(481g) Kinetic Description of Site Ensembles on Catalytic Surfaces

We demonstrate that the ubiquitously-used Langmuir-Hinshelwood formalism is an incomplete kinetic description and is inappropriate even for catalytic reactions as simple as A + ½B₂→ AB. The Langmuir-Hinshelwood kinetic description is predicated on the Hinshelwood assumption – that all adsorbates are randomly-distributed on the surface. The utility of this approximation is in reducing coverages of multi-site ensembles (e.g. two-site A^*–B^*) to a product of coverages of constituent single-site ensembles (e.g. one-site A^* and B^*). For example, the rate of surface reaction between neighboring A^* and B^* species is rigorously r = k_rθ_{A*– B*} where θ_A*–B* is the fraction of pairs of sites which contain one A^* and one B^* species. The Langmuir-Hinshelwood formalism simplifies the rate to r = k_rθ_A*θ_B* by application of the Hinshelwood approximation – mathematically, that the mean-field metric, μ_ij = θ_ij(θ_iθ_j)^-1, is unity for all site pairs ij, giving θ_A*–B* = θ_A*θ_B*.

The Hinshelwood approximation, however, crucially neglects the propensity of multi-site elementary steps (e.g. two-site A^*–B^* → *–* + AB) to engender (i) aggregation (μ_ij >> 1) of slowly-consumed ensembles and (ii) partitioning (μ_ij << 1) of rapidly-consumed ensembles. Accurate description of partitioning and clustering phenomena requires derivation of higher-order, ensemble-specific rate terms which (i) quantify the unique kinetic influence each ensemble exerts on each elementary step and (ii) explicate the effect of partitioning/clustering to engender profound changes in rates, selectivities, and identities of rate-determining steps unidentifiable in the Langmuir-Hinshelwood formalism – as we demonstrate in the context of (i) the A + ½B₂ → AB reaction and (ii) the industrially-relevant ammonia synthesis reaction for which we predict kinetically-relevant clustering of N^*–N^* pairs (μ_N*–N* ~ 10⁵) resultant from the well-known difficulty of activating N≡N triple bonds in rate-determining N₂adsorption.