Non-Arrhenius behaviour

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. 

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]. 

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. 

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... 

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.

As also shown in Figure 4, the transport properties of water display a strongly non-Arrhenius behaviour at subzero temperatures. Thus, the viscosity of water, when extrapolated to -90°C, is of the same order as that of glycerol at room temperature. This rapid viscosity rise at low temperatures plays a role in limiting the cooling rates that can be achieved in practice. 

As discussed for DSC earlier, disadvantages of microcalorimetry include its chemical non-specificity and also a possibility that unpredictable physical changes might lead to non-Arrhenius behaviour. Such changes include unexpected phase transformations, water transfer between excipients and drugs, improperly defined rate constants, and parallel reactions of the same order but with different activation energies. 

In what follows we review very briefly some of the results obtained in recent experiments at low and ultra-low temperatures. Examples are chosen to illustrate the diversity of non-Arrhenius behaviour which has been discovered in our kinetic experiments below room temperature. In the final section, we attempt to review what has been learnt in the limited number of experiments so far and to provide some cautious guidance to modellers of interstellar clouds as to how to estimate reasonable rate constant values for reactions between neutral species. 

In this section, for a number of selected reactions, I compare the results of kinetic experiments with those of theoretical calculations, especially those using transition state methods. A disproportionately large fraction of the reactions selected are those that my colleagues and I have worked on in the past. The other criteria for inclusion have been to select reactions for which rate constants have been measured over a wide range of temperature, and which exhibit non-Arrhenius behaviour. Although in the previous section I have emphasised bimolecular reactions, I choose to start this comparison of experimental and theoretical data by considering unimolecular reactions. 

In this chapter I have sought to show that the temperature-dependence of the rate constants for elementary reactions are frequently not well-matched by the simple Arrhenius equation, eqn (1.2)— it could be said that we live in a post-Arrhenius age . The relatively common observation of non-Arrhenius behaviour has been brought about largely by advances in experimental methods and especially the ability to measure rate constants more accurately, for a wider range of reactants and over a wider range of temperature than before. Some examples of reactions that exhibit non-Arrhenius behaviour are considered in Section 1.4. 

M. Celina, K.T. Gillen, and R.A. Assink, Accelerated aging and lifetime prediction Review of non-arrhenius behaviour due to two competing processes. Polymer Degradation and Stability, 90(3) 395-404, December 2005. 

Celina, M., Gillen, K., Assink, R. Accelerated aging and lifetime prediction review of non-Arrhenius behaviour due to two competing processes. Polym. Degrad. Stab. 90, 395-404... 

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