Diffusion measurements microscopic measurement

Comparison between xf a as determined on the basis of Eq. (3.1.15) from the microscopically determined crystallite radius and the intracrystalline diffusivity measured by PFG NMR for sufficiently short observation times t (top left of Figure 3.1.1), with the actual exchange time xintra resulting from the NMR tracer desorption technique, provides a simple means for quantifying possible surface barriers. In the case of coinciding values, any substantial influence of the surface barriers can be excluded. Any enhancement of xintra in comparison with x a, on the other side, may be considered as a quantitative measure of the surface barriers. 

While microscopic techniques like PFG NMR and QENS measure diffusion paths that are no longer than dimensions of individual crystallites, macroscopic measurements like zero length column (ZLC) and Fourrier Transform infrared (FTIR) cover beds of zeolite crystals [18, 23]. In the case of the popular ZLC technique, desorption rate is measured from a small sample (thin layer, placed between two porous sinter discs) of previously equilibrated adsorbent subjected to a step change in the partial pressure of the sorbate. The slope of the semi-log plot of sorbate concentration versus time under an inert carrier stream then gives D/R. Provided micropore resistance dominates all other mass transfer resistances, D becomes equal to intracrystalline diffusivity while R is the crystal radius. It has been reported that the presence of other mass transfer resistances have been the most common cause of the discrepancies among intracrystaUine diffusivities measured by various techniques [18]. 

If the activation energies of surface diffusion vary over a wide range from one element to another and from one surface to another, the diffusivity, or the pre-exponential factor, D0, does not. Within the very limited accuracy of the field ion microscope measurements, usually no better than one order of magnitude because of the narrow temperature range within which a measurement can be conveniently done, all measured values of D0 are consistent with eq. (4.22) by taking AS = 0, and v0 = kTIh where h is the Planck constant, or D0 are about a few 10-3 cm2/s. This has been pointed out repeatedly by the author126 since there is... 

Adatom diffusion, at least under the low temperature of field ion microscope measurements, almost always follows the direction of the surface channels. Thus adatoms on the W (112) and Rh (110) surfaces diffuse in one direction along the closely packed atomic rows of the surface channels. Such one-dimensional surface channel structures and random walks can be directly seen in the field ion images, and thus the diffusion anisotropy is observed directly through FIM images. Unfortunately, for smoother surfaces such as the W (110) and the fee (111), no atomic or surface channel structures can be seen in field ion images. But even in such cases, diffusion anisotropy can be established through a measurement of the two-dimensional displacement distributions, as discussed in the last section. Because of the anisotropy of a surface channel structure, the mean square displacements along any two directions will be different. In fact this is how diffusion anisotropy on the W (110) surface was initially found in an FIM observation.120... 

C.J.Burton, IEC 35, 120-5(l943)(Electron microscope and cellulose) 19)E.Ott, "Cellulose and Derivatives , Interscience, NY(1943) 20)Hackh s(1944), 178 21)N.Gral6n, "Sedimentation and Diffusion Measurements on Cellulose and Cellulose Derivatives , Almqvist Wiksells, Uppsala(1944) 22)E.Heuser, "The Chemistry of Cellulose , Wiley, NY(1944) 22a)... 

These abilities provide the site selective laser techniques with unique capabilities to determine the changes in defect equilibria at a microscopic level. They are complementary to conductivity, diffusion, dielectric and other bulk measurements which measure nonlocal properties that must be modeled to extract microscopic details. 

The diffusion coefficient may be measured via several experimental techniques. The most prominent ones at present are the direct observation of a diffusion boundary in either a field electron microscope [159, 160] or a photoelectron emission microscope [158] or via laser desorption experiments [161, 162], In the latter case a short laser pulse is used to heat the surface to momentarily desorb the adsorbate from a well defined region of the crystal. Subsequent laser pulses with well defined time delays with respect to the first one, and measurement of the number of particles leaving the surface, allow one to determine the rate of diffusion into the depicted zone. Other methods to determine surface diffusion are spectroscopic measurements which cover the proper time window, for example magnetic resonance-based methods [163, 164]. In favorable cases these methods may even be applied to single crystal surfaces [165],... 

A general experimental result is the difference between measured rates of diffusion in macroscopic experiments and measurements of self-diffusion by spectroscopic techniques such as gradient field NMR [80-84]. The difference between the microscopic measurement and the macroscopic experiment is desorption and reentry of molecules in zeolite microcrystallites. In this respect, it is important to remember the Biot condition, which states the condition when the measured rate of diffusion is independent of the rate of desorption ... 

For details on the derivation of this formula the reader is referred to section 4.5.1 of Frenkel and Smit (1996). The physical message to be taken away from this discussion is that by carefully observing the statistics of particle trajectories it is possible to reconcile the relevant microscopic motions seen in a molecular dynamics simulation with the macroscopic reflection of these motions, namely, the existence of a diffusion constant. On the other hand, we have not fully owned up to the rarity of diffusion events as measured on the time scale of atomic vibrations. This topic will be taken up again in chap. 12. 

Many of the macroscopic techniques can be apphed to the measurement of self-diffusion by using isotopically labeled tracers. Such methods, first introduced by Barrer and Fender [97], have been widely applied in order to obtain data which should be directly comparable with microscopic self-diffusion measurements. Such comparisons are presented in several of the chapters within the present volume. 

Measurements by interference microscopy are, under favorable conditions, capable of yielding both internal diffusivities and apparent diffusivities based on overall sorption rates. The former tend to approach the values obtained from microscopic measurements while the latter yield values similar to those obtained by other macroscopic methods. Of necessity these studies have been carried out in large zeolite crystals. One may expect that smaller crystals may be less defective, although the influence of surface resistance may be expected to be greater. The extent to which these conclusions are applicable to the small zeolite crystals generally used in commercial zeolite catalysts and adsorbents remains an open question. 

Abstract In this chapter the main macroscopic experimental methods for measuring diffusion in microporous solids are reviewed and the advantages and disadvantages of the various techniques are discussed. For several systems experimental measurements have been made by more than one technique, and in Part 3 the results of such comparative studies are reviewed. While in some cases the results show satisfactory consistency, there are also many systems for which the apparent intracrystaUine diffusivities derived from macroscopic measurements are substantially smaUer than the values from microscopic measurements such as PFG NMR. Recent measurements of the transient intracrystalline concentration profiles show that sirnface resistance and intracrystalline barriers are both... 

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]. 

The techniques outlined above have been used to study diffusion in a wide range of zeolite systems. In general we find that there is reasonable agreement between the different macroscopic methods and also between the microscopic methods (QENS, and PFG NMR). However, although for several systems the macroscopic and microscopic measurements are also consistent, there are many systems for which we see significant discrepancies between the two classes of measurements. 

Diffusion measurements fall into two broad classes. Under macroscopic equilibrium, i.e. if the overall concentration within the sample remains constant, molecular diffusion can only be studied by following the diffusion path of the individual molecules ( microscopic measurement by quasielastic neutron scattering (QENS) [48,183,184], nuclear magnetic relaxation and line-shape analysis, PFG NMR) or by introducing differently labelled (but otherwise identical) molecules into the sample and monitoring their equilibration over the sample ( macroscopic measurements by tracer techniques) [185,186]. The process of molecular movement studied under such conditions is called self-diffusion. 

For the FTIR microscopic diffusion measurements (micro-FTIR spectroscopy) [30-32] the same Perkin-Elmer 1800 spectrometer was used, but a so-called IR microscope (Spectra Tech model IR-Plan) and an appropriate flow-through micro-cell were attached (see Figures 4a,b). 

Microscopic Measurement of Transport Diffusion and Permeation Through Transport Resistances on the Crystal Surface... 

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