Relevance of saddle-splay elasticity in complex nematic geometries

Flow-induced periodic chiral structures in an achiral nematic liquid crystal

Supramolecular chirality typically originates from either chiral molecular building blocks or external chiral stimuli. Generating chirality in achiral systems in the absence of a chiral input, however, is non-trivial and necessitates spontaneous mirror symmetry breaking. Achiral nematic lyotropic chromonic liquid crystals have been reported to break mirror symmetry under strong surface or geometric constraints. Here we describe a previously unrecognised mechanism for creating chiral structures by subjecting the material to a pressure-driven flow in a microfluidic cell. The chirality arises from a periodic double-twist configuration of the liquid crystal and manifests as a striking stripe pattern. We show that the mirror symmetry breaking is triggered at regions of flow-induced biaxial-splay configurations of the director field, which are unstable to small perturbations and evolve into lower energy structures. The simplicity of this unique pathway to mirror symmetry breaking can shed light on the requirements for forming macroscopic chiral structures.

On the elusive saddle-splay and splay-bend elastic constants of nematic liquid crystals

The elastic behavior of nematics is commonly described in terms of the three so-called bulk deformation modes, i.e., splay, twist, and bend. However, the elastic free energy contains also other terms, often denoted as saddle-splay and splay-bend, which contribute, for instance, in confined systems. The role of such terms is controversial, partly because of the difficulty of their experimental determination. The saddle-splay (K24) and splay-bend (K13) elastic constants remain elusive also for theories; indeed, even the possibility of obtaining unambiguous microscopic expressions for these quantities has been questioned. Here, within the framework of Onsager theory with Parsons-Lee correction, we obtain microscopic estimates of the deformation free energy density of hard rod nematics in the presence of different director deformations. In the limit of a slowly changing director, these are directly compared with the macroscopic elastic free energy density. Within the same framework, we derive also closed microscopic expressions for all elastic coefficients of rodlike nematics. We find that the saddle-splay constant K24 is larger than both K11 and K22 over a wide range of particle lengths and densities. Moreover, the K13 contribution comes out to be crucial for the consistency of the results obtained from the analysis of the microscopic deformation free energy density calculated for variants of the splay deformation.

Neural networks determination of material elastic constants and structures in nematic complex fluids

Supervised machine learning and artificial neural network approaches can allow for the determination of selected material parameters or structures from a measurable signal without knowing the exact mathematical relationship between them. Here, we demonstrate that material nematic elastic constants and the initial structural material configuration can be found using sequential neural networks applied to the transmmited time-dependent light intensity through the nematic liquid crystal (NLC) sample under crossed polarizers. Specifically, we simulate multiple times the relaxation of the NLC from a random (qeunched) initial state to the equilibirum for random values of elastic constants and, simultaneously, the transmittance of the sample for monochromatic polarized light. The obtained time-dependent light transmittances and the corresponding elastic constants form a training data set on which the neural network is trained, which allows for the determination of the elastic constants, as well as the initial state of the director. Finally, we demonstrate that the neural network trained on numerically generated examples can also be used to determine elastic constants from experimentally measured data, finding good agreement between experiments and neural network predictions.

Topological phases and curvature-driven pattern formation in cholesteric shells

We study the phase behaviour of cholesteric liquid crystal shells with different geometries. We compare the cases of tangential anchoring and no anchoring at the surface, focussing on the former case, which leads to a competition between the intrinsic tendency of the cholesteric to twist and the anchoring free energy which suppresses it. We then characterise the topological phases arising close to the isotropic-cholesteric transition. These typically consist of quasi-crystalline or amorphous tessellations of the surface by half-skyrmions, which are stable at lower and larger shell sizes, respectively. For ellipsoidal shells, defects in the tessellation couple to a local curvature, and according to the shell size, they either migrate to the poles or distribute uniformly on the surface. For toroidal shells, the variations in the local curvature of the surface stabilise heterogeneous phases where cholesteric or isotropic patterns coexist with hexagonal lattices of half-skyrmions.

Spontaneous Twisting of Achiral Hard Rod Nematics

Since Onsager's seminal work, hard rods have been taken as a prototype of nematic liquid crystals, characterized by uniaxial order and a uniform director field as a ground state. Here, using Onsager theory to calculate the free energy in the presence of arbitrary deformations, we find that hard rod nematics have an intrinsic tendency to twist around their ordering axis (double twist), driven by a mechanism in which the orientational fluctuations of particles play a key role. The anisotropic hard core potential used here is arguably the simplest form of interaction able to originate spontaneous breaking of mirror symmetry in a 3D fluid. Our results are discussed in relation to the recent discovery of a double twisted ground state in cylindrically confined lyotropic chromonic liquid crystals.

Foray into Concepts of Design and Evaluation of Microemulsions as a Modern Approach for Topical Applications in Acne Pathology

With a fascinating complexity, governed by multiple physiological processes, the skin is considered a mantle with protective functions which during lifetime are frequently impaired, triggering dermatologic disorders. As one of the most prevalent dermatologic conditions worldwide, characterized by a complex pathogenesis and a high recurrence, acne can affect the patient's quality of life. Smart topical vehicles represent a good option in the treatment of a versatile skin condition. By surpassing the stratum corneum known for diffusional resistance, a superior topical bioavailability can be obtained at the affected place. In this direction, the literature study presents microemulsions as a part of a condensed group of modern formulations. Microemulsions are appreciated for their superior profile in matters of drug delivery, especially for challenging substances with hydrophilic or lipophilic structures. Formulated as transparent and thermodynamically stable systems, using simplified methods of preparation, microemulsions have a simple and clear appearance. Their unique structures can be explained as a function of the formulation parameters which were found to be the mainstay of a targeted therapy.

Chiral nematic liquid crystals in torus-shaped and cylindrical cavities

We present a Monte Carlo simulation study of chiral nematic liquid crystals confined in torus-shaped and cylindrical cavities. For an achiral nematic with planar degenerate anchoring confined to a toroidal or cylindrical cavity, the ground state is defect free, with an untwisted director field. As chirality is introduced, the ground state remains defect free but the director field becomes twisted within the cavity. For homeotropic anchoring, the ground state for an achiral nematic within a toroidal cavity consists of two disclination rings, one large and one small, that follow the major circumference of the torus. As chirality is introduced and increased, this ground state becomes unstable with respect to twisted configurations. The closed nature of the toroidal cavity requires that only a half integer number of twists can be formed and this leads to the ground state being either a single disclination line that encircles the torus twice or a pair of intertwined disclination rings forming stable, knotted defect structures.

Programming emergent symmetries with saddle-splay elasticity

The director field adopted by a confined liquid crystal is controlled by a balance between the externally imposed interactions and the liquid's internal orientational elasticity. While the latter is usually considered to resist all deformations, liquid crystals actually have an intrinsic propensity to adopt saddle-splay arrangements, characterised by the elastic constant [Formula: see text]. In most realisations, dominant surface anchoring treatments suppress such deformations, rendering [Formula: see text] immeasurable. Here we identify regimes where more subtle, patterned surfaces enable saddle-splay effects to be both observed and exploited. Utilising theory and continuum calculations, we determine experimental regimes where generic, achiral liquid crystals exhibit spontaneously broken surface symmetries. These provide a new route to measuring [Formula: see text]. We further demonstrate a multistable device in which weak, but directional, fields switch between saddle-splay-motivated, spontaneously-polar surface states. Generalising beyond simple confinement, our highly scalable approach offers exciting opportunities for low-field, fast-switching optoelectronic devices which go beyond current technologies.

Effects of chiral dopants on double-twist configurations of lyotropic chromonic liquid crystals in a cylindrical cavity

We investigate how chiral dopants affect the chiral symmetry breaking of lyotropic chromonic liquid crystals (LCLCs) focusing on the double-twist (DT) director configurations in a cylindrical capillary. LCLCs of unusual elastic properties tend to exhibit chiral director configurations under confinement despite the absence of intrinsic chirality. The DT director configuration in a cylindrical cavity with a degenerate planar anchoring, resulting from the large saddle-splay-to-twist elastic modulus ratio, is a representative example. Here we start by reexamining the DT configuration of nematic disodium cromoglycate in a cylindrical capillary and estimate the ratio of saddle splay to bend modulus K_{24}/K_{3}=0.5±0.1. Additionally, we study the DT configurations of the chiral nematic LCLCs with chiral dopants. The DT configuration becomes homochiral when the dopant concentration surpasses the critical concentration. We characterize these chiral DT configurations and provide a theoretical model on their energetics. Finally, we observe how the enantiomeric excess of chiral dopants determines the director configuration when dopants of two different handednesses are mixed.

In Silico Measurement of Elastic Moduli of Nematic Liquid Crystals

Experiments on confined droplets of the nematic liquid crystal 5CB have questioned long-established bounds imposed on the elastic free energy of nematic systems. This elasticity, which derives from molecular alignment within nematic systems, is quantified through a set of moduli which can be difficult to measure experimentally and, in some cases, can only be probed indirectly. This is particularly true of the surfacelike saddle-splay elastic term, for which the available experimental data indicate values on the cusp of stability, often with large uncertainties. Here, we demonstrate that all nematic elastic moduli, including the saddle-splay elastic constant k_{24}, may be calculated directly from atomistic molecular simulations. Importantly, results obtained through in silico measurements of the 5CB elastic properties demonstrate unambiguously that saddle-splay elasticity alone is unable to describe the observed confined morphologies.

Lassoing saddle splay and the geometrical control of topological defects

Systems with holes, such as colloidal handlebodies and toroidal droplets, have been studied in the nematic liquid crystal (NLC) 4-cyano-4'-pentylbiphenyl (5CB): Both point and ring topological defects can occur within each hole and around the system while conserving the system's overall topological charge. However, what has not been fully appreciated is the ability to manipulate the hole geometry with homeotropic (perpendicular) anchoring conditions to induce complex, saddle-like deformations. We exploit this by creating an array of holes suspended in an NLC cell with oriented planar (parallel) anchoring at the cell boundaries. We study both 5CB and a binary mixture of bicyclohexane derivatives (CCN-47 and CCN-55). Through simulations and experiments, we study how the bulk saddle deformations of each hole interact to create defect structures, including an array of disclination lines, reminiscent of those found in liquid-crystal blue phases. The line locations are tunable via the NLC elastic constants, the cell geometry, and the size and spacing of holes in the array. This research lays the groundwork for the control of complex elastic deformations of varying length scales via geometrical cues in materials that are renowned in the display industry for their stability and easy manipulability.