PFG NMR measurements

As a typical example, in the long time limit, t —> oo, of diffusion confined to spheres of radius R, the effective diffusivity of PFG NMR measurements is found to be [4, 8, 10]... 

Nowak et al. (63) presented a comparative study of the diffusivities of rigid models of methane, ethane, and propane in silicalite. (The details of the calculation are reported in the preceding section.) The calculated diffusion coefficients decreased as the length of the carbon chain increased, and the effect was found to be far more pronounced for ethane than propane. The calculated diffusivities, in units of 108 m2/s, were 0.62, 0.47, and 0.41 for methane, ethane, and propane, respectively. The ethane value is in satisfactory agreement with PFG-NMR measurements [0.38 (77), 0.3 (80), 0.4 (42) for silicalite. The value for propane, however, was calculated to be almost an order of magnitude larger than the NMR results of Briscoe et al. (80). [The agreement with the value of Caro et al. (71) is better, but still an overestimation.]... 

The diffusion coefficient was estimated to be 4 x 10 9 m2/s. Experimental values for benzene in faujasites range from 10 10 to 10"13 m2/s, depending on the measurement technique (24, 97). PFG-NMR measurements are the closest to the MD value, which was admitted by the authors to be a crude estimate (mainly on grounds of a short simulation and inflexible molecules). The simulation time was too short to permit a calculation of the residence times of the benzene at either the cation or the window site or inside a particular cage. The cage residence times were estimated to be at least an order of magnitude longer than those for methane in NaY zeolite (43). 

NMR Sorption Comparison Diffusion of the large tri-ethylamine molecule is sufficiently slow that reliable dif-fusivities can be determined from uptake rate measurements in 50]jm crystals(57) at least over a limited range of conditions. A comparative study, carried out with the same zeolite samples showed good agreement between the sorption and PFG NMR measurements, both as to the magnitude of the diffusivity ( 10 cm2.s- at 445K) and the trends with concentration and temperature(41). 

The Li+ migration in AMILs is confirmed by pfg-NMR measurement of the two salts containing Li+. However, its migration is less diffusive than that of the organic... 

This result is in agreement with recent PFG NMR measurements with oriented ZSM-5 crystals, where the mean self-diffusivity of methane averaged over the straight and sinusoidal channels (i.e., in the x, y plane) has been found to be larger by a factor of 3-5 than the self-diffusivity in the c direction, perpendicular to those 42,43). For the self-diffusion of methane in ZSM-5/silicalite-I, the MD simulations were in very satisfactory agreement with the experimental PFG NMR and QENS self-diffusion data (cf. Refs. 34-38). Furthermore, the degree of a mass transport anisotropy in the MFI framework as predicted by MD simulations (34-38) is compatible with the experimental findings (42,43,49). 

Figure 1. Results of PFG NMR measurements of the self-diffusivities of acetone, isopropanol, propene, and water in NaX...

Figure 11 Scanning electron micrograph of the surface of a capillary matrix used for the PFG NMR measurements with aligned ZSM-5 crystals, showing two crystals at the orifice of a capillary. (From Ref. 153.)...

Comparative investigations between the conventional adsorption/desorption method and PFG NMR have been carried out with aromatics in zeolite NaX. It was pointed out in Table 2 that there is still some divergence between the data obtained by both methods on intracrystalline diffusion. Table 3 compares the values for Tjnira and Tjn,ra determined by the NMR methods [143,175,176]. H PFG NMR measurements of these systems are complicated by the rather short transverse nuclear magnetic relaxation times, which range over milliseconds and lead to mean errors up to 50%. However, as with the n-paraffins in NaX, there is no indication of a significant enhancement of Tjn,ra 0 comparison with Tin,ra° " as... 

Figure 33 shows the time dependence of the diffusivities of the reactant molecules (cyclopropane) and of the product molecules (propene) as well as of their relative amount, as determined by an analysis of the contributions of both molecular species to the NMR signal following the first tt/2 pulse (free induction decay) under reaction conditions (208]. The diffusivities of these reactant and product molecules happen to be quite close to each other, so there is no essential change in the diffusivity of either of the components with increasing reaction time. It is remarkable that this result may be predicted already on the basis of PFG NMR measurements at lower temperatures (i.e., far away from reaction conditions), where both diffusivities are also found to be nearly identical and independent of the composition (208]. In such a case the self-diffusivity should apparently coincide with the coefficient of counterdiffusion. 

Diffusion of benzene in silicahte has been studied by several different macroscopic techniques with broadly consistent results (Fig. 12). However, diffusion in this system is too slow to allow rehable PFG NMR measurements so no comparison between micro and macro techniques is possible. 

The consistency between sorption rate measurements and PFG NMR measurements in large crystals of 5A zeolite was noted many years ago. In more recent studies a similar pattern of consistency between sorption rate, ZLC, and PFG NMR data has been observed for Xe, CO2, and C3H8 in 5A zeoHte (Fig. 13). 

If the mean molecular displacements in the interval between the two field-gradient pulses are much larger than the crystalhte diameters, the diffusivity resulting from PFG NMR measurements reflects the rate of molecular propagation through the bed of crystalhtes. This coefficient of long-range diffusion may be shown to be determined by [84]... 

Fig. 10 The different patterns of concentration dependence of intracrystalline self-diffusivities as determined from PFG NMR measurements. From Keil et al. [232], based on experimental data from Karger and Pfeifer [202]...

PFG NMR measurements are generally performed with closed samples containing the adsorbate in equilibrium with the adsorbent. In general, the measurements are carried out hours or even days after the introduction of the adsorbate into the activated sample. Moreover, the process of equilibration may be accelerated by keeping the sample at an elevated temperature. Once equilibrium is established, the measurements may be repeated as often as desired. There are examples [162], where more than 20 years after the first measurement, PFG NMR measurement of an adsorbate-adsorbent system within a closed sample tube yielded identical diffusivities. 

Fig. 22 Self-diffusivities of the inert CF4 probe during ethene conversion in H-ZSM-5 at 343 K resulting from in-situ PFG NMR measurements during the chemical reaction. From [236] with permission...

Such one-dimensional motion of particles through a narrow pore such that two particles caimot cross each other is actually well-known in the literature and is termed single-file diffusion. In the case of normal diffusion the mean-square displacement of particles is proportional to time, whereas in single-file diffusion it is proportional to the square root of time. The single-file diffusion mode was recently confirmed experimentally by an NMR study of water confined in a CNT of diameter 1.4 A. It was found that the mean-square displacement is indeed proportional to the square root of time from the pulse-field gradient (PFG) NMR measurements (see Figure 18.3). 

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