Characterization of the non-Arrhenius behavior of supercooled liquids by modeling nonadditive stochastic systems

Rosa, A. C. P.; Cruz, Clebson; Santana, Wanisson Silva; Moret, Marcelo A.

doi:10.1103/physreve.100.022139

Cited by 10 publications

(7 citation statements)

References 52 publications

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Section: Discussionmentioning

confidence: 99%

“…The effort to cope with the curvature of the Arrhenius plot is very old and many phenomenological equations have been published, e.g., Equations ( 4)-( 7), ( 9) and (10). Some of them have been published and used only a few times but, e.g., the supplement of C/(RT) 2 as an addend in Equation ( 5) (or exp[C/(RT) 2 ] as a multiplicand before logarithmization) causing curvature of the Arrhenius plot) has been used very often as a so-called Bässler-like factor [3,34].…”

Section: Discussionmentioning

confidence: 99%

“…Deviation from the linear shape of the Arrhenius plot (from “Arrhenius behaviour”) is often referred to as the “non-Arrhenius behaviour” [ 10 ] and is distinguished into the “super-Arrhenius behaviour” (concave curve) and “sub-Arrhenius behaviour” (convex curve), e.g., [ 10 , 11 ]. Many authors distinguish only between “concave Arrhenius plot” and “convex Arrhenius plot”, but some of them interchange the terms “concave” and “convex”, e.g., [ 12 ].…”

Section: Introductionmentioning

confidence: 99%

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Modified Arrhenius Equation in Materials Science, Chemistry and Biology

Kohout

2021

Molecules

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The Arrhenius plot (logarithmic plot vs. inverse temperature) is represented by a straight line if the Arrhenius equation holds. A curved Arrhenius plot (mostly concave) is usually described phenomenologically, often using polynomials of T or 1/T. Many modifications of the Arrhenius equation based on different models have also been published, which fit the experimental data better or worse. This paper proposes two solutions for the concave-curved Arrhenius plot. The first is based on consecutive A→B→C reaction with rate constants k1 ≪ k2 at higher temperatures and k1 ≫ k2 (or at least k1 > k2) at lower temperatures. The second is based on the substitution of the temperature T the by temperature difference T − T0 in the Arrhenius equation, where T0 is the maximum temperature at which the Arrheniusprocess under study does not yet occur.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modified Arrhenius Equation in Materials Science, Chemistry and Biology

Kohout

2021

Molecules

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“…As discussed in this article the approach turns out to be a powerful tool, capable of establishing a connection between canonical data and microcanonical information, permitting comparisons among apparently uncorrelated formulations: it also allows interpretation of empirical parameters, for example for the AM, ASCC, VFT and NTS formulas considered in this paper. Previous (Tsallis and Bukman, 1996; Lenzi et al, 2001; JiangLin et al, 2006; Zhou and Du, 2013) and concomitant (Zhou and Du, 2014; Guo and Du, 2015; Rosa et al, 2016; Junior et al, 2019) efforts have been dedicated to provide also a connection of anomalous kinetic diffusion effects while surmounting a potential barrier via variants of Fokker-Planck equation, tackling a class of phenomenologically physicochemical diffusion process.…”

Section: Additional and Final Remarksmentioning

confidence: 99%

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

2019

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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.

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“…There are some examples in the literature [29,[69][70][71] where there is evidence that our language the classical thermodynamic limit is reached due to the magnitude of Avogadro number O 10 24 . Considering this number, the statistical mechanics treatment indicates that fluctuations of energy in a canonical ensemble turn out extremely sharp and narrow.…”

Section: Avoiding the Thermodynamic Limit Describes Nonlinearities Of Arrhenius Plotsmentioning

confidence: 95%

From the Kinetic Theory of Gases to the Kinetics of Rate Processes: On the Verge of the Thermodynamic and Kinetic Limits

2020

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A variety of current experiments and molecular dynamics computations are expanding our understanding of rate processes occurring in extreme environments, especially at low temperatures, where deviations from linearity of Arrhenius plots are revealed. The thermodynamic behavior of molecular systems is determined at a specific temperature within conditions on large volume and number of particles at a given density (the thermodynamic limit): on the other side, kinetic features are intuitively perceived as defined in a range between the extreme temperatures, which limit the existence of each specific phase. In this paper, extending the statistical mechanics approach due to Fowler and collaborators, ensembles and partition functions are defined to evaluate initial state averages and activation energies involved in the kinetics of rate processes. A key step is delayed access to the thermodynamic limit when conditions on a large volume and number of particles are not fulfilled: the involved mathematical analysis requires consideration of the role of the succession for the exponential function due to Euler, precursor to the Poisson and Boltzmann classical distributions, recently discussed. Arguments are presented to demonstrate that a universal feature emerges: Convex Arrhenius plots (super-Arrhenius behavior) as temperature decreases are amply documented in progressively wider contexts, such as viscosity and glass transitions, biological processes, enzymatic catalysis, plasma catalysis, geochemical fluidity, and chemical reactions involving collective phenomena. The treatment expands the classical Tolman’s theorem formulated quantally by Fowler and Guggenheim: the activation energy of processes is related to the averages of microscopic energies. We previously introduced the concept of “transitivity”, a function that compactly accounts for the development of heuristic formulas and suggests the search for universal behavior. The velocity distribution function far from the thermodynamic limit is illustrated; the fraction of molecules with energy in excess of a certain threshold for the description of the kinetics of low-temperature transitions and of non-equilibrium reaction rates is derived. Uniform extension beyond the classical case to include quantum tunneling (leading to the concavity of plots, sub-Arrhenius behavior) and to Fermi and Bose statistics has been considered elsewhere. A companion paper presents a computational code permitting applications to a variety of phenomena and provides further examples.

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Characterization of the non-Arrhenius behavior of supercooled liquids by modeling nonadditive stochastic systems

Cited by 10 publications

References 52 publications

Modified Arrhenius Equation in Materials Science, Chemistry and Biology

Modified Arrhenius Equation in Materials Science, Chemistry and Biology

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

From the Kinetic Theory of Gases to the Kinetics of Rate Processes: On the Verge of the Thermodynamic and Kinetic Limits

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