Theory of Elastic Interaction of the Colloidal Particles in the Nematic Liquid Crystal Near One Wall and in the Nematic Cell

Abstract

We apply the method developed in Ref. [S.B.Chernyshuk and B.I.Lev, Phys.Rev.E, \textbf{81}, 041701 (2010)] for theoretical investigation of colloidal elastic interactions between axially symmetric particles in the confined nematic liquid crystal (NLC) 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 \textit{one} particle with the wall and within the nematic cell are found as well as corresponding \textit{two particle} elastic interactions. A set of new 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 \textit{isotropic attraction} is predicted for large distances $r>r_{dd}=4.76h$; maps of attraction and repulsion zones are crucially changed for all interactions near the planar wall and in the planar cell; one dipole particle in the homeotropic nematic cell was found to be shifted by the distance ${\delta }_{eq}$ from the center of the cell \textit{independent} of the thickness $L$ 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 taken from [M.Vilfan et al. Phys.Rev.Lett. {\bf 101}, 237801, (2008)] in the range $1÷1000kT$.

18 pages, 23 figures

References in corpus (5)

• Elasticity-mediated self-organization and colloidal interactions of solid spheres with tangential anchoring in a nematic liquid crystal
• Ordered droplet structures at the liquid crystal surface and elastic-capillary colloidal interactions
• Forces between elongated particles in a nematic colloid
• Elastic interaction between colloidal particles in confined nematic liquid crystals
• Effective interactions of colloids on nematic films

Cited by in corpus (8)

• Transport of Particles in Liquid Crystals
• Tunable colloid trajectories in nematic liquid crystals near wavy walls
• Theory of elastic interaction between colloidal particles in the nematic cell in the presence of the external electric or magnetic field
• Particle selection through topographic surface patterns in nematic colloids
• Elastic octopoles and colloidal structures in nematic liquid crystals
• Freedericksz-like positional transition of a micro-droplet suspended in a nematic cell
• Surface induced structures in nematic liquid crystal colloids
• Formation of a fast "lane" for positional transition in a microparticle-suspended nematic liquid crystal cell