Arrhenius representation

From experimental results obtained at different temperatures, an Arrhenius representation of the above equation gives (Fig. 51) a Aft of 21.3 kJ mol-1. All these results are quite close to those obtained from other experiments. 

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)...

Plotting wo as a function of the reciprocal temperature T-1 (Arrhenius representation), one can derive the activation energy from the slope. The temperature dependent pre-exponential factor vq = ,oT2rru is then obtained from the axis cutoff T-1 —> 0 K-1. 

Fig. 5.15. Arrhenius representation. Data are derived from Fig. 5.13. The activation energy and pre-exponential factors are defined in the text...

Strong Temperature Dependence of Drift Mobility. Figure 6 is an Arrhenius representation of hole drift mobility data on a 0.2 1 TNF-PVK film (iO). The apparent activation in this representation is field dependent,... 

From these data is also possible to calculate the activation energy in pores of given water content from an Arrhenius representation of the calculated diffusion coefficients [63], The results show no indication of a substantial increase in activation energy at water levels as low as A = 4, contrary to the results in [23] and more in line with results from Kreuer (see Fig. 6 and [50]). Rather, the activation energy for proton transfer remains low at all studied water contents. Thus, it appears that in an individual pore the Grotthus mechanism remains rate-determining whereas the surface mechanism does not dominate the transport behavior. Similar results as in slab pores were also found in cylinder pores [63],... 

Arrhenius representation of the dependence with temperature of the diffusion coefficients for the PMMA/methanol system. 

Figure 5. Arrhenius representation of liquid viscosity illustrating Angel s strong-fragile classification scheme. Here Tg is the glass transition temperature defined in terms of r/(Tg) = 1013 poise. (Reproduced from Ref. 44.)...

Figure 2 Bimolecular quadruplex analysis, (a) Melting and cooling profiles of the Oxy 1.5 sequence (G4T4G4) in 0.11 M Na with a temperature gradient of 0.2°C min (b) Arrhenius representation of the association (In (K Co) open circles) and dissociation (In (Kg ) filled circles) rates of the bimolecular quadruplex f ormed by G4T4G4...

Figure 3 Tetramolecular quadruplex dissociation, (a) Example of an irreversible melting curve (TG4T) in 0.11 M Na recorded at 245 nm with a temperature gradient of 0.2°C min Directions of temperature changes are indicated by arrows. The small difference observed at high temperature between the heating and cooling profiles results from a partial evaporation of the sample, (b) Arrhenius representation of the dissociation rate (In (k ff) shown on the left Y-scale) and lifetime (right Y-scale) of the TG4T (DNA) and IIG4U (RNA) quadruplexes in 0.11 M Na" (ref 27)...

The growth kinetics of the acetylacetonate-complex of tin was studied by Maruyama and Ikuta [176]. The deposition rate increased exponentially with the evaporation temperature, and the Arrhenius representation of the growth rate indicates two different reaction mechanisms. At low temperatures, up to about 400 °C, it is diffusion-con-... 

Figure 6. Variations of the observed kinetic constant of liquid decomposition with wall temperature in an Arrhenius representation. A comparison with the scheme of Diebold (14).

Bimolecular rate constants measured in Ar below 2 atm [14,15,18] were combined in a single Arrhenius representation, k(Ar) = 10 -° exp[-(15300 600)/RT] cm mor s" [14]. Data measured in experiments for M = N2 [14] were admittedly not very reliable. At high experimental scatter and, as compared to M = Ar, an unexpectedly low Arrhenius preexponential factor (in the high-pressure limit) gave rise to some doubt [14]. It was mentioned that trace impurities of O2 (ca. 0.01%) in Ar enhanced the rate of N2F4 dissociation [17]. 

FIGURE 2.6 Activation energies of proton transport Nafion 117, extracted from the Arrhenius representation of condnctivity data at varying water contents. (With kind permission from Springer Science+Business Media Fuel Cells I, Fhoton-conducting polymer electrolyte membranes Water and structnre in charge, 2(X)8, pp. 15-54, Eikerling, M., Kornyshev, A. A., and... 

At the macroscopic level, proton transport can be studied with electrochemical impedance spectroscopy (EIS). Cappadonia et al. (1994,1995) performed EIS studies to explore variations of proton conductivity with water content and temperature for Nafion 117. The Arrhenius representation of conductivity data revealed activation energies between 0.36 eV at lowest hydration and 0.11 eV at highest hydration, as shown in Figure 2.6. The transition occurs at a critical water content of A-crit 3. At fixed X, the transition between low and high activation energies was observed at 260 K for well-hydrated membranes. This finding was interpreted as a freezing point suppression due to confinement of water in small pores. 

In chemical kinetics one characterizes the role of energy in chemical reactivity by the temperature dependence of the reaction rate constant. In Section 3.1 we review the input from chemical kinetics - the Arrhenius representation of the rate constant - then go from the rate constant to the reaction cross-section. Next we go in the opposite direction, from the microscopic reaction cross-section to the macroscopic rate constant. What we obtain thereby is the Tolman interpretation of the activation energy as the (mean) excess energy of those collisions that lead to reaction. 

Figure 10. Arrhenius representation of effective rate coefficient /c = j for OH + H2(i = 1)->H20 -h H for different [Ar]/[OH] ratios. Also shown is the thermal rate coefficient for equilibrium (---) and nonequilibrium (.) conditions.

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