Coverage-Dependent Rate-Driving Force Relationships: Hydrogen Transfer from Cerium Oxide Nanoparticle Colloids

Rate-driving force relationships, known as Brønsted-Evans-Polanyi (BEP) relations, are central to many methods for predicting the performance of heterogeneous catalysts and electrocatalysts. Methods such as Tafel plots and "volcano" analyses often assume that the effect of adsorbate coverage on reaction rates across different materials is constant and known. Here, we use UV-visible spectroscopy to test these assumptions by measuring rates of net hydrogen atom transfer from colloidal cerium oxide nanoparticles (nanoceria) to organic reagents at varying surface CeO-H bond strengths and surface coverages. The resulting rate constants follow a linear BEP relationship, Δlog(k) = αΔlog(K_eq), across two sizes of nanoceria, two organic reagents, and a ∼10 kcal mol^-1 range of CeO-H bond strengths. Interestingly, the Brønsted slope is only 0.2, demonstrating that the rate constants are far less sensitive to CeO-H bond strength than would commonly be assumed for a heterogeneous nanomaterial. Furthermore, we observe a Brønsted slope >1 when altering the reaction driving force via the organic reagent bond strength instead of that of CeO-H. The implications of these Brønsted slopes for either concerted or stepwise mechanisms are discussed. To our knowledge, these are the first solution-phase measurements of BEP relationships for hydrogen coverage on a (nano)material.