NEMATIC TO SMECTIC-A TRANSITION IN THE ASYMPTOTIC LIMIT OF VERY LONG HARD SPHEROCYLINDERS

We study a system of hard spherocylinders with rotational freedom in which the length-to-diameter ratio of the spherocylinder L/D is large. The asymptotic expressions for the one-particle distribution function and the free-energy functional in the limit L/D --> infinity are found. The virial expansion of the free energy is used to study the nematic to smectic-A transition by means of a bifurcation analysis and the third-order term of the expansion is taken into account. Then the bifurcation analysis is extended to the next order to determine the order of the transition. We also compare our results with computer simulations and other density-functional theories.