Single 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... 

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. 

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