Nematic liquid crystals have been known for more than a century, but it was not until the 60s-70s that, with the development of room temperature nematics, they became widely used in applications. Polar nematic phases have been long-time predicted, but have only been experimentally realized recently. Synthesis of materials with nematic polar ordering at room temperature is certainly challenging and requires a deep understanding of its formation mechanisms, presently lacking. Here, we compare two materials of similar chemical structure and demonstrate that just a subtle change in the molecular structure enables denser packing of the molecules when they exhibit polar order, which shows that reduction of excluded volume is in the origin of the polar nematic phase. Additionally, we propose that molecular dynamics simulations are potent tools for molecular design in order to predict, identify and design materials showing the polar nematic phase and its precursor nematic phases.
Recent experiments have reported a novel splay nematic phase, which has alternating domains of positive and negative splay. To model this phase, previous studies have considered a 1D splay modulation of the director field, accompanied by a 1D modulation of polar order. When the flexoelectric coupling between splay and polar order becomes sufficiently strong, the uniform nematic state becomes unstable to the formation of a modulated phase. Here, we re-examine this theory in terms of a new approach to liquid crystal elasticity, which shows that pure splay deformation is double splay rather than …
Different liquid crystalline phases with long-range orientational but not positional order, so-called nematic phases, are scarce. It rarely occurs that a new nematic phase is discovered and such event is inevitably accompanied by a great interest. Here, we describe a transition from uniaxial to novel nematic phase characterized by a periodic splay modulation of the director. In this new nematic phase, defect structures not present in the uniaxial nematic are observed, which indicates that the new phase has lower symmetry than the ordinary nematic phase. The phase transition is weakly first ord…
While twist-bend nematic phases have been extensively studied, the experimental observation of two dimensional, oscillating splay-bend phases is recent. We consider two theoretical models that have been used to explain the formation of twist-bend phases -- flexoelectricity and bond orientational order -- as mechanisms to induce splay-bend phases. Flexoelectricity is a viable mechanism, and splay and bend flexoelectric couplings can lead to splay-bend phases with different modulations. We show that while bond orientational order circumvents the need for higher order terms in the free energy, th…
The twist-bend nematic phase (NTB) is characterized by a conically twisting director and by a dramatic softening of the bend elastic constant before the transition to NTB phase. In the recently found splay nematic phase (NS) the splay elastic constant tends to zero, resulting in a splay modulation perpendicular to the director. We model both phases with a single Q-tensor free energy including a term that breaks the degeneracy between the splay and bend elastic constant, and a flexoelectric term coupling the divergence of the Q-tensor with polarization. NTB or NS phase is obtained by a change o…
The recent discovery of nematic liquid crystals with polar order (ferroelectric nematic) has created immense interest. Despite intensive research, several physical properties of this liquid crystal are yet to be investigated and understood. Here, we report experimental studies on the birefringence and exoelectric coefficient of a polar nematic (NF) liquid crystal. Our experiments directly reveal that the splay fluctuations influence the birefringence several degrees above the nonpolar (N) to polar-nematic (NF) phase transition temperature and the heat capacity exponent obtained from the tilt a…
The symmetry breaking Freedericksz transitions, when a uniformly aligned nematic state is replaced by a homogeneously or periodically distorted state, have been extensively studied before. Here we analyse the influence of the saddle-splay elasticity on the non-linear ground state of nematic liquid crystal in presence of magnetic field above the Freedericksz threshold. We identify the bifurcation point when the kink-soliton is linearly unstable with respect to the perturbations of the wave vector in the direction perpendicular to the initial plane of soliton. This instability occurs only if the…
We establish a macroscopic description of the splay--density coupling in semiflexible main-chain nematic polymers with hairpins, using a vectorial continuity constraint for the "recovered" polar order of the chain tangents and introducing chain backfolds (hairpins) as its new type of sources besides chain ends. We treat both types of sources on a unified basis as a mixture of two ideal gases with fixed composition. Performing detailed Monte Carlo simulations of nematic monodomain melts of "soft" worm-like chains with variable length and flexibility, we show via their structure factors that the…
The recent discovery of the ferroelectric splay nematic phase has opened the door to experimental investigation of one of the most searched liquid crystal phases in decades, with high expectations for future applications. However, at this moment, there are more questions than answers. In this work, we examine the formation and structure of large polar nematic domains of the ferroelectric splay nematic material RM734 in planar liquid crystals cells with different aligning agents and specifications. We observe that confining surfaces have a strong influence over the formation of different types …
Recently, Tavarone et al. (J. Chem. Phys. 143, 114505 (2015)) discussed phase behavior of zig-zag and bow-shaped particles composed of three needles. The authors presented very interesting results of extensive Monte Carlo simulations with periodic boundary conditions in the constant-NVT and the constant-NPT ensembles. In addition to isotropic, nematic, and smectic phases, they identified a modulated nematic, which is actually the nematic splay-bend phase ($N_{SB}$), long-anticipated for bent-core systems (Europhys. Lett. 56, 247 (2001)). They also described isotropic-nematic and nematic-smecti…
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…
Nematics with a broken polar symmetry is one of the fascinating recent discoveries in the field of soft matter. High spontaneous polarisation and the fluidity of the ferroelectric nematic $N_{\mathrm{F}}$ phase make such materials attractive for future applications and interesting for fundamental research. Here we explore the polar and mechanical properties of a room-temperature ferroelectric nematic and its behaviour in a magnetic field. We show that $N_{\mathrm{F}}$ is much less susceptible to the splay deformation than to the twist. The strong splay rigidity can be attributed to the electro…
We present a theoretical study of director fields in toroidal geometries with degenerate planar boundary conditions. We find spontaneous chirality: despite the achiral nature of nematics the director configuration show a handedness if the toroid is thick enough. In the chiral state the director field displays a double twist, whereas in the achiral state there is only bend deformation. The critical thickness increases as the difference between the twist and saddle-splay moduli grows. A positive saddle-splay modulus prefers alignment along the short circle of the bounding torus, and hence stimul…
We propose an extension of Frank-Oseen's elastic energy for bulk nematic liquid crystals which is based on the hypothesis that the fundamental deformations allowed in nematic liquid crystals are splay, twist and bend. The extended elastic energy is a fourth order form in the fundamental deformations. The existence of bulk spontaneous modulated or deformed nematic liquid crystal ground states is investigated. The analysis is limited to bulk nematic liquid crystals in the absence of limiting surfaces and/or external fields. The non deformed ground state is stable only when Frank-Oseen's elastic …
We develop a lattice model for the splay flexoelectric effect in nematic liquid crystals. In this model, each lattice site has a spin representing the local molecular orientation, and the interaction between neighboring spins represents pear-shaped molecules with shape polarity. We perform Monte Carlo simulations and mean-field calculations to find the behavior as a function of interaction parameters, temperature, and applied electric field. The resulting phase diagram has three phases: isotropic, nematic, and polar. In the nematic phase, there is a large splay flexoelectric effect, which dive…
Splay and polar order in a system of hard pear-like molecules: confrontation of Monte Carlo numerical simulations with density functional theory calculations
We study dynamical optical response of a nematic liquid crystal cell that undergoes the splay-bend transition after applying the voltage across the cell. We formulate a simplified model that takes into account both the flexoelectric coupling and the surface rotational viscosity. The dynamic equations of the model were solved numerically to calculate temporal evolution of the director profile and the transmittance. We evaluate the response time as a function of a number of parameters characterising dielectric and elastic anisotropies, asymmetry of the surface pretilt angles, anchoring energy, s…
The physics of light interference experiments is well established for nematic liquid crystals. Using well-known techniques, it is possible to obtain important quantities, such as the differential scattering cross section and the saddl-splay elastic constant $K_{24}$. However, the usual methods to retrieve the latter involves an adjusting of computational parameters through the visual comparisons between the experimental light interference pattern or a $^{2}H-NMR$ spectral pattern produced by an escaped-radial disclination, and their computational simulation counterparts. To avoid such comparis…
We study the organization of topological defects in a system of nematogens confined to the two-dimensional sphere (S^2). We first perform Monte Carlo simulations of a fluid system of hard rods (spherocylinders) living in the tangent plane of S^2. The sphere is adiabatically compressed until we reach a jammed nematic state with maximum packing density. The nematic state exhibits four +1/2 disclinations arrayed on a great circle rather than at the vertices of a regular tetrahedron. This arises from the high elastic anisotropy of the system in which splay (K_1) is far softer than bending (K_3). W…
This article re-examines a classic question in liquid-crystal physics: What are the elastic modes of a nematic liquid crystal? The analysis uses a recent mathematical construction, which breaks the director gradient tensor into four distinct types of mathematical objects, representing splay, twist, bend, and a fourth deformation mode. With this construction, the Oseen-Frank free energy can be written as the sum of squares of the four modes, and saddle-splay can be regarded as bulk rather than surface elasticity. This interpretation leads to an alternative way to think about several previous re…
Double Splay Nematic Order in Confined Polar Fluids
Southern University of Science and Technology（南方科技大学）；The Hongkong University of Science and Technology（香港科技大学）；South China Advanced Institute for Soft Matter Science and Technology (AISMST), School of Emergent Soft Matter, South China University of Technology（华南理工大学 emergent soft matter 学院 / 华南软物质科学与技术先进研究院）；Guangdong Provincial Key Laboratory of Functional and Intelligent Hybrid Materials and Devices, South China University of Technology（华南理工大学 广东省功能与智能杂化材料器件重点实验室）
We analyze stability of the planar orientational structure in a nematic liquid crystal (NLC) cell with planar anchoring conditions at both substrates. Specifically, we study the instabilities of the ground state caused by surface elasticity at large saddle-splay elastic constant, $K_{24}$. For relatively small $K_{24}$ violating the Ericksen inequalities the theory predicts that the critical fluctuation mode of the wavelength, $λ_c$, will render the structure unstable when the thickness of the cell is below its critical value, $d_c$. The parity of the critical mode changes as the twist-splay r…
Using dynamic light scattering, we measure for the first time the temperature-dependent elastic moduli and associated orientational viscosity coefficients of the nematic phase in a self-assembled lyotropic chromonic liquid crystal. The bend K3 and splay K1 moduli are an order of magnitude higher than the twist K2 constant. The ratio K3/K1 shows an anomalous increase with temperature; we attribute this to the shortening of the aggregates as temperature increases. The viscosity coefficients also show a significant anisotropy, as well as a strong temperature dependence; in particular, the bend vi…
The dielectric spectra of the twist bend nematic phase of the bent shaped achiral liquid crystal dimer are studied for the determination of the different relaxation modes. The two molecular processes were assigned one to the precessional rotation of the longitudinal components of the cyanobiphenyl groups and the second to the spinning rotation of the transverse component of the dimer. The low frequency peak shows a peculiar temperature behavior at the twist bend nematic to nematic transition. This peak can be assigned to a collective fluctuation of the tilt angle of the coarse grained director…
Active systems comprised of self-propelled units show fascinating transitions from Brownian-like dynamics to collective coherent motion. Swirling of swimming bacteria is a spectacular example. This study demonstrates that a nematic liquid crystal environment patterned as a spiral vortex controls individual-to-collective transition in bacterial swirls and defines whether they expand or shrink. In dilute dispersions, the bacteria swim along open spiral trajectories, following the pre-imposed molecular orientation. The trajectories are nonpolar. As their concentration exceeds some threshold, the …
Placing colloidal particles in predesigned sites represents a major challenge of the current state-of-the-art colloidal science. Nematic liquid crystals with spatially varying director patterns represent a promising approach to achieve a well-controlled placement of colloidal particles thanks to the elastic forces between the particles and the surrounding landscape of molecular orientation. Here we demonstrate how the spatially varying director field can be used to control placement of non-spherical particles of boomerang shape. The boomerang colloids create director distortions of a dipolar s…
Mono-layers of stearic and behenic acids deposited with the Langmuir-Blodgett technique, were used as aligning films in nematic liquid crystal cells. During the filling process the liquid crystal adopts a deformed quasi-planar alignment with splay-bend deformation and preferred orientation along the filling direction. This state is metastable and transforms with time into homeotropic once the flow has ceased. The transition is accompanied by formation of disclination lines which nucleate at the edges of the cell. The lifetime of the metastable splay-bend state was found to depend on the cell t…
We report experimental studies on optical (birefringence, $Δn$), dielectric $(Δ\varepsilon)$ and bend-splay elastic anisotropies ($ΔK=K_{33}-K_{11})$ of a few mixtures of two nematic liquid crystals, namely CCH-7 and CCN-47, made of highly polar molecules with identical cores and antagonistic orientation of permanent dipoles. In particular, the polar group (-CN) attached to the bicyclohexane core of CCH-7 is oriented along the longitudinal direction whereas, in CCN-47, it is oriented along the transverse direction. We show that apart from the significant contribution to the optical and dielect…
Surface interactions are responsible for many properties of condensed matter, ranging from crystal faceting to the kinetics of phase transitions. Usually, these interactions are polar along the normal to the interface and apolar within the interface. Here, we demonstrate that polar in-plane surface interactions of a ferroelectric nematic NF produce polar monodomains in micron-thin planar cells and stripes of an alternating electric polarization, separated by 180 degree domain walls, in thicker slabs. The surface polarity binds together pairs of these walls, yielding a total polarization rotati…
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…
A thermal gradient-induced circular motion of particles placed on ferroelectric nematic liquid crystal sessile drops is demonstrated and explained. Unlike hurricanes and tornadoes that are the prime examples for thermal motors and where turbulent flows are apparent, here the texture without tracer particles appears completely steady indicating laminar flow. We provide a simple model showing that the tangential arrangement of the ferroelectric polarization combined with the vertical thermal gradient and the pyroelectricity of the fluid drives the rotation of the tracer particles that become ele…
We present a generalization of the Maier-Saupe (MS) theory that incorporates the description of the ferroelectric nematic phase (NF) within its scope of application. The extension of the theory is carried out in a natural way, by adding to the nematic potential of MS a term proportional to cosθ and to the polar order parameter <cosθ >, where θ is the angle between the long molecular axis and the spontaneous polarization. The NF phase can be reached by cooling from the isotropic phase with or without the formation of an intermediate normal nematic phase, depending on the relative intensity of t…
We have structurally characterized the liquid crystal phase that appears as an intermediate state when a dielectric nematic, having polar disorder of its molecular dipoles, transitions to the almost perfectly polar-ordered ferroelectric nematic. This intermediate phase, which fills a 100-year-old void in the taxonomy of smectics and which we term the "smectic $Z_A$", is antiferroelectric, with the nematic director and polarization oriented parallel to smectic layer planes, and the polarization alternating in sign from layer to layer. The period of this polarization wave ($\sim$180 A) is mesosc…
Adiabatic scanning calorimetry (ASC) is capable of providing simultaneously the specific enthalpy h(T) and the specific heat capacity cp(T), and is an important tool to determine the order of transitions and to render high-resolution information on pretransitional thermal behavior. Here we report on ASC results on the compound DIO and on mixtures with RM734. Both compounds exhibit a low-temperature ferroelectric nematic phase (NF) and a high-temperature paraelectric nematic (N). In DIO these two phases are separated by an intermediate phase (Nx). Detailed data of h(T) and cp(T), indicated that…
Elasticity-Driven Periodic Polarization Patterns in Confined Chiral Ferroelectric Nematic Fluid
Jožef Stefan Institute（约瑟夫·斯特凡研究所）；Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学与物理学院）；CENN Nanocenter（CENN纳米中心）；Department of Physics, Faculty of Science and Technology, University of the Basque Country UPV/EHU（巴斯克国立大学理学院物理系）；School of Chemistry, University of Leeds（利兹大学化学学院）；School of Physics and Astronomy, University of Leeds（利兹大学物理与天文学院）
Direct visualization of local electric fields in a layer of a ferroelectric nematic liquid
Jožef Stefan Institute（约瑟夫·斯特凡研究所）；Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学与物理学院）；School of Chemistry, University of Leeds（利兹大学化学学院）；School of Physics and Astronomy, University of Leeds（利兹大学物理与天文学学院）
