Self-diffusivities loading

F[G, 25. Self-diffusion coefficients of methane (open symbols) and water (hlied mbols) in zeolites NaCaA, NaX, and ZSM-5 (loading, approximately 1 CH4 or H2O molecule per 24 T atoms, 296 K) (5). 

FlC. 26. Self-diffusion coefficients of methanol (squares) and water (circles) in their binary mixtures sorbed in HZSM-5 for two total loadings 35 mg (H2O + CH3OH) g" (open m-bols) and 50 mg g (filled symbols) at 300 K (725). Comparison with the self-diffusivity in liquid methanol/water mixtures (126,127) dotted line, D(CH30H) dashed lines, D(H20). 

Flo. 37. NMR intracrystalline self-diffusion coefficient Dm, (a) and effective self-diffusivity Dcir ( ) of methane in HZSM-5 crystals that were coked for different times by n-hexane cracking (131-133). Before loading with methane (9.2 CHa per u.c.), the coked ZSM-5 crystals were carefully outgassed at 623 K and 10 Pa. The remaining carbonaceous residues were defined as coke. Amounts of coke after different times on stream 1 h, 0.8 wt% C 2 h, 1.3 wt% C 6 h, 3.2 wt% C 16 h, 4.8 wt% C. The starting self-diffusion coefficient is 8.1 x 10" m s . ... 

Dubbeldam et al.46S use random walk theory and extended dynamically corrected transition state theory in order to compute the self-diffusivity of adsorbed molecules in nanoporous confined systems at nonzero loading. The results are compared with MD simulation results with good agreement. 

Fig. 1 Comparison of experimental and simulated self-diffusivities of benzene in NaX zeolite (supercage depicted in inset) vs. inverse temperature for three loadings, 0, indicated. (View this art in color at www.dekker.com.)...

Figs. 1 and 2 depict the result of hierarchical training of a KMC model of benzene in the NaX lattice by simultaneously fitting self-diffusivity data at different loadings 0 (number of benzene molecules per cage) and adsorption isotherms, respectivelyThe optimized... 

Figure 9 Self-diffusion coefficients of propane (loading ca 2.5 molecules per channel intersection) in polycrystalline grains of fresh H ZSM-5 and after 1 h (corresponding to 3.6 mass X coke) and 12 h (corresponding to 4.3 mass % coke) on n-hsxane stream for different observation times h at 296 K (Reproduced with permission from Ref. 33. Copyright 1987 Elsevier)...

This expression contains two different diffusion coefficients oa which characterizes the frictional resistance with the pore walls and ab which characterizes the interaction between the two differing species (the mutual dif-fusivity). For self-diffusion Nb=- N and 0 = 0a + 0b (the total fractional loading), so that for diffusion in the z direction ... 

In tracer ZLC (TZLC) [28,51,58] the experiment is similar to the standard method, but the monitored species is the deuterated form of the sorbate. This introduces an additional cost for the material and the requirement for an online mass spectrometer. The advantages are the eUmination of all possible heat effects, strict Unearity of the equiUbrium between the fluid phase and the adsorbed phase, and the possibility of measuring directly the tracer diffusivities (which shoifld be the same as the microscopically measured self-diffusivity) over a wide range of loading. To reduce the costs the carrier is prepared with a mixture of pure and deuterated hydrocarbons. It has been shown that small imbalances in the concentration of the carrier and the purge streams do not affect the desorption dynamics [58]. 

Fig. 14 Diffusion of methanol in NaX zeolite crystals at 100 °C. a Tracer ZLC response curves, b Variation of self-diffusivity with loading showing comparison of ZLC and PFG NMR data. From Brandani et al. [71]...

Figure 11 shows the self-diffusion coefficients obtained from the TEX-PEP experiments for both alkanes as a function of the gas-phase mixture composition. Evidently, we find that the self-diffusivity of n-hexane is an order of magnitude higher than that of the 2-methylpentane. Indeed, the kinetic diameter of n-hexane (4.3 A) is smaller than that of isohexane (5.0 A) [51]. Moreover, we observe a decrease in mobility with increasing fraction of the branched alkane in the gas phase. Analogous behavior was found for CH4/CF4 mixtures, where the self-diffusivity of both components decreased as the loading of the slower diffusing tetrafiuoromethane increased [52]. 

Fig. 11 Self-diffusivities of mixture components in silicalite as a function of the 2-methyl-pentane fraction in the gas phase (left) and as a function of the 2-methylpentane loading (total hydrocarbon pressure 6.6 kPa, 433 K)...

Around a value of the gas-phase fraction of 2-methylpentane of about 0.83, the influence of the acid sites on the n-hexane diffusivity is not dominant anymore in comparison to the pore occupation of slow-diffusing 2-methyl-pentane. Figure 14 shows the dependence of the diffusivities of both components versus the concentration of adsorbed 2-methylpentane in terms of molecules per unit cell. The diffusivities of n-hexane in silicalite-1 and H-ZSM-5 become nearly equal when the concentration of 2-methylpentane reaches approximately 2.75 molecules per unit cell. For 2-methylpentane we And that the self-diffusivity in silicalite-1 becomes very close to the value in H-ZSM-5 at the same loading. 

Fig. 14 Self-diffusivities of mixture components in both MFI-type zeolites as a function of 2-methylpentane loading, 433 K...

Summarizing, we observe that the presence of acid sites causes a decrease in the self-diffusivity of n-hexane and 2-methylpentane. In H-ZSM-5, we find that the diffusivity of n-hexane in mixtures with its branched isomer is determined by two factors (i) the interaction with acid sites, strong for the linear alkane, which decreases the diffusivity and (ii) the presence of 2-methylpentane which has an order of magnitude lower diffusivity. At low 2-methylpentane loadings the influence of the acid sites is dominating. However, at a loading of about 2.7 molecules per unit cell, the effect of pore blocking by the preferential location of the branched alkane in the intersections dominates. The diffusivities are then more or less equal in silicalite-1 and H-ZSM-5. 

Fig. 17 Self-diffusivity of n-pentane in silicalite-1 at various temperatures and loadings...

Figure 20 shows the self-diffusivities of n-pentane and n-hexane as a function of gas mixture composition. The loadings of both components depend on the gas phase composition fraction. Note that in these experiments the total hydrocarbon pressure is kept constant (6.6 kPa). The loading of a feed of pure n-hexane under these conditions (433 K, 6.6 kPa) is 3.6 molecules per unit cell. Unexpectedly, we observe a lower diffusion coefficient for pure n-pentane than for n-pentane in a mixture with n-hexane. Tentatively, we ascribe this to the more drastic increase in n-hexane dif-fusivity with loading than for n-pentane. As discussed earlier, this can be ascribed to stronger repulsive interactions for the longer hexane hydrocarbons. It is clear from Fig. 20 that at low n-hexane concentrations, its diffusion is slower than of n-pentane. The diffusivity of hexane increases with n-hexane loading, while the diffusivity of pure n-pentane was found to be independent on the concentration at this temperature. Repulsion between n-pentane... 

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