Temperature dependence of chemical and biophysical rate processes: Phenomenological approach to deviations from Arrhenius law

Abstract

a b s t r a c tArrhenius plots, which are used to represent the effects of temperature on the rates of chemical and biophysical processes and on various transport phenomena in materials science, may exhibit deviations from linearity. Account of curvature is provided here by a formula which involves a deformation of the exponential function, of the kind recently encountered in treatments of non-extensivity in statistical mechanics. We present here examples on diverse topics -respiration rates of plants, speed of gliding of bacteria, quantum mechanical tunneling in a chemical reaction -illustrating the variety of possible applications and the additional insight that can be gained.

Kinetics of low-temperature transitions and a reaction rate theory from non-equilibrium distributions

“…The relationship was first given in [28,29] (see also [20]). The expansion (2.6) in (2.3), as detailed previously [27,28], leads to a linear first-order differential equation for k(β) of the Bernoulli type that can be integrated by quadrature. It is immediate, but reassuring, to recover the Arrhenius equation within the validity of the first term, i.e.…”

Complex angular momentum theory of state-to-state integral cross sections: resonance effects in the F + HD → HF(v′ = 3) + D reaction

“…1 At low temperatures, reaction rates are often strongly influenced by quantum mechanical resonances and tunneling, which may cause large deviations of the rate constants from the Arrhenius law. [2][3][4] Modelling of resonance phenomena, in which the reactants form an intermediate complex before breaking up into products, requires large scale dynamical calculations on highly accurate potential surfaces. No less important is the task of interpreting the resonance patterns observed in the differential (DCS) and integral (ICS) cross sections.…”

Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces

“…The contribution of Aquilanti and co-workers [41] reviews their recent work on a reaction rate theory that is able to generalize the Arrhenius behaviour to low temperatures and to distributions of molecular states which do not follow Boltzmann statistics [42,43]. Different applications are given, from transport phenomena to quantum-mechanical tunnelling and to reactions that are strongly hindered.…”