Preexponential factor

A more recent model for the preexponential factor including viscous flow across the solid-liquid interface is [14]... 

For example, van den Tempel [35] reports the results shown in Fig. XIV-9 on the effect of electrolyte concentration on flocculation rates of an O/W emulsion. Note that d ln)ldt (equal to k in the simple theory) increases rapidly with ionic strength, presumably due to the decrease in double-layer half-thickness and perhaps also due to some Stem layer adsorption of positive ions. The preexponential factor in Eq. XIV-7, ko = (8kr/3 ), should have the value of about 10 " cm, but at low electrolyte concentration, the values in the figure are smaller by tenfold or a hundredfold. This reduction may be qualitatively ascribed to charged repulsion. 

With the aid of (B1.25.4), it is possible to detennine the activation energy of desorption (usually equal to the adsorption energy) and the preexponential factor of desorption [21, 24]. Attractive or repulsive interactions between the adsorbate molecules make the desorption parameters and v dependent on coverage [22]- hr the case of TPRS one obtains infonnation on surface reactions if the latter is rate detennming for the desorption. 

A preexponential factor in which the frequency of chain addition increases with the surface area of the embryo. This, in turn, increases with increasing r. 

The Arrhenius equation relates the rate constant k of an elementary reaction to the absolute temperature T R is the gas constant. The parameter is the activation energy, with dimensions of energy per mole, and A is the preexponential factor, which has the units of k. If A is a first-order rate constant, A has the units seconds, so it is sometimes called the frequency factor. 

Tests of the collision theory consist of comparisons between calculated and experimental values of the preexponential factor, the comparison often being made in terms of a ratio P defined by... 

The preexponential factor of the Arrhenius equation is approximately given by... 

Collision theory leads to this equation for the rate constant k = A exp (-EIRT) = A T exp (,—EIRT). Show how the energy E is related to the Arrhenius activation energy E (presuming the Arrhenius preexponential factor is temperature independent). 

In Eq. (6-1), A is called the preexponential factor and is the activation energy. In this section we are concerned with the experimental evaluation of A and and with their uses. 

A more interesting possibility, one that has attracted much attention, is that the activation parameters may be temperature dependent. In Chapter 5 we saw that theoiy predicts that the preexponential factor contains the quantity T", where n = 5 according to collision theory, and n = 1 according to the transition state theory. In view of the uncertainty associated with estimation of the preexponential factor, it is not possible to distinguish between these theories on the basis of the observed temperature dependence, yet we have the possibility of a source of curvature. Nevertheless, the exponential term in the Arrhenius equation dominates the temperature behavior. From Eq. (6-4), we may examine this in terms either of or A//. By analogy with equilibrium thermodynamics, we write... 

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... 

For copolymers of acrylamide with sodium acrylate, the preexponential factor K and exponent a of [tj] = KM depend on copolymer composition (Table 3). 

Several points are worth noting about these formulae. Firstly, the concentrations follow an Arrhenius law except for the constitutional def t, however in no case is the activation energy a single point defect formation energy. Secondly, in a quantitative calculation the activation energy should include a temperature dependence of the formation energies and their formation entropies. The latter will appear as a preexponential factor, for example, the first equation becomes... 

Finally, the total preexponential factor includes the stoichimetry deviation represented by c°(, or c° so an extrapolated Arrhenius plot will show an intercept which is very sensitive to composition. Experimental data will be hard to reproduce both because of stoichiometry variations and because of the slow approach to thermal equilibrium. 

The attention of the authors was particularly directed toward the increased activity of the nickel catalyst film when copper was added. This increase is revealed in a change of the initial reaction rate of copper itself and of all the alloys (except those containing 25-35% nickel) they are more active than nickel itself. A respectively similar difference was observed for the activation energy and the preexponential factor. 

Energy of Desorption, of the Order of Desorption and of the Preexponential Factor. 365... 

When the temperature of the analyzed sample is increased continuously and in a known way, the experimental data on desorption can serve to estimate the apparent values of parameters characteristic for the desorption process. To this end, the most simple Arrhenius model for activated processes is usually used, with obvious modifications due to the planar nature of the desorption process. Sometimes, more refined models accounting for the surface mobility of adsorbed species or other specific points are applied. The Arrhenius model is to a large extent merely formal and involves three effective (apparent) parameters the activation energy of desorption, the preexponential factor, and the order of the rate-determining step in desorption. As will be dealt with in Section II. B, the experimental arrangement is usually such that the primary records reproduce essentially either the desorbed amount or the actual rate of desorption. After due correction, the output readings are converted into a desorption curve which may represent either the dependence of the desorbed amount on the temperature or, preferably, the dependence of the desorption rate on the temperature. In principle, there are two approaches to the treatment of the desorption curves. 

In principle, the formal preexponential factor kd can be a function of 6 and T. However, often it is more or less correctly assumed that this dependence is but weak as compared with the terms 0 and exp(—Ed/RT), and therefore it cannot be accurately enough determined from the experimental data which usually exhibit a considerable scatter. 

In the following, the traditional treatment of the rate equation (3) will be adopted, taking the preexponential factor as a constant. Evidently, no other procedure is available at present. Even if a quantitative theory of the outlined problems were available, mathematical difficulties would render it possible to present only selected computerized data. 

The preexponential factor determines the rate of incidence of the gas particles onto the free surface at a unit pressure and has a dimension of (mole sec g-1 cm-1). 

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