Abstract
The role of environment in shaping material properties is of great significance, but less is known about how non-trivial topology of the environment couples to material states, which can be of non-trivial topology themselves. In this paper, we demonstrate the role of the topology of the environment on the formation of complex nematic fields and defect structures, specifically in the system of nematic colloidal knots. The topological environments around knotted colloidal particles are suggested to exist as spherical surface-patterned nematic cavities imposing radial, uniform or hyperbolic nematic profiles. We show that topologically different nematic environments significantly affect and create differences in the colloidal field structure created within the environment, such as the location, profile and number of topological defects. Specifically, we demonstrate that topological environments in combination with knotted colloidal particles of non-trivial topology lead to the formation of diverse nematic knotted and linked fields. These fields are different adaptations of the knotted shape of the colloidal particles, creating knots and links of topological defects as well as escaped-core defect-like solitonic structures. These are observed in chiral nematic media but here are stabilised in achiral nematic media as a result of the distinct shape of the knotted colloidal particle, with a double helix segment and nematic environmental patterns. More generally, this paper is a contribution towards understanding the role of environment, especially its topology, on the response and defect formation in elastic fields, such as in nematic liquid crystal colloids.
Highlights
An inseparable element in the design of topological soft materials is the environment – for example, imposed by the surface, confinement or geometry – which on one hand can pose constraints on the material design but on the other hand can generate possibilities for new material structures.[1,2,3] A common role of the environment in the design of topological soft matter is that it primarily affects the energetics of the material, such as making structures stable or metastable
We explore the role of the topology of the environment on the formation and stabilisation of complex nematic fields and defect structures, in the system of nematic colloidal knots confined within a spherical cavity of non-trivial surface-imposed topology fields
We considered three different designs for the topological structures of the environment in a system of trefoil and pentafoil nematic colloidal knots
Summary
An inseparable element in the design of topological soft materials is the environment – for example, imposed by the surface, confinement or geometry – which on one hand can pose constraints on the material design but on the other hand can generate possibilities for new material structures.[1,2,3] A common role of the environment in the design of topological soft matter is that it primarily affects the energetics of the material, such as making structures stable or metastable. The first method employs ionic surfactants to make the droplets’ anchoring pattern modifiable under the application of a dc electric field.[45] The second method is a mechanical modification technique in which the anchoring pattern is dynamically modified through the diffusion of droplets from a layer of sodium dodecyl sulfate (SDS), where they have a homeotropic anchoring, into a layer of pure glycerol, inducing planar degenerate anchoring.[43] patchy droplets with well-defined fractions of homeotropic and degenerate planar anchoring can be generated at the interface between SDS and glycerol, and upon photo-polymerization the patches can be created with a desired relative size These recent developments clearly show that anchoring patterns can be controllably designed at a complex level. We illustrate that these differences between the topological states originate from an interplay between the screening ability of the particle and the nematic ordering effects of the environment
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