Theoretically informed Monte Carlo simulation of liquid crystals by sampling of alignment-tensor fields

Armas-Pérez, Julio C.; Londoño-Hurtado, Alejandro; Guzmán, Orlando; Hernández-Ortíz, Juan P.; Pablo, Juan J. de

doi:10.1063/1.4926790

Cited by 25 publications

(33 citation statements)

References 63 publications

(60 reference statements)

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“…Monte Carlo (MC) studies of hard spherocylinders have been performed, where ellipsoidal clusters with homogeneous director orientation are nucleated [4,16]. More recently, spherical nanodroplets with a radial hedgehog defect, accompanied by a Saturn-ring at the core and bipolar pole-centered boojum defects with uniform field structure have been reported [17]. It is worth mentioning that kinetic pathways in MC simulations can be misleading, as the algorithm samples the Gibbs distribution in equilibrium without obeying the natural dynamics of the system.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

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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“…7 Since then, it has been demonstrated that this anisometry can be directly controlled through various means, 8,9 the simplest of which is by uniaxial mechanical stretching of the PDLC film to produce highly prolate spheroidal domains ( Figure 1b). 10,11 While a significant body of past mesoscale simulation work exists for cylindrical nematic capillaries 12,13 and spherical droplets, [14][15][16] elliptic or ellipsoidal domains have been far less studied. [17][18][19][20] Furthermore, of this work, most use theoretical models which are unable to accurately capture nematic defects and phase transition.…”

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confidence: 99%

Formation and field-driven dynamics of nematic spheroids

Abukhdeir

2017

Soft Matter

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Emerging technologies based on liquid crystal (LC) materials increasingly leverage the presence of nanoscale defects, unlike the canonical application of LCs -LC displays. The inherent nanoscale characteristics of LC defects present both significant opportunities and barriers for the application of this fascinating class of materials.Simulation-based approaches to the study of the effects of confinement and interface anchoring conditions on LC domains has resulted in significant progress over the past decade, where simulations are now able to access experimentally-relevant micron-scales while simultaneously capturing nanoscale defect structures. In this work, continuum simulations were performed in order to study the dynamics of micron-scale nematic LC droplets of varying spheroidal geometry. Nematic droplets are one of the simplest inherently defect-containing LC structures and are also relevant to polymer-dispersed 1 arXiv:1702.05404v1 [cond-mat.soft]

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“…Therefore, the method of choice for the shape parameter optimization was the tensor Laplacian from the global RBF. The results in Figure are in qualitative agreement with experimental and theoretical observations of phases present in LC droplets under different conditions . The relative error, using the global as the standard value, was order 10 − 3 (0.1%), and it was independent of W .…”

Section: Resultsmentioning

confidence: 99%

Educating local radial basis functions using the highest gradient of interest in three dimensional geometries

Palacio‐Betancur

Villada‐Gil

Pablo

et al. 2016

Numerical Meth Engineering

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Summary We present a novel methodology to effectively localize radial basis function approximation methods in three dimensions. The local scheme requires shape parameter‐dependent functions that can be used to approximate gradients of scattered data and to solve partial differential operators. The optimum shape parameter is obtained from the highest gradient of interest, where a known analytical function, when boundary conditions are not present, or a shape parameter‐free global approximation are used to educate the localized scheme. The later option is applicable to problems where the operator needs to be solved multiple times, like in time evolution or stochastic integration. Past shape parameter's optimizations, for two‐dimensional domains, based on the condition number of the interpolant matrix, were unable to provide satisfactory approximations. The applicability of our method is illustrated in the context of an analytical expression interpolation and during a Ginzburg–Landau relaxation of a free energy functional. In general, the optimum shape parameter depends on geometry, node distribution, and density, whereas the approximation errors decrease as the node density and the local stencil size increase. The effective localization of radial basis functions motivates its use in moving boundary problems and accelerates solutions through sparse matrix solvers. Copyright © 2016 John Wiley & Sons, Ltd.

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Theoretically informed Monte Carlo simulation of liquid crystals by sampling of alignment-tensor fields

Cited by 25 publications

References 63 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

Formation and field-driven dynamics of nematic spheroids

Educating local radial basis functions using the highest gradient of interest in three dimensional geometries

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