Saddle–splay elasticity induced chiral structures in achiral liquid crystals within cylindrical geometry

ABSTRACT

On the basis of Landau–de Gennes theory and the finite-difference iterative method, spontaneous chiral structures in cylinders with degenerate planar boundary conditions are investigated. A double-twist director configuration can be achieved by the saddle–splay contribution, corresponding to the L₂₄ term in Landau–de Gennes theory. The twist angle increases as the radius R of the cylinder is reduced because the curvature of the cylindrical surface becomes larger. Moreover, we find fine structures of the domain walls and point defects between opposite-handed domains. An energy comparison shows that domain walls are the stable state for K₂₄/K> 0.6 (K₁₁ = K₃₃ = K, K₁₁, K₃₃ and K₂₄ are the splay, bend, saddle–splay elastic constants in Frank theory), whereas point defects are the stable state for K₂₄/K< 0.6.

Graphical abstract

Schematic of the chiral director configuration for domain walls (a, c) and point defects (b, d), induced by saddle-splay elasticity.

KEYWORDS:

• Landau–de Gennes theory
• chiral structures
• saddle–splay elasticity
• elastic anisotropy
• cylindrical geometry

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [under Grant No. 11374087 and No. 11447179].