(639b) How to Write the Rate of a* + a*

Analytical kinetic descriptions of rates of reactions on catalytic surfaces based on the Langmuir-Hinshelwood formalism considers surface-bound adsorbates to adhere to Langmuir’s postulates describing interactions of fluid phase species with surfaces and Hinshelwood’s postulate that adsorbates are randomly distributed on the surface (i.e., are combinatorially ideal). Hinshelwood’s postulate, formulated mathematically, assumes that the mean-field μ_ij ≡ θ_ij(θ_iθ_j)^-1 is unity for all pairs of site occupants i and j. This approximation neglects the propensity of multi-site elementary steps (e.g. two-site A* + A* → A₂) to engender clustering (isolation) of slowly-consumed (rapidly-consumed) surface species. Consequently, the Langmuir-Hinshelwood formalism incorrectly asserts that the rate, kinetic influence, and coverage-dependence of each elementary step is equivalent with respect to each site ensemble.

An accurate kinetic description requires improvement upon the mean-field (i.e. Hinshelwood) assumption. We demonstrate the utility of a formalism which explicitly describes dynamics of multi-site ensembles by inclusion of higher-order rate terms specific to each ensemble and each elementary step in context of the reaction A* + A*.

We illustrate in context of this example, adsorbate clustering and isolation is caused by disparate elementary step rates and site-size requirements engendering (i) aggregation (μ_ij >> 1) of slowly-consumed ensembles and (ii) partitioning (μ_ij << 1) of rapidly-consumed (i.e. highly-reactive) ensembles – resulting in a ‘poorly-mixed’ or ‘transport-limited’ surface. Adsorbate surface diffusion resolves rate-controlling ‘transport limitations’ by dispersing clustered species and allying highly-reactive, isolated species. Only, in the limit of infinitely-fast surface diffusion (i.e. a reaction-limited, rather than transport-limited surface), does adsorbate distribution randomize and the Hinshelwood approximation become valid.