Final Report Summary - ACTOIDS (Active liquid crystal colloids) The work of ACTOIDS explored vibrant multidisciplinary science of complex soft matter materials, as driven by fundamental questions of activity generated dynamics and technologically attractive self-assembled structuring of colloids in complex fluids. The research based theory and numerical computer modelling revealed several challenging research concepts including: (i) confined active flows in capillaries; (ii) prediction of experimental regimes for determination of continuum active parameters; (iii) modelling of make-by-order knots and links in complex nematic fluids; and (iv) self-assembly of three-dimensional (3D) colloidal crystals in chirality frustrated nematics. (i) Research of ACTOIDS revealed active nematic flows in complex confinement of a cylindrical capillary. We find active flow modes, which can be controlled by surfaces, activity, and size of the confining cavity. They show helical flow motifs, highlighting the importance of both primary and secondary flow. If topological defects are imposed by the boundary conditions in such confined active fluids, they act as local pumps driving the flow. At higher activity, we demonstrate escape of the active defects and flow into the third dimension, indicating the importance of dimensionality in active materials. (ii) ACTOIDS show that measuring the magnitude of the active flow as a function of the size of the confining cavity, such as capillary radius, could allow for determination of a value for the activity coefficient. Namely, in specific active nematic geometries with scalable orientational profiles, the activity-driven stress in the fluid can be mapped into local forcing which then leads to clear dependence of continuum active parameters on the size of the system. (iii) In collaboration with experimental partners, we demonstrated formation and self-assembly of topological defect lines in nematic liquid crystal colloids into arbitrary microscopic knots and links. All knots and links with up to six crossings, including the Hopf link, the Star of David, and the Borromean rings, are demonstrated, stabilising colloidal particles into an unusual soft matter. Modelling revealed the structure of the topological tangles in clusters of particles and in 2D particle arrays - as the elementary building blocks of the knots. (iv) Using the mobility of the fellow, in collaboration with the Ljubljana group, we find a novel method for the assembly of 3D colloidal crystals using blue phase complex nematic fluids. The assembly is based on blue phases providing a 3D template of trapping sites for colloidal particles. The particle configuration is determined by the orientational order of the LC molecules: Specifically, face-centred cubic colloidal crystals form in type-I blue phases, whereas body-centred crystals form in type-II blue phases. For typical 100-nm particle diameters the effective binding energy can reach up to a few 100 kT, implying robustness against mechanical stress and temperature fluctuations. Moreover, the colloidal particles substantially increase the thermal stability range of the blue phases, for a factor of two and more. Complex fluids, colloids, and activity were explored by using a continuum mean-field model of complex fluids. We developed a custom-written computer code, based on a hybrid Lattice Boltzmann algorithm that is able to model various, practically general, 3D geometries of complex active and passive flow and ordering of complex fluids. Specifically, the code can directly switch between passive and active complex nematic fluids. We believe the code -beside the already presented research results- offers an exciting novel tool that could give further access to interesting phenomena in soft matter science, either for academia or high-tech oriented research. The research was constantly complemented by training the fellow in a diversity of skills and competencies. ACTOIDS was implemented at the University of Oxford, an experienced academic environment, which trained the fellow also on highest standards in communication and presentation skills, teaching, intellectual property rights, ethical issues, language proficiency, and cultural awareness. The mobility of the fellow led to genuine - professional and personal ties with the host group and collaborators which can and will contribute to the European excellence also beyond the project.
