Hard Disks Confined within a Narrow Channel

We employ inhomogeneous integral equation theory to investigate the equilibrium properties of hard disks confined to a channel of width L by hard parallel walls. If the channel width is narrowed below two disk diameters, then the system enters a quasi-one-dimensional regime for which the particles cannot move past each other. In the limit when L is equal to one particle diameter, the system reduces to the one-dimensional bulk along the center of the channel. We study first the dimensional crossover properties of the inhomogeneous Percus-Yevick (PY) integral equation as L is reduced and then investigate the behavior of a quasi one-dimensional system as the packing of the particles is increased for a fixed value of L. We find that the inhomogeneous PY equation is highly accurate for situations of quasi-one-dimensional confinement and that it predicts the onset of a structural transition to a zigzag state at higher packing. The excellent performance of this integral equation method and the ease with which it handles confinement-induced dimensional crossover is a consequence of the improved resolution which comes from treating explicitly the inhomogeneous two-body correlation functions.