Non-Arrhenius dependence

In fact, with small particles or clusters, a range of excited state lifetimes could be observed by spectroscopic methods . The observed non-Arrhenius dependence indicated the importance of multiphonon electron tunnelling, probably to preexistent traps. The shorter lifetimes observed at shorter emission wavelenths indicated significant coulombic interaction between traps. 

On average, a carrier located at can continue its motion only after thermal excitation. If all carriers were located at and a transport level existed at e = 0, the center of the DOS, the temperature dependence of the mobility should follow a non-Arrhenius dependence of the form exp[-(a/ 7)-2]. This temperature dependence has been recovered by both EMA studies and Monte Carlo simulations, although with a constant in the exponent of less than unity that accounts for the statistics of occupational energies. The predicted temperature dependence of the zero-field mobility is... 

The structure of the intermediate states in Rh7 and Rh8 has been studied recently by theoretical investigation [42], Regarding the proton translocation model, it should be noted that the excitation photon density was extremely high in the low-temperature picosecond experiments [10,35]. Therefore, the non-Arrhenius dependence of the formation rate of bathorhodopsin on temperature and the deuterium isotope effect may be results which could be detected only under intense excitation conditions. In fact, a deuterium isotope effect was not observed in the process from photorhodopsin to bathorhodopsin under weak excitation conditions [43],... 

The activation plot of relaxation time for the non-Arrhenius dependence present in the low frequency range below 80 °C (Fig. 2.11) was obtained using the empirical HN [20]. For secondary relaxations with Arrhenius behavior, we used the Cole-Cole simple model [9] to obtain the activation plot for relaxation time. Some authors [21, 61] have used the model of HN to describe relaxations in polysaccharides. However, this requires more adjustable parameters. On the other hand, several authors have shown that these secondary relaxations are well described by the simpler Cole-Cole model (HN model with = 1) this model has been successfully applied for the fitting of lateral group motions representing the [ -relaxation [18, 62-64] and for describing the motion of ions ascribed to the a-relaxation [65]. 

Historically, the free-volume concept was developed to explain the non-Arrhenius dependence of the fluidity or viscosity of liquids on temperature. " The most well-known formulation of... 

It is noteworthy that the above rule connects two quite different values, because the temperature dependence of is governed by the rate constant of incoherent processes, while A characterizes coherent tunneling. In actual fact, A is not measured directly, but it is calculated from the barrier height, extracted from the Arrhenius dependence k T). This dependence should level off to a low-temperature plateau at 7 < This non-Arrhenius behavior of has actually been observed by Punnkinen [1980] in methane crystals (see fig. 1). A similar dependence, also depicted in fig. 1, has been observed by Geoffroy et al. [1979] for the radical... 

The temperature dependence of the reaction rate constant closely (but not exactly) obeys the Arrhenius equation. Both theories, however, predict non-Arrhenius behavior. The deviation from Arrhenius behavior can usually be ignored over a small temperature range. However, non-Arrhenius behavior is common (Steinfeld et al., 1989, p. 321). As a consequence, rate constants are often fitted to the more general expression k = BTnexp( —E/RT), where B, n, and E are empirical constants. 

The dispersion of this waiting time distribution, i.e., its second central moment, is a measure that we can use to define a homogenization time scale on which the dispersion is equal to that of a homogeneous (Poisson) system on a time scale given by the torsional autocorrelation time. The homogenization time scale shows a clear non-Arrhenius temperature dependence and is comparable with the time scale for dielectric relaxation at low temperatures.156... 

Non-linear Eyring or Arrhenius dependences per se do not indicate tunneling... 

The non-Arrhenius temperature-dependence of the relaxation time. It shows a dramatic increase when the glass transition temperature region is approached. This temperature dependence is usually well described in terms of the so called Vogel-Fulcher temperature dependence [114,115] ... 

Energy transfer limitations have long been recognized to affect the rates and mechanisms of fission and association reactions (Robinson and Holbrook, 1972 Laidler, 1987). In addition, it is increasingly being recognized that many exothermic bimolecular reactions can exhibit pressure-(density)-dependent rate parameters if they proceed via the formation of a bound intermediate. When energy transfer limitations exist, the rate coefficients exhibit non-Arrhenius temperature dependencies—i.e., the plots of ln(k) as a function of l/T are curved. 

J. Troe Professor Marcus, you were mentioning the 2D Sumi-Marcus model with two coordinates, an intra- and an intermolecu-lar coordinate, which can provide saddle-point avoidance. I would like to mention that we have proposed multidimensional intramolecular Kramers-Smoluchowski approaches that operate with highly nonparabolic saddles of potential-energy surface [Ch. Gehrke, J. Schroeder, D. Schwarzer, J. Troe, and F. Voss, J. Chem. Phys. 92, 4805 (1990)] these models also produce saddle-point avoidances, but of an intramolecular nature the consequence of this behavior is strongly non-Arrhenius temperature dependences of isomerization rates such as we have observed in the photoisomerization of diphenyl butadiene. 

The effect of temperature on the photoinduced electron transfer from [Ru(bpy)3]2+ to methyl viologen solubilized in cellophane has been investigated 98 K The first-order rate constant which depends exponentially on the distance between the reactants shows a non-Arrhenius type of behavior in the temperature interval from 77 to 294 K. This phenomenon, previously found to be of great importance in biological systems, is quantitatively interpreted in terms of a nonadiabatic multiphonon non-radiative process. 

TEMPO, which is commercially available, traps carbon-centred radicals with rate constants an order of magnitude lower than the diffusion-controlled limit in most organic solvents at <120°C (e.g. kc = 3.1 x 108 dm3 mol-1 s 1 with benzyl radical at 50°Cin tert-butylbenzene) [6], and somewhat more slowly if the radical is sterically congested (e.g. kc = 5.7x 107 dm3 mol-1 s 1 with cumyl radical under the same conditions, Scheme 10.6) [6]. Non-Arrhenius behaviour or non-temperature dependence has been observed for several radical coupling reactions [6, 7]. 

Given the broad distribution of r s in rls, it is not surprising that the temperature dependence of the relaxation time corresponding to Tm is found to be non-Arrhenius. This is clearly shown for pmn in Figure 15.9, which gives results at 1 bar and 4-8 kbar. The departure from Arrhenius behavior can be generally satisfactorily described in a variety of ways many of which can be expressed [14,28] in the form of the Vogel-Fulcher (V-F) equation... 

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