Biaxiality at the isotropic-nematic interface with planar anchoring

Kamil, S. M.; Bhattacharjee, Anup Kumar; Adhikari, R.; Menon, Gautam I.

doi:10.1103/physreve.80.041705

Cited by 11 publications

(9 citation statements)

References 12 publications

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“…The codirector l and the secondary director m (not shown) also have a singular structure with B 2 reaching a maximum on a noncircular ring embedded in the outer region of the droplet. This is consistent with the understanding that a planar interface exhibits local biaxiality for large κ [48]. When approximating the droplets to be circular, the critical droplet size can be estimated in terms of the parameters in the GLdG free energy.…”

Section: Nucleation In Supercooled Isotropic Phasesupporting

confidence: 84%

Stochastic kinetics reveal imperative role of anisotropic interfacial tension to determine morphology and evolution of nucleated droplets in nematogenic films

Bhattacharjee¹

2017

Sci Rep

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For isotropic fluids, classical nucleation theory predicts the nucleation rate, barrier height and critical droplet size by ac- counting for the competition between bulk energy and interfacial tension. The nucleation process in liquid crystals is less understood. We numerically investigate nucleation in monolayered nematogenic films using a mesoscopic framework, in par- ticular, we study the morphology and kinetic pathway in spontaneous formation and growth of droplets of the stable phase in the metastable background. The parameter κ that quantifies the anisotropic elastic energy plays a central role in determining the geometric structure of the droplets. Noncircular nematic droplets with homogeneous director orientation are nucleated in a background of supercooled isotropic phase for small κ. For large κ, noncircular droplets with integer topological charge, accompanied by a biaxial ring at the outer surface, are nucleated. The isotropic droplet shape in a superheated nematic background is found to depend on κ in a similar way. Identical growth laws are found in the two cases, although an unusual two-stage mechanism is observed in the nucleation of isotropic droplets. Temporal distributions of successive events indi- cate the relevance of long-ranged elasticity-mediated interactions within the isotropic domains. Implications for a theoretical description of nucleation in anisotropic fluids are discussed.

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Section: Nucleation In Supercooled Isotropic Phasesupporting

confidence: 84%

Stochastic kinetics reveal imperative role of anisotropic interfacial tension to determine morphology and evolution of nucleated droplets in nematogenic films

Bhattacharjee¹

2017

Sci Rep

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“…SMOL is a stochastic generalization of the deterministic method of lines approach 59 that relies on discretizing the spatial derivates without a temporal discretization, thus yielding to a set of ordinary differential equations in time, that can be easily integrated using the standard numerical libraries 60 . Though spatial accuracy can be increased by using spectral collocation method 61 , obtained solution is usually limited by the temporal accuracy of the integrator. SMOL is numerically stable without computational hindrance with convergence, is less computationally overloaded, spatiotemporally second order accurate, satisfies discrete FDT and can faithfully reproduce lab-based experiments in silico 7 , 13 , 20 , 29 , 30 .…”

Section: Methodsmentioning

confidence: 99%

Controlling motile disclinations in a thick nematogenic material with an electric field

Bhattacharjee

2018

Sci Rep

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Manipulating topological disclination networks that arise in a symmetry-breaking phase transformation in widely varied systems including anisotropic materials can potentially lead to the design of novel materials like conductive microwires, self-assembled resonators, and active anisotropic matter. However, progress in this direction is hindered by a lack of control of the kinetics and microstructure due to inherent complexity arising from competing energy and topology. We have studied thermal and electrokinetic effects on disclinations in a three-dimensional nonabsorbing nematic material with a positive and negative sign of the dielectric anisotropy. The electric flux lines are highly nonuniform in uniaxial media after an electric field below the Fréedericksz threshold is switched on, and the kinetics of the disclination lines is slowed down. In biaxial media, depending on the sign of the dielectric anisotropy, apart from the slowing down of the disclination kinetics, a nonuniform electric field filters out disclinations of different topology by inducing a kinetic asymmetry. These results enhance the current understanding of forced disclination networks and establish the presented method, which we call fluctuating electronematics, as a potentially useful tool for designing materials with novel properties in silico.

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“…homeotropic, planar, or oblique anchoring) on the nematic state. It turns out that the relative sizes of different elastic coefficients also play important roles on anchoring conditions on the interface, see Kamil-Bhattacharjee-Adhikari-Menon [25,26]. There are proposed forms of the surface energy by Chanderashka [5], Ericksen [11] based on a phenomenological theory.…”

Section: Isotropic and Nematic Phase Transitionsmentioning

confidence: 99%

“…For example, it was shown by Popa-Nita-Sluckin-Wheeler [43] a region proximate to the interface can exhibit biaxiality within the LGdG theory, even if the stable nematic phase is purely uniaxial, provided planar anchoring is enforced on the interface. Such a biaxiality is absent if the anchoring is homeotropic [6], see also [25,26].…”

Section: Isotropic and Nematic Phase Transitionsmentioning

confidence: 99%

Isotropic-Nematic Phase Transition and Liquid Crystal Droplets

Lin¹,

Wang²

2020

Preprint

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Liquid crystal droplets are of great interest from physics and applications. Rigorous mathematical analysis is challenging as the problem involves harmonic maps (and in general the Oseen-Frank model), free interfaces and topological defects which could be either inside the droplet or on its surface along with some intriguing boundary anchoring conditions for the orientation configurations. In this paper, through a study of the phase transition between the isotropic and nematic states of liquid crystal based on the Ericksen model, we can show, when the size of droplet is much larger in comparison with the ratio of the Frank constants to the surface tension, a Γ-convergence theorem for minimizers. This Γ-limit is in fact the sharp interface limit for the phase transition between the isotropic and nematic regions when the small parameter ε, corresponding to the transition layer width, goes to zero. This limiting process not only provides a geometric description of the shape of the droplet as one would expect, and surprisingly it also gives the anchoring conditions for the orientations of liquid crystals on the surface of the droplet depending on material constants. In particular, homeotropic, tangential, and even free boundary conditions as assumed in earlier phenomenological modelings arise naturally provided that the surface tension, Frank and Ericksen constants are in suitable ranges.

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Biaxiality at the isotropic-nematic interface with planar anchoring

Cited by 11 publications

References 12 publications

Stochastic kinetics reveal imperative role of anisotropic interfacial tension to determine morphology and evolution of nucleated droplets in nematogenic films

Stochastic kinetics reveal imperative role of anisotropic interfacial tension to determine morphology and evolution of nucleated droplets in nematogenic films

Controlling motile disclinations in a thick nematogenic material with an electric field

Isotropic-Nematic Phase Transition and Liquid Crystal Droplets

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