Stability of cholesteric blue phases in the presence of a guest component

We investigate theoretically, with the aid of numerical calculations based on a Landau–de Gennes theory, how two cubic cholesteric blue phases of a chiral liquid crystal, BP I and BP II, are stabilized when a guest component, such as a polymer network, is introduced and replace energetically costly defect regions. We show that the temperature range of stable BP I is significantly widened by the guest component, while the stability of BP II is only modestly enhanced.

Figure 1

Calculated phase diagram in the presence of a guest component of volume fraction $\phi$. For reference, the boundary between BP II and Iso ($\tau \simeq 0.224$) is also shown as a dotted line. Inset is a magnified one around $\tau =0$.

Figure 2

Plots of ${\overline{\varphi }}_{\mathrm{BPII}}\left(\phi \right)-{\overline{\varphi }}_{\mathrm{BPI}}\left(\phi \right)$ (red solid line) and ${\overline{\varphi }}_{\mathrm{BPI}}\left(\phi \right)-{\varphi }_{{\mathrm{N}}^{*}}$ (green dashed line) for $\tau =$ (a) $0.2$, (b) 0, (c) $-1$, and (d) $-10$. In (c) and (d), the values of $\phi$ satisfying ${\overline{\varphi }}_{\mathrm{BPII}}\left(\phi \right)-{\overline{\varphi }}_{\mathrm{BPI}}\left(\phi \right)$ and $F_{{\mathrm{BP}}_{\mathrm{I}}}=F_{{\mathrm{BP}}_{\mathrm{I}}\mathrm{I}}$ are highlighted by a cross ($\times$) and a vertical dashed line, respectively. Irregular oscillations of ${\overline{\varphi }}_{\mathrm{BPII}}\left(\phi \right)-{\overline{\varphi }}_{\mathrm{BPI}}\left(\phi \right)$ at small $\phi$ are a numerical artifact. Insets are the plots of ${\overline{\varphi }}_{\mathrm{BPII}}\left(\phi \right)$ (green dashed line), ${\overline{\varphi }}_{\mathrm{BPI}}\left(\phi \right)$ (red solid line), and, for reference, ${\varphi }_{{\mathrm{N}}^{*}}$ (blue dotted horizontal line).

Figure 3

Isosurfaces of free energy density at (a) and (b) $\tau =0$ and (c) and (d) $\tau =-1$. The value of $\varphi$ is (a) $0.01$, (b) $-0.005$, (c) $-0.06$, and (d) $-0.3$.