Structural properties of hard-disk fluids under single-file confinement

The structural properties of confined single-file hard-disk fluids are studied analytically by means of a mapping of the original system onto a one-dimensional mixture of non-additive hard rods, which is exact in the polydisperse limit. Standard statistical-mechanical results are used as a starting point to derive thermodynamic and structural properties of the one-dimensional mixture, where the condition that all particles have the same chemical potential must be taken into account. Analytical results are then provided for the $n$th neighbor probability distribution function, the radial distribution function, and the structure factor. Comparison with simulation data shows a very good agreement of all data analyzed.