Elastic moduli of blue phases of cholesteric liquid crystals with low chirality

A new theoretical approach has been developed to describe the elastic properties of cubic blue phases of cholesteric liquid crystals (LCs). Blue phases are three-dimensional periodic chiral liquids with local anisotropy of the average orientation of molecules, and due to their periodicity, they have lattice elastic moduli characteristic of ordinary crystalline solids. The rigid tensor approximation, which works well at low chirality parameter ($\kappa\ll1$), was used to calculate the elastic moduli of the experimentally observed blue phases $O^8$ (BPI) and $O^2$ (BPII). It is shown that in the one-constant approximation for Frank moduli of LCs ($K_{11}=K_{22}=K_{33}$), the cubic lattice of blue phases has isotropic elasticity, and the Lam\'e's first parameter $\lambda_\mathrm{L}$ and Poisson's ratio $\nu$ are equal to zero. It is found that the sign of the Poisson's ratio is determined by the ratio of elastic moduli $K_0/K_1$; in particular, when $K_0>K_1$, the Poisson's ratio is negative.