Tunable entangled photon-pair generation in a liquid crystal.

Liquid crystals, with their ability to self-assemble, strong response to an electric field and integrability into complex systems, are key materials in light-beam manipulation1. The recently discovered ferroelectric nematic liquid crystals2,3 also have considerable second-order optical nonlinearity, making them a potential material for nonlinear optics4,5. Their use as sources of quantum light could considerably extend the boundaries of photonic quantum technologies6. However, spontaneous parametric down-conversion, the basic source of entangled photons7, heralded single photons8 and squeezed light9, has so far not been observed in liquid crystals-or in any liquids or organic materials. Here we implement spontaneous parametric down-conversion in a ferroelectric nematic liquid crystal and demonstrate electric-field tunable broadband generation of entangled photons, with an efficiency comparable to that of the best nonlinear crystals. The emission rate and polarization state of photon pairs is markedly varied by applying a few volts or twisting the molecular orientation along the sample. A liquid-crystal source enables a special type of quasi-phase matching10, which is based on the molecular twist structure and is therefore reconfigurable for the desired spectral and polarization properties of photon pairs. Such sources promise to outperform standard nonlinear optical materials in terms of functionality, brightness and the tunability of the generated quantum state. The concepts developed here can be extended to complex topological structures, macroscopic devices and multi-pixel tunable quantum light sources.

Collective and non-collective molecular dynamics in a ferroelectric nematic liquid crystal studied by broadband dielectric spectroscopy.

A great deal of effort has been recently devoted to the study of dielectric relaxation processes in ferroelectric nematic liquid crystals, yet their interpretation remains unclear. In this work, we present the results of broadband dielectric spectroscopy experiments of a prototypical ferroelectric nematogen in the frequency range 10 Hz-110 MHz at different electrode separations and under the application of DC bias fields. The results evidence a complex behavior in all phases due to the magnitude of polar correlations in these systems. The observed modes have been assigned to different relaxation mechanisms based on existing theoretical frameworks.

Polarization patterning in ferroelectric nematic liquids via flexoelectric coupling.

The recently discovered ferroelectric nematic liquids incorporate to the functional combination of fluidity, processability and anisotropic optical properties of nematic liquids, an astonishing range of physical properties derived from the phase polarity. Among them, the remarkably large values of second order optical susceptibility encourage to exploit these new materials for non-linear photonic applications. Here we show that photopatterning of the alignment layer can be used to structure polarization patterns. To do so, we take advantage of the flexoelectric effect and design splay structures that geometrically define the polarization direction. We demonstrate the creation of periodic polarization structures and the possibility of guiding polarization by embedding splay structures in uniform backgrounds. The demonstrated capabilities of polarization patterning, open a promising new route for the design of ferroelectric nematic based photonic structures and their exploitation.

DNMR measurements of an asymmetric odd liquid crystal dimer: determination of the intramolecular angle and the degree of order of the two rigid cores.

In this work, we present a Deuteron Nuclear Magnetic Resonance (DNMR) study of the non-symmetric odd liquid crystal dimer α-(4-cyanobiphenyl-4'-yloxy)-ω-(1-pyrenimine-benzylidene-4'-oxy) heptane (CBO7O.Py), formed by a pro-mesogenic cyanobiphenyl unit and a bulky pyrene-containing unit, linked via alkoxy flexible chain. We have synthesized two partially deuterated samples: one with the deuterium atoms in the cyanobiphenyl moiety (dCBO7O.Py) and the other one with the deuterium atoms in the pyrenimine-benzylidene unit (CBO7O.dPy). We have performed angular distribution analysis in the SmA glassy state, obtaining the degree of order of both rigid cores and an estimation of the internal molecular angle between both structures. With the results from the angular study, we have been able to determine the degree of order of both rigid units in either the N phase and the SmA phase, far enough from the glass transition. Both rigid cores have the same degree of order close to the nematic-isotropic phase transition, but as the compound is cooled down, the degree of order of the cyanobiphenyl moiety is clearly higher than that of the pyrene-containing unit. The critical behaviour of the order parameter of the pyrene-containing moiety is consistent with the fact that, for CBO7O.Py, the N-I phase transition is tricritical, which seems to indicate that the uniaxial order parameter of the dimer is dominated by the degree of order of the pyrene-containing core.

Ferroelectric nematic liquid-crystalline phases.

Recent experimental realization of ferroelectric nematic liquid crystalline phases stimulated material development and numerous experimental studies of these 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 to date, e.g., giant dielectric permittivity values, polarization values an order of magnitude larger than in classical ferroelectric liquid crystals, and nonlinear optical coefficients comparable with several ferroelectric solid materials. Key observations of anchoring and electro-optic behavior will also be examined. The collected contributions lead to a final discussion on open challenges in materials development, theoretical description, experimental explorations, and possible applications of the ferroelectric phases.

Understanding self-assembly at molecular level enables controlled design of DNA G-wires of different properties.

A possible engineering of materials with diverse bio- and nano-applications relies on robust self-assembly of oligonucleotides. Bottom-up approach utilizing guanine-rich DNA oligonucleotides can lead to formation of G-wires, nanostructures consisting of continuous stacks of G-quartets. However, G-wire structure and self-assembly process remain poorly understood, although they are crucial for optimizing properties needed for specific applications. Herein, we use nuclear magnetic resonance to get insights at molecular level on how chosen short, guanine-rich oligonucleotides self-assemble into G-wires, whereas complementary methods are used for their characterization. Additionally, unravelling mechanistic details enable us to guide G-wire self-assembly in a controlled manner. MD simulations provide insight why loop residues with considerably different properties, i.e., hydrogen-bond affinity, stacking interactions, electronic effects and hydrophobicity extensively increase or decrease G-wire length. Our results provide fundamental understanding of G-wire self-assembly process useful for future design of nanomaterials with specific properties.

On the molecular origins of the ferroelectric splay nematic phase.

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.

Supramolecular Polymorphism of (G4C2)n Repeats Associated with ALS and FTD.

Guanine-rich DNA sequences self-assemble into highly stable fourfold structures known as DNA-quadruplexes (or G-quadruplexes). G-quadruplexes have furthermore the tendency to associate into one-dimensional supramolecular aggregates termed G-wires. We studied the formation of G-wires in solutions of the sequences d(G4C2)n with n = 1, 2, and 4. The d(G4C2)n repeats, which are associated with some fatal neurological disorders, especially amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD), represent a challenging research topic due to their extensive structural polymorphism. We used dynamic light scattering (DLS) to measure translational diffusion coefficients and consequently resolve the length of the larger aggregates formed in solution. We found that all three sequences assemble into longer structures than previously reported. The d(G4C2) formed extremely long G-wires with lengths beyond 80 nm. The d(G4C2)2 formed a relatively short stacked dimeric quadruplex, while d(G4C2)4 formed multimers corresponding to seven stacked intramolecular quadruplexes. Profound differences between the multimerization properties of the investigated sequences were also confirmed by the AFM imaging of surface films. We propose that π-π stacking of the basic G-quadruplex units plays a vital role in the multimerization mechanism, which might be relevant for transformation from the regular medium-length to disease-related long d(G4C2)n repeats.

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.

Ferroelectric-Ferroelastic Phase Transition in a Nematic Liquid Crystal.

Ferroelectric ordering in liquids is a fundamental question of physics. Here, we show that ferroelectric ordering of the molecules causes the 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 imaging, which additionally allowed for determination of the splay modulation period to be of the order of 5-10 microns, also confirmed by polarized optical microscopy. The observations can be quantitatively described by a Landau-de Gennes type of macroscopic theory.

Optical second harmonic generation in a ferromagnetic liquid crystal.

A comparative experimental investigation of the dependence of second harmonic generation (SHG) on an applied external voltage between a standard nematic liquid crystalline material and an analogue ferromagnetic nematic liquid crystalline material was performed by using a fundamental optical beam at an 800 nm wavelength. For the ferromagnetic material, the dependence of SHG on an applied magnetic field was also examined. Three different polarization combinations of the fundamental and the second harmonic radiation were analysed. The SHG signal observed in the former material is attributed to a combination of electric field-induced SHG (EFISHG) and flexoelectric deformation-induced SHG, while the SHG signal observed in the latter material is attributed solely to flexoelectric deformation-induced SHG. The obtained dependences of the SHG signal on the associated optical retardation show that, in the most favourable polarization combination, the two contributions generate about the same effective nonlinear optical susceptibility.

Polar Order, Mirror Symmetry Breaking, and Photoswitching of Chirality and Polarity in Functional Bent-Core Mesogens.

In recent years, liquid crystals (LCs) responding to light or electrical fields have gained significant importance as multifunctional materials. Herein, two new series of photoswitchable bent-core liquid crystals (BCLCs) derived from 4-cyanoresorcinol as the central core connected to an azobenzene based wing and a phenyl benzoate wing are reported. The self-assembly of these molecules was characterized by differential scanning calorimetry (DSC), polarizing light microscopy (POM), electro-optical, dielectric, second harmonic generation (SHG) studies, and XRD. Depending on the direction of the COO group in the phenyl benzoate wing, core-fluorination, temperature, and the terminal alkyl chain length, cybotactic nematic and lamellar (smectic) LC phases were observed. The coherence length of the ferroelectric fluctuations increases continuously with decreasing temperature and adopts antipolar correlation upon the condensation into superparaelectric states of the paraelectric smectic phases. Finally, long-range polar order develops at distinct phase transitions; first leading to polarization modulated and then to nonmodulated antiferroelectric smectic phases. Conglomerates of chiral domains were observed in the high permittivity ranges of the synclinic tilted paraelectric smectic phases of these achiral molecules, indicating mirror symmetry breaking. Fine-tuning of the molecular structure leads to photoresponsive bent-core (BC)LCs exhibiting a fast and reversible photoinduced change of the mode of the switching between ferroelectric- and antiferroelectric-like as well as a light-induced switching between an achiral and a spontaneous mirror-symmetry-broken LC phase.

Interplay between structure and relaxation in polyurea networks: the point of view from a novel method of cooperativity analysis of dielectric response.

The influence of structural constraints on the relaxation dynamics of three polyurea networks with a varying degree of crosslinking, has been studied by means of a thorough analysis of broadband dielectric spectroscopy measurements. Two different relaxation processes are observed, namely, a fast process involving the soft poly(propylene oxide) chains, and a slower and much broader process associated with the immediate surroundings of the hard crosslinkers. Microphase separation in soft and hard domains characterizes the systems in the presence of hydrogen bonding. In this case, different confinement conditions are explored by varying the soft chain length; overall, so called "adsorption" effects dominate. With respect to both cooperativity and the rearrangement energy threshold in fast relaxation, it is found that the enhancement of configurational constraints is similar to cooling, but only on qualitative grounds. An upper bound of the hard domains' interface thickness, in which the slow relaxation is believed to take place, is estimated from the analysis of the fast relaxation in the system characterized by the highest degree of confinement, taking into account the results of the structural analysis. Dropping the hydrogen bonding mechanism, phase separation does not occur anymore and the configurational constraints at the ends of the soft chains are reduced, leaving just those imposed by the rigid crosslinkers. This leads to a significant increase in cooperativity on approaching the glass transition, and to a complex behavior that is thoroughly discussed in comparison with those observed in the micro-segregated systems.

Director reorientation dynamics of ferromagnetic nematic liquid crystals.

Successful realization of ferromagnetic nematic liquid crystals has opened up the possibility to experimentally study a completely new set of fundamental physical phenomena. In this contribution we present a detailed investigation of some aspects of the static response and the complex dynamics of ferromagnetic liquid crystals under the application of an external magnetic field. Experimental results are then compared with a macroscopic model. Dynamics of the director were measured by optical methods and analyzed in terms of a theoretical macroscopic model. A dissipative cross-coupling coefficient describing the dynamic coupling between the two system order parameters, the magnetization and the nematic director, is needed to explain the results. In this contribution we examine the dependency of this coefficient on material parameters and the saturation magnetization and the liquid crystal host. Despite the complexity of the system, the theoretical description allows for a proper interpretation of the results and is connected to several microscopic aspects of the colloidal suspension.

Cooperative behavior of molecular motions giving rise to two glass transitions in the same supercooled mesophase of a smectogenic liquid crystal dimer.

In the present work, a detailed analysis of the glassy behavior and the relaxation dynamics of the liquid crystal dimer α-(4-cyanobiphenyl-4'-yloxy)-ω-(1-pyrenimine-benzylidene-4'-oxy) heptane (CBO7O.Py) throughout both nematic and smectic-A mesophases by means of broadband dielectric spectroscopy has been performed. CBO7O.Py shows three different dielectric relaxation modes and two glass transition (T_{g}) temperatures: The higher T_{g} is due to the freezing of the molecular motions responsible for the relaxation mode with the lowest frequency (µ_{1L}); the lower T_{g} is due to the motions responsible for the two relaxation modes with highest frequencies (µ_{1H} and µ_{2}), which converge just at their corresponding T_{g}. It is shown how the three modes follow a critical-like description via the dynamic scaling model. The two modes with lowest frequencies (µ_{1L} and µ_{1H}) are cooperative in the whole range of the mesophases, whereas the highest frequency mode (µ_{2}) is cooperative just below some crossover temperature. In terms of fragility, at the glass transition, the ensemble (µ_{1H}+µ_{2}) presents a value of the steepness index and µ_{1L} a different one, meaning that fragility is a property intrinsic to the molecular motion itself. Finally, the steepness index seems to have a universal behavior with temperature for the dielectric relaxation modes of liquid crystal dimers, being almost constant at high temperatures and increasing drastically when cooling the compound down to the glass transition from a temperature about 3/4T_{NI}.

Magneto-optic dynamics in a ferromagnetic nematic liquid crystal.

We investigate dynamic magneto-optic effects in a ferromagnetic nematic liquid crystal experimentally and theoretically. Experimentally we measure the magnetization and the phase difference of the transmitted light when an external magnetic field is applied. As a model we study the coupled dynamics of the magnetization, M, and the director field, n, associated with the liquid crystalline orientational order. We demonstrate that the experimentally studied macroscopic dynamic behavior reveals the importance of a dynamic cross-coupling between M and n. The experimental data are used to extract the value of the dissipative cross-coupling coefficient. We also make concrete predictions about how reversible cross-coupling terms between the magnetization and the director could be detected experimentally by measurements of the transmitted light intensity as well as by analyzing the azimuthal angle of the magnetization and the director out of the plane spanned by the anchoring axis and the external magnetic field. We derive the eigenmodes of the coupled system and study their relaxation rates. We show that in the usual experimental setup used for measuring the relaxation rates of the splay-bend or twist-bend eigenmodes of a nematic liquid crystal one expects for a ferromagnetic nematic liquid crystal a mixture of at least two eigenmodes.

Doping of nematic cyanobiphenyl liquid crystals with mesogen-hybridized magnetic nanoparticles.

Magnetic nanoparticles (MNPs) functionalized with (pro-)mesogenic ligands are implemented into a nematic liquid crystal (LC) and studied regarding both colloidal stability and magneto-optical behavior. In this study, the particle surface is specifically engineered to tune the MNP interactions with the LC host. For this purpose, four types of (pro-)mesogenic ligands (ML) are synthesized, which are composed of three structural parts, i.e., a rigid, LC motif (i.e., cyanobiphenyl) and a functional group for nanoparticle binding, both linked via a flexible spacer of different alkyl chain lengths. Electrostatically stabilized CoFe2O4 and γ-Fe2O3 nanoparticles with narrow size distribution and sizes below 3 nm are obtained via co-precipitation and subsequently functionalized to yield MNP@ML nanoparticles. Studies on the behaviour of the MNP@ML nanoparticles in the commercial LC host (i.e., 4-pentyl-4'-cyanobiphenyl (5CB)) in the bulk and in thin films in LC test cells, reveal the initial formation of some heterogeneities after transition from the isotropic to the nematic phase. Homogenous MNP@ML-5CB hybrids with long-term, colloidal stability, however, are obtained after magnetic separation of initially formed particle aggregates. In particular, MLs with carboxy groups and high structural flexibility (i.e., long linker lengths) are shown to be well suited to form stable MNP colloids, allowing for high MNP doping levels. As compared to undoped 5CB, the CoFe2O4@MLx-5CB hybrids show an increased sensitivity to the magnetic field, affecting the Fréedericksz transition. The strongest effect, however, is observed in magnetic and electric fields. The coupling of the ultrasmall, spherical MNPs with the LC director in the magnetic field suggests the formation of LC-induced, anisometric MNP clusters.

Emergence of polar order and tilt in terephthalate based bent-core liquid crystals.

A new bent-core liquid crystalline material consisting of a 4-cyanoresorcinol unit with two terephthalate based rod-like wings and terminated by two short alkyl chains was synthesized. Its liquid crystalline (LC) self-assembly and the development of polar order in the LC phases were investigated. The polar order is characterised using second harmonic generation and dielectric spectroscopy techniques in addition to XRD and DSC characterisations of the mesophase structure and investigation of freely suspended films. We demonstrate the growth of ferroelectric domains in the paraelectric SmA phase (SmAPR), which adopt antipolar correlations (SmAPAR) and eventually condense into a weakly tilted antiferroelectric smectic phase (SmCaPA).

Molecular dynamics of a binary mixture of twist-bend nematic liquid crystal dimers studied by dielectric spectroscopy.

We report a comprehensive dielectric characterization of a liquid crystalline binary mixture composed of the symmetric mesogenic dimer CB7CB and the nonsymmetric mesogenic dimer FFO9OCB. In addition to the high-temperature nematic phase, such a binary mixture shows a twist-bend nematic phase at room temperature which readily vitrifies on slow cooling. Changes in the conformational distribution of the dimers are reflected in the dielectric permittivity and successfully analyzed by means of an appropriate theoretical model. It is shown that the dielectric spectra of the mixture reflect the different molecular dipole properties of the components, resembling in the present case the characteristic dielectric spectra of nonsymmetric dimers. Comparison of the nematic and twist-bend nematic phases reveals that molecular dynamics are similar despite the difference in the molecular environment.

Polar Order and Symmetry Breaking at the Boundary between Bent-Core and Rodlike Molecular Forms: When 4-Cyanoresorcinol Meets the Carbosilane End Group.

Two isomeric achiral bent-core liquid crystals involving a 4-cyanoresorcinol core and containing a carbosilane unit as nanosegregating segment were synthesized and were shown to form ferroelectric liquid-crystalline phases. Inversion of the direction of one of the COO groups in these molecules leads to a distinct distribution of the electrostatic potential along the surface of the molecule and to a strong change of the molecular dipole moments. Thus, a distinct degree of segregation of the carbosilane units and consequent modification of the phase structure and coherence length of polar order result. For the compound with larger dipole moment (CN1) segregation of the carbosilane units is suppressed, and this compound forms paraelectric SmA and SmC phases; polar order is only achieved after transition to a new LC phase, namely, the ferroelectric leaning phase (SmCLs PS ) with the unique feature that tilt direction and polar direction coincide. The isomeric compound CN2 with a smaller dipole moment forms separate layers of the carbosilane groups and shows a randomized polar SmA phase (SmAPAR ) and ferroelectric polydomain SmCs PS phases with orthogonal combination of tilt and polar direction and much higher polarizations. Thus, surprisingly, the compound with the smaller molecular dipole moment shows increased polar order in the LC phases. Besides ferroelectricity, mirror-symmetry breaking with formation of a conglomerate of macroscopic chiral domains was observed in one of the SmC phases of CN1. These investigations contribute to the general understanding of the development of polar order and chirality in soft matter.