Smectic-A and smectic-A2 phases in aligned cylinders with a cylindrical attractive square well at one end.

Abstract

Nematic (N), smectic-A (Sm-A), and bilayer smectic-${\mathit{A}}_{2}$ (Sm-${\mathit{A}}_{2}$) phases are studied for an aligned fluid of cylinders with a cylindrical attractive square well at one end. The smectic phases are treated using an extension of the theory of Hosino, Nakano, and Kimura [J. Phys. Soc. Jpn. 46, 1709 (1979)]. The smectic-${\mathit{A}}_{2}$ phase has a modulation in the probability of a molecule pointing up (or down) in addition to the density modulation of a smectic-A phase. As for the smectic-A density wave this second modulation requires an order parameter. A theory including the two order parameters is developed and the phase diagram calculated. This phase diagram shows N--Sm-A, N--Sm-${\mathit{A}}_{2}$, and Sm-A--Sm-${\mathit{A}}_{2}$ phase transitions that are second order, first order, and second order at high temperature above a tricritical point and first order below, respectively. Somewhat surprisingly, there is also a Sm-A--Sm-A transition; this is bracketed by a critical point at high temperature and the Sm-A--Sm-${\mathit{A}}_{2}$ transition at low temperature. There is thus a triple point where the Sm-A--Sm-A and Sm-A--Sm-${\mathit{A}}_{2}$ transitions meet. The two coexisting Sm-A phases differ in both the density and the wavelength of the smectic density modulation. Also notable is the very weak dependence on temperature of the N--Sm-A transition, in contrast to earlier work on cylinders with saturable attractive forces such that only dimers form [R. P. Sear and G. Jackson, Mol. Phys. 83, 961 (1994)].