Helfrich-Hurault elastic instabilities driven by geometrical frustration

Blanc, Christophe; Durey, Guillaume; Kamien, Randall D.; Lopez-Leon, Teresa; Lavrentovich, Maxim O.; Tran, Lisa

doi:10.1103/revmodphys.95.015004

Helfrich-Hurault elastic instabilities driven by geometrical frustration

Journal Article · Fri Mar 31 00:00:00 EDT 2023 · Reviews of Modern Physics

DOI:https://doi.org/10.1103/revmodphys.95.015004· OSTI ID:2424899

^[1]; Durey, Guillaume ^[2]; ^[3]; ^[4]; Lavrentovich, Maxim O. ^[5]; ^[6]

Université Montpellier (France)
Brown University, Providence, RI (United States); Université PSL, Paris (France)
University of Pennsylvania, Philadelphia, PA (United States)
Université PSL, Paris (France)
University of Tennessee, Knoxville, TN (United States)
Utrecht University (Netherlands)

Here, the Helfrich-Hurault (HH) elastic instability is a well-known mechanism behind patterns that form as a result of strain upon liquid crystal systems with periodic ground states. In the HH model, layered structures undulate and buckle in response to local, geometric incompatibilities in order to maintain the preferred layer spacing. Classic HH systems include cholesteric liquid crystals under electromagnetic field distortions and smectic liquid crystals under mechanical strains, where both materials are confined between rigid substrates. However, richer phenomena are observed when undulation instabilities occur in the presence of deformable interfaces and variable boundary conditions. Understanding how the HH instability is affected by deformable surfaces is imperative for applying the instability to a broader range of materials. In this review, the HH mechanism is reexamined and special focus is given to how the boundary conditions influence the response of lamellar systems to geometrical frustration. Lamellar liquid crystals confined within a spherical shell geometry are used as the model system. Made possible by the relatively recent advances in microfluidics within the past 15 years, liquid crystal shells are composed entirely of fluid interfaces and have boundary conditions that can be dynamically controlled at will. Past and recent work that exemplifies how topological constraints, molecular anchoring conditions, and boundary curvature can trigger the HH mechanism in liquid crystals with periodic ground states is examined. The review ends by identifying similar phenomena across a wide variety of materials, both biological and synthetic. The fact that the HH mechanism is a generic and often overlooked response of periodic materials to geometrical frustration is highlighted.

View Accepted Manuscript (DOE)

Research Organization:: US Department of Energy (USDOE), Washington, DC (United States). Office of Science, Basic Energy Sciences (BES)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); French National Research Agency; National Science Foundation (NSF); Simons Foundation; European Commission

OSTI ID:: 2424899

Alternate ID(s):: OSTI ID: 1968914

Journal Information:: Reviews of Modern Physics, Journal Name: Reviews of Modern Physics Journal Issue: 1 Vol. 95; ISSN 0034-6861

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cholesteric liquid crystals
Confinement
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Smectic liquid crystals

Helfrich-Hurault elastic instabilities driven by geometrical frustration

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