Arrangement dependence of interparticle force in nematic colloids

We have experimentally and theoretically studied the interparticle force between two colloidal particles with different sizes accompanied by hyperbolic hedgehog defects in a nematic liquid crystal. The force $f$ was directly measured using dual-beam optical tweezers and calculated theoretically from the equilibrium tensor field around the particles. The dependence of $f$ on the center-to-center distance between particles of different sizes $R$ is different from that for particles with the same size. The magnitude of $f$ depends on the relative arrangement of the particles: $f$ is larger when a defect between the particles belongs to the larger particle. From the theoretical calculation, the difference in $f$ between the two arrangements, $\delta f$, monotonically increases with increasing size difference. The difference $\delta f$ was experimentally and theoretically found to be proportional to $R^{-4.6}$ at large $R$. The obtained exponent is comparable to the exponent of $-5$ predicted by electrostatic analogy.

Figure 1

Possible arrangements of two particles with different sizes. (a) Type A: the larger particle is on the left side $\left(a_2>a_1\right)$. (b) Type B: the smaller particle is on the left side $\left(a_2<a_1\right)$. The two particles (dipoles) are aligned parallel to the far-field director.

Figure 2

(Color online) Dependence of the interparticle force $f$ on the center-to-center interparticle distance $R$ for particles with radii of 2.55 and $2.0\mu \text{m}$. The force curves in a logarithmic plot are shown in (b). Filled circles (red online): type A. Empty circles (blue online): type B. Empty squares (green online): particles with the same size (radius of $2.55\mu \text{m}$). The solid lines in (b) are the best fits to experimental data using Eq. (1). The dotted line in (b) shows $R^{-4}$ dependence as a guide to the eye.

Figure 3

(Color online) Dependence of dimensionless interparticle force $\overline{f}$ on the reduced interparticle distance $D$. (a) Particles in type A arrangement $\left(a_1\le a_2\right)$. (b) Particles in type B arrangement $\left(a_1\ge a_2\right)$.

Figure 4

(Color online) Comparison between experimentally obtained force curves and theoretical calculations. The calculated force curves are scaled to fit the experimental result for type A arrangement (filled circles).

Figure 5

(Color online) Dependence of the difference in the interparticle force between the two arrangements $\delta f$ on the reduced interparticle distance $D$. The dotted line (black online) is proportional to $D^{-5}$, which is expected from the electrostatic analogy. The best-fitted slope to the theoretical calculation, drawn as a thick line (blue online), is proportional to $D^{-4.6}$.