Theory of Tracer Exchange in Single-File Systems

Tracer exchange in single-file systems (one-dimensional diffusional systems where the particles are not able to pass each other) shows peculiar and interesting features which differ considerably from that of transport diffusion or from the behaviour known from ordinary diffusional systems. A formalism relating the tracer exchange curve (as the observable of the tracer exchange experiment) to the residence time distribution (describing the intracrystalline diffusional mechanism) and the boundary condition (describing the situation outside) is introduced. The formalism is guite general and valid for any diffusional regime. Typical examples of the residence time distribution of a single-file system can be inferred from the tracer exchange curves obtained in a previous study by numerical simulations. Based on these examples, the tracer exchange curves for the single-file system subject to different boundary conditions (corresponding to a variety of experimental set-ups) are plotted and discussed.