Compensation phenomena in heterogeneous catalysis: General principles and a possible explanation

The compensation phenomenon in heterogeneous catalysis takes the form of a sympathetic linear correlation between the observed parameters of the Arrhe nius equation E-app and ln A(app) for a series of related reactions or cata lysts: ln A(app) = mE(app) + c Exact obedience to this Cremer-Constable relation requires all Arrhenius pl ots in the set to intersect at the isokinetic temperature (T-i). When this is established with statistical rigor (which is rare), the term "isokinetic relationship" (IKR) is used, the term "compensation" being reserved for ca ses in which this has not been done. Early work suggested that T-i equated to that at which the catalysts were prepared, but this observation has not been generally confirmed. Experimental error in the Arrhenius plots and oth er causes, such as a change in mechanism or the onset of diffusion limitati on, can give rise to false ''apparent'' compensation which is of no real si gnificance. The scope of this review is strictly limited to heterogeneously catalyzed r eactions; thermal desorption is excluded. Explanations advanced include (1) distribution of active-site energy and (2) an enthalpy-entropy relation or iginating either in the thermodynamics of chemisorption, or in the activati on parameters of the Transition State Theory, or in the process of energy t ransfer between initial and final states. The distinction between apparent (E-app and ln A(app)) and true (E-t and In A,) Arrhenius parameters is clea rly drawn: The latter are observed only where the catalyst exhibits a high affinity for the adsorbate(s) and where, therefore, the coverage is high an d independent of temperature within the range of measurement; zero-order ki netics then apply. Structure insensitivity is often observed under these co nditions. Compensation is only seen with apparent Arrhenius parameters, whi ch occur when chemisorption is weaker: The resulting lower coverages are te mperature dependent and sensitive to many variables such as catalyst compos ition and the nature of the reactant(s). Reaction orders are then greater t han zero, and under these conditions, structure sensitivity is often found. Values of E-t then exceed those of E-app by the appropriate adsorption ent halpy terms. Model calculations based on Langmuir-Hinshelwood bimolecular k inetics show that compensation may occur within a single system, due simply to a change of coverage with reactant pressure: Consequential changes in t he exponential term exp(-E-app/RT) are greater than changes in rate, so tha t compensation is inevitable. These concepts are illustrated by reference to three systems: (1) acid-cata lyzed hydrocarbon transformations, where independent measurements of adsorp tion enthalpies are available; (2) metal-catalyzed hydrogenation of benzene and its homologs, where mathematical modeling extracts values for E-t and adsorption enthalpies; and (3) metal-catalyzed hydrogenolysis of alkanes, w here the endothermic initial C-H bond splitting causes the value of E-app t o be larger than E-t, thus explaining inter alia the variation of E-app wit h chain length. If, in a set of reaction systems, conditions far measuring the temperature dependence of rate are chosen such that adsorbed reactant concentrations va ry to an appreciable degree, values of E-app will necessarily differ, and c ompensation will appear if accompanying changes in rate are small (i.e., if T-i lies within or close to the temperature range used).