Director reorientation dynamics of ferromagnetic nematic liquid crystals

Electrically Tuneable Optical Diffraction Gratings Based on a Polymer Scaffold Filled with a Nematic Liquid Crystal

We present an experimental and theoretical investigation of the optical diffractive properties of electrically tuneable optical transmission gratings assembled as stacks of periodic slices from a conventional nematic liquid crystal (E7) and a standard photoresist polymer (SU-8). The external electric field causes a twist-type reorientation of the LC molecules toward a perpendicular direction with respect to initial orientation. The associated field-induced modification of the director field is determined numerically and analytically by minimization of the Landau–de Gennes free energy. The optical diffraction properties of the associated periodically modulated structure are calculated numerically on the basis of rigorous coupled-wave analysis (RCWA). A comparison of experimental and theoretical results suggests that polymer slices provoke planar surface anchoring of the LC molecules with the inhomogeneous surface anchoring energy varying in the range 5–20 μJ/m². The investigated structures provide a versatile approach to fabricating LC-polymer-based electrically tuneable diffractive optical elements (DOEs).

Structure and rheology of soft hybrid systems of magnetic nanoparticles in liquid-crystalline matrices: results from particle-resolved computer simulations

Hybrid mixtures composed of magnetic nanoparticles (MNP) in liquid crystalline (LC) matrices are a fascinating class of soft materials with intriguing physical properties and a wide range of potential applications, e.g., as stimuli-responsive and adaptive materials. Already in the absence of an external stimulus, these systems can display various types of orientationally disordered and ordered phases, which are enriched by self-assembled structures formed by the MNPs. In the presence of external fields, one typically observes highly nonlinear macroscopic behavior. However, an understanding of the structure and dynamics of such systems on the particle level has, so far, remained elusive. In the present paper we review recent computer simulation studies targeting the structure, equilibrium dynamics and rheology of LC-MNP systems, in which the particle sizes of the two components are comparable. As a numerically tractable model system we consider mixtures of soft spherical or elongated particles with a permanent magnetic dipole moment and ellipsoidal non-magnetic particles interacting via a Gay-Berne potential. We address, first, equilibrium aspects such as structural organization and self-assembly (cluster formation) of the MNPs in dependence of the orientational state of the matrix, the role of the size ratio, the impact of an external magnetic field, and the translational and orientational diffusion of the two components. Second, we discuss the non-equilibrium dynamics of LC-MNP mixtures under planar shear flow, considering both, spherical and non-spherical MNPs. Our results contribute to a detailed understanding of these intriguing hybrid materials, and they may serve as a guide for future experiments.

Magnetically Tunable Liquid Crystal-Based Optical Diffraction Gratings

We present a theoretical analysis of optical diffractive properties of magnetically tunable optical transmission gratings composed of periodically assembled layers of a polymer and a ferromagnetic liquid crystal (LC). The orientational structure of the LC layers as a function of an applied magnetic field is calculated by minimization of the Landau-de Gennes free energy for ferromagnetic LCs, which is performed numerically and also analytically by using the one-constant approximation and the approximations of the high and the low magnetic fields. Optical diffractive properties of the associated diffraction structure are calculated numerically in the framework of rigorous coupled-wave analysis (RCWA). The presented methodology provides a basis for designing new types of diffractive optical element based on ferromagnetic LCs and simulating their operation governed by the in-plane magnetic field.

Molecular-statistical theory of ferromagnetic liquid crystal suspensions

A tensor variant of molecular-statistical theory is developed, within the framework of which it is possible to describe the appearance of spontaneous magnetization of anisotropic ferromagnetic nanoparticles dispersed in a nematic liquid crystal. Along with the tensor order parameters characterizing the orientational ordering of the liquid crystal and dispersed anisometric particles, the vector order parameter determining the magnetization of the ensemble of particles is additionally taken into account. A comparison between the previously known phenomenological theories of ferronematics and the proposed molecular-statistical theory is made. Phase diagrams of the suspension are constructed and the mean-field theory parameters are calculated on the basis of experimental data available in the literature.

Magnetically tunable optical diffraction gratings based on a ferromagnetic liquid crystal

Transmission optical diffraction gratings composed of periodic slices of a ferromagnetic liquid crystal and a conventional photoresist polymer are demonstrated. Dependence of diffraction efficiencies of various diffraction orders on an in-plane external magnetic field is investigated. It is shown that diffraction properties can be effectively tuned by magnetic fields as low as a few mT. The tuning mechanism is explained in the framework of a simple empirical model and also by numerical simulations based on the rigorous coupled wave analysis (RCWA). The obtained results provide a proof of principle of operation of magnetically tunable liquid crystalline diffractive optical elements applicable in contactless schemes for control of optical signals.

Torque-induced reorientation in active fibre-reinforced materials

We introduce a continuum model for a fibre reinforced material in which the reference orientation of the fibre may evolve with time, under the influence of external stimuli. The model is formulated in the framework of large strain hyperelasticity and the kinematics of the continuum is described by both a position vector and by a remodelling tensor which, in the present context, is an orthogonal tensor representing the fibre reorientation process. By imposing suitable thermodynamical restrictions on the constitutive equation, we obtain an evolution equation of the remodelling tensor governed by the Eshelby torque, whose stationary solutions are studied in absence of any external source terms. It is shown that the fibres reorient themselves in a configuration that minimises the elastic energy and get aligned along a direction that may or may not be of principal strain. The explicit analysis of the Hessian of the strain energy density allows us to discriminate among the stationary solutions, which ones are stable. Examples are given for passive reorientation processes driven by applied strains or external boundary tractions. Applications of the proposed theory to biological tissues, nematic or magneto-electro active elastomers are foreseen.

A ferronematic slab in external magnetic fields

The behavior of a uniformly magnetized ferronematic slab is investigated numerically in a situation in which an external magnetic field is applied parallel and antiparallel, respectively, to its initial magnetization direction. The employed numerical method allows one to determine hysteresis curves from which a critical magnetic field strength (i.e., the one at which the ferronematic sample becomes distorted) as a function of the system parameters can be inferred. Two possible mechanisms of switching the magnetization by applying a magnetic field in the antiparallel direction are observed and characterized in terms of the coupling constant between the magnetization and the nematic director and in terms of the coupling strength of the nematic liquid crystal and the walls of the slab. Suitably prepared walls allow one to combine both switching mechanisms in one setup, such that one can construct a cell, the magnetization of which can be reversibly switched off.