Aquilanti–Mundim deformed Arrhenius model in solid-state reactions

Abstract

Although the theoretical framework supporting the use of non-extensive statistical theory for the study of chemical reaction kinetics and solid-state diffusive reactions is well established, direct evaluation of the parameters involved-such as the case of pair (d, e) appearing in the d-Arrhenius model-in the pertinent experimental data has yet to be generalized. This study proposes the use of ''d-Arrhenius log-log plots'' instead of Arrhenius semilog plots as a tool to determine the kinetic parameters of a reaction and their application to two different solid-state reactions obtained by DSC measurements in an Al-Fe-Si alloy. The paper goes on to show that the data obtained by DSC using the Arrhenius law generate a single k(T), whereas resorting to the Aquilanti-Mundim deformed Arrhenius model generates a set of (d, e) parameter pairs capable of reproducing the experimental data. Different (d, e) pairs generate different k(T) (d = 0, e = Q) corresponding to the Arrhenius pair. The effect of the different (d, e) pairs on the different functions related to the kinetics of the reaction is examined.Graphical Abstract AMDA graph showing linearity for different (d, e) pairs obtained from the precipitation reaction Guinier-Preston zones measured by DSC in an AA8011 commercial alloy (Superior) and Q activation energy for different pairs (bottom). The pair of Arrhenius (0, Q) in both graphs is represented by perpendicular and horizontal lines, respectively.

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

“…The super-Arrhenius behaviour is one that deserves particular attention, and its occurrence is varied and demanding (figure 1). It often manifests because of collective phenomena, such as those amenable to treatment by the non-extensive thermodynamics of Tsallis, and covers an ample set of phenomena: rates of enzymatic catalysis-promoted processes [53][54][55], food preservation processes [56,57] and basic features of the dynamics of complex or glass-forming liquids and solids [58][59][60][61][62][63].…”

“Transitivity”: A Code for Computing Kinetic and Related Parameters in Chemical Transformations and Transport Phenomena

“…A characterizing feature of the code is the consistent use of the d-formulation, which recently culminated in a series of successful applications from phenomenological to first-principles descriptions of pure and applied chemical kinetics and material science. Examples are available:From the phenomenology of elementary processes (such as the H 2 + F [94], OH + HBr [80], F + HD [65] and C + CH + [95] reactions) to complex processes (such as food systems [96], plant respiration [25], plasma chemistry [97], and solid-state diffusive reaction [98]);Calculation of the kinetic rate constants for chemical reactions from the potential energy surface features profile, such as the CH 4 + OH [60], CH 3 OH + H [99], OH + HCl [44], OH + HI [43], to proton rearrangement of enol forms of curcumin [100], OH + H 2 [101], and chiral nucleophilic substitution reaction [102]. …”

“…From the phenomenology of elementary processes (such as the H 2 + F [94], OH + HBr [80], F + HD [65] and C + CH + [95] reactions) to complex processes (such as food systems [96], plant respiration [25], plasma chemistry [97], and solid-state diffusive reaction [98]);…”