Arrhenius behaviour

The mobility of the boundary should be closely related to the volume diffusion process in the solid, and would therefore be expected to show an Arrhenius behaviour with an activation energy close to the volume diffusion activation energy. 

For temperatures above 71, the deviation from an Arrhenius behaviour... 

Experiments were also performed at various temperatures in the presence of DPPH. Although the data fitted the conventional Arrhenius relationship (Eq. 5.39), it gave an activation energy which was negative i. e. inverse Arrhenius behaviour. 

Fig. 4.22 Arrhenius representation of the relaxation rates obtained from fitting stretched exponentials to the spectra of PB at Q=1.88 A" at different temperatures. The three symbols represent three different sets of experiments carried out in separate experimental runs. The solid line displays the viscosity time scale. The dashed line indicates the Arrhenius behaviour of the low-temperature branch. (Reprinted with permission from [188]. Copyright 1992 The American Physical Society)...

The feasibility of hydrogen abstraction at the peptidyl a-carbon hydrogen bond by 1,4-aryl diradicals has been determined by examining a model reaction, i.e. abstraction of deuterium from dideuterioglycine by aryl radicals. The results have biological implications for the reactivity of the enediyne anti-tumour antibiotics with proteins. The non-Arrhenius behaviour of hydrogen-abstraction reactions by radicals has been investigated. For a number of reactions studied the enthalpy of activation was found either to increase or to decrease as a function of temperature. 

Isotope effects and element effects associated with hydron-transfer steps during methoxide promoted dehydrohalogenation reactions of jo-CF3C6H4C HClCH2X (X=Br, Cl, or F) have also been discussed, with regard to distinction between E2 and multi-step pathways. The Arrhenius behaviour of hydrogen isotope effects was used to calculate the amounts of internal hydrogen return associated with the two-step mechanism. 

The single particle auto-correlation time tc in Eq. 9 can, of course, exhibit also a non-critical temperature dependence. Consider a set of independent hydrogen bonds with symmetric double well potentials and a barrier a between the wells. In this case the motion is thermally activated and tc shows an Arrhenius behaviour ... 

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]. 

Since k2 is a constant, the dependence of k,x, on temperature should show strict Arrhenius behaviour, giving a linear plot of loge kfx, versus 1 IT. 

The equation for the high pressure rate constant predicts strict Arrhenius behaviour, and also a non-linear plot for l/kobs versus 1/[A], both in agreement with experiment. 

However, there is no molecular trapping in this system, so the Arrhenius behaviour does not come from full or partial thermalization prior to dissociation. A simple analytic model provides an explanation for this behaviour. We assume that the main effect of increasing the energy in the surface oscillator is to downshift the threshold for the rotational or vibrational transition. If we make a linear approximation... 

Rate coefficients of elementary processes have been assumed to follow an Arrhenius behaviour. The values of kinetic parameters were chosen from the literature (reviews and tables), or calculated from the kinetic parameters of reverse reactions, or by structural analogies. A geometric mean relationship has been assumed for crossed recombination rate coefficients. In conclusion, both the model and its parameters have been built up a priori, without any model fitting to experimental data. Edelson and Allara [71] qualify these models as fundamental as opposed to fitted models. 

The 2-site 120° jump motion for the basal molecules switches between these two hydrogen bonding arrangements and clearly requires correlated jumps of the hydroxyl groups of all three basal molecules. On the assumption of Arrhenius behaviour for the temperature dependence of the jump frequencies, the activation energies for the jump motions of the apical and basal deuterons were estimated to be 10 and 21 kj mol-1, respectively. This dynamic model was further supported by analysis of the dependence of the quadrupole echo 2H NMR lineshape on the echo delay and consideration of 2H NMR spin-lattice relaxation time data. 

Lomellini P (1992) Williams-Landel-Ferry versus Arrhenius behaviour polystyrene melt viscoelasticity revised. Polymer 33 4983-89. 

Mechanistic studies of alkoxide-promoted dehydrohalogenations of C6H5CH2CH2X and various derivatives YC6H4CHX CH2X and YC6H4CHX CHp2X (where X = Br, Cl, or F and X = Br or Cl) have been extended to include MeO /MeOH-promoted dehydrohalogenations of (8a-c) and interpreted with reference to Scheme 1 The Arrhenius behaviour of the primary KIEs, = 3.40, 3.49, 2.19 and... 

The decreasing values of A from I to III are consistent with the extra loss of entropy of activation (ca 18JK moF per lost rotation) in the emerging electron-delocalized radicals. The data base is probably reliable to a factor of 2 between 600 and 1200 K unless there is a very marked non-Arrhenius behaviour in i. Below 600 K, (1) is far too slow to influence events and above 1200 K, reaction (lA) will dominate unless the O2 pressure is very high (ca 20 atms) (Table 1.11). 

Theoretical efforts in this field have included the use of TST to investigate non-Arrhenius behaviour, the validity of additive empirical rate expressions and attempts have been made to calculate rate coefficients for these relatively simple reactions from first principles. We conclude Section 2.3.5 with a brief review of abstractions by other radical species and a comparison of time-resolved measurements with alternative techniques. 

Transition state theory can also give us some insight into the non-Arrhenius behaviour of rate coefficients as epitomized by Fig. 2.6 for the OH + ethane reaction. Curvature of the Arrhenius plot can arise from a number of factors. 

Arrhenius behaviour in ethyne hydrogenation over palladium catalysts. Appl Catal 55 L5... 

Th( nsactions show a non-linear Arrhenius behaviour. For the O + CH4 reaction, this is attributed to spin-orbit interactions and tunneling. For the H + CH4 reaction, tunneling plays the major role. At high temperature, the curvature is also caused by the vibrational excitations of the CH4 reactant, which can significantly enhance the reaction. 

Dielectric measurements combined with thermal analysis revealed two transitions a, a glass-rubber transition between 295-340 K (10 Hz), and B, a sub-glass transition exhibiting Arrhenius behaviour. 

The parallel reaction model [99] assumes that the reaction complexity can be represented by a set of independent parallel processes each with its own values of A and ,. Such a reaction system can lead to non-Arrhenius behaviour [99] so the following simplifications may be used, (i) All of the reactions are assumed to have the same pre-exponential factor and the differences in reactivity are represented by... 

Data shown in Fig. 6 lead to the following conclusions at temperatures near 0 the desorption rate demonstrates Arrhenius behaviour with the effective activation energy of 50 4 kJ/mol, which is much greater than the value predicted by the simple MP mechanism (25-35 kJ/mol). Also, at temperatures above -40 C, the ice vaporization rate exceeds the desorption rate predicted by the simple MP model. In summary, the mobile precursor mechanism, as formulated by Somorjai and Davy, fails to describe the desorption kinetics of ice at temperatures near its melting point. 

Fig. 17. The Arrhenius plots for the rate constants A (diamonds), A/3 (stars), and SAciass (fuU triangles) for 8, reported in Ref. 51. The arrow marks the singularity on the Adass (T) curve the occurrence of which is an indirect indication of the inadequacy of the AB model to the system investigated. On the other hand, the kifT) and kfT) curves are smooth. A non-Arrhenius behaviour of kifT) is remarkable.

It may be noted that if Sc A/r /k (=B) in AG equation were to be a constant, it requires that liquids exhibiting Arrhenius behaviour at high temperature possess constant value of Sc - temperature independent configurational entropy, which is not correct. 

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