Triply-Periodic Smectics

Details Triply-Periodic Smectics Triply-Periodic Smectics

2006-09-22

arxiv.org/abs/cond-mat/0609596v1

Phys. Rev. E 75 (2007) 011702

Physics

Condensed Matter

Soft Condensed Matter

13 pages, 7 figures

Scientific paper

10.1103/PhysRevE.75.011702

Twist-grain-boundary phases in smectics are the geometrical analogs of the Abrikosov flux lattice in superconductors. At large twist angles, the nonlinear elasticity is important in evaluating their energetics. We analytically construct the height function of a pi/2 twist-grain-boundary phase in smectic-A liquid crystals, known as Schnerk's first surface. This construction, utilizing elliptic functions, allows us to compute the energy of the structure analytically. By identifying a set of heretofore unknown defects along the pitch axis of the structure, we study the necessary topological structure of grain boundaries at other angles, concluding that there exist a set of privileged angles and that the \pi/2 and \pi/3 grain boundary structures are particularly simple.

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