Colloidal nanoparticles trapped by liquid-crystal defect lines: A lattice Monte Carlo simulation

Lattice-based Monte Carlo simulations are performed to study a confined liquid crystal system with a topological disclination line entangling a colloidal nanoparticle. In our microscopic study the disclination line is stretched by moving the colloid, as in laser tweezing experiments, which results in a restoring force attempting to minimize the disclination length. From constant-force simulations we extract the corresponding disclination line tension, estimated as $\sim 50$ pN, and observe its decrease with increasing temperature.

Figure 1

Schematic of the simulated nanochannel: dashed lines at the top and bottom surfaces represent the director field. The colloidal particle under study (white) is at the center and the smaller pinning particle (black) is at the channel top and bottom (note the periodic boundary conditions). The disclination (dark gray line) runs along the channel axis. The particle in a shifted position along with the stretched disclination is also shown in lighter shades. The defect structure around the particles is not explicitly shown.

Figure 2

Top row shows defect structures (yellow) entangling a colloidal particle (red) of radius $10a$, obtained with (a) the particle positioned at origin for $T^{*}=1.0$, averaged over MC sweeps (MDS) and, (b)–(f) with $x_c$ = 0, 10, 20, 30, and 40 for $T^{*}=0.1$ from an equilibrated instantaneous configuration (IDS). Bottom row displays similar structures for a smaller particle of radius $5a$. Disclinations are visualized as $c_l^i$ isosurfaces for a threshold of 0.85 and 0.28 at the lower and higher temperatures, respectively. (The corresponding bulk values are approximately 0.98 and 0.6.) Note the apparent variation in the looping of disclination line around the colloid, and the thickness of the line away from the particle, at both temperatures. See text for a more detailed description and Supplemental Material [22] for the movies. The small particle seen at the top and bottom in each plate serves to pin the disclination line.

Figure 3

Trail of the particle as the system evolves from an initially stretched entangled disclination with particle at $x_c=20$, along $x$ at $T^{*}=0.1$ (black) and 0.15 (gray).

Figure 4

(a) Equilibrium colloidal particle position versus applied force for different temperatures. Straight lines represent Hookean linear fits. (b) Temperature dependence of the force constant inverse $1/k^{*}$.