Department of Physics Papers

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Journal Article

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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 π/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 π/2 and π/3 grain boundary structures are particularly simple.


Suggested Citation:
C.D. Santangelo and R.D. Kamien. (2007). Triply periodic smectic liquid crystals. Physical Review E 75, 011702.

© 2007 The American Physical Society

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Date Posted: 19 May 2011

This document has been peer reviewed.