Journal article
Saddle-splay screening and chiral symmetry breaking in toroidal nematics
Soft matter, Vol.10(23), pp.4192-4198
01 Jan 2014
PMID: 24780941
Abstract
We present a theoretical study of director fields in toroidal geometries with degenerate planar boundary conditions. We find spontaneous chirality: despite the achiral nature of nematics the director configuration shows a handedness if the toroid is thick enough. In the chiral state the director field displays a double twist, whereas in the achiral state there is only bend deformation. The critical thickness increases as the difference between the twist and saddle-splay moduli grows. A positive saddle-splay modulus prefers alignment along the meridian of the bounding torus, and hence promotes a chiral configuration. The chiral-achiral transition mimics the order-disorder transition of the mean-field Ising model. The role of the magnetisation in the Ising model is played by the degree of twist. The role of the temperature is played by the aspect ratio of the torus. Remarkably, an external field does not break the chiral symmetry explicitly, but shifts the transition. In the case of toroidal cholesterics, we do find a preference for one chirality over the other - the molecular chirality acts as a field in the Ising analogy.
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Details
- Title
- Saddle-splay screening and chiral symmetry breaking in toroidal nematics
- Creators
- Vinzenz Koning - Lorentz InstituteBenjamin C. van Zuiden - Lorentz InstituteRandall D. Kamien - Department. of Physics and Astronomy, University of Pennsylvania, Philadelphia, USAVincenzo Vitelli - Lorentz Institute
- Publication Details
- Soft matter, Vol.10(23), pp.4192-4198
- Publisher
- Royal Soc Chemistry
- Number of pages
- 7
- Grant note
- DMR12-62047 / NSF; National Science Foundation (NSF) Stichting Fundamenteel Onderzoek der Materie (FOM); FOM (The Netherlands) Simons Foundation
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Center for Functional Fabrics
- Identifiers
- 991019167995204721
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