Interactions of carbon nanotubes in a nematic liquid crystal. I. Theory.

Elongated and rodlike objects such as carbon nanotubes (CNTs) are studied when immersed in a nematic liquid crystal. Their interaction energy in a uniform nematic field depends on their orientation relative to the director n, and its minimum determines if they stabilize parallel or perpendicular to n. Using free energy calculations, we deduce the orientation at equilibrium that they choose in a uniform director field n or when they are in contact with a splay-bend disclination line. Naturally, the CNT orientations also depend on the anchoring conditions at their surface. Essentially, three types of anchorings are considered, planar, homeotropic, and Janus anchorings in the cases of weak and strong anchoring strengths. In the presence of a splay-bend disclination line, they are attracted toward it and ultimately, they get out of the colloidal dispersion to stick on it. Their orientation relative to the line is found to be parallel or perpendicular to it, again depending on the anchoring conditions. When a sufficient number of particles are deposited on a disclination line, we finally obtain a micro- or nanonecklace in the shape of a thin thread or of a bottle brush, according to the CNTs being oriented parallel or perpendicular to the disclination line, respectively. The system exhibits a rich versatility even if up to now the weak anchorings appear to be difficult to control. As discussed in the associated experimental paper, these necklaces could be a step toward interesting applications for realizing nanowires self-connected in three dimensions to predesignated electrodes. This method could provide a way to increase the number of transistors that may be connected together on a small volume.