60th Annual Report on Research 2015

Geometric shape and topology of constituent particles can alter many colloidal properties such as Brownian motion, self-assembly, and phase behavior. So far, only single-component building blocks of colloids with connected surfaces have been studied, although topological colloids, with constituent particles shaped as freestanding knots and handlebodies of different genus, have been recently introduced. In our first article (published in PNAS, 2014) that emerges from this project we develop a new topological class of colloids shaped as multicomponent links. Using two-photon photopolymerization, we fabricate colloidal microparticle analogues of the classic examples of links studied in the field of topology, the Hopf and Solomon links, which we disperse in nematic fluids that possess orientational ordering of anisotropic rod-like molecules. The surfaces of these particles are treated to impose tangential or perpendicular boundary conditions for the alignment of liquid crystal molecules, so that they generate a host of topologically nontrivial field and defect structures in the dispersing nematic medium, resulting in an elastic coupling between the linked constituents. The interplay between the topologies of surfaces of linked colloids and the molecular alignment field of the nematic host reveals that linking of particle rings with perpendicular boundary conditions is commonly accompanied by linking of closed singular defect loops, laying the foundations for fabricating complex, composite materials with interlinking-based structural organization. Colloidal dispersions are abundant in nature, fundamental science, and technology, with examples ranging from fog and milk to colloidal models of atomic crystals and glasses and colloidal quantum dots used in fabricating the third generation solar cells. Despite the recent progress in exquisite control of geometric shape and topology of constituent colloidal particles, so far only single-component colloidal building blocks have been fabricated or found occurring in nature. We develop multicomponent linked colloidal particles lacking connectivity of their surfaces, with each component behaving as a genus-one colloidal particle itself but being topologically linked with the other components within a colloidal building block. As an example, the attached TOC shows optical micrographs and 3D multiphoton fluorescence based images of Hopf and Solomon link colloidal particles. Using such colloidal particles dispersed in a liquid crystal (LC) host fluid, we uncover topological property-defining behavior of such colloidal particles when dispersed in a nematic liquid crystal medium. In this work, we have developed a class of topological colloidal particles with multiple linked components. We have demonstrated that, when dispersed in nematic fluids, linked colloidal building blocks induce field-defect configurations that can be topologically distinct from each other, but always satisfy the topological constraints. Although we considered only uniform tangential and perpendicular boundary conditions on all surfaces of colloidal building blocks, this study can be extended to patched, mixed and optically controlled boundary conditions, potentially allowing for dynamic re-configurability. In addition to linked genus-one rings, one can envision complex but interesting behavior of linked particles with larger genus and larger number of linked components. For example, a defect line emanating from the surface of one linked large-genus colloidal component with tangential boundary conditions could terminate on another one, binding both components. In this way valence-like interactions between the components of the colloidal building blocks could emerge. Experimental study of implications of linking of particles and defect loops in terms of the topology-dictated appearance of additional defects could also allow for new means of probing symmetry of LC phases, e.g. distinguishing between uniaxial and biaxial nematics, as well as expands the diversity of soft matter systems generating topologically nontrivial configurations. Other needed future explorations include stability analysis and study of structural phase diagrams, as well as how cell confinement, kinetic processes, chirality, surface nonorientability of linked colloidal components, and external fields control them. Linked multicomponent particles dispersed in LC or isotropic hosts, with the components made of the same or different materials, are of practical interest as they can enrich colloidal self-assembly and response to external stimuli.