Effect of correlated flights on particle mobilities during single-file diffusion

When large adsorbates diffuse in the pores of zeolites and molecular sieves, they can undergo single-file diffusion. The mean-square displacement of particles during single-file diffusion, 〈${\mathrm{x}}^2$(t)〉, is proportional to ${\mathrm{t}}^{1\mathrm{/}2}$. By contrast, in the absence of other particles, an isolated adsorbate will perform normal diffusion with a tracer diffusion coefficient ${\mathrm{D}}_0$. An important goal of theoretical treatments of single-file diffusion is to relate ${\mathrm{D}}_0$ and the single-file mobility, F=〈${\mathrm{x}}^2$(t)〉/${2\mathrm{t}}^{1\mathrm{/}2}$. One physical feature that is ubiquitous in activated diffusion in periodic potentials, such as the diffusion of adsorbates in zeolites, is the appearance at sufficiently high temperatures of correlated flights that pass through multiple binding sites. We show that when isolated particles can perform multisite flights, the expression usually used to relate ${\mathrm{D}}_0$ and F is not exact, and we investigate methods that can lead to more accurate expressions. We discuss how the existence of long flights affects equilibrium adsorbate structures and comment on the implications of our results for the interpretation of experimental measurements of single-file diffusion.