Dynamics and Thermodynamics of Pd–PdO Phase Transitions: Effects of Pd Cluster Size and Kinetic Implications for Catalytic Methane Combustion

Methane oxidation rates uncorrupted by nonchemical effects of transport, taken together with stoichiometric oxygen uptake (oxidation cycle) and evolution (decomposition cycle) data, are used to establish for the first time a set of conditions required for true thermodynamic equilibrium during metal-to-oxide interconversions in small Pd clusters (1.8–8.8 nm). These conditions allow us to assess the intrinsic thermodynamics of small Pd clusters and their catalytic effects in CH4 oxidation. PdO decomposition in the absence of CH4 deviates from equilibrium, as this step is limited by the nucleation of an oxygen vacancy ensemble on oxide domains. The nucleation bottleneck is removed by CH4 during its catalytic sojourns, when CH4 pressure and the related rates exceed a critical value, because CH4 effectively removes the oxygen adatoms near an oxygen vacancy site via C–H bond activation on an oxygen–oxygen vacancy site pair that converts the O* adatom to a hydroxyl intermediate, which desorbs as H2O in sequential steps. CH4 oxidation turnovers promote the nucleation of oxygen vacancy ensembles at conditions that maintain the global oxygen equilibration, as confirmed from the absence of CH4 oxidation rate hysteresis in both Pd oxidation and PdO decomposition cycles and from coincidence of rate and oxygen content profiles during Pd oxidation. A theoretical construction decoupling the inherent cluster size variance from cluster diameter effects shows marked effects of size on bulk phase transition. The bulk phase transition occurs at lower oxygen chemical potentials for the smaller clusters, which confirm their more negative Gibbs free energy for PdO formation than the large structures. The bulk phase transition converts O*–O* adatom sites to Pd2+–O2– ion pairs that are more effective for the kinetically relevant C–H bond activation in CH4. These effects of size on the thermodynamics and reactivities of small clusters illustrated in this study are general and extend beyond the Pd–PdO system.