Arrhenius plots for diffusivities

R is the gas constant Dq and activation energy Eu are constants derived from an Arrhenius plot for diffusion coefficients applying at different temperatures, and solubility coefficient was obtained from a separate permeation test at TiK. Suitable testing using a specially constmcted permeation cell water-cooled at one end provided good validation data. 

Fig. 4.26 An Arrhenius plot for diffusion of a Si adatom on the W (110) surface, derived from —360 heating periods of observation with one Si adatom. From the slope of the plot one obtains Ed = 0.70 0.07 eV. From the intercept one obtains D0 = 3.1 x 10 1 X 10 L28 cm2/s.

Figure 5.5 Arrhenius plots for diffusion of solar 4He and 20Ne in a magnetic separate from a Pacific Ocean sediment. The results of two duplicate samples (solid and open symbols) are shown. For 20Ne, both the data corrected (large open circles) for the atmospheric component, i.e., excess 2<>Ne and the data uncorrected (small open circles) are shown. The times required for 99% gas release are also shown for corresponding Dla2 values. After Hiyagon (1993).

Fig. 16 Arrhenius plots for diffusivities of n-hexane left) and of 2-methylpentane right) in silicalite-1 and H-ZSM-5...

Fig. 8. Arrhenius plots for diffusion coefficient D of intertu g groups in dynamic quenching of ben-zophenone triplet by phenyl, phenylene, and est groups in polysQrrene ( , A), polycarbonate (O, A), and PMMA ( )...

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.

At high temperatures there is experimental evidence that the Arrhenius plot for some metals is curved, indicating an increased rate of diffusion over that obtained by linear extrapolation of the lower temperature data. This effect is interpreted to indicate enhanced diffusion via divacancies, rather than single vacancy-atom exchange. The diffusion coefficient must now be represented by an Arrhenius equation in the form... 

Figure 5.19 Arrhenius plot of diffusion data, In D versus 1/T. The slope of the straight-line graph allows the activation energy of diffusion, a, to be determined, and the intercept at 1/T = 0 gives a value for the pre-exponential factor.

In most ordinary solids, bulk diffusion is dominated by the impurity content, the number of impurity defects present. Any variation in D0 from one sample of a material to another is accounted for by the variation of the impurity content. However, the impurity concentration does not affect the activation energy of migration, Ea, so that Arrhenius plots for such crystals will consist of a series of parallel lines (Fig. 5.21a). The value of the preexponential factor D0 increases as the impurity content increases, in accord with Eq. (5.13). 

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. 1.5 Arrhenius plot of diffusion coefBcients versus reciprocal temperatures for various minerals. Data from phases reacted under wet conditions are given as solid lines, whereas dry conditions are represented by dashed lines. Note that the rates for dry systems are generally lower and have higher activation energies (steeper slopes). (Modified after Cole and Chakraborty 2001)...

Fig. 3. The Arrhenius plot for a heterogeneous reaction showing regions in which the rate is diffusion-controlled and reaction-controlled.

The isomerizations of n-butenes and n-pentenes over a purified Na-Y-zeolite are first-order reactions in conversion as well as time. Arrhenius plots for the absolute values of the rate constants are linear (Figure 2). Similar plots for the ratio of rate constants (Figure 1), however, are linear at low temperatures but in all cases except one became curved at higher temperatures. This problem has been investigated before (4), and it was concluded that there were no diffusion limitations involved. The curvature could be the result of redistribution of the Ca2+ ions between the Si and Sn positions, or it could be caused by an increase in the number of de-cationated sites by hydrolysis (6). In any case the process appears to be reversible, and it is affected by the nature of the olefin involved. In view of this, the following discussion concerning the mechanism is limited to the low temperature region where the behavior is completely consistent with the Arrhenius law. 

The expected Arrhenius plot for cation self-diffusion in KC1 doped with Ca++ is shown in Fig. 8.13. The two-part curve reflects the intrinsic behavior at high temperatures and extrinsic behavior at low temperatures. 

Figure 8.13 Arrhenius plot for self-diffusivity on the cation sublattice, DK, in KC1...

Figure 7.14 Arrhenius plot for noble gas diffusion from noble gas-implanted target minerals. Samples are the same as those in Figure 7.13. After Futagami et al. (1993).

Although originally derived for membrane transport phenomena, the mechanisms outlined above can also provide potential explanations for non-linear, upwardly-concave Arrhenius plots for passive diffusion (Silvius and McElhaney, 1981 Klein, 1982). Other... 

Fig. 5. Arrhenius plot for a catalysed reaction showing the transition between diffusion control at high temperatures and surface control at low temperatures.

Figure 3. Arrhenius plot for experiments micropore diffusivity data...

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

The choice of these two substrates prevents complications associated with changes in the balance between kisc and kc as the temperature is varied. Figure 11 shows the Arrhenius plots for these two substrates based on their time-resolved quenching of 02(1Ag) luminescence. Both show two distinct regions with a positive slope at high temperature (pre-equilibrium limit) and a negative slope at low temperature (diffusion limit). This latter limit was confirmed by comparison with the corresponding data for /1-carotene, an... 

Figure 2. Primary yields (g-values) of the reducing (left hand panel) and oxidising (right hand panel) species produced in the radiolysis of D2O. The data points are from [3], The solid lines are calculated as described in Section 5 [32] the broken lines in the left hand panel are the results obtained using a linear extrapolation of the Arrhenius plot for A(e , + e , ) above 130 C instead of equation (8). The sensitivity of the calculations to a 10% uncertainty in the diffusion coefBcients and rate constants is shown by the error bars. 

Corresponding Arrhenius plots for the diffusion of 2-methylpentane in silicalite-1 and H-ZSM-5 are presented in Fig. 16, and the results are collected in Table 4. The diffusivities have been measured in the temperature interval... 

Figure 7,4 Log diffusion coefScienC vs i/7 plot (Arrhenius plot) for the di0tision of oxygen m selected minerals. The numbers in parencbeses are the activation energies In kcal/g-atom O (after Farver, 1989).

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