Athermal reactions

In contrast to the situation in real systems, the collision probability on lattices between two units is always fixed to unity because of the structural specificity of lattices [19,58-61]. Mathematically, this can be explained by the absence of the entropy term, v/V, in the intermolecular reaction on lattices. Consider an athermal reaction, and let Nbe the number of FUs. then the respective intermolecular reaction rates of Eqs. (38) and (69) can be simplified as follows... 

The parameter is a measure of the heat evolved (or absorbed), being close to zero for athermal reactions. The nondimensional continuity equation follows ... 

Every hopping step that corresponds to an elementary step is characterized by identical activation energy values E and E, the former being for the forward reaction and the latter for the reverse one. It is therefore an athermal reaction for which (see Figure 5.2) ... 

For the endothermic reaction , the equilibrium constant decreases, and the equilibrium is shifted to the left, in the endothermic direction. For the athermal reaction (D, the change in temperature has no effect. For the endothermic reaction (D, the increase in T brings about an increase in K and the reaction is shifted to the right. 

The quantity x is called the Flory-Huggins interaction parameter It is zero for athermal mixtures, positive for endothermic mixing, and negative for exothermic mixing. These differences in sign originate from Eq. (8.39) and reaction (8.A). 

Finally, at even lower transformation temperatures, a completely new reaction occurs. Austenite transforms to a new metastable phase called martensite, which is a supersaturated solid solution of carbon in iron and which has a body-centred tetragonal crystal structure. Furthermore, the mechanism of the transformation of austenite to martensite is fundamentally different from that of the formation of pearlite or bainite in particular martensitic transformations do not involve diffusion and are accordingly said to be diffusionless. Martensite is formed from austenite by the slight rearrangement of iron atoms required to transform the f.c.c. crystal structure into the body-centred tetragonal structure the distances involved are considerably less than the interatomic distances. A further characteristic of the martensitic transformation is that it is predominantly athermal, as opposed to the isothermal transformation of austenite to pearlite or bainite. In other words, at a temperature midway between (the temperature at which martensite starts to form) and m, (the temperature at which martensite... 

There is sfill some dispufe about how microwave irradiation accelerates reactions. Besides the generally accepted thermal effects, one beheves that there are some specific (but also thermal) microwave effects, such as the formation of hot spots . There is still some controversy about the existence of non-thermal (athermal) microwave effects. At the present time, new techniques such as coohng while heating are being investigated and the problem of upscahng... 

The essential questions raised by the assumption of athermal or specific effects of microwaves are, then, the change of these characteristic terms (free energy of reaction and of activation) of the reaction studied. Hence, in relation to previous conclusions, five criteria or arguments (in a mathematical sense) relating to the occurrence of microwave athermal effects have been formulated by the author [25], More details can be found in comprehensive papers which analyze and quantify the likelihood of nonthermal effects of microwaves. This paper provides guidelines which clearly define the character of nonthermal effects. 

If AHf( NF4+) were 236 dt 10 kcal./mole, then from the known heats of formation of NF3, NF2, and NFS+ the following ion-molecule reaction would be athermal ... 

Methyl acetate may be produced by the elementary equilibrium-limited acid-catalyzed esterification reaction of methyl alcohol and acetic acid which also by-produces water. The reaction is nearly athermic, with an equilibrium constant on the order of unity. 

Table 10.3 Calculated redox energies (eV) for tetragonal La2Cu04 and Nd2Cu04. Details of reactions 1-7 are given in the text. Energies all refer to the athermal limit except for those in brackets, which refer to 1000 K.

Moreover, in order to improve the yields, the formation of poiyalkylated derivatives is limited by using excess benzene in the reaction zone, and an attempt is made, after having separated those that have been produced, to achieve their transalkylation. This operation, which is practically athermic, takes place in conditions similar to those required for alkylation and, depending on the catalyst employed, can take place in the same reactor or in a different unit. v... 

Experimental time-temperature-transformation (TXT) diagram for Ti-Mo. Xhe start and finish times of the isothermal precipitation reaction vary with temperature as a result of the temperature dependence of the nucleation and growth processes. Precipitation is complete, at any temperature, when the equilibrium fraction of a is established in accordance with the lever rule. Xhe solid horizontal line represents the athermal (or nonthermally activated) martensitic transformation that occurs when the p phase is quenched. 

If the reaction is associative, it must then be athermic except if the product has vibrational modes in which the excess energy can be dissipated or if the product is formed in an electronically excited state. In both cases, these reactions are formally exothermic and are called radiative associations [2,4,5]. If the reaction is dissociative, it can be exothermic with no restriction. 

We shall now consider the exit channels, either athermic or exothermic, for the triplet and singlet potential energy surfaces oftheSi+ -t-NHa reaction. Upon inspection of the... 

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