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We report a model to predict equilibrium density profiles for different shaped colloids in two-dimensional liquid, nematic, and crystal states in nonuniform external fields. The model predictions are validated against Monte Carlo simulations and optical microscopy experiments for circular, square, elliptical, and rectangular colloidal particles in AC electric fields between parallel electrodes. The model to predict the densities of all states of different shaped particles is based on a balance of the local quasi-2D osmotic pressure against a compressive force due to induced dipole-field interactions. The osmotic force balance employs equations of state for hard ellipse liquid, nematic, and crystal state osmotic pressures, which are extended to additional particle shapes. The resulting simple analytical model is shown to accurately predict particle densities within liquid, liquid crystal, and crystal states for a broad range of particle shapes, system sizes, and field conditions. These findings provide a basis for quantitative design and control of fields to assemble and reconfigure colloidal particles in interfacial materials and devices. 

Simulations of colloids on spherical surfaces show that self-diffusion, local density, and topological defects are curvature-independent until freezing, after which topological charge distribution mediates curvature-dependent diffusion. 

We report a method to predict equilibrium concentration profiles of hard ellipses in nonuniform fields, including multiphase equilibria of fluid, nematic, and crystal phases. Our model is based on a balance of osmotic pressure and field mediated forces by employing the local density approximation. Implementation of this model requires development of accurate equations of state for each phase as a function of hard ellipse aspect ratio in the range k = 1–9. The predicted density profiles display overall good agreement with Monte Carlo simulations for hard ellipse aspect ratios k = 2, 4, and 6 in gravitational and electric fields with fluid–nematic, fluid–crystal, and fluid–nematic–crystal multiphase equilibria. The profiles of local order parameters for positional and orientational order display good agreement with values expected for bulk homogeneous hard ellipses in the same density ranges. Small discrepancies between predictions and simulations are observed at crystal–nematic and crystal–fluid interfaces due to limitations of the local density approximation, finite system sizes, and uniform periodic boundary conditions. The ability of the model to capture multiphase equilibria of hard ellipses in nonuniform fields as a function of particle aspect ratio provides a basis to control anisotropic particle microstructure on interfacial energy landscapes in diverse materials and applications. 

We measure and model monolayers of concentrated diffusing colloidal probes interacting with polymerized liquid crystal (PLC) planar surfaces. At topological defects in local nematic director profiles at PLC surfaces, we observe time-averaged two-dimensional particle density profiles of diffusing colloidal probes that closely correlate with spatial variations in PLC optical properties. An inverse Monte Carlo analysis of particle concentration profiles yields two-dimensional PLC interfacial energy landscapes on the kT -scale, which is the inherent scale of many interfacial phenomena ( e.g. , self-assembly, adsorption, diffusion). Energy landscapes are modelled as the superposition of macromolecular repulsion and van der Waals attraction based on an anisotropic dielectric function obtained from the liquid crystal birefringence. Modelled van der Waals landscapes capture most net energy landscape variations and correlate well with experimental PLC director profiles around defects. Some energy landscape variations near PLC defects indicate either additional local repulsive interactions or possibly the need for more rigorous van der Waals models with complete spectral data. These findings demonstrate direct, sensitive measurements of kT -scale van der Waals energy landscapes at PLC interfacial defects and suggest the ability to design interfacial anisotropic materials and van der Waals energy landscapes for colloidal assembly. 

Assembling different shaped particles into ordered microstructures is an open challenge in creating multifunctional particle-based materials and devices. Here, we report the two-dimensional (2D) AC electric field mediated assembly of different shaped colloidal particles into amorphous, liquid crystalline, and crystalline microstructures. Particle shapes investigated include disks, ellipses, squares, and rectangles, which show how systematic variations in anisotropy and corner curvature determine the number and type of resulting microstructures. AC electric fields induce dipolar interactions to control particle positional and orientational order. Microstructural states are determined via particle tracking to compute order parameters, which agree with computer simulations and show how particle packing and dipolar interactions together produce each structure. Results demonstrate how choice of particle shape and field conditions enable kinetically viable routes to assemble nematic, tetratic, and smectic liquid crystal structures as well as crystals with stretched 4- and 6-fold symmetry. Results show it is possible to assemble all corresponding hard particle phases, but also show how dipolar interactions influence and produce additional microstructures. Our findings provide design rules for the assembly of diverse microstructures of different shaped particles in AC electric fields, which could enable scalable and reconfigurable particle-based materials, displays, and printing technologies. 

We construct a reduced, data-driven, parameter dependent effective Stochastic Differential Equation (eSDE) for electric-field mediated colloidal crystallization using data obtained from Brownian dynamics simulations. 

We report computer simulations of two-dimensional convex hard superellipse particle phases vs. particle shape parameters including aspect ratio, corner curvature, and sidewall curvature. Shapes investigated include disks, ellipses, squares, rectangles, and rhombuses, as well as shapes with non-uniform curvature including rounded squares, rounded rectangles, and rounded rhombuses. Using measures of orientational order, order parameters, and a novel stretched bond orientational order parameter, we systematically identify particle shape properties that determine liquid crystal and crystalline phases including their coarse boundaries and symmetry. We observe phases including isotropic, nematic, tetratic, plastic crystals, square crystals, and hexagonal crystals (including stretched variants). Our results catalog known benchmark shapes, but include new shapes that also interpolate between known shapes. Our results indicate design rules for particle shapes that determine two-dimensional liquid, liquid crystalline, and crystalline microstructures that can be realized via particle assembly.