Spontaneous Fluctuations in Mesoscopic Simulations of Nematic Liquid Crystals

Híjar, Humberto; Halver, René; Sutmann, Godehard

doi:10.1142/s0219477519500111

Cited by 12 publications

(17 citation statements)

References 28 publications

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“…Specifically [ 48 ],

which yields

. It is worth noticing that due to their anisotropic character, actual nematic solvents have more than one viscosity coefficient, whereas N-MPCD approximates the momentum transport through the solvent as isotropic [ 55 ]. However, this approximation has shown consistent results for simulations of CPs driven by nematic flow [ 29 , 36 ] and can be considered as a first attempt to reproduce the hydrodynamic behaviour on the mesoscopic scale.…”

Section: Resultsmentioning

confidence: 99%

“…

is the ratio of viscous-to-elastic effects and is customarily defined as

where

is a rotational viscosity and

(

) is a characteristic velocity (length). The ratio

can be estimated from the spectrum of director fluctuations as discussed in References [ 55 , 61 ]. Using the same set of MPCD parameters as here but with

, it is obtained

[ 61 ].…”

Section: Resultsmentioning

confidence: 99%

“…To quantify the elastic energy stored in the nematic medium, the Frank free energy density is considered under the one-constant approximation, which has been proven to be valid for the present implementation of N-MPCD [ 36 , 51 , 55 ]. The total elastic energy of the nematic solvent is

where K is the elastic constant and

indicates summation over all collision cells.…”

Section: Methodsmentioning

confidence: 99%

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Nonequilibrium Dynamics of a Magnetic Nanocapsule in a Nematic Liquid Crystal

Armendáriz¹,

Híjar²

2021

Materials

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Colloidal particles in nematic liquid crystals show a beautiful variety of complex phenomena with promising applications. Their dynamical behaviour is determined by topology and interactions with the liquid crystal and external fields. Here, a nematic magnetic nanocapsule reoriented periodically by time-varying magnetic fields is studied using numerical simulations. The approach combines Molecular Dynamics to resolve solute–solvent interactions and Nematic Multiparticle Collision Dynamics to incorporate nematohydrodynamic fields and fluctuations. A Saturn ring defect resulting from homeotropic anchoring conditions surrounds the capsule and rotates together with it. Magnetically induced rotations of the capsule can produce transformations of this topological defect, which changes from a disclination curve to a defect structure extending over the surface of the capsule. Transformations occur for large magnetic fields. At moderate fields, elastic torques prevent changes of the topological defect by tilting the capsule out from the rotation plane of the magnetic field.

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“…Specifically [ 48 ],

which yields

Section: Resultsmentioning

confidence: 99%

“…

is the ratio of viscous-to-elastic effects and is customarily defined as

where

is a rotational viscosity and

(

) is a characteristic velocity (length). The ratio

can be estimated from the spectrum of director fluctuations as discussed in References [ 55 , 61 ]. Using the same set of MPCD parameters as here but with

, it is obtained

[ 61 ].…”

Section: Resultsmentioning

confidence: 99%

where K is the elastic constant and

indicates summation over all collision cells.…”

Section: Methodsmentioning

confidence: 99%

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Nonequilibrium Dynamics of a Magnetic Nanocapsule in a Nematic Liquid Crystal

Armendáriz¹,

Híjar²

2021

Materials

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“…Numerical experiments were conducted using the same simulation parameters ∆t, k B T, m,N c , a, and L, given in section 3.2. Nematic order was simulated using U = 20k B T. For this mean-field strength, it has been shown that the average scalar order parameter produced in collision cells,S c = 0.947, is in agreement with predictions of self-consistent models of NLCs [32]. Two main features of hydrodynamic correlation functions in MPCD-N will be explored.…”

Section: Measurementsmentioning

confidence: 91%

“…Dynamic equations for director fluctuations can be obtained by replacing equations (3.11) and (5.1) into equations (5.2) and (5.4), and retaining only linear contributions. In a first approximation, mass and momentum transport can be assumed to be still given by equations (3.1) and (3.2), thus neglecting the effects of backflow [32]. In section 5.1, the validity of this assumption will be explored.…”

Section: Fluctuating Nematodynamicsmentioning

confidence: 99%

Hydrodynamic correlations in isotropic fluids and liquid crystals simulated by multi-particle collision dynamics

Híjar¹

2019

Condens. Matter Phys.

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Multi-particle collision dynamics is an appealing numerical technique aiming at simulating fluids at the mesoscopic scale. It considers molecular details in a coarse-grained fashion and reproduces hydrodynamic phenomena. Here, the implementation of multi-particle collision dynamics for isotropic fluids is analysed under the so-called Andersen-thermostatted scheme, a particular algorithm for systems in the canonical ensemble. This method gives rise to hydrodynamic fluctuations that spontaneously relax towards equilibrium. This relaxation process can be described by a linearized theory and used to calculate transport coefficients of the system. The extension of the algorithm for nematic liquid crystals is also considered. It is shown that thermal fluctuations in the average molecular orientation can be described by an extended linearized scheme. Flow fluctuations induce orientation fluctuations. However, orientational changes produce observable effects on velocity correlation functions only when simulation parameters exceed their values from those used in previous applications of the method. Otherwise, the flow can be considered to be independent of the orientation field. and energy. This property allows MPCD to recover, over long simulation times, the hydrodynamic equations of mass, momentum, and heat propagation. In addition, the stochastic character of MPCD produces fluctuations and Brownian forces [7,8].A considerable number of soft condensed matter systems have been successfully simulated under MPCD schemes. Recent examples include sediment-water interface flow [9], bistable biochemical systems [10], and two-dimensional one-component plasma [11], to mention but a few. Furthermore, modified MPCD rules have been used to extend simulations towards complex solvents, e.g., viscoelastic fluids [12] and binary mixtures [13]. Very recently, algorithms for simulating nematic liquid crystals (NLCs) using the principles of MPCD have been also proposed [14,15]. They allow one to reproduce hydrodynamic and elastic characteristics of such phases, still being potentially able to be coupled with microscopic degrees of freedom. These algorithms simulate isotropic-nematic phase transitions, consistent dynamics for annihilation of defects, and molecular reorientation under flow.Here, basic implementations of MPCD for simple liquids and NLCs are considered. Simulations for equilibrium states are presented, where systems are in contact with the thermal bath based on an Andersen thermostat that keeps them at a fixed temperature. In order to exhibit the ability of MPCD to reproduce hydrodynamic behaviour and to emphasise its stochastic character, attention is focused on the analysis of the spectra of hydrodynamic fluctuations produced by the algorithm in both simple liquids and nematics. There is discussed a very good agreement that exists between correlation functions obtained from the numerical implementation with those derived from linearized hydrodynamic models of liquids and LCs. Following the MPCD model for nematics (MPCD-N) i...

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