摘要

The liquid crystalline phase behaviour of a chiral two-site hard Gaussian overlap fluid is examined using the well-known Parsons-Lee extension of the theory of Onsager. The hard-core model is constructed such that the vector connecting the centers of two hard Gaussian segments is perpendicular to the long axes of both segments. The microscopic chirality of the particle can be controlled with the dihedral angle between the long axes of the hard Gaussian segments, the distance between the two segments, and the length-to-breath ratios of each segment. In the framework of the Parsons-Lee approach three different types of phases are considered, namely, the isotropic liquid state, and the nematic and the chiral nematic (cholesteric) liquid crystalline states. For simplicity, the orientation of the particles is restricted to the plane perpendicular to the twist axis, and the particles do not have internal freedom to rotate around their main symmetry axes. The geometric condition for the formation of a chiral nematic phase, the properties of the helical structure, and the phase boundary of the ordering transition are determined by means of a free energy minimization. It is shown that steric (shape) chirality always gives rise to a helical structure in the nematic phase, and that the low density chiral systems can undergo a transition from an isotropic liquid to a twisted nematic phase on increasing the density. Analytical expressions are obtained for the twist period (pitch) in the limit of parallel stacking of the rod-like segments in layers normal to the helical axis, which are only valid for systems characterized by weak chiral strengths. A key finding of the numerical calculations is that the pitch is very sensitive to the segment separation, but not to the density or aspect ratio. It is interesting to note that the inverse of the pitch is predicted to depend linearly on the dihedral angle in all of the cases studied.

  • 出版日期2011