Phase equilibria of a nematic and smectic-A mixture

A phase diagram of a mixture consisting of nematic and smectic liquid crystals has been calculated self-consistently by combining Flory–Huggins (FH) theory for isotropic mixing and Maier–Saupe–McMillan (MSM) theory for smectic-A ordering. However, the MSM theory can be deduced to the original Maier–Saupe (MS) theory for nematic ordering. To describe the phase transitions involving induced smectic phase and nematic + smectic equilibrium, two nematic and two smectic order parameters for the nematic/smectic mixtures have been coupled through the normalized partition function and the orientation distribution function. Self-consistent numerical solution has been sought in establishing nematic/smectic phase diagrams involving (i) phase separation between nematic and smectic liquid crystals and (ii) occurrence of induced smectic in a nematic/smectic mixture. The predictive capability of this combined FH/MSM theory has been tested critically with a reported phase diagram of a nematic/smectic liquid-crystal mixture and also with our experimental phase diagram of a mixture consisting of a nematic side-on side-chain liquid-crystalline polymer and a smectic low molar mass liquid crystal.