We derive a Föppl-von Kármán-type constitutive model for solid liquid crystalline plates where the nematic director may or may not rotate freely relative to the elastic network. To obtain the reduced two-dimensional model, we rely on the deformation decomposition of a nematic solid into an elastic deformation and a natural shape change. The full solution to the resulting equilibrium equations consists of both the deformation displacement and stress fields. The model equations are applicable to a wide range of thin nematic bodies subject to optothermal stimuli and mechanical loads. For illustration, we consider certain reversible natural shape changes in simple systems which are stress free, and their counterparts, where the natural deformations are blocked and internal stresses appear. More general problems can be addressed within the same framework.
A spontaneous buckling transition in thin layers of monodomain nematic liquid crystalline gel was observed by polarized light microscopy. The coupling between the orientational ordering of liquid crystalline solvent and the translational ordering of crosslinked polymer backbones inside the nematic gel contributes to such buckling transition. As the nematic mesogens become more ordered when the gel is cooled down from a higher gelation temperature, the polymeric backbones tend to elongate along the direction parallel to the nematic director, which is perpendicular to the rigid glass surfaces in…
Using x-ray photon correlation spectroscopy, we studied the dynamics in the nematic phase of a nanorodsuspension. The collective diffusion coefficient in the plane perpendicular to the director varies sharply with the wave vector. Combining the structure factor and the diffusion coefficient, we find that the hydrodynamic function of the phase decreases by more than a factor of 10 when going from length scales comparable to the interparticle distance toward larger values. Thus, the collective dynamics of the nematic phase experiences strong and scale-dependent slowing down, in contrast with iso…
Recent experimental realization of ferroelectric nematic liquid crystalline phases stimulated material development and numerous experimental studies of these new phases, guided by their fundamental and applicative interest. In this Perspective, we give an overview of this emerging field by linking history and theoretical predictions to a general outlook of the development and properties of the materials exhibiting ferroelectric nematic phases. We will highlight the most relevant observations up-to-date, e.g., giant dielectric permittivity values, polarization values an order of magnitude large…
We investigated the effect of a photovoltaic field generated on the surface of iron-doped lithium niobate crystals on droplets of a ferroelectric nematic liquid crystalline and a standard nematic liquid crystalline material deposited on this surface. When such assembly is illuminated with a laser beam, a wide range of dynamic phenomena are initiated. Droplets located outside the laser spot are dragged in the direction of the illuminated area, while droplets located inside the illuminated region tend to bridge each other and rearrange into tendril-like structures. In the ferroelectric nematic p…
We investigate the connections between some simple Maier-Saupe lattice models, with a discrete choice of orientations of the microscopic directors, and a recent proposal of a two-tensor formalism to describe the phase diagrams of nematic liquid-crystalline systems. This two-tensor proposal is used to formulate the statistical problem in terms of fully-connected lattice Hamiltonians, with the local nematic directors restricted to the Cartesian axes. Depending on the choice of interaction parameters, we regain all of the main features of the original mean-field two-tensor calculations. With a st…
The stability of demixing phase transition in binary mixtures of hard plates (with thickness L and diameter D) and hard spheres (with diameter $σ$) is studied by means of Parsons-Lee theory. The isotropic-isotropic demixing, which is found in mixtures of large spheres and small plates, is very likely to be preempted by crystallization. In contrast, the nematic-nematic demixing, which is obtained in mixtures of large plates and small spheres, can be stabilized at low diameter ratios ($σ$/D) and aspect ratios (L/D). At intermediate values of $σ$/D, where the sizes of the components are similar, …
We theoretically study the phase behaviour of monolayers of hard rod-plate mixtures using a fundamental-measure density functional in the restricted-orientation (Zwanzig) approximation. We consider both species to be subject to an attractive potential proportional to the particle contact area on the surface and with adsorption strengths that depend on the species type. Particles have board-like shape, with sizes chosen using a symmetry criterion: same volume and same aspect ratio $κ$. Phase diagrams were calculated for $κ=10$, 20 and 40 and different values of adsorption strengths. For small a…
The influence of the molecular structure of the nematic liquid crystal (NLC) on the photoalignment process at the NLC -- polymer interface has been investigated experimentally. NLCs having exclusively phenyl-, or cyclohexane rings in the rigid core, as well as NLCs containing both phenyl and cyclohexane groups have been considered. Substantial differences have been found in the photoalignment process depending on the molecular structure of the NLC, supporting the assumption that the polymer -- NLC interface should be regarded as a coupled system, where the two components mutually influence eac…
We studied dielectric properties of a polar nematic phase (NF) sandwiched between two gold or ITO electrodes, serving as a cell surfaces. In bulk, NF is expected to exhibit a Goldstone mode (phason), because polarization can uniformly rotate with no energy cost. However, because the coupling between the direction of nematic director and polarization is finite, and the confinement, even in the absence of the aligning surface layer, induces some energy cost for a reorientation of polarization, the phason dielectric relaxation frequency is measured in a kHz regime. The phason mode is easily quenc…
We investigate by means of continuum percolation theory and Monte Carlo simulations how spontaneous uniaxial symmetry breaking affects geometric percolation in dispersions of hard rod-like particles. If the particle aspect ratio exceeds about twenty, percolation in the nematic phase can be lost upon adding particles to the dispersion. This contrasts with percolation in the isotropic phase, where a minimum particle loading is always required to obtain system-spanning clusters. For sufficiently short rods, percolation in the uniaxial nematic mimics that of the isotropic phase, where the addition…
In the shear flow of liquid crystalline polymers (LCPs) the nematic director orientation can align with the flow direction for some materials, but continuously tumble in others. The nematic dumbbell (ND) model was originally developed to describe the rheology of flow-aligning semi-flexible LCPs, and flow-aligning LCPs are the focus in this paper. In the shear flow of monodomain LCPs it is usually assumed that the spatial distribution of the velocity is uniform. This is in contrast to polymer solutions, where highly non-uniform spatial velocity profiles have been observed in experiments. We ana…
We consider textures of biaxial nematics confined between two parallel plates. The boundary conformations at the bordering plates are supposed to be identical, the gradients of the order parameter being generally nonzero. We claim that for any texture (including stable uniform order parameter alignment) there exists its counterpart texture which is also a minimum of the gradient elastic energy. Our arguments are based on the topological analysis of the conformation of the order parameter.
We examine the ordering behavior of hard plate-like particle in a very narrow slit-like pore using the Parsons-Lee density functional theory and the restricted orientation approximation. We observe that the plates are orientationally ordered and align perpendicularly (face-on) to the walls at low densities, a first order layering transition occurs between uniaxial nematic structures having n and n+1 layers at intermediate densities and even a phase transition between a monolayer with parallel (edge-on) orientational order and n layers with perpendicular one can be detected at high densities. I…
We have numerically studied a liquid composed of achiral, bent-shaped molecules built of tangent spheres. The system is known to spontaneously break mirror symmetry, as it forms a macroscopically chiral, twist-bend nematic phase [Phys. Rev. Lett. 115, 147801 (2015)]. Here, we have examined the full phase diagram of such liquid and observed several phases characterized by orientational and/or translational ordering of molecules. Apart from conventional nematic, smectic A, and the above-mentioned twist-bend nematic phase, we have identified antiferroelectric smectic A phase. For large densities …
We predict theoretically the existence of a class of colloidal structures in nematic liquid crystal (NLC) cells, which are induced by surface patterns on the plates of the cell (like cells with UV-irradiated polyimide surfaces using micron size masks). These bulk structures arise from non-zero boundary conditions for the director distortions at the confining surfaces. In particular, we demonstrate that quadrupole spherical particles (like spheres with boojums or Saturn-ring director configurations) form a square lattice inside a planar NLC cell, which has checkerboard patterns on both its plat…
Phase behavior of liquid crystals is of long-standing interest due to numerous applications, with one of the key issues being how the presence of impurities affects the liquid crystalline order. Here we study the orientational order of 4-cyano-4$^{'}$-pentylbiphenyl (5CB) and 4-cyano-4$^{'}$-hexylbiphenyl (6CB) nematic liquid crystals in the presence of varying concentrations of water and n-hexane molecules serving as impurities, by carrying out both fully atomistic simulations and experiments. Our results reveal that mixing of the impurities (in case of hexane) with the host liquid crystals c…
We present experiments where anisometric colloidal microparticles dispersed in a nematic liquid crystal cell with homeotropic anchoring conditions are dynamically assembled by means of liquid-crystal-enabled electrophoresis (LCEEP) using an AC electric field perpendicular to the confining plates. A nematic host with negative dielectric anisotropy leads to a driving force parallel to the cell plates. We take advantage of the resulting gliding anchoring conditions and the degeneracy in the direction of particle motion to design reconfigurable trajectories using a photosensitive anchoring layer (…
This paper reviews the research work on the liquid crystalline (LC) polymer vesicles (polymersomes), where the thermotropic nematic and smectic phases are displayed in the lyotropic bilayer polymer membrane. LC polymersomes possess the properties of both liquid crystals and polymers, the two essential soft matters. LC polymersomes offer, on the one hand, novel examples of the interplay between orientational order and the curved geometry of a two dimensional membrane. Spherical, ellipsoidal and tetrahedral vesicles are discussed. On the other hand, LC polymersomes enable novel design of stimuli…
The phase-field-crystal model is used to access the structure and thermodynamics of interfaces between two coexisting liquid crystalline phases in two spatial dimensions. Depending on the model parameters there is a variety of possible coexistences between two liquid crystalline phases including a plastic triangular crystal (PTC). Here, we calculate numerically the profiles for the mean density and the nematic order tensor across the interface for isotropic-PTC and columnar-PTC respectively smectic A-PTC coexistence. As a general finding, the width of the interface with respect to the nematic …
Dispersions of rodlike colloidal particles exhibit a plethora of liquid crystalline states, including nematic, smectic A, smectic B, and columnar phases. This phase behavior can be explained by presuming the predominance of hard-core volume exclusion between the particles. We show here how the self-organization of rodlike colloids can be controlled by introducing a weak and highly localized directional attractive interaction between one of the ends of the particles. This has been performed by functionalizing the tips of filamentous viruses by means of regioselectively grafting fluorescent dyes…
We investigate the self-organization of a binary mixture of similar sized rods and dipolar soft spheres by means of Monte-Carlo simulations. We model the interparticle interactions by employing anisotropic Gay-Berne, dipolar and soft-sphere interactions. In the limit of vanishing magnetic moments we obtain a variety of fully miscible liquid crystalline phases including nematic, smectic and lamellar phases. For the magnetic mixture, we find that the liquid crystalline matrix supports the formation of orientationally ordered ferromagnetic chains. Depending on the relative size of the species the…
We studied the dynamics of isotropic-nematic transitions in liquid crystalline polymers by integrating time-dependent Ginzburg-Landau equations. In a concentrated solution of rodlike polymers, the rotational diffusion constant Dr of the polymer is severely suppressed by the geometrical constraints of the surrounding polymers, so that the rodlike molecules diffuse only along their rod directions. In the early stage of phase transition, the rodlike polymers with nearly parallel orientations assemble to form a nematic polydomain. This polydomain pattern with characteristic length l, grows with se…
We study the flow behaviour of a twist-bend nematic $(N_{TB})$ liquid crystal. It shows three distinct shear stress ($σ$) responses in a certain range of temperatures and shear rates ($\dotγ$). In Region-I, $σ\sim\sqrt{\dotγ}$, in region-II, the stress shows a plateau, characterised by a power law $σ\sim{\dotγ}^α$, where $α\sim0.1-0.4$ and in region-III, $σ\sim\dotγ$. With increasing shear rate, $σ$ changes continuously from region-I to II, whereas it changes discontinuously with a hysteresis from region-II to III. In the plateau (region-II), we observe a dynamic stress fluctuations, exhibitin…
In this paper, based on the numerical calculation of total energy utilizing the Green's function method, we found that the external electric field applied to a microparticle-suspended nematic liquid crystal cell, if reaching a critical value, combined with its direction, surface anchoring feature and molecular dielectric anisotropy, is possible to create an anisotropic "bubble" around the microparticle with a vertical fast "lane", in which the microparticle can, driven by the asymmetric buoyant force, vertically move swiftly from the cell's midplane to a new equilibrium position, triggering a …
Physical properties of composite materials can be pre-engineered by controlling their structure and composition at the mesoscale. Yet, approaches for achieving this are limited and rarely scalable. We introduce a new breed of self-assembled nematogels formed by an orientationally ordered network of thin cellulose nanofibers infiltrated with a thermotropic nematic fluid. The interplay of orientational ordering within the nematic network and that of the small-molecule liquid crystal around it yields a composite with highly tunable optical properties. By means of combining experimental characteri…
We consider a nematic liquid crystal, in coexistence with its isotropic phase, in contact with a substrate patterned with rectangular grooves. In such a system, the nematic phase may fill the grooves without the occurrence of complete wetting. There may exist multiple (meta)stable filled states, each characterised by the type of distortion (bend or splay) in each corner of the groove and by the shape of the nematic-isotropic interface, and additionally the plateaux that separate the grooves may be either dry or wet with a thin layer of nematic. Using numerical simulations, we analyse the dynam…
Orientational and positional ordering properties of liquid crystal monolayers are examined by means of Fundamental-Measure Density Functional Theory. Particles forming the monolayer are modeled as hard parallelepipeds of square section of size $σ$ and length $L$. The particle centers of mass are restricted to a flat surface and three possible and mutually perpendicular orientations (in-plane and along the layer normal) of their uniaxial axes are allowed. We find that the structure of the monolayer depends strongly on particle shape and density. In the case of rod-like shapes, particles align a…
We consider a microscopic field theoretical approach for interacting active nematic particles. With only steric interactions the self-propulsion strength in such systems can lead to different collective behaviour, e.g., synchronized self-spinning and collective translation. The different behaviour results from the delicate interplay between internal nematic structure, particle shape deformation and particle-particle interaction. For intermediate active strength an asymmetric shape emerges and leads to chirality and self-spinning crystals. For larger active strength the shape is symmetric and t…
The article presents a straightforward experiment that directly and illustratively demonstrates double refraction. For this purpose, two liquid crystalline cells were designed, which enable qualitative and quantitative measurements of the extraordinary refractive index direction dependency in a uniaxial nematic liquid crystal.
Isotropic-genesis nematic elastomers (IGNEs) are liquid crystalline polymers (LCPs) that have been randomly, permanently cross-linked in the high-temperature state so as to form an equilibrium random solid. Thus, instead of being free to diffuse throughout the entire volume, as they would be in the liquid state, the constituent LCPs in an IGNE are mobile only over a finite length-scale controlled by the density of cross-links. We address the effects that such network-induced localization have on the liquid-crystalline characteristics of an IGNE, as probed via measurements made at high temperat…
Eppur si muove: Shape of topological defects -- and consequent motion -- in active nematics
CY Cergy Paris Université（塞吉-蓬图瓦兹CY大学）；CEA, CNRS Université Paris-Saclay（法国原子能与替代能源委员会，CNRS巴黎萨克雷大学）；Sorbonne Université（索邦大学）；Laboratoire Jean Perrin, Sorbonne Université and CNRS（让·佩兰实验室，索邦大学和CNRS）
Sessile droplets of a ferroelectric nematic liquid crystalline material were exposed to surface electric fields produced by pyroelectric and photogalvanic (photovoltaic) effects in X-cut iron-doped lithium niobate crystals. The resulting dynamic processes were monitored by polarization optical (video)microscopy (POM). During heating/cooling cycles, at first, the droplets change their shape from spherical to extended ellipsoidal. Then they start to move rapidly along the surface electric field, i.e., along the crystal's polar axis (c-axis). During this motion, several droplets merge into runnin…
Ferroelectric ordering in liquids is a fundamental question of physics. Here, we show that ferroelectric ordering of the molecules causes formation of recently reported splay nematic liquid-crystalline phase. As shown by dielectric spectroscopy, the transition between the uniaxial and the splay nematic phase has the characteristics of a ferroelectric phase transition, which drives an orientational ferroelastic transition via flexoelectric coupling. The polarity of the splay phase was proven by second harmonic generation (SHG) imaging, which additionally allowed for determination of the splay m…
Nematic phase is the most fundamental mesophase exhibited by most of the rod shaped anisotropic liquid crystalline molecules. Nematics are orientationally ordered fluids whose average orientation direction can be manipulated on application of electric and magnetic fields. Carbon nanotube (CNT), a highly shape anisotropic object can find numerous industrial application because of its interesting electronic and mechanical properties. The self-organizing properties of nematics can be used to align CNTs dispersed in them. We have dispersed functionalized CNTs in nematic liquid crystal and carried …
Free interfaces of liquid crystals tend to minimise both capillarity and anchoring forces. Here we study nematic films in planar and radial geometries with antagonistic anchoring boundary conditions and one deformable interface. Assuming a perturbation ansatz we study possible couplings of the director configuration with the shape of free interfaces. In the long-wavelength limit independent of the surface tension, we find analytically threshold thickness when flat film becomes unstable. Next we quantify the bifurcation of a circular ring towards structures with $m$-fold rotational symmetry, in…
Understanding and controlling the director field configuration, shape, and orientation in nematic and cholesteric liquid crystals is of fundamental importance in several branches of science. Liquid crystalline droplets, also known as tactoids, which spontaneously form by nucleation and growth within the biphasic region of the phase diagram where isotropic and nematic phases coexist, challenge our current understanding of liquid crystals under confinement, due to the influence of anisotropic surface boundaries at vanishingly small interfacial tension and are mostly studied under quiescent, quas…
While studies of active nematics in two dimensions have shed light on various aspects of the flow regimes and topology of active matter, three-dimensional properties of topological defects and chaotic flows remain unexplored. By confining a film of active nematics between two parallel plates, we use continuum simulations and analytical arguments to demonstrate that the crossover from quasi-2D to 3D chaotic flows is controlled by the morphology of the disclination lines. For small plate separations, the active nematic behaves as a quasi-2D material, with straight topological disclination lines …
