 177 (2006) 149 – 157
Fig. 8. Plots of the electrode polarization resistance (R E) for the reaction in wet CH4 as a function of the LSCM/YSZ composite composition, measured at different temperatures.
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load [13,14]. Thus, the use of Pt or Au paste [11] could partly lead to the improvement in the electrode performance through the increased contact areas between the LSCM anode and current collector. Fig. 6 shows the SEM micrographs of the surface of the LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes sintered at different temperatures after testing. For the anode sintered at 1100 -C, the microstructure of the LSCM/YSZ composite anode is characterized by relatively large LSCM grains covered by fine YSZ particles. However, it appears that the contact between the LSCM and YSZ particles is poor as there is little necking formation between the particles. This may imply the poor interface between the LSCM/YSZ composite anode and YSZ electrolyte. The poor interface contact between the LSCM and YSZ electrolyte is indirectly indicated by the high cell resistance (R V = 3.0– 3.5 V cm2) and relatively high electrode polarization resistance for the anodes sintered at 1100 -C (Fig. 5). As the sintering
(a) (b)
2 µm (c)
2 µm (d)
2 µm (e)
2 µm (f)
2 µm
5 µm
Fig. 9. SEM micrographs of the surface of (a) LSCM (30 wt.%)/YSZ (70 wt.%), (b) LSCM (50 wt.%)/YSZ (50 wt.%), (c) LSCM (60 wt.%)/YSZ (40 wt.%), (d) LSCM (70 wt.%)/YSZ (30 wt.%) and (e) pure LSCM anodes. The cross-section of LSCM (50 wt.%)/YSZ (50 wt.%) composite anode is given in (f).
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temperature increases, there is significant grain growth of LSCM and in particular YSZ in the composite anodes. The particle size of YSZ was ¨ 0.5 Am, significantly larger than ¨ 0.2 Am for the anode sintered at 1100 -C. Moreover, there is clearly necking formation between the YSZ and LSCM particles (Fig. 6b). The necking formation leads to the intimate contact between the LSCM-to-LSCM, YSZ-to-YSZ and YSZ-to-LSCM particles in the composite, resulting in the formation of the continuous network of both ionic and electronic conduction [15]. This also indicates the good interfacial contact between the LSCM/YSZ anode and YSZ electrolyte. Thus, the low R V and low electrode polarization resistance for the LSCM/YSZ composite anodes sintered at 1200 -C are most likely due to the significant enhancement of the interface contact between the LSCM and YSZ phases. Further increasing the sintering temperature would simply cause the grain growth with no additional benefit to the interface contact between the LSCM and YSZ. However, the rather rapid increase of the electrode polarization resistance indicates that sintering at 1300 -C has significant detrimental effect on the electrode electrocatalytic activity for the methane oxidation reaction probably due to the resistive layer formation at the LSCM and YSZ interface. The formation of the resistive phase such lanthanum zirconate at the LSCM and YSZ interface may be similar to that between the A-site stoichiometry Sr-doped LaMnO3 and YSZ [16,17]. Thus in the following sections, all LSCM/YSZ composite anodes were sintered at 1200 -C without specification. 3.4. Effect of LSCM/YSZ composite composition
microstructure of the LSCM/YSZ composite anodes depends on the composition. For LSCM (30 wt.%)/YSZ (70 wt.%) composite anode, the microstructure is characterized by the large LSCM particles completely embedded in the fine YSZ particles. Pores were in the range of 0.3 –0.8 Am and were uniformly distributed. The porosity appears to be small (Fig. 9a). As the LSCM content in the composite increases, there is gradually an increase in the porosity and the number of large pores. In the case of LSCM (50 wt.%)/YSZ (50 wt.%), the distribution of LSCM large particles and YSZ fine particles is clearly visible and there is a formation of small and large pores (Fig. 9b). A good interface contact between the LSCM/YSZ composite anode and YSZ electrolyte is formed (Fig. 9f). The porosity increased significantly as compared to that of the LSCM (30 wt.%)/YSZ (70 wt.%) composite anode. Despite the open structure of the LSCM/YSZ composite anode, it appears that LSCM and YSZ particles are networked to form continuous LSCM-to-LSCM and YSZ-to-YSZ contact. Such open structure with good distribution of fine and coarse pores is consistent with the low electrode polarization resistance measured for the methane oxidation. Increasing the LSCM content to 70 wt.% resulted in the reduction in porosity (Fig. 9d). This may be caused by the significant grain growth of the LSCM phase due to the reduced inhibiting effect of YSZ phases in the composite. For pure LSCM anodes, the particles were in the range of 1 –2 Am and porosity is very small (Fig. 9e). In some part of the pure LSCM electrode coating, nanosized fiber-like deposits were also found, indicating the poor conversion of methane on the LSCM. This explains the high R E values for the reaction for the pure LSCM and LSCM/YSZ
The LSCM/YSZ composite anodes with LSCM contents in the range of 30– 100 wt.% were studied. In this case, no significant variation of the cell resistance, R V, with the composition of the LSCM/YSZ composite was found. Fig. 7 shows typically the impedance responses of the LSCM (30 wt.%)/YSZ (70 wt.%), LSCM (50 wt.%)/YSZ (50 wt.%), and LSCM (70 wt.%)/YSZ (30 wt.%) composite anodes in wet CH4 at 900 -C. The electrode polarization performance clearly depends on the LSCM/YSZ composition. For the CH4 oxidation reaction on the LSCM/YSZ composite anodes, the electrode polarization resistance is low for the anodes with LSCM content close to 50 wt.%. As shown in the figure, the LSCM content in the composite anode primarily affects the low frequency impedance responses. Fig. 8 shows the plots of the electrode polarization resistance for the reaction in wet CH4 as a function of the LSCM/YSZ composite composition, measured at different temperatures. Electrode polarization resistance (R E) of pure LSCM anodes is high and decreases significantly with the increase of LSCM contents in the composite. In the case of pure LSCM, delamination of the anode was also observed. The results indicate that the best performance of the LSCM/ YSZ composite is the composite anode with 50– 60 wt.% LSCM. SEM micrographs of the LSCM/YSZ composite anodes with various compositions are presented in Fig. 9. The
Fig. 10. Impedance curves for the oxidation reaction in wet CH4 at different temperatures on a LSCM (50 wt.%)/YSZ (50 wt.%) composite anode. Symbols are experimental data and lines are fitted results. Numbers are frequency in Hz.
S.P. Jiang et al. / Solid State Ionics 177 (2006) 149 – 157
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Fig. 11. The equivalent circuit used for the fitting of the collected impedance data of LSCM (50%)/YSZ (50%) composite anodes. In the figure, L is the inductance, R S the electrolyte resistance, R 1 and Q 1 the electrode polarization resistance and constant phase element (CPE) of the high frequency arc, R 2 and Q 2 the electrode polarization resistance and constant phase element (CPE) of the medium frequency arc, and R 3 and Q 3 the electrode polarization resistance and constant phase element (CPE) of the low frequency arc.
composite anodes with LSCM content higher than 70 wt.% (Fig. 8). 3.5. Oxidation reaction in wet CH4 Fig. 10 is the impedance curves for the CH4 oxidation reaction on a LSCM (50 wt.%)/YSZ (50 wt.%) composite anode in wet CH4 at different temperatures under open circuit condition. Symbols are the experimental data and lines are the fitted results. The equivalent circuit for the fitting is shown in Fig. 11. Table 1 gives the fitted results for the reaction at different temperatures. Good fitting between the equivalent circuit and the observed data is observed. Most interesting, as the operation temperature increases, the impedance responses particularly at low frequencies decrease significantly. Three impedance arcs are clearly separated at high, medium and low frequencies. This indicates that the electrochemical oxidation of CH4 on LSCM/YSZ composite anodes is limited by at least three electrode steps. For the reaction at 800 -C, the characteristic frequencies for the high, medium and low frequency arcs are 501, 3.16 and 0.02 Hz, respectively (Fig. 10b). Fig. 12 is the activation energy plots of the electrode polarization resistance for the oxidation reaction in wet CH4 on the LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes. For the methane oxidation, the activation energies are 159, 168 and 150 kJ mol 1 for the electrode process at high, medium and low frequency arcs. The activation energy of the overall electrode resistance for the methane oxidation reaction is 160 kJ mol 1. High activation energy of 160– 200 kJ mol 1 was also reported by Primdahl et al. [18] for the H2 oxidation reaction on La0.8Sr0.2Cr0.97V0.03O3 anode. In the temperature range studied, it is clear that the oxidation reaction in wet CH4 is dominated by the low frequency impedance process. For the H2 oxidation reaction on Ni/YSZ cermet anodes, the reaction is generally considered to be limited by two electrode steps, namely, hydrogen dissociative adsorption and diffusion on the Ni surface or hydrogen gas diffusion inside the porous anode, and the charge transfer
reaction at the electrode and electrolyte interface [19]. The electrode process associated hydrogen dissociative adsorption has much lower activation energy (0 –50 kJ mol 1) as compared to the charge transfer process [19,20]. The three phase boundary areas between the Ni electrode, YSZ electrolyte and H2 reactant gas play a very important role in the reaction kinetics of the H2 oxidation reaction in the Ni and Ni/YSZ cermet anodes [15,21]. The high activation energy, 150 kJ mol 1, of the electrode process associated with low frequency arc on the LSCM/YSZ composite anodes indicates that the low frequency impedance is not dominated by the gas phase diffusion inside the porous LSCM/YSZ composite anodes. Such high energetic process also implies that the low impedance response for the CH4 oxidation reaction on the LSCM/YSZ composite anodes could not be the gas diffusion impedance due to the stagnant gas outside the porous anode, as reported by Primdahl and Mogensen for the H2 oxidation reaction on porous Ni/YSZ cermet anodes [22]. According to the Adler – Lane – Steele (ALS) model [23,24] on the oxygen reduction on the mixed ionic and electronic conducting (MIEC) oxides, the electrode impedance is consisted of charge transfer and noncharge transfer processes ZE ¼ Zelectronic þ Zionic þ Zchem
ð1Þ
where Z electronic is the impedance of electron transfer process occurring at the current collector/electrode interface, and Z ionic is the impedance of the ionic transfer process at the electrode/electrolyte interface. Z chem is the convoluted contribution of noncharge transfer processes including oxygen surface exchange, solid-state diffusion, and gas-phase diffusion inside and outside the electrode. Tao and Irvine [25] studied the H2 oxidation reaction on the mixed conducting oxide Sc0.15Y0.05Zr0.62Ti0.18O1.9 (ScYZT) in 5% H2. The impedance responses were characterized by three separated arcs. The characteristic frequency of the low frequency arc at 900 -C is 0.025 Hz, similar to that for the methane oxidation reaction on the LSCM/YSZ composite anodes in the present
Table 1 Impedance fitting results for the methane oxidation on the LSCM (50 wt.%)/YSZ (50 wt.%) composite anode in wet CH4 Temperature (-C)
R s (V cm2)
High frequency arc 2
R 1 (V cm ) 800 850 900
4.01 2.9 2.0
0.63 0.18 0.12
Medium frequency arc 2
n
Q 1 (V cm s ) 3
1.10 10 9.70 10 3 6.22 10 4
2
Low frequency arc 2
n
n1
R 2 (V cm )
Q 2 (V cm s )
n2
R 3 (V cm2)
Q 3 (V cm2 sn )
n3
0.9 0.8 1
1.70 0.80 0.43
0.17 0.15 0.18
0.7 0.7 0.7
9.94 4.08 2.07
0.69 0.68 0.58
1 0.9 0.8
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S.P. Jiang et al. / Solid State Ionics 177 (2006) 149 – 157 Table 2 Concentration of each component in the H2O – CH4 system before and after the system reaches equilibrium condition CH4
H2O
CO CO2 O2 H2
Initial concentration a b 0 Equilibrium concentration a – x 1 – x 2 b – x 1 – 2x 2 – 2x 3 x 1
Fig. 12. Activation energy plots for the oxidation reaction in wet CH4 on the LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes.
study. Tao and Irvine also observed the increase of the high frequency impedance with the increased polarization potential. This appears to be consistent with the reduced electronic conductivity of the ScYZT at low partial pressure of O2 due to the increased overpotential. For O2 reduction on MIEC cathodes such as (La,Sr)(Co,Fe)O3 and GDC-impregnated (La,Sr)MnO3, the electrode impedance is generally characterized by two impedance arcs [26,27]. The disappearance of the electrode impedance associated with the electronic transfer process could be explained by the high electronic conductivity of the LSCF and GDC-impregnated LSM materials. LSCM is a p-type conductor and shows limited mixed ionic and electronic conductivity under SOFC operation conditions [11]. The substitution of Sr into the A-site of the LSCM perovskite results in a charge-compensating transition of Cr3+/ Mn3+ to Cr4+/Mn4+ and at low partial pressure of oxygen, the compensation is achieved by the formation of oxygen vacancies. The concentration of oxygen vacancies would increase under reducing conditions. Thus, similar to the H2 oxidation on the ScYZT anodes [25], the electrode impedance for the methane oxidation on the LSCM/YSZ composite anodes can be in principle represented by the impedances of the electrode processes at the current collector/anode interface, the anode/electrolyte interface and the chemical processes according to Eq. (1). This is supported by the observation of the distinctive three impedance arcs for the methane oxidation on the LSCM/YSZ composite anodes (see Fig. 10). The high and medium frequency impedance responses are likely related to the electronic current exchange and ionic exchange processes, respectively, while the low frequency impedance to the noncharge processes including oxygen surface exchange and diffusion reactions. The chemical nature of the electrode process at low frequencies is also indicated by the high value of the constant phase element or the pseudo capacitant, Q 3 (see Table 1). Sakai et al. [28] studied the oxygen transport properties of La0.8Ca0.2CrO3 and the activation energy is 160 and 167 kJ mol 1 for the bulk and grain boundary diffusion, respectively, which are close to the high activation energies
0 x2
0 x3
0 x4
observed for the electrode polarization resistance at high, medium and low frequency arcs for the methane oxidation on the LSCM/YSZ composite anodes. This indicates that the methane oxidation reaction on the LSCM/YSZ composite anodes could be essentially controlled by the high energetic process of the oxygen vacancy diffusion in the LSCM perovskites. The dominance of the electrode process associated with low frequency arc may indicate that the noncharge process may be limited by the oxygen exchange rate at the surface of the LSCM/YSZ composite electrodes. Nevertheless, the methane oxidation is a complex process and more work will be needed in order to fundamentally understand the reaction mechanism and kinetics of this importance reaction in SOFC. 4. Conclusions The La0.75Sr0.25Cr0.5Mn0.5O3 (LSCM)/YSZ composites have been synthesized and studied as the alternative anode materials for the direct utilization of methane in SOFCs. Electrochemical performance of pure stoichiometric LSCM was low probably due to the poor conversion of methane, low porosity and poor adhesion between LSCM electrode and YSZ electrolyte. Addition of YSZ phase greatly improved the adhesion and reduced the electrode polarization resistance. LSCM/YSZ composite anodes show relatively good performance for the methane oxidation reaction in wet CH4 and the best electrode performance was achieved for the composite with LSCM contents of 50 – 60 wt.% with polarization resistances of 2– 3 V cm2 in wet CH4 at 850 -C without using of Pt or Au paste. The impedance for the methane oxidation on
Fig. 13. Calculated OCP for the cell with H2O – CH4 fuel and air at different temperatures.
S.P. Jiang et al. / Solid State Ionics 177 (2006) 149 – 157
157
the LSCM/YSZ composite anodes is characterized by three separable arcs and could be explained based on the ALS model for the reaction on the MIEC electrode. The high activation energies of the methane oxidation reaction imply that electrocatalytic activity of the LSCM/YSZ composite anodes may be limited by the oxygen ion conductivity. This could be enhanced by impregnation of high oxygen ion conducting phase such as Gd-doped ceria into the composite [27].
Fig. 13 is the theoretical OCP for the cell with H2O –CH4 fuel and air at different temperatures. Sfeir et al. [8] calculated the thermodynamic equilibrium concentration in the 56% CH/ 41% Ar/3% H2O/air system and the theoretical OCP is 1.205 V at 800 -C. This is close to 1.228 V for the 3% H2O – 97% CH4/ air at the same temperature in the present study.
Appendix A. Calculated open circuit potential in H2O – CH4/air system
[1] S.P. Jiang, S.H. Chan, Mater. Sci. Technol. 20 (2004) 1109. [2] S.P. Jiang, S.H. Chan, J. Mater. Sci. 39 (2004) 4405. [3] J.-H. Koh, Y.-S. Yoo, J.-W. Park, H.C. Lim, Solid State Ionics 149 (2002) 157. [4] C.M. Chun, J.D. Mumford, T. Ramanarayanan, J. Electrochem. Soc. 147 (2000) 3680. [5] P.V. Hendriksen, S.C. Singhal, H. Tagawa (Eds.), SOFC-V, vol. 97-40, The Electrochem. Soc., Penington, NJ, 1997, p. 1319. [6] M. Mori, Y. Hier, J. Am. Ceram. Soc. 84 (2001) 2573. [7] J. Vulliet, B. Morel, J. Laurencin, G. Gauthier, L. Bianchi, S. Giraud, J.-Y. Henry, F. Lefebvre-Joud, S.C. Singhal, M. Dokiya (Eds.), SOFC-VIII, vol. 2003-07, The Electrochem. Soc., Pennington, NJ, 2003, p. 803. [8] J. Sfeir, P.A. Buffat, P. Mo¨ckli, N. Xanthopoulos, R. Vasquez, H.J. Mathieu, J. Van herle, K.R. Thampi, J. Catal. 202 (2001) 229. [9] J. Sfeir, J. Power Sources 118 (2003) 276. [10] S. Tao, J.T.S. Irvine, Nat. Mater. 2 (2003) 320. [11] S. Tao, J.T.S. Irvine, J. Electrochem. Soc. 151 (2004) A252. [12] F.T. Ciacchi, K.M. Crane, S.P.S. Badwal, Solid State Ionics 73 (1994) 49. [13] S.P. Jiang, J.G. Love, L. Apateanu, Solid State Ionics 160 (2003) 15. [14] S. Koch, P.V. Hendriksen, Solid State Ionics 168 (2004) 1. [15] S.P. Jiang, J. Electrochem. Soc. 150 (2003) E548. [16] A. Mitterdorfer, L.J. Gauckler, Solid State Ionics 111 (1998) 185. [17] S.P. Jiang, J.-P. Zhang, K. Foger, J. Eur. Ceram. Soc. 23 (2003) 1865. [18] S. Primdahl, J.R. Hansen, L. Grahl-Madsen, P.H. Larsen, J. Electrochem. Soc. 148 (2001) A74. [19] S.P. Jiang, S.P.S. Badwal, Solid State Ionics 123 (1999) 209. [20] S.P. Jiang, W. Wang, Y.D. Zhen, J. Power Sources 147 (2005) 1. [21] A. Bieberle, L.P. Meier, L.J. Gauckler, J. Electrochem. Soc. 148 (2001) A646. [22] S. Primdahl, M. Mogensen, J. Electrochem. Soc. 146 (1999) 2827. [23] S.B. Adler, J.A. Lane, B.C.B. Steele, J. Electrochem. Soc. 144 (1997) 1884. [24] S.B. Adler, Solid State Ionics 135 (2000) 603. [25] S. Tao, J.T.S. Irvine, J. Electrochem. Soc. 151 (2004) A497. [26] A. Esquirol, N.P. Brandon, J.A. Killer, M. Mogensen, J. Electrochem. Soc. 151 (2004) A1847. [27] S.P. Jiang, W. Wang, J. Electrochem. Soc. 152 (2005) A1398. [28] N. Sakai, K. Yamaji, T. Horita, H. Yokokawa, T. Kawada, M. Dokiya, J. Electrochem. Soc. 147 (2000) 3178.
The OCP in H2O–CH4/air system can be calculated from the thermodynamic equilibrium concentration of the mixture gases, CH4, CO, O2, CO2, H2O and H2, according to the following four main chemical reactions: CH4 þ 2O2 6CO2 þ 2H2 O
ð2Þ
CH4 þ H2 O6CO þ 3H2
ð3Þ
CH4 þ CO2 62CO þ 2H2
ð4Þ
CO þ H2 O6CO2 þ H2
ð5Þ
The initial and equilibrium concentrations of each component are shown in Table 2. Defining that K 1, K 2, K 3 and K 4 are the equilibrium constants of the above four reactions, the four unknown parameters, x 1, x 2, x 3 and x 4, can be obtained from following equations. K1 ¼
x2 ðb x1 2x2 2x3 Þ2 ða x1 x2 Þx23
ð6Þ
K2 ¼
x1 x34 ða x1 x2 Þðb x1 2x2 2x3 Þ
ð7Þ
K3 ¼
x1 x24 ða x1 x2 Þx2
ð8Þ
K4 ¼
x1 x4 x1 ðb x1 2x2 2x3 Þ
ð9Þ
The above equations can be solved using nonlinear least square method. As the concentration of the oxygen in air is 0.21 atm, the open circuit potential of the cell can be calculated as: RT 0:21 ln OCP ¼ ð10Þ 4F x3
References
(La0.75Sr0.25)(Cr0.5Mn0.5)O3/YSZ composite anodes for methane oxidation reaction in solid oxide fuel cells S.P. Jiang *, X.J. Chen, S.H. Chan, J.T. Kwok, K.A. Khor School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore Received 19 April 2005; received in revised form 10 August 2005; accepted 7 September 2005
Abstract The synthesis and performance of (La0.75Sr0.25)(Cr0.5Mn0.5)O3/Y2O3 – ZrO2 (LSCM/YSZ) composites are investigated as alternative anodes for the direct utilization of methane (i.e., natural gas) in solid oxide fuel cells. Addition of YSZ phase greatly improves the adhesion and reduces the electrode polarization resistance of the LSCM/YSZ composite anodes. LSCM/YSZ composite anodes show reasonably good performance for the methane oxidation reaction in wet CH4 and the best electrode performance was achieved for the composite with LSCM contents of 50 – 60 wt.% with polarization resistances of 2 – 3 V cm2 in 97% CH4/3% H2O at 850 -C. The electrode impedance for the methane oxidation in wet CH4 on the LSCM/YSZ composite anodes was characterized by three separable arcs and the electrode behavior could be explained based on the ALS model for the reaction on the MIEC electrode. The results indicate that electrocatalytic activity of the LSCM/YSZ composite anodes for the methane oxidation is likely limited by the oxygen vacancy diffusion in the substituted lanthanum chromite-based materials. D 2005 Elsevier B.V. All rights reserved. PACS: 84.60.D Keywords: Alternative anodes; LSCM/YSZ composite; Methane oxidation; Solid oxide fuel cells
1. Introduction It is well known that Ni/Y2O3 –ZrO2 (Ni/YSZ) cermet anodes of solid oxide fuel cells (SOFC) have excellent catalytic properties and stability for the H2 oxidation of hydrogen fuel at SOFC operation conditions [1,2]. However, Ni/YSZ-based anode suffers a number of drawbacks in systems where hydrocarbon fuel is used such as sulfur poisoning and carbon deposition [2]. Carbon deposition covers the active sites of the anode, resulting in the loss of the cell performance [3]. Under high carbon activity environment, Ni metal could be corroded by a process known as metal dusting [4]. As Ni is a good catalyst for hydrocarbon cracking reaction, Ni/YSZ cermet anodes can only be directly used in hydrocarbon fuels if excess steam is present to ensure the complete fuel reforming and to suppress the carbon deposition. High steam/ carbon ratio is not attractive for fuel cells as it lowers the electrical efficiency of the fuel cells by diluting the fuel. The
* Corresponding author. Fax: +65 6791 1859. E-mail address: [email protected] (S.P. Jiang). 0167-2738/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2005.09.010
endothermic nature of the steam reforming reaction can also cause local cooling and steep thermal gradients potentially capable of mechanically damaging the cell stack [5]. Thus, development of structurally stable anodes with high electrocatalytic activity for hydrocarbon fuel oxidation is vital for the natural gas fuel-based SOFC. Replacing Ni/YSZ cermet anodes by Ni-free oxides such as ceria, titanate and lanthanum chromite-based oxides has attracted a great attention recently. Doped LaCrO3-based materials have been extensively investigated as interconnect material in SOFC [6]. LaCrO3-based oxide such as (LaSr)CrO3 was shown to have very low activity towards carbon deposition [7]. Catalytic activity of LaCrO3 for methane oxidation can also be substantially enhanced by partial substitution at A- and Bsites. Sfeir et al. [8,9] studied the thermodynamic stability and the catalytic activity of (LaA)(CrB)O3 system (A= Ca, Sr and B = Mg, Mn, Fe, Co, Ni) as alternative anode materials under simulated SOFC operation conditions. Thermodynamically, Sr and Mn substitution maintains the stability of the perovskite while other substitutes destabilize the system. However, transition metal substituted LaCrO3 did not decompose easily under reducing conditions, indicating that the decomposition of
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the substituted LaCrO3 would be hindered kinetically. Ca and Sr substitution at the A-site improves the catalytic activity and for B-site substitution, Co and Mg show an inhibiting effect while Mn, Fe and Ni improve the activity. Recently, Tao and Irvine [10,11] reported promising results of La0.75Sr0.25Cr0.5Mn0.5O3 (LSCM) as anode for SOFC. LSCM is a p-type conductor with conductivity of ¨ 38 S cm 1 in air and 1.5 S cm 1 in 5% H2 at 900 -C. The electrode polarization resistance for the oxidation reactions in wet CH4 and H2 at 900 -C was 0.85 V cm2 and 0.26 V cm2, respectively. The performances are considered to be compatible to the Ni/YSZ cermet anodes. Addition of the ionic conducting phase such YSZ allows delocalization of the reaction in the entire electrode volume, increasing the reaction sites and enhancing the performance of the electrode. Thus, it would be interesting to investigate the performance of LSCM/YSZ composite anodes. In this report, the fabrication and performance of LSCM/YSZ composite anodes were investigated to assess their feasibility as alternative anodes for methane oxidation reactions for SOFC. The process and reaction mechanism of the CH4 oxidation reaction in wet CH4 (3% H2O) are discussed. 2. Experimental YSZ electrolyte substrates were prepared from 8 mol% yttria-stabilized zirconia (YSZ, Tosoh, Japan) powders by die pressing and sintered at 1550 -C for 4 h. The diameter and thickness of the YSZ electrolyte were ¨ 20 mm and ¨ 1 mm, respectively. The surface of YSZ discs was ground using sandpapers to increase the roughness of the surface and the contact between the electrode and the YSZ electrolyte. The composition of LSCM was chosen as La0.75Sr0.25 Cr0.5Mn0.5O3 (LSCM) [10,11]. LSCM was prepared from La2O3, SrCO3, Cr2O3 and MnCO3 (all from Aldrich) by solid-state reaction. La2O3 was heat-treated at 1000 -C to get rid of the moisture. The powders were mixed and ball-milled for 4 h with propanol. The mixture was then heated at 1200 -C for 20 h in air. LSCM/YSZ composites with various weight ratios were made by ball milling for 1 h. The mixture of LSCM and YSZ was again mixed thoroughly with addition of PG400 in mortar for another 30 min to form slurry. Carbon (5 wt.%) was added to the composite slurry as pore-former. LSCM and LSCM/YSZ composite electrodes were applied to the electrolyte disk by slurry painting. To study the sintering temperature, LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes were sintered at 1100, 1200 and 1300 -C in air, respectively, for 2 h. The thermal expansion coefficients of the LSCM and LSCM (50%)/YSZ (50%) composites were measured by a Perkin Helmer Dynamic Mechanical Analyzer. The samples were pressed into cylinder with a diameter of 10 mm and a length of 5 mm. After sintering at 1200 -C for 2 h, the diameter of the cylinders shrank to ¨ 8 mm. Temperature was raised from 30 -C to 900 -C with heating rate of 10 -C min 1. Data were recorded and thermal expansion coefficient (TEC) was calculated from the slope of the curve.
Platinum paste was painted onto the center of the other side of the electrolyte substrate as the counter electrode and the reference electrode was painted as a ring at the edge of the electrolyte substrate. Pt mesh was used as current collector for both anode and counter electrode. Different to the experimental settings reported by Tao and Irvine [11], no additional Pt or Au paste was applied to the coating surface of the anode. The distance between the counter and ring reference electrodes was ¨ 4 mm. Methane humidified at room temperature (97% CH4/ 3% H2O) was used as fuel and air was used as oxidant. The fuel flow rate was controlled at 100 sccm. Electrochemical impedance spectroscopy was carried out using a Solartron 1255 frequency response analyzer coupled to a Solartron 1287 electrochemical interface. The impedance spectra of the electrochemical cell were recorded at open circuit voltage (OCV) with amplitude of 10 mV over the frequency range 0.01 Hz to 1 MHz. The ohmic resistance of the electrolyte and the anode (R V) was estimated from the high frequency intercept of the impedance curves and the overall electrode polarization (interface) resistance (R E) was directly measured from the differences between the low and high frequency intercepts on the impedance curves. The impedance responses were analyzed using an equivalent circuit method. The measurement was carried out in the temperature range of 800 to 950 -C. Microstructure of the anodes after the performance testing was inspected by scanning electron microscopy (SEM, Leica 360, Germany). 3. Results and discussions 3.1. The phase and thermal expansion coefficient Fig. 1 is the X-ray diffraction (XRD) pattern of a LSCM powder sintered at 1200 -C. The patterns are identical to the La0.75Sr0.25Cr0.5Mn0.5O3 obtained at 1400 -C [11], indicating the formation of the perovskite phase of the LSCM powder. Fig. 2 shows the thermal expansion of pure LSCM and LSCM (50%)/YSZ (50%) composite. The linear thermal expansion coefficient (TEC) of LSCM is 9.2 10 6 K 1 in the
Fig. 1. XRD pattern of La0.75Sr0.25Cr0.5Mn0.5O3 (LSCM) powder sintered at 1200 -C for 20 h.
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151
Fig. 4. Impedance curves of the reaction on LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes sintered at different temperatures. The EIS was measured at 850 -C in wet CH4. Fig. 2. The TEC of La0.75Sr0.25Cr0.5Mn0.5O3 (LSCM) and LSCM (50%)/YSZ (50%) at high temperatures in air.
temperature range of 34 – 135 -C and 13.7 10 6 K 1 between 161 -C and 900 -C. There is a slope change at 135 –161 -C. The average TEC between 30 -C and 900 -C is 11.4 10 6 K 1, which is higher than 9.3 10 6 K 1 reported by Tao and Irvine [11] for the same oxide. Addition of YSZ phase reduces the thermal expansion of the composite. In the case of LSCM (50%)/YSZ (50%) composites, the TEC is 8.4 10 6 K 1 and 12.2 10 6 K 1 in the temperature range of 30– 243 -C and 291– 900 -C, respectively. The slope change occurred between 243 and 291 -C. The average TEC between 30 and 900 -C is 10.3 10 6 K 1, identical to that of the YSZ electrolyte. This indicates that matching of the TEC of the LSCM/YSZ composites with YSZ electrolyte can be achieved. 3.2. Open circuit potential (OCP) behavior The open circuit potential (OCP) of the LSCM (50 wt.%)/ YSZ (50 wt.%) composite anodes was recorded at different
Fig. 3. Open circuit potentials (OCP) of the LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes at different temperatures in wet CH4. The composite anodes were sintered at different temperatures. The solid lines are the theoretical OCP for the systems of 97% CH4/3% H2O and 97% H2/3% H2O fuels and air as oxidant.
temperatures in 97% CH4/3% H2O (wet CH4), as shown in Fig. 3. In the figure, the solid lines are the theoretical open circuit potentials based on the equilibrium of the 97% CH4/3% H2O fuel and air as oxidant (the theoretical calculation for H2O – CH4/air system is given in Appendix A). In comparison, the theoretical OCP and the measured OCP on a LSCM (50 wt.%)/ YSZ (50 wt.%) composite anode sintered at 1200 -C in 97% H2/3% H2O is also given in the figure. For the LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes in wet CH4, the OCP was typically in the range 0.91 to 0.93V at 850 -C and decreased slightly with the increase in the sintering temperature of the anodes. The OCP in wet CH4 decreases with the decrease in temperature and shows the same trend as the calculated OCP based on the thermodynamic equilibrium in the 97% CH4/3% H2O fuel. However, the theoretical OCP at 97% CH4/3% H2O is 1.246 V at 850 -C, much higher than that measured on the LSCM/YSZ composite anodes. The very low observed OCP as compared to the theoretical OCP is most likely due to the low conversion of methane on the substituted lanthanum chromites [8]. This is also supported by the observation that addition of small amount of Ni (¨ 5 wt.%)
Fig. 5. Electrode polarization resistance, R E, of the reaction on LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes as a function of anode sintering temperature. EIS was measured at open circuit in wet CH4 at different temperatures.
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(a) 1100°C
(b) 1200°C
(c) 1300°C
2 µm
Fig. 6. SEM micrographs of the surface of the LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes sintered at different temperatures after testing.
to the LSCM/YSZ composite anodes significantly increased the OCP values for the reaction in wet CH4. For example, for the reaction on a 5 wt.% Ni added LSCM (50 wt.%)/YSZ (50 wt.%) composite anode in wet CH4, the OCP increased to ¨ 1.19 V at 850 -C, which is much higher than ¨ 0.92 V observed on the same composite anodes without Ni addition at the same temperature. However, we found no significant improvement of the electrochemical performance of the Ni added LSCM/YSZ composite anodes for the methane oxidation reaction. In wet H2, as would be expected, the OCP for the H2 oxidation reaction on LSCM/YSZ composite anode increases with the decrease in temperature and is close to that calculated for the 97% H2/3% H2O system. This indicates that the lower OCP observed on LSCM/YSZ composite anodes in wet CH4 as compared to the calculated one is not due to the leakage of the system.
example, for the LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes sintered at 1100 -C, R V was 3.0– 3.5 V cm2 at 900 -C. When the sintering temperature increased to 1200 -C, R V at 900 -C decreased significantly to 1.3 –1.6 V cm2. Further increase in the anode sintering temperature only slightly increased the R V values to ¨ 2.0 V cm2. At 900 -C, the conductivity for the Tosoh YSZ powder was reported as 0.109 S cm 1 [12]. Thus, the ohmic contribution of the YSZ electrolyte with thickness of 1 mm would be 0.92 V cm2 at 900 -C. The higher resistance of the cell with the LSCM/YSZ composite anodes as compared to the electrolyte resistance indicates the ohmic resistance of the LSCM/YSZ composite is not negligible and this is probably due to the low conductivity of the LSCM material in reducing environment [11]. Nevertheless, the significant variation of the R V with the sintering temperature shows the cell resistance of LSCM/YSZ anode also depends on the anode sintering temperatures. Fig. 4 is the impedance curves of the methane oxidation reaction on LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes sintered at different temperatures. For the purpose of comparison, the high frequency intercept of the impedance responses was adjusted to zero. For the methane oxidation at 850 -C, the electrode polarization resistance was 11.5, 2.3 and 12.7 V cm2 for the LSCM/YSZ composite anodes sintered at 1100, 1200 and 1300 -C, respectively. Clearly, the composite anode sintered at 1200 -C has the lowest electrode polarization resistance (R E). It is interesting to note that the sintering temperature has significant effect on the impedance responses at low frequencies. This is also the case for the electrode polarization resistance measured at other temperatures. Minimum R E was obtained for the composite anodes sintered at 1200 -C, as shown in Fig. 5. The electrode performance for the LSCM/YSZ composite anode in the present study is lower than that reported for the graded LSCM anodes (R E is ¨ 0.8 V cm2 in wet CH4 at 900 -C [11]). This is probably due to the fact that we did not use Pt or Au paste on the anode coating and have not attempted to optimize the electrode structure and structure of the composite anodes using functional graded electrode approaches. As shown recently, the resistance and polarization performance of the fuel cell depends significantly on the contact area between the electrode coating and the current collector and the mechanical
3.3. Effect of composite anode sintering temperature The electrolyte and electrode ohmic resistance, R V, varied significantly with the anode sintering temperatures. For
Fig. 7. Impedance curves of the LSCM (30 wt.%)/YSZ (70 wt.%), LSCM (50 wt.%)/YSZ (50 wt.%) and LSCM (70 wt.%)/YSZ (30 wt.%) composite anodes in wet CH4 at 900 -C.
S.P. Jiang et al. / Solid State Ionics 177 (2006) 149 – 157
Fig. 8. Plots of the electrode polarization resistance (R E) for the reaction in wet CH4 as a function of the LSCM/YSZ composite composition, measured at different temperatures.
153
load [13,14]. Thus, the use of Pt or Au paste [11] could partly lead to the improvement in the electrode performance through the increased contact areas between the LSCM anode and current collector. Fig. 6 shows the SEM micrographs of the surface of the LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes sintered at different temperatures after testing. For the anode sintered at 1100 -C, the microstructure of the LSCM/YSZ composite anode is characterized by relatively large LSCM grains covered by fine YSZ particles. However, it appears that the contact between the LSCM and YSZ particles is poor as there is little necking formation between the particles. This may imply the poor interface between the LSCM/YSZ composite anode and YSZ electrolyte. The poor interface contact between the LSCM and YSZ electrolyte is indirectly indicated by the high cell resistance (R V = 3.0– 3.5 V cm2) and relatively high electrode polarization resistance for the anodes sintered at 1100 -C (Fig. 5). As the sintering
(a) (b)
2 µm (c)
2 µm (d)
2 µm (e)
2 µm (f)
2 µm
5 µm
Fig. 9. SEM micrographs of the surface of (a) LSCM (30 wt.%)/YSZ (70 wt.%), (b) LSCM (50 wt.%)/YSZ (50 wt.%), (c) LSCM (60 wt.%)/YSZ (40 wt.%), (d) LSCM (70 wt.%)/YSZ (30 wt.%) and (e) pure LSCM anodes. The cross-section of LSCM (50 wt.%)/YSZ (50 wt.%) composite anode is given in (f).
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temperature increases, there is significant grain growth of LSCM and in particular YSZ in the composite anodes. The particle size of YSZ was ¨ 0.5 Am, significantly larger than ¨ 0.2 Am for the anode sintered at 1100 -C. Moreover, there is clearly necking formation between the YSZ and LSCM particles (Fig. 6b). The necking formation leads to the intimate contact between the LSCM-to-LSCM, YSZ-to-YSZ and YSZ-to-LSCM particles in the composite, resulting in the formation of the continuous network of both ionic and electronic conduction [15]. This also indicates the good interfacial contact between the LSCM/YSZ anode and YSZ electrolyte. Thus, the low R V and low electrode polarization resistance for the LSCM/YSZ composite anodes sintered at 1200 -C are most likely due to the significant enhancement of the interface contact between the LSCM and YSZ phases. Further increasing the sintering temperature would simply cause the grain growth with no additional benefit to the interface contact between the LSCM and YSZ. However, the rather rapid increase of the electrode polarization resistance indicates that sintering at 1300 -C has significant detrimental effect on the electrode electrocatalytic activity for the methane oxidation reaction probably due to the resistive layer formation at the LSCM and YSZ interface. The formation of the resistive phase such lanthanum zirconate at the LSCM and YSZ interface may be similar to that between the A-site stoichiometry Sr-doped LaMnO3 and YSZ [16,17]. Thus in the following sections, all LSCM/YSZ composite anodes were sintered at 1200 -C without specification. 3.4. Effect of LSCM/YSZ composite composition
microstructure of the LSCM/YSZ composite anodes depends on the composition. For LSCM (30 wt.%)/YSZ (70 wt.%) composite anode, the microstructure is characterized by the large LSCM particles completely embedded in the fine YSZ particles. Pores were in the range of 0.3 –0.8 Am and were uniformly distributed. The porosity appears to be small (Fig. 9a). As the LSCM content in the composite increases, there is gradually an increase in the porosity and the number of large pores. In the case of LSCM (50 wt.%)/YSZ (50 wt.%), the distribution of LSCM large particles and YSZ fine particles is clearly visible and there is a formation of small and large pores (Fig. 9b). A good interface contact between the LSCM/YSZ composite anode and YSZ electrolyte is formed (Fig. 9f). The porosity increased significantly as compared to that of the LSCM (30 wt.%)/YSZ (70 wt.%) composite anode. Despite the open structure of the LSCM/YSZ composite anode, it appears that LSCM and YSZ particles are networked to form continuous LSCM-to-LSCM and YSZ-to-YSZ contact. Such open structure with good distribution of fine and coarse pores is consistent with the low electrode polarization resistance measured for the methane oxidation. Increasing the LSCM content to 70 wt.% resulted in the reduction in porosity (Fig. 9d). This may be caused by the significant grain growth of the LSCM phase due to the reduced inhibiting effect of YSZ phases in the composite. For pure LSCM anodes, the particles were in the range of 1 –2 Am and porosity is very small (Fig. 9e). In some part of the pure LSCM electrode coating, nanosized fiber-like deposits were also found, indicating the poor conversion of methane on the LSCM. This explains the high R E values for the reaction for the pure LSCM and LSCM/YSZ
The LSCM/YSZ composite anodes with LSCM contents in the range of 30– 100 wt.% were studied. In this case, no significant variation of the cell resistance, R V, with the composition of the LSCM/YSZ composite was found. Fig. 7 shows typically the impedance responses of the LSCM (30 wt.%)/YSZ (70 wt.%), LSCM (50 wt.%)/YSZ (50 wt.%), and LSCM (70 wt.%)/YSZ (30 wt.%) composite anodes in wet CH4 at 900 -C. The electrode polarization performance clearly depends on the LSCM/YSZ composition. For the CH4 oxidation reaction on the LSCM/YSZ composite anodes, the electrode polarization resistance is low for the anodes with LSCM content close to 50 wt.%. As shown in the figure, the LSCM content in the composite anode primarily affects the low frequency impedance responses. Fig. 8 shows the plots of the electrode polarization resistance for the reaction in wet CH4 as a function of the LSCM/YSZ composite composition, measured at different temperatures. Electrode polarization resistance (R E) of pure LSCM anodes is high and decreases significantly with the increase of LSCM contents in the composite. In the case of pure LSCM, delamination of the anode was also observed. The results indicate that the best performance of the LSCM/ YSZ composite is the composite anode with 50– 60 wt.% LSCM. SEM micrographs of the LSCM/YSZ composite anodes with various compositions are presented in Fig. 9. The
Fig. 10. Impedance curves for the oxidation reaction in wet CH4 at different temperatures on a LSCM (50 wt.%)/YSZ (50 wt.%) composite anode. Symbols are experimental data and lines are fitted results. Numbers are frequency in Hz.
S.P. Jiang et al. / Solid State Ionics 177 (2006) 149 – 157
155
Fig. 11. The equivalent circuit used for the fitting of the collected impedance data of LSCM (50%)/YSZ (50%) composite anodes. In the figure, L is the inductance, R S the electrolyte resistance, R 1 and Q 1 the electrode polarization resistance and constant phase element (CPE) of the high frequency arc, R 2 and Q 2 the electrode polarization resistance and constant phase element (CPE) of the medium frequency arc, and R 3 and Q 3 the electrode polarization resistance and constant phase element (CPE) of the low frequency arc.
composite anodes with LSCM content higher than 70 wt.% (Fig. 8). 3.5. Oxidation reaction in wet CH4 Fig. 10 is the impedance curves for the CH4 oxidation reaction on a LSCM (50 wt.%)/YSZ (50 wt.%) composite anode in wet CH4 at different temperatures under open circuit condition. Symbols are the experimental data and lines are the fitted results. The equivalent circuit for the fitting is shown in Fig. 11. Table 1 gives the fitted results for the reaction at different temperatures. Good fitting between the equivalent circuit and the observed data is observed. Most interesting, as the operation temperature increases, the impedance responses particularly at low frequencies decrease significantly. Three impedance arcs are clearly separated at high, medium and low frequencies. This indicates that the electrochemical oxidation of CH4 on LSCM/YSZ composite anodes is limited by at least three electrode steps. For the reaction at 800 -C, the characteristic frequencies for the high, medium and low frequency arcs are 501, 3.16 and 0.02 Hz, respectively (Fig. 10b). Fig. 12 is the activation energy plots of the electrode polarization resistance for the oxidation reaction in wet CH4 on the LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes. For the methane oxidation, the activation energies are 159, 168 and 150 kJ mol 1 for the electrode process at high, medium and low frequency arcs. The activation energy of the overall electrode resistance for the methane oxidation reaction is 160 kJ mol 1. High activation energy of 160– 200 kJ mol 1 was also reported by Primdahl et al. [18] for the H2 oxidation reaction on La0.8Sr0.2Cr0.97V0.03O3 anode. In the temperature range studied, it is clear that the oxidation reaction in wet CH4 is dominated by the low frequency impedance process. For the H2 oxidation reaction on Ni/YSZ cermet anodes, the reaction is generally considered to be limited by two electrode steps, namely, hydrogen dissociative adsorption and diffusion on the Ni surface or hydrogen gas diffusion inside the porous anode, and the charge transfer
reaction at the electrode and electrolyte interface [19]. The electrode process associated hydrogen dissociative adsorption has much lower activation energy (0 –50 kJ mol 1) as compared to the charge transfer process [19,20]. The three phase boundary areas between the Ni electrode, YSZ electrolyte and H2 reactant gas play a very important role in the reaction kinetics of the H2 oxidation reaction in the Ni and Ni/YSZ cermet anodes [15,21]. The high activation energy, 150 kJ mol 1, of the electrode process associated with low frequency arc on the LSCM/YSZ composite anodes indicates that the low frequency impedance is not dominated by the gas phase diffusion inside the porous LSCM/YSZ composite anodes. Such high energetic process also implies that the low impedance response for the CH4 oxidation reaction on the LSCM/YSZ composite anodes could not be the gas diffusion impedance due to the stagnant gas outside the porous anode, as reported by Primdahl and Mogensen for the H2 oxidation reaction on porous Ni/YSZ cermet anodes [22]. According to the Adler – Lane – Steele (ALS) model [23,24] on the oxygen reduction on the mixed ionic and electronic conducting (MIEC) oxides, the electrode impedance is consisted of charge transfer and noncharge transfer processes ZE ¼ Zelectronic þ Zionic þ Zchem
ð1Þ
where Z electronic is the impedance of electron transfer process occurring at the current collector/electrode interface, and Z ionic is the impedance of the ionic transfer process at the electrode/electrolyte interface. Z chem is the convoluted contribution of noncharge transfer processes including oxygen surface exchange, solid-state diffusion, and gas-phase diffusion inside and outside the electrode. Tao and Irvine [25] studied the H2 oxidation reaction on the mixed conducting oxide Sc0.15Y0.05Zr0.62Ti0.18O1.9 (ScYZT) in 5% H2. The impedance responses were characterized by three separated arcs. The characteristic frequency of the low frequency arc at 900 -C is 0.025 Hz, similar to that for the methane oxidation reaction on the LSCM/YSZ composite anodes in the present
Table 1 Impedance fitting results for the methane oxidation on the LSCM (50 wt.%)/YSZ (50 wt.%) composite anode in wet CH4 Temperature (-C)
R s (V cm2)
High frequency arc 2
R 1 (V cm ) 800 850 900
4.01 2.9 2.0
0.63 0.18 0.12
Medium frequency arc 2
n
Q 1 (V cm s ) 3
1.10 10 9.70 10 3 6.22 10 4
2
Low frequency arc 2
n
n1
R 2 (V cm )
Q 2 (V cm s )
n2
R 3 (V cm2)
Q 3 (V cm2 sn )
n3
0.9 0.8 1
1.70 0.80 0.43
0.17 0.15 0.18
0.7 0.7 0.7
9.94 4.08 2.07
0.69 0.68 0.58
1 0.9 0.8
156
S.P. Jiang et al. / Solid State Ionics 177 (2006) 149 – 157 Table 2 Concentration of each component in the H2O – CH4 system before and after the system reaches equilibrium condition CH4
H2O
CO CO2 O2 H2
Initial concentration a b 0 Equilibrium concentration a – x 1 – x 2 b – x 1 – 2x 2 – 2x 3 x 1
Fig. 12. Activation energy plots for the oxidation reaction in wet CH4 on the LSCM (50 wt.%)/YSZ (50 wt.%) composite anodes.
study. Tao and Irvine also observed the increase of the high frequency impedance with the increased polarization potential. This appears to be consistent with the reduced electronic conductivity of the ScYZT at low partial pressure of O2 due to the increased overpotential. For O2 reduction on MIEC cathodes such as (La,Sr)(Co,Fe)O3 and GDC-impregnated (La,Sr)MnO3, the electrode impedance is generally characterized by two impedance arcs [26,27]. The disappearance of the electrode impedance associated with the electronic transfer process could be explained by the high electronic conductivity of the LSCF and GDC-impregnated LSM materials. LSCM is a p-type conductor and shows limited mixed ionic and electronic conductivity under SOFC operation conditions [11]. The substitution of Sr into the A-site of the LSCM perovskite results in a charge-compensating transition of Cr3+/ Mn3+ to Cr4+/Mn4+ and at low partial pressure of oxygen, the compensation is achieved by the formation of oxygen vacancies. The concentration of oxygen vacancies would increase under reducing conditions. Thus, similar to the H2 oxidation on the ScYZT anodes [25], the electrode impedance for the methane oxidation on the LSCM/YSZ composite anodes can be in principle represented by the impedances of the electrode processes at the current collector/anode interface, the anode/electrolyte interface and the chemical processes according to Eq. (1). This is supported by the observation of the distinctive three impedance arcs for the methane oxidation on the LSCM/YSZ composite anodes (see Fig. 10). The high and medium frequency impedance responses are likely related to the electronic current exchange and ionic exchange processes, respectively, while the low frequency impedance to the noncharge processes including oxygen surface exchange and diffusion reactions. The chemical nature of the electrode process at low frequencies is also indicated by the high value of the constant phase element or the pseudo capacitant, Q 3 (see Table 1). Sakai et al. [28] studied the oxygen transport properties of La0.8Ca0.2CrO3 and the activation energy is 160 and 167 kJ mol 1 for the bulk and grain boundary diffusion, respectively, which are close to the high activation energies
0 x2
0 x3
0 x4
observed for the electrode polarization resistance at high, medium and low frequency arcs for the methane oxidation on the LSCM/YSZ composite anodes. This indicates that the methane oxidation reaction on the LSCM/YSZ composite anodes could be essentially controlled by the high energetic process of the oxygen vacancy diffusion in the LSCM perovskites. The dominance of the electrode process associated with low frequency arc may indicate that the noncharge process may be limited by the oxygen exchange rate at the surface of the LSCM/YSZ composite electrodes. Nevertheless, the methane oxidation is a complex process and more work will be needed in order to fundamentally understand the reaction mechanism and kinetics of this importance reaction in SOFC. 4. Conclusions The La0.75Sr0.25Cr0.5Mn0.5O3 (LSCM)/YSZ composites have been synthesized and studied as the alternative anode materials for the direct utilization of methane in SOFCs. Electrochemical performance of pure stoichiometric LSCM was low probably due to the poor conversion of methane, low porosity and poor adhesion between LSCM electrode and YSZ electrolyte. Addition of YSZ phase greatly improved the adhesion and reduced the electrode polarization resistance. LSCM/YSZ composite anodes show relatively good performance for the methane oxidation reaction in wet CH4 and the best electrode performance was achieved for the composite with LSCM contents of 50 – 60 wt.% with polarization resistances of 2– 3 V cm2 in wet CH4 at 850 -C without using of Pt or Au paste. The impedance for the methane oxidation on
Fig. 13. Calculated OCP for the cell with H2O – CH4 fuel and air at different temperatures.
S.P. Jiang et al. / Solid State Ionics 177 (2006) 149 – 157
157
the LSCM/YSZ composite anodes is characterized by three separable arcs and could be explained based on the ALS model for the reaction on the MIEC electrode. The high activation energies of the methane oxidation reaction imply that electrocatalytic activity of the LSCM/YSZ composite anodes may be limited by the oxygen ion conductivity. This could be enhanced by impregnation of high oxygen ion conducting phase such as Gd-doped ceria into the composite [27].
Fig. 13 is the theoretical OCP for the cell with H2O –CH4 fuel and air at different temperatures. Sfeir et al. [8] calculated the thermodynamic equilibrium concentration in the 56% CH/ 41% Ar/3% H2O/air system and the theoretical OCP is 1.205 V at 800 -C. This is close to 1.228 V for the 3% H2O – 97% CH4/ air at the same temperature in the present study.
Appendix A. Calculated open circuit potential in H2O – CH4/air system
[1] S.P. Jiang, S.H. Chan, Mater. Sci. Technol. 20 (2004) 1109. [2] S.P. Jiang, S.H. Chan, J. Mater. Sci. 39 (2004) 4405. [3] J.-H. Koh, Y.-S. Yoo, J.-W. Park, H.C. Lim, Solid State Ionics 149 (2002) 157. [4] C.M. Chun, J.D. Mumford, T. Ramanarayanan, J. Electrochem. Soc. 147 (2000) 3680. [5] P.V. Hendriksen, S.C. Singhal, H. Tagawa (Eds.), SOFC-V, vol. 97-40, The Electrochem. Soc., Penington, NJ, 1997, p. 1319. [6] M. Mori, Y. Hier, J. Am. Ceram. Soc. 84 (2001) 2573. [7] J. Vulliet, B. Morel, J. Laurencin, G. Gauthier, L. Bianchi, S. Giraud, J.-Y. Henry, F. Lefebvre-Joud, S.C. Singhal, M. Dokiya (Eds.), SOFC-VIII, vol. 2003-07, The Electrochem. Soc., Pennington, NJ, 2003, p. 803. [8] J. Sfeir, P.A. Buffat, P. Mo¨ckli, N. Xanthopoulos, R. Vasquez, H.J. Mathieu, J. Van herle, K.R. Thampi, J. Catal. 202 (2001) 229. [9] J. Sfeir, J. Power Sources 118 (2003) 276. [10] S. Tao, J.T.S. Irvine, Nat. Mater. 2 (2003) 320. [11] S. Tao, J.T.S. Irvine, J. Electrochem. Soc. 151 (2004) A252. [12] F.T. Ciacchi, K.M. Crane, S.P.S. Badwal, Solid State Ionics 73 (1994) 49. [13] S.P. Jiang, J.G. Love, L. Apateanu, Solid State Ionics 160 (2003) 15. [14] S. Koch, P.V. Hendriksen, Solid State Ionics 168 (2004) 1. [15] S.P. Jiang, J. Electrochem. Soc. 150 (2003) E548. [16] A. Mitterdorfer, L.J. Gauckler, Solid State Ionics 111 (1998) 185. [17] S.P. Jiang, J.-P. Zhang, K. Foger, J. Eur. Ceram. Soc. 23 (2003) 1865. [18] S. Primdahl, J.R. Hansen, L. Grahl-Madsen, P.H. Larsen, J. Electrochem. Soc. 148 (2001) A74. [19] S.P. Jiang, S.P.S. Badwal, Solid State Ionics 123 (1999) 209. [20] S.P. Jiang, W. Wang, Y.D. Zhen, J. Power Sources 147 (2005) 1. [21] A. Bieberle, L.P. Meier, L.J. Gauckler, J. Electrochem. Soc. 148 (2001) A646. [22] S. Primdahl, M. Mogensen, J. Electrochem. Soc. 146 (1999) 2827. [23] S.B. Adler, J.A. Lane, B.C.B. Steele, J. Electrochem. Soc. 144 (1997) 1884. [24] S.B. Adler, Solid State Ionics 135 (2000) 603. [25] S. Tao, J.T.S. Irvine, J. Electrochem. Soc. 151 (2004) A497. [26] A. Esquirol, N.P. Brandon, J.A. Killer, M. Mogensen, J. Electrochem. Soc. 151 (2004) A1847. [27] S.P. Jiang, W. Wang, J. Electrochem. Soc. 152 (2005) A1398. [28] N. Sakai, K. Yamaji, T. Horita, H. Yokokawa, T. Kawada, M. Dokiya, J. Electrochem. Soc. 147 (2000) 3178.
The OCP in H2O–CH4/air system can be calculated from the thermodynamic equilibrium concentration of the mixture gases, CH4, CO, O2, CO2, H2O and H2, according to the following four main chemical reactions: CH4 þ 2O2 6CO2 þ 2H2 O
ð2Þ
CH4 þ H2 O6CO þ 3H2
ð3Þ
CH4 þ CO2 62CO þ 2H2
ð4Þ
CO þ H2 O6CO2 þ H2
ð5Þ
The initial and equilibrium concentrations of each component are shown in Table 2. Defining that K 1, K 2, K 3 and K 4 are the equilibrium constants of the above four reactions, the four unknown parameters, x 1, x 2, x 3 and x 4, can be obtained from following equations. K1 ¼
x2 ðb x1 2x2 2x3 Þ2 ða x1 x2 Þx23
ð6Þ
K2 ¼
x1 x34 ða x1 x2 Þðb x1 2x2 2x3 Þ
ð7Þ
K3 ¼
x1 x24 ða x1 x2 Þx2
ð8Þ
K4 ¼
x1 x4 x1 ðb x1 2x2 2x3 Þ
ð9Þ
The above equations can be solved using nonlinear least square method. As the concentration of the oxygen in air is 0.21 atm, the open circuit potential of the cell can be calculated as: RT 0:21 ln OCP ¼ ð10Þ 4F x3
References
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