Phase behavior of the thermotropic melt of asymmetric V-shaped molecules

The phase behavior of the monodisperse melt of V-shaped molecules composed of two rigid segments of different lengths joined at their ends at an external angle alpha has been examined within the Landau-de Gennes approach. Each rigid segment consists of a sequence of monomer units; the anisotropic interactions in the system are assumed to be of the Maier-Saupe form. The coefficients of the Landau-de Gennes free-energy expansion have been found from a microscopic model of V-shaped molecule. A single Landau point at which the system undergoes direct continuous transition from isotropic to biaxial nematic phase is found for asymmetry parameter phi = 1/3 or phi = 2/3, where f is the number fraction of monomer units in one of the segments. Two Landau points are found in a range 1/3 < phi < 2/3. Only isotropic and nematic states are found to be stable for 0 <= phi < 1/3 and 2/3 < phi <= 1. Regions of stability of isotropic, prolate uniaxial, and biaxial nematic phases are found for phi = 1/3 and phi = 2/3. In addition, a stable oblate uniaxial phase is revealed if asymmetry parameter falls in the range 1/3 < phi < 2/3. The region of stability of the biaxial nematic phase becomes smaller as parameter f increases from 1/3 to 1/2 (or decreases from 2/3 to 1/2). Coefficients of the gradient terms have been found; for certain values of asymmetry parameter these coefficients can become negative in some ranges of angles.