Uniform description of non-Arrhenius temperature dependence of reaction rates, and a heuristic criterion for quantum tunneling vs classical non-extensive distribution

• Published in: Chemical physics letters 2013-12, Vol.590, p.201-207
• Main Authors: Silva, Valter H.C., Aquilanti, Vincenzo, de Oliveira, Heibbe C.B., Mundim, Kleber C.
• Format: Article
• Language: English
• ISSN: 0009-2614; 1873-4448
• DOI: 10.1016/j.cplett.2013.10.051

•Concave or convex deviations from linearity of Arrhenius plots at low temperatures.•Quantum and classical (collective) nature of the Sub- and Super-Arrhenius regimes.•Linearization of the inverse activation energy vs inverse temperature relationship.•Phenomenological uniform formula correlated with Tsallis non-extensivity parameter.•Connection established with features of quantum mechanical underbarrier tunneling. To account for frequently documented low-temperature deviations from Arrhenius rate law, the proposed expansion of inverse activation energy against inverse temperature is shown to yield a first order linearizing parameter which is formally correlated with Tsallis non-extensive classical statistical mechanics. Its sign provides a heuristic criterion, especially appealing in biochemistry, for assigning deviations as due either: (i) to quantum mechanical under-barrier tunneling, or (ii) to ‘classical’ collective phenomena. For (i), an explicit relationship is here derived in terms of barrier features. Case (ii) typically occurs in enzymatic or heterogeneous catalysis, in membrane mediated processes and in those controlled by diffusion or by transport in general.