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.

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.

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.

Long- and short-range order in the mesophases of laterally substituted calamitic mesogens and their radial octapodes.

The mesomorphic behavior of a calamitic mesogen (4'-undecyloxybiphenyl-4-yl-4-octyloxy-2-(pent-4-en-1-yloxy)benzoate) and of a supermesogenic octapode formed by the side-on attachment of the mesogen to a octasilsesquioxane central core is studied by X-ray diffraction and polarizing optical microscopy. The calamitic compound is found to have a nematic phase that has biaxial domains (cybotactic clusters) of tilted layers throughout its entire temperature range. Domains of analogous structure are also found in both the nematic and the hexagonal columnar mesophases exhibited by the obctapode compound. The spacing of the layers forming the domains is found to have the same, essentially temperature independent value for the calamitic monomer and for the octapode, in both its mesophases. Comparison with compounds of analogous structure shows that this value is determined by the length of the rigid part of the mesogenic unit. Variation of the latter length is shown to have no effect on the size of the hexagonal lattice of the octapode columnar phase or on the stacking distance within the columns. The presence of the biaxial domains in the nematic phase is discussed in connection with the phase biaxiality that has been observed in structurally related tetrapode compounds and the possibility of field induced macroscopic biaxial nematic order.

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.

Columnar phase structures of an organic-inorganic hybrid functionalized with eight calamitic mesogens.

A liquid-crystalline octapode, formed by laterally connecting calamitic mesogens to an inorganic silsesquioxane cube through flexible siloxane spacers, is studied using polarized light microscopy, differential scanning calorimetry (DSC) and X-ray diffraction (XRD). The studies are extended to mixtures of the octapode with the respective monomer mesogens. The monomer and the octapode show a nematic phase. At lower temperatures, the octapode exhibits additionally a columnar hexagonal phase (6 lattice), which, on further cooling, undergoes a transition to a columnar rectangular phase (2 lattice). A similar phase-transition sequence is observed for mixtures of the octapode with moderate concentrations of the monomer. The columnar-columnar transition is discussed combining XRD and DSC results, and a possible model of the molecular self-organization is presented.

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.

Direct Measurement of the Angular Pair Correlation Coefficients in Molecular Liquids Using NMR. Benchmarking Force Fields for Atomistic Simulations.

High-field deuterium NMR spectroscopy is used to characterize a number of molecular liquids and their mixtures in order to probe the directional part of the intermolecular interactions through the orientational ordering induced in the isotropic liquid phase by the spectrometer magnetic field. The systems studied include benzene, chloroform, hexafluorobenzene, and thiophene at various concentrations and in mixtures. Dilution with the magnetically isotropic tetramethylsilane provides quantification of ordering at "infinite magnetic dilution", that is, in the absence of magnetic intermolecular correlations, and thereby allows identification of the contribution of these correlations to the orientational ordering in neat phases and at various degrees of magnetic dilution. Such contributions are conveyed by angular pair correlation coefficients, which, in addition to being accessible to direct NMR measurement, are also possible to evaluate directly from molecular dynamics simulations. By using various force fields, simulations provide benchmark quantities for testing and possibly further improving the force field performance, particularly with respect to the directional components of the intermolecular interactions. The latter are critical for the simulation of self-assembly generally and particularly in biological systems.

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.

Liquid-State Structure via Very High-Field Nuclear Magnetic Resonance Discriminates among Force Fields.

Deuterium nuclear magnetic resonance ((2)H NMR) spectra of labeled molecular liquids obtained at high fields, for example, |B| = 22.3 T (950 MHz proton NMR), exhibit resolved quadrupolar splittings that reflect the average orientation of the molecules relative to B. Those residual nuclear spin interactions exhibited by benzene and chloroform provide an experimental determination of the leading tensor component of the pair correlation function for these two molecular liquids. In this way, very high-field (2)H NMR may be used to extract unambiguous information about liquid-state structure. Additionally, replicating the experimentally derived pair correlation function using molecular dynamics simulations provides a critical test of simulation force fields.

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.

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.