Iris B. Liu

Capillary migration of microdisks on curved interfaces.

The capillary energy landscape for particles on curved fluid interfaces is strongly influenced by the particle wetting conditions. Contact line pinning has now been widely reported for colloidal particles, but its implications in capillary interactions have not been addressed. Here, we present experiment and analysis for disks with pinned contact lines on curved fluid interfaces. In experiment, we study microdisk migration on a host interface with zero mean curvature; the microdisks have contact lines pinned at their sharp edges and are sufficiently small that gravitational effects are negligible. The disks migrate away from planar regions toward regions of steep curvature with capillary energies inferred from the dissipation along particle trajectories which are linear in the deviatoric curvature. We derive the curvature capillary energy for an interface with arbitrary curvature, and discuss each contribution to the expression. By adsorbing to a curved interface, a particle eliminates a patch of fluid interface and perturbs the surrounding interface shape. Analysis predicts that perfectly smooth, circular disks do not migrate, and that nanometric deviations from a planar circular, contact line, like those around a weakly roughened planar disk, will drive migration with linear dependence on deviatoric curvature, in agreement with experiment.

Elastocapillary interactions on nematic films

Significance In this research we demonstrate complementary roles for elastic and capillary interactions for particles on thin nematic liquid crystal films. A priori estimates would suggest that surface tension effects would dominate over those associated with bend, twist, or splay of nematic director fields. This work is the first to our knowledge to clearly demonstrate complementary roles for both effects and extends significantly the means for developing oriented anisotropic assemblies. Anisotropic particles create strong capillary interactions that can dictate assembly. These assemblies obey orientations dictated by director fields in oriented planar nematic films. Curved interfaces add another degree of freedom, because curvature capillary-driven alignment competes with elastic-driven orientations. Experimental results are supported by analysis. Rod-like colloids distort fluid interfaces and interact by capillarity. We explore this interaction at the free surface of aligned nematic liquid crystal films. Naive comparison of capillary and elastic energies suggests that particle assembly would be determined solely by surface tension. Here, we demonstrate that, under certain circumstances, the capillary and elastic effects are complementary and each plays an important role. Particles assemble end-to-end, as dictated by capillarity, and align along the easy axis of the director field, as dictated by elasticity. On curved fluid interfaces, however, curvature capillary energies can overcome the elastic orientations and drive particle migration along curvature gradients. Domains of dominant interaction and their transition are investigated.

Curvature-driven assembly in soft matter.

Control over the spatial arrangement of colloids in soft matter hosts implies control over a wide variety of properties, ranging from the system’s rheology, optics, and catalytic activity. In directed assembly, colloids are typically manipulated using external fields to form well-defined structures at given locations. We have been developing alternative strategies based on fields that arise when a colloid is placed within soft matter to form an inclusion that generates a potential field. Such potential fields allow particles to interact with each other. If the soft matter host is deformed in some way, the potential allows the particles to interact with the global system distortion. One important example is capillary assembly of colloids on curved fluid interfaces. Upon attaching, the particle distorts that interface, with an associated energy field, given by the product of its interfacial area and the surface tension. The particle’s capillary energy depends on the local interface curvature. We explore this coupling in experiment and theory. There are important analogies in liquid crystals. Colloids in liquid crystals elicit an elastic energy response. When director fields are moulded by confinement, the imposed elastic energy field can couple to that of the colloid to define particle paths and sites for assembly. By improving our understanding of these and related systems, we seek to develop new, parallelizable routes for particle assembly to form reconfigurable systems in soft matter that go far beyond the usual close-packed colloidal structures. This article is part of the themed issue ‘Soft interfacial materials: from fundamentals to formulation’.

Capillary Assembly of Colloids: Interactions on Planar and Curved Interfaces

In directed assembly, small building blocks are assembled into an organized structure under the influence of guiding fields. Capillary interactions provide a versatile route for structure formation. Colloids adsorbed on fluid interfaces distort the interface, which creates an associated energy field. When neighboring distortions overlap, colloids interact to minimize interfacial area. Contact line pinning, particle shape, and surface chemistry play important roles in structure formation. Interface curvature acts like an external field; particles migrate and assemble in patterns dictated by curvature gradients. We review basic analysis and recent findings in this rapidly evolving literature. Understanding the roles of assembly is essential for tuning the mechanical, physical, and optical properties of the structure.

Directed micro assembly of passive particles at fluid interfaces using magnetic robots

We combine strategies for passive particle assembly in soft matter with robotics to develop new means of controlled interaction. In capillary assembly, particles distort fluid interfaces and move in directions that minimize the surface area. In particular, they move along principle axes on curved interfaces to sites of high curvature via capillary migration. We propose a robot that serves as a programmable source of fluid curvature and allows the collection of passive particles. When settled on a fluid interface, the magnetic robot distorts the interface, which strongly influences curvature capillary migration. The shape of the robot dictates the interface shape. Preferred assembly site can be created by imposing high interface curvature near corners. This freedom to manipulate interface curvature dynamically and to migrate laterally on the interface creates new possibilities for directed bottom-up particle assemblies and precise manipulation of these complex assembled structures. Since the passive particles can be functionalized to sense, report and interact with their surroundings, this work paves the way to new schemes for creation and control of functionalized micro robots.

Smectic Gardening on Curved Landscapes

Focal conic domains (FCDs) form in smectic-A liquid crystal films with hybrid anchoring conditions with eccentricity and size distribution that depend strongly on interface curvature. Assemblies of FCDs can be exploited in settings ranging from optics to material assembly. Here, using micropost arrays with different shapes and arrangement, we assemble arrays of smectic flower patterns, revealing their internal structure as well as defect size, location, and distribution as a function of interface curvature, by imposing positive, negative, or zero Gaussian curvature at the free surface. We characterize these structures, relating free surface topography, substrate anchoring strength, and FCD distribution. Whereas the largest FCDs are located in the thickest regions of the films, the distribution of sizes is not trivially related to height, due to Apollonian tiling. Finally, we mold FCDs around microposts of complex shape and find that FCD arrangements are perturbed near the posts, but are qualitatively similar far from the posts where the details of the confining walls and associated curvature fields decay. This ability to mold FCD defects into a variety of hierarchical assemblies by manipulating the interface curvature paves the way to create new optical devices, such as compound eyes, via a directed assembly scheme.