Dimensional crossover of hard parallel cylinders confined on cylindrical surfaces

functional in turn is obtained from the corresponding two-dimensional functional for a fluid of hard disks of radius R on a flat surface with centers of mass confined onto a circumference of radius R-0. From the density functional of circular arcs, and by applying a dimensional expansion procedure to the spatial dimension orthogonal to the plane of the circumference, we finally obtain the density functional of curved rectangles of edge lengths sigma and L. The phase behavior of a fluid of aligned curved rectangles is obtained by calculating the free-energy branches of smectic, columnar, and crystalline phases for different values of the ratio R-0/R in the range 1 < R-0/R <= 4; the smectic phase turns out to be the most stable except for R-0/R = 4, where the crystalline phase becomes reentrant in a small range of packing fractions. When R-0/R < 1 the transition is absent, since the density functional of curved rectangles reduces to the 1D Percus functional.

Dimensional crossover of hard parallel cylinders confined on cylindrical surfaces Articles