Arrhenius behavior temperature

Exploration of the region 0 < T < requires numerical calculations using eqs. (2.5)-(2.7). Since the change in /cq is small compared to that in the leading exponential term [cf. (2.14) and (2.18)], the Arrhenius plot k(P) is often drawn simply by setting ko = coo/ln (fig. 5). Typical behavior of the prefactor k and activation energy E versus temperature is presented in fig. 6. The narrow intermediate region between the Arrhenius behavior and the low-temperature limit has width... 

The PES found by Smedarchina et al. [1989] has two cis-form local minima, separated by four saddle-points from the main trans-form minima. The step-wise transfer (trans-cis, cis-trans) - because of endoergicity of the first stage - displays Arrhenius behavior even at T < T. . The concerted transfer of two hydrogen atoms was supposed to become prevalent at sufficiently low temperatures. However, because of too high a barrier for the concerted trans-trans transition, this... 

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 conductivity of ionic liquids often exhibits classical linear Arrhenius behavior above room temperature. However, as the temperatures of these ionic liquids approach their glass transition temperatures (T s), the conductivity displays signif-... 

FIGURE 13.23 An Arrhenius plot is a graph of In A against 11T. If, as here, the line is straight, then the reaction is said to show Arrhenius behavior in the temperature range studied. This plot has been constructed from the data in Example 13.8. 

FIGURE 5.1 Arrhenius behavior over a large temperature range. (Data from Monat, J. P., Hanson, R. K., and Kruger, C. H., Shock tube determination of the rate coefficient for the reaction N2 + O- NO + N, Seventeenth Symposium (International) on Combustion, Gerard Faeth, Ed., The Combustion Institute, Pittsburgh, 1979, pp. 543-552.)... 

A good model is consistent with physical phenomena (i.e., 01 has a physically plausible form) and reduces crresidual to experimental error using as few adjustable parameters as possible. There is a philosophical principle known as Occam s razor that is particularly appropriate to statistical data analysis when two theories can explain the data, the simpler theory is preferred. In complex reactions, particularly heterogeneous reactions, several models may fit the data equally well. As seen in Section 5.1 on the various forms of Arrhenius temperature dependence, it is usually impossible to distinguish between mechanisms based on goodness of fit. The choice of the simplest form of Arrhenius behavior (m = 0) is based on Occam s razor. 

A plot of the adatom density versus T is shown in Fig. 4. An anomalous increase in the density is observed at high temperatures. The dashed line represents the adatom population that would be predicted if there were no lateral interactions. However, the LJ potential between adatoms tends to stabilize them at the higher coverages, and it is this effect that causes the deviation from Arrhenius behavior at high temperatures. A similar temperature dependence is observed in the rate of mass transport on some metal surfaces (8,9), and it is possible that it is caused by the enhanced population of the superlayer at high temperatures. 

This behavior is in between that of a liquid and a solid. As an example, PDMS properties obey an Arrhenius-type temperature dependence because PDMS is far above its glass transition temperature (about — 125°C). The temperature shift factors are... 

A method is described for fitting the Cole-Cole phenomenological equation to isochronal mechanical relaxation scans. The basic parameters in the equation are the unrelaxed and relaxed moduli, a width parameter and the central relaxation time. The first three are given linear temperature coefficients and the latter can have WLF or Arrhenius behavior. A set of these parameters is determined for each relaxation in the specimen by means of nonlinear least squares optimization of the fit of the equation to the data. An interactive front-end is present in the fitting routine to aid in initial parameter estimation for the iterative fitting process. The use of the determined parameters in assisting in the interpretation of relaxation processes is discussed. 

These results support the idea that Arrhenius curvature in the rearrangements of MeCCl60 (and MeCBr61) may be associated with QMT, although the theoretical analysis found that QMT dominated the 1,2-H(D) shift only below —73°C at higher temperatures, the classical process became more important.63 The benzylchlorocarbene case is less clear. QMT is clearly important in matrices at 10-34 K, where the KIE for 1,2-H(D) shift is 2000 59 cf. Section IV.A. However, the nonlinear Arrhenius behavior exhibited by 10a or 10b in solution is largely due to the intervention of intermolecular reactions (Section IV.C) which obscure any contribution of QMT.71... 

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. 

To see more clearly the temperature effect on ion conduction, the logarithmic molal conductivity was plotted against the inverse of temperature, and the resultant plots showed apparent non-Arrhenius behavior, which can be nicely fitted to the Vogel— Tamman-Fulcher (VTF) equation ... 

Reaction behavior that fails to agree with the Arrhenius temperature dependence. Enzyme-catalyzed reactions have been reported to display anti-Arrhenius behavior. As the temperature rises, the temperature dependence of the reaction rate does exhibit a normal Arrhenius pattern however, at elevated temperatures, the reaction velocity falls off as a result of denaturation. 

A reaction for which the mechanism changes in a temperature-dependent manner may also exhibit anti-Arrhenius behavior. See Arrhenius Equation Arrhenius Plot, Nonlinear... 

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