Nonlinear Arrhenius Plots

Nonlinear Arrhenius Plots For most organic reactions, plots of In k versus l/T are linear, and afford and A values in accord with the Arrhenius equation." However, for systems where QMT is involved, rate constants fall off less steeply than expected as temperatures are lowered, which often leads to upwardly curved Arrhenius plots as illustrated in Figure 10.2 ... 

Arrhenius plots of both 1u( h) and ln(A D) versus T were found to be curved significantly, exhibiting decreasing dependence on temperature at lower temperatures. As described in the Introduction, such nonlinear Arrhenius plots are telling indicators of QMT as temperature is lowered, the classical overbarrier reaction slows more significantly than does one that proceeds via tunneling. Later work showed that the abstraction reaction of 2 to 3 persisted at a measurable rate at least down to 28 K in frozen media, where the decay became nearly temperature independent. 

Effect of Inhibitors on Arrhenius Plots. The presence of inhibitors can lead to nonlinear Arrhenius plots as well as an increase in E. For example, jack bean urease exhibits a linear Arrhenius plot in the absence of an inhibitor, but a curved plot in the presence of 34 mM sodium sulfite . 

Finally, yet another issue enters into the interpretation of nonlinear Arrhenius plots of enzyme-catalyzed reactions. As is seen in the examples above, one typically plots In y ax (or. In kcat) versus the reciprocal absolute temperature. This protocol is certainly valid for rapid equilibrium enzymes whose rate-determining step does not change throughout the temperature range studied (and, in addition, remains rapid equilibrium throughout this range). However, for steady-state enzymes, other factors can influence the interpretation of the nonlinear data. For example, for an ordered two-substrate, two-product reaction, kcat is equal to kskjl ks + k ) in which ks and k are the off-rate constants for the two products. If these two rate constants have a different temperature dependency (e.g., ks > ky at one temperature but not at another temperature), then a nonlinear Arrhenius plot may result. See Arrhenius Equation Owl Transition-State Theory van t Hoff Relationship... 

To a first approximation over the relatively small temperature range encountered in the troposphere, A is found to be independent of temperature for many reactions, so that a plot of In k versus T l gives a straight line of slope —E.d/R and intercept equal to In A. However, the Arrhenius expression for the temperature dependence of the rate constant is empirically based. As the temperature range over which experiments could be carried out was extended, nonlinear Arrhenius plots of In k against T 1 were observed for... 

The electron mobilities at 296 and 420°K are given for several Cr-doped and -doped samples in Table II. The data for the Cr-doped crystals should be considered less accurate since a mixed-conductivity analysis was necessary in most cases (Look, 1980). However, the temperature dependences are not unlike those of conductive GaAs samples with similar impurity concentrations (1016—1018 cm-3). At least two of the crystals (MA 287/80 and MOR 56/76) appeared to be inhomogeneous, as evidenced by nonlinear Arrhenius plots. However, it is doubtful that the bulk of the data require a percolation-type conduction mechanism to be operative, as has been suggested (Robert et ai,... 

Although not directly related to TET, Scaiano [63] had also obtained linear Arrhenius plots in the 227-313 K range and KIE of 3 for 2 -methylacetophenone photoenolization, and concluded that thermal activation was dominant for this reaction. However, it was later shown that tunnelling was the dominant mechanism for this and other related reactions [64], which clearly show nonlinear Arrhenius plots at lower temperatures and a KIE of 150 at 180K. Marcantonatos exciplex mechanism was also shown to be inconsistent with experimental data on uranyl ion quenching and the role of radiationless transitions was emphasized [65]. 

Nonlinear Arrhenius plots. QMT will become relatively more important as the temperature is decreased and this will lead to curved Arrhenius plots with the curvature being more pronounced for H transfer than for D transfer. This is clearly seen in Fig. 28.1. Moreover, if the reaction rate can be monitored at sufficiently low temperatures, there will be little or no thermal activation and the reaction will only occur because of QMT. This means that at very low temperatures the rate should become essentially independent of the temperature. This is clearly the case for IJ, isomerization (see Fig. 28.1) and presumably would also have been true for IJjhad it been possible to make measurements at lower temperatures. 

Some other systems in which nonlinear Arrhenius plots have been found at subzero temperatures have been reported by Douzou (2). There is no reason at present to assume that the observed changes in... 

The rate of formation of the product of a reaction is found to give a nonlinear Arrhenius plot, the line being convex to the l/T axis (i.e., the activation energy is higher at higher temperatures). Suggest a reason for this type of behavior. 

Nonlinear Arrhenius plots were found for the reactions (148)... 

Before the evidence for tunneling can be considered as established, possible alternative explanations of a nonlinear Arrhenius plot in solution must be considered and ruled out (23). According to Caldin (23), a change of solvation with temperature, such as we discussed in our Section V, can be ruled out when the Arrhenius line exhibits a comparatively sharp bend at some low temperature, instead of a curvature over the whole temperature range, as represented by Eq. 12. A change of solvent structure at the unusually low temperatures at which these reactions are carried out has also to be considered (23). For a series of similar reactions in a given solvent, such an effect should make itself felt always at the same temperature this is not the case for the protonation of the anion of 2,4,6,-trinitrotoluene (see Fig. 8). 

F. W. Cope, Critical Exponent Analysis of Activation Energies of Nonlinear Arrhenius Plots as a Test for Cooperative Interactions in Amorphous Semiconductors and in Biological Systems, Physiol. Chem. Phys. 9(4, 5), 329, 443 (1977). 

A long extrapolation of a plot of experimental data may produce an inaccurate value for In A. Therefore, an alternative approach is to calculate In A from the calculated Ej value and data for the reaction rate coiwtant at some temperature in the middle of the range of experimental temperature-rate data. Kalantar, A. H. /. Phys. Chem. 1986,90,6301 discussed the precision of Ea and A measurements. For a discussion of nonlinear Arrhenius plots, see Hulett, J. R. Q. Rev. Chem. Soc. 1964, 18, 227. 

It was shown by sensitization experiments that —>Z and Z—> isomerization can proceed via the triplet state. As the quantum yield for sensitized and direct photoisomerization are different, it was concluded that direct photoisomerization proceeds mainly — if not completely — via singlet excited states. From the observation that < 1 nd from nonlinear Arrhenius plots, it was concluded that more than... 

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