Length and occupancy dependence of the tracer exchange in single-file systems

The tracer exchange between a finite single-file channel (in which the diffusing guest particles are not able to pass each other) and its surroundings is considered. A mean-field calculation shows that the mean intracrystalline residence time τintra is proportional to the 3rd power of the channel length L. Further, it is proportional to Θ/(1−Θ), where Θ denotes the relative occupancy. Monte Carlo simulations confirm these results to a satisfactory accuracy, especially at high occupancy. The essential mechanism of tracer exchange is considered in more detail.