Design of effective bulk potentials for nematic liquid crystals via colloidal homogenisation

We consider a Landau–de Gennes model for a suspension of small colloidal inclusions in a nematic host. We impose suitable anchoring conditions at the boundary of the inclusions, and we work in the dilute regime — i.e. the size of the inclusions is much smaller than the typical separation distance between them, so that the total volume occupied by the inclusions is small. By studying the homogenised limit, and proving rigorous convergence results for local minimisers, we compute the effective free energy for the doped material. In particular, we show that not only the phase transition temperature, but also any coefficient of the quartic Landau–de Gennes bulk potential can be tuned, by suitably choosing the surface anchoring energy density.

Electrostatically controlled surface boundary conditions in nematic liquid crystals and colloids

Differing from isotropic fluids, liquid crystals exhibit highly anisotropic interactions with surfaces, which define boundary conditions for the alignment of constituent rod-like molecules at interfaces with colloidal inclusions and confining substrates. We show that surface alignment of the nematic molecules can be controlled by harnessing the competing aligning effects of surface functionalization and electric field arising from surface charging and bulk counterions. The control of ionic content in the bulk and at surfaces allows for tuning orientations of shape-anisotropic particles like platelets within an aligned nematic host and for changing the orientation of director relative to confining substrates. The ensuing anisotropic elastic and electrostatic interactions enable colloidal crystals with reconfigurable symmetries and orientations of inclusions.

Steady electrical and micro-rheological response functions for uncharged colloidal inclusions in polyelectrolyte hydrogels

The electric-field-induced response of an uncharged colloidal sphere embedded in a quenched polyelectrolyte hydrogel is calculated from a model where the polymer network is treated as an elastic, porous skeleton saturated with an aqueous electrolyte. We present exact analytical solutions for the steady response to a uniform electric field, as well as the steady susceptibility, defined as the ratio of the particle displacement to the strength of an optical or magnetic force. Even though the particle is uncharged, it attains a finite electric-field-induced displacement owing to hydrodynamic coupling with electroosmotic flow. The steady susceptibility decreases with increasing charge and decreasing electrolyte concentration; in general, charge imparts a small correction to the classical theory for an uncharged linearly elastic continuum.