Estimation of Surface Coverages on H2/H2o Electrode in Reversible Operation of Solid Oxide Fuel Cell/ Electrolysis Cell Using Electrochemical Kinetics with Optimized Parameter By Genetic Algorithm
Authors: Koga Yasutomo , Hasegawa Kei , Iida Yuta , Kameda Keisuke , Ihara Manabu 
Published: December 2020

Solid oxide fuel cell / electrolysis cell (SOFC / EC) can be expected as energy converters with high efficiency. In SOFC / EC material developments, the coverages of the chemical species at the three-phase boundary (TPB) are directly linked to the electrode performance. Accordingly, it is important to estimate the surface coverages at TPB to develop a new electrode. However, it is difficult to directly analyze and evaluate the coverages at the reaction field of the oxide / metal composites at high temperature (> 600 °C). Therefore, it is required to construct electrochemical kinetics with the various parameters, such as reaction constants and adsorption equilibrium constants.
In order to determine the coverages at the TPB, it has demands not only to construct an appropriate electrochemical model but also both to develop a method for fitting a large number of parameters included in the model and to acquire a series of various experimental data sufficient for fitting. These requirements are not fully satisfied in previous researches [1-2]. Therefore, the chemical properties of the electrode surface have not been clarified while the reaction mechanism on the H2 electrode has been understood in FC operation.
In this study, the determination method of surface coverage using an electrochemical reaction model for H2 / H2O porous electrodes composed of Ni / YSZ was established. We considered that the local equilibrium between oxygen and oxide ions is achieved in the solid electrolyte, and proposed a H2 electrode reaction model consisting of a competitive adsorption reaction as Langmuir-Hinshelwood type at TPB. Using the model, a relational expression between the electric current density and the coverage could be obtained.
The equation includes the parameters of current density (i), oxygen activity (a
O), the partial pressures of hydrogen (P
H2) and water (P
H2O), the kinetics constant of the water generation reaction at FC operation (k
a), and the adsorption equilibrium constant of H, O, OH and H2O (K
H, K
O, K
OH and K
H2O). a
O(eq) is the oxygen activity at equilibrium potential. The i, P
H2, P
H2O, a
O and a
O(eq) could be obtained by experimental conditions and data while ka
, K
H, K
O, K
OH and K
H2O are unknown constants without appropriate fitting. The simple optimization method cannot approximate optimal solutions and determine the coverages because this model is multivariate function, which has 5 parameters.
As a method for quantifying the coverage of chemical species by fitting the experimental data to the reaction model, the method using a genetic algorithm was applied. The genetic algorithm is one of the multivariable optimization methods, which efficiently approximates the optimized value of the parameters by alternation of generations created by operations composed of selection, crossover, and mutation [3]. By taking advantage of the characteristics of the genetic algorithm that randomly generates and converges initial value candidates during optimization, multiple optimal solutions can be efficiently obtained with preventing the drop to local optimum by increasing the number of trials. The most effective optimal solution could be determined from them.
As the various electrochemical data for estimating the surface coverage at a temperature of 900 °C, the electrochemical data of both FC / EC under 12 conditions, in which P
H2 and P
H2O were changed were got using the same cell. The current interruption method was used to separate the overvoltage and ohmic voltage loss of the H2/H2O electrode during power generation and electrolysis under constant current, and then, the oxygen activity was calculated from the ohmic free-anode potential (vs. 1 atom O2). Using genetic algorithm, optimization schemes were attempted more than 50,000 times and searched for the parameter set with the smallest error between the experimental value and the estimated value from the obtained optimal solutions. The outline of the optimization process was shown in Fig. 1.
As a result of fitting various reaction constants to the model with optimal solutions, the relationship between i and a
O could be roughly expressed by multiple reaction rate constants and equilibrium constants, and the coverages could be quantified. Furthermore, it was possible to draw the chemical state at TPB of Ni / YSZ electrodes during FC operation.
[1] W. G. Bessler et al., Phys. Chem. Chem. Phys., 12, 13888 (2010).
[2] M. Ihara et al., J. Electrochem. Soc., 148(3), A209 (2001).
[3] M. Srinivas et al., IEEE, 27(6), 17 (1994).

Figure 1