Stabilization of blue phases by the variation of elastic constants

We study theoretically the effect of the variation of the elastic constants on the stability of cholesteric blue phases (BPs). We demonstrate that the stability of BPs is greatly enhanced when the bend elastic constant $K_{33}$ is smaller, in agreement with recent experimental findings. Larger splay ($K_{11}$) and twist ($K_{22}$) elastic constants also stabilize BPs. Our argument sheds light on the subtle effect of the variation of the elastic constants on the stability of BPs, and could guide the synthesis of liquid crystals with a wider temperature range of stable BPs.

Figure 1

(a) Plots of $t(1,K_{22}/K,K_{33}/K)$ with the variation of $K_{33}/K$ (solid red lines) and $t(K_{11}/K,K_{22}/K,1)$ with the variation of $K_{11}/K$ (dashed blue lines) for $K_{22}/K=1$ and $0.5$. (b) Plot of $t(1,K_{22}/K,1)$ as a function of $K_{22}/K$. Equation (8) is used for the evaluation of $t$.

Figure 2

(a) Plots of $t(1,K_{22}/K,K_{33}/K)$ with the variation of $K_{33}/K$ (solid red lines) and $t(K_{11}/K,K_{22}/K,1)$ with the variation of $K_{11}/K$ (dashed blue lines) for $K_{22}/K=1$ and $0.5$. (b) Plot of $t(1,K_{22}/K,1)$ as a function of $K_{22}/K$. Equation (9) is now used for the evaluation of $t$.