Description
- Abstract:
- Colloidal membranes are monolayers of rod-like particles and provide a model system of liquid crystals to study chirality, elasticity, and geometry. In this thesis, we study chiral colloidal membranes in both curved and planar geometries. We consider the competition between Frank elasticity and tilt coupling determining how chiral mem- branes respond to curvature and director dynamics of skyrmions in planar colloidal membranes. In the case of curved surface, we study the interplay of curvature, the tilt coupling favoring alignment of the directors to the normal of the surface, and liquid crystal elasticity on a cylinder. We show that when the tilt coupling is sufficiently large, the curvature of the cylinder leads to a discontinuous transition between the twisted state and the state with all directors normal to the surface. We also study the metastable twisted conformations above the transition corresponding to two sharp twist domain walls (π-walls) that wrap around the cylinder in helical paths. Our nu- merical work is supported by analytic calculations that approximately capture the transition as well as the trend of increasing pitch with increasing penalty for tilt away from the surface normal. Finally, we explore the role of the Gaussian curvature of the surface by determining the conformation of a chiral liquid crystal on a family of unduloids, which smoothly vary from the cylinder to a string of spheres. In the case of planar membranes, we analyze a phenomenological model for the dynamics of a skyrmion in a colloidal membrane, disregarding membrane and solvent flow. The skyrmion corresponds to a configuration with a circular twist wall. Numerically solv- ing this model, we find that chirality determines whether a circular twist wall expands or contracts. The transition point is consistent with the criteria for the formation of a straight twist wall in the plane. By fitting the numerical calculation with the results of experiments, we estimate the rotational viscosity of the rods. Our results match well with other theoretical approximations, giving a more precise range of chirality to form a colloidal skyrmion. We also perform simulations based on Landau–de Gennes theory using FEniCS. We find two mechanisms that make the straight π-walls relax faster than the curved π-walls. One is the anisotropy in the elastic constants. An- other is that the dissipation is confined to the ends of the straight π-wall but takes place all along the length of the curved π-wall.
- Notes:
- Thesis (Ph. D.)--Brown University, 2026
Citation
Liu, Zifei,
"Chiral Colloidal Membranes: effects of curvature and dynamics of π-walls"
(2026).
Physics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://repository.library.brown.edu/studio/item/bdr:rt3w5bku/
