Liquid-mesophase-solid transitions: systematics of a density-wave theory

Abstract

The density-wave theory of Ramakrishnan and Yussouff is used to study phase transitions between liquid, liquid-crystalline, and crystalline phases. The different phases considered are liquid, nematic, smectic, discotic, bcc plastic crystal, orientationally ordered bcc, and a new incommensurate bcc crystal with orientational order. The direct correlation function, required as an input for the theory, is expressed approximately in terms of five generalized Fourier coefficients. The theory is then used to obtain sections through the phase diagram in the five-dimensional space of these coefficients. Simple approximations for the direct correlation function of hard ellipsoids of revolution are used to compare these phase diagrams with those obtained from experiments and numerical simulations. Molecular-field theories of smectic and discotic ordering are reexamined, and, given the potentials they use, it is shown that an orientationally ordered bcc crystal has a lower free energy than either the smectic or the discotic phase. The conditions required to stabilize smectic and discotic phases are examined.