Non-Arrhenius behavior and fragile-to-strong transition of glass-forming liquids

On the pseudo-hyperbolic behavior of charge transfer resistance-temperature dependence in corrosion behavior of Nickel based glass alloy

Temperature plays an important role in promoting the corrosion of metals. The Arrhenius plot can interpret the corrosion rate-temperature dependence, where the Arrhenius behavior gives a geometrical meaning and makes explicit a positive or negative linear dependence of charge transitivity and temperature. In addition, according to the Arrhenius interpretation, it represents the energy that the molecule in the initial state of the process must acquire before it can take part in the reaction, whether it is a physical, or a chemical process. Taking into account the deviation from the linearity, we have extended the Arrhenius-type expression by one term in 1/T² and we have given some physical meaning to the new related coefficients for which it is found that they depend closely on the number of acid hydrogen atoms in the polyacid for the corrosion and passivation of the Nickel based metallic glass alloy of the composition Ni_82.3Cr₇Fe₃Si_4.5B_3.2. Moreover, we can consider that the deviation to the Arrhenius linear behavior as a super-Arrhenius behavior In addition, a mathematical analysis of the trend of experimental scatter points of the charge transfer resistance with temperature permits us to reveal an interesting homographic behavior which leads us to suggest an original empirical model with only two optimal adjustable parameters, as well as a new pseudo-power dependence of the number of hydrogen atoms in the polyacid.

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

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.