Dipole-dipole correlations in the nematic phases of symmetric cyanobiphenyl dimers and their binary mixtures with 5CB.

We report on the temperature dependence of birefringence and of the static dielectric permittivity tensor in a series of binary mixtures between the symmetric, bent-shaped, 1'',9''-bis(4-cyanobiphenyl-4'-yl)nonane (CB9CB) dimer and the monomeric nematogen 5CB. In the studied composition range the mixtures exhibit two nematic phases with distinct birefringence and dielectric features. Birefringence measurements are used to estimate the temperature dependence of the tilt between the axis defining the nanoscale helical modulation of the low temperature nematic phase with the (local) direction of the maximal alignment of the cyanobiphenyl units. Planar as well as magnetically and/or electrically aligned samples are used to measure the perpendicular and parallel components of the dielectric permittivity in both nematic phases. A self-consistent molecular field theory that takes into account flexibility and symmetry of the constituent mesogens is introduced for the calculation of order parameters and intra-molecular orientational dipolar correlations of the flexible dimers as a function of temperature/concentration. Utilising the tilt angle, as calculated from the birefringence measurements, and the predictions of the molecular theory, dielectric permittivity is modelled in the framework of the anisotropic version of the Kirkwood-Fröhlich theory. Using the inter-molecular Kirkwood correlation factors as adjustable parameters, excellent agreement between theory and permittivity measurements across the whole temperature range and composition of the mixtures is obtained. The importance of the orientational, intra- and inter-molecular, dipolar correlations, their relative impact on the static dielectric properties, as well as their connection with the local structure of the nematic phases of bent-shaped bimesogens, is discussed.

Field-induced anti-nematic and biaxial ordering in binary mixtures of discotic mesogens and spherical magnetic nanoparticles.

Using computer simulations we explore the equilibrium structure and response to external stimuli of complex magnetic hybrids consisting of magnetic particles in discotic liquid crystalline matrices. We show that the anisotropy of the liquid crystalline matrix (either in the nematic or in the columnar phase) promotes the collective orientational ordering of self-assembled magnetic particles. Upon applying an external homogeneous magnetic field in an otherwise isotropic state, the magnetic particles self-assemble into linear-rodlike-chains. At the same time structural changes occur in the matrix. The matrix transforms from an isotropic to a non-conventional anti-nematic state in which the symmetry axis of the discs is, on average, perpendicular to the magnetic field. In addition, a stable biaxial nematic state is found upon applying an external field to an otherwise uniaxial discotic nematic state. These observed morphologies constitute an appealing alternative to binary mixtures of rigid rod-disc system and indicate that non-trivial biaxial ordering can be obtained in the presence of a uniaxial external stimulus.

A molecular theory of nematic-nematic phase transitions in mesogenic dimers.

We study theoretically the molecular origins of the fascinating, and still debated, nematic-nematic phase transition exhibited by symmetric, statistically achiral, mesogenic dimers. A simple molecular model that mimics the key features and symmetry (C2V) of this class of mesogens is presented. In the mean-field approximation, the model yields up to three positionally disordered phases, one isotropic and two nematic. The low temperature nematic phase (NX) has a local two-fold symmetry axis, which is also a direction of molecular polar ordering and is tightly twisted about a macroscopic phase axis. The onset of polar ordering generates spontaneous chiral symmetry breaking and the formation of chiral domains of opposite handedness, manifested primarily by the twisting of the polar director. Within these domains the statistical balance between the enantiomer conformations is slightly shifted and the principal axes of the ordering tensors of the molecular segments twist at constant tilt angles with the helical axis. Key experimental results on the NX phase of liquid crystalline dimers are discussed in the light of the theoretical predictions of the model, which are also contrasted with the predictions of the twist-bend nematic model.

On the structure of the Nx phase of symmetric dimers: inferences from NMR.

NMR measurements on a selectively deuterated liquid crystal dimer CB-C9-CB, exhibiting two nematic phases, show that the molecules in the lower temperature nematic phase, N(X), experience a chiral environment and are ordered about a uniformly oriented director throughout the macroscopic sample. The results are contrasted with previous interpretations that suggested a twist-bend spatial variation of the director. A structural picture is proposed wherein the molecules are packed into highly correlated chiral assemblies.

Comparative Study of the Optical and Dielectric Anisotropy of a Difluoroterphenyl Dimer and Trimer Forming Two Nematic Phases.

We present a comparative study of the optical and dielectric anisotropy of a laterally fluorinated liquid crystal dimer and its homologous trimer, both exhibiting two nematic phases. In the high-temperature nematic phase, both oligomers exhibit positive optical anisotropy with similar magnitude, which, however, is lower in comparison with the optical anisotropy of the monomer. In the same temperature range, the dielectric permittivity along and perpendicular to the nematic director, measured on magnetically aligned samples, reveals negative dielectric anisotropy for both oligomers, which saturates as the temperature approaches the N-N phase transition temperature. Comparison of the dielectric anisotropies of the oligomers with the corresponding anisotropy of the monomer indicates a systematic variation of its magnitude with the number of the linked mesogenic units. Results are compared with the corresponding anisotropies of the cyanobiphenyl dimers, the archetypal compounds with two nematic phases, and are discussed in terms of the dipolar structure of the mesogens and the dipolar correlations in their nematic phases.

All Structures Great and Small: Nanoscale Modulations in Nematic Liquid Crystals.

The nature of the nanoscale structural organization in modulated nematic phases formed by molecules having a nonlinear molecular architecture is a central issue in contemporary liquid crystal research. Nevertheless, the elucidation of the molecular organization is incomplete and poorly understood. One attempt to explain nanoscale phenomena merely "shrinks down" established macroscopic continuum elasticity modeling. That explanation initially (and mistakenly) identified the low temperature nematic phase (NX), first observed in symmetric mesogenic dimers of the CB-n-CB series with an odd number of methylene spacers (n), as a twist-bend nematic (NTB). We show that the NX is unrelated to any of the elastic deformations (bend, splay, twist) stipulated by the continuum elasticity theory of nematics. Results from molecular theory and computer simulations are used to illuminate the local symmetry and physical origins of the nanoscale modulations in the NX phase, a spontaneously chiral and locally polar nematic. We emphasize and contrast the differences between the NX and theoretically conceivable nematics exhibiting spontaneous modulations of the elastic modes by presenting a coherent formulation of one-dimensionally modulated nematics based on the Frank-Oseen elasticity theory. The conditions for the appearance of nematic phases presenting true elastic modulations of the twist-bend, splay-bend, etc., combinations are discussed and shown to clearly exclude identifications with the nanoscale-modulated nematics observed experimentally, e.g., the NX phase. The latter modulation derives from packing constraints associated with nonlinear molecules-a chiral, locally-polar structural organization indicative of a new type of nematic phase.

Two-dimensional ordered porous patterns by molecular design.

We demonstrate by computer experiments that the spontaneous formation of two-dimensional regularly patterned molecular networks containing voids may be an entirely entropy-driven process. On the basis of a simple model of core-(soft) shell half-disk-shaped particles, we show that, even without the mediation of any attractive interparticle forces, such particles self-organize to stable and macroscopically ordered patterns with regularly distributed voids. The morphology of these supramolecular porous motifs depends critically on the size of the core relative to the coronal halo. The reverse engineering analysis of these precise two-dimensional supramolecular porous templates suggests molecular-shape complementarity and polyphilicity as key design parameters for the bottom-up engineering of such functional substrates.

Symmetries and alignment of biaxial nematic liquid crystals.

The possible symmetries of the biaxial nematic phase are examined against the implications of the presently available experimental results. Contrary to the widespread notion that biaxial nematics have orthorhombic symmetry, our study shows that a monoclinic (C(2h)) symmetry is more likely to be the case for the recently observed phase biaxiality in thermotropic bent-core and calamitic-tetrapode nematic systems. The methodology for differentiating between the possible symmetries of the biaxial nematic phase by NMR and by IR spectroscopy measurements is presented in detail. The manifestations of the different symmetries on the alignment of the biaxial phase are identified and their implications on the measurement and quantification of biaxiality as well as on the potential use of biaxial nematic liquid crystals in electro-optic applications are discussed.

Molecular modeling of liquid crystalline self-organization of fullerodendrimers: columnar to lamellar phase transitions driven by temperature and/or concentration changes.

The molecular cubic-block model [ J. Chem. Phys. 2005, 123, 164904 ] is used to study a class of poly(benzyl ether) fullerodendrimers that have recently been reported to form columnar liquid crystal phases. In agreement with experiment, the model-molecules are found to self-assemble into columns which form hexagonal or rectangular lattices. The columnar cross sections are elongated in the rectangular phase. Transitions to the isotropic phase, either directly or through the intermediate formation of smectic phases, have been found. The effects of dissolving small amounts of nonbonded fullerene molecules have been explored. The results predict that the fullerene solutes restrict the range of stability of the columnar phase and may induce transitions from the columnar to the smectic or the isotropic phase.

Self-organisation of fullerene-containing conical supermesogens.

A molecular model of cubic building blocks is used to describe the mesomorphism of conical fullerenomesogens. Calculations based on density functional molecular theory and on Monte Carlo computer simulations give qualitatively similar results that are also in good agreement with the experimentally observed mesomorphic behaviour. The columnar and lamellar mesophases obtained are non-polar, and their relative stability is controlled by a single model parameter representing the softness of the repulsive interactions among the building blocks of the conical molecules.

Polar Molecular Ordering in the NX Phase of Bimesogens and Enantiotopic Discrimination in the NMR Spectra of Rigid Prochiral Solutes.

The potential of mean torque governing the orientational ordering of prochiral solutes in the two nematic phases (N and NX) formed by certain classes of symmetric achiral bimesogens is formulated and used for the analysis of existing NMR measurements on solutes of various symmetries dissolved in the two phases. Three distinct attributes of the solvent phase, namely polarity of the orientational ordering, chirality of the constituent molecules, and spatial modulation of the local director, are identified as underlying three possible mechanisms for the generation of chiral asymmetry in the low temperature nematic phase (NX). The role and quantitative contribution of each mechanism to enantiotopic discrimination in the NX phase are presented and compared with the case of the conventional chiral nematic phase (N*). It is found that polar ordering is essential for the appearance of enantiotopic discrimination in small rigid solutes dissolved in the NX phase and that such discrimination is restricted to solutes belonging to the point group symmetries Cs and C2v.

Homogeneous alignment of liquid crystalline dendrimers confined in a slit-pore. A simulation study.

In this work we present results from isobaric-isothermal (NPT) Monte Carlo simulation studies of model liquid crystalline dendrimer (LCDr) systems confined in a slit-pore made of two parallel flat walls. The dendrimers are modelled as a collection of spherical and ellipsoidal particles corresponding to the junction points of the dendritic core and to the mesogenic units respectively. Assuming planar uniform (unidirectional) soft anchoring of the mesogenic units on the substrates we investigate the conformational and alignment properties of the LCDr system at different thermodynamic state points. Tractable coarse grained force fields have been used from our previous work. At low pressures the interior of the pore is almost empty, since almost all LCDrs are anchored to the substrates forming two-dimensional smectic-like structures with the mesogens aligned along the aligning direction of the substrates. As the pressure grows the LCDrs occupy the whole pore. However, even at low temperatures, the smectic organization does not transmit in the interior of the pore and is preserved for distances of 2-3 mesogenic diameters from the walls. For this reason, the global orientational order decreases with increasing pressure (density). In the vicinity (2-3 mesogenic diameters) of the pore walls, mesogenic units preserve the smectic structure whose layers are separated by layers of spherical beads. In this region individual LCDrs possess a rod like shape.

Molecular Interactions in Chiral Nematic Liquid Crystals and Enantiotopic Discrimination through the NMR Spectra of Prochiral Molecules I: Rigid Solutes.

We have developed a molecular theory for enantiotopic discrimination in prochiral solutes dissolved in chiral nematic solvents by means of NMR spectroscopy. The leading rank tensor contributions to the proposed potential of mean torque include symmetric as well as antisymmetric terms with respect to spatial inversion; these lead to consistent determination of all prochiral solute symmetries for which enantiotopes are distinguishable by NMR and also to excellent quantitative agreement when tested against the available experimental data for the rigid solutes acenaphthene and norbornene as well as for the moderately flexible ethanol molecule.

Molecular simulation study of polar order in orthogonal bent-core smectic liquid crystals.

We explore the phase behavior and structure of orthogonal smectic liquid crystals consisting of bent-core molecules (BCMs) by means of Monte Carlo molecular simulations. A simple athermal molecular model is introduced that describes the basic features of the BCMs. Phase transitions between uniaxial and biaxial (antiferroelectric) orthogonal smectics are obtained. The results indicate the presence of local in-plane polar correlations in the uniaxial smectic phase. The macroscopic uniaxial-biaxial transformation is rationalized in terms of local polar correlations giving rise to polar domains. The size of these polar domains grows larger under the action of an external vector field and their internal ordering is enhanced, leading to field-induced biaxial order-disorder transitions.

Supramolecular nature of the nematic-nematic phase transitions of hard boardlike molecules.

The phase behavior of hard boardlike biaxial particles of relative dimensions close to the clamitic to discotic crossover is explored by means of Monte Carlo molecular simulations. Transitions between two distinct biaxial nematic phases as well as transitions from a biaxial nematic to a uniaxial Sm-A phase are obtained. The formation of anisotropic supramolecular assemblies is demonstrated and is quantified by means of rotationally invariant pair correlation functions.

Molecular simulation of hierarchical structures in bent-core nematic liquid crystals.

The structure of nematic liquid crystals formed by bent-core mesogens (BCMs) is studied in the context of Monte Carlo simulations of a simple molecular model that captures the symmetry, shape, and flexibility of achiral BCMs. The results indicate the formation of (i) clusters exhibiting local smectic order, orthogonal or tilted, with strong in-layer polar correlations and antiferroelectric juxtaposition of successive layers and (ii) large homochiral domains through the helical arrangement of the tilted smectic clusters, while the orthogonal clusters produce achiral (untwisted) nematic states.

Polymer brushes on periodically nanopatterned surfaces.

Structural properties of polymer brushes tethered on a periodically nanopatterned substrate are investigated by computer simulations. The substrate consists of an alternating succession of two different types of equal-width parallel stripes, and the polymers are end-tethered selectively on every second stripe. Three distinct morphologies of the nanopatterned brush have been identified, and their range of stability has been determined in terms of a single universal parameter that combines the grafting density, the polymer length, and the stripe width. We propose scaling relations for the average brush height and for the architectural properties of the outer surface of the nanopatterned brush under good solvent conditions. Our analysis provides guidelines for fabricating well-defined and tunable nanopatterned polymeric films.

Thermotropic biaxial nematic liquid crystals: spontaneous or field stabilized?

An intermediate nematic phase is proposed for the interpretation of recent experimental results on phase biaxiality in bent-core nematic liquid crystals. The phase is macroscopically uniaxial but has microscopic biaxial, and possibly polar, domains. Under the action of an electric field, the phase acquires macroscopic biaxial ordering resulting from the collective alignment of the domains. A phenomenological theory is developed for the molecular order in this phase and for its transitions to purely uniaxial and to spontaneously biaxial nematic phases.

Self-organization and pattern formation of janus particles in two dimensions by computer simulations.

The phase behavior and associated pattern formation of two-dimensional systems of hard disks decorated with amphiphilic coronae (Janus disks) are studied by means of Monte Carlo computer simulations. A primitive interaction potential that captures the essential interparticle interactions is introduced. Despite its simplicity, the system exhibits a very rich phase polymorphism. Apart from the isotropic phase and depending upon the coronal thickness, the simulated systems self-organize in a number of two-dimensional mesophases of various symmetries exhibiting a variety of novel patterns. The results of these simulations suggest that 2D Janus particles are promising candidates for bottom-up design of precise two-dimensional templates.