Theory of polygonal phases self-assembled from T-shaped liquid crystalline molecules

Abstract

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.

Figures (10)

• Figure 1: Schematic of TLCM chain containing a rigid backbone block $R$ (blue), two ends flexible blocks $A$ (red), and a flexible side block $B$ (green).
• Figure 2: Layered structures self-assembled from TLCMs. $\rm \bf{Smectic}$-$\rm \bf{A}$$\bf{phases}$ (a1) SmA-AR; (a2) SmA-ABR; $\rm \bf{Smectic}$-$\rm \bf{P}$$\rm \bf{phases}$ (b1) SmP-ABR; (b2) SmP-BR; $\rm \bf{Cholesteric}$$\rm \bf{phases}$ (c1) Chol-AR; (c2) Chol-ABR; and $\rm \bf{Zigzag}$$\rm \bf{phase}$ (d) Zig-ABR. In the second column, red, green, and blue represent components $A$, $B$, and $R$ with high concentration, respectively. The third, fourth and fifth columns present the density distributions of components $A$, $B$ and $R$, respectively. The sixth column exhibits the orientation distribution of the region framed by the white line in the second column. The last column shows the main diffraction peaks of components $A$ (red) and $B$ (green).
• Figure 3: Simple polygonal phases self-assembled from TLCMs. (a) Triangle; (b) Square; (c) Diamond; (d) Pentagon; (e) Hexagon; (f) Dual-Pentagon. The second column presents the morphologies combined with schematic arrangement diagrams, in which $A$-, $B$-, and $R$-rich domains are plotted in red, green and blue colors, respectively. The third, fourth and fifth columns show the density distributions of components $A$, $B$ and $R$, respectively. The last column shows the main diffraction peaks of components $A$ (red) and $B$ (green).
• Figure 4: Giant polygonal phases: (g) $\rm Diamond_{8}$; (h) $\rm Square_{8}$; (i) $\rm Hexagon_{8}$; (j) $\rm Pentagon_{9}$; (k) $\rm Square_{10}$. The meanings represented by subfigures are similar with Fig. \ref{['fig:simplehoney']}.
• Figure 5: Giant polygonal phases: (l) $\rm Pentagon_{10}$; (m) S-$\rm Hexagon_{10}$; (n) $\rm Hexagon_{10}$; (o) $\rm Square_{12}$; (p) $\rm Hexagon_{12}$. The meanings of each subfigure are similar with Fig. \ref{['fig:simplehoney']}.