Thermally activated processes, rate

In other fracture processes, the ideas presented here would be couched somewhat differently. For instance, if fracture occurred through a rate-controlled thermally activated process, such as might apply in the dynamic... 

From the Arrhenius form of Eq. (70) it is intuitively expected that the rate constant for chain scission kc should increase exponentially with the temperature as with any thermal activation process. It is practically impossible to change the experimental temperature without affecting at the same time the medium viscosity. The measured scission rate is necessarily the result of these two combined effects to single out the role of temperature, kc must be corrected for the variation in solvent viscosity according to some known relationship, established either empirically or theoretically. 

The Monte Carlo method as described so far is useful to evaluate equilibrium properties but says nothing about the time evolution of the system. However, it is in some cases possible to construct a Monte Carlo algorithm that allows the simulated system to evolve like a physical system. This is the case when the dynamics can be described as thermally activated processes, such as adsorption, desorption, and diffusion. Since these processes are particularly well defined in the case of lattice models, these are particularly well suited for this approach. The foundations of dynamical Monte Carlo (DMC) or kinetic Monte Carlo (KMC) simulations have been discussed by Eichthom and Weinberg (1991) in terms of the theory of Poisson processes. The main idea is that the rate of each process that may eventually occur on the surface can be described by an equation of the Arrhenius type ... 

To conclude this elementary discussion, it can be said that the quantum mechanical interconversion step is a necessary and sufficient condition for the reaction to happen, although the rate is not necessarily determined by this step. It is this aspect which leaves any general quantum theory of reaction rates devoid of substance. There can be a general quantum theory of the chemical interconversion step only. Thermally activated processes form a special category for which quantum theories exist [36, 39, 67, 76]. 

The formalism for treating primary isotope effects on unimolecular processes follows analogously to the development above, once due account is taken of the difference in zero point energies on isotope substitution at the reaction site (which is reflected in an isotopic difference in the threshold energy Eo). For thermal activation the rate ratio in the high pressure limit is straightforwardly obtained from Equation 14.25. For H/D effects... 

As field evaporation is a thermally activated process, the field evaporation rate is given by... 

As with other thermally activated processes, the rate of nucleation, N, can be expressed by an Arrhenius equation with AG as the activation energy,... 

The Marcus Inverted Region (MIR) is that part of the function of rate constant versus free energy where a chemical reaction becomes slower as it becomes more exothermic. It has been observed in many thermal electron transfer processes such as neutralization of ion pairs, but not for photoinduced charge separation between neutral molecules. The reasons for this discrepancy have been the object of much controversy in recent years, and the present article gives a critical summary of the theoretical basis of the MIR as well as of the explanations proposed for its absence in photoinduced electron transfer. The role of the solvent receives special attention, notably in view of the possible effects of dielectric saturation in the field of ions. The relationship between the MIR and the theories of radiationless transitions is a topic of current development, although in the Marcus-Hush Model electron transfer is treated as a thermally activated process. 

The rate constants do not follow any type of Arrhenius-Eyring relationship, especially at low temperatures where they level off to some constant value this is thought to be an indication that electron tunnelling takes over from the thermally activated process, a concept altogether foreign to the classical Marcus model — and there would be no M.I.R. in such cases [71]. 

In the early 1980s, the classical Marcus theory was reanalyzed to consider the influence of quantum effects, notably electron tunneling [23]. Qualitatively, this gives the right direction, since it increases the observed rate constants when the thermally activated process becomes slow but it was concluded that it could not account for the quantitative discrepancies of observed Rehm-Weller type plots from Marcus behaviour. For this reason the hypothesis was retained that the... 

The growth kinetics describes the nucleation processes on the atomic scale. Thermally activated processes as adsorption, desorption, and diffusion at the surface and in the volume, nucleation, and crystallization/ recrystallization determine the film structure and can be controlled by the substrate temperature and the growth rate. Using a diagram ln(J ) over 1/ T, R being the deposition rate and T the growth temperature, three different growth modes (epitaxial, polycrystalline, and amorphous) can be... 

Thermal Activation. A slightly different formulation must be employed for excitation of M by a thermal activation process since the stabilization products cannot be measured directly and the rate of activation is related to a rate of collision. The usual Lindemann mechanism... 

We shall see that throughout the literature there has been an implicit assumption of thermally activated processes, both for cure kinetics and for the intrinsic dipolar and ionic mobilities. However, it is well known that reaction kinetics become diffusion controlled at the later stages of cure, which leads to deviations from simple rate... 

The classical inversion mechanism is a thermally activated process 2>, activation energies being determined from the variation of inversion rates with temperature. The corresponding rates for passage over the barrier may be calculated from the absolute reaction rate theory 2>. The rate constant is given by the Eyring rate equation ... 

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