Classes de universalidades em cinética de reações químicas sob regime de Tunelamento quântico : função transitividade guiando aos limites de Wigner

Abstract

The kinetics of the physicochemical processes is related to the temperature by the Arrhenius law, so that the logarithm of the kinetic constant in relation to the temperature (1/T) was linearized showing constant activation energy throughout the process, however at low- temperature deviations can be observed, they are the sub-Arrhenius and super-Arrhenius cases, in which the kinetic constant starts to assume overestimated and underestimated values, respectively. As a result, new improvements were needed so that reliable kinetic constant values could be made available in several areas, such as enzymatic kinetics, combustion chemistry, atmospheric reactions, food preservation, storage of super-cold fluids, among others. The super- Arrhenius shifts are related to classical factors, while the sub-Arrhenius shifts are associated with quantum factors and needed an adequate probabilistic treatment, as well as interpretations, focused on the microscopic properties involved in endothermic and exothermic reactions. These have different behavior in quantum tunneling regimes close to the Wigner limits where the collision energies are considerably low at low temperatures. As several studies were effective in proving the variation of the activation energy with the temperature of the system, the transitivity (γ), given as the inverse of the activation energy, emerged as an alternative to give mathematical meaning to these processes, making it possible to obtain kinetic parameters and describe new functional expressions by relating transitivity and temperature. It was demonstrated in this work that the processes known until then, including those that have a non-Arrhenius behavior, have similar behavior and the same variables and associated constants, therefore, they can be grouped into universality classes with the transitivity varying with respect to beta, so that the kinetics of the processes can be described by an equation dependent on the universality coefficients “ζ”, “ι” and “τ”, which can have values that give rise to equations that relate the value assumed by the transitivity in a certain temperature, providing a field for the development of even new relationships. In this work, five endothermic reactions and five exothermic reactions were adjusted, which made it possible to obtain not only the universality coefficients but also the energy barrier (ℰ‡), the zero reactivity energy (ℰ†) and the zero reactivity temperature (T†), being possible to observe that the behavior of the transitivity in relation to the temperature in the sub-Arrhenius deviations was similar to that predicted in the approached literature.