Reverse Water Gas Shift versus Carbon Dioxide Electro-Reduction: The Reaction Pathway Responsible for Carbon Monoxide Production in Solid Oxide Co-Electrolysis Cells

Abstract

Solid oxide co-electrolysis cells can utilize renewable energy sources for the conversion of steam and carbon dioxide into valuable chemicals and feedstocks. An important challenge in the analysis of these devices is understanding the reaction pathway(s) that govern carbon monoxide generation. Studies in which co-electrolysis polarization lies between those of pure steam and pure carbon dioxide electrolysis suggest that carbon dioxide electro-reduction (CO₂ER) and the reverse water gas shift (RWGS) reaction are both contributors to CO generation. However, experiments in which co-electrolysis polarization overlaps that of pure steam electrolysis propose that the RWGS reaction dominates CO production and CO₂ER is negligible. Supported by dimensional analysis, thermodynamics, and reaction kinetics, this work elucidates the reasons for which the latter conclusion is infeasible, and provides evidence for why the observed overlap between co-electrolysis and pure steam electrolysis is a result of the slow kinetics of CO₂ER in comparison to that of steam, with the RWGS reaction being inconsequential. For sufficiently thin cathode current collectors, we reveal that CO₂ER is dominant over the RWGS reaction, while the rate of steam electro-reduction is much higher than that of carbon dioxide, which causes the co-electrolysis and pure steam electrolysis polarization curves to overlap. This is contrary to what has been proposed in previous experimental analyses. Ultimately, this work provides insight into how to design solid oxide co-electrolysis cells such that they can exploit a desired reaction pathway in order to improve their efficiency and product selectivity.

1. Introduction

Solid oxide co-electrolysis cells (SOco-ECs) are a promising technology with the capacity to convert CO₂ and steam into syngas (a mixture of H₂ and CO) using renewable and intermittent sources of energy [1,2,3]. The produced syngas can be delivered to Fischer-Tropsch reactors to generate liquid synthetic fuel and polymers [4,5], which can therefore alleviate society’s dependence on fossil fuels and conventional means of manufacturing plastics [6]. A comprehensive overview of the background, application, and importance of SOco-ECs can be found in Refs. [7,8]. One of the key challenges in the analysis and understanding of SOco-ECs is determining the reaction pathway(s) responsible for CO production [7]. Researchers in previous electrochemical analyses have observed different contributions of the reverse water gas shift (RWGS) reaction:

$$\begin{array}{c}\hfill {\mathrm{CO}}_2+{\mathrm{H}}_2\leftrightarrow \mathrm{CO}+{\mathrm{H}}_2\mathrm{O}\end{array}$$

(1)

and carbon dioxide electro-reduction (CO₂ER):

$$\begin{array}{c}\hfill {\mathrm{CO}}_2+2{\mathrm{e}}^{-}\to \mathrm{CO}+{\mathrm{O}}^{2-}\end{array}$$

(2)

alongside steam electro-reduction (H₂OER) to generate hydrogen:

$$\begin{array}{c}\hfill {\mathrm{H}}_2\mathrm{O}+2{\mathrm{e}}^{-}\to {\mathrm{H}}_2+{\mathrm{O}}^{2-}\end{array}$$

(3)

resulting in conflicting arguments in terms of the co-electrolysis reaction pathways [7]. Some researchers have suggested that CO generation is largely attributed to the RWGS reaction [9,10], since the polarization curves of pure steam electrolysis and co-electrolysis overlap each other. Therefore, they surmised that CO₂ER is inconsequential to CO production. Conversely, other studies have shown that the polarization curves corresponding to co-electrolysis lie between those of pure steam and pure carbon dioxide electrolysis [11,12,13], thus indicating the RWGS reaction and CO₂ER are both contributors [14,15]. Both hypotheses may be plausible, and their different findings could be a result of experiments having been performed in different transport regimes (i.e., diffusion limited versus reaction limited). It is important to develop an understanding of the reaction pathways that govern the generation of CO, since they have a significant impact on the energy demands to perform CO₂ER and H₂OER.

Numerical models of SOco-ECs have been developed to make sense of the results discussed above, but have also yielded varying conclusions. Researchers have determined that CO₂ER is the predominant mechanism for CO generation [16], while others have concluded the RWGS reaction is the dominant pathway [17]. Additionally, Luo et al. [18] and Ni [19] revealed the RWGS reaction can play a significant role, but can transition to consuming carbon monoxide, depending on the operating temperature, inlet gas composition, and flow velocity. Luo et al. conducted additional numerical analyses to investigate how the microstructural properties [20] and thickness [21] of the cathode affect the contribution of electrochemical and heterogeneous chemical reactions. The study revealed that using a cathode with a thickness of 700 μm leads to a contribution from both CO₂ER and the RWGS reaction, while, on the other hand, they suggested that employing a cathode with a thickness of ∼30 μm results in CO production through only the RWGS reaction. The latter conclusion was based on the observation that the polarization curves of co-electrolysis and pure steam electrolysis overlap with each other. This latter explanation is counter-intuitive, however, since reducing the thickness of the cathode current collector decreases the amount of catalyst available to facilitate the RWGS reaction. Hence, we believe that reducing the thickness of the cathode current collector makes the RWGS reaction negligible and promotes CO₂ER, therefore causing the polarization curves of co-electrolysis and pure steam electrolysis to overlap each other.

In this work, we develop a physics-based approach to untangle the different behaviour of SOco-ECs reported in previous experiments. A dimensional analysis of the reaction rates corresponding to CO production is initially undertaken to reveal how the contribution of the RWGS reaction and CO₂ER scale with the thickness of the cathode current collector, and we further demonstrate the thickness at which the RWGS reaction is negligible. We then apply the first and second laws of thermodynamics to illustrate the conditions required for the polarization curves of co-electrolysis and pure steam electrolysis to overlap each other. This is followed by a comparison of the kinetics of CO₂ER and H₂OER using Butler-Volmer kinetics. This analysis is intended to provide an enhanced understanding of the behaviour of SOco-ECs, and can help designers make informed decisions on how to construct a cell to exploit a desired reaction pathway in order to reduce the electrical work input.

2. Theoretical Formulation and Experimental Comparison

The current approach is based on the SOco-EC illustrated in Figure 1, which is valid for planar, radial, and tubular systems, wherein steam, carbon dioxide, hydrogen, and carbon monoxide are supplied to the cathode channel with inlet molar flow rates $J_i^{c,in}$. Steam and carbon dioxide are subsequently transported through the cathode current collector, towards the triple phase boundary, at which point they are electrochemically reduced to generate hydrogen and carbon monoxide, according to reactions (1) and (2) in Figure 1. Since steam, carbon dioxide, hydrogen, and carbon monoxide co-exist in the Ni-YSZ cathode current collector, the RWGS reaction can also occur (reaction (3) in Figure 1), while it is assumed in this analysis that the influence of other possible reactions is negligible. Furthermore, we make the assumption that electrochemical reactions take place at the interface between the electrolyte and cathode current collector [22,23,24,25], and we assume that both electrochemical and chemical kinetics occur within a single, rate-determining step. However, when examining a specific cell, it may become necessary to consider the distribution of electrochemical reactions within the active catalyst layers. It is crucial to ensure that these layers are sufficiently thin so that treating the triple phase boundary as an interface remains valid.

2.1. Carbon Monoxide Reaction Pathways

The two reaction pathways under investigation are the heterogeneous RWGS reaction in the cathode current collector and CO₂ER at the triple phase boundary. The rate of production of carbon monoxide can be determined by evaluating its utilization factor, which is characterized as the difference between the inlet and outlet molar flow rates across the length of a cell divided by the inlet value:

$$\begin{array}{c}\hfill U_{\mathrm{CO}}^c=\frac{J_{\mathrm{CO}}^{c,in}-J_{\mathrm{CO}}^{c,out}}{J_{\mathrm{CO}}^{c,in}}=-\underset{U_{\mathrm{CO},\mathrm{RWGS}}^c}{\underbrace{\frac{LW{\int }_0^{{\delta }^c}{R}_{\mathrm{RWGS}}^{c}dy}{W{H}^c{\overline{V}}^{c,in}{c}_{\mathrm{CO}}^{c,in}}}}-\underset{U_{\mathrm{CO},elec}^c}{\underbrace{\frac{LW{i}_{{\mathrm{CO}}_2}}{n_{{\mathrm{CO}}_2}FW{H}^c{\overline{V}}^{c,in}{c}_{\mathrm{CO}}^{c,in}}}}\end{array}$$

(4)

where $U_{\mathrm{CO}}^c$ is the utilization factor of carbon monoxide, $J_{\mathrm{CO}}^{c,in}$ and $J_{\mathrm{CO}}^{c,out}$ are its inlet and outlet molar flow rates, respectively, L is the length of the cell, W is its width, $H^c$ is the height of the cathode channel, ${\delta }^c$ is the thickness of the cathode current collector, ${\overline{V}}^{c,in}$ is the average inlet flow velocity, $c_{\mathrm{CO}}^{c,in}$ is the inlet concentration, $R_{\mathrm{RWGS}}^c$ is the RWGS reaction rate, $n_{{\mathrm{CO}}_2}$ is the number of electrons transferred in CO₂ER, F is the Faraday constant, $i_{{\mathrm{CO}}_2}$ is the current density corresponding to CO₂ER, $U_{\mathrm{CO},\mathrm{RWGS}}^c$ is the utilization factor of carbon monoxide due to the RWGS reaction, and $U_{\mathrm{CO},elec}^c$ is that corresponding to CO₂ER. Carbon monoxide utilization due to the RWGS reaction and CO₂ER are written as negative terms in Equation (4), since both reaction pathways produce CO (i.e., negative utilization). For the RWGS reaction rate, $R_{\mathrm{RWGS}}^c$, we utilize the expression derived by Haberman and Young [26], which is expressed as:

$$\begin{array}{c}\hfill R_{\mathrm{RWGS}}^c=k_{\mathrm{RWGS}}^c{R}^2{T}^2\left(c_{{\mathrm{CO}}_2}{c}_{{\mathrm{H}}_2}-c_{{\mathrm{H}}_2\mathrm{O}}{c}_{\mathrm{CO}}/K_{\mathrm{RWGS}}\right)\end{array}$$

(5)

where $k_{\mathrm{RWGS}}^c$ is the RWGS reaction rate constant, R is the universal gas constant, T is the operating temperature, $K_{\mathrm{RWGS}}$ is the reaction equilibrium constant, and $c_i$ is the concentration of component i. The current density corresponding to CO₂ER can be evaluated using the concentration gradient at the triple phase boundary (tpb), according to:

$$\begin{array}{c}\hfill i_{{\mathrm{CO}}_2}=n_{{\mathrm{CO}}_2}F{D}_{{\mathrm{CO}}_2}\frac{d{c}_{{\mathrm{CO}}_2}}{dy}{|}_{y=tpb}\end{array}$$

(6)

where $D_{{\mathrm{CO}}_2}$ is the effective diffusion coefficient in the cathode current collector. Details for how to compute $D_{{\mathrm{CO}}_2}$ is provided in Supplementary Note S1 and Supplementary Table S1 lists the resultant values. We now introduce the following dimensionless parameters: $\tilde{y}\equiv y/{\delta }^c$ and ${\tilde{c}}_i\equiv c_i/c_{tot}^{c,in}$ and substitute Equations (5) and (6) into Equation (4) to yield:

$$\begin{array}{c}\hfill U_{\mathrm{CO}}^c=-\underset{U_{\mathrm{CO},\mathrm{RWGS}}^c}{\underbrace{\frac{L{k}_{\mathrm{RWGS}}^c{R}^2{T}^2{c}_{tot}^{c,in}{\delta }^c}{H^c{\overline{V}}^{c,in}{\tilde{c}}_{\mathrm{CO}}^{c,in}}{\int }_0^1\left({\tilde{c}}_{{\mathrm{CO}}_2}{\tilde{c}}_{{\mathrm{H}}_2}-{\tilde{c}}_{{\mathrm{H}}_2\mathrm{O}}{\tilde{c}}_{\mathrm{CO}}/K_{\mathrm{RWGS}}\right)d\tilde{y}}}-\underset{U_{\mathrm{CO},elec}^c}{\underbrace{\frac{L{D}_{{\mathrm{CO}}_2}}{H^c{\overline{V}}^{c,in}{\delta }^c{\tilde{c}}_{\mathrm{CO}}^{c,in}}\frac{d{\tilde{c}}_{{\mathrm{CO}}_2}}{d\tilde{y}}{|}_{\tilde{y}=tpb}}}\end{array}$$

(7)

It is shown in Equation (7) that the utilization of carbon monoxide due to the RWGS reaction is directly proportional to the thickness of the cathode current collector ($U_{\mathrm{CO},\mathrm{RWGS}}^c\sim {\delta }^c$), while CO₂ER is inversely proportional ($U_{\mathrm{CO},elec}^c\sim ({\delta }^c$)${}^{-1}$). This means that decreasing the thickness of the cathode current collector reduces the contribution of the RWGS reaction, while doing so promotes CO₂ER. In extreme cases when ${\delta }^c\to 0$, the contribution of heterogeneous chemical reactions in the cathode current collector to the production of carbon monoxide are effectively eliminated ($U_{\mathrm{CO},\mathrm{RWGS}}^c\to 0$), leaving only CO₂ER to produce carbon monoxide.

To further clarify the above conclusion, we evaluate the ratio of the RWGS reaction rate to that of CO₂ER (see Supplementary Note S2 for detailed derivation), in order to obtain the following dimensionless parameter [27,28]:

$$\begin{array}{c}\hfill {\Gamma }_{\mathrm{RWGS}}^c\equiv \frac{k_{\mathrm{RWGS}}^c{R}^2{T}^2{c}_{tot}^{c,in}{\left({\delta }^c\right)}^2}{D_{{\mathrm{CO}}_2}}=\frac{\mathrm{reverse}\mathrm{water}\mathrm{gas}\mathrm{shift}\mathrm{reaction}\mathrm{rate}}{\mathrm{rate}\mathrm{of}\mathrm{carbon}\mathrm{dioxide}\mathrm{electro-reduction}}\end{array}$$

(8)

Values of ${\Gamma }_{\mathrm{RWGS}}^c\ll 1$ indicate the RWGS reaction is negligible ($U_{\mathrm{CO},\mathrm{RWGS}}^c\sim 0$), resulting in only CO₂ER, while values of ${\Gamma }_{\mathrm{RWGS}}^c\sim 1$ suggest that both processes occur at approximately the same rate. We compare the experimental data from various studies to determine their resultant value of ${\Gamma }_{\mathrm{RWGS}}^c$, which are illustrated in Figure 2. The studies in which ${\Gamma }_{\mathrm{RWGS}}^c\ll 1$ (i.e., CO₂ER dominant regime) illustrate that the co-electrolysis and pure steam electrolysis polarization curves overlap each other, while studies with values of ${\Gamma }_{\mathrm{RWGS}}^c\sim 1$ (i.e., mixed CO₂ER and RWGS reaction regime) demonstrate that the co-electrolysis polarization curve lies between pure steam and pure carbon dioxide electrolysis. This approach demonstrates that dimensionless parameter ${\Gamma }_{\mathrm{RWGS}}^c$ can effectively characterize the behaviour of SOco-ECs with different geometries (button cells versus cell stacks) and operating conditions, and is relevant for all cathode current collector materials and microstructural properties due to its dimensionless nature.

Thus far, we have proven that the RWGS reaction and other possible heterogeneous chemical reactions are inconsequential to the transport behaviour of SOco-ECs when the cathode current collector’s thickness is sufficiently thin, which in turn promotes CO₂ER for the production of carbon monoxide, and is contrary to what has been proposed in previous analyses [9,10,21]. However, this finding alone does not explain why the polarization curves of both co-electrolysis and pure steam electrolysis overlap one another for sufficiently thin cathodes (i.e., ${\Gamma }_{\mathrm{RWGS}}^c\ll 1$). To explain this phenomenon, we now shift our attention to the thermodynamics of the system, and subsequently Butler-Volmer kinetics for a comparison of the rates of CO₂ER and H₂OER.

2.2. Thermodynamics of Solid Oxide Co-Electrolysis

The rate of work required for the CO₂ER and H₂OER reactions is determined by the product of the operating current and operating potential, according to:

$$\begin{array}{c}\hfill \dot{W}=EI\end{array}$$

(9)

and the operating current is proportional to the sum of the rate at which the CO₂ER and H₂OER reactions occur, which is expressed as:

$$\begin{array}{c}\hfill I=2F\left(U_{{\mathrm{H}}_2\mathrm{O},elec}^c{J}_{{\mathrm{H}}_2\mathrm{O}}^{c,in}+U_{{\mathrm{CO}}_2,elec}^c{J}_{{\mathrm{CO}}_2}^{c,in}\right)\end{array}$$

(10)

Here, $U_{{\mathrm{H}}_2\mathrm{O},elec}^c$ and $U_{{\mathrm{CO}}_2,elec}^c$ represent the electrochemical utilization factors of steam and carbon dioxide, respectively. Additionally, the rate of work for this system, based on the first and second laws of thermodynamics (see Supplementary Note S3 for the derivation), can be expressed as:

$$\begin{array}{c}\hfill \dot{W}=U_{{\mathrm{H}}_2\mathrm{O},elec}^c{J}_{{\mathrm{H}}_2\mathrm{O}}^{c,in}{\Delta }_r{g}_{{\mathrm{H}}_2\mathrm{O}}+U_{{\mathrm{CO}}_2,elec}^c{J}_{{\mathrm{CO}}_2}^{c,in}{\Delta }_r{g}_{{\mathrm{CO}}_2}\end{array}$$

(11)

where ${\Delta }_r{g}_{{\mathrm{H}}_2\mathrm{O}}$ and ${\Delta }_r{g}_{{\mathrm{CO}}_2}$ are the Gibbs free energy required to facilitate the H₂OER and CO₂ER reactions. By substituting Equations (10) and (11) into Equation (9) and solving for the operating potential, we obtain:

$$\begin{array}{c}\hfill E=\frac{{\zeta }_{{\mathrm{H}}_2\mathrm{O}}{\Delta }_r{g}_{{\mathrm{H}}_2\mathrm{O}}+{\zeta }_{{\mathrm{CO}}_2}{\Delta }_r{g}_{{\mathrm{CO}}_2}}{2F}\end{array}$$

(12)

In Equation (12), ${\zeta }_{{\mathrm{H}}_2\mathrm{O}}$ and ${\zeta }_{{\mathrm{CO}}_2}$ represent the ratios of the rate of electrochemical utilization of steam and carbon dioxide, respectively, to the total rate of the electrochemical conversion of both, which are expressed as:

$$\begin{array}{c}\hfill {\zeta }_{{\mathrm{H}}_2\mathrm{O}}=\frac{U_{{\mathrm{H}}_2\mathrm{O},elec}^c{J}_{{\mathrm{H}}_2\mathrm{O}}^{c,in}}{U_{{\mathrm{H}}_2\mathrm{O},elec}^c{J}_{{\mathrm{H}}_2\mathrm{O}}^{c,in}+U_{{\mathrm{CO}}_2,elec}^c{J}_{{\mathrm{CO}}_2}^{c,in}}\end{array}$$

(13)

and:

$$\begin{array}{c}\hfill {\zeta }_{{\mathrm{CO}}_2}=\frac{U_{{\mathrm{CO}}_2,elec}^c{J}_{{\mathrm{CO}}_2}^{c,in}}{U_{{\mathrm{H}}_2\mathrm{O},elec}^c{J}_{{\mathrm{H}}_2\mathrm{O}}^{c,in}+U_{{\mathrm{CO}}_2,elec}^c{J}_{{\mathrm{CO}}_2}^{c,in}}\end{array}$$

(14)

respectively. Assuming there are equal inlet molar flow rates of carbon dioxide and steam supplied to the system ($J_{{\mathrm{H}}_2\mathrm{O}}^{c,in}=J_{{\mathrm{CO}}_2}^{c,in}$), which is often the case, Equations (13) and (14) are further simplified to:

$$\begin{array}{c}\hfill {\zeta }_{{\mathrm{H}}_2\mathrm{O}}=\frac{U_{{\mathrm{H}}_2\mathrm{O},elec}^c/U_{{\mathrm{CO}}_2,elec}^c}{U_{{\mathrm{H}}_2\mathrm{O},elec}^c/U_{{\mathrm{CO}}_2,elec}^c+1}\end{array}$$

(15)

and:

$$\begin{array}{c}\hfill {\zeta }_{{\mathrm{CO}}_2}=\frac{1}{U_{{\mathrm{H}}_2\mathrm{O},elec}^c/U_{{\mathrm{CO}}_2,elec}^c+1}\end{array}$$

(16)

It is shown in Equations (15) and (16) that if the electrochemical utilization of steam is much higher than that of carbon dioxide ($U_{{\mathrm{H}}_2\mathrm{O},elec}^c\gg U_{{\mathrm{CO}}_2,elec}^c$), then ${\zeta }_{{\mathrm{H}}_2\mathrm{O}}\to 1$ and ${\zeta }_{{\mathrm{CO}}_2}\to 0$, causing the operating potential of co-electrolysis in Equation (12) to converge towards that of pure steam electrolysis ($E\approx {\Delta }_r{g}_{{\mathrm{H}}_2\mathrm{O}}/2F$). Conversely, if $U_{{\mathrm{H}}_2\mathrm{O},elec}^c\ll U_{{\mathrm{CO}}_2,elec}^c$, then ${\zeta }_{{\mathrm{H}}_2\mathrm{O}}\to 0$ and ${\zeta }_{{\mathrm{CO}}_2}\to 1$, and the operating potential will overlap that of pure CO₂ER. Based on experiments which have shown the polarization curves of co-electrolysis and pure steam electrolysis to overlap each other [9,10], it is expected the electrochemical utilization of steam is significantly higher than that of carbon dioxide ($U_{{\mathrm{H}}_2\mathrm{O},elec}^c\gg U_{{\mathrm{CO}}_2,elec}^c$), and below we provide an explanation for why this is the case.

2.3. Electrochemical Kinetics and Mass Transport

In order to compare the electrochemical utilization factor and kinetics of steam and carbon dioxide, we need to apply the Butler-Volmer equation to both components. For an infinitesimally thin active catalyst layer, the Butler-Volmer equation can be expressed as a boundary condition:

$$\begin{array}{c}\hfill i_i=n_{i}F{D}_i\frac{d{c}_i}{dy}{|}_{y=tpb}=n_{i}F{c}_i{|}_{y=tpb}{k}_i\lambda \left[exp\left(\frac{{\alpha }_i{n}_{i}F}{RT}{\eta }_i^c\right)-exp\left(\frac{-(1-{\alpha }_i)n_{i}F}{RT}{\eta }_i^c\right)\right]\end{array}$$

(17)

where $n_i$ is the number of electrons transferred in electrochemical reaction i, ${\eta }_i^c$ is the cathode activation overpotential, ${\alpha }_i$ is the charge transfer coefficient, $\lambda$ is the cathode triple phase boundary length, and $k_i$ is the electrochemical reaction rate constant of either steam or carbon dioxide. Substituting the above dimensionless parameters into Equation (17) produces the following expression:

$$\begin{array}{c}\hfill \frac{d{\tilde{c}}_i}{d\tilde{y}}{|}_{\tilde{y}=tpb}=\frac{{\delta }^c\lambda k_i}{D_i}{\tilde{c}}_i{|}_{\tilde{y}=tpb}\left[exp\left(\frac{{\alpha }_i{n}_{i}F}{RT}{\eta }_i^c\right)-exp\left(\frac{-(1-{\alpha }_i)n_{i}F}{RT}{\eta }_i^c\right)\right]\end{array}$$

(18)

which can then be substituted into the electrochemical utilization factor of steam:

$$\begin{array}{c}\hfill U_{{\mathrm{H}}_2\mathrm{O},elec}^c=\frac{L{D}_{{\mathrm{H}}_2\mathrm{O}}}{H^c{\overline{V}}^{c,in}{\delta }^c{\tilde{c}}_{{\mathrm{H}}_2\mathrm{O}}^{c,in}}\frac{d{\tilde{c}}_{{\mathrm{H}}_2\mathrm{O}}}{d\tilde{y}}{|}_{\tilde{y}=tpb}\end{array}$$

(19)

and that of carbon dioxide:

$$\begin{array}{c}\hfill U_{{\mathrm{CO}}_2,elec}^c=\frac{L{D}_{{\mathrm{CO}}_2}}{H^c{\overline{V}}^{c,in}{\delta }^c{\tilde{c}}_{{\mathrm{CO}}_2}^{c,in}}\frac{d{\tilde{c}}_{{\mathrm{CO}}_2}}{d\tilde{y}}{|}_{\tilde{y}=tpb}\end{array}$$

(20)

Doing so reveals that the electrochemical utilization factor of steam and carbon dioxide are directly proportional to their respective electrochemical rate constant (i.e., $U_{{\mathrm{H}}_2\mathrm{O},elec}^c\sim k_{{\mathrm{H}}_2\mathrm{O}}$ and $U_{{\mathrm{CO}}_2,elec}^c\sim k_{{\mathrm{CO}}_2}$). Previous studies have demonstrated that $k_{{\mathrm{H}}_2\mathrm{O}}$ can be up to 3-times higher than that of carbon dioxide [29,30], while Liang et al. [11] recently found that it can be up to 9-times higher. This correspondingly increases $U_{{\mathrm{H}}_2\mathrm{O},elec}^c$ over $U_{{\mathrm{CO}}_2,elec}^c$, increases ${\zeta }_{{\mathrm{H}}_2\mathrm{O}}$ while decreasing ${\zeta }_{{\mathrm{CO}}_2}$ (see Equations (15) and (16)), and therefore causes the operating potential of co-electrolysis to approach that of pure steam electrolysis ($E\approx {\Delta }_r{g}_{{\mathrm{H}}_2\mathrm{O}}/2F$). Additionally, given the enhanced mass transport characteristics of steam versus carbon dioxide, in tandem with hydrogen’s increased capacity to diffuse from the triple phase boundary in comparison to that of carbon monoxide, the concentration of steam at the triple phase boundary will be higher than that of carbon dioxide (${\tilde{c}}_{{\mathrm{H}}_2\mathrm{O}}{{|}_{\tilde{y}=tpb}>{\tilde{c}}_{{\mathrm{CO}}_2}|}_{\tilde{y}=tpb}$). This further promotes the electrochemical utilization of steam over carbon dioxide (i.e., $U_{{\mathrm{H}}_2\mathrm{O},elec}^c\sim {\tilde{c}}_{{\mathrm{H}}_2\mathrm{O}}{|}_{\tilde{y}=tpb}$ versus $U_{{\mathrm{CO}}_2,elec}^c\sim {\tilde{c}}_{{\mathrm{CO}}_2}{|}_{\tilde{y}=tpb}$) and causes the co-electrolysis polarization curve to coincide with that of pure steam electrolysis, which has been reported in previous experiments [9,10].

In summary, for sufficiently thin cathodes (i.e., ${\Gamma }_{\mathrm{RWGS}}^c\ll 1$), we find that H₂OER is dominant over CO₂ER, causing the co-electrolysis polarization curve to overlap with that of pure steam electrolysis. Additionally, implementing a thin cathode makes the contribution of the RWGS reaction to the production of carbon monoxide negligible, while promoting CO₂ER (i.e., $U_{{\mathrm{H}}_2\mathrm{O},elec}^c\gg U_{{\mathrm{CO}}_2,elec}^c\gg U_{\mathrm{CO},\mathrm{RWGS}}^c$). This analysis enables designers and researchers to select an appropriate value for the thickness of the cathode current collector, in order to exploit a desired reaction pathway to improve the performance and product selectivity of SOco-ECs.

3. Conclusions

This work has provided evidence for the fact that the RWGS reaction is not the reaction pathway responsible for CO generation when the polarization curves of co-electrolysis and pure steam electrolysis coincide with each other. Using dimensional analysis, we demonstrated that reducing the cathode current collector thickness diminishes the contribution of the RWGS reaction, while doing so promotes CO₂ER. We also showed that the RWGS reaction is negligible for sufficiently thin cathode current collectors, which is opposite to what was concluded in previous studies [9,10,21]. We have also derived a dimensionless parameter that characterizes the behaviour of SOco-ECs observed in previous experiments. Furthermore, we have utilized the first and second laws of thermodynamics, coupled with the enhanced electrochemical kinetics and mass transport properties of steam in comparison to carbon dioxide, to determine why the polarization curves of both co-electrolysis and pure steam electrolysis overlap one another. We found that the faster kinetics of H₂OER over CO₂ER, in tandem with CO₂ER being dominant in comparison to the RWGS reaction for sufficiently thin cathode current collectors, cause the pure steam electrolysis and co-electrolysis polarization curves to coincide. The goals of this analysis are to develop an improved understanding of the transport phenomena that govern the performance of SOco-ECs, and to illustrate the value of dimensional analysis when investigating such systems.