Colloidal nematostatics

Abstract

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...

Transport of particles in liquid crystals

“…The ring structure can be stabilized in a thin cell of thickness close to 2 R 34 , for relatively small R or for relatively weak anchoring strength 35 , under a high electric or magnetic field 36,37 . Besides the configurations shown in Fig.1, more complex structures, including twisted ones, around particles of various shapes have been considered, see, for example, [38][39][40][41][42][43] and references therein. Figure 2 shows the optical microscopy textures of a sphere with normal anchoring and accompanying hyperbolic hedgehog and its modification by a strong alternating current (AC) electric field.…”

“…The dipolar model is only a rough approximation, as discussed in Ref. 39,137,155 . Its validity is diminished by the following factors: (a) shortness of separating distances at the stage of collisions; (b) field-induced torques that modify the interactions; (c) high flow velocities that modify n 156 , etc.…”

Anisotropic shift of surface plasmon resonance of gold nanoparticles doped in nematic liquid crystal

“…Recently, new perspectives of liquid crystals (LCs) have been shown in optics and photonics [1], display devices [2], virus detection by understanding its interaction with LC [3], and studying the interaction of LC with nanomaterials for enhanced applications [4][5][6][7][8][9][10][11][12][13]. Nanomaterials are emerging as a prototype to enrich the properties of LC materials.…”

“…The active research in this direction has been focused on the analysis and control of the interaction between LC molecules and gold nanoparticles (GNP) at nanoscale dimension. Some mathematical models have been presented to understand the alignment of LC molecular director around nanomaterials in the form of Saturn rings, hedgehogs, and boojams [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. The inclusion of GNPs in nematic LC can create some stable defects with possible integral strength ± 1 or ± ½ depending on the interaction of LC with GNPs.…”

“…The inclusion of GNPs in nematic LC can create some stable defects with possible integral strength ± 1 or ± ½ depending on the interaction of LC with GNPs. The theoretical approach on the linearized director distortion in nematic LC formed by particles analyzes several properties like elastic charge density, multipole particles, mechanical torque balance on the basis of electrostatic interactions, and defect symmetry [12]. The anisotropic alignment of LC molecules is due to breaking of mirror symmetry and it leads to the dipolar interaction between colloidal particles in LC [13].…”