Quantification of PEFC Catalyst Layer Saturation via In Silico, Ex Situ, and In Situ Small-Angle X-ray Scattering

The complex nature of liquid water saturation of polymer electrolyte fuel cell (PEFC) catalyst layers (CLs) greatly affects the device performance. To investigate this problem, we present a method to quantify the presence of liquid water in a PEFC CL using small-angle X-ray scattering (SAXS). This method leverages the differences in electron densities between the solid catalyst matrix and the liquid water filled pores of the CL under both dry and wet conditions. This approach is validated using ex situ wetting experiments, which aid the study of the transient saturation of a CL in a flow cell configuration in situ. The azimuthally integrated scattering data are fitted using 3D morphology models of the CL under dry conditions. Different wetting scenarios are realized in silico, and the corresponding SAXS data are numerically simulated by a direct 3D Fourier transformation. The simulated SAXS profiles of the different wetting scenarios are used to interpret the measured SAXS data which allows the derivation of the most probable wetting mechanism within a flow cell electrode.


Determination of the liquid saturation level by Invariant calculation
Invariant is related to the electron density and the volume fraction of the material by the following equation expressed for 3-phase system.
The value of K obtained from Equation 2 was then use in Equation 1 to solve the C or volume fraction of liquid (see Equation 3). .
In the case of absolute-scaled intensity of a two-phase material can be experimentally obtained, K in Equation 2 equals to 1 (experimental Invariant equals to theoretical Invariant).
The porosity (1-solid fraction A ) can be calculated if the SLD ( A ) of the solid fraction in void is known.
A SLD of hydrophilic porous PVDF membrane 15.15x10 10 cm -2 and porosity of 70% were used. The SLD of the dry catalyst layer structure is the volume-weighted average of the SLD of ionomer and carbon, which are 17.82x10 10 cm -2 and 16.36x10 10 cm -2 . The SLD of water is 9.45 x10 10 cm -2 and of decane is 7.16 x10 10 cm -2 . All SLDs are calculated based on 11.2 keV beam energy using Equation 4, where Z is the atomic number of the i th element in the molecular volume vm and re = 2.81 X 10 -13 cm, is the classical radius of the electron.

Details on Intersected Boolean Model
The geometrical covariogram of randomly distributed spherical grains reads where is the real space coordinate, and Θ() the Heaviside step function, being 1 for a positive argument and 0 otherwise. The solid covariance C11(r) is the probability that a stick with length , with random position and direction, has both of its ends in the solid phase of the two-phase pore structure. It can be calculated from the geometrical covariogram ( ). With where is the number density of grains in the simulation box. The number density of grains is adjusted such that 1 = ∏ =1 (1 − 0, ) equals the total volume fraction of the solid phase. The model scattering intensity I(q) is obtained by numerically integrating.
This model scattering intensity is fitted to the measured intensity. The grain sizes , the number density of grains , and the prefactor are constant during the experiment and are solved as fitting parameters.

Figure S4
Cross section of 3D synthetic structure with pore size threshold applied and without, Pt particles are more concentrated in certain areas when threshold is applied.

Figure S5
The different mechanisms of wetting in the pores of C only structure (intermediate towards Pt/C): I) smaller pores filling first, II) larger pores filling first, II) thin film formation.

Figure S6
Simulated SAXS profiles of carbon only structure of different saturation levels in the three wetting mechanisms explored, and its corresponding relative intensities (wet/dry) to visualize better the intensity change (b-I-III). Color coded to the 3D structures in Figure S5. In order to assess the morphological stability of the Pt/C catalyst layer, a multitude of SAXS measurements were implemented on one spot of the dry electrode. The probed location accumulated a total X-ray exposure of 26.95 s, which is more than twice higher than the accumulated exposure of the individual measurement spots during the 10-minute in situ wetting experiment. While the log-scale representation of the intensity profiles are virtually overlapping (see Figure S7a), relative intensity changes (normalized by the intensity after 1 s exposure, see Figure S7b) reveal that there is an observable decrease in intensity at lower q (max -5%) and increase at higher q (up to +10%). The effect of X-ray exposure can be seen more detailed in Figure S7c, showing a general increase (red area) in high-q and intensity decrease (green area) at low-q with higher exposure time. The changes in X-ray scattering are During the in situ experiment in the flow cell, the full SAXS intensity data was recorded for ~100 minutes. In the beginning, the open-circuit-voltage (OCV) was measured and was followed by the recording of a linear sweep down to 0.05 VRHE. Cyclic voltammetry (CV) was carried out in between chronoamperometric (CA) measurements at increasingly negative potentials to evolve hydrogen (specifically at -0.1 VRHE) and therewith reduce the Pt and increase its utilization. From the SAXS profiles, an increase in intensity at higher-q can be observed with time (see Figure S8a).

Radiation damage test to dry sample with continuous X-ray exposure
Oscillations of the signal from high-q with respect to the potential are more clearly revealed by relative intensity plot in Figure S8b. These oscillations may stem from the formation and subsequent reduction of oxide depending on the applied potential during the CVs between 0.05 VRHE and 1.1 VRHE 4 . With increasing time and increasing number of cycles, the location of intensity increase (indicated by the pink arrow in Figure S8a) shifts to lower-q. This shift may originate from the increase of Pt size due to Oswald ripening 5 or the dissolution of smaller Pt nanoparticles and subsequent preferential redeposition on larger Pt nanoparticles. Continuous X-ray exposure may also speed up the Pt growth as seen in the radiation damage test, minor intensity increase at higher q.
Since the Pt contribution to the liquid water saturation level determination is found to be significant, before calculating the invariant to determine the saturation level of liquid water, a careful extraction of the constant contribution of Pt is needed. A fit to the Pt region (0.6 < q < 1.5 nm -1 ) of the in situ SAXS profile to the analytical solution of sphere form factor with lognormal distribution was carried out using the JScatter Python package 6 by assuming that the pores near the Pt are fully filled or in other words assuming the contrast change is from particle size only. This may not be the case during the potential holds at 0 V and -0.1 V, as H2-bubbles may have been produced near the Pt's surface, hence the particle size change may also hide small nanobubble development. The mean diameter of the Pt size increased from ~2.2 to 2.6 nm (see Figure S8c), mean diameter from the fit in pink and moving average in black). By subtracting the contribution of Pt using the analytical fit result, a relatively constant saturation level throughout the electrochemical procedure was observed (see Figure S8d). Before the potential hold, the Pt utilization derived from CVs in Figure S9 indicated as red dots in Figure S8d  After applying a 3D FFT to the 3D image, the zero frequency of the resulting 3D FFT data is shifted to the center of the image. The 3D FFT arrays consist of real and imaginary parts.
The 3D array of SAXS intensity is obtained by the squared magnitude of the 3D FFT array.
The resulting of 3D intensity array was then subjected to spherical averaging of intensities with the same distance to the center creating a 1D intensity array (intensity versus distance to the center of the 3D array). The distance from cube's center can be related to reciprocal space, qmin = 2 * ℎ and qmax = , with spacing between points of q equals to qmin.
The 1D simulated intensity profile then was convolved with a sinc function to reduce artifacts in the high-q due to the cubic voxel structure. The resulting intensity is in units of length -1 , with the simulation box in units of length. For example, if the voxel size is user-defined as 1 nm, the intensity will have unit of nm -1 . It is to note that by doing spherical averaging, the resulting intensity profile is equivalent to having intensities averaged from all potential orientations of the sample relative to the X-ray beam, thus eliminating, or averaging out any anisotropy in the reciprocal-space map or in the 3D structure. This averaging is justified by observing that the SAXS patterns from the Pt/C catalyst layer are isotropic.

IMG2SAS verification
In order to validate IMG2SAS we applied it to functions for which an analytical solution is known, namely a spherical form factor, core-shell form factor, and a cubic form factor. These geometries were created with raster-geometry Python package. The resulting profiles from IMG2SAS are then compared to the analytical solution from JScatter Python package.
For the spherical form factor, the simulation with IMG2SAS is limited to the simulation box size used (denoted as a) and voxel size (denoted as v). Figure S11 shows the result for the form factor of spheres with different parameters of the simulation box size in nm, voxel size in nm, radius in nm, electron density contrast against air/vacuum in nm -2 (eta). Results for simulated SAXS profiles for a core and a shell are shown in Figure S12, for variations of the core radius, the shell thickness, as well as the scattering length densities of both.

Figure S12
Simulated SAXS profiles (dots) obtained by IMG2SAS for core-shell spheres compared to analytical solutions (lines); parameters in the brackets of the legend entries are IMG2SAS(box size in nm, voxel size in nm, core shell radius in nm, shell thickness in nm, core SLD in nm -2 , shell SLD in nm -2 ).
Results for simulated SAXS profiles cubes are show in Figure S13, where the simulation code receives different edge length of the cubes. For anisotropic objects such as cylinders, the resulting form factor from IMG2SAS is comparable to the analytical solution when the cylinder is averaged from all directions, as shown in Figure S14. To demonstrate the applicability of IMG2SAS to more complex structures, an artificial porous media (see Figure S15a) was generated with the Porespy package 9 with different pore sizes with the Union Boolean Model (UBM) approach. The created structure was then characterized with the granulometry procedure of Geodict2021 to calculate pore size distribution as shown in Figure S15b. The SAXS analytical solution of the UBM is compared to the simulated numerical SAXS from the 3D voxel representation by IMG2SAS in Figure   S15c, showing a good agreement for the accessible q-range of the IMG2SAS result.

Aperiodic structure effects in IMG2SAS
The 3D FFT algorithm that is used in IMG2SAS (and 3D FFT in general) assumes periodicity of the structure. However, in this manuscript the structures are not always periodic due the pore geometry and the water structure therein. In this section, two methods to deal with aperiodicity and edge effects are presented: 1) padding of the 3D structure plus mirroring along edge axes 20 and 2) window function to taper the edges of the 3D structure so that the edge values equal to 0.

Figure S16
2D Cross section of a) an initial CL structure that undergoes modifications to eliminate boundary effects: b) padded and c) tapered.
Padding the structure results in an eight times larger structure compared to the initial structure (see Figure S16b compared to S16a), hence causing longer computation time. The padding method has an advantage over windowing as the porosity and hence the saturation level of the initial structure are conserved. The intensity profiles corresponding to the initial structures in Figure 6 with padding treatment reveals a similar trend to the structure without padding for the proposed wetting scenarios (see Figure S17) as well as similar saturation level by Invariant calculation in Figure S19a.   Figure   6.
The alternative is to taper the edges of the 3D structure, modifying the initial electron density values. A tapered cosine window with 5% of the 3D structure in the boundary region is chosen as an example (see Figure S16c). The trend of intensity change during wetting is recovered by using the tapered structure (see Figure S18). However, since tapering modifies the electron density, the intensity profiles are different from the initial structures -particularly at low q, where the intensity profiles seem smoother. The discrepancy is also reflected in the obtained saturation levels (see Figure S19b) and mainly affects the large saturation levels. Hence, the usage of tapering is not recommended.   Chord length distribution for the void fraction of NNMC and Pt/C d).