Article From The Kinetic Theory Of Gases To The Kinetics Of Rate Processes On The Verge Of The Thermodynamic And Kinetic Limits Valter H Carvalhosilva by Valter H. Carvalho-silva, Nayara D. Coutinho, Vincenzo Aquilanti instant download after payment.

doi:10.3390/molecules25092098

Abstract: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.

Keywords:Maxwell–Boltzmann path; Euler’s formula for the exponential; activation; transitivity;
transport phenomena