Effect of confining walls on the interaction between particles in a nematic liquid crystal

Fukuda, Jun Ichi; Lev, B. I.; Yokoyama, Hiroshi

doi:10.1088/0953-8984/15/23/301

Cited by 23 publications

(22 citation statements)

References 47 publications

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“…Consideration of finite anchoring effects in colloidal nematostatics requires incorporation of a finite-size source, and theories, based on the approximation of point-like sources, encounter difficulties. For instance, the treatment of finite anchoring in [61,62], based on the approach [43,44,63], required an introduction of an artificial director field inside the colloids' material. In our approach, the anchoring effects can be easily included.…”

Section: Incorporation Of Real Surfaces and Finite Anchoringmentioning

confidence: 99%

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Colloidal nematostatics

Pergamenshchik¹,

Uzunova²

2010

Condens. Matter Phys.

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We give a review of the theory of large distance colloidal interaction via the nematic director field. The new area of nematic colloidal systems (or nematic emulsions) has been guided by the analogy between the colloidal nematostatics and electrostatics. The elastic charge density representation of the colloidal nematostatics [V.M. Pergamenshchik, V.O. Uzunova, Eur. Phys. J. E, 2007, 23, 161; Phys. Rev. E, 2007, 76, 011707] develops this analogy at the level of charge density and Coulomb interaction. The analogy is shown to lie in common mathematics based on the solutions of Laplace equation. However, the 3d colloidal nematostatics substantially differs from electrostatics both in its mathematical structure and physical implications. The elastic charge is a vector fully determined by the torque exerted upon colloid, the role of Gauss' theorem is played by conservation of the torque components. Elastic multipoles consist of two tensors (dyads). Formulas for the elastic multipoles, the Coulomb-like, dipole-dipole, and quadrupole-quadrupole pair interaction potentials are derived and illustrated by particular examples. Based on the tensorial structure, we list possible types of elastic dipoles and quadrupoles. An elastic dipole is characterized by its isotropic strength, anisotropy, chirality, and its longitudinal component. An elastic quadrupole can be uniaxial and biaxial. Relation between the multipole type and its symmetry is discussed, sketches of some types of multipoles are given. Using the mirror image method of electrostatics as a guiding idea, we develop the mirror image method in nematostatics for arbitrary director tilt at the wall. The method is applied to the charge-wall and dipole-wall interaction. : 61.30.Dk, 61.30.Jf, 82.70Dd, 01.55.+b 1. The intrigue of nematic colloids: similarity to the electrostatics, its origin, and how it is developed in this article. Key words: nematic colloid, electrostatic analogy, elastic charge and multipoles PACSIsotropic liquids doped with colloidal particles or just colloids are the classical many-particle systems which, over many decades , have been studied using the methods of molecular and statistical physics, electrolyte theory, physical chemistry, and so on [1,2]. Colloidal particles can be of different physical and chemical origin, but in all cases their interaction via isotropic liquid is of a short range [3], even if the colloids are charged since their electric field is rapidly screened by a numerous couterions. The nematic colloids, that have become widely known just over the last 15 years, are fundamentally different: interaction of colloids mediated by distortions of the nematic director is of a long range. That is why nematic colloids are usually compared not with standard isotropic colloids, but with a system of electric charges. The similarity with the electrostatics has always been a powerful, if not dominating, factor of the development of the field of nematic colloids. But what is the origin of this similarity?The interaction of particles in a ne...

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Section: Incorporation Of Real Surfaces and Finite Anchoringmentioning

confidence: 99%

“…As in electrostatics, these effects can be addressed by introducing image-multipoles behind the confining surface [59][60][61][62][63]. The image method for finite-size colloids [59,60] is presented in section 3.4.…”

Section: -7mentioning

confidence: 99%

Colloidal nematostatics

Pergamenshchik¹,

Uzunova²

2010

Condens. Matter Phys.

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“…If both particles have the same height h = h ′ then ρ = r and ϕ = θ. In this case the dipole-dipole energy of interaction (27) between two parallel dipoles at the same height h near the wall with planar anchoring conditions ( Fig.8.a) can be presented as: Let's analyze dipole-dipole interaction (31) which corresponds to the usual dipole configuration on the Fig.8.a. First remarkable behavior is the dipole-dipole isotropic attraction on far distances.…”

Section: Interaction Between Two Particles Near One Planar Wallmentioning

confidence: 99%

“…Authors received formula similar to (46) but with unknown multiplier Γ and without the constant 3πKβ 2 a 6 L 5 ζ(5). If we set Γ = 2πKc = −2βπKa 3 in [27] we receive the same formula (46) up to a constant.…”

Section: Interaction Of the One Particle With Nematic Cellmentioning

confidence: 99%

Theory of elastic interaction of colloidal particles in nematic liquid crystals near one wall and in the nematic cell

Chernyshuk

Lev

2011

Phys. Rev. E

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We apply the method developed [Chernyshuk and Lev, Phys. Rev. E 81, 041701 (2010)] for theoretical investigation of colloidal elastic interactions between axially symmetric particles in the confined nematic liquid crystal near one wall and in the nematic cell with thickness L. Both cases of homeotropic and planar director orientations are considered. Particularly, dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole interactions of the one particle with the wall and within the nematic cell are found as well as corresponding two particle elastic interactions. A set of results has been predicted: The effective power of repulsion between two dipole particles at height h near the homeotropic wall is reduced gradually from inverse 3 to 5 with an increase of dimensionless distance r / h; near the planar wall, the effect of dipole-dipole isotropic attraction is predicted for large distances r > r(dd) = 4.76 h; maps of attraction and repulsion zones are crucially changed for all interactions near the planar wall and in the planar cell; and one dipole particle in the homeotropic nematic cell was found to be shifted by the distance δ(eq) from the center of the cell. The proposed theory fits very well with experimental data for the confinement effect of elastic interaction between spheres in the homeotropic cell [Vilfan et al., Phys. Rev. Lett. 101, 237801 (2008)] in the range 1-1000 kT. The influence of the K(24) and K(13) terms as well as connection with other theoretical approaches are discussed.

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“…In that paper authors have found exponential screening effects for quadrupole-quadrupole interaction between spherical particles in homeotropic NLC cell. From our viewpoint there was only one theoretical approach for description of colloidal particles in confined NLC performed in papers [13,14].In this paper we propose the new approach for quantitative description of the axial colloidal particles in confined NLC. This method enables to find self energy of one colloidal particle and interaction energy between two particles in arbitrary confined NLC with strong anchoring condition n µ (s) = 0 on the bounding surface.…”

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confidence: 99%

Elastic interaction between colloidal particles in confined nematic liquid crystals

Chernyshuk

Lev

2010

Phys. Rev. E

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The theory of elastic interaction of micron size axially symmetric colloidal particles immersed into confined nematic liquid crystal has been proposed. General formulas are obtained for the self energy of one colloidal particle and interaction energy between two particles in arbitrary confined NLC with strong anchoring condition on the bounding surface. Particular cases of dipole-dipole interaction in the homeotropic and planar nematic cell with thickness L are considered and found to be exponentially screened on far distances with decay length λ dd = L π . It is predicted that bounding surfaces in the planar cell crucially change the attraction and repulsion zones of usual dipole-dipole interaction. As well it is predicted that the decay length in quadrupolar interaction is two times smaller than for the dipolar case. . The first theoretical approach was developed in [1,10] with help of ansatz functions for the director and using multiple expansion in the far field area. Another approach [11,12] gave possibility to find approximate solutions in terms of geometrical shape of particles. Recently authors of [15,16] proposed a method for finding elastic interaction between colloids based on the fixing of director field on the surface of virtual sphere surrounding the real particle. The predicted dipole-dipole forces are three times weaker and quadrupole-quadrupole five times weaker than results of [10]. On the other hand authors of [9] recently have measured experimentally both interactions and found that experimental results are in accordance with Lubensky et al. prediction [10] with about 10% accuracy. This allows to justify assumptions of [10] for spherical particles for intinite nematic liquid crystal. In this paper we suggest to generalize that approach for the case of the confined nematic liquid crystals as practically always NLC has to be confined with walls, cells or containers. In a broader context, understanding the elasticity-mediated colloidal interactions in confined media is of great importance not only in the field of regular thermotropic liquid crystals, but also for understanding interactions in more complex media with orientational order, for example, in solutions of DNA, f-actin and other biologically relevant molecules. Up to now almost all experimental studies did not take into account quantitatively confinement effects besides the article of Vilfan et al. [4]. In that paper authors have found exponential screening effects for quadrupole-quadrupole interaction between spherical particles in homeotropic NLC cell. From our viewpoint there was only one theoretical approach for description of colloidal particles in confined NLC performed in papers [13,14].In this paper we propose the new approach for quantitative description of the axial colloidal particles in confined NLC. This method enables to find self energy of one colloidal particle and interaction energy between two particles in arbitrary confined NLC with strong anchoring condition n µ (s) = 0 on the bounding surface. We apply general form...

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Effect of confining walls on the interaction between particles in a nematic liquid crystal

Cited by 23 publications

References 47 publications

Colloidal nematostatics

Colloidal nematostatics

Theory of elastic interaction of colloidal particles in nematic liquid crystals near one wall and in the nematic cell

Elastic interaction between colloidal particles in confined nematic liquid crystals

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