  Extensive experimental studies have shown that numerous ordered phases can be
formed via the self-assembly of T-shaped liquid crystalline molecules (TLCMs)
composed of a rigid backbone, two flexible end chains and a flexible side
chain. However, a comprehensive understanding of the stability and formation
mechanisms of these intricately nanostructured phases remains incomplete. Here
we fill this gap by carrying out a theoretical study of the phase behaviour of
TLCMs. Specifically, we construct phase diagrams of TLCMs by computing the free
energy of different ordered phases of the system. Our results reveal that the
number of polygonal edges increases as the length of side chain or interaction
strength increases, consistent with experimental observations. The theoretical
study not only reproduces the experimentally observed phases and phase
transition sequences, but also systematically analyzes the stability mechanism
of the polygonal phases.
