Arrhenius plot of diffusion coefficient

Fig. 47. Arrhenius plot of diffusion coefficient for (a) H and (b) D atoms on the (110) face of a tungsten crystal at coverage degree 0.1-0.9 as indicated. The cusps on the curves correspond to the phase transition.

Figure 7. Arrhenius plots of diffusion coefficients for Rb, Cs, and Sr. Solid lines are high temperature data (numbers are literature references). Dashed lines are extrapolated coefficients based on Equation 5. Open circles are from this study.

Fig. 14. Arrhenius plots of diffusion coefficients in tow density polyethylene ( ) tetralin,...

Figure 5. Arrhenius plots of diffusion coefficients for water in the two copolymers (a) P(VdC/VC) and (b) P(VdC/AcN).

Figure 4. Arrhenius plots of diffusion coefficient, D, of interacting groups for dynamic quenching of benzophenone triplet by phenyl, phenylene, and ester groups in polystyrene ( , ), polycarbonate (Q. ), and PMMA ( ), respectively.

Fig. 47. (i) Arrhenius plot of diffusion coefficient (Df) and the reciprocal switching time (rs) in a Gd film, (ii) Variation in diffusion coefficient and switching time as a function of added hydrogen, (iii) Potential dependence of diffusion coefficient and reciprocal switching time, (iv) Variation in diffusion coefficient and reciprocal switching time as a function of film thickness for two applied potentials, 1.0 V (square) and 1.1 V (triangle) (Di Vece et al., 2003c). 

In addition to following the isothermal effects, it is also quite important to understand the changes that take place in the observed activation energy for diffusion as a function of the composition. The ease of oxygen ion diffusion in perovskite structure is usually attributed to the value of the apparent aetivation energy estimated from the Arrhenius plots of diffusion coefficient. This apparent activation energy, Ea, however, consists of several terms, as indicated in the following equation ... 

Figure 7.7 An Arrhenius plot of diffusion data In D versus l/T. Note D, diffusion coefficient T, temperature (in kelvin) Dq, pre-exponential, or frequency, factor...

Arrhenius plots of conductivity for the four components of the elementary cell are shown in Fig. 34. They indicate that electrolyte and interconnection materials are responsible of the main part of ohmic losses. Furthermore, both must be gas tight. Therefore, it is necessary to use them as thin and dense layers with a minimum of microcracks. It has to be said that in the literature not much attention has been paid to electrode overpotentials in evaluating polarization losses. These parameters greatly depend on composition, porosity and current density. Their study must be developed in parallel with the physical properties such as electrical conductivity, thermal expansion coefficient, density, atomic diffusion, etc. 

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].

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

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...

Membrane Diffusion in Nonaqueous Solvent Environments. Self-diffusion coefficients of Na+ and Cs+ for 1200 EW Nafion membranes in dilute methanol and acetonitrile solutions have been measured (5). Arrhenius plots of these results are shown in Figure 7 along with corresponding results for aqueous experiments activation energies of diffusion are listed in Table IV. Diffusion coefficients of Na+ in methanol and water-equilibrated membranes are very similar, and the activation energy of diffusion for the methanol system is only slightly higher than the respective value for Na+ in pure methanol solvent, 12.9 kJ mol 1 (27). Thus a solution-like diffusion mechanism is inferred for both solvent systems. Cesium ion diffusion in the methanol equilibrated membrane is much slower than sodium ion diffusion in fact the... 

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. 

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

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

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].

Figure 7.14 Arrhenius plots of temperature-dependent diffusivity coefficients of C6 alkanes within silicalite indicate that diffusion is increasingly hindered in the medium-pore channels as the degree of branching increases. Cyclohexane also diffuses very slowly. [Reproduced from reference 133 with permission. Copyright 1995 American Chemical Society.]...

F. 28 Arrhenius plots of (a) measured dye diffusion coefficient ( )) and (b) steady-shear viscosity for poly(butyl acrylate)s with UPy side groups. The cartoons emphasize that molecular diffusion is determined by the equilibrium association constant, whereas viscous relaxation is determined by the rate of bond dissociation. RevCTsibly associating copolymers (RAC) contain UPy side groups and control copolymtas (CCP) do not. Adapted from [149] with permission of The Royal Society of Chemistry... 

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).

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. 

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.

The Arrhenius plot of 1/r for benzophenone in poly(methyl acrylate) (PMA) showed another break at 40 °C (above T of PM A), which corresponds to the crossover of k j given by Eq. (14) from a diffusion-controlled to an activation-controlled reaction. The diffusion coefficient D for reacting carbonyl groups calculated from the values of 1/t and B also showed a break at each transition temperature, as exemplified in Fig. 8 for PMMA, polystyrene, and polycarbonate. It should be iK>ted that D in Fig. 8 refers to the reacting functional groups but not to the molecule. The diffusion proc at temperatures below T would be caused by rotation of the benzojdienone molecule and by the cooperative motion of a few successive monomer units of the matrix polymer. Nevertheless, the values of D in these polymers at 100 °C are comparable to the value of D = 5.6 x 10 an /s for mass diffusion of ethylbenzene in polj tyrene at 30 °C. The reaction radius R was estimated to be 3-5 A. The transition temperatures... 

An interesting report in this area concerns the kinetics of dimerization of Ag(CO)3 to Aga(CO>4 in a solid CO matrix between 30 and 37 K. Not surprisingly the rates are diffusion controlled and from calculations of diffusion coefficients at various temperatures an Arrhenius plot gave Ea= 1.86 0.3 kcal mol for the reaction. If it is assumed that Ag(CO)3 dimerizes by moving through the matrix via a CO vacancy mechanism the activation energy will be similar to that of self-diffusion in CO. A calculated value of a=2.05 kcal mol" for such a process can therefore be cited as reasonable evidence for such a mechanism. 

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