Eyring’s reaction rate theory

According to Eyring s reaction-rate theory,90 the elementary bimolecular chemical reaction between reactant species A and B proceeds through a transition-state... 

The relation between the frequency v of local jumps, shear stress r, temperature T and macroscopic rate of creep e was well established by Eyring s reaction rate theory [41]. Let us consider that a number of vl0 thermally activated structural units attempt per unit time to cross a potential barrier Ur, the net flow v, of units that will succeed is then given by ... 

The values between brackets are calculated from Eyring s reaction rate theory in this calculation it was supposed ... 

The formation of syndiotacticity and isotacticity can be related to rate constants and ki, respectively. From Eyring s reaction rate theory one can derive that... 

Based on the known vibrational modes, as well as the energy and geometry characteristics of the studied reactions, the rate constants can be estimated according to Eyring s Transition State Theory (TST). The canonical rate constant for a bimolecular reaction at a given temperature proceeds according to the following equation ... 

This paper deals with some aspects of the theory of photochemical reactions, and necessarily makes contact with the theory of unimolecular reactions and the theory of energy transfer. The indirect influence of Henry Eyring s work is manifest in much of what follows since, in part, we are concerned with the validity of the usual concepts of unimolecular reaction rate theory. 

Henry Eyring s courses in statistical mechanics and reaction rate theory opened a new world to me when I took them in 1947-48 while a graduate student in physiology. My most vivid memories of these courses are the clarity of his lectures, his enthusiasm for his subject, and the insight he imparted into the behavior of matter at the molecular level. The brilliance of his lectures was emphasized when Henry was out of town and his post-doctoral students had to substitute for him they suffered in the inevitable comparison. 

The relations of Eyring s equations to other formulations of the statistical reaction rate theory will be discussed in the next section in the framework of the adiabatic approximation to the exact collision theory. 

The relation (184 111) could be considered a definition of a characteristic temperature Tj corresponding to Eyring s formulation of activated complex theory /20b/. However, when the non-adiabatic condition (72.Ill) is really fulfilled, equation (184.III) actually represents only a relation of equivalency of the collision and statistical formulations of reaction rate theory in the high temperature region T >T /2 to which both the formulas (177.Ill) and (183.Ill) refer. This means that if T < T, the formula (183.III) cannot be used in the temperature range TjJ/2 < T < Tj /2 for physical reasons. 

Bosse et al. [40] proposed a new model to predict binary Maxwell-Stefan diffusion coefficients Dij, based on Eyring s absolute reaction rate theory [41]. A correlation from Vignes [42], which was shown to be valid only for ideal systems of similar sized molecules without energy interactions [43] was extended with a Gibbs excess energy term... 

From a chemical viewpoint, bond scission under stress is a particular case of a un-imolecular dissociation reaction whose rate is enhanced by mechanical stress. As such, it could be treated with Eyring s transition-state theory [Eq. (37)], which permits one to bring the treatment of rate processes within the scope of thermodynamic arguments. By combining de Boer s thermodynamic formulation and the transition-state theory, Tobolsky and Eyring in 1943 developed the rate theory for thermally activated fracture of polymeric threads. When put into an Arrhenius-... 

One conclusion from this study of the simple form of Eyring s absolute reaction rate theory is that we can obtain Al/f and AS using two equations in two unknowns over a limited temperamre range. However, the more general analytical formulas show that the values are definitely dependent on the temperature. Considering the many ways to make errors in these calculations, it might occur to a... 

Figure 4.9 illustrates the sequential process of nucle-ation, which shows AG(N) against N. AG (A ) corresponds to critical nano-nucleation. In the nucleation theory, the so-called net flow of nucleation (j) plays an important role in the nucleation process as illustrated in Figure 4.9 (also see Section 4.4). As the zero-th approximation, critical nano-nucleation should become the main controlling process with an activation barrier in nucleation following Eyring s kinetic theory of absolute reaction rate (theory of absolute reaction rate) [30]. Hence,y can be given by... 

S. Glasstone, K. J. Laidler, and H. Eyring, "Theory of Rate Processes", McGraw-Hill, New York (1941) H. S. Johnston, "Gas Phase Reaction Rate Theory", Ronald Press, New York (1966) ... 

Several attempts to relate the rate for bond scission (kc) with the molecular stress ( jr) have been reported over the years, most of them could be formally traced back to de Boer s model of a stressed bond [92] and Eyring s formulation of the transition state theory [94]. Yew and Davidson [99], in their shearing experiment with DNA, considered the hydrodynamic drag contribution to the tensile force exerted on the bond when the reactant molecule enters the activated state. If this force is exerted along the reaction coordinate over a distance 81, the activation energy for bond dissociation would be reduced by the amount ... 

The transition state theory provides a useful framework for correlating kinetic data and for codifying useful generalizations about the dynamic behavior of chemical systems. This theory is also known as the activated complex theory, the theory of absolute reaction rates, and Eyring s theory. This section introduces chemical engineers to the terminology, the basic aspects, and the limitations of the theory. 

Although the formulation of such a theory has never been achieved, Eyring s absolute reaction rate model [123] has several features in common with such theory. 

The critical nucleus of a new phase (Gibbs) is an activated complex (a transitory state) of a system. The motion of the system across the transitory state is the result of fluctuations and has the character of Brownian motion, in accordance with Kramers theory, and in contrast to the inertial motion in Eyring s theory of chemical reactions. The relationship between the rate (probability) of the direct and reverse processes—the growth and the decrease of the nucleus—is determined from the condition of steadiness of the equilibrium distribution, which leads to an equation of the Fourier-Fick type (heat conduction or diffusion) in a rod of variable cross-section or in a stream of variable velocity. The magnitude of the diffusion coefficient is established by comparison with the macroscopic kinetics of the change of nuclei, which does not consider fluctuations (cf. Einstein s application of Stokes law to diffusion). The steady rate of nucleus formation is calculated (the number of nuclei per cubic centimeter per second for a given supersaturation). For condensation of a vapor, the results do not differ from those of Volmer. 

Robson Wright M., Fundamental Chemical Kinetics, Horwood, Chichester, 1999. Laidler K.J., Theories of Chemical Reaction Rates, McGraw-Hill, New York, 1969. Glasstone S., Laidler K.J. and Eyring H., Theory of Rate Processes, McGraw-Hill, New York, 1941. 

Chapter 8 provides a unified view of the different kinetic problems in condensed phases on the basis of the lattice-gas model. This approach extends the famous Eyring s theory of absolute reaction rates to a wide range of elementary stages including adsorption, desorption, catalytic reactions, diffusion, surface and bulk reconstruction, etc., taking into consideration the non-ideal behavior of the medium. The Master equation is used to generate the kinetic equations for local concentrations and pair correlation functions. The many-particle problem and closing procedure for kinetic equations are discussed. Application to various surface and gas-solid interface processes is also considered. 

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