Colloidal liquid crystals in rectangular confinement: theory and experiment

Abstract

We theoretically and experimentally study nematic liquid crystal equilibria within shallow rectangular wells. We model the wells within a two-dimensional Oseen-Frank framework, with strong tangent anchoring, and obtain explicit analytical expressions for the director fields and energies of the 'diagonal' and 'rotated' solutions reported in the literature. These expressions separate the leading-order defect energies from the bulk distortion energy for both families of solutions. The continuum Oseen-Frank study is complemented by a microscopic mean-field approach. We numerically minimize the mean-field functional, including the effects of weak anchoring, variable order and random initial conditions. In particular, these simulations suggest the existence of higher-energy metastable states with internal defects. We compare our theoretical results to experimental director profiles, obtained using two types of filamentous virus particles, wild-type fd-virus and a modified stiffer variant (Y21M), which display nematic ordering in rectangular chambers, as found by confocal scanning laser microscopy. We combine our analytical energy expressions with experimentally recorded frequencies of the different equilibrium states to obtain explicit estimates for the extrapolation length, defined to be the ratio of the nematic elastic constant to the anchoring coefficient, of the fd-virus.

Ordering transitions of weakly anisotropic hard rods in narrow slitlike pores

“…This transition survives even in the extreme confinement limit 0  H ; therefore, it is interpreted as the isotropic-nematic transition of two-dimensional (2D) hard rods [24,25]. Along these lines, both experimental and theoretical studies have been devoted to the capillary nematisation and the surface ordering in strongly confined lyotropic and thermotropic liquid crystals [10,[26][27][28][29][30]. Even a second order isotropic-nematic phase transition can be observed in extremely confined semiflexible polymer solutions [31].…”

Direct calculation of distortion energies in colloidal liquid crystals from single-particle data

“…in microfluidics channels, adds elastic stress to the material. A wall often forces a certain orientation of the particles close to it (anchoring), and when a liquid crystal is confined between two or more such walls, anchoring and distortion energies must compete to determine the configuration of the director field, which is often different from that seen in bulk [2]. It has previously been shown for this particular system that anchoring is very strong and, depending on the opening angle of the wedge, the director field will either form a splay deformation or a combination of splay and bend deformations [1].…”

“…recent work by [1][2][3][4][5][6]. For colloidal liquid crystals, the effects of confinement may even be more pronounced with confinement down to the particle level.…”

Nematic Equilibria on a Two‐Dimensional Annulus

“…We employ the popular Rapini–Papoular surface energy , which in normalized form reads as where consists of two concentric circles, with radii and , and dσ is arc‐length element along . The dimensionless anchoring strength is the ratio of the outer radius to the extrapolation length ξ, , and the three key modeling parameters are then δ, ρ, and α. The extrapolation length, , is the ratio of the bending elastic constant to the physical surface anchoring strength parameter W , such that describes the strong anchoring regime .…”