Single intracrystalline diffusion

When only a single intracrystalline diffusion process occurs in a microporous system, the characteristic functions are [2,3]... 

Fig. 3.1.11 Relative effective intracrystalline diffusivities D(t)/D0 as function of JDot for n-hexane under single-component adsorption (circles) and for n-hexane (triangles) and tetrafluoromethane (rectangles) under two-...

If a NS monocrystal takes up a single component from a fluid phase and Intercrystalline transport does not influence the uptake rate, one should be aware of the possibility that, besides intracrystalline diffusion, the following processes may either contribute or even govern the uptake rate ... 

It is well known that, under the assumption that the exchange between the product molecules in the interior of the zeolite crystallites and the reactant molecules in the intercrystalline space is limited by intracrystalline diffusion, the effectiveness of reactions catalyzed by the internal surface of zeolite crystallites is a function of a single parameter, the Thiele modulus [3. It is defined by the relation... 

It has been demonstrated by numerical simulations [9] that, with this definition, eq. 2 provides a reasonable order-of-magnitude estimate of the effectiveness factor also in the case of single-file diffusion. While in the case of ordinary diffnsion the intracrystalline mean life time may be easily correlated with the crystal size and the internal mobility [11], similar analytical expressions for single-file diffusion have not been established. The rule-of-thumb given in Ref. [10] on the basis of a few first numerical simulations turned out to be of rather limited validity in recent more refined considerations [12]. 

Most importantly, combining the expressions for the intracrystalline mean life time Eq. 23 and the effective self-diffusivity (Eq. 19), in the case of singlefile diffusion the mean time of molecular exchange is found to scale with L, rather than with the dependence typical of normal diffusion. Therefore, under the conditions of single-file diffusion, the exchange rate with zeoUte crystallites decreases even more pronounced with increasing crystal sizes as in the case of normal diffusion. 

The method is in principle applicable also to the measurement of micropore or intracrystalline diffusivities, but the practical difficulties of mounting and sealing a single small zeolite crystal have hitherto prevented such applications. However, these difficulties have been overcome and the results of two studies have been recently reported in which diffusion through a single (iOO /tm) zeolite crystal, mounted in a metal plate, was measured by this method. 

The prerequisites of the evaluation of data characteristic of intracrystalline processes in the case of zeolite sorbents are discussed, along with the conditions under which diffusion can be compared to self-diffusion. Selected results of investigations carried out in the author s laboratory are given in order to demonstrate the consistency of sorption kinetic data with intracrystalline mobility data of single components on molecular sieves (HS). Various types of surface barrier which may influence the uptake rate are also described. 

Diffusion measurements under nonequilibrium conditions are more complicated due to the difficulties in ensuring well defined initial and boundary conditions. IR spectroscopy has proved to be a rather sensitive tool for studying simultaneously the intracrystalline concentration of different diffusants, including the occupation density of catalytic sites [28], By choosing appropriate initial conditions, in this way both co- and counterdiffusion phenomena may be followed. Information about molecular transport diffusion under the conditions of multicomponent adsorption may also be deduced from flow measurements [99], As in the case of single-component adsorption, the diffusivities arc determined by matching the experimental data (i.e. the time dependence of the concentration of the effluent or the adsorbent) to the corresponding theoretical expressions. 

Galwey and Laverty [13] concluded, from complementary kinetic investigations, that dehydration of Ca(OH)2 was satisfactorily represented by the first-order equation. The overall rate of H2O release was sensitive to the locally prevailing water vapour pressure and its distribution within the reactant mass. Kinetic characteristics were strongly influenced by the rates of intracrystalline and intercrystalline diffusive escape of product water which strongly depended on reactant compaction/dispersal within the heated zone. Measured values of and for Ca(OH)2 dehydration could not be identified with a single reaction step because... 

Once coarsening and recrystallization stops, graphite flakes will preserve isotope composition due to slow diffusion. Intracrystalline zoning of 5 C has been detected in some crystals by most studies that have evaluated it. This has been demonstrated by delamination of single flakes at the 20-100 pm-scale (Wada 1988, Arita and Wada 1990, Kitchen and Valley 1995, Satish-Kumar 2000), by ion microprobe (Farquar et al. 1999) or, more simply, by analysis of large vs. small flakes from the same rock (Kitchen and Valley 1995). 

Grenier, P., et al.. Single-step thermal method to measure intracrystalline mass diffusion in adsorbents, AlChE J., 41(9), 2047-2057 (1995). 

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