Temperature Dependence of Rate Processes Beyond Arrhenius and Eyring: Activation and Transitivity.

Valter H. Carvalho-Silva,Vincenzo Aquilanti,Nayara D. Coutinho

doi:10.3389/fchem.2019.00380

Valter H. Carvalho-Silva, Vincenzo Aquilanti + Show 1 more

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https://doi.org/10.3389/fchem.2019.00380

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Abstract

Advances in the understanding of the dependence of reaction rates from temperature, as motivated from progress in experiments and theoretical tools (e. g., molecular dynamics), are needed for the modeling of extreme environmental conditions (e.g., in astrochemistry and in the chemistry of plasmas). While investigating statistical mechanics perspectives (Aquilanti et al., 2017b, 2018), the concept of transitivity was introduced as a measure for the propensity for a reaction to occur. The Transitivity plot is here defined as the reciprocal of the apparent activation energy vs. reciprocal absolute temperature. Since the transitivity function regulates transit in physicochemical transformations, not necessarily involving reference to transition-state hypothesis of Eyring, an extended version is here proposed to cope with general types of transformations. The transitivity plot permits a representation where deviations from Arrhenius behavior are given a geometrical meaning and make explicit a positive or negative linear dependence of transitivity for sub- and super-Arrhenius cases, respectively. To first-order in reciprocal temperature, the transitivity function models deviations from linearity in Arrhenius plots as originally proposed by Aquilanti and Mundim: when deviations are increasingly larger, other phenomenological formulas, such as Vogel-Fulcher-Tammann, Nakamura-Takayanagi-Sato, and Aquilanti-Sanches-Coutinho-Carvalho are here rediscussed from the transitivity concept perspective and with in a general context. Emphasized is the interest of introducing into this context modifications to a very successful tool of theoretical kinetics, Eyring's Transition-State Theory: considering the behavior of the transitivity function at low temperatures, in order to describe deviation from Arrhenius behavior under the quantum tunneling regime, a “d-TST” formulation was previously introduced (Carvalho-Silva et al., 2017). In this paper, a special attention is dedicated to a derivation of the temperature dependence of viscosity, making explicit reference to feature of the transitivity function, which in this case generally exhibits a super-Arrhenius behavior. This is of relevance also for advantages of using the transitivity function for diffusion-controlled phenomena.

Highlights

To understand and control the physical chemistry of materials in an ample variety of environments that may be encountered in basic and applied scientific research, information on the kinetics of the involved elementary processes and their role in global mechanisms is needed: of particular interest are the rates, and often in a wide range of conditions— of temperature
From the early Arrhenius (1889) and Eyring (1935) formulations, demands emerge for interpretative theoretical tools to study the kinetics of chemical reactions and to phenomenological account of reaction rate data as generated from exact quantum benchmarks or from approximate semiclassical and classical trajectory approaches
Traditional and recent phenomenological reaction rate constant formulas and transitivity function are presented to deal with sub- and super-Arrhenius behavior with larger deviations than those not accounted for the AM d-Arrhenius formula: VFT, ASCC, and NTS

Summary

Introduction

To understand and control the physical chemistry of materials in an ample variety of environments that may be encountered in basic and applied scientific research, information on the kinetics of the involved elementary processes and their role in global mechanisms is needed: of particular interest are the rates, and often in a wide range of conditions— of temperature. In generic super-Arrhenius behavior, sometimes high-order terms in the transitivity function are to be introduced to describe a sequence of processes, yielding concavities in the transitivity plot and moving the minimum temperature T† at lower values (Figure 2); ii) in sub-Arrhenius cases, the linear growth of γ as β increases may be accelerated at low temperatures: actual experimental information (Limbach et al, 2006; Tizniti et al, 2014; Meng et al, 2015) is confirmed by computations (Aquilanti et al, 2005; De Fazio et al, 2006; Cavalli et al, 2014; De Fazio, 2014; Coutinho et al, 2018b) and is eventually governed by Wigner’s limit (Wigner, 1948): before the latter limit is accessed interference effects may superimpose to quantum tunneling effects, which can be studied through microcanonical exact computations (Aquilanti et al, 2005; De Fazio et al, 2006; Coutinho et al, 2018b).

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Conclusion