Arrhenius region

The bifurcational diagram (fig. 44) shows how the (Qo,li) plane breaks up into domains of different behavior of the instanton. In the Arrhenius region at T> classical transitions take place throughout both saddle points. When T < 7 2 the extremal trajectory is a one-dimensional instanton, which crosses the maximum barrier point, Q = q = 0. Domains (i) and (iii) are separated by domain (ii), where quantum two-dimensional motion occurs. The crossover temperatures, Tci and J c2> depend on AV. When AV Vq domain (ii) is narrow (Tci — 7 2), so that in the classical regime the transfer is stepwise, while the quantum motion is a two-proton concerted transfer. This is the case when the tunneling path differs from the classical one. The concerted transfer changes into the two-dimensional motion at the critical value of parameter That is, when... 

The measured dependence of kn(T) and T) consists of an Arrhenius region ( = 9.6 kcal/mol) going over to the low-temperature plateau below IlOK, where k 10 s . The isotope effect grows as the temperature drops, kn/ko — 20 at T = 100 K (fig. 15). Tunneling is promoted by the torsional vibrations of the OH and CH groups, as well as the oxy-group bending vibration. 

A few comments on (2.27), (2.29), and (1.12) are appropriate at this point. The activation energy in the Arrhenius region is independent of 17, since friction changes only the velocity at which a classical particle crosses the barrier and thus affects only the preexponential factor. However, friction reduces both kc and Tc and thereby widens the Arrhenius region. Dissipation has a noticeable effect on the temperature dependence of... 

The temperature dependence of this rate constant was measured by Al-Soufi et al. [1991], and is shown in Figure 6.17. It exhibits a low-temperature limit of rate constant kc = 8x 105 s 1 and a crossover temperature 7 C = 80K. In accordance with the discussion in Section 2.5, the crossover temperature is approximately the same for hydrogen and deuterium transfer, showing that the low-temperature limit appears when the low-frequency vibrations, whose masses are independent of tunneling mass, become quantal at Tisotope effect increases with decreasing temperature in the Arrhenius region by about two orders of magnitude and approaches a constant value kH/kD = 1.5 x 103 at T[Pg.174]

The solid-state environment prevents diffusion of radicals, so reactions are only possible with neighboring Cl2 molecules. Reaction (9.15) can therefore occur only in clusters (RH-C12) , where > 2. Products are observed only when the mole fraction of chlorine in the mixture is greater than 0.1. The k(T) dependence includes an Arrhenius region (60-90 K) in which the activation energy (2-4 kcal/mol) is 1.5-2 times larger than in the corresponding gas-phase reactions. The low-temperature plateau occurs below 40-50 K where kc is 5 x 10-3 s-1 and 2 x 10 2 s-1 for the radicals of n-butylchloride and methylcyclohexane, respectively. 

Since at the probability of transition becomes equal to m, the integral (5) is divided into two summands the second is proportional to exp (- V Kb T) and determines the constant value of the activation energy in the Arrhenius region where all transitions are the over -barrier ones. With falling temperature the contribution of transitions corresponding to the region w( ) lo increases, and apparent activation energy E, ... 

Later experimental researches have shown that the temperature relationship of X(r) comprised of the Arrhenius region and low-temperature plateau is typical of various solid-state chemical reactions. The set of kinetic data is given in Figure 4. 

The K T) relationships for photochlorination of butyl chloride [124], methylcyclohexane [125], and other hydrocarbons [126] are composed of the low-temperature plateau at T < 50 K and the Arrhenius region with... 

Table III in Section V covered this topic with examples for three polymers, showing below Til, above T/p, as well as in the region between T / and Tip. We have tried with limited success to expand this study to include a larger variety of polymers. Prior to our work, literature uniformly, except for Utracki, indicated log t]q - T data above Tg as exhibiting continuous curvature until above a temperature which we believe to be T/p where linearity was found, i.e., the so-called Arrhenius region. Several studies have been made of AH (T>Tip) as a function of chemical structure.

Ngai and Plazekl O fjnd g strong correlation between in the Arrhenius region and barriers to internal rotation. The only polymer data reported are for PE and hydrogenated PBD. This work supports our assignment of Tip as occurring when the polymer chain first overcomes intramolecular barriers to rotation. 

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