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.

When liquid crystals are confined to finite volumes, the competition between the surface anchoring imposed by the boundaries and the intrinsic orientational symmetry-breaking of these materials gives rise to a host of intriguing phenomena involving topological defect structures. For synthetic molecular mesogens, like the ones used in liquid-crystal displays, these defect structures are independent of the size of the molecules and well described by continuum theories. In contrast, colloidal systems such as carbon nanotubes and biopolymers have micron-sized lengths, so continuum descriptions are expected to break down under strong confinement conditions. Here, we show, by a combination of computer simulations and experiments with virus particles in tailor-made disk- and annulus-shaped microchambers, that strong confinement of colloidal liquid crystals leads to novel defect-stabilized symmetrical domain structures. These finite-size effects point to a potential for designing optically active microstructures, exploiting the as yet unexplored regime of highly confined liquid crystals.

We study the nematic phase of rodlike fd -virus particles confined to channels with wedgestructured walls. Using laser scanning confocal microscopy we observe a splay-to-bend transition at the single particle level as a function of the wedge opening angle. Lattice Boltzmann simulations reveal the underlying origin of the transition and its dependence on nematic elasticity and wedge geometry. Our combined work provides a simple method to obtain the splay-to-bend elasticity ratios and offers a way to control the position of defects through the confining boundary conditions. PACS numbers:Packing and confinement problems emerge in fields ranging from biology to engineering. In biological systems the organization of the cell is determined, among other things, by the packing of fibril-like particles (actin filaments, DNA) [1,2]. An example of the subtlety of packing phenomena is the plethora of liquid crystalline phases that can be found in arrangements of anisotropic particles by increasing concentration [3,4]. Confinement of liquid crystals adds to the complexity, since the interactions of the particles with the walls may lead to structures that compete with those formed in the bulk [5,6]. Many of the next generation liquid crystal display devices exploit this interplay by using structured or patterned surfaces as an essential element of their design [7,8]. Very recently, the ordering at sawtoothed structures has been studied theoretically within a Landau-De Gennes framework [9,10], with a focus on the wetting behaviour. In this Letter, in a combined experimental and theoretical effort, we show the rich phenomenology that emerges when confining a nematic liquid crystal to a microfluidic channel with a wedge structured wall. We seek to disentangle how the wedge geometry and elasticity of the fd -virus' nematic phase determine the adopted deformation in the wedge. We introduce a new method for estimating elastic constants suitable to colloidal and biological systems, as an alternative to previous methods using magnetic fields [11] or light scattering [12]. Specifically, we determine the transition from a splay to a bend director field, with increasing wedge angle.We use the fd -virus, which is an excellent model liquid crystal system for both static and dynamic behaviour [13][14][15][16]. The virus' contour length and diameter are 0.88 µm and 6.6 nm, respectively. These dimensions allow for the 3D determination of the position and orientation of individual particles by means of laser scanning confocal microscopy (LSCM). Thus we obtain detailed mechanistic insights on a single particle level of the director field. Moreover, due to the relatively large size of the particles, we can study effects of wall structures that are, when translated to the scale of thermotropic liquid crystals, very small and inaccessible. The particles were grown following standard protocols [17] and dispersed in 20 mM tris buffer at pH 8.15 with 100 mM NaCl and 15% EtOH. The ethanol was added to prevent the growth of bacteria. The virus concent...