Curvature and confinement effects on chiral liquid crystal morphologies.

Chiral liquid crystals (ChLCs) exhibit an inherent twist that originates at the molecular scale and can extend over multiple length scales when unconstrained. Under confinement, the twist is thwarted, leading to formation of defects in the molecular order that offer distinct optical responses and opportunities for colloidal driven assembly. Past studies have explored spheroidal confinement down to the nanoscopic regime, where curved boundaries produce surface defects to accommodate topological constraints and restrict the propagation of cuboidal defect networks. Similarly, strict confinement in channels and shells has been shown to give rise to escaped configurations and skyrmions. However, little is known about the role of extrinsic curvature in the development of cholesteric textures and Blue Phases (BP). In this paper, we examine the palette of morphologies that arises when ChLCs are confined in toroidal and cylindrical cavities. The equilibrium morphologies are obtained following an annealing strategy of a Landau-de Gennes free energy functional. Three dimensionless groups are identified to build phase diagrams: the natural twist, the ratio of elastic energies, and the circumscription of a BP cell. Curvature is shown to introduce helical features that are first observed as a Double Twist, and progress to Chiral Ribbons and, ultimately, Helical BP and BP. Chiral ribbons are examined as useful candidates for driven assembly given their tunability and robustness.

Strongly Chiral Liquid Crystals in Nanoemulsions.

Liquid crystal (LC) emulsions represent a class of confined soft matter that exhibit exotic internal organizations and size-dependent properties, including responses to chemical and physical stimuli. Past studies have explored micrometer-scale LC emulsion droplets but little is known about LC ordering within submicrometer-sized droplets. This paper reports experiments and simulations that unmask the consequences of confinement in nanoemulsions on strongly chiral LCs that form bulk cholesteric and blue phases (BPs). A method based on light scattering is developed to characterize phase transitions of LCs within the nanodroplets. For droplets with a radius to the pitch ratio (Rv /p0 ) as small as 2/3, the BP-to-cholesteric transition is substantially suppressed, leading to a threefold increase of the BP temperature interval relative to bulk behavior. Complementary simulations align with experimental findings and reveal the dominant role of chiral elastic energy. For Rv /p0  ≈ 1/3, a single LC phase forms below the clearing point, with simulations revealing the new configuration to contain a τ-1/2 disclination that extends across the nanodroplet. These findings are discussed in the context of mechanisms by which polymer networks stabilize BPs and, more broadly, for the design of nanoconfined soft matter.

Directing the far-from-equilibrium assembly of nanoparticles in confined liquid crystals by hydrodynamic fields.

The assembly of nematic colloids relies on long-range elastic interactions that can be manipulated through external stimuli. Confinement and the presence of a hydrodynamic field alter the defect structures and the energetic interactions between the particles. In this work, the assembly landscape of nanoparticles embedded in a nematic liquid crystal confined in a nanochannel under a pressure-driven flow is determined. The dynamics of the liquid crystal tensor alignment field is determined through a Poisson-Bracket framework, namely the Stark-Lubensky equations, coupled with the zero-Reynolds momentum equations and the liquid crystal Landau-de Gennes free energy functional. A second order semi-implicit time integration and a three-dimensional Galerkin finite element method are used to resolve flow and nematic fields under several conditions. In general, the zero Reynolds flow displaces the defects around the particles in the upstream direction and renders the surface anchoring ineffective when the flow strength dominates over the nematic elasticity. More importantly, the potential of mean force for particle assembly is non-monotonic independent of surface anchoring. Our results show that the confinement length scale determines the repulsion/attraction transition between colloids, while the flow strength modifies the static defect structure surrounding the particles and determines the magnitude of the energetic barrier for successful assembly. In the attractive regime, the particles move at different rates through the nematic until one particle eventually catches up with the other. This process occurs against or along the direction of flow depending on the flow strength. Ultimately, these results provide a template for engineering and controlling the transport and assembly of nanoparticles under far-from equilibrium conditions in anisotropic media.

Cuboidal liquid crystal phases under multiaxial geometrical frustration.

Cuboidal liquid crystal phases - the so-called blue phases - consist of a network of topological defects arranged into a cubic symmetry. They exhibit striking optical properties, including Bragg reflection in the visible range and fast response times. Confining surfaces can interfere with the packing of such a network, leading to structures that have not been explored before. In this work, a Landau-de Gennes free energy formalism for the tensor alignment field Q is used to investigate the behavior of chiral liquid crystals under non-isotropic confinement. The underlying free energy functional is solved by relying on a Monte Carlo method that facilitates efficient exploration of configuration space. The results of simulations are expressed in terms of phase diagrams as a function of chirality and temperature for three families of spheroids: oblate, spherical, and prolate. Upon deformation, blue phases adapt and transform to accommodate the geometrical constraints, thereby resulting in a wider range of thermal stability. For oblate spheroids, confinement interferes with the development of a full blue phase structure, resulting on a combination of half skyrmions. For prolate spheroids, the blue phases are hybridized and exhibit features of blue phases I and II. More generally, it is shown that mechanical deformation provides an effective means to control, manipulate and stabilize blue phases and cholesterics confined in tactoids.

Reconfigurable Multicompartment Emulsion Drops Formed by Nematic Liquid Crystals and Immiscible Perfluorocarbon Oils.

Liquid crystalline (LC) oils offer the basis of stimuli-responsive LC-in-water emulsions. Although past studies have explored the properties of single-phase LC emulsions, few studies have focused on complex multicompartment emulsions containing co-existing isotropic and LC domains. In this paper, we report a study of multiphase emulsions using LCs and immiscible perfluoroalkanes dispersed in water or glycerol (the latter continuous phase is used to enable characterization). We found that the nematogen 4'-pentyl-4-biphenylcarbonitrile (5CB) anchors homeotropically (perpendicularly) and weakly at liquid perfluorononane (F9) interfaces, consistent with the smectic layering of 5CB molecules. The proposed role of smectic layering is supported by experiments performed with 4-(trans-4-pentylcyclohexyl)benzonitrile, a nematogen that possesses a cyclohexyl group that frustrates the smectic packing and leads to tilted orientations at the F9 interface. By employing perfluorocarbon and hydrocarbon surfactants in combination with multiphase 5CB and F9 emulsion droplets dispersed in a continuous water or glycerol phase, we observe a range of emulsion droplet morphologies to form, including core-shell and Janus structures, with internal organizations that reflect an interplay of interfacial (anchoring energies; F9 and glycerol) and elastic energies within the confines of the geometry of the emulsion droplet. By comparing experimental observations to simulations of the LC-perfluorocarbon droplets based on a Landau-de Gennes model of the free energy, we place bounds on the orientation-dependent interfacial energies that underlie the internal ordering of these complex emulsions. Additionally, by forming core-shells emulsion droplets from 5CB (shell) and perfluoroheptane (cores), we demonstrate how a liquid-to-vapor phase transition in the perfluorocarbon core can be used to actuate the droplet and rapidly thin the nematic shell. Overall, the results reported in this paper demonstrate that multiphase LC emulsions formed from mixtures of perfluoroalkanes and LCs provide new opportunities to engineer hierarchical and stimuli-responsive emulsion systems.

Fluctuations and phase transitions of uniaxial and biaxial liquid crystals using a theoretically informed Monte Carlo and a Landau free energy density.

In this work, we explore fluctuations during phase transitions of uniaxial and biaxial liquid crystals using a phenomenological free energy functional. We rely on a continuum-level description of the liquid crystal ordering with a tensorial parameter and a temperature dependent Landau polynomial expansion of the tensor's invariants. The free energy functional, over a three-dimensional periodic domain, is integrated with a Gaussian quadrature and minimized with a theoretically informed Monte Carlo method. We reconstruct analytical phase diagrams, following Landau and Doi's notations, to verify that the free energy relaxation reaches the global minimum. Importantly, our relaxation method is able to follow the thermodynamic behavior provided by other non-phenomenological approaches; we predict the first order character of the isotropic-nematic transition, and we identify the uniaxial-biaxial transition as second order. Finally, we use a finite-size scaling method, using the nematic susceptibility, to calculate the transition temperatures for 4-Cyano-4'-pentylbiphenyl (5CB) and N-(4-methoxybenzylidene)-4-butylaniline (MBBA). Our results show good agreement with experimental values, thereby validating our minimization method. Our approach is an alternative towards the relaxation of temperature dependent continuum-level free energy functionals, in any geometry, and can incorporate complicated elastic and surface energy densities.