Curved Arrhenius diagrams

Relaxation mechanisms of dipoles located in dissimilar environments, or originating from complex forms of molecular or ionic motion, usually exhibit curved Arrhenius diagrams. This curvature is usually interpreted in terms of the semiempirical Williams-Landel-Ferry (WLF) equation (Williams et al. 1955)... 

Figure 8. Arrhenius diagram of the gamma-ray initiated polymerization of acrylonitrile in bulk 1161 Curve 1 Initial rates" curve 2 Pseudostationary rates. ...

Figure 5 Nucleation and growth kinetics of Pd clusters on MgO(l 00) from a TEAS study, (a) Series of nucleation kinetics curves for various substrate temperatures (atomic beam flux 1.1 x 1013 cm-2 s-2. (b) Arrhenius diagram of the saturation density, (c) Growth kinetics at various substrate temperatures. Atomic beam flux 1.1 x 1013 cm-2 s-2.

Arrhenius diagram), the general curve depicted in Fig. 3 is obtained. At a lower temperature the chemical reaction is slow and thereby rate controlling. Concentration and temperature remain constant over the entire cross-section of the catalyst pellet (see Fig. 2a). In this region, the slope of the curve in Fig. 3 is proportional to the intrinsic activation energy Ea-... 

Figure 6.28 Arrhenius diagrams of the HH-transfer (a) in a substituted acetyiporphyrin according to Ref [20] and (b) in meso-tetraphenyiisobacteriochiorin (upper curves) [19a] and in meso-tetraphenyichiorin (iow/er curves) dissoived in organic soivents [19d].

Figure 6.34 Arrhenius diagram for the double proton and deuteron transfer in the cyclic trimers of solid DMP. Adapted from Ref [25aj. The solid curves were calculated using the Bell-Limbach tunneling model as described in the text.

Firstly, let us discuss the example of a thermophilic alcohol dehydrogenase from Bacillus stearothermophilus (bsADH) studied by Kohen et al. [91, 92]. This enzyme catalyzes the abstraction of a hydride to the nicotinamide cofactor NAD+ as depicted in Fig. 6.54. The Arrhenius diagram is depicted in Fig. 6.54(a) a sudden decrease in the apparent slope and the apparent intercept of the Arrhenius curves is observed around room temperature (Fig. 6.54(b)). The puzzling observation is that the kinetic isotope effects are independent of temperature in the high-temper-ature regime but dependent on temperature in the low-temperature regime. 

It follows that, when the values of and V IF q corresponding to the different experiments are substituted in Eq. (c) or Eq. (d) k becomes a function of n only for each experiment. The point of intersection of the k versus n curves should give the value of k at the temperature considered and the unique value of n. This is shown in Fig. 5 for 750 C. The order is found to be 1.5, also at 730° and 710°C. This order is quite plausible on the basis of radical mechanisms for the reaction. The values of k are given in Table 1. The Arrhenius diagram for k is shown in Fig. 6. 

Fig. 3.15. Arrhenius-Diagram of the temperature dependence of the ductile-brittle transition and stress crack-oxidative degradation transition in the stress rupture curve of HDPE pipes, a 1. ductile-brittle transition of Hostalen 5010. b ductile-brittle transition of Hostalen GM 5010 T2 (see Fig. 3.14a), c start of oxidative degradation of resins GM 5010 and GM 5010 T2 (see Fig. 3.14a). The figure has been taken from reference (Koch et al. 1988)...

Right temperature-time curve (thermai iong-term diagram) representing the temperature index (Arrhenius diagram)... 

Where the WLF master curve was particularly bad and essentially a scatter diagram or the Arrhenius plot was far from a straight line no prediction could be made. Fiowever, there was apparently not good correlation between relatively poor WLF or Arrhenius plots and wrong or unreasonable predictions, nor between particularly good plots and good predictions. This is probably because poor predictions are more related to the shapes and direction of the property-time curves at elevated temperatures. 

The Yukawa diagram (Figure 7.5a), for a onepressure increases with temperature in an Arrhenius-type fashion up to the critical point, and a GS curve at low temperature and pressure. 

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