Diffusivities of n-alkanes

FIGURE 7.16 Effect of calcium exchange for sodium in zeolite A on hydrocarbon adsorption. Replacement of four sodium ions by two calcium ions permits easy diffusion of n-alkanes into the zeolite channels. 

Dumont and Bougeard (68, 69) reported MD calculations of the diffusion of n-alkanes up to propane as well as ethene and ethyne in silicalite. Thirteen independent sets of 4 molecules per unit cell were considered, to bolster the statistics of the results. The framework was held rigid, but the hydrocarbon molecules were flexible. The internal coordinates that were allowed to vary were as follows bond stretching, planar angular deformation, linear bending (ethyne), out-of-plane bending (ethene), and bond torsion. The potential parameters governing intermolecular interactions were optimized to reproduce infrared spectra (68). 

The coefficients of intraciystalline self-diffusion of the n-alkanes from propane to n-hexane adsorbed in zeolite ZSM-5 are studied by means of the PFG NMR technique over a temperature range from -20 to 380 °C (96). The diffusivities are found to decrease monotonically with increasing chain lengths. Over the considered temperature range, the diffusivities in ZSM-5 are found to be intermediate between those for Na X and NaCa A zeolite, and the diffusivities of n-alkanes are independent of the Si/Al ratio of the zeolite lattice (96). 

Fig. 23 Variation of the diffusivity of n-alkanes in zeolite Na,Ca-A with the carbon number at 473 K as observed with different techniques [QENS spin-echo technique (NSE), 12 carbon atoms per cavity x PFG NMR, 1 molecule per cavity A, (more recent data), 2 molecules per cavity ZLC, limit of vanishing concentration , o (more recent data)]. From [176], with permission...

Various experimental and theoretical methods have been used to determine the diffusivities of n-alkanes in silicahte or ZSM-5 zeoHtes. Branched alkanes are expected to be slower, but the ratio of the diffusivities between a normal alkane and a mono-methyl isomer may vary experimentally between a factor 5 to 1,000 [39,40]. With a rigid framework, the value of this ratio obtained from simulations varies between two and six orders of magnitude [41-43]. The first QENS measurements on hydrogenated isobutane in ZSM-5 were performed on a back-scattering instrument [40]. The broadenings were small, only 10-20% of the instrumental resolution. The self-diffusivities, which were extracted, were 2-5 x 10 m s , for temperatures ranging between 450 and 570 K [40]. 

Harmandaris, V.A., Doxastakis, M., Mavrantzas, V.G., and Theodorou, D.N., 2002, Detailed molecular dynamics simulation of the self-diffusion of n-alkane and cis-1,4 polyisoprene oligomer melts , J. Chem. Phys. 116,436. 

Leroy, F., and Rousseau, B. 2004. Self-diffusion of n-alkanes in MFl type zeolite using molecular dynamics simulations with an anisotropic united atom (AUA) forcefield Mol. Simul. Vol. 30 pp 617-620. 

Sorption and Diffusion of n-Alkanes and Alcohols in Poly(l-trimethylsilyl-l-propyne)... 

The analysis of the literature data shows that zeolites modified with nobel metals are among perspective catalysts for this process. The main drawbacks related to these catalysts are rather low efficiency and selectivity. The low efficiency is connected with intracrystalline diffusion limitations in zeolitic porous system. Thus, the effectiveness factor for transformation of n-alkanes over mordenite calculated basing on Thiele model pointed that only 30% of zeolitic pore system are involved in the catalytic reaction [1], On the other hand, lower selectivity in the case of longer alkanes is due to their easier cracking in comparison to shorter alkanes. 

In Figure 5 the generally accepted reaction path (14) for hydroisomerization of n-alkanes has been represented along with different possibilities for the cracking step. The n-alkane molecules are adsorbed at a dehydrogenation/hydrogenation site where n-alkenes are formed. After desorption and diffusion to an acidic site chemisorption yields secondary carbenium ions that rearrange... 

The observations of the n-alkane diffusion triggered extensive theoretical investigations, mostly employing Monte Carlo (MC) and Molecular Dynamics (MD) simulations [63-69]. From systematic simulations of a series of n-alkanes (n-CsHs, n-CeHi4, n-CioH22 and n-C2oH42) on W(001) the trends observed experimentally on Ru(001) were confirmed in the 300-1000 K... 

Koszinowski, J. Diffusion and Solubility of n-Alkanes in Polyolefins. J. Appl. Poly. Sci. 1986, 31 1805-1826. 

The equation for the diffusion coefficient in a gaseous state, Dc, is the starting point for the derivation of an equation for diffusion coefficients in an amorphous solid state (S). The homologous series of n-alkanes is used as a reference class of chemical compounds which asymptotically reach an unlimited molecular chain in the form of poly methylene. The diffusion coefficient, DSji, is derived theoretically for a member of the series with j carbon atoms at infinite dilution in a matrix of a n-alkane with i carbon atoms in the molecule. In addition, the diffusion in polymethylene, which is considered as the reference structure for all polymers is also derived theoretically. 

The corresponding diffusion coefficient in the liquid state (L), DLderived from Ds.ji and Dc. Starting from the reference class of n-alkanes, diffusion coefficients can be estimated for any solute and matrix with corresponding specific values for the critical temperature and critical pressure of the matrix and the critical molar volume of the solute. 

Figure 6-2 Logarithm of diffusion coefficients of n-alkanes in polyolefins at 23 °C as a function of the relative molecular mass.

Reference Eq. (6-20) for an infinite chain of covalently bonded methylene groups can be considered to be an asymptotic limit for the homologous series of n-alkanes. By substitution of w into the exponent of Eq. (6-20) by the corresponding term, wI (., which represents a matrix composed of a paraffin with i carbon atoms, an equation for the diffusion coefficient Dski for trace amounts of a paraffin with k carbon atoms results ... 

Taking into account that, for the reference homologous series of n-alkanes the relative molecular masses of the member i in the series is Mni = 2+14 i, the self-diffusion coefficient DL i can be calculated with Eqs. (6-27) and (6-28). This can be done using only two values based on experimental results, the limit value of the critical temperature, Tc, and the mean value for the ratio, VcJMni. 

The cage or window effect was proposed by Gorring (48) to explain the nonlinear effect of chain length observed in hydrocracking of various n alkanes over T zeolite, chabazite (CHA) and erionite (ERI). Thus, when a nC22 alkane is cracked over erionite, there are two maxima in the size distribution of the product molecules at carbon numbers of 4 and 11 and a minimum at carbon number of 8. The diffiisivities of n-alkanes also change in a similar periodic manner by over two orders of magnitude between the minimum at C8 and the maxima. This shows that for diffusion, and hence for shape selective effects, not only the size but also the structure of the reactant and product molecules need to be considered. 

Matthews-Akgerman The free-volume approach of H ildebrand was shown to be valid for binary, dilute liquid paraffin mixtures (as well as self-diffusion), consisting of solutes from Cj to Cie and solvents of Ce and C12. The term they referred to as the diffusion volume was simply correlated with the critical volume, as Vp = 0.308 V . We can infer from Table 5-15 that this is approximately related to the volume at the melting point as Vp = 0.945 V . Their correlation was valid for diffusion of linear alkanes at temperatures up to 300°C and pressures up to 3.45 MPa. Matthews et al. and Erkey and Akger-man completed similar studies of diffusion of alkanes, restricted to n-hexadecane and n-octane, respectively, as the solvents. 

Kinetic studies of ion exchange on partially ion-exchanged type A zeolites of Mg Ca and Mn " revealed that mini-mums and maximums characterize the differential coefficients of internal diffusion for every exchange of 2 Na " ions for one divalent cation per unit cell of the zeolite. On the basis of these observations, assuming definite interactions between the cations and the zeolite lattice, predictions can be made concerning the distribution and arrangement of cations in the unit cells of a type A zeolite. Research on liquid phase adsorption of n-alkanes on partially ion-exchanged type A zeolites indicated that the differential diffusion coefficients for alkane adsorption are influenced likewise by cation distribution in the unit cells of the zeolite. 

Typical applications of zeolite membranes in reactors include i) conversion enhancement either by equilibrium displacement (product removal) or by removal of catalyst poisons/ inhibitors and ii) selectivity enhancement either by control of residence time or by control of reactant traffic. A large number of examples are reported and discussed in [49,50,52], Several of them are reported in fable 3. The use of a zeolite membrane as a distributor for a reactant has been attempted for the partial oxidation of alkanes such as propane to propene [137], or n-butane to maleic anhydride [138]. Limited performances were obtained because the back-diffusion of the alkane is hardly controllable with this type of microporous membrane [139]. 

Fig. 5.14 High-pressure (saturated vapour pressures—SVP) isobars for self-diffusion at T = 473 K of a number of n-alkanes plotted as a function of the molecular weight, M .

Fig. 16 Comparison of diffusivities for n-alkanes in silicalite measured by different experimental methods o, , MD simulations +, QENS V, single crystal membrane A, PEG NMR A, ZLC. Data are from various sources. From Jobic [96] with permission...

As shown in Fig. 12, a monotonous decrease in the self-diffusion coefficient was measured by PPG NMR for a series of n-alkanes in Na-X [50]. A similar trend was observed in ZSM-5 by QENS. From the NSE experiments performed in 5A, one finds that Dt drops to a minimum at Cs and has a clear maximiun at Ci2. A similar variation is obtained for Do after correcting from the thermodynamic correction factor (the number of carbon atoms per cavity is the same). Recent PEG NMR results indicate also a small minimum for Ds at Cg and a small maximum at Cm [51]. The NSE data obtained for longer n-alkanes in 5A are in contradiction with simulations which predict increasing diffusivities from C12 to Ci7 [52] whereas a decreasing trend is observed (Fig. 12). Finally, the activation energies derived from the NSE measurements show a minimum for C12, in agreement with the explanation in terms of the window effect. These results are related to similar concepts such as resonant diffusion [53] or the levitation effect, which corresponds to a maximum in self-diffusivity when the size of the diffusant is comparable to the diameter of the void [54]. 

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