Tracer exchange curves

For an estimate of the correlation between t he intracrystalline mean life time and the system properties, the exchange curve between the (labelled) molecules of a single-file system and the (unlabelled) surroundings ( tracer exchange curve ) may be assumed to be determined by a single dimensionless parameter... 

With the TEX-PEP technique experiments on the diffusion and adsorption of mixture of n-hexane/2-methylpentane in large silicalite-1 crystals have been performed. By modeling the experimental tracer exchange curves values of intracrystalline diffusion coefficient and adsorption constant were obtained. Slight preference for the adsorption of /t-hexane was found. Diffusivity of -hexane sharply decreases with increasing fraction of its isomer, since the last one occupies channel intersections thus blocking zeolite network. 

Fig. 3 The normalized tracer exchange curves in single-file systems obtained by dynamic Monte Carlo (DMC) simulations for various file lengths (=L in the figiu e) and loadings (0) (points). The dashed and solid lines show the best fit lines for 0 = 0.5 with the slope of 1/2 and 1/4 expected for the mechanism of normal and single-file diffusion, respectively, in the limit of short times. From [57] with permission...

It is interesting to note that the residence time distribution may also be used as a generating function for the tracer exchange curve as introduced in Sect. 3.2. The relative amount of tracer exchange at a certain time t is simply the sum over all molecules which have entered and remained in the system between time zero and the present instant, or, in other words, the residence... 

Fig. 9 Probability distribution function (p r) (a) and effectiveness factor rj k) (b) corresponding to the tracer exchange curves in the limiting cases of dominating single-file diffusion, normal diffusion and surface barriers as a function of the quotient of r and Tintra- From [74] with permission...

Figure 9 displays the probability distribution function (p r) and the effectiveness factor r] k), which have been calculated via Eqs. 36 and 34 from the tracer exchange curves in the limiting cases of single-hle diffusion, normal diffusion and barrier confinement. The fact that in all cases the residence time distribution function is found to decrease monotonically may be easily rationalized as a quite general property. Due to the assumed stationarity of the residence time distribution function, the number of molecules with a residence time r is clearly the same at any instant of time. The number of molecules with a residence time r + At may therefore be considered as the number of molecules with a residence time r minus the number of molecules which will leave the system in the subsequent time interval At. Therefore, (p x) must quite generally be a monotonically decaying function. 

Fig. 12 Tracer exchange curve of propane in AIPO4-5 at 293 K and a loading of 0.7 molecules per unit cell. From [75] with permission...

The methods described so far for studying self-diffusion are essentially based on an observation of the diffusion paths, i.e. on the application of Einstein s relation (eq 3). Alternatively, molecular self-diffusion may also be studied on the basis of the Fick s laws by using iso-topically labeled molecules. As in the case of transport diffusion, the diffusivities are determined by comparing the measured curves of tracer exchange between the porous medium and the surroundings with the corresponding theoretical expressions. As a basic assumption of the isotopic tracer technique for studying self-diffusion, the isotopic forms are expected to have... 

A plot of the relative intensity of the broad constituent versus the observation time (i.e. the separation between the two field gradient pulses) contains information which is analogous to that of a tracer exchange experiment between a particular crystallite containing e.g. labelled molecules and the unlabelled surroundings. Therefore, this way of analysis of PFG NMR data of zeolitic diffusion has been termed the NMR tracer desorption technique [60]. The first statistical moment ( time constant ) of the NMR tracer desorption curve represents the intracrystalline mean lifetime Tintra of the molecules under study. 

The tracer response -curve is calculated by numerically integrating Equation (15.56) and using the concentration-time curve at the inlet. The amount of tracer that does not exchange with the film shows up in the -curve as a sharp peak, where the width of the peak is only determined by the tracer injection curve. The amount of tracer that is transferred to the film is slowly released to subsequent slugs and appears in the -curve as a long tail. 

If the fluid that bypasses the catalyst bed as well as the fluid that passes through the bed were both in plug flow, and if there were no exchange of fluid between the two regions, the tracer response curve might resemble the one shown below. 

Figure 12. Extent of dissolution and re-precipitation between aqueous Fe(III) and hematite at 98°C calculated using Fe-enriched tracers. A. Percent Fe exchanged (F values) as calculated for the two enriched- Fe tracer experiments in parts B and C. Large diamonds reflect F values calculated from isotopic compositions of the solution. Small circles reflect F values calculated from isotopic compositions of hematite, which have larger errors due to the relatively small shifts in isotopic composition of the solid (see parts B and C). Curves show third-order rate laws that are fit to the data from the solutions. B. Tracer experiment using Fe-enriched hematite, and isotopically normal Fe(lll). C. Identical experiment as in part B, except that solution Fe(lll) is enriched in Te, and initial hematite had normal isotope compositions. Data from Skulan et al. (2002).

Figure 6.9 Elution curve for W-tracer modelling the seaborgium separation in ARCAII using a solution of 0.1 M HNO3/5 x 10" 4 M HF with a flow rate of 1 ml min-1. The 1.6 x 8 mm columns are filled with the cation exchange resin Aminex A6. Reproduced with permission from Schadel etal. (1997b). 1997 R. Oldenbourg Verlag.

FIG. 3. Flow-limited and barrier-limited exchange. Outflow curves for an extracellular tracer with plasma flows of 0.2 (diamonds), 1.0 (circles), and 2.0 (squares) ml g min", (a) How-limited exchange with PSg of 100 ml g min", (b) Curves from (a) scaled by their mean transit times, T, showing similarity scaling, (c) Barrier-limited exchange with PSg of 10 ml g min", (d) Transit time scaled curves from (c). 

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