Thermodynamic Equilibrium versus Kinetic Trapping: Thermalization of Cluster Catalyst Ensembles Can Extend Beyond Reaction Time Scales
Patricia Poths, Santiago Vargas, Philippe Sautet, Anastassia N. Alexandrova
Abstract
The fluxionality of sub-nanocluster catalysts is essential to understand their behavior at an atomistic level. Up until now, when it has been considered, fluxionality has been treated primarily thermodynamically, representing relevant isomer populations as their Boltzmann populations. Previous work supported this, suggesting that the Pt 7 /Al 2 O 3 ensemble should be kinetically accessible at 700 K, based on the barrier heights for isomerization. In the current work, we explore the isomerization kinetics of gas-phase and surface-supported Pt 4 H x clusters, using kinetic Monte Carlo (kMC) based on first-principles energetics to explore the evolution of isomer populations with time as a function of temperature. We additionally revisited the previously obtained Pt 7 /Al 2 O 3 network. This allows us to determine the temperature-dependent time scales at which the ensembles of these sub-nanoclusters reach thermal equilibrium. Gas-phase clusters readily thermalize within nanoseconds by 350 K, while surface-supported clusters require temperatures between 500 and 700 K to thermalize within μs. Ultimately, thermalization time scales depend on the heights of the barriers between low-lying isomers, which in turn depend on the extent of the structural difference between isomers. We therefore show that it is essential to compute the barriers for isomerization between low-lying isomers in order to accurately determine either thermalization time scales or nonequilibrium steady-state populations. These thermalization time scales can extend to longer than catalytically relevant time scales depending on the reaction in question, indicating not only that isomerization can be an essential feature of the reaction coordinate of a catalytic reaction but also that a catalytic supported cluster system can remain out-of-equilibrium even at industrial time scales under mild conditions.