Experimental realization of the “lock-and-key” mechanism in liquid crystals

Abstract

The ability to control the movement and assembly of particles in liquid crystals is not only an important route to design functional materials, but also sheds light on the mechanisms of colloidal interactions. In this study we place micron-sized particles with "Saturn ring" defects near a wall with hills and dales that impose perpendicular (homeotropic) molecular anchoring. The strong splay distortion at the wall interacts with the distortion around the particles in the near field and favors their migration towards the dales via the so-called "lock-and-key" mechanism. We demonstrate experimentally that the lock-and-key mechanism can robustly localize a particle at specific topographical features. We observe the complex trajectories traced by the particles as they dock on the dales, estimate the binding energy, and explore a range of parameters that favor or disfavor the docking event, thus exploiting the capabilities of our experimental system. We extend the study to colloids with homeotropic anchoring but with an associated point defect instead of a Saturn ring and show that they find a different preferred location, i.e. we can place otherwise identical particles at well defined sites according to their topological defect structure. Finally, for deep enough wells, confinement drives topological transitions of Saturn rings to dipoles. This ability to tailor wall geometry to guide colloids to well defined sites within nematic liquid crystals represents an important new tool in directed assembly.Fabrication through directed self-assembly provides a major simplification in processing, creating, and controlling supramolecular materials. This approach has revolutionized polymer science and is a modality that pervades biology.[1, 2] Soft materials are ideal systems to create long-range interactions by molding the associated free energy fields within which inclusions move, interact and assemble. For 1 arXiv:1602.05639v4 [cond-mat.soft]

Tunable colloid trajectories in nematic liquid crystals near wavy walls

“…However, at larger λ, the range of interaction increases only weakly. A simple calculation for the director field near a wavy wall in an unbounded medium in the one constant approximation and assuming small slopes predicts that the distortions from the wall decay over distances comparable to λ [23]. However, when λ T , thickness of the cell, confinement by the top and bottom slides truncates this range (See SI and Fig.…”

“…The energy dissipated to viscous drag along a trajectory U can be used to infer the total elastic energy change; we perform this intergration and find U ∼ 5000 k B T . In this calculation, we correct the drag coefficient for proximity to the wavy wall according to [34] and for confinement between parallel plates according to [35] (see [23] for more details). The dissipation calculation shows that gradients are weak far from the wall and steeper in the vicinity of the wall.…”

Wetting of Nematic Liquid Crystals on Crenellated Substrates: A Frank–Oseen Approach

“…where r = (x, y) and r 0 = (x 0 , y 0 ). To solve Equation (15) and evaluate F e from Equation (13), we discretize the boundary L in a number of straight segments, typically of order of 100. Then, Equation (15) reduces to a set of linear equations where the unknowns are the values of ν · ∇θ ns , which are supposed to be constant on each segment.…”

“…The study of nematic liquid crystals in contact with microstructured substrates has been an active area of research in the last decades [1][2][3], with practical applications such as zenithally bistable devices [4][5][6][7][8][9] and tailoring of soft rails for colloidal transport on surfaces [10][11][12][13][14][15][16]. Structured substrates frustrate the nematic orientational order, and thus elastic distortions of the nematic and, in some cases, topological defects arise driven by the substrate relief.…”

Controlling placement of nonspherical (boomerang) colloids in nematic cells with photopatterned director

“…The reason is that orientational order of the nematic medium and anisotropy of surface energy at the colloid-nematic interfaces makes the colloidal interactions long-range and anisotropic, thus producing a broad spectrum of ordered patterns. The LC orientational order leads to long-range anisotropic colloidal interactions which can be used to form linear chains, anisotropic clusters, 2D and 3D periodic colloidal assemblies through interactions with flat, curved, templated interfaces and topological defects (3,5,(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19). The LC mediated colloidal self-assembly further expands the spectrum of possible design pathways when combined with the external stimuli such as electromagnetic fields, temperature, or confinement.…”