Determination with a Genetic Algorithm of Reactant Coverages on H2/H2O Electrodes Based on Electrochemical Kinetics Under Reversible SOFC/EC Operation ▴

A scheme to quantify surface coverages of reactants at triple phase boundary (TPB) by electrochemical measurements was constructed to evaluate the electrode performance of solid oxide fuel cells and electrolysis cells (SOFC/EC). The developments of electrode requires that the intrinsic properties of materials separated from the effect of geometric structure of the electrode. The proposed reaction model at TPB of H2/H2O electrodes is composed of competitive adsorptions and Langmure‐type surface reactions under the relationship between oxygen activity (aO) and the electrode potential. To determine the reaction constant (ka) and four adsorption equilibrium constants at TPB (KH, KH2O, KO and KOH), a mashine learning approach with a genetic algorithm as an optimization method and the experimental data of reversible SOFC/ECs with different H2/H2O partial pressures as the learning data was developed. As a result, even though all experimental curves of the current density vs. aO in SOFC operation were fitted by numerous sets of the five constants, the coverages under different conditions could be uniquely determined. Results suggest that TPB at 900 °C was almost vacant with a small amount of H2O in SOEC operation, and was not vacant and the OH coverage increased with increasing aO in SOFC operation.


Introduction
Expectation for solid oxide fuel cells/electrolysis cells (SOFC/ECs) are increasing with the increasing demand for large-scale, low cost energy storage [1][2][3]. Although it is necessary to reduce the SOFC/EC cost, improving the cell characteristics, that is, improving the power density for SOFCs and the current density at the heat neutral point for ECs, is directly linked to the cost reduction of the entire system [4][5][6][7][8]. In addi-tion, the cost can be reduced by the integrated type that utilizes reversible operation [4,5]. On the other hand, SOFCs have been extensively researched from materials to devices, however electrode development related to SOECs is in progress, and most materials and devices are based on SOFCs [5][6][7][8][9][10][11]. And not only top performance but also characteristics, such as characteristics with a wide range of loads, followabil--Invited paper related to the Topical Issue on ''High-Temperature Electrolysis using Solid Oxide Electrolyzer Cell (HT-SOEC)''.
ity and efficiency during transient operation are important, in order to respond to fluctuating power sources and fluctuating demand derived from renewable energy. Therefore, it is crucial to evaluate the SOFC/EC electrodes and establish a comprehensive kinetics model for quantitative electrode reactions, especially surface chemical/electrochemical reactions, toward new development.
One of the challenges in SOFC/EC material development is that it is difficult to directly analyze and evaluate the state of the reaction field in the oxide/metal composite at high temperature. It is important to clarify the state of the electrode surface, because the electrode kinetics is directly linked to the coverage of reactive species or their relative values on the electrode surface, especially the triple phase boundary (TPB) [12][13][14][15][16][17][18][19][20][21][22]. However, it is difficult to separate the effect of the porous structure with three dimensional TPB from the intrinsic characteristics of the materials. In Gd-doped CeO x with fluorite structure [23,24] and ion conductive oxides with perovskite structure, especially in proton conductive oxides, such as BaCe 0.9 Y 0.1 O 3-d [25], SrZr 1-x Y x O 3-d , SrZr 1-x Yb x O 3-d [26], SrCe 1-x Yb x O 3-d [27], and Pr-Doped Ba 2 In 2 O 5 [28], the amount of oxygen vacancy depends on the surface gas atmosphere such as oxygen partial pressure. Thus, not only the surface coverages of reactants but also the interior bulk properties change under a vacuum condition and/or different gas atmospheres, thus making it difficult to detect the surface coverage independently. Although certain in situ spectroscopic measurement technologies, such as Raman spectroscopy [29], have enabled to detect NiO in the cermet electrode or ambient pressure. X-ray photoelectron spectroscopy (XPS) [30] have enabled measurement of the oxidized state of the oxide material surface, but it is difficult to observe the coverage of chemical species on the electrode surface. Also, a method for quantifying the adsorbed species (H, OH, etc.) at the TPB has not yet been established. Determining the state of chemical species at the TPB requires the development of a comprehensive approach based on electrochemical evaluation of electrodes.
Hydrogen oxidation kinetics on SOFC hydrogen electrodes and water reduction on SOEC water electrodes have been extensively discussed, based on a pair of reversible reactions at TPB and developed the reaction models including the surface coverage of the reactants as the parameters [12][13][14][15][16][17][18][19][20][21][22]. The configurations of the anode were Ni pattern electrodes on YSZ to define the length of TPB [12,18,22] or the porous cermet electrode as the commercial cells [13][14][15][16]19]. Mizusaki et al. proposed a reaction kinetics model that assumed equilibrium of the oxide ion in the electrolyte and the oxygen adsorbent at TPB, and assumed local equilibrium of O 2-, O, and eat YSZ in the electrode [12]. Under these equilibrium assumptions, the oxygen activity (a O ) and the surface coverage of oxygen (q O ) correspond to the electrode potential. This reaction model was discussed in terms of the reaction order (i.e., current density (i) vs. a O , and electrode interface conductivity vs. partial pressure of H 2 or H 2 O (P H2 , P H2O )) measured via experiments on the pattern anode. The coverages of reactants on the active site of TPB were assumed to be the coverage of the vacancy (q V ) as~1. Based on those assumptions, Wen et al. described the relationship between i and the anode overpotential with the adsorption/desorption equilibrium and the surface chemistry under the assumption of q V~1 , and suggested that the overpotential can be reduced by keeping H 2 O ad at an appropriate level [13]. Jiang et al. proposed a reaction model in which adsorbed oxygen on Ni acts as an effective adsorption site of hydrogen based on the effect of P H2O on the anode overpotential measured by AC impedance measurement at low P H2O . [14]. The relationship between P H2O , P H2 and the exchange current density (i 0 ) in the Butler-Volmer equation was discussed and the existence of optimum P H2O to minimize the overpotential was suggested [15].
On the other hand, even though numerous researchers have evaluated the reaction on Ni/YSZ electrodes, the relationship between P H2 or P H2O , and the electrode performances have varied even at same operating conditions of P H2 , P H2O and temperature [16]. Thus, Ihara et al. proposed a comprehensive reaction model of SOFC/EC reaction using Langmuir competitive adsorption that enables description of such varied effect of P H2 /P H2O on DC polarization properties and on AC impedance properties [16]. In an actual SOFC electrode, the surface state at TPB, such as the crystal phase of each material, can depend on the source materials and/or preparation process. As a result, the properties of DC polarization and/or AC impedance at different P H2 /P H2O ratio can be varied depending on the surface coverage of reactants at TPB. Thus, by assuming local equilibrium in the electrolyte and equilibrium with competitive adsorption at TPB, the proposed model is based on a Langmuir-type kinetics equation of SOFC/EC which are both higher and lower a O than the equilibrium potential [16]. Variation in the reaction order of a O , P H2 , and P O2 to i represents the coverage ratio of chemical reactants vs. q V . By using the model, the kinetics constant (k), which depends on the geometric structure of the porous electrode, and the equilibrium constant (K), which is intrinsic properties of the material surface, can be separately discussed. By applying the model to FC/EC data under a wide range of a O , P H2 , and P H2O , the relationship between the FC/EC conditions and the coverage of the reactants can be directly determined.
Based on those investigations, a number of studies have proposed anode reaction models [17][18][19][20][21][22]. From the viewpoint of determining the surface coverage of the reactants of the electrode by data fitting, these models can be organized based on the following four factors: (i) rate determining reaction; (ii) assumption of the local equilibrium of oxygen, oxide ion and electron in the electrolyte, and/or the equilibrium between oxide ion in the electrolyte and the oxygen adsorbents on the active site, both of which correspond to the relationship among the oxygen coverage, oxygen activity and the anode potential; (iii) assumption of Langmuir-type reaction based on competitive adsorption on the electrode surface, and thus enables calculation of the coverage; and (iv) approximations in the model equations. Bieberle [17,18]. The model uses the mass balance equation with q O , q H , q OH , and q H2O at TPB and numerically calculates those q at the steady state. In contrast to the models in [12,13,16], in this model the competitive adsorption to occupy the limited number of active sites by the reactants (iii) was not investigated, nor was the local equilibrium of oxygen in the electrolyte, oxide ion and electron assumed, and the ratio of oxygen vacancy in the electrolyte (ii) was kept constant, namely, independent of the anode potential, and thus the coverage of each reactant did not depend on the potential of the electrode. Zhu [19]. Then, in order to understand the reaction mechanism of a H 2 /H 2 O electrode, the group applied the model to SOFC/EC data on the patterned electrode reported by Mizusaki et al. [12] under various P H2 and P H2O and determined the symmetric factor (b) in the Butler-Volmer equation as the comprehensive constant of the reaction [20]. The model equation was a polynomial with the coverage of multiple species x (q x ) under the assumption of competitive adsorption (iii). Although neither the local equilibrium of the oxygen, oxide ion and electron in the electrolyte nor equilibrium between the oxide ion and the surface oxygen adsorbent were assumed (ii), the coverage of each species depends on the activation potential in the Butler-Volmer equation, and thus the coverage of each reactant can be determined by appropriate data fitting. In those works, fitting of the comprehensive Butler-Volmer equation and the current-overpotential curves under the assumption that q O2-,YSZ @ 1 enabled the coverage of only OHon YSZ to be determined. Bessler et al. developed a scheme to simulate the SOFC reaction by generalizing the approach of Bieberle et al. [17]. In this scheme, the rate equation of each specific process in an SOFC, such as gas flow, adsorption/desorption of reactants, surface diffusion and chemical/electrochemical reactions and the ion transport were prepared, the equations of the total mass and charge balance with a general electrochemical equation were constructed, and the steady state at TPB were derived numerically [21]. Furthermore, the rate constant of each process without the charge transfer reaction was not determined by fitting the experimental data but by substituting the value obtained from literature as a physical property [31][32][33][34]. Based on this scheme, Volger et al. simultaneously investigated multiple possible reaction pathways [22]. A reaction pathway including one or two charge transfer processes was assumed, and then previously reported values were substituted for the values of the kinetics constants of other processes, such as adsorption/desorption [31][32][33][34], or chemical reaction on Ni or on YSZ [31,32], including their temperature dependence. By applying this model [21] to the AC impedance properties under different P H2 , P H2O and temperature [18], the suggested reaction pathway which sufficiently describes the data includes the charge transfer reaction of H ad on Ni and O 2on YSZ or H ad on Ni and OHon YSZ across TPB, and the rate determining step was assumed to be one of these reactions (i). By these methods, the steady state coverage of the reactants, including the vacant site, can be determined by calculating the rate constant of charge transfer by data fitting, but the specific values strongly depend both on the set of kinetics constant and the equilibrium constants obtained from literature and on the reliability of those parameters under actual SOFC/EC conditions. Also, as the model suggested by Bieberle et al. [17], the local equilibrium of the oxygen, oxide ion and electron in the electrolyte and the equilibrium between the oxide ion and the surface oxygen adsorbent were not assumed (ii), and the ratio of oxygen vacancy in the electrolyte was assumed to be constant and thus independent of the electrode potential. Thus, the coverage of each reactant and the electrode potential were the independent of each other.
Thus, in order to develop the scheme to evaluate the chemical characteristics of the electrode materials by quantitatively determining the coverages of reactants at TPB, to select and/ or establish the appropriate reaction model is required. Also, to apply any model to quantify the state of chemical species at TPB, sufficient set of experimental data and the appropriate multiple regression method are necessary. However, because both of them are not sufficient, although many of the proposed reaction models work as the method to understand the reaction mechanism on the electrodes, the chemical properties at TPB in the electrode have not been quantitatively determined. Although the number of studies focusing on the hydrogen generation reaction of SOEC based on the discussion of SOFC reaction models is increasing [7][8][9][10][35][36][37], the comprehensive understanding of SOFC/EC reaction to determine the electrode properties with applying the knowledge of the SOFC models are still ongoing. Thus, in order to quantitatively understand the reaction kinetics of SOFC/EC and to enhance the development of the electrode performance, it is necessary to determine the chemical characteristics, such as surface coverage. In order to establish the scheme, all of the three components are required as (i) to establish the appropriate electrochemical model based on the existed SOFC reaction models, (ii) to develop the procedure for the data fitting of the multiple variables to the experimental data, and (iii) to obtain series of the sufficient number of experimental data to determine and validate the variables.
Technology is needed for optimizing the multiple variables and to efficiently obtain the global optimum by fitting the reaction model with experimental data. Recently, machinelearning technologies are rapidly developing and have been widely applied in the research field, such as the multiple regression, i. e., supervised learning with the experimental data as the learning data. A common multivariate analysis method is the so-called ''genetic algorithm'', which is an evolutionary calculation method. This method efficiently approximates parameters to obtain optimal solutions by decreasing the possibility to terminate the optimization procedure at the local optimum by alternation of generations created by selection, crossover, and mutation operations [38,39]. Ohenoja et al. applied a real-coded genetic algorithm to optimize seven parameters of an electrochemical model for polymer electrolyte membrane fuel cells, and tried to specify the range of each of those parameters [40]. Bozorgmehri et al. constructed an artificial neural network model whose objective function was the cell voltage for anode-supported SOFCs, and then optimized the maximum power density by using a genetic algorithm with four parameters, namely, anode support thickness, anode support porosity, electrolyte thickness and functional layer cathode thickness [41]. By applying such technologies into the multiple regression, the global optimal solution for a set of parameters can be obtained by iteration of the genetic algorithm.
In our work reported here, in order to develop a scheme to determine the surface coverage of the reactants at TPB on the electrode based on electrochemical measurement data, we applied the electrochemical reaction model developed by Ihara et al. [16] by considering the following three factors: (i) the coverage changes depending on the electrode potential (based on the assumption of local equilibrium between oxygen, oxide ion and electron in the electrolyte and on assumption of equilibrium between the oxide ion in the electrolyte and the oxygen adsorbent on the electrode surface); (ii) the model was constructed under the assumption of competitive adsorption, which is a common assumption in the thermochemical catalyst research field; and (iii) the model was composed of each elementally reaction step without approximations. This reaction model describes the i value that corresponds to the reaction rate as the competitive adsorption reaction of a chemical species, such as H, O, H 2 O and OH, and to the Langmuir reaction among these species. Then, in this work, the multiple regression, i. e., supervised learning with the experimental data as the learning data, was investigated with applying a genetic algorithm as an optimization method to determine the set of kinetics constant and equilibrium constants in our kinetics model. In order to determine the multiple variables by applying the reaction model and the algorism of data fitting, we obtained a series of experimental data of both SOFC and SOEC reaction across the equilibrium potential under different gas conditions with H 2 /H 2 O/Ar mixture and a single cell with a commonly used cermet H 2 /H 2 O electrode of nickel (Ni)/yttria stabilized zirconia (YSZ) with well-defined structure. Finally, we developed the method to determine the sur-face property of SOFC/EC electrode, namely, the coverages of reactant at TPB by applying our kinetics model, the procedure to data optimization algorism and the series of reversible SOFC/EC data. As a result, the experimental curves i vs. a O under 4 different P H2 3 different P H2O approximately fitted in SOFC region using one set of five independent variables. The coverage of chemical species at the TPB of Ni/YSZ during the SOFC power generation under wide range of the different oxygen activity was quantitatively determined.

Cell Fabrication and Power Generation Experiments
Electrolyte-support type SOFC/EC cell was prepared using 8 mol.%-Y 2 O 3 -ZrO 2 (8-YSZ; 20-mm diameter, 0.25-mm thick, TOSOH Co., Tokyo) as an electrolyte disc. For the H 2 /H 2 O electrode, a mixture paste of NiO (Kusaka Rare Metal Products, Co. Ltd., Tokyo) and 8-YSZ (TOSOH Co., Tokyo) was prepared at a weight ratio of 3:2 with adding ethylcellulose and a-terpineol at a weight ratio of 10:74. The paste was coated on the disc and was calcined on a 8-YSZ disc in air at 1,300°C for 4 h. Then, for the O 2 electrode, a mixture paste of La 0.8 Sr 0.2 MnO 3 (AGC Seimi Chemical Co. Ltd., Kanagawa) and ScSZ (Daiichi Kigenso Kagaku Kogyo Co., Ltd., Osaka) at a weight ratio of 1:1 was coated on the other side of the disc and calcined on the other side of the 8-YSZ disc in air at 1,200°C for 4 h. Both H 2 /H 2 O electrode and O 2 electrode were divided into working electrode (0.52 cm 2 ) and reference electrode (0.15 cm 2 ) with 2 mm in distance between them, as described in ref. [16] and shown in Figure 1a The cell was set in the SOFC/EC apparatus described in [16]. The apparatus is composed of the multiple mullite tubes. The H 2 /H 2 O electrode was contacted to Au mesh and oxygen electrode contacted to Pt mesh as the current collector. Both side electrodes with current collectors are attached to the end of inner tubes as the upper gas stream (10 mm in diameter). They were inserted into outer tubes as the downer gas stream (21 mm in diameter). The Pyrex glass ring, with the softening Fig. 1  In the measurement as reversible operation of SOFC/EC, the current density i applied with the interval of 50 mA cm -2 from 0 to 1,000 mA cm -2 and the interval of 100 mA cm -2 from 1,000 to 1,900 mA cm -2 in the FC region and the interval of at most 25 mA cm -2 until the potential difference between H 2 /H 2 O and O 2 working electrode reached 1.5 V across OCV.

Measurement of i vs. E a at different gas conditions
All the data with the number of total data points as 360 including the V at equilibrium with i = 0 in FC region and 177 in EC region among 12 conditions were obtained from the experiment at each i in different P H2 and P H2O , as described in 2.1 and as shown in Figure 2 using one cell. To minimize the effects of concentration overpotential and a shift in the Nernst potential in the measurement, the H 2 utilization at FC mode were kept lower than 7.8% and the water utilization at EC mode were kept lower than 24%, as shown in Table 1. As shown in Figure  The ohmic voltage loss of the HW and OW including ohmic voltage loss of the electrolyte, were identified using the current interruption method measured by an oscilloscope. The abrupt voltage change occurred in 5 μs and was defined as the ohmic voltage loss, and the ohmic voltage loss of HW and OW was defined as the difference between the voltage before the current interruption and the average voltage from 5 to 20 μs on V HW-HR and V OR-OW , respectively. Then, the H 2 /H 2 O electrode overvoltage (η h ) was calculated as -V HW-HR minus ohmic voltage loss. Here, the ohmic-free anode potential (E a ) defined as V OR-HW minus ohmic voltage loss of HW was confirmed by calculating the sum η h + V OR-HR .
Also, in general, the reaction between H 2 /O 2 and H 2 O in the gas phase at the H 2 /H 2 O electrode in SOFC/EC, as shown in Eq. (1), reaches thermal equilibrium (equilibrium constant, K = 10 8.153 at 900°C, thermodynamic data obtained from MALT, Materials-oriented Little Thermodynamic Database, Kagaku-Gijutsu Sha, Tokyo).
Thus, the actual P H2O during the electrochemical measurements at each i was also estimated based on the assumption of the equilibrium reaction Eq. (1) using P O2 , which was calculated from V OR-HR (P O2 = 1 at the O 2 electrode). Fig. 2 Configuration of four-electrode cell. Current flows between OW and HW (red line). P H2O was calculated from P O2 determined by voltage difference between OR and HR (green line). a O at site 3 was calculated from ohmic-free voltage difference between OR (site 1) and HW (site 2) (blue line). Here, a O as shown in Eq. (2) was calculated from the ohmic-free anode potential via the following derivation process: where E a is expressed as E a = -(V HW-OW + ΔV ohmic + h o ), V HW-OW is the potential difference between HW and OW, ΔV ohmic is ohmic voltage loss of HW and OW, h o is O 2 electrode overvoltage between OW and OR, F is Faraday constant, R is gas constant, and T is the temperature. The experimental cell was composed of four electrodes, as shown in Figure 1a and Figure 2: HW, HR, OW and OR on the electrolyte. The ohmic-free E a at TPB (site 3 in Figure 2) was determined by measuring the potential difference between OR (site 1) and HW (site 2) by the current interruption method. The a O was calculated from the electrochemical potential (Φ) of the HW TPB as follows. The measured voltage difference between sites 1 and 2 (E), which corresponds to the difference in Φ of electrons (Φ e ) between these two sites ( Figure 2), is described in Eq. (3), where the number in parentheses is the site number.
When the following local equilibrium in oxide ion conductors such as YSZ or ScSZ, can be assumed as Eq. (4), then Φ of e -, O and O 2can be described, as shown in Eqs. (5) and (6).
Because O is a neutral oxygen atom in the oxides and does not have any charge, its potential (Φ O ) is described as Eq. (9).
where F O is the standard electrochemical potential of O in the oxides. Thus, Eq. (8) becomes Eq. (10) When pure O 2 is supplied at the ideal state to the O 2 electrode, a O (1) can be considered as 1.
Here, we assumed a homogeneous a O in the oxide ion conductor of porous cermet H 2 /H 2 O electrode. Thus, a O (3), which corresponds to a O at TPB, is calculated as Eq. (11) and is also described as Eq. (2).

Relationship of a O and i on Different P H2 and P H2O
Figures 3a-3d show the I-V and I-P plots for the fuel cell for different gas mixtures at different P H2 and P H2O . The I-V is plotted both at the FC mode (positive i) and EC mode (nega- tive i), and I-P is plotted at FC mode. In all 12 conditions, i > 1.9 A cm -2 were observed. The maximum power density was depending mainly on P H2 , and achieved 601 mW cm -2 at P H2 = 0.99 and P H2O = 0.01. The maximum power density changed slightly depending on P H2O . Any obvious voltage drops at a high i region caused by concentration overvoltage were not observed in any conditions. The open circuit potential (i = 0) depended on P H2O and quantitatively agreed with the calculated value by assuming thermal equilibrium of reaction Eq. (1). Figure 4 shows i vs. P H2O at the EC region of V OW-HW = 1.3 V and 1.4 V at different P H2 . In this region, i was approximately linear to P H2O 0.60~0.75 and slightly depended on P H2 . The maximum i in the EC mode region was not high compared to that reported in the literature obtained at P H2O > 0.9 A cm -2 [42][43][44], because range of P H2O was 0.01-0.05 in this present study. Figure 5 shows the relationship between log a O (calculated based on ohmic-free E a ) and log ‰i‰ for different gas mixtures at different P H2 and P H2O . In these plots ( Figure 5), the gradients of the slopes correspond to the nominal order of each reaction (guide y = x are shown in each graph). The gradient of the slopes in the FC mode was around 1 and decreased with increasing a O , and that in the EC mode was less than 1 and became more gradual at lower a O . The a O vs. i at each condition qualitatively agreed with previously reported data [16]. The curves at EC mode and the a O(eq) varied depending on both P H2O and P H2 , and the variation in i vs. a O at the FC mode for the three different P H2O decreased at a high a O region (> 10 -8.5 ). The trend in the gradient was reflected by the coverage of each reactant at TPB. For example, the gradient of each slope at low a O in FC mode (i.e., near the equilibrium potential) was steeper than 1, due to partial cathodic current (= EC reaction), and then gradually decreased with increasing a O . This tendency can be qualitatively explained by the increasing coverage of reactant at TPB with increasing a O . Details and quantitative analysis of those slopes are described in the following sections.

Investigation of Models Based on Previous Literature
This work develops a scheme to determine the coverage of the reactants at TPB with a reaction model and a set of SOFC/EC measurement data. To select the reaction model, we investigated previously reported models with considering the existence of the following factors: (i) rate limiting reaction; (ii) assumptions in determining the relationship among the electrode potential, oxygen activity and oxygen coverage are the local equilibrium among oxygen, oxide ion and electron in the electrolyte and the equilibrium between the oxide ion in the electrolyte and the oxygen adsorbent on the surface; (iii) assumption in describing the relationship between the reaction rate and the coverage is competitive adsorption at TPB; and (iv) simplification or approximation of the relationship between the reaction rate and the coverage. The reaction models we investigated as candidates with these factors are shown in Table 2.   [12].
Under these equilibrium conditions, the relationship between electrode potential and a O and that between a O and q O are uniquely determined. The reaction model has been discussed with the reaction order of a O , P H2 , and P H2O to i. Under the above assumptions, the rate limiting reaction was assumed to be the reaction between O ad at TPB and H 2 . Wen et al. discussed the relationship between P H2 /P H2O and i based on the relationship between anode overpotential and a O [13]. For both studies, P H2 and P H2O were low, q V was assumed to bẽ 1, and the competitive adsorption was not discussed [12,13].
On the other hand, the previous literatures including those two studies showed different relationships between P H2 or P H2O and the electrode performance even though measurements were carried out with the common electrode material Ni/YSZ. Thus, Ihara et al. proposed a comprehensive SOFC/ EC reaction model that can account for variation in DC polarization properties and AC impedance properties under different P H2 and P H2O [16]. The model described the reaction as a Langmuir-type kinetics equation with competitive adsorption on TPB under local equilibrium in the electrolyte and under equilibrium between oxide ion and O ad . That equation can be separated into two parts. One part is composed of the coverage ratio represented by adsorption equilibrium constants, which are independent of the geometric structure of the electrode and dependent only on the physical properties of Ni-YSZ. The other part is the kinetics constant, which depends on both the physical properties and geometric structure, such as porous structure or TPB length. The variation in reaction order of a O , P H2 and P O2 to i represents the values of the coverage ratio of chemical reactants vs. q V , and thus q at different conditions can be directly quantified.
Bieberle et al. established a scheme to simulate the reaction on a Ni/YSZ electrode based on six reversible reactions, as summarized in Section 1 (i.e., charge transfer  [17]. In contrast to refs. [12,13,16], in this scheme, the ratio O O x / V O .. was assumed to be constant, and thus independent of the anode potential. The mass balance equations of the adsorbents on TPB were described and the steady state coverages q O , q H , q OH , and q H2O were numerically calculated. The kinetics constant of the six reversible reactions were fitted to the AC impedance data [18] for different P H2 and P H2O , and the results suggested that the rate limiting step is the charge transfer reaction between the oxide ion and the surface oxygen adsorbents. In this model, the local equilibrium of oxygen in the electrolyte, oxide ion and electron was not assumed and the ratio of oxygen vacancy in the electrolyte was constant, independent of the anode potential, and thus the coverage of each reactant did not depend on the potential of the electrode. Also, the competitive adsorption to occupy the limited number of active sites was not investigated. Because the rate limiting step was suggested to be the charge transfer between the oxide ion and the surface oxygen, the coverage of each reactant was determined by the equilibrium of the reversible reaction in the model. Zhu et al. proposed a reaction model with the sequential charge transfer pathway, as shown in Eqs. (15) and (16), assuming the rate limiting reaction, as Eq. (16) [19,20] The model was developed under the following equilibrium assumptions: (i) equilibrium of the dissociative adsorption, (ii) equilibrium of H ad on Ni, (iii) adsorption equilibrium of H 2 O ad on YSZ, (iv) equilibrium between the O 2in YSZ bulk and the surface (by this equilibrium, the coverage of O 2ad on YSZ is independent of the electrode potential), and (v) quasiequilibrium of the electrochemical reaction, as shown in Eq. (15). By solving Eqs. (15) and (16) simultaneously with those equilibrium assumptions, the coverages q H,Ni , q V,YSZ , q O2-,YSZ , q OH-,YSZ , and q H2O,YSZ (q V,YSZ + q O2-,YSZ + q OH-,YSZ + q H2O,YSZ = 1) were determined and the relationship between i and the ohmic-free anode potential vs. the potential at the center of the electrolyte (E a ) was described based on the Butler-Volmer type equation, as shown in Eq. (17): where l TPB is the length of TPB, b a and b c are anodic and cathodic symmetric factors (b a + b c = 1), and k a and k c are anodic and cathodic kinetics constants. In this model, whereas the local equilibrium of electrons and the equilibrium between O 2in the electrolyte and O ad on the electrode were not assumed, the coverage of each species can be determined by fitting the model with two parameters, namely, the exchange i (i 0 ) and b, to actual data. In this work, on the other hand, only the relationship between the overpotential and the coverage of OHwas calculated by using the approximated equation under the assumption that q O2-,YSZ @ 1 [19,20]. Bessler et al. developed a reaction model of the SOFC/EC reaction [21] by generalizing the model developed by Bieberle et al. [17]. One reaction path or a series of two reaction paths was assumed and i was described as the difference between the rate of oxidation and reduction reactions, and each reaction rate was described by q a νa q b νb q c νc K where νx is the reaction order vs. q x . Then, the mass balance equations were described, based on all of the rate process including mass transfer, adsorption/desorption, reaction and/or charge transfer. The set of q i values for steady state were numerically calculated, and the framework to simulate the relationship between i and the overpotential was proposed. By those methods, the multiple possible reaction pathways have been simultaneously investigated by Volger et al. [22] by substituting the following parameters of all of the processes without the charge transfer reaction, namely, the equilibrium constant of H 2 , H 2 O adsorption/desorption on Ni or YSZ [31][32][33][34], and the rate constant of the surface chemical reaction on Ni [31,32] along with their temperature dependence from literature, the appropriate reaction path was suggested to be the reaction shown in Eqs. (15) and (16), and one of these two reactions was suggested as the rate determining step. In this method, because all of the rate constants are determined by fitting the rate of charge transfer reaction from reported data, the steady state coverage including the vacancy and the exponent of coverages corresponding to the kinetics order can be calculated. However, the accuracy of the values strongly depends on the equilibrium constants and rate constants obtained from literature. On the other hand, the electrode materials and/or the temperatures obtained from literature are not always the same as those in actual SOFC operations. For example, whereas most of the equilibrium constants and rate constants were obtained from the surface reaction and the adsorption/desorption equilibrium on Ni from calculated values of the heat of adsorption or the activation energy of the reaction on the metal surface including Ni (111) surface [45,46], other constant values were obtained by using the extrapolated value from the temperature programmed desorption below 200°C [47], or using the experimental value for that on a rhodium (111) surface [45]. The constant value for the adsorption/desorption and the reaction on YSZ were obtained from the respective value at a temperature below 700°C at which the YSZ surface was mostly covered by OH [34]. Thus, quantifying the coverage at TPB by using the model [21,22] involved using both a set of appropriate values of the rate and/or equilibrium constants obtained under conditions similar to an actual SOFC/EC reaction and a series of electrochemical measurement data under a wide range of conditions. Also, the model did not assume competitive adsorption, local equilibrium of oxygen, oxide ion and electron in the electrolyte, nor equilibrium of the oxide ion and the oxygen adsorbents, and thus the coverages of the reactants are determined independently by the electrode potential in the model.
Thus, this present work applies the electrochemical model to a H 2 /H 2 O electrode where the coverages of the reactants changes depending on the electrode potential assuming local equilibrium of oxygen, oxide ion and electron in the electrolyte and assuming equilibrium of the oxide ion and oxygen adsorbents [12,13,16]. Due to the competitive adsorption reaction, which is the general kinetics model in the thermochemical reaction, these assumptions are appropriate in the electrochemical model [16,19]. Also, because the model by Ihara et al. [16] was developed with bottom-up with the elementary reactions without approximation of the equations, we decided to apply the model based on the model in ref. [16] into the scheme to determine the coverage of the reactants at TPB. The dependence of q x /q V on a O , P H2 and P H2O becomes a component of the denominator in the Langmuir-type rate equation, and the value of q x /q V appears as the reaction order of i vs. a O , P H2 and P H2O . Conversely, based on the reaction order of i vs. a O , P H2 and P H2O obtained in a wide range of experimental conditions, the value of q x under such wide-ranging conditions can be determined. Thus, in this work, by applying the appropriate experimental data and using the method to optimize the multiple constants that are related to each other, the model can be used to determine the coverage q x , which is independent of the geometric structure of the electrodes. In addition, in the model in ref [16], whereas the rate limiting reaction was assumed to be the three-atom reaction of two  [13]. Therefore, the surface chemical reaction in the model which we applied was modified as the consecutive reaction from O ad and H ad to OH ad and H ad , which have been described as the simultaneous reaction of O ad and 2H ad in [16].

Construction of the Model
Our kinetics model of the SOFC anode at TPB is composed of the Langmuir-type reaction model under competitive adsorption and equilibrium of charge transfer. The two candidates for the rate-determining reaction of the power generation, namely, reaction between H and O or between H and OH adsorbing on Ni near TPB can be represented, as in Eqs. (18) and (19) where k a1 , k a2 and k c1 k c2 are rate constants of anodic and cathodic reactions, and V ad is the density of vacant sites for adsorption at TPB. The total current density (i) is expressed with anodic and cathodic current (i a and i c ), as shown in Eqs. (20) or (21) where q H , q O , q H2O , q OH , and q V , respectively, represent the coverage ratio of H ad , O ad , H 2 O ad , OH ad , and V ad on the absorption site. In both cases (Eqs. (18) and (19)), H 2 O and H 2 are the respective competitive adsorption equilibrium states between the gas phase and Ni surface, as shown in Eqs. (22) and (23) is assumed to be the combined equilibrium of reactions, as shown in Eqs. (25) to (27).
Thus, q H , q O , and q H2O were obtained using the equilibrium assumptions, as shown in Eqs. (29) to (34).
Here, q OH depends on which reaction (Eq. (18) or (19)) is the rate-determining reaction. We assumed one of them as a quasi-equilibrium due to their fast reaction rate, while the other one as the rate-determining reaction: Under this equilibrium case Eq. (36) is Thus, q OH , and q V are obtained using Eqs. (30) and (32) as Eqs. (37) and (38).
Based on Eq. (39), the range of the nominal reaction order of a O , P H2 and P H2O to i can be represented as follows, depending on the variation in magnitude between the terms in the dominator of Eq. (39).
Under a fully polarized anodic condition, i can be assumed to be i a if q OH /q V is relatively lower than 1, which means q OH is much lower than q V, and thus i of the power generation based on Eq. (39) can be approximated as The range of the nominal reaction orders of a O , P H2 , P H2O to i can be considered as follows. For example, if q O /q V = K O a O is relatively much larger than 1 þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi K H P H2 p þ K H2O P H2O , Eq. (40) becomes and if q O /q V is much smaller than 1, Eq. (40) becomes Finally, the range of the nominal reaction orders of a O , P H2 , P H2O to i a are included in Eq. (43).
On the other hand, if q OH /q V is relatively much higher than 1 þ K O a O þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi K H P H2 p þ K H2O P H2O , Eq. (39) can be approxi-mated as Eq. (44) and the nominal reaction order can be represented as following Eq. (45).
Under a fully polarized anodic condition, i can be assumed to be i a if q OH /q V is relatively lower than 1, which means q OH is much lower than q V, and thus i of the power generation based on Eq. (50) can be approximated as Eq. (51) and if q O /q V is smaller than 1, Eq. (51) becomes On the other hand, if q OH /q V is relatively larger than þ K H2O P H2O , then Eq. (50) can be approximated as Eq. (54) and the nominal reaction order can be represented as follows.
Finally, the range of the nominal reaction orders of a O , P H2 , P H2O to i a are included in the range as follows: Thus, the rate determining reaction at TPB can be assumed to be the nominal reaction orders of a O , P H2 , P H2O to i at the fully polarized anodic region as i = i a . As shown in Figure 5 (a-d), regardless of P H2 and P H2O , the reaction order of a O to i a was around 1, which allows both Cases 1 and 2. As for P H2 and P H2O , Figure 6 shows i vs. P H2O (a-d) and i vs. P H2 (e-h) with a double logarithm axis under the fully polarized anodic region, -8.3 < log a O < -8.0, with line guides y = -x (a-d) and y = x (e-h). The gradient of the plots corresponds to the reaction order of P H2O (a-d) or P H2 (e-h) to i a . The reaction order of P H2O to i a was -0.33~0 and depended on a O and P H2 . It was higher at larger a O and/or at smaller P H2 . That of P H2 to i a was around 1 regardless of a O and P H2O . In Case 1, the reaction order of P H2 to i a was -1.5~0.5 at low q OH /q V or 1.5 at high q OH /q V , and thus Case 1 cannot describe the experimental data, where the reaction order of P H2 to i is around 1 regardless of a O and P H2O . In Case 2, on the other hand, the reaction order of P H2 to i was 1, when q H /q V and q OH /q V were relatively low, and thus Case 2 can describe the experimental data with the appropriate set of K O , K H , K H2O , and K OH . Thus, Case 2 with the kinetics Eq. (50) is valid for SOFC reaction. Although the rate determining step of the anode reaction has been extensively discussed, the process of hydrogen oxidation reaction is a common step. For example, Wen et al. assumed the rate of H 2 O ad generation from H ad and OH ad is the key to decrease the anode overpotential [13], and Zhu et al. assumed the rate determining step as the reaction of H Ni + OH -YSZ [19,20]. In the following discussion, for convenience, k a2 , k c2 , and, respectively. K OH1 in Eq. (50) are denoted as k a , k c , and K OH .
Thus, the reaction model of the present work is described as Eq.  1 (b, f), -8.2 (c, g), and -8.3 (d, h). P H2 , P H2O , and a O as shown in then denominator in Eq. (50), then the values of q x /q V reflects the reaction order of x to i. Thus, by preparing a sufficient number and wide range of experimental data of i vs. a O at both SOFC region with higher a O than a O at equilibrium (a O(eq) ) and EC regions with lower a O than a O(eq) under different P H2 and P H2O , the values of q x /q V under the different a O , P H2 , and P H2O can be determined. Also, because the relationship between i and each K x is not independent from each other, particularly, q OH /q V is described with the combination of multiple variables as K OH-K O a O (K H P H2 ) 1/2 , an appropriate method to optimize the multiple parameters is required. By optimizing the values of equilibrium constant by those experimental data and optimization algorism, Eqs. (29), (31), (33), and (47), q H , q H2O , q O , and q OH on the active site of TPB can be determined.

Balance of Kinetics Constant Between FC and EC
First, a O(eq) in which there is no current in either the EC or FC direction, can be set in the model as shown in Eq. (56): In this case, according to Eq. (50), it becomes as shown in Eq. (57).
Then, k c / k a is described in terms of other variables and k c becomes a dependent variable as Eq. (58): /P H2O is a constant value of 10 -8.153 at 900°C, because the H 2 /H 2 O electrode reaches the thermal equilibrium of reaction Eq. (1), and the P O2 at the H 2 /H 2 O electrode is exp(4FE a(eq) /RT) when P O2 at the O 2 electrode is 1. Thus, P H2 a O(eq) /P H2O also becomes constant at 7 10 -9 for any P H2 /P H2O , and finally k c /k a can be described as a constant value, and K H , K OH , K O , K H2O and k c become dependent variables in Eq. (50).
As a result, i can be described based on Eq. (50) as Eq. (59) by using a O(eq) , which can be calculated by the equilibrium of H 2 /H 2 O/O 2 under P H2 and P H2O , and be confirmed experimentally by OCV.
Thus, the remaining independent variables are k a , K H , K O , K H2O , and K OH .

Genetic Algorithm to Determine the Kinetics Constant and Equilibrium Constants
The next step is to determine the kinetics constant k a and the equilibrium constants K O , K H , K H2O , and K OH by data fitting of the power generation data for SOFC/EC. The supervised machine learning approach with the experimental data as the learning data and the genetic algorism as an optimization method was developed. The real-coded genetic algorithm was applied to determine the optimal values of these five parameters of the model equation Eq. (59) for the power generation data. Figure 7 shows the flowchart of the analysis method using the genetic algorithm. It is a repetitive process of the following overall steps: (i) generate the first population of multiple individuals which are candidates for the parameter set (individual is defined here as the set of five parameters) [38,39]; (ii) generate the next population composed of the same number of individuals as the first population by using three operations, namely, selection, crossover, and mutation [38,39]; (iii) evaluate each new individual based on a quantitative index, such as the mean squared error (MSE). First, we prepared 200 individuals, where each had a set of five random numbers with the ranges of -500 < log k a or log K x < 500 as the process of (1) in Figure 7. To generate a new population, the tournament selection method, which is a common selection method, was applied to obtain 30 individuals [39] by selecting two candidates randomly from the previous generation and then choosing the individual with the lower MSE, as shown in Figures 7 (2) and 7 (3). In the two-point crossover method used here, one of the parameters (except K H2O as explained in the next paragraph) is exchanged between the randomly selected 2 individuals from the 30 individuals selected by the tournament selection method [39]. Thus, 30 new individuals were created by conducting such crossover for each of the four other parameters, thus generating a total of 120 individuals, as shown in Figure 7 (4). In the mutation method, after picking one individual selected by the tournament selection method, one of the five parameters in that individual was randomly changed. In our work, 10 individuals were randomly picked to apply mutation for each of the five parameters, thus generating a total of 50 individuals, as shown in Figure 7 (5). Next, a new generation population of 200 individuals was created (whose number was the same as that in the previous generation population) by merging the 30 new individuals from the selection, the 120 from crossover, and the 50 from mutation, as shown in Figure 7 (6).
In the genetic algorithm, the balance between the calculation cost, i.e., computational complexity, and the probability to achieve the global optimal solution can be controlled by adjusting the number of individuals in the crossover and mutation operations in generating the next-generation candidates from the previous generation [39]. In preliminary analysis operation, we initially used 500 individuals per population, including the crossover of every parameter including K H2O , and performed 100 iterations of the entire process. As a result, K H2O was determined as an unique value in the early iterations, and thus crossover operation on K H2O did not work efficiently. Consequently, to reduce the calculation time in the formal analysis operation, the number of individuals was reduced to 200, and only mutation was applied to K H2O . The process was repeated by creating a new generation via selection, crossover, and mutation until the MSEs of all 30 individuals from the selection operation converged to almost the same value. As a result, 80 was set as the final number of generations because the values converged in about 80 iterations, as shown in Figure 7 (7). The solution obtained by the genetic algorithm was used as the initial solution, and the optimal solution was converged by using the gradient descent method, as shown in Figure 7 (8). Considering the possibility that the obtained optimal solution is a local optimal solution, the global optimal solution was searched by repeating the following process more than 50,000 times using the simulation tool MATLAB/ SIMULINK, as shown in Figure 7 (9). The MSE was used as an index for determining the goodness of fit, and is the error function expressed as in Eq. (60)

ORIGINAL RESEARCH PAPER
where i exp is the experimental value of i, and i calc is the value calculated by using our kinetics model Eq. (60) (in this work, N = 348 is the total number of data points of SOFC operation under 12 conditions). As a result, the optimal solution with the smallest MSE (0.06345) was observed as the global optimal solution among the obtained optimal solutions. In this analysis, 2,272 sets of global optimal solution combinations were detected in more than 50,000 optimal solutions. Figure 8 shows the 2,272 sets of optimal solution candidates of K OH (a), K H (b), K O (c), K H2O (d), and k a (e) obtained by the fitting method using the genetic algorithm. The horizontal axis shows the data number when K OH is arranged in ascending order, and the vertical axis shows the exponent of each parameter. Here, log K H2O was 0.5044 for all the parameter sets. In contrast, as K OH increased, the range of k a , K H2 , and K O broadened. Nine representative examples of these optimal solution candidates are plotted as different colored circles in Figure 8, and summarized in Table 3 , and P H2 (a O -a O(eq) ), was also detemined to be a constant value. Finally, all terms of Eq. (59) under the different a O , P H2O , and P H were determined as a unique values.
A sensitivity analysis was carried out for K O , K H , K H2O , and K OH to confirm that the obtained solutions are globally optimal solutions. Each reaction and equilibrium constant was fixed, and optimization was performed using the other four parameters. Figure 9 shows the sensitivity analysis results. K H2O has the unique value that MSE was minimum when log K H2O was 0.5044 as shown in Figure 9b. The minimum MSE was observed when log K H < -9 (Figure 9a), log K O < 5 (Figure 9c), and log K OH > 8 (Figure 9d). The values of the parameters in Table 3 and Figure 8 are in this range. In the Supporting Information, figure S1 shows additional sets of K x values, focusing on K H (red circles), K O (black), and K OH (green). For example, the red circles in Figures S1b-S1d show the values of log K H2O , log K O , and log K OH when optimized by fixing log K H = -100 ( Figure  S1a). The circles and triangles show the parameter values when the MSE was the minimum and the squares show when the MSE was the local optimal solution. The circles and triangles were in the range of log K H < -9, log K O <5, and log K OH > 8 for all parameters, and log K H2O converged at 0.5044. In contrast, the squares reveal that none of the parameters reached the global optimal solution. Therefore, the solution obtained in our analysis is a global optimum solution. When log K O > 12, log K H > 8, and log K OH < 2, MSE had a constant value and the parameters had converged on local minimum.

Evaluation of Coverage at TPB by the Kinetics Model
Based on the results shown in Section 3.3, the relationship between the coverage of each adsorbent on the active site of TPB (q H , q O , q H2O , q OH and q V ) and a O at different P H2 and P H2O were evaluated, as shown in Figures 10a-10c. The coverage curves were fitted by using the parameter set of the nine representative examples of the optimal solution candidate in Table 3 and superimposed on each plot (Figures 10a-10c). When all the parameter sets in Figure 8 were superimposed on each plot, the curves for q H2O , q OH , and q V were all the same in every conditions. In contrast, q H and q O show different curves depending on the multiple optimized parameter set, but had negligibly small values even in high a O and P H2 . , and k a (e) obtained by the fitting method using the genetic algorithm; horizontal axis shows the data number when K OH is arranged in ascending order, and the vertical axis shows the exponent of each parameter; the representative optimal solutions (No. 1-9) listed in Table 3 are plotted. Table 3 Parameter sets of representative examples of these optimal solution groups in Figure 8. All of the 2,272 parameter sets show the same result, namely, q H2O , q OH , and q V had the same curves, and q H and q O had small values. Therefore, the coverages were uniquely determined for any combination despite the existence of many optimal parameters. Finally, by applying Eq. (61), i can be approximated as follows: The constant values of K H2O = 3.194, K OH K O K H 1/2 = 1.146 10 7 and k a K H 1/2 = 12.27 were determined by our experimental data in this work. In the range of 10 -9 < a O < 10 -7 , the range of each coverage was 0.94 > q V > 0.35, 0.15 > q H2O > 0.049, 0.022 < q OH < 0.57, q H < 10 -6 and q O < 10 -4 . The coverage q OH depended on a O and P H2 but not on P H2O , and was negligibly small at a O <10 -9 and relatively high at a O > 10 -8 . The coverage q H2O depended on both the feedstock P H2O condition and a O . It increased with increasing a O because H 2 O is the reaction product of fuel cells, and P H2O increases with increasing i and then q H2O decreases with further increasing a O , due to the increase in q OH and the decrease in q V . Figure S2 (a-c) shows the relationship between i and q x and Figure S3 (a-c) shows the relationship between i and q x /q V (see Supporting Information). Whereas q OH and q H2O depended on i, both P H2 and P H2O and their variation correspond to the variation in q V , and q H2O /q V was independent of P H2O and linearly increased with increasing i. This trend suggests that q H2O /q V simply depends on P H2O at the H 2 /H 2 O electrode, where H 2 O comes both from the feedstock and from the power generation reaction. Both q H and q O were negligibly small, regardless of a O , P H2 , and P H2O . Thus, in FC mode, q V is governed mainly by q OH and q H2O . In our previous study [16], the nominal reaction order against P H2 at higher P H2 was less than 1, which seems to differ compared to this present work. The difference might be due to the increase in q OH /q V and q H2O /q V at high a O and high i region, because the higher i at higher P H2 causes an increase in both q OH /q V and q H2O /q V , as shown in Eq.  [19,31,32], and thus the coverages of many of the reactants are independent of the electrode potential. On the other hand, our scheme determines the coverages from the relationship between i and a O in our data, which is a relationship based on the competitive adsorption equilibrium and can be used to estimate the coverages that depends on a O . In the present work, even though multiple sets of K O , K H , K H2O , and K OH were obtained as the optimum by our genetic algorithm and did not be determined as one set, the set of coverages were uniquely determined values by the set of experimental data without any assumptions or preset parameters. While each term in the denominator of Eq. (50) corresponds to the coverage ratio of each reactant and the value of the coverage ratio determines the reaction order, q OH /q V is not a simple term consisting of multiple K. In contrast, q H /q V , q O /q V , and q H2O /q V can be described simply with one K x and one experimental parameter. Thus, in order to determine each K x , a machine learning technique, such as a genetic algorithm, is necessary to obtain the global optimum set of multiple parameters. Also required for determination of q is a sufficient set of experimental i vs. a O data including a O(eq) under various P H2 and P H2O . By applying the optimization algorithm and the experimental data set to the reaction model, the intrinsic properties of the electrode material, i.e.,  coverages of reactants, were quantified independently from the effect of the geometric structure of the electrode. Based on our results with the optimization algorithm and the experimental data, in the reversible SOFC/ EC reaction at 900°C, TPB is almost vacant but also partially covered with H 2 O in P H2O = 0.01-0.05. Also, at FC reaction with a high i, a large amount of OH was covered with the TPB, but not fully. These properties will be suitable as a reaction field of an FC, because the coverage of TPB is kept sufficiently low. On the other hand, it is not clear that the TPB with Ni/YSZ is suitable for water electrolysis with a high P H2O , because too high coverage of H 2 O can inhibit the electrolysis reaction. Further study at a high P H2O is required to evaluate the effect of q H2O . Also, by applying our scheme to determine the coverage of reactant, as shown in Section 3.3, to different electrode materials, porous electrode structures and/or reactant species, the material properties can be directly evaluated. This will promote development of SOFC/ECs. Thus, applying the kinetics model with the optimization by applying the genetic algorithm to the series of data with a sufficient range of gas conditions will be an efficient method to evaluate material properties by using TPB coverages. Figure 11 shows superimposed log a O vs. log i curves fitted by using the nine representative parameter sets of the optimal solution candidate in Table 3, and also shows measured data at both EC and FC regions. Similar to the coverage, every k a and K x set represented exactly the same curves. Also, the curves in all four different P H2 three different P H2O prepared by one set of k a and K x approximately fitted the experimental data at each condition. These results suggest that the kinetics which is governed by the coverage of each adsorbent can be described by Eq. (61) with the constant values of K H2O , K OH- The model curves at 0.99 P H2 , at 0.01 P H2O , and at 0.97 P H2O , 0.03 P H2O were lower than the experimental data, possibly due to the effect of initial degradation of the cell. Figure 12 shows the I-V and I-P curves, both of which are the same, as shown in Figure 3, but with fitting curves showing the calculated i vs. V or P as Eq. (61). At the FC region, most of the fitting curves, especially at P H2 = 0.80 (b) and 0.50 (c) at any P H2O , approximately fit to the experimental data. There are some small gaps between the experimental data and the fitting curves at P H of 0.99-0.97 ( Figure 12a) and wide gaps at i >1.2 A cm -2 at P H2 of 0.3 (d). One reason for the wide gaps in the high i region is that MSE as the evaluation index (Eq. (60)) was based on the relationship between log i exp and log i calc . Compared using the linear scale i as an evaluation index, the effect of larger i region on the MSE became smaller, thus resulted in the error in the high i region becoming larger to obtain a smaller MSE.

Fitting Results of Reversible FC/EC Reaction
Thus, by obtaining a series of i vs. a O data that includes the equilibrium potential under different P H2 and P H2O in one cell and applying the optimization method with the genetic algorithm, the relationship between a O and the chemical state of the reactants at TPB, i.e., coverage of reactants at TPB in FC region, can be quantified based on the reaction model. Also, these results suggest that in the EC region with small a O < 10 -9 the active site of TPB will be almost vacant with a small amount of H 2 O ad , whereas it is partially covered with OH ad and H 2 O ad at FC region with large a O > 10 -8 .  Table 3 are superimposed.
On the other hand, the model could not determine the relationship between the i and a O at the EC region with a O < 10 -10 . The maximum measured i at the EC region was 3-6 times larger than that determined by the model at any P H2O and P H2 . The tendencies were observed both in Figures 11 and 12. At lower a O , the difference between experimental and calculated i increases. Assuming that the balance between i a and i c is fixed by a O(eq) in the model and that i reaches its maximum value, i c(max) at the minimum a O~0 as Eq. (62): In the experimental data as shown in Figure 11, on the other hand, i continuously increased with decreasing log a O .

Possible Modification of Electrolysis Reaction Kinetics
From Eq. (50), i in the EC region is almost independent of a O because a O is relatively small, but the experimental data shows dependence of i on a O . To describe the relationship between i and a O in the EC region, another variable that depends on a O is required. Even if the kinetics of electrolysis in Eq. (21) is changed in the model, the equilibrium a O(eq) limits the balance between i a and i c . So we reinvestigated the equilibrium of the comprehensive adsorption shown in Eqs. (22) to (24), particularly between a O and O ad as shown in Eqs. (25) to (27). We assumed the equilibrium of electron activity on Ni and YSZ to be variable (i.e., dependent on a O ) and set the electron activity ratio, a e-YSZ /a e-Ni , as another variable. Figure 13 shows schematics of the reaction kinetics and the equilibrium on Ni around TPB in the original model ( Figure 13a) and this modified model (Figure 13b) (64): where K e is the new equilibrium constant between a e-YSZ and a e-Ni . Thus, i is described as in Eqs. (65) and (66):   By this modified equation with this additional independent variable a e-YSZ /a e-Ni , i = f(a O ) changes as follows. In the power generation region (e.g., a O > 10 -9 ), a e-YSZ /a e-Ni is fixed at 1 and i in Eqs. (50) and (66) become the same value. In the EC region (e.g., a O < 10 -9 ), a e-YSZ /a e-Ni increases when a O decreases, and i also increases although it reaches a constant value in the original model described in Eq. (50). Figure 14a shows i vs. a O with the curves calculated using the modified model and shows the experimental data at P H2 = 0.80. Fig. 14(b) shows q H2O , q OH , and q V dependence on log a O calculated by the original model and by the modified kinetics model at P H2 = 0.80 and P H2O = 0.03. Significant difference appeared in q OH ; whereas it linearly decreased with decreasing a O in the original model, the gradient became smaller in the electrolysis region in the new model. The a e-on metal is 1, so the electron activity on YSZ increases due to the static charge balance of YSZ near TPB and changes due to the negative voltage. When a e-YSZ /a e-Ni > 1, the equilibrium constant between O(YSZ) and O ad , as shown in Eq. (24) increases and O ad increases at the same a O . Also, the coverage of OH ad increases by the equilibrium Eq. (46). Thus, the O 2flux can increase and finally the cathodic current can increase. As a result, the negative charge of YSZ near TPB by applying voltage causes a shift in the equilibrium between O(YSZ), O ad and OH ad , and thus enhances the flux of O 2at the electrolysis region. Similar phenomena have been discussed as ''electrochemical promotion of catalyst (EPOC)'' or ''non-faradic electrochemical modification of catalytic activity (NEMCA)'' effect which occurs on the metal catalysts on the ion conductive oxide support to enhance a catalytic activity of non-faradaic reaction by electrochemically modifying the surface ad/desorption equilibrium [48][49][50]. However, further investigation is needed to confirm our modified EC electrochemical model based on the shift in a e-YSZ /a e-Ni . To develop a method to quantify the relationship among O ad , OH ad , a O and a e-YSZ /a e-Ni in different materials, electrode structures, or temperature, unifying the kinetics model of electrolysis and power generation will be key to establish the methodology to predict the performance of SOECs from that of SOFCs.

Conclusions
This study developed a method to quantify the coverage of chemical reactants at TPB by electrochemical measurement to establish a scheme to evaluate electrode materials and structures of SOFC/ECs. In this work, to determine the coverages, (i) a kinetics model based on comprehensive adsorption reaction on a H 2 /H 2 O electrode under the local equilibrium of O 2-, O and ein the electrolyte and under the equilibrium between O 2in YSZ and O ad on TPB was applied, (ii) multiple variables including k a and K H , K O , K H2O , K OH by machine learning process using a genetic algorithm as the optimization method was developed, and (iii) experimental i vs. a O data was obtained for a reversible SOFC/EC using an electrolyte support cell with YSZ electrolyte and Ni/YSZ H 2 /H 2 O electrode in H 2 /H 2 O/Ar mixture gas. By determining K x and k a , the material properties and the effect of the porous structure of an electrode can be independently discussed. By applying the genetic algorithm, the fitting curve and coverage were uniquely determined for any set of k a and K H , K O , K H2O , K OH although numerous optimal parameters were confirmed in the fitting results. As a result, under SOFC conditions, q H and q O were relatively low, and q OH was low at oxygen activity (a O ) < 10 -9 and high at a O > 10 -8 . When 10 -9 < a O < 10 -7 , each coverage was 0.94 > q V > 0.35, 0.15 > q H2O > 0.049, 0.022 < q OH < 0.57, q H < 10 -6 and q O < 10 -4 . Finally, one set of K x and k a approximately described the i vs. a O curves at all of four

ORIGINAL RESEARCH PAPER
FUEL CELLS 20, 2020, No. 6, 661-681 2020 The Authors. Fuel Cells published by Wiley-VCH GmbH P H2 three P H2O conditions at SOFC regions. Those result suggests that the active site at TPB under SOFC power generating condition at 900°C is partially covered with H 2 O or OH. As for the SOEC, on the other hand, the data showed over 4 times larger i at the electrolysis region compared to that based on our original kinetics model. Therefore, we proposed the modified EC electrochemical model by reconsidering the equilibrium of electrons between YSZ and Ni. In the modified model, another independent variable of the electron activity ratio (a e-YSZ /a e-Ni ) was applied as a comprehensive electrochemical reaction model of reversible SOFC/ECs. Although further investigation is needed to confirm our modified EC electrochemical model, the results revealed that the increase in cathodic current came from the increased OH coverage (q OH ) due to the shift in local charge balance caused by the increase in a e-YSZ .

Acknowledgements
Part of this work was supported by JST-Mirai Program Grant Number JP18077648, Japan. Coverage of x on the surface of y at TPB / -

Data Availibility Statement
The data that supports the findings of this study are available in the supplementary material of this article.