Arrhenius factor measurement

The measured growth rates are illustrated by the circles in Fig. 7. The interface velocity is plotted versus the interface temperature T. The value of T is always greater than Tq because of the release of the latent heat at the interface. Dimensionless units for T and the velocity are used here. The maximum velocity corresponds to 80m /s for argon. The most surprising aspect is the rapid crystallization at low temperatures. Most materials exhibit sharply reduced rates at low temperatures, as expected for an activated growth process. That is, the kinetics can be represented as the product of an Arrhenius factor F(T) and a term that accounts for the net production of crystalline material as a result of the atoms ordering and disordering at the interface,... 

A certain kind of radical transfer can be modelled by the transfer of a hydrogen atom from an alkane molecule to a small alkyl radical. This reaction was studied in detail in the gas phase. With hydrocarbon partners, heats of reaction are a fairly safe measure of the relative rate of transfer, as the pre-exponential Arrhenius factors remain approximately constant for a series of transfers to a given radical. Tabulated thermodynamic data indicate, however, [31, 32] that the correlation between the heat of reaction and the transfer rate is not valid for reactions of a radical with polar substrates [32, 33], In condensed phases, transfer reactions have not been sufficiently studied. Polymerizations themselves are the source of the most valuable, though incomplete, information. 

For C-H bond cleavage, Equation (4) predicts a KIE equal to kH/kD 7 at room temperature. In the limit where the semiclassical theory is valid, experimentalists measure the Schaad-Swain exponent, ln(kH/A T)/ln(kD/kT). In the special case that the pre-Arrhenius factor A is the same for all isotopes (which is not true in most cases) then semiclassical theory predicts for this exponent a value 3.26. Deviations from this value are often interpreted as signs of increased tunneling, but in our opinion this line of argument is based on an oversimplified model of quantum transfer in condensed phases. Note that in tunneling reactions where the ratio Au/AD l, the semiclassical theory predicts an exponent that is not equal to 3.26 and is temperature dependent. 

Figure 6.20(b) depicts the case where the formation of the reactive state involves a positive entropy and enthalpy. Such a case could happen if the reaction partners AH and B are involved in strong interactions with other species. For example, AH could be hydrogen bonded to any proton acceptor, or B to any proton donor, which requires this interaction to be broken before the partners can react. Now, the reacting state predominates at high temperatures and the non-reactive state at low temperatures. Only at high temperatures is the true Arrhenius curve measured, exhibiting a normal pre-exponential factor of about 13. At low temperatures, the... 

If measurements are carried out over a wide range in l/T there is no reason to expect that either the Arrhenius factor or the activation energy is independent of temperature. Therefore a strict definition of the activation energy... 

The classical experiment tracks the off-gas composition as a function of temperature at fixed residence time and oxidant level. Treating feed disappearance as first order, the pre-exponential factor and activation energy, E, in the Arrhenius expression (eq. 35) can be obtained. These studies tend to confirm large activation energies typical of the bond mpture mechanism assumed earlier. However, an accelerating effect of the oxidant is also evident in some results, so that the thermal mpture mechanism probably overestimates the time requirement by as much as several orders of magnitude (39). Measurements at several levels of oxidant concentration are useful for determining how important it is to maintain spatial uniformity of oxidant concentration in the incinerator. 

Activation Parameters. Thermal processes are commonly used to break labile initiator bonds in order to form radicals. The amount of thermal energy necessary varies with the environment, but absolute temperature, T, is usually the dominant factor. The energy barrier, the minimum amount of energy that must be suppHed, is called the activation energy, E. A third important factor, known as the frequency factor, is a measure of bond motion freedom (translational, rotational, and vibrational) in the activated complex or transition state. The relationships of yi, E and T to the initiator decomposition rate (kJ) are expressed by the Arrhenius first-order rate equation (eq. 16) where R is the gas constant, and and E are known as the activation parameters. 

It is important to distinguish clearly between the surface area of a decomposing solid [i.e. aggregate external boundaries of both reactant and product(s)] measured by adsorption methods and the effective area of the active reaction interface which, in most systems, is an internal structure. The area of the contact zone is of fundamental significance in kinetic studies since its determination would allow the Arrhenius pre-exponential term to be expressed in dimensions of area"1 (as in catalysis). This parameter is, however, inaccessible to direct measurement. Estimates from microscopy cannot identify all those regions which participate in reaction or ascertain the effective roughness factor of observed interfaces. Preferential dissolution of either reactant or product in a suitable solvent prior to area measurement may result in sintering [286]. The problems of identify-... 

The temperature dependence of a rate is often described by the temperature dependence of the rate constant, k. This dependence is often represented by the Arrhenius equation, /c = Aexp(- a/i T). For some reactions, the temperature relationship is instead written fc = AT" exp(- a/RT). The A term is the frequency factor for the reaction, which reflects the number of effective collisions producing a reaction. a is known as the activation energy for the reaction, and is a measure of the amount of energy input required to start a reaction (see also Benson, 1960 Moore and Pearson, 1981). 

We wish to account for (i.e., interpret) the Arrhenius parameters A and EA, and the form of the concentration dependence as a product of the factors c (the order of reaction). We would also like to predict values of the various parameters, from as simple and general a basis as possible, without having to measure them for every case. The first of these two tasks is the easier one. The second is still not achieved despite more than a century of study of reaction kinetics the difficulty lies in quantum mechanical... 

Temperature is a direct measure of the heat energy available at release (Edwards and Lawrence, 1993). Temperature is the most important factor influencing reaction rate as shown in the Arrhenius equation. In practice an increase in temperature of 10°C will increase a specific reaction rate by two to four times depending on the energy of activation (CCPS, 1995a). 

Following the conceptual idea introduced by Milliken [68], Takahashi and Glassman [53] have shown, with appropriate assumptions, that, at a fixed temperature, i/c could correlate with the number of C—C bonds in the fuel and that a plot of the log ipc versus number of C—C bonds should give a straight line. This parameter, number of C—C bonds, serves as a measure of both the size of the fuel molecule and the C/H ratio. In pyrolysis, since the activation energies of hydrocarbon fuels vary only slightly, molecular size increases the radical pool size. This increase can be regarded as an increase in the Arrhenius pre-exponential factor for the overall rate coefficient and hence in the pyrolysis and precursor formation rates so that the C/H ratio determines the OH concentration [12]. The 4>c versus C—C bond plot is shown in Fig. 8.14. When these... 

Fig. 4.10 a Characteristic relaxation times determined from dielectric measurements [137] (diamonds), and from NSE spectra at (triangles) for triol (open symbols) and PU (solid symbols). The full lines correspond to Vogel-Fulcher and the dotted lines to Arrhenius descriptions, b Relaxation times from NSE spectra have been arbitrarily multiplied by a factor 6 for triol and 40 for PU to build a normalized relaxation map. (Reprinted with permission from [127]. Copyright 2002 Elsevier)... 

Fig. 4.20 Temperature dependence of the average relaxation times of PIB results from rheological measurements [34] dashed-dotted line), the structural relaxation as measured by NSE at Qmax (empty circle [125] and empty square), the collective time at 0.4 A empty triangle), the time corresponding to the self-motion at Q ax empty diamond),NMR dotted line [136]), and the application of the Allegra and Ganazzoli model to the single chain dynamic structure factor in the bulk (filled triangle) and in solution (filled diamond) [186]. Solid lines show Arrhenius fitting curves. Dashed line is the extrapolation of the Arrhenius-like dependence of the -relaxation as observed by dielectric spectroscopy [125]. (Reprinted with permission from [187]. Copyright 2003 Elsevier)...

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