Unintuitive Inverse Dependence of the Apparent Turnover Frequency on Precatalyst Concentration: A Quantitative Explanation in the Case of Ziegler-Type Nanoparticle Catalysts Made from [(1,5-COD)Ir(μ‑O2C8H15)]2 and AlEt3

The Ziegler-type hydrogenation precatalyst dimer, [(1,5-COD)­Ir­(μ-O2C8H15)]2 (1,5-COD = 1,5-cyclooctadiene; O2C8H15 = 2-ethylhexanoate) plus added AlEt3 stabilizer has recently been shown to form AlEt3-stabilized, Ziegler-type Ir(0)∼4–15 nanoparticles initially, which then grow to larger Ziegler-type Ir(0)∼40–50 nanoparticles during the catalytic hydrogenation of cyclohexene (Alley, W. M.; Hamdemir, I. K.; Wang, Q.; Frenkel, A. I.; Li, L.; Yang, J. C.; Menard, L. D.; Nuzzo, R. G.; Özkar, S.; Johnson, K. A.; Finke, R. G. Inorg. Chem. 2010, 49, 8131–8147). An interesting observation for this Ziegler-type nanoparticle catalyst system is that the apparent TOF (TOFapp = k obs/[Ir]) for cyclohexene hydrogenation increases with decreasing concentration of the precatalyst, [Ir] (defined as 2­[{(1,5-COD)­Ir­(μ-O2C8H15)}2], that is, twice the starting precatalyst concentration since that dimer contains 2 Ir). A perusal of the literature reveals that such an intuitively backward, inverse relationship between the apparent turnover frequency, TOFapp, and the concentration of precatalyst or catalyst has been seen at least eight times before in other, disparate systems in the literature. However, this effect has previously never been satisfactorily explained, nor have the mixed, sometimes opposite, explanations offered in the literature been previously tested by the disproof of all reasonable alternative explanations/mechanistic hypotheses. Herein, five alternative mechanistic explanations have been tested via kinetic studies, Z-contrast STEM microscopy of the nanoparticle product sizes, and other evidence. Four of the five possible explanations have been ruled out en route to the finding that the only mechanism of the five able to explain all the evidence, as well as to quantitatively curve-fit the inverse TOFapp vs [Ir] data, is a prior, dissociative equilibrium, in which x ≈ 3 equiv of the surface-bound, AlR3-based nanocluster stabilizer is dissociated, Ir(0) n ·[AlEt3] m ⇄ xAlEt3 + Ir(0) n ·[AlEt3] m−x , with the resulting, more coordinatively unsaturated Ir(0) n ·[AlEt3] m−x being the faster, kinetically dominant catalyst. The implication is that such unusual, inverse TOFapp vs [precatalyst or catalyst] concentration observations in the literature are, more generally, likely just unintentional, unwitting measurements of a component of the rate law for such systems. The results herein are significant (i) in providing the first quantitative, disproof-tested explanat