Single-file systems profile

Fig.4 Comparison of the concentration profiles of tagged particles obtained by DMC simulations for tracer exchange in single-file systems of length L (oscillating solid lines) with the concentration profiles for normal diffusion, with Dsim and N given in Table 1 (solid lines) at times ti = 0.93 x 10 r, t2 = 2.1 x 10 r, t = 3.7 x 10 , and t4 = 7.6 x 10 r (r is the duration of the elementary diffusion step). From [57] with permission...

SO far only been attained by Monte Carlo simulations. Figure 5 illustrates the situation due to the combined effect of diffusion and catalytic reaction in a single-file system for the case of a monomolecular reaction A B [1]. For the sake of simplicity it is assumed that the molecular species A and B are completely equivalent in their microdynamic properties. Moreover, it is assumed that in the gas phase A is in abimdance and that, therefore, only molecules of type A are captured by the marginal sites of the file. Figure 5 shows the concentration profile of the reaction product B within the singlefile system imder stationary conditions. A parameter of the representation is the probabiUty k that during the mean time between two jump attempts (t), a molecule of type A is converted to B. It is related to the intrinsic reactivity k by the equation... 

Fig. 5 Concentration profiles of the molecules of species B within the single-file system under stationary conditions and comparison with the dependence to be expected for ordinary diffusion (broken line, Eq. 29). The quantity 2L(klDy (the Thiele modulus 0) in Eq. 29 has been chosen to coincide with the generalized Thiele modulus (cf. Eq. 30) of the single-file reaction for k = 1.27 x 10 (0 = 2.77). z denotes the distance from the middle of the file and L = NX its length. From [1] with permission...

Fig. 8 Average residence time profile (in units of the time r between two jump attempts) of the particles in the single-file systems considered in Fig. 7. From [72] with permission...

In complete agreement with the fact that the product molecules in a singlefile system are prevented from leaving the system by their file neighbors, the concentration profiles in the single-file cases show a much more pronounced tendency of accumulation of the reaction products in the file center than in the case of normal diffusion. Under stationary conditions, the effective reactivity k is related to the intrinsic reactivity k by the equation... 

Fig. 6 T-G (temperature-field) phase diagram for a system that exhibits first-order transitions (solid line) that are terminated at a single critical point of the water-vapour type. The supercritical evolution emanates further from the critical point along a Widom line (dashed line). The heat-capacity Cp and order-parameter S temperature profiles corresptmding to different G values are shown in file graph. The dotted lines represent the discrmtinuity in the Cp(T) and S(J) profiles, corresponding to the phase-coexistoice regirai in which the latent heat is released...

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