Temperature-independent factor

Like b0, the temperature independent factor of the velocity coefficient, fco, can be calculated theoretically. For a kinetic estimate, we assume that fc0 equals the number of adsorption places multiplied by the probability that an adsorbed molecule reacts when in possession of the activation energy. This probability, according to usual assumptions, is a vibration frequency v of the order of 1013 sec-1. Thus, we arrive at ... 

Attention was drawn by Semenov to the fact that explosive substances are characterized by a high value of the activation energy E, as well as of the temperature-independent factor B. 

This, however, confronts us with the fundamental problem expressed by Beeck as a Challenge to the physicist, i.e., how to account for the fact that the activity differences are located in the temperature-independent factors. The problem as stated by Beeck appeared the more mysterious, since it was reported for films that the dependency of the rate on the pressures of the reactants was essentially the same for all the metals discussed here, being first order in the hydrogen pressure and zero order in the ethylene pressure. Our results, however, show differences that appear significant. The exponents connected with the hydrogen and ethylene pressure as they occur in Equation (42) were calculated in the same way as indicated for Ni and tabulated in Table IX. There appears to be a trend in n, the exponent... 

Hence, it is not surprising that the relative activity of the metal is observed in the temperature-independent factor, while it can also be understood that there is no substantial variation of E from metal to metal. A necessary demand arising from this explanation, however, is that the kinetics have to be different for metals with different activities, an expectation that is confirmed by the experimental results. 

KIEs to transition state structure, has a very broad maximum. Unfortunately, this means that these KIEs will not be useful in determining transition state structure in, S n2 reactions. The temperature-independent factor (imaginary frequency ratio) and the tunnelling contribution to the KIE ranged from 57.5 to 69.0% of the total KIE. 

In the first and second equation, E is the energy of activation. In the first equation A is the so-called frequency factor. In the second equation AS is the entropy of activation, the interatomic distance between diffusion sites, k Boltzmann s constant, and h Planck s constant. In the second equation the frequency factor A is expressed by means of the universal constants X2 and the temperature independent factor eAS /R. For our purposes AS determines which fraction of ions or atoms with a definite energy pass over the energy barrier for reaction. 

The plot of Fig. 14 shows a straight line relationship from which an energy of activation of 27,400 cal./mol is calculated for the oxidation of tantalum. The temperature independent factors e s /B are evaluated from Equation (5) mentioned above. A similar analysis of the data on columbium oxidation yields an activation energy of 22,800 cal./mol. 

Figure 29. Dielectric spectra of several type A glass formers shifted by a temperature independent factor k to provide coincidence at highest frequencies, i.e., in the region of the excess wing (compiled from [137,142,230]) note that although the spectra exhibit virtually the same excess wing the a-peak itself is different along different a values of the GGE distribution, cf. Eq. 36.

The temperature-independent factor A has now been given a physical significance and an estimated magnitude. 

A plot of (7) against T shows that for an atomic weight 10 and the potential curve of Fig. the quantum correction becomes insignificant above 0° C. It seems, therefore, that apart from reactions involving H, the tunnelling effect cannot be made responsible at ordinary temperatures for any large decrease of the temperature independent factor. 

These considerations have a particular reference to the dissociation of N2O in which the temperature independent factor was found to be about io times the value obtained by estimating (4). This was taken, for awhile, as an indication of the non-adiabatic nature of the reaction,2 which was suggested by the fact that it violates the spin conservation law. However, it has been shown by Zener on the basis of the interaction integrals obtained from the intensities of forbidden... 

Both the Rouse and Zimm models, as well as other molecular models to be discussed in Chapter 9, tacitly assume that the relaxation time associated with each mode has the same temperature dependence. Each mode s relaxation time is the product of temperature-independent factors and the... 

The assumed temperature-independent factor Sn can be determined from Eq. (6.70) by the least squares fitting procedure or by testing the linearity of the rearranged Eq. (6.70) as it was proposed by Bratland et al. (1966)... 

The use of the Slater (/w2//ti)W as the temperature independent factor does not obviously follow from a consideration of the potential energy surface, and thus its use must be regarded as an intermingling of the Eyring and the Slater approaches. 

We now consider the same model for the reaction but calculate the temperature independent factor from the considerations with regard to potential surfaces given in Section III. In addition, it is convenient to avoid the calculation of the frequency shift, Avv and evaluate the quantum correction through an approximation (see Eq. 11.30) based on the method of the first quantum correction. One. obtains at 4006K... 

This same quantum correction can be used with the Slater coordinate for the temperature independent factor. This would give kjnk3 = 1.045 at 400°K, and would not change the conclusions to be reached. 

The method was to calculate the concentration of molecules in the van der Waals layer by statistical mechanics, and to formulate the rate of exchange by activated complex theory (52). The results for the temperature-independent factor B,ink=B for a catalyst area of 1 cm., ... 

We j hall first consider the isotope effects to be expected from an oversimplified model of the activated complex namely, all frequencies in the activated complex are identical with those in the normal molecule except the C—C stretching frequency, which becomes a translation. The temperature independent factor will, first, be calculated from the Slater coordinate. 

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