Diffusion samples, configuration

The apparent simplicity of this approach is, however, deceptive. For measurement of intracrystalline diffusion the method works well when diffusion is relatively slow (large crystals and/or low diffusivity), but when sorption rates are rapid the uptake rate may be controlled by extracrystalline diffusion (through the interstices of the adsorbent bed) and/or by heat transfer. The intrusion of such effects is not always obvious from the shape of the uptake curve, but it may generally be detected by changing the sample quantity and/or the sample configuration. It is in principle possible to allow for such effects in the mathematical model used to interpret the uptake curves (Fig. 2), and indeed the modeling of nonisothermal systems has been studied in considerable detail [8-12]. However, any such intrusion will obviously diminish the accuracy and confidence with which the intracrystalline diffusivities can be determined. 

Fig. 1.8. Sample configuration used for diffuse reflectance. After Perkins [56]. Reprinted with permission from W.D. Perkins, in Practical Sampling Techniques for Infrared Analysis (P.B. Coleman, ed.), CRC Press, Boca Raton (1993). Copyright CRC Press, Boca Raton, Florida.

Do we expect this model to be accurate for a dynamics dictated by Tsallis statistics A jump diffusion process that randomly samples the equilibrium canonical Tsallis distribution has been shown to lead to anomalous diffusion and Levy flights in the 5/3 < q < 3 regime. [3] Due to the delocalized nature of the equilibrium distributions, we might find that the microstates of our master equation are not well defined. Even at low temperatures, it may be difficult to identify distinct microstates of the system. The same delocalization can lead to large transition probabilities for states that are not adjacent ill configuration space. This would be a violation of the assumptions of the transition state theory - that once the system crosses the transition state from the reactant microstate it will be deactivated and equilibrated in the product state. Concerted transitions between spatially far-separated states may be common. This would lead to a highly connected master equation where each state is connected to a significant fraction of all other microstates of the system. [9, 10]... 

The comparison with experiment can be made at several levels. The first, and most common, is in the comparison of derived quantities that are not directly measurable, for example, a set of average crystal coordinates or a diffusion constant. A comparison at this level is convenient in that the quantities involved describe directly the structure and dynamics of the system. However, the obtainment of these quantities, from experiment and/or simulation, may require approximation and model-dependent data analysis. For example, to obtain experimentally a set of average crystallographic coordinates, a physical model to interpret an electron density map must be imposed. To avoid these problems the comparison can be made at the level of the measured quantities themselves, such as diffraction intensities or dynamic structure factors. A comparison at this level still involves some approximation. For example, background corrections have to made in the experimental data reduction. However, fewer approximations are necessary for the structure and dynamics of the sample itself, and comparison with experiment is normally more direct. This approach requires a little more work on the part of the computer simulation team, because methods for calculating experimental intensities from simulation configurations must be developed. The comparisons made here are of experimentally measurable quantities. 

In the worse case, where either sample temperature, pressure or reactor integrity issues make it impossible to do otherwise, it may be necessary to consider a direct in situ fiber-optic transmission or diffuse reflectance probe. However, this should be considered the position of last resort. Probe retraction devices are expensive, and an in situ probe is both vulnerable to fouling and allows for no effective sample temperature control. Having said that, the process chemical applications that normally require this configuration often have rather simple chemometric modeling development requirements, and the configuration has been used with success. 

The most common separators include the Ryhage or jet diffusion separator (74), the Watson-Biemann or pore diffusion separator (75), and the membrane solution diffusion separator originally developed by Llewellyn (75). The first two separators involve direct passage of the sample into the mass spectrometer the low molecular weight helium diffuses more readily and is pumped away. The membrane separator involves diffusion of the sample through a silicone membrane while the carrier gas vents to the atmosphere carrier gas is thus not confined to helium. There is no best separator the choice depends on the nature of the compounds, the temperature range over which it will be operated, and most usually what is available in a particular laboratory. A convenient configuration for a double-beam mass spectrometer such as the AEI MS-30 is two different separators, one into each beam, which permits rapid evaluation of separator performance. 

Raman spectra were taken on a home built system, composed of Spectra-Physics 2020 series lasers, coupled with a Dilor XY-800 triple spectrometer and a Whight Instruments nitrogen cooled CCD. All samples were measured at room temperature in a backscattering configuration, with 514.53 nm Ar+ laser excitation. The laser power was tuned between 1 mW and 30 mW. UV-VIS diffuse reflectance spectra were taken on a Varian Cary 5 spectrophotometer, equipped with a specially designed Praying Mantis diffuse reflectance attachment of Harrick. 

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