Calculation of the absolute free energy of a smectic-A phase

In this paper, we provide a scheme to compute the absolute free energy of a smectic-A phase via the "indirect method." The state of interest is connected through a three-step reversible path to a reference state. This state consists of a low-density layer of rods coupled to two external fields maintaining these rods close to the layer's plane and oriented preferably normal to the layer. The low-density free energy of the reference state can be computed on the basis of the relevant second virial coefficients between two rods coupled to the two external fields. We apply this technique to the Gay-Berne potential for calamitics with a parameter set leading to stable isotropic (I), nematic (N), smectic-A (SmA), and crystal (Cr) phases. We locate the I-SmA phase transition at low pressure and the sequence of phase transitions I-N-SmA along higher-pressure isobars and we establish the location of the I-N-SmA triple point. Close to this triple point, we show that the N-SmA transition is clearly first order. Our results are compared to the coexistence lines of the approximate phase diagram elucidated by de Miguel et al. [J. Chem. Phys. 121, 11183 (2004)] established through the direct observation of the sequence of phase transitions occurring along isobars under heating or cooling sequences of runs. Finally, we discuss the potential of our technique in studying similar transitions observed on layered phases under confinement.