Diffusion activation energies

The mobility of the boundary should be closely related to die volume diffusion process in the solid, and would therefore be expected to show an Anlienius behaviour widi an activation energy close to the volume diffusion activation energy. 

Diffusion activation energy for diffusion defined by equation 12.3.84... 

Figure 8. Apparent diffusion activation energies of alkali metals as a function ionic radii. Data are from this study and cited references.

For single-component gas permeation through a microporous membrane, the flux (J) can be described by Eq. (10.1), where p is the density of the membrane, ris the thermodynamic correction factor which describes the equilibrium relationship between the concentration in the membrane and partial pressure of the permeating gas (adsorption isotherm), q is the concentration of the permeating species in zeolite and x is the position in the permeating direction in the membrane. Dc is the diffusivity corrected for the interaction between the transporting species and the membrane and is described by Eq. (10.2), where Ed is the diffusion activation energy, R is the ideal gas constant and T is the absolute temperature. 

The critical input parameters are then (1) the grain size, which should be known for each case, (2) the Aci temperature which is calculated from thermodynamics, (3) the effective diffusion activation energy, Qea, and (4) the empirical constants aj for each element. Qea and aj were determined by empirically fitting curves derived using Eq. (11.12) to experimentally observed TTT curves, and the final formula for calculating r was given as... 

Table 12 The alkali-metal ion diffusion activation energies (eV) in Ti02 anatase.

The diffusion activation energy ED depends on the temperature, the size of the gas molecule d, and the glass transition temperature of the polymer. This relationship is well represented in Fig. 2.61 [62] with the size of nitrogen molecules, d 2 as a reference. Table 2.17 contains values of the effective cross section size of important gas molecules. 

Figure 2.61 Graph to determine the diffusion activation energy Ed as a function of...

In the temperature range between room temperature and 250°C, and with high surface area samples, behaviour intermediate between surface exchange and bulk diffusion has been observed by two sets of workers [90, 99] who obtained essentially similar results. As the temperature is raised, the second, third and fourth layers can be observed to exchange separately with activation energies of about 0.56—0.78 eV for the second layer, 1.17 for the third layer, and for the fourth layer either a similar value to the third [90] or a value close to the bulk diffusion activation energy of 1.61 eV [99]. The depth to which the solid behaves significantly differently from bulk properties correlates quite well with the... 

X parameter accounts for the deviation of the diffusion activation energy in the con sidered polymer from the reference activation energy (EA) - 15.1.1... 

By analyzing the interaction between a chain center and the centers from adjacent chains, a relation for the potential interaction energy in both the normal and activated state was obtained (43). This formula was eventually used to develop a relationship for the calculation of the diffusion activation energy Ed. To use this relation... 

The parameter AP accounts for a specific contribution of the plastic material to the diffusion process. Phenomenologically speaking AP has the role of a conductance of the polymer matrix towards the diffusion of the migrant (Chapter 6). Higher values of AP in such polymers as PE lead to increased DP-values while in stiff chain polymers such as polyesters and polystyrenes lower AP-values account for smaller diffusion coefficients for the same migrant. The parameters b and c account for the specific contributions of the migrant and the diffusion activation energy respectively. 

The 1.5 eV diffusion activation energy, needed to release hydrogen from the Si—H bond into an interstitial site, is smaller than the... 

The hydrogen diffusion activation energy increases with time because of the dispersive hydrogen motion. The relaxation of defects and dopants typically involves a much shorter hydrogen diffusion distance than in measurements of the diffusion coefficient, so that the activation energy of t is smaller than of Dg and is given by... 

In Table XV. 1 are summarized some data for fast reactions in solution which are presumed to be diffusion-controlled. The range in rate constants of about 10 is probably a reflection of the different entropy changes on association. What is of special interest is the low values of the activation energy, which are in the range of diffusion activation energies. 

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