2006/09/22 by Christian D. Santangelo, Randall D. Kamien · 8 citations
Chemistry · Materials Science · Mathematics · Physics and Astronomy · #Boundary (topology) #Chemistry #Condensed matter physics #Crystallography #Elastic energy #Geometry #Grain boundary #Lattice (music) #Liquid Crystal Research Advancements #Liquid crystal #Materials science #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Microstructure #Nonlinear system #Physics #Quantum mechanics #Superconductivity #Surface (topology) #Theoretical and Computational Physics #Twist #cond-mat.soft
paper · pdf · doi:10.1103/physreve.75.011702
published in Physical Review E 75(1), 011702 (American Physical Society) · 13 pages, 7 figures
arxiv created 2006/09/22 · openalex publication_date 2007/01/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 pi2 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 pi2 and pi3 grain boundary structures are particularly simple.