# Imaging Liquid Water in a Polymer Electrolyte Fuel Cell with High-Energy X-ray Compton Scattering
## 4 Results and Discussion
Finally, the relationship between the amount of generated liquid water and that of Pt catalysts is investigated using the Pearson correlation coefficient [34]. Figure 8 shows both the Compton scattering intensity and the Pearson correlation coefficient in the vicinity of the cathode layer as a function of the current density. Here, the Compton scattering intensity is obtained by integrating the counts over the Compton scattering peak. The intensity increases with current density in 0-500 mA/cm\({}^{2}\), indicating that the amount of generated water increases with the increase in the current densities. In contrast, in 500-900 mA/cm\({}^{2}\), the intensity is slightly decreased. This finding suggests that the amount of water generated in the cathode catalyst layer exceeds a certain threshold, resulting in the formation of paths where the water flows from the cathode CL to the channel through the GDL. This is consistent with Figures 5f,g and 7c. Here, the Pearson correlation coefficient (\(r_{\text{Pt-H2O}}\)) is defined as  
\[r_{\text{Pt-H2O}}=\frac{\sum_{i}\big{(}I_{\text{Pt}}^{i}-\overline{I}_{\text{Pt }}\big{)}\big{(}I_{\text{H2O}}^{i}-\overline{I}_{\text{H2O}}\big{)}}{\sqrt{ \sum_{i}\big{(}I_{\text{Pt}}^{i}-\overline{I}_{\text{Pt}}\big{)}^{2}\big{(}I _{\text{H2O}}^{i}-\overline{I}_{\text{H2O}}\big{)}^{2}}} \tag{3}\]  
where \(I_{\text{Pt}}^{i}\) is the intensity of the X-ray fluorescence of Pt-K\(\alpha\) and \(I_{\text{H2O}}^{i}\) is the differentiated intensity of Compton-scattered X-rays in the \(i\)-th pixel, respectively. \(I_{\text{Pt}}\) and \(\overline{I}_{\text{H2O}}\) are their  
Figure 8: Trends of the Compton scattering intensity (black) and Pearson correlation coefficient (red) in the vicinity of the cathode layer as a function of the current density. Figure 7: (**a,b**) Compton scattering images of the channel-rib layer; (**c**) subtracted image at 500 mA/cm\({}^{2}\). mean values. If this value is close to 1, it means that there is very high correlation between Pt and water, and they are distributed in the same location. If it is close to 0, it means that there is no correlation between them. As shown in Figure 8, the Pearson correlation coefficient is about 0.1 at 100 mA/cm\({}^{2}\) and about 0.8 at 300 mA/cm\({}^{2}\) and higher. The correlation maps between Pt and water at 100 and 500 mA/cm\({}^{2}\) are presented in Figure 9b,c, together with the image of Pt-Ka fluorescent X-ray intensities in Figure 9a. In Figure 8, the value of \(r_{\rm Pt-H2O}\) increases when increasing the current density from 0 mA/cm\({}^{2}\) to 300 mA/cm\({}^{2}\) and is almost constant or slightly decreased in 400-900 mA/cm\({}^{2}\). The overall trend is almost the same to that of the generated water. These facts show that water is dispersed in the CL without any correlation with the amount of Pt catalysts at low current densities, and water tends to be distributed in the Pt-rich areas at high current densities. This finding is consistent with the fact that the chemical reaction takes place at the Pt catalysts. This work has demonstrated that the study of correlations between liquid water and a specific element is feasible with the simultaneous measurements of Compton-scattered X-rays and fluorescent X-rays. This method can be applied to the study of the relationship between Ce scavengers and liquid water in an operating PEFC.