Analogy between periodic patterns in thin smectic liquid crystal films and the intermediate state of superconductors

Abstract

Spontaneous breaking of symmetry in liquid crystal (LC) films often reveals itself as a microscopic pattern of molecular alignment. In a smectic-A LC, the emergence of positional order at the transition from the nematic phase leads to periodic textures that can be used as optical microarrays, templates for soft lithography, and ordering matrices for the organization and manipulation of functional nanoparticles. While both 1d and 2d patterns have been obtained as a function of the LC film thickness and applied fields, the connection has not been made between pattern formation and the peculiar critical behavior of LCs at the nematic–smectic transition, still eluding a comprehensive theoretical explanation. In this article, we demonstrate that an intense bend distortion applied to the LC molecular director while cooling from the nematic phase produces a frustrated smectic phase with depressed transition temperature, and the characteristic 1d periodic texture previously observed in thin films and under applied electric fields. In light of De Gennes’ analogy with the normal-superconductor transition of a metal, we identify the 1d texture as the equivalent of the intermediate state in type I superconductors. The bend distortion is analog to the magnetic field in metals and penetrates in the frustrated phase as an array of undercooled nematic domains, periodically intermixed with bend-free smectic-A domains. Our findings provide fundamental evidence for theories of the nematic–smectic transition, highlighting the deep connection between phase frustration and pattern formation, and perspectives on the design of functional smectic microarrays.

On the measurement of the bend elastic constant in nematic liquid crystals close to the nematic-to-SmA and the nematic-to-NTBphase transitions

“…5b). In practice this texture forms in a very narrow interval of temperature above T N A , which depends on the sample thickness [23]. In a 25 µm-thick sample of 8CB this interval of temperature is of the order of 0.02 • C. Needless to say that our optical method to determine κ 31 can no longer be applied in this interval of temperature, which is a limitation of this method.…”

Structural Landscapes in Geometrically Frustrated Smectics

“…Such methods could be of great benefit to structure prediction where the defects cannot be observed optically, for example, in thin films [39][40][41][42][43]. Furthermore, scenarios where partial smectic order exists, such as during the transition from the nematic to the smectic phase, may exhibit very complicated pretransitional structures [37,38,44,45], and few studies have addressed the connection between pattern formation and the peculiar critical behavior of liquid crystals at the nematicsmectic transition [46]. Dynamical phenomena-such as time-varying layer spacing [47], interactions between embedded particles [31], and the evolution of smectic films and bubbles [48][49][50]-also present difficult problems that appear to require numerical modeling.…”

Self-assembled liquid crystal architectures for soft matter photonics

“…It was found that the director field geometry of nematics would strongly affect the geometry of subsequent smectic topological defects during the phase transition, which is rationalized by illustrating the similarity of ordering between nematics and smectics. Zappone et al 103 examined the smectic pattern conversion from one-dimensional (1D) streaks to 2D fan-shaped FCD arrays when cooling from nematics to smectics, Fig. 5b .…”