Thermophoresis of colloids in nematic liquid crystal.

Thermophoresis, or the directional motion of colloidal particles in liquids driven by a temperature gradient, is of both fundamental interest and practical use. In this work we explore the thermophoresis of colloids suspended in nematic liquid crystals (LCs). We observe that the motion of these colloids is fundamentally different from that in isotropic systems as a result of elastic distortions in the director fields caused by the colloidal inclusions. In the case of a sufficiently large local temperature and gradient, the elastic energy drives negative thermophoresis of immersed particles, which has a strongly nonlinear dependence on temperature. We develop a theory that incorporates elastic energy minimization into the traditional thermophoretic formulation and demonstrated a good agreement with experimental observations. We also examine the temperature dependence of the effective viscosity of the colloids and highlight the large magnitude of the Soret coefficient (|ST| > 5000), which results from the inherent enhancement in thermophoresis due to elastophoretic considerations and suppression of Brownian diffusion in LC media.

Making waves in a photoactive polymer film.

Oscillating materials that adapt their shapes in response to external stimuli are of interest for emerging applications in medicine and robotics. For example, liquid-crystal networks can be programmed to undergo stimulus-induced deformations in various geometries, including in response to light. Azobenzene molecules are often incorporated into liquid-crystal polymer films to make them photoresponsive; however, in most cases only the bending responses of these films have been studied, and relaxation after photo-isomerization is rather slow. Modifying the core or adding substituents to the azobenzene moiety can lead to marked changes in photophysical and photochemical properties, providing an opportunity to circumvent the use of a complex set-up that involves multiple light sources, lenses or mirrors. Here, by incorporating azobenzene derivatives with fast cis-to-trans thermal relaxation into liquid-crystal networks, we generate photoactive polymer films that exhibit continuous, directional, macroscopic mechanical waves under constant light illumination, with a feedback loop that is driven by self-shadowing. We explain the mechanism of wave generation using a theoretical model and numerical simulations, which show good qualitative agreement with our experiments. We also demonstrate the potential application of our photoactive films in light-driven locomotion and self-cleaning surfaces, and anticipate further applications in fields such as photomechanical energy harvesting and miniaturized transport.

Gradient-driven diffusion and pattern formation in crowded mixtures.

Gradient-driven diffusion in crowded, multicomponent mixtures is a topic of high interest because of its role in biological processes such as transport in cell membranes. In partially phase-separated solutions, gradient-driven diffusion affects microstructure, which in turn affects diffusivity; a key question is how this complex coupling controls both transport and pattern formation. To examine these mechanisms, we study a two-dimensional multicomponent lattice gas model, where "tracer" molecules diffuse between a source and a sink separated by a solution of sticky "crowder" molecules that cluster to form dynamically evolving obstacles. In the high-temperature limit, crowders and tracers are miscible, and transport may be predicted analytically. At intermediate temperatures, crowders phase separate into clusters that drift toward the tracer sink. As a result, steady-state tracer diffusivity depends nonmonotonically on both temperature and crowder density, and we observe a variety of complex microstructures. In the low-temperature limit, crowders rapidly aggregate to form obstacles that are kinetically arrested; if crowder density is near the percolation threshold, resulting tracer diffusivity shows scaling behavior with the same scaling exponent as the random resistor network model. Though highly idealized, this simple model reveals fundamental mechanisms governing coupled gradient-driven diffusion, phase separation, and microstructural evolution in crowded mixtures.

Brownian motion of arbitrarily shaped particles in two dimensions.

We implement microfabricated boomerang particles with unequal arm lengths as a model for nonsymmetric particles and study their Brownian motion in a quasi-two-dimensional geometry by using high-precision single-particle motion tracking. We show that because of the coupling between translation and rotation, the mean squared displacements of a single asymmetric boomerang particle exhibit a nonlinear crossover from short-time faster to long-time slower diffusion, and the mean displacements for fixed initial orientation are nonzero and saturate out at long times. The measured anisotropic diffusion coefficients versus the tracking point position indicate that there exists one unique point, i.e., the center of hydrodynamic stress (CoH), at which all coupled diffusion coefficients vanish. This implies that in contrast to motion in three dimensions where the CoH exists only for high-symmetry particles, the CoH always exists for Brownian motion in two dimensions. We develop an analytical model based on Langevin theory to explain the experimental results and show that among the six anisotropic diffusion coefficients only five are independent because the translation-translation coupling originates from the translation-rotation coupling. Finally, we classify the behavior of two-dimensional Brownian motion of arbitrarily shaped particles into four groups based on the particle shape symmetry group and discussed potential applications of the CoH in simplifying understanding of the circular motions of microswimmers.

Brownian motion of boomerang colloidal particles.

We investigate the Brownian motion of boomerang colloidal particles confined between two glass plates. Our experimental observations show that the mean displacements are biased towards the center of hydrodynamic stress (CoH), and that the mean-square displacements exhibit a crossover from short-time faster to long-time slower diffusion with the short-time diffusion coefficients dependent on the points used for tracking. A model based on Langevin theory elucidates that these behaviors are ascribed to the superposition of two diffusive modes: the ellipsoidal motion of the CoH and the rotational motion of the tracking point with respect to the CoH.

Monte Carlo studies of the XY model on two-dimensional curved surfaces.

To explore the interaction between topological defects and curvature in materials with orientational order, we perform Monte Carlo studies of the two-dimensional XY model on the surface of curved substrates. Each curved surface is patterned with a random lattice constructed via random sequential absorption, and an XY spin is positioned at each lattice site. Spins lie in the plane locally tangent to the surface and interact with neighbors defined via a distance cutoff. We demonstrate that the relative phase associated with vortices is significant in curved geometries and plays a role in microstructural evolution. We also observe that any nonuniform curvature, e.g., on the surface of a torus, induces spontaneous segregation of positive and negative vortices and promotes the formation of deeply metastable defect microstructures. Though qualitative in nature, these observations provide novel insights into the patterning of topological defects in curved geometries and suggest that the Kosterlitz-Thouless transition may be altered in geometries with nonuniform curvature.