Deformable homeotropic nematic droplets in a magnetic field.

We present a Frank-Oseen elasticity theory for the shape and structure of deformable nematic droplets with homeotropic surface anchoring in the presence of a magnetic field. Inspired by recent experimental observations, we focus on the case where the magnetic susceptibility is negative, and find that small drops have a lens shape with a homogeneous director field for any magnetic-field strength, whereas larger drops are spherical and have a radial director field, at least if the magnetic field is weak. For strong magnetic fields the hedgehog configuration transforms into a split-core line defect that, depending on the anchoring strength, can be accompanied by an elongation of the tactoid itself.

Connectedness percolation of elongated hard particles in an external field.

A theory is presented of how orienting fields and steric interactions conspire against the formation of a percolating network of, in some sense, connected elongated colloidal particles in fluid dispersions. We find that the network that forms above a critical loading breaks up again at higher loadings due to interaction-induced enhancement of the particle alignment. Upon approach of the percolation threshold, the cluster dimensions diverge with the same critical exponent parallel and perpendicular to the field direction, implying that connectedness percolation is not in the universality class of directed percolation.

Connectivity percolation of polydisperse anisotropic nanofillers.

We present a generalized connectedness percolation theory reduced to a compact form for a large class of anisotropic particle mixtures with variable degrees of connectivity. Even though allowing for an infinite number of components, we derive a compact yet exact expression for the mean cluster size of connected particles. We apply our theory to rodlike particles taken as a model for carbon nanotubes and find that the percolation threshold is sensitive to polydispersity in length, diameter, and the level of connectivity, which may explain large variations in the experimental values for the electrical percolation threshold in carbon-nanotube composites.

Continuum percolation of polydisperse nanofillers.

We show that a generalized connectedness percolation theory can be made tractable for a large class of anisotropic particle mixtures that potentially contain an infinite number of components. By applying our methodology to carbon-nanotube composites, we explain the huge variations found in the onset of electrical conduction in terms of a percolation threshold that turns out to be sensitive to polydispersity in particle length and diameter. The theory also allows us to model the influence of the presence of nonconductive species in the mixture, such as is the case for single-walled nanotubes, showing that these raise the percolation threshold proportionally to their abundance.

Shape and director field deformation of tactoids of plate-like colloids in a magnetic field.

We investigated by means of polarization microscopy the influence of a magnetic field on the shape and director field of nematic droplets in dispersions of plate-like colloidal particles. To interpret the experimental observations, we put forward a simple theory in which we presume strong anchoring and a sphero-cylindrical droplet shape. This model allows us to extract values for the interfacial tension and the splay elastic constant from the experimental data.

Capillary rise of an isotropic-nematic fluid interface: surface tension and anchoring versus elasticity.

A theoretical study is presented on the shape of the interface between coexisting isotropic and nematic phases in contact with a solid vertical wall. The interface profile is determined by a competition between three surface tensions, two anchoring strengths, gravity, and the Frank elastic constants of the director field. In the weak-anchoring limit, the director field is rigid and uniform, and we find the capillary rise height to depend nontrivially on the orientation of the director field relative to the solid-fluid interface.