Elastic interaction between colloidal particles in confined nematic liquid crystals

Abstract

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...

Effects of gas interparticle interaction on dissipative wake-mediated forces

“…Simple analytical expressions for density perturbation and dissipative forces for the ensemble of widely separated small obstacles can be obtained using the qualitative approach described in Appendix A. This approach is similar to that based on the method of molecular field that was used to describe the elastic interaction of colloidal particles in a liquid crystal, see [58]. In particular, the gas density perturbation far from an isolated obstacle can be written as…”

“…The latter means that the interaction between two inclusions cannot be separated out of the influence of all other inclusions. This is a general property of a nonlinear response or nonlinear systems, see [58]. The employed approach allows one to consider the non-linear response and to represent expressions for δn and f kj in the form similar to that given by the linear response for moving probe-particles (cf.…”

“…Equation (A6) can be simplified by applying an approach similar to the self-consistent molecular field approach [58]. Since distribution U of the heavy component is localized near the inclusion centers R j and has compact carriers u j (r) = u(r − R j ) ≤ 1, we may consider u j (r) as a probability density distribution and the integral in (A6) as an average (Ω, ∇G) j associated with this distribution.…”

Colloidal particles in liquid crystal films and at interfaces

“…The effective interaction potential between two dipolar particles was also directly measured as a function of their separation d [61]. However, the accuracy of the measurements did not make it possible to compare them to the theoretical predictions, which concluded that the dipole-dipole power law of d −3 is exponentially screened for distances larger than the thickness of the cell, with an extended crossover region between the two regimes [103].…”

Surface-induced structures in nematic liquid crystal colloids

“…where U ij is the pair interaction energy between the i-th and j-th particles and U i +U pattern i is the one-particle energy. Both U ij and U i arise from the bulk and zero boundary conditions n µ (s) = 0 at the surfaces Σ and were discussed earlier in [20,21]. The last summand U pattern i originates from non-zero patterns n µ (s) = 0 at the surfaces Σ…”