Arrhenius plots of the diffusion coefficients

Fig. 5 Arrhenius plots of the diffusion coefficients of the cations squares) and anions (circles) of a pure (closed) and a 97% pure (open) sample of [bmim]PF6 [36]. Reproduced with permission...

Arrhenius plots of the diffusion coefficient yielded values of activation energies in the range of 8-10 kcal/grmole that are of the same order of magnitude as the heat of adsorption on molecular sieves. The activation energy was found to increase slightly with increasing SO2 partial pressure. 

Fig. 18 Comparison of the Arrhenius plots of the diffusion coefficients of propane in theta-1 (cf. [65]) ( ) and in sUicalite-1 (cf. [65]) ( )...

The activation energy for the diffusion coefficient, obtained from an Arrhenius plot of the diffusion coefficient versus temperature, is 1700 J/mol in the 15°C to 28°C temperature range. 

Fig. 79. Arrhenius plot of the diffusion coefficients evaluated from the description of the kinetics of solid-state ion exchange in the systems CuCl/Na-Y and CuCl/Na-M through a diffusion model (for details, see text after [289], with permission)...

Figure 5.3 Arrhenius plots of self-diffusion coefficients of the anions and cations for (a) EMIBF4 and EMITFSI and (b) BPBF4 and BPTFSi.

Figure 25.7 Arrhenius-type plot of the diffusion coefficient D [cm s ] versus the inverse temperature [1 /K] for the three hydrogen isotopes (H, D, and T) adsorbed on the tungsten (110) surface (low coverage regime (0 = 0.1)). Clearly evident is that (T-independent) tunneling dominates in the low temperature range, whereas classical diffusion takes over at higher temperatures. After Auerbach et al. [45].

The Arrhenius plots of the diffusive permeability coefficient, P of water for the pol)nner/artificial amphiphile composite membranes reveal a distinct jump in the vicinity of the phase transition temperature of artificial amphiphiles. This striking increase of P may be caused by activation of thermal molecular motion which is closely related to the crystal-mesomorphic phase transition behavior. 

As illustrated in Fig. 5.10, the temperature dependence of the diffusion coefficient of transition metals into liquid aluminium is well described by the Arrhenius equation, D = D0 exp (-E/R.T), giving a linear plot of In I) against T l. Values of the pre-exponential factor, D0, and the activation energy, E, for some of them are given in Table 5.10. 

This expression has the Arrhenius form and E is the maximum value of the potential energy, an activation energy for deposition. This is expected because the potential profile of fig. 2 resembles the plot of the energy against reaction coordinate used in the theory of rate processes. The factor /(//m) accounts for the dependence of the diffusion coefficient on the distance and evaluations show that it can decrease the frequency factor in eqn (16) by two orders of magnitude. 

Fig. 12. Arrhenius plot of the apparent diffusion coefficient for PMMA/SAN-31.5(50/50)(31.5 wt% AN in SAN). The apparent diffusion coefficients results after temperature jumps from 210°C to different annealing temperatures below the LOST (cf. Fig. 1 la). Phase separation of the blend starts at 200 JC...

Figure 5.3 depicts the Arrhenius plots of the apparent self-diffusion coefficient of the cation (Dcation) and anion (Oanion) for EMIBF4 and EMITFSI (Figure 5.3a) and for BPBF4 and BPTFSI (Figure 5.3b). The Arrhenius plots of the summation (Dcation + f anion) of the cationic and anionic diffusion coefficients are also shown in Figure 5.4. The fact that the temperature dependency of each set of the self-diffusion coefficients shows convex curved profiles implies that the ionic liquids of interest to us deviate from ideal Arrhenius behavior. Each result of the self-diffusion coefficient has therefore been fitted with VFT equation [6].

The Arrhenius plot is valid for the temperature dependence of the diffusion coefficient D in a particular combination polymer/stabilizer. The value of D is independent of stabilizer concentration and was mostly determined by quantification of data dealing with the transfer of a stabilizer from a doped into a virgin polymer. The values of D of antioxidants in PP decrease approximately with increasing molecular weight of AO, with branching of substituents, increasing difference between the polarity of the polymer and that of stabilizer. A generalization is, however, very difficult [27, 30]. 

Figure 7. Arrhenius plot of the corrected diffusion coefficients Dq for the system benzene - Ga-MFI ---------- Dependence of D...

Fig. 9 Arrhenius-plot of the parabolic rate constant measured for the growth of CoO on Co in air [91] compared with that calculated from Wagners theory and the tracer diffusion coefficient for Co in CoO [89, 90].

The values of the diffusion coefficients increase rapidly as the temperature increases. Figure 6.31 presents the Arrhenius plot of the data in Table 6.1. 

Fig. 83. Arrhenius plot of the oxygen tracer self-diffusion coefficient Z>. Comparison of the data of Conder et al. (1994b) with those of Rothman et al. (1989, 1991). After Conder et al. (1994b).

Liquid-encapsulated Czochralski-grown InP S samples, annealed for 0.5h in various ambients at 550C, exhibited diffusion fronts which suggested an extremely rapid out-diffusion of S. The Arrhenius plot of the temperature dependence of the diffusion coefficient in vacuum anneals yielded,... 

Figure 8. Arrhenius plot of tracer diffusion data of O, Al and and diffusion data extracted from dehydration and hydration from Ruscher et al. single crystals (2 1). Dc and Dh are diffusion coefficients obtained for mullite calculated as given in the text.

FIGURE 4.45. Arrhenius plot of the apparent chemical diffusion coefficient for undoped NiO at different surface... 

Fig. 23. Arrhenius plots of the oxygen chemical diffusion coefficient (D ) measured on two...

Figure 9. Arrhenius plot of the self diffusion coefficients of Si, O and Na in SiC>2 and sodium silicates plotted vs. inverse temperature. Straight lines indicate the Anbenius relations, D

Figure 12. Arrhenius plot of the self-diffusion coefficients of Si, O tmd A1 in Si02 and (Al203)2(Si02) melts. In the case of Si02, curves shown represent fits according to mode coupling theory (D (1 - r jTcY, Tc = 3330 K, 7 st 2 broken curves) and according to the Arrhenius relation, respectively. In the case of aluminium-disilicate, curves are guides to the eye only. From Winkler et al. [56].

FIGURE 7.19 Analysis of the limited valance model with = 4. Isodiffusivity lines with the spinodal (left panel) and dependence of the diffusion coefficient along the isochores indicated as a function of the inverse temperature (right panel). The thick line at the bottom of the left panel shows the expected glass line from the Arrhenius plots. (From Zaccarelli E. et al. 2006. J. Chem. Phys. 124 124908. With permission.)... 

Figure 79 shows an Arrhenius plot of the thus-determined values of In (Dto/R ) vs. 1/T, where D, to, R, T represent the diffusion coefficient, selected time after beginning of the exchange process, particle radius and the exchange temperature, respectively. From the slopes of the straight lines activation energies of 70 kj moE were derived. 

Figure 24 Arrhenius plots of the rotational diffusion coefficients / s-...

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