On the calculation of the absolute grand potential of confined smectic-A phases

We determine the absolute grand potential Λ along a confined smectic-A branch of a calamitic liquid crystal system enclosed in a slit pore of transverse area A and width L, using the rod–rod Gay–Berne potential and a rod–wall potential favouring perpendicular orientation at the walls. For a confined phase with an integer number of smectic layers sandwiched between the opposite walls, we obtain the excess properties (excess grand potential Λexc, solvation force fs and adsorption Γ) with respect to the bulk phase at the same μ (chemical potential) and T (temperature) state point. While usual thermodynamic integration methods are used along the confined smectic branch to estimate the grand potential difference as μ is varied at fixed L, T, the absolute grand potential at one reference state point is obtained via the evaluation of the absolute Helmholtz free energy in the (N, L, A, T) canonical ensemble. It proceeds via a sequence of free energy difference estimations involving successively the cost of locali...