Mechanically Induced Biaxial Transition in a Nanoconfined Nematic Liquid Crystal with a Topological Defect

Using an atomic force microscopy, we have measured the separation dependence of the force between an atomically flat mica sheet and a micrometer-sized glass sphere immersed in the nematic liquid crystal. As the mica surface induces a strong parallel alignment and the treated glass sphere induces a strong perpendicular alignment on the liquid crystal, a repulsive force is observed due to the elastically deformed nematic liquid crystal. We observe that below a critical separation $d_{\mathrm{th}}\approx 10\mathrm{nm}$, the system undergoes a structural transition, thus relaxing the distortion. The results are interpreted within the eigenvalue exchange mechanism using the Landau–de Gennes tensorial approach.

Figure 1

Force (open circles) mediated by a thin hybrid 5CB nematic layer confined between a homeotropic sphere and a planar mica surface. The force is monotonically repulsive for $d>15\mathrm{nm}$ and follows the Frank-Derjaguin model (solid line). When $d\sim {\xi }_b$, the force becomes nonmonotonic but still repulsive and is described by the tensorial LdG model for a hybrid cell with defect (dashed line). In the inset, the small separation region is enlarged.

Figure 2

Orientation of the molecules in a thin film of a nematic liquid crystal 5CB, which is confined between a DMOAP covered glass sphere and a flat mica surface. The alignment is planar on the flat mica surface and homeotropic on the curved surface of the sphere. The topological constraint creates a disclination line, passing through the contact point.

Figure 3

Biaxiality $\mathcal{B}$ in a thin hybrid nematic layer with different thicknesses: (a) $d=200\mathrm{nm}$, (b) $d=30\mathrm{nm}$, (c) $d=14\mathrm{nm}$, and (d) $d=10\mathrm{nm}$. At large separation [(a) and (b)], the system is uniaxial everywhere except for a small region surrounding the defect core. As the gap is decreased, the defect core is deformed (c) and below some threshold gap $d_{\mathrm{th}}$ (d), the defect is expelled through the creation of a biaxial wall which connects the perpendicular and the parallel orientations. The lateral size is 300 nm.

Figure 4

Average molecular orientation described by $\cos (\theta {)}^2$ inside of the hybrid layer for (a) $d=200\mathrm{nm}$ and (b) $d=10\mathrm{nm}$. $\theta$ is the angle between the average orientation of molecular long axis (i.e., the director) and the $x$ direction.