Small angle X-ray scattering study for investigating 3D nanoparticle packing structure of Pt catalyst on Gd-doped CeO₂ supports for fuel cells

Small-angle X-ray scattering probes structural features over length scales ranging from individual nanoparticles to larger aggregates without destroying the sample. Unlike microscopy, which examines relatively small regions, SAXS measures the bulk material, providing statistically representative information about particle size, aggregation, and pore structure. When combined with structural modeling, it can reconstruct realistic three-dimensional arrangements of catalyst particles throughout the sample.

SAXS measurements alone provide reciprocal-space scattering data rather than direct real-space structures. Reverse Monte Carlo modeling iteratively adjusts particle positions within a simulated three-dimensional structure until the calculated scattering closely matches the experimental data. This process generates structural models that are consistent with the measured scattering and enables calculation of properties such as coordination numbers and pore size distributions.

The modeling indicates that only a fraction of the nominal platinum loading behaves as uniformly dispersed nanoparticles throughout the catalyst. As platinum loading increases, much of the additional Pt appears to become clustered or localized rather than evenly distributed. This results in fewer GDC particles having neighboring Pt particles despite the higher overall platinum content.

Increasing Pt loading decreases the average coordination number between Pt nanoparticles and GDC support particles. Higher-loading samples contain a greater proportion of support particles with no adjacent Pt nanoparticles, indicating that additional platinum preferentially forms localized concentrations instead of creating a more uniformly connected catalytic network.

The pore network controls how reactant gases reach catalytic sites and how reaction products are removed. Pore size and connectivity directly influence gas transport, catalyst utilization, and overall electrochemical performance. Three-dimensional structural models make it possible to evaluate these pore characteristics alongside nanoparticle distributions within the same framework.

The pore size distributions calculated from the reconstructed three-dimensional models were compared with pore sizes obtained from nitrogen adsorption measurements using the Barrett-Joyner-Halenda (BJH) method. The lower quartiles and median pore diameters showed good agreement between the two approaches, providing confidence that the reconstructed structures realistically represent the catalyst morphology.

Traditional Debye scattering calculations become computationally impractical for large nanoparticle systems because they require evaluating every particle pair. The modified Debye scattering equation reduces this computational burden by treating short-range and long-range particle correlations differently while preserving the accuracy needed to model large, multicomponent catalyst structures. This enables practical simulation of systems containing hundreds of thousands of nanoparticles.

Once a realistic structural model has been reconstructed, it can be used to investigate properties that are difficult to measure directly, including gas diffusivity, electrical conductivity, particle connectivity, and catalyst accessibility. This provides a pathway for correlating nanoscale structure with electrochemical performance and optimizing catalyst formulations for improved efficiency and durability.