SMECTIC-A AND SMECTIC-A(2) PHASES IN ALIGNED CYLINDERS WITH A CYLINDRICAL ATTRACTIVE SQUARE-WELL AT ONE END

Nematic (N), smectic-A (Sm-A), and bilayer smectic-A(2) (Sm-A(2)) phas es are studied for an aligned fluid of cylinders with a cylindrical at tractive square well at one end. The smectic phases are treated using an extension of the theory of Hosino, Nakano, and Kimura [J. Phys. Sec . Jpn. 48, 1709 (1979)]. The smectic-A(2) phase has a modulation in th e probability of a molecule pointing up (or down) in addition to the d ensity modulation of a smectic-A phase. As for the smectic-A density w ave, this second modulation requires an order parameter. A theory incl uding the two order parameters is developed and the phase diagram calc ulated. This phase diagram shows N-Sm-A, N-Sm-A(2), and Sm-A-Sm-A(2) p hase transitions that are second order, first order, and second order at high temperature above a tricritical point and first order below, r espectively. Somewhat surprisingly, there is also a Sm-A-Sm-A transiti on; this is bracketed by a critical point at high temperature and the Sm-A-Sm-A(2) transition at low temperature. There is thus a triple poi nt where the Sm-A-Sm-A and Sm-A-Sm-A(2) transitions meet. The two coex isting Sm-A phases differ in both the density and the wavelength of th e 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 fo rm [R.P. Sear and G. Jackson, Mol. Phys. 83, 961 (1994)].