Simple Model and Spectral Analysis for a Fluxional Catalyst: Intermediate Abundances, Pathway Fluxes, Rates, and Transients

Abstract

The fluxional interconversion of a catalyst between forms with different structures and properties complicates mechanistic analyses and kinetic modeling efforts. We construct a simple model for a catalyst with two fluxionally interconverting forms, inspired by the interconverting flat (*) and stacked (▲) forms of noble metal sub-nanoclusters. Using a detailed balance, free energy relations, non-dimensionalization, and representative equilibrium constants from ab initio calculations in the literature, ten initial rate parameters are reduced to two. The two remaining parameters control the fluxional interconversion rate and the reactant concentration. For a wide range of these two parameters, we compute the steady-state turnover frequencies, pathway fluxes, intermediate abundances, as well as transient intermediate relaxation rates. The results demonstrate how steady-state abundances and dominant pathways can change with the degree of fluxionality, even when equilibrium constants are unchanged. We conclude that accurate rate expressions must account for non-equilibrium steady-state abundances and fluxes, beyond equilibrium populations. Furthermore, in contrast to the short-lived transients for a non-fluxional catalyst, we show that non-steady transients may persist through many turnovers when fluxional interconversion is slow.

Unraveling Multiscale Kinetics over Subnanometer Cluster Catalysts: H2 Desorption from Pt3(-H)2/γ-Al2O3(110)

“…Beyond an estimation of the time scales based on intermediate coverage trajectories, the time scales of the reaction network can be quantified by spectral analysis. The Pt 3 (-H) x cluster populations evolve along the eigenmodes of the Jacobian of their population ODEs ( M̂ ; see Section ), where each eigenmode’s characteristic relaxation time is approximated from the inverse of its eigenvalue. ,, For the state-to-state reaction network considered here, the Jacobian depends only on temperature and the activity of reactive species; thus, analyzing transients this way bypasses bias due to initial populations. It has been shown that, for a transient catalytic reaction, the dependence of the instantaneous rate on the kinetic parameters can be unraveled by perturbing a desired kinetic rate constant while keeping the eigenvalues constant .…”

“…It becomes increasingly evident that single atoms are not necessarily the most active ones, and small clusters could be more efficient. Due to the low metal–metal coordination, the metal sites are strongly affected by the support (the ligand, using terminology from homogeneous catalysis) and the composition of the surrounding gas. − Under reaction conditions, an ensemble of site configurations most likely exist and a cluster may restructure, − as dictated by thermodynamic and kinetic factors. This situation is further complicated by the fact that the experimentally determined structure is ensemble-averaged or of limited spatial area resolution. ,− This renders the understanding of this class of catalysts hard.…”

Active Site Engineering via Optimizing the Heterogeneous Support Structure for Single-Atom Catalysis

“…The eigenvalues of the transition matrix are found to control the TOF and other kinetic properties of the network. A somewhat different spectral analysis was recently proposed by Peters . In order to explore the method, for the 2D problem, we shall actually compute the full chemistry network and locate the (HTS,LINT) pairs appropriate to each value of x .…”

“…A somewhat different spectral analysis was recently proposed by Peters. 54 In order to explore the method, for the 2D problem, we shall actually compute the full chemistry network and locate the (HTS,LINT) pairs appropriate to each value of x. For the larger 3D problem, we use this information to simplify the network.…”

Promoter-poison partnership protects platinum performance in coked cluster catalysts

“…This is in agreement with work by Peters, which emphasizes the importance of isomer interconversion flux and reaction production leading to deviations of populations from their equilibrium concentrations. 42 Thus reactivity may not be identifiable from equilibrium populations alone. For experimental validation of the electronic origin of the Ge effects on coking and stability, we compare our DFT results to ISS and TPD data for Pt 4 and Pt 4 Ge, before and after varying numbers of ethylene TPD cycles.…”