Eyring expression

The temperature dependence of the corrected diffusivity follows the usual Eyring expression... 

The strain rate dependence of the yield stress is shown at various temperatures in Fig. 20. To go further in the analysis, it is interesting to use the Eyring approach presented in Sect. 2.2.1.1. For this purpose, the ratio oy/T, K is plotted versus log( , s-1) at various temperatures in Fig. 21. A linear dependence is observed at each temperature, in agreement with the Eyring expression. However, the slopes show two different temperature regimes at low and high temperatures. Of course, the activation volume, Vo, directly related to the slope, reflects the change in behaviour, as shown in Fig. 22. At low temperature, the activation volume is small (around 0.1 nm3) and independent of temperature, whereas it increases rapidly above room temperature... 

Fig. 1. The classical (a) and the semi-classical (b-d) representations of the Marcus theory for X — 1.0 eV at T = 300 K. In the classical expression (Eq. 1), X determines both the position of the maximum and the breadth of the parabola. The maximum keI is determined by the frequency factor (Z, here taken as 6 x 10 1 s ) in the Eyring expression (ket = KZexp( — AGlJkbT) where k is the transmission coefficient, usually taken to be unity). In the semi-classical approach the reorganization energy is explicitly divided into Xh (here equal 0.2 eV) and 2a (0.8 eV). The value of V is chosen to...

Zwolinski and Eyring expressed the deviation of the actual rate from the equilibrium rate by forming the ratio jT of the above calculated rate to the rate determined on the assumption... 

In a fiormal analogy to the expressions for the thenuodynamical quantities one can now defiine the standard enthalpy // and entropy ofiactivation. This leads to the second Eyring equation. ... 

The effect of temperature on diffusivities in zeolite ciystals can be expressed in terms of the Eyring equation (see Ruthven, gen. refs.). 

Eyring s transition-state reaction rate expression is... 

According to the theory of rate processes (Eyring et al., 1941), reaction rate constants are determined by the expression... 

Since the discovery of the deuterium isotope in 1931 [44], chemists have long recognized that kinetic deuterium isotope effects could be employed as an indicator for reaction mechanism. However, the development of a mechanism is predicated upon analysis of the kinetic isotope effect within the context of a theoretical model. Thus, it was in 1946 that Bigeleisen advanced a theory for the relative reaction velocities of isotopic molecules that was based on the theory of absolute rate —that is, transition state theory as formulated by Eyring as well as Evans and Polanyi in 1935 [44,45]. The rate expression for reaction is given by... 

The idea that an activated complex or transition state controls the progress of a chemical reaction between the reactant state and the product state goes back to the study of the inversion of sucrose by S. Arrhenius, who found that the temperature dependence of the rate of reaction could be expressed as k = A exp (—AE /RT), a form now referred to as the Arrhenius equation. In the Arrhenius equation k is the forward rate constant, AE is an energy parameter, and A is a constant specific to the particular reaction under study. Arrhenius postulated thermal equilibrium between inert and active molecules and reasoned that only active molecules (i.e. those of energy Eo + AE ) could react. For the full development of the theory which is only sketched here, the reader is referred to the classic work by Glasstone, Laidler and Eyring cited at the end of this chapter. It was Eyring who carried out many of the... 

The Marcus classical free energy of activation is AG , the adiabatic preexponential factor A may be taken from Eyring s Transition State Theory as (kg T /h), and Kel is a dimensionless transmission coefficient (0 < k l < 1) which includes the entire efiFect of electronic interactions between the donor and acceptor, and which becomes crucial at long range. With Kel set to unity the rate expression has only nuclear factors and in particular the inner sphere and outer sphere reorganization energies mentioned in the introduction are dominant parameters controlling AG and hence the rate. It is assumed here that the rate constant may be taken as a unimolecular rate constant, and if needed the associated bimolecular rate constant may be constructed by incorporation of diffusional processes as ... 

Eyring also stated (Ref 3> p 98, as quoted in Ref 4, p 201) that release of energy by lateral expansion of the products permits stabilization of one of the sub-ideal states in the shock front. Of the hydro-dynamic equations only that of continuity, expressing the constancy of mass velocity, is perturbed by the expansion... 

Eyring and co-workers (G5) and others have shown that rate processes are determined by the activation energy (free-energy change needed to initiate the process) and by the temperature. For nucleation the expression becomes... 

The general equation expressing the rate constant of a reaction is the Eyring equation... 

According to Eyring s absolute rate theory (1), in which there is postulated the establishment of a quasiequilibrium between the reactants and an active complex, the rate constant may be expressed as... 

This expression has seen many developments through the years and has evolved into the so-called London-Eyring-Polanyi-Sato (LEPS) surface in which expression (30) is multiplied by an empirical factor (1 + k)" which is supposed to take account of overlap effects (90). The coulomb and exchange integrals are calculated from the singlet and triplet potential curves of the diatomics, given by the expressions... 

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