Separation-Independent Attractive Force between Like Particles Mediated by Nematic-Liquid-Crystal Distortions

We investigate numerically with the aid of the Landau–de Gennes continuum theory the interaction between two spherical particles carrying the same topological charges $+1$ mediated by the elastic distortion of a nematic liquid crystal. We consider the case where an escaped nontopological ring disclination is situated between the particles; the director is continuous everywhere and no counterdefects are present. We find that the interaction is attractive and its potential energy depends linearly on the interparticle distance $D$. This behavior yields the $D$-independent interaction force, which was observed experimentally by Poulin, Cabuil, and Weitz [Phys. Rev. Lett. 79, 4862 (1997)] in the presence of narrow strings of birefringent regions (“bubble-gum” configuration) between the particles.

Figure 1

Schematic illustration of the initial condition prepared for small $D(\le 6.6R_0)$.

Figure 2

(a)–(c) The orientation profiles of a nematic liquid crystal shown by gray-scale plots of $Q_{zz}^2$ for $D=$ (a) $2.2R_0$, (b) $4.0R_0$, and (c) $6.0R_0$. The $z$ axis is along the horizontal direction. (d) The orientation profile shown by a gray-scale plot of $Q_{yy}^2(\varphi =0)$ for $D=6.0R_0$.

Figure 3

The width $w$ of the region with positive $Q_{yy}(\varphi =0)$ as a function of the interparticle distance $D$.

Figure 4

The reduced free energy of the host nematic liquid crystal $\overline{F}$ as a function of $D$. The dashed line is $0.00208+0.000488\times (D/R_0)$. The solid line is the reduced free energy of parallel dipoles (see the text). The inset is a magnified plot for $2\le D/R_0\le 3$.

Figure 5

The reduced force acting on the particle from the host nematic liquid crystal $\overline{f}$ as a function of $D$. $\overline{f}<0$ implies an attractive force.