*Electrodialysis*

thickness depending on the ionic conductivity of the composite. In the present simulations, both conductivities (electronic and ionic) and gas transport have been computed, and the competition between gas, ions, and electrons was investigated. The simulation results highlight a complex distribution of electrochemical active areas (see **Figure 6**). Due to the competition effect between gas (water) diffusion and ionic charge transport occurring in "countercurrent," the current source terms are located close to both interfaces. In order to obtain better comprehensions, the current sources distributions have been analyzed. **Figure 6** presents diagrams of

*Solid Oxide Steam Electrolyzer: Gas Diffusion Steers the Design of Electrodes*

*DOI: http://dx.doi.org/10.5772/intechopen.90352*

electrode thickness has been divided into 10 layers from the electrolyte/cathode interface to the cathode/gas channel interface, and the ratio of the current sources to the whole current for each layer is plotted versus the electrode thickness. The results are expressed in percentage of the total current generation. Since the most interesting phenomena occurs under the edges of the collector pin, the current

The competition between the transport of ions and the diffusion of gases is highlighted. Electron transport is not a limiting step as the electronic conductivity is about 10<sup>4</sup> times higher than the ionic one. When the water diffusion coefficient decreases, the competition between O<sup>2</sup> and gas transport is distorted, and a relocation of current sources toward the cathode/gas channel interface occurs (**Figure 6**). Therefore, gas access implies a higher reactivity of the electrode/gas

On all 40 μm thick electrodes, all layers exhibit a reactivity higher than 5% of the total generated current. However, the 80 μm electrode generates roughly 65% of the total current within the first 24 μm of electrode thickness and 30% within the last 16 μm (**Figure 6c**). In other terms, 50% of the electrode thickness is responsible for 95% of the current generation. The thinner the electrode, the more homogeneous

**Figure 7a** shows the current source generation along the 80 μm electrode thickness located in the middle of the gas channel (abscissa x = 0 mm). It can be seen that more than 70% of the total current generation comes from the first 30% of the electrode thickness. That observation is coherent with Hussain et al. [30] who consider that the electrochemical reaction is occurring exclusively at the interface electrode/electrolyte. **Figure 7a**, **b** show that increasing electrode thickness leads to

) along the cathode thickness for the studied cases. The

Faradic currents (A m<sup>3</sup>

channel interfaces than expected.

the current sources seem to be.

**Figure 5.**

**103**

*Polarization curves for cases A, B, C, and D.*

source terms are considered at abscissa x = 1 mm.

**Figure 3.**

*Current sources (A m<sup>3</sup> ) through SOEC cell for a cell potential close to 1.3 V, for case A (left, a) and case B (right, b).*

#### **Figure 4.**

*Steam concentration (mol m<sup>3</sup> ) through the SOEC cathode for a cathodic overpotential equal to 0.5 V (cell voltage = 1.3 V) for case A.*

performed. Consequently, as seen in **Figure 3b**, no water depletion is observed in case B when considering a perfectly collected current without the collector pin. The current–voltage characteristics for cases A, B, C, and D are presented in **Figure 5**.

As expected, a homogeneous current collecting significantly improves the performance. Gaseous reactants and products are not impeded by the collector pin anymore. Decreasing the water diffusion coefficient induces a large shift of the current-tension characteristic toward lower currents and thus increases concentration overpotentials. According to Juhl et al. [29], increasing the electrode thickness improves the electrode performance for LSM/YSZ composite cathode of SOFC using thicknesses between 2 and 12 μm. Nevertheless, Virkar et al. [22] have computed that SOFC cathode overpotential increases or decreases with electrode

#### *Solid Oxide Steam Electrolyzer: Gas Diffusion Steers the Design of Electrodes DOI: http://dx.doi.org/10.5772/intechopen.90352*

thickness depending on the ionic conductivity of the composite. In the present simulations, both conductivities (electronic and ionic) and gas transport have been computed, and the competition between gas, ions, and electrons was investigated. The simulation results highlight a complex distribution of electrochemical active areas (see **Figure 6**). Due to the competition effect between gas (water) diffusion and ionic charge transport occurring in "countercurrent," the current source terms are located close to both interfaces. In order to obtain better comprehensions, the current sources distributions have been analyzed. **Figure 6** presents diagrams of Faradic currents (A m<sup>3</sup> ) along the cathode thickness for the studied cases. The electrode thickness has been divided into 10 layers from the electrolyte/cathode interface to the cathode/gas channel interface, and the ratio of the current sources to the whole current for each layer is plotted versus the electrode thickness. The results are expressed in percentage of the total current generation. Since the most interesting phenomena occurs under the edges of the collector pin, the current source terms are considered at abscissa x = 1 mm.

The competition between the transport of ions and the diffusion of gases is highlighted. Electron transport is not a limiting step as the electronic conductivity is about 10<sup>4</sup> times higher than the ionic one. When the water diffusion coefficient decreases, the competition between O<sup>2</sup> and gas transport is distorted, and a relocation of current sources toward the cathode/gas channel interface occurs (**Figure 6**). Therefore, gas access implies a higher reactivity of the electrode/gas channel interfaces than expected.

On all 40 μm thick electrodes, all layers exhibit a reactivity higher than 5% of the total generated current. However, the 80 μm electrode generates roughly 65% of the total current within the first 24 μm of electrode thickness and 30% within the last 16 μm (**Figure 6c**). In other terms, 50% of the electrode thickness is responsible for 95% of the current generation. The thinner the electrode, the more homogeneous the current sources seem to be.

**Figure 7a** shows the current source generation along the 80 μm electrode thickness located in the middle of the gas channel (abscissa x = 0 mm). It can be seen that more than 70% of the total current generation comes from the first 30% of the electrode thickness. That observation is coherent with Hussain et al. [30] who consider that the electrochemical reaction is occurring exclusively at the interface electrode/electrolyte. **Figure 7a**, **b** show that increasing electrode thickness leads to

**Figure 5.** *Polarization curves for cases A, B, C, and D.*

performed. Consequently, as seen in **Figure 3b**, no water depletion is observed in case B when considering a perfectly collected current without the collector pin. The current–voltage characteristics for cases A, B, C, and D are presented in **Figure 5**. As expected, a homogeneous current collecting significantly improves the performance. Gaseous reactants and products are not impeded by the collector pin anymore. Decreasing the water diffusion coefficient induces a large shift of the current-tension characteristic toward lower currents and thus increases concentration overpotentials. According to Juhl et al. [29], increasing the electrode thickness improves the electrode performance for LSM/YSZ composite cathode of SOFC using thicknesses between 2 and 12 μm. Nevertheless, Virkar et al. [22] have computed that SOFC cathode overpotential increases or decreases with electrode

*) through the SOEC cathode for a cathodic overpotential equal to 0.5 V (cell*

*) through SOEC cell for a cell potential close to 1.3 V, for case A (left, a) and case B*

**Figure 4.**

**102**

**Figure 3.**

*Electrodialysis*

*(right, b).*

*Current sources (A m<sup>3</sup>*

*Steam concentration (mol m<sup>3</sup>*

*voltage = 1.3 V) for case A.*

**Figure 6.**

*Current sources distribution through cathodes for cases A (a), B (b), C (c), and D (d), at abscissa separating the gas channel and the current collector (x = 1 mm and cell voltage = 1.3 V).*

**Figure 7.**

**105**

*Current sources distribution though case C (80 μm electrode) cathode (a) and anode (b) at abscissa located in*

*the middle of the gas channel (x = 0 mm and cell voltage = 1.3 V).*

*Solid Oxide Steam Electrolyzer: Gas Diffusion Steers the Design of Electrodes*

*DOI: http://dx.doi.org/10.5772/intechopen.90352*

*Solid Oxide Steam Electrolyzer: Gas Diffusion Steers the Design of Electrodes DOI: http://dx.doi.org/10.5772/intechopen.90352*

#### **Figure 7.**

*Current sources distribution though case C (80 μm electrode) cathode (a) and anode (b) at abscissa located in the middle of the gas channel (x = 0 mm and cell voltage = 1.3 V).*

**Figure 6.**

*Electrodialysis*

**104**

*Current sources distribution through cathodes for cases A (a), B (b), C (c), and D (d), at abscissa separating*

*the gas channel and the current collector (x = 1 mm and cell voltage = 1.3 V).*

current being generated closer to the collector pin. This is compensated by a higher reactivity in the interface vicinity. Those edge effects, obvious in all cases, can be attributed to the electronic ohmic drop. Moreover, the ionic ohmic drop also controls the distribution of anodic current sources. **Figure 7b** displays the anodic equivalent to **Figure 7a**. Contrary to the cathode, no control of the faradaic currents by gas access exists at the anode, since the gas is being produced. Nevertheless, both electrodes display similar current sources distributions. Such observation remains valid for all simulations. Consequently the anodic current sources distribution is driven by electrical cathodic behavior.

#### **4.2 Influence of graded grain diameter**

It is generally accepted that the performances of composite electrodes as well as graded cathodes in SOFCs are largely governed by TPB number, mass transport, and ohmic drop. It is well known that the polarization resistance decreases [31, 32] when using graded electrodes. The improvement of the microstructure is one of the key parameters to reach high electrochemical performances.

In the context of current collecting considerations, this work has emphasized the effects of functionally graded electrodes on overall cell behavior (i.e., current collectors/electrodes/electrolyte). Thus, the influence of grain size distribution was investigated via the simulations gathered in **Table 6**. A gradient of grain diameter distribution was introduced, leading to either the cathode or the anode presenting several layers of different grain diameters. The effects of such a change in microstructure on the currents obtained and their distribution were investigated. In this work, electrodes are constituted of two layers, each presenting a specific grain size. Their responses were modeled and the results analyzed. For each cathode and anode, five simulations were performed, referenced from I to V, with the subscripts "a" and "c" referring to anode and cathode, respectively. One goal of this work was to investigate the influence of the grain diameter on the reaction location and the cell performances. However, as Eq. (10) shows, the exchange current density is modified by the microstructure. To be able to compare the currents obtained for the different samples, the average exchange current density i0,a*=*c, given by Eq. (25) over the whole electrode thickness was kept constant:


$$\overline{i\_{0,a/c}} = \frac{1}{L} \left( \int\_0^{aL} i\_{0,a/c} \left( d\mathbf{g}\_{a/c}^{0\text{ to all}} \right) + \int\_{aL}^L i\_{0,a/c} \left( d\mathbf{g}\_{a/c}^{\text{all, to L}} \right) \right) d\mathbf{x} \tag{25}$$

**Figure 8.**

**107**

*Polarization curves for cathode simulations Ic to Vc (a) and anode simulations Ia to Va (b).*

*Solid Oxide Steam Electrolyzer: Gas Diffusion Steers the Design of Electrodes*

*DOI: http://dx.doi.org/10.5772/intechopen.90352*

#### **Table 6.**

*Summary of the simulated microstructures.*

*Solid Oxide Steam Electrolyzer: Gas Diffusion Steers the Design of Electrodes DOI: http://dx.doi.org/10.5772/intechopen.90352*

**Figure 8.** *Polarization curves for cathode simulations Ic to Vc (a) and anode simulations Ia to Va (b).*

current being generated closer to the collector pin. This is compensated by a higher reactivity in the interface vicinity. Those edge effects, obvious in all cases, can be attributed to the electronic ohmic drop. Moreover, the ionic ohmic drop also controls the distribution of anodic current sources. **Figure 7b** displays the anodic equivalent to **Figure 7a**. Contrary to the cathode, no control of the faradaic currents by gas access exists at the anode, since the gas is being produced. Nevertheless, both electrodes display similar current sources distributions. Such observation remains valid for all simulations. Consequently the anodic current sources distribution is

It is generally accepted that the performances of composite electrodes as well as graded cathodes in SOFCs are largely governed by TPB number, mass transport, and ohmic drop. It is well known that the polarization resistance decreases [31, 32] when using graded electrodes. The improvement of the microstructure is one of the

In the context of current collecting considerations, this work has emphasized the effects of functionally graded electrodes on overall cell behavior (i.e., current collectors/electrodes/electrolyte). Thus, the influence of grain size distribution was investigated via the simulations gathered in **Table 6**. A gradient of grain diameter distribution was introduced, leading to either the cathode or the anode presenting several layers of different grain diameters. The effects of such a change in microstructure on the currents obtained and their distribution were investigated. In this work, electrodes are constituted of two layers, each presenting a specific grain size. Their responses were modeled and the results analyzed. For each cathode and anode, five simulations were performed, referenced from I to V, with the subscripts "a" and "c" referring to anode and cathode, respectively. One goal of this work was to investigate the influence of the grain diameter on the reaction location and the cell performances. However, as Eq. (10) shows, the exchange current density is modified by the microstructure. To be able to compare the currents obtained for the different samples, the average exchange current density i0,a*=*c, given by Eq. (25)

driven by electrical cathodic behavior.

*Electrodialysis*

**4.2 Influence of graded grain diameter**

key parameters to reach high electrochemical performances.

over the whole electrode thickness was kept constant:

*ω*ð *L*

@

**Cathode Anode**

*i*0,*a=<sup>c</sup> dg*0 to <sup>α</sup><sup>L</sup> *a=c* � � þ ð *L*

� � <sup>0</sup>

**% thickness <sup>ω</sup> dg<sup>ω</sup> [μm] dg1**�**<sup>ω</sup> [μm] Quote % thickness <sup>ω</sup> dg<sup>ω</sup> [μm] dg1**�**<sup>ω</sup> [μm] Quote** 2.0 4.048 Ic 20 2.0 4.048 Ia 1.8 6.654 IIc 20 1.8 6.654 IIa 2.0 3.324 IIIc 10 2.0 3.324 IIa 1.8 3.563 IVc 10 1.8 3.563 IVa 1.5 4.950 Vc 10 1.5 4.950 Va

*ωL*

*i*0,*a=<sup>c</sup> dg*<sup>α</sup>L to L *a=c*

1

A*dx* (25)

0

*<sup>i</sup>*0,*a=<sup>c</sup>* <sup>¼</sup> <sup>1</sup> *L*

*Summary of the simulated microstructures.*

**Table 6.**

**106**

To do so in multilayer samples, the increase in exchange current density caused by a layer composed of smaller particles was compensated by a larger particle layer. The different grain diameters were adapted according to the thickness of the layer so that the average exchange current density remains constant. The layer displaying the thinner grains is always closer to the electrolyte and will be referred to as layer ω

The current–voltage characteristics obtained for the five cathodic and anodic cases are displayed in **Figure 8a**, **b**. On the cathode side, sample Vc seems to present an obvious performance increase if compared to the other modified cathodes. Additionally, case IVc shows higher current densities than case IIc, even if both electrodes are composed of grain of equal diameter in the layer closest to the electrolyte. On the other hand, the microstructural changes do not influence significantly the electrical

Ni et al. [15, 33] have evaluated the potential of functionally graded materials for SOEC electrodes. These authors have compared [33] conventional nongraded electrodes with particle size-graded electrodes. For graded electrodes with a particle size decreasing by 50% from the gas/electrode interface (dg = 1 μm) to the electrode/electrolyte interface (dg = 0.5 μm), a negligible reduction in potential is observed in comparison with nongraded electrode. For a higher gradient of particle

electrode overvoltage has been observed. The present study exhibits similar results. In **Figure 8**, the bilayer with a 50% decrease in particle size (Ic: dg = 4.048 ➔ 2 μm) showed poor improvement of performance. In addition, a 70% grain diameter decrease (Vc: dg = 4.95 ➔ 1.5 μm) led to a large enhancement of the current

Thin particles at the electrode/electrolyte interface (cathode interlayer thickness) decrease the area-specific resistance (ASR). This increase in performance goes along with the relocation of the electrochemical reaction at the electrode/electrolyte interfaces. As shown in **Figure 9**, 80% of the cathodic current arises from the first 10% of electrode thickness (case Vc), and on the anode side, more than 90% is generated by the first 20% (case IIa). The relocation in the volume observed for the smallest particles can easily be explained by the dependence of exchange current densities on grain diameter Eq. (10). Furthermore, forcing the current generation close to the electrolyte interface enables decreasing the ionic current path length.

The results show the influence of current collectors on gas access. Relevant control of material microstructures improves the diffusion of gaseous reactants and the current collecting. When diffusion is the limiting step, a relocation of the current sources within the volume of the electrodes is observed. On the contrary, if ionic ohmic drop becomes the rate determining step, current density sources are located close to the electrode/electrolyte interface. In some specific cases, the assumption that all electrochemical reactivity is located in the electrolyte interface vicinity cannot be made. That observation is emphasized when the competition between gas and ion transport is intentionally distorted, since a second reactive

It has been shown that it is possible to force the reaction to occur close to the electrolyte/electrode interfaces by layering the electrodes and introducing gradients of grain diameters. The obtained relocation is as high as 80% of the current being generated within the first 4 μm of the cathode thickness. The ohmic losses are

and expressed as a percentage of the total thickness of the electrode.

*Solid Oxide Steam Electrolyzer: Gas Diffusion Steers the Design of Electrodes*

*DOI: http://dx.doi.org/10.5772/intechopen.90352*

anode behavior. The polarization curves can barely be differentiated.

size decreasing by 70% (i.e., dg = 1 ➔ 0.3 μm) a significant saving of H2

generated by the cell.

**5. Conclusion**

**109**

layer appears close to the cathodic gas channel.

reduced and gas access facilitated.

#### **Figure 9.**

*Current sources distribution through both electrodes underneath the middle of the gas channel (x = 0 mm) for case A and cases displaying the best performance in the grain size investigation (Vc and IIa) at cell voltage = 1.3 V.*

#### *Solid Oxide Steam Electrolyzer: Gas Diffusion Steers the Design of Electrodes DOI: http://dx.doi.org/10.5772/intechopen.90352*

To do so in multilayer samples, the increase in exchange current density caused by a layer composed of smaller particles was compensated by a larger particle layer. The different grain diameters were adapted according to the thickness of the layer so that the average exchange current density remains constant. The layer displaying the thinner grains is always closer to the electrolyte and will be referred to as layer ω and expressed as a percentage of the total thickness of the electrode.

The current–voltage characteristics obtained for the five cathodic and anodic cases are displayed in **Figure 8a**, **b**. On the cathode side, sample Vc seems to present an obvious performance increase if compared to the other modified cathodes. Additionally, case IVc shows higher current densities than case IIc, even if both electrodes are composed of grain of equal diameter in the layer closest to the electrolyte. On the other hand, the microstructural changes do not influence significantly the electrical anode behavior. The polarization curves can barely be differentiated.

Ni et al. [15, 33] have evaluated the potential of functionally graded materials for SOEC electrodes. These authors have compared [33] conventional nongraded electrodes with particle size-graded electrodes. For graded electrodes with a particle size decreasing by 50% from the gas/electrode interface (dg = 1 μm) to the electrode/electrolyte interface (dg = 0.5 μm), a negligible reduction in potential is observed in comparison with nongraded electrode. For a higher gradient of particle size decreasing by 70% (i.e., dg = 1 ➔ 0.3 μm) a significant saving of H2 electrode overvoltage has been observed. The present study exhibits similar results. In **Figure 8**, the bilayer with a 50% decrease in particle size (Ic: dg = 4.048 ➔ 2 μm) showed poor improvement of performance. In addition, a 70% grain diameter decrease (Vc: dg = 4.95 ➔ 1.5 μm) led to a large enhancement of the current generated by the cell.

Thin particles at the electrode/electrolyte interface (cathode interlayer thickness) decrease the area-specific resistance (ASR). This increase in performance goes along with the relocation of the electrochemical reaction at the electrode/electrolyte interfaces. As shown in **Figure 9**, 80% of the cathodic current arises from the first 10% of electrode thickness (case Vc), and on the anode side, more than 90% is generated by the first 20% (case IIa). The relocation in the volume observed for the smallest particles can easily be explained by the dependence of exchange current densities on grain diameter Eq. (10). Furthermore, forcing the current generation close to the electrolyte interface enables decreasing the ionic current path length.
