Rate Expressions in Mean Field Microkinetic Models Incorporating Multiple Types of Active Sites

05 August 2022, Version 3
This content is a preprint and has not undergone peer review at the time of posting.

Abstract

It is well known that heterogenous catalysts exhibit a distribution of sites/structures, some more active than others but more than one often being important to the underlying reaction mechanism(s). The inclusion of this reality in mean field microkinetic models has been largely avoided in favor of lattice-based models like cluster expansions where in principle different types of sites can be explicitly defined. Here, we develop a thermodynamically self-consistent theory of multi-site microkinetics from first principles-based statistical mechanics to show how multiple site types can be represented in mean field microkinetic models. The theory incorporates local enthalpies and entropies, lateral molecular interactions, and macroscopic configurational entropy; generating thermodynamic activities for any number of site types that deviate significant from those of idealized models. We provide the resultant rate expressions for rates of adsorption/desorption and surface diffusion between the site types. Contrary to what is typically assumed, even when a species has access to many different sites or binding configurations, only one rate, which is driven by the average adlayer chemical potential, can be defined for desorption from the surface. The approach in this work correctly describes adsorption/desorption and diffusion for a multi-site model of a heterogenous catalyst and differs from the commonly used law of mass action.

Keywords

Heterogeneous Catalysis
Microkinetic Modeling
Site Distributions
Chemical Kinetics
Reactive Surface Chemistry
Statistical Mechanics
Mean Field
Lattice Gas
Ideal Gas
Thermodynamic Activity
Site Blocking
Lateral Interactions
Intermolecular Interactions
Partition Function
Chemical Potential
Transition State Theory
Boudart

Supplementary materials

Title
Description
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Title
Supplementary Information
Description
Section S1. Relationship Between Partial Differentials and Site-Specific Chemical Potentials 4 Section S2. Full List of Possible Critical Points for a 3- and 4-Site Model 6 Section S3. Macroscopic Configurational Entropy: Cases II – IV 8 Section S4. Differential Mole Balance for Models α and β in Scenario 1 11 Section S5. Site Coverages During Thermal Excitations 12
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