Topological fine structure of smectic grain boundaries and tetratic disclination lines within three-dimensional smectic liquid crystals

Monderkamp, Paul A.; Wittmann, René; Vrugt, Michael te; Voigt, Axel; Wittkowski, Raphael; Löwen, Hartmut

doi:10.48550/arxiv.2201.01736

Cited by 1 publication

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References 116 publications

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“…However, these same properties contrive to make lamellar fluids notoriously difficult to model and understanding their structural dynamics in complex geometries remains an outstanding challenge. Molecular dynamics [29][30][31], Monte-Carlo [32][33][34], density functional approaches [24,35,36] and neural networks [37] have offered exciting results, but a major hurdle remains the difficulty of performing numerical simulations on macroscopic length scales. The primary source of difficulty faced by macroscopic theories is that complex scalar order parameters for smectics are not truly a single-valued functions of position and so possess ambiguity [38,39].…”

Section: Introductionmentioning

confidence: 99%

Smectic layering: Landau theory for a complex-tensor order parameter

Paget

Alberti

Mazza

et al. 2022

J. Phys. A: Math. Theor.

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Composed of microscopic layers that stack along one direction while maintaining fluid-like positional disorder within layers, smectics are excellent systems for exploring topology, defects and geometric memory in complex confining geometries. However, the coexistence of crystalline-like characteristics in one direction and fluid-like disorder within layers makes lamellar liquid crystals notoriously difficult to model—especially in the presence of defects and large distortions. Nematic properties of smectics can be comprehensively described by the Q-tensor but to capture the features of the smectic layering alone, we develop a phenomenological Landau theory for a complex-tensor order parameter E, which is capable of describing the local degree of lamellar ordering, layer displacement, and orientation of the layers. This theory can account for both parallel and perpendicular elastic contributions. In addition to resolving the potential ambiguities inherent to complex scalar order parameter models, this model reduces to previous employed models of simple smectics, and opens new possibilities for numerical studies on smectics possessing many defects, within complex geometries and under extreme confinement.

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