Effect of arm-length polydispersity on the phase behaviour of V-shaped molecules

Phase behaviour of a melt of polydisperse V-shaped particles is considered within the Landau theory of phase transitions. It is assumed that particles are composed of two semi-flexible segments, one of which has a constant length, while the other has an arbitrary length distribution; the segments are joined at an external angle. The contributions up to the sixth order into the Landau–de Gennes free energy expansion in terms of the alignment tensor are presented in a diagrammatic form. The phase diagrams have been obtained for a special case characterised by rigid segments and Schulz–Zimm distribution for the length of the segment. It is shown that an increase in the polydispersity index of the segment leads to an increase of the isotropic–nematic transition temperature, substantial increase of the stability region of a uniform biaxial nematic (NB) phase, and a decrease in the area occupied by a uniform oblate nematic phase.