Diffusional activation energy

The diffusional activation energies, listed in Table III, show a clear correlation with the critical diameters of the sorbite molecules (calculated as the diameter of the smallest cylinder which cap circumscribe the molecule). The data for the olefins are of particular interest since propylene, 1-butene, and frcms-2-butene, which all have the same critical diameter,... 

Diffusional Activation Energies and Pre-Exponential Factors of the Eyring Equation for the Diffusion of H-ZSM-11 and H-SSZ-24 Zeolites at Different... 

Variation of diffusional activation energy with van der Waals radius (aG) for diffusion in 4A and 5A zeolites... 

Comparison of diffusivities and diffusional activation energies for linear paraffins as free liquids and adsorbed on NaX zeolite. 

Using for V0 the experimental value of the diffusional activation energy one may estimate theoretical values for the pre-exponential factors D and Kg, which may then be compared with the experimental values. Such a comparison is shown in table 1 and it is evident that in spite of the obvious approximations, the model provides a good representation of the behaviour of these systems at low concentrations. 

Thus, it is suspected that strong contact ion pairing in the case of the carboxylate is responsible for the low sodium ion diffusion coefficients and high diffusional activation energies. For the sulfonate, sodium ions that function as exchange-site counterions may be less strongly bound than for the carboxylate case, resulting in more facile sodium ion self-diffusion in the polymer. 

Figure 5. Variation of diffusional activation energy with carbon number for n-paraffins in 5A zeolite crystals. (Data from refs. 9, 21, 22, 29, 15.)...

The contribution of surface diffusion to the overall effective diffusivity, however, depends on the product KD rather than on the surface diffusivity alone (Eq. (5.20)]. Since the diffusional activation energy ( ) is generally smaller than the heat of sorption, this product, and therefore the relative contribution of surface diffusion, normally decreases with increasing temperature. Such a trend is illustrated by the data given in Table 5.1. 

FIGURE 5.12. Variation of diffusional activation energy with van der Waals diameter for diffusion in 4A and 5A zeolites and 5A molecular sieve carbon. Van der Waals diameters are estimated according to Eq. (2.5) from values of the van der Waals co-volume b) given in the Handbook of Physics and Chemistry, 55lh ed. C.R.C Press 1974, (Diffusivity data are from refs. 1-3, 48, 49,51-53, and 81.)... 

For systems in which the diffusivity ratio is smaller a more gradual variation in diffusivity and diffusional activation energy with ion exchange is predicted. The theoretical curve calculated from this model provides a good representation of the experimental data for diffusion of butane in Na-Ca zeolite A, as may be seen from Figure 5.13b. 

The size of these crystals and the conditions of dehydration are essentially similar to those used in the preparation of commercial 5A adsorbents. It is remarkable that the diffusional activation energy determined from the tracer desorption results for the small crystals dehydrated at high temperature (2.8 kcal/molc) is almost the same as the value determined from the earlier adsorption rate measurements with small commercial Linde crystals (3.0 kcal/mole). The absolute values of the diffusivities for the severely de-... 

FIGURE 5.19. Comparison of self-diffusivities and diffusional activation energies for linear paraffins as free liquids and adsorbed on 13X zeolite crystals. Data of Karger cl (Reprinted with permission from ref. 46, Copyright 1983 American Chemical Society.)... 

The temperature dependence of the corrected diffusivity is illustrated in Figure 5.23, and the correlation of diffusional activation energy with van der Waals radius is indicated in Figure 5.12. It is evident that the trend is very similar to that observed with 4A zeolite although the magnitude is somewhat larger. 

The positive diffusional activation energy is larger in absolute value than the negative AH, and so the overall permeability increases as temperature increases, but to a lower degree than the diffusion coefficient itself It should be noted that the use of equation 34 is only strictly valid when the diffusion and solubility coefficients are independent of concentration. 

Fig 4 16 Vanation of diffusional activation energy with van der Waak diameter for diffusion in 4 A and S A zeolites and S A molecular sieve carbon (Reproduced with permission by Ruthven, M, Principles Adsorption and Adsorption Processes, p 148, John Wiley and Sons, New York (I98S))... 

In nanoporous materials diffusion is sterically hindered so that the diffusional activation energy (and hence the permeance) are strongly dependent on molecular size (see Fig. 2), thus giving rise to the possibility of size selective molecular sieve separations. In extreme cases where one of the components is sterically excluded from the pore system a highly efficient molecular sieve separation may be achieved (provided that the membrane is coherent). However,... 

For several reasons the reliable measurement of micropore-diffusion has proved to be far more difficult than expected. A wide range of different experimental techniques have been applied (see Table 3). We now know that when the diameter of the diffusing molecule is even slightly smaller than the pore diameter, diffusion within an ideal micropore is surprisingly fast and difficult to measure by macroscopic methods since the size of available zeolite crystals is limited. Such fast processes can, however, be measured relatively easily by PFG NMR and QENS. As the molecular diameter of the sorbate approaches (or even exceeds) the minimum diameter of the pore the diffusional activation energy increases and the diffusivity drops by orders of magnitude. Slow transport-diffusion (for example ethane, propane, etc. in CHA or Zeolite A - see Fig. 7) is easily measured macroscopically but inaccessible to microscopic techniques. The range of systems and experimental conditions where reliable measurements can be made by both macroscopic and microscopic methods is therefore quite restricted. 

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