Dynamic interaction between suspended particles and defects in a nematic liquid crystal

Abstract

Insertion of spherical particles into a uniform nematic liquid crystal gives rise to the formation of topological defects. In the present work, we investigate how a spherical particle accompanied by its topological defects interacts with neighboring disclination lines. We perform two- and three-dimensional dynamic simulations to analyze the effect of a particle on the annihilation process of two disclination lines. The dynamics of the liquid crystal is described by a time-dependent evolution equation on the symmetric traceless order parameter that includes some of the salient features of liquid crystalline materials: excluded volume effects, or equivalently, short-range order elasticity and long-range order elasticity. At the surface of the particle, the liquid crystal is assumed to exhibit strong homeotropic anchoring. The particle is located between two disclination lines of topological charges +1/2 and -1/2. Two-dimensional simulations indicate that the topological defects bound to the particle mediate an interaction between the two disclination lines which increases the attraction between them. This result is confirmed by three-dimensional simulations that provide a complete description of the director field and of the order parameter around the particle. These simulations indicate that a spherical particle between two disclination lines can be surrounded by a Saturn ring, and suggest that the dynamic behavior of disclination lines could be used to report the structure of a defect around the particle.

Interactions between spherical colloids mediated by a liquid crystal: A molecular simulation and mesoscale study

“…From previous studies we know that a single sphere in this system would be accompanied by a stable Saturn ring defect. 23 If the spheres are very far apart, each should be surrounded by an identical Saturn ring of characteristic radius a; we have already discussed how this characteristic of isolated rings can be used to establish a correspondence between the length scales of 0 and . We now pose a question of how do these rings interact at close range.…”

“…The Saturn ring configuration can also be stabilized for micron-sized particles by confinement. 4,23 In a previous paper, 13 we have presented our results from simulation and field theory for a one-colloid system confined between parallel walls, including density and orientational profiles, structure of the Saturn ring defect, and the potential of mean force ͑PMF͒ between the colloid and the cell's walls.…”

“…Systems of LCs and one or two colloids have been studied by experimental, 4 -8 simulation, [9][10][11][12][13][14] and theoretical methods [15][16][17][18][19][20][21][22][23][24] in connection with their associated defect structures and effective interactions. The simplest case corresponds to a single spherical colloid embedded in a nematic fluid, with strong homeotropic ͑perpendicular͒ anchoring at the colloid surface.…”

Slow dynamics of thin nematic films in the presence of adsorbed nanoparticles

“…16 In the nematic phase, also amounts to several molecular lengths and corresponds to the characteristic spatial extension of the core defects. 28,20 We also introduce 0 ϭ͉6DA(1ϪU/3)͉ Ϫ1 , corresponding to the characteristic time scale for changes of the order parameter. For the parameter values used in this work, 29 the relaxation time is on the order of 100 ns.…”

“…The characteristic dimensions of the film are large compared to the nematic coherence length ( Ϸ20 nm), 16,17 while the size of the nanoparticles is on the order of a few coherence lengths: the biological particles that are the targets of the experimental sensors have a size on the order of tens or hundreds of nanometers, hence in the model sensor that we present the adsorbed particles have a radius Rϭ2.4 , which is large compared to the coherence length of the bulk nematic. The relaxation of the nematic is described by a time evolution equation for the tensor order parameter 17 18 The tensor order parameter formulation has been successfully applied to study the defect structure around an individual particle, 19,20 or a group of particles. 6,7,21 The system is first equilibrated in the isotropic phase; after a sudden quench into the nematic phase, its evolution is analyzed through the correlation function of the tensor order parameter for different concentrations of particles.…”