Eyring’s equation

Some workers in this field have used Eyring s equation, relating first-order reaction rates to the activation energy d(7, whereas others have used the Arrhenius parameter E. The re.sults obtained are quite consistent with each other (ef. ref. 33) in all the substituted compounds listed above, AG is about 14 keal/mole (for the 4,7-dibromo compound an E value of 6 + 2 keal/mole has been reported, but this appears to be erroneous ). A correlation of E values with size of substituents in the 4- and 7-positions has been suggested. A/S values (derived from the Arrhenius preexponential factor) are... 

Eyring s equation may be regarded as a good phenomenological description of yield stress as a function of test parameters (T, e), but it cannot be related to physical processes at the molecular scale. The equation can be used at high e for impact properties and for the prediction of the ductile brittle transition temperature. Eyring s equation can be modified with two sets of parameters if two relaxations are involved in the range of temperatures and strain rates (Bauwens-Crowet et al., 1972). 

Eyring s equation is the only relationship describing, with a good agreement, the dependence of yield stress on both temperature and strain rate. Unfortunately, this equation is phenomenological, and the determined constants have no physical meaning. 

The macroscopic upper yield stress is lineary related to Tg — T for a given strain rate, and can be adjusted with Argon s, Bowden s, and Kitagawa s models. The influence of strain rate is well represented by the phenomenological Eyring s equation. 

There are two models that quantitatively describe the relationship between temperature and rate constants, the Arrhenius theory and the Eyring theory [2, 3], Engineers prefer the Arrhenius equation because it is slightly simpler, while kineti-cists prefer the Eyring equation because its parameters (entropy and enthalpy of activation, AS and AH, respectively) can be interpreted more directly. Here, we will use Eyring s equation. 

Further, eqn. (8) may easily be integrated over a Boltzmann distribution to recover Eyring s equation [7] (still neglecting total rotation). It was shown earlier that... 

This result was obtained by expanding exp (—h v /fcBT) in a power series and keeping only the first two terms. Thus finally we obtain Eyring s equation for the rate constant ... 

However, Eq. (14.20) fails when it tries to describe the yield behavior of polymers over a wide range of temperatures. This has led to a modification of the model (20,21) that assumes that the deformation process involves two different flow processes that have different values of AE and V. Finally, another simple modification of Eyring s equation [Eq. (14.20)] (22) is to include the effect of hydrostatic pressure. This modification reflects the different yield behavior of polymers observed in tension and those in compression. 

Eyring s equation assumes that a thermodynamic equilibrium exists between the transition state and the state of the reactants and that the reaction rate is proportional to the concentration of particles at the high-energy transition state, k accounts for the fraction of molecules going into product state and AG represents the difference between Gibbs energy of transition state and reactants. If AG is expressed in terms of enthalpy (AH ) and entropy (AS ) of activation, fromEq. 3.114 ... 

Finally, it is important to add some comments on the advantages of the above derivations of Eyring s equation (91.Ill) or (94.Ill) The usual derivation of these equations (with % = 1) is based on... 

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. 

We note that additional approximations are not necessary to represent the equations of the adiabatic rate theory in a thermodynamic form (94.Ill) of Eyring s expression, as seen in a comparison with the exact equations (107.Ill) and (130.Ill), as well as with the approximate ones (135.Ill) and (138.Ill), which correspond to the high temperature limits of the former. There is, of course, an essential difference between the free energies of activation in Eyring s equation and the two kinds of formulations of the adiabatic theory this difference results from the varying definitions of the activated complex in each of these cases. 

III). In conditions of vibration-rotational adiabaticity, will represent an apparent tunneling correction which is necessary only to obtain the correct values of the rate constant when using the collision theory expression (51.Ill), instead of Eyring s equation (67.Ill) (corrected by the real tunneling factor ). 

The relations (6.IV) can obviously be directly derived from Eyring s equation (98.Ill) of the activated complex theory under the assumption that zf = Z, which means that the "activated complex"... 

Eyring s equation t ac represent the real tunneling correction for an electronically adiabatic reaction only if = 1. ... 

Hirschfelder, Curtiss and Bird have shown that Eyring s equation of state for dense... 

Crazing can be considered as a type of inhomogenous localized yielding. A major factor affecting ESC is yield strength CTj, and this can be expressed in terms of thermally activated shear flow, as described by Eyring s equation ... 

Eyring and Wynne-Jones (99) have extended Eyring s equation for the diffusion constant by introducing the entropy of activation and the heat of activation The... 

Table 111. Degrees of freedom in acquiring energy of activation far diffusion from Wheeler s equation, and the entropy of activation from Wynne-Jones arid Eyring s equation...

The activation energy in Eyring s equation has to be corrected by the effect of the electrochemical potential jump through the adlayer (compact layer). This potential can be, for example, estimated from [14,15]... 

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