Normalized tracer exchange curves

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...

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. 

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).

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