Numerical method of lines for the relaxational dynamics of nematic liquid crystals

Bhattacharjee, Anup Kumar; Menon, Gautam I.; Adhikari, R.

doi:10.1103/physreve.78.026707

Cited by 25 publications

(32 citation statements)

References 35 publications

(66 reference statements)

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“…In each case we consider situations with either positive (∆ > 0) or negative (∆ < 0) dielectric anisotropies. The parameters used in the simulations are ∆x = ∆y = 1, ∆t = 0.1 and A = −0.1, B = −0.5, C = 2.67, R 1 = 1.0, R 2 = 0.0, Γ = 1.0, corresponding to a uniaxial nematic phase [19]). The amplitude of the applied rectangular electric field pulse is taken to be E = 0.025/ |∆ |.…”

Section: Numerical Implementationmentioning

confidence: 99%

“…Hence, computer simulations are an important complement in the study of the evolution of liquid crystalline systems with defects. Lattice simulations have been used extensively in the study of liquid crystals (see, for example, [15][16][17][18][19]) since the pioneering work of Lebwohl and Lasher [20]. An order parameter is usually attached to each point of the lattice with orientational degrees of freedom only, so that the liquid does not flow but each molecule is free to orient itself in three-dimensional space.…”

Section: Introductionmentioning

confidence: 99%

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Nematic liquid crystal dynamics under applied electric fields

et al. 2010

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In this paper we investigate the dynamics of liquid crystal textures in a two-dimensional nematic under applied electric fields, using numerical simulations performed using a publicly available LIquid CRystal Algorithm (LICRA) developed by the authors. We consider both positive and negative dielectric anisotropies and two different possibilities for the orientation of the electric field (parallel and perpendicular to the two-dimensional lattice). We determine the effect of an applied electric field pulse on the evolution of the characteristic length scale and other properties of the liquid crystal texture network. In particular, we show that different types of defects are produced after the electric field is switched on, depending on the orientation of the electric field and the sign of the dielectric anisotropy.

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Section: Numerical Implementationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nematic liquid crystal dynamics under applied electric fields

et al. 2010

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“…Recall that the alignment tensor is symmetric and traceless, and out of its nine cartesian components, only five are actual degrees of freedom. Therefore, it can be expressed in terms of an orthonormal tensor basis, as originally discussed by Hess and co-workers 52 and, more recently, by Bhattacharjee et al, 11,53 …”

Section: Uniform Monte Carlo Minimization Algorithmmentioning

confidence: 97%

“…The model consists of a free energy functional which is minimized by resorting to well-known minimization techniques, e.g., by direct solution of the corresponding Euler-Lagrange equations, 9 or through dynamic relaxation in terms of a time-dependent GinzburgLandau (GL) formalism. [10][11][12][13] An important challenge in this type of work is that of finding relevant global free energy minima.…”

Section: Introductionmentioning

confidence: 99%

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

Armas-Pérez

Londoño-Hurtado

Guzmán

et al. 2015

The Journal of Chemical Physics

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A theoretically informed coarse-grained Monte Carlo method is proposed for studying liquid crystals. The free energy functional of the system is described in the framework of the Landau-de Gennes formalism. The alignment field and its gradients are approximated by finite differences, and the free energy is minimized through a stochastic sampling technique. The validity of the proposed method is established by comparing the results of the proposed approach to those of traditional free energy minimization techniques. Its usefulness is illustrated in the context of three systems, namely, a nematic liquid crystal confined in a slit channel, a nematic liquid crystal droplet, and a chiral liquid crystal in the bulk. It is found that for systems that exhibit multiple metastable morphologies, the proposed Monte Carlo method is generally able to identify lower free energy states that are often missed by traditional approaches. Importantly, the Monte Carlo method identifies such states from random initial configurations, thereby obviating the need for educated initial guesses that can be difficult to formulate.

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“…[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]), colloidal membranes and smectic stacks have been the subject of more recent modeling (e.g. [4,5,7,[9][10][11][40][41][42][43][44][45][46][47]).…”

Section: Introductionmentioning

confidence: 99%

Probing a self-assembledfdvirus membrane with a microtubule

2016

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The self-assembly of highly anisotropic colloidal particles leads to a rich variety of morphologies, whose properties are just beginning to be understood. This article uses computer simulations to probe a particle-scale perturbation of a commonly studied colloidal assembly, a monolayer membrane composed of rodlike fd viruses in the presence of a polymer depletant. Motivated by experiments currently in progress, we simulate the interaction between a microtubule and a monolayer membrane as the microtubule "pokes" and penetrates the membrane face-on. Both the viruses and the microtubule are modeled as hard spherocylinders of the same diameter, while the depletant is modeled using ghost spheres. We find that the force exerted on the microtubule by the membrane is zero either when the microtubule is completely outside the membrane or when it has fully penetrated the membrane. The microtubule is initially repelled by the membrane as it begins to penetrate but experiences an attractive force as it penetrates further. We assess the roles played by translational and rotational fluctuations of the viruses and the osmotic pressure of the polymer depletant. We find that rotational fluctuations play a more important role than the translational ones. The dependence on the osmotic pressure of the depletant of the width and height of the repulsive barrier and the depth of the attractive potential well is consistent with the assumed depletion-induced attractive interaction between the microtubule and viruses. We discuss the relevance of these studies to the experimental investigations.

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Numerical method of lines for the relaxational dynamics of nematic liquid crystals

Cited by 25 publications

References 35 publications

Nematic liquid crystal dynamics under applied electric fields

Nematic liquid crystal dynamics under applied electric fields

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

Probing a self-assembledfdvirus membrane with a microtubule

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