Paper HC+SS-MoM5
The Apparent Activation Energy for Complex Mechanisms: A Simple Relationship via Degrees of Rate Control

Monday, October 21, 2019, 9:40 am, Room A212

Reactions on surface usually consists of several elementary steps. It is known that the observed reaction kinetics often represents a composite of the contribution from each of these elementary steps. The “rate-determining step” (RDS) assumption is a common approach for dealing with multistep mechanisms, where a single step is assumed to dominate the reaction kinetic behaviors and the kinetic parameters of this RDS (e.g., net rate, activation energy) are good estimation for those of the overall reaction. However, RDS is not a rigorous concept in mathematics and there is no universal definition for RDS. Efforts have been made to clarify the actual physical meaning behind RDS, and the “Degree of Rate Control” (DRC) was raised as a rigorous mathematical approach to quantify to what extent the change of the Gibbs free energy of a species in the reaction scheme can affect the rate of the overall reaction. DRC analysis to reaction kinetics elucidates that there are only rate-determining species with non-negligible DRCs instead of rate-determining steps.

The apparent activation energy E_app is determined by fitting the temperature dependence of the reaction rate to the Arrhenius law. It is believed that E_app is a direct measurement of energy information in the RDS, which has been challenged by DRC analysis. A general and accurate elaboration of the microscopic origin of E_app has not been reported except in cases where there is an analytical rate expression. Here a simple but general mathematical expression of E_app in terms of the enthalpies of species in the reaction and their DRCs is derived. To verify the accuracy of this equation, microkinetic modelling of methanol synthesis through CO₂ hydrogenation on Cu-based model catalysts under three different conditions was carried out based on previously-published DFT energetics. On pure Cu(211) at 450 K, there are only one transition state and only one intermediate with non-negligible DRCs, and E_app estimated using our equation is within 1 kJ/mol of the true value. When the temperature is raised to 570 K, the surface sites are mostly unoccupied; and, when the model catalyst is promoted by Zn, there are four transition states with non-negligible DRCs, which means the single RDS assumption is not true. In both these complicated cases, the error of the estimated value for E_app is still <1 kJ/mol.