Antiphase structures in polar smectic liquid crystals and their molecular origin

Accessing the electronic structure of liquid crystalline semiconductors with bottom-up electronic coarse-graining

Understanding the relationship between multiscale morphology and electronic structure is a grand challenge for semiconducting soft materials. Computational studies aimed at characterizing these relationships require the complex integration of quantum-chemical (QC) calculations, all-atom and coarse-grained (CG) molecular dynamics simulations, and back-mapping approaches. However, these methods pose substantial computational challenges that limit their application to the requisite length scales of soft material morphologies. Here, we demonstrate the bottom-up electronic coarse-graining (ECG) of morphology-dependent electronic structure in the liquid-crystal-forming semiconductor, 2-(4-methoxyphenyl)-7-octyl-benzothienobenzothiophene (BTBT). ECG is applied to construct density functional theory (DFT)-accurate valence band Hamiltonians of the isotropic and smectic liquid crystal (LC) phases using only the CG representation of BTBT. By bypassing the atomistic resolution and its prohibitive computational costs, ECG enables the first calculations of the morphology dependence of the electronic structure of charge carriers across LC phases at the ∼20 nm length scale, with robust statistical sampling. Kinetic Monte Carlo (kMC) simulations reveal a strong morphology dependence on zero-field charge mobility among different LC phases as well as the presence of two-molecule charge carriers that act as traps and hinder charge transport. We leverage these results to further evaluate the feasibility of developing mesoscopic, field-based ECG models in future works. The fully CG approach to electronic property predictions in LC semiconductors opens a new computational direction for designing electronic processes in soft materials at their characteristic length scales.

External field induced defect transformation in circular confined Gay-Berne liquid crystals

Normally, defects in two-dimensional, circular, confined liquid crystals can be classified into four types based on the position of singularities formed by liquid crystal molecules, i.e., the singularities located inside the circle, at the boundary, outside the circle, and outside the circle at infinity. However, it is considered difficult for small aspect ratio liquid crystals to generate all these four types of defects. In this study, we use molecular dynamics simulation to investigate the defect formed in Gay-Berne, ellipsoidal liquid crystals, with small aspect ratios confined in a circular cavity. As expected, we only find two types of defects (inside the circle and at the boundary) in circular, confined, Gay-Berne ellipsoids under static conditions at various densities, aspect ratios, and interactions between the wall and liquid crystals. However, when introducing an external field to the system, four types of defects can be observed. With increasing the strength of the external field, the singularities in the circular, confined system change from the inside to the boundary and the outside, and the farthest position that the singularities can reach depends on the strength of the external field. We further introduce an alternating, triangular wave, external field to the system to check if we can observe the transformation of different defects within an oscillating period. We find that the position of the singularities greatly depends on the oscillating intensity and oscillating period. By changing the oscillating intensity and oscillating period of the external field, the defect types can be adjusted, and the transformation between different defects can be easily observed. This provides a feasible way to modulate liquid crystal defects and investigate the transformation between different defects.

A chiral smectic phase induced by an alternating external field

Using simple achiral building blocks modulated by an external field to achieve chiral liquid crystal phases remains a challenge. In this study, a chiral helix liquid crystal phase is obtained for a simple Gay-Berne ellipsoid model under an alternating external field by using molecular dynamics simulations. Our results show that the chiral helix liquid crystal phase can be observed in a wide range of external field strengths when the oscillation period is smaller than the rotational characteristic diffusion timescale of ellipsoids. In addition, we find that the pitch and tilt angle of the helix structure can also be adjusted by changing the strength and oscillation period of the applied alternating external field. This may provide a feasible route for the regulation of chiral liquid crystal phases by an alternating external field.

Can off-centre mesogen dipoles extend the biaxial nematic range?

We have investigated the possibility of extending the stability range of the biaxial nematic phase by adding an off-centre dipole of various strengths and orientations to elongated biaxial Gay-Berne (GB) mesogens yielding a relatively narrow biaxial nematic (N_bx) phase, and a smectic (S_bx) phase when dipole-less. The effect of dipoles is not easy to predict, and our previous investigations have shown the limited benefits of having a central dipole. Here we show, employing molecular dynamics (MD) simulations, that a not too strong off-centre dipole positioned along the longest axis of the nematogen can extend the temperature range of stability of the biaxial nematic phase, also shifting it towards lower temperatures.

Doping liquid crystals with nanoparticles. A computer simulation of the effects of nanoparticle shape

Molecular-scale Monte Carlo simulations of liquid crystal-nanoparticle dispersions show the effect on the orientational order and on the clearing temperature of shape and concentration of the dopant nanoparticles.

Monte Carlo computer simulation of sedimentation of charged hard spherocylinders

In this article we present a NVT Monte Carlo computer simulation study of sedimentation of an electroneutral mixture of oppositely charged hard spherocylinders (CHSC) with aspect ratio L/σ = 5, where L and σ are the length and diameter of the cylinder and hemispherical caps, respectively, for each particle. This system is an extension of the restricted primitive model for spherical particles, where L/σ = 0, and it is assumed that the ions are immersed in an structureless solvent, i.e., a continuum with dielectric constant D. The system consisted of N = 2000 particles and the Wolf method was implemented to handle the coulombic interactions of the inhomogeneous system. Results are presented for different values of the strength ratio between the gravitational and electrostatic interactions, Γ = (mgσ)/(e(2)/Dσ), where m is the mass per particle, e is the electron's charge and g is the gravitational acceleration value. A semi-infinite simulation cell was used with dimensions Lx ≈ Ly and Lz = 5Lx, where Lx, Ly, and Lz are the box dimensions in Cartesian coordinates, and the gravitational force acts along the z-direction. Sedimentation effects were studied by looking at every layer formed by the CHSC along the gravitational field. By increasing Γ, particles tend to get more packed at each layer and to arrange in local domains with an orientational ordering along two perpendicular axis, a feature not observed in the uncharged system with the same hard-body geometry. This type of arrangement, known as tetratic phase, has been observed in two-dimensional systems of hard-rectangles and rounded hard-squares. In this way, the coupling of gravitational and electric interactions in the CHSC system induces the arrangement of particles in layers, with the formation of quasi-two dimensional tetratic phases near the surface.

Ferroelectric order in liquid crystal phases of polar disk-shaped ellipsoids

The demonstration of a spontaneous macroscopic ferroelectric order in liquid phases in the absence of any long range positional order is considered an outstanding problem of both fundamental and technological interest. Recently, we reported that a system of polar achiral disklike ellipsoids can spontaneously exhibit a long searched ferroelectric nematic phase and a ferroelectric columnar phase with strong axial polarization. The major role is played by the dipolar interactions. The model system of interest consists of attractive-repulsive Gay-Berne oblate ellipsoids embedded with two parallel point dipoles positioned symmetrically on the equatorial plane of the ellipsoids. In the present work, we investigate in detail the profound effects of changing the separation between the two symmetrically placed dipoles and the strength of the dipoles upon the existence of different ferroelectric discotic liquid crystal phases via extensive off-lattice N-P-T Monte Carlo simulations. Ferroelectric biaxial phases are exhibited in addition to the uniaxial ferroelectric fluids where the phase biaxiality results from the dipolar interactions. The structures of all the ferroelectric configurations of interest are presented in detail. Simple phase diagrams are determined which include different polar and apolar discotic fluids generated by the system.

Monte Carlo simulations of spontaneous ferroelectric order in discotic liquid crystals

The demonstration of a spontaneous macroscopic ferroelectric order in liquid phases in the absence of any long-range positional order is considered as an outstanding problem of great fundamental and technological interest. We report here off-lattice Monte Carlo simulations of a system of polar achiral disklike ellipsoids which spontaneously exhibit a novel ferroelectric nematic phase which is a liquid in three dimensions, considering attractive-repulsive pair interaction suitable for the anisotropic particles. At lower temperature, the ferroelectric nematic phase condenses to a ferroelectric hexagonal columnar fluid with an axial macroscopic polarization. A spontaneous ferroelectric order of dipolar origin is established here for the first time in columnar liquid crystals. Our study demonstrates that simple dipolar interactions are indeed sufficient to produce a class of novel ferroelectric fluids of essential interest. The present work reveals the structure-property relationship of achieving long searched ferroelectric liquid crystal phases and transitions between them, and we hope these findings will help in future development of technologically important fluid ferroelectric materials.

Smectic order parameters via liquid crystal NMR spectroscopy: Application to a partial bilayer smectic A phase

Solute molecules were dissolved in the liquid crystal 4-cyano-4'-n-octyloxybiphenyl (8OCB), known to form a partial bilayer smectic-A phase. Through measurement of solutes' and solvent's orientational order parameters via nuclear magnetic resonance spectroscopy, and their analysis via a statistical thermodynamic density functional theory, values of the solvent's positional order parameters and solutes' positional-orientational distribution functions were obtained. Near to the transition to the nematic phase, the main positional order parameter of the smectic liquid crystal turned out to be comprised in the interval 0.4-0.6, though the quality of the fittings assuming the phase as nematic all across the temperature range investigated was only slightly worse. This may be ascribed to the looseness of the partial bilayer smectic structure. Solutes were found to preferentially lie in those regions where liquid crystal molecule terminal chains are located.

Frustration in smectic layers of polar Gay-Berne systems

The main focus of the present paper is studying dipolar frustration within smectic- A(d) layers as induced by dipole-dipole interactions. Our reference point is the Gay-Berne system with kappa=4, kappa'=5, mu=2 and nu=1, which in the phase diagram shows a stable "island" of smectic- A phase with a short-range hexagonal order within each layer [Phys. Rev. E 57, 6685 (1998)]. We carry out isothermal-isobaric Monte Carlo simulations for a dipolar version of this model, where the Gay-Berne interaction is supplemented by interaction between longitudinal dipole moments. For a fixed off-center position of the dipoles we increase value of the dipole moment and follow evolution of the liquid-crystalline part of the phase diagram focusing on changes of the nematic-smectic- A phase boundaries and on structural response of the smectic- A layers. For weak dipoles only the classical smectic- A phase is stabilized, which then transforms into smectic- A(d) with layers being formed by two ferroelectrically polarized sublayers of opposite polarization. Average positions of dipoles that contribute to the polarization of a sublayer are located in a common plane, referred to as a dipolar plane. For not too strong dipole-dipole interactions increasing magnitude of the dipole moment causes stabilization of nematic at the expense of smectic- A(d). Under the same conditions the layer spacing increases and the distance between the dipolar planes within layers decreases. Each smectic sublayer is characterized by a short-range hexagonal order of the molecular centers of mass. With the dipole moment exceeding the threshold value, the polarization planes that built up the layers start to merge, which sets in the dipolar frustration. This, in turn, forces the system to develop a competition between frustrated hexagonal- and frustration-free tetragonal local order within each layer. When the local hexagonal order is transformed into the tetragonal one the stability range of smectic-A(d) increases with increasing dipole moment at the expense of the nematic phase. Similar competition is observed in crystalline phases. For small dipole moment only crystalline structures with long-range hexagonal order appear stable. They evolve with dipolar strength into monoclinic and tetragonal lattices.

Core charge distribution and self assembly of columnar phases: the case of triphenylenes and azatriphenylenes

BACKGROUND

The relation between the structure of discotic molecules and columnar properties, a crucial point for the realization of new advanced materials, is still largely unknown. A paradigmatic case is that hexa-alkyl-thio substituted triphenylenes present mesogenic behavior while the corresponding azatriphenylenes, similar in shape and chemical structure, but with a different core charge distribution, do not form any liquid crystalline mesophase. This study is aimed at investigating, with the help of computer simulations techniques, the effects on phase behaviour of changes of the charge distribution in the discotic core.

RESULTS

We described the shape and the pair, dispersive and electrostatic, interactions of hexa alkyl triphenylenes by uniaxial Gay-Berne discs with embedded point charges. Gay-Berne parameters were deduced by fitting the dispersive energies obtained from an atomistic molecular dynamics simulation of a small sample of hexa-octyl-thio triphenylene molecules in columnar phase, while a genetic algorithm was used to get a minimal set of point charges that properly reproduces the ab anitio electrostatic potential. We performed Monte Carlo simulations of three molecular models: the pure Gay-Berne disc, used as a reference, the Gay-Berne disc with hexa-thio triphenylene point charges, the Gay-Berne disc with hexa-thio azatriphenylene point charges. The phase diagram of the pure model evidences a rich polymorphism, with isotropic, columnar and crystalline phases at low pressure, and the appearance of nematic phase at higher pressure.

CONCLUSION

We found that the intermolecular electrostatic potential among the cores is fundamental in sta-bilizing/destabilizing columnar phases; in particular the triphenylene charge distribution stabilizes the columnar structure, while the azatriphenylene distribution suppresses its formation in favor of the nematic phase. We believe the present model could be successfully employed as the basis for coarse-grained level simulations of a wider class of triphenylene derivatives.

Two-dimensional chiral model for liquid crystals, bent hard needles: A Monte Carlo simulation

The liquid crystalline behavior of a two dimensional (2D) model of hard needles bent into a "zigzag shape" is studied. This model, originally designed to study two dimensional chiral segregation, also shows liquid crystalline behavior and has some anomalous features which are contrasted in relation to the following: (i) Most of the microscopical models used to study liquid crystals have a symmetry axis that coincides with a molecular axis; (ii) in three-dimensions, chiral molecules can form cholesteric instead of nematic phases; (iii) the smectic phase is usually found when attractions are present or at least when the molecules have finite volume. Despite the fact that the present 2D model does not have any of these characteristics, numerical evidence is found for the occurrence of nematic and smectic phases. Since these molecules are athermal, infinitely repulsive, and infinitesimally thin, the liquid crystalline characteristics are attributed to excluded volume effects. To determine the mesophases of the model, both nematic and smectic order parameters as well as distribution functions are computed.

A Monte Carlo study of the mesophases formed by polar bent-shaped molecules

Liquid crystal phases formed by bent-shaped (or "banana") molecules are currently of great interest. Here we investigate by Monte Carlo computer simulations the phases formed by rigid banana molecules modeled combining three Gay-Berne sites and containing either one central or two lateral and transversal dipoles. We show that changing the dipole position and orientation has a profound effect on the mesophase stability and molecular organization. In particular, we find a uniaxial nematic phase only for off-center dipolar models and tilted phases only for the one with terminal dipoles.

A novel mesophase formed by top-shaped molecules in the bulk and unsupported thin films: A molecular dynamics study

We have used molecular dynamics simulations to investigate the ordering of top-shaped molecules in bulk phases and in unsupported thin films. Each rigid anisotropic molecule was composed of 11 Lennard-Jones interaction centers (beads). In an attempt to enhance the nematic stability in preference to smectic, the three central beads were assigned a larger Lennard-Jones diameter than the tail beads, giving the molecule a shape resembling a top. The molecular model was found to exhibit an unusual bulk mesophase with long-range orientational order and with molecular center-of-mass positions arranged in parallel interdigitated layers, with layer spacing smaller than half the length of the long axis of a molecule. However, despite the toplike molecular shape, no nematic phase was observed in the pressure range studied. Unsupported films of the isotropic liquid were cooled in order to locate a triple point between the novel mesophase, vapor, and isotropic liquid. At temperatures slightly above the triple point, enhanced surface ordering of molecules was found to occur in the unsupported film. At temperatures slightly below the triple point, the preferred molecular alignment in the unsupported film was parallel to the interface, in violation of arguments that have been proposed based on the relative enthalpies of various cleavage planes for close-packed structures.

Dipolar interactions, molecular flexibility, and flexoelectricity in bent-core liquid crystals

The effects of dipolar interactions and molecular flexibility on the structure and phase behavior of bent-core molecular fluids are studied using Monte Carlo computer simulations. Some calculations of flexoelectric coefficients are also reported. The rigid cores of the model molecules consist of either five or seven soft spheres arranged in a "V" shape with external bend angle gamma. With purely repulsive sphere-sphere interactions and gamma = 0 degrees (linear molecules) the seven-sphere model exhibits isotropic, uniaxial nematic, and untilted and tilted smectic phases. With gamma > or = 20 degrees the untilted smectic phases disappear, while the system with gamma > or = 40 degrees shows a direct tilted smectic-isotropic fluid transition. The addition of electrostatic interactions between transverse dipole moments on the apical spheres is generally seen to reduce the degree of molecular inclination in tilted phases, and destabilizes the nematic and untilted smectic phases of linear molecules. The effects of adding three-segment flexible tails to the ends of five-sphere bent-core molecules are examined using configurational-bias Monte Carlo simulations. Only isotropic and smectic phases are observed. On the one hand, molecular flexibility gives rise to pronounced fluctuations in the smectic-layer structure, bringing the simulated system in better correspondence with real materials; on the other hand, the smectic phase shows almost no tilt. Lastly, the flexoelectric coefficients of various nematic phases--with and without attractive sphere-sphere interactions--are presented. The results are encouraging, but a large computational effort is required to evaluate the appropriate fluctuation relations reliably.

Coarse grained models for flexible liquid crystals: Parameterization of the bond fluctuation model

We extend the bond fluctuation model, originally devised to investigate polymer systems, to contain anisotropic interactions suitable for the simulation of large flexible molecules such as liquid crystalline polymers and dendrimers. This extended model coarse grains the interaction between the flexible chains at a similar level of detail to the mesogenic units. Suitable interaction parameters are obtained by performing trial simulations on a low molar mass liquid crystalline system. The phase diagram of this system is determined as a function of the molecular stiffness. The nematic to isotropic transition temperature is found to increase with increasing stiffness.

Structure of liquids composed of shifted dipole linear molecules

Simulation results for liquids composed of linear molecules interacting through dispersion forces and off-center dipoles are presented. Remarkable differences are found on the vapor-liquid equilibrium respect to that of centered dipole molecules. Even more remarkable is the appearance of additional short-range liquid structure at relatively large dipoles and aspect ratios. The existence of dipole dimers is clearly established, and some suggestions allowing for the correspondence between a particular macroscopic phenomenology and a particular dispersion potential function are presented.

Molecular dipoles and tilted smectic formation: a Monte Carlo study

We investigate the possibility of forming a tilted smectic liquid crystal phase by suitably positioning two permanent dipoles in a rodlike molecule. We show, using Monte Carlo simulations, that a tilted smectic is formed from ellipsoidal Gay-Berne particles with two off-center outboard dipoles when these are directed along or at 60 degrees from the rod axis where they are located, but not when they are perpendicular to it. The properties of the phases obtained are studied in some detail.

Computer simulation of apolar bent-core and rodlike molecules

Bent-core molecules have received much interest due to their biaxiality and novel phase ordering. It is, therefore, of interest to model the characteristic shape of these molecules and observe the effect on liquid crystal mesophase formation in a computer simulation study. A simple model of the interaction employed a two-site Gay-Berne potential with the sites separated by +/-0.5 reduced units for all models. The angle between the two sites, 180 degrees -gamma, was varied from gamma=0 degrees to gamma=70 degrees and influenced the phase behavior markedly. The rodlike model formed isotropic, nematic, smectic-A, and smectic-B, phases. Results for the bent-core models show that as the angle gamma increases the transition temperature to the ordered phase decreases. As gamma increases the nematic phase is first destabilized then stabilized with respect to the smectic phase and a tilted smectic-B phase is seen at gamma=20 degrees. For gamma=40 degrees a "TGB-like" phase is identified as the system cools whereas for gamma=70 degrees no ordered phase is formed.

Dielectric and elastic properties of liquid crystals

The structural properties, the static and relaxation dielectric coefficients [epsilon(j) and epsilon(j)(omega) (j= ||, perpendicular)], the rotational diffusion constants D( perpendicular) and D( ||), the orientational correlation times tau(1)(i0) (i=0,1), and the bulk elastic constants K(i) (i=1,2,3) are investigated for polar liquid crystals, such as 4-n-pentyl-4(')-cyanobiphenyl (5CB). epsilon(j) are calculated by a combination of the existing molecular theory and statistical-mechanical approach (SMA) that takes into account translational and orientational correlations as well as their coupling, whereas epsilon(j)(omega) are calculated by combining SMA and nuclear magnetic resonance relaxation theory, both based on a rotational diffusion model in which the reorientation of an individual molecule is assumed as stochastic Brownian motion in a potential of mean torque. Reasonable agreement between the calculated and experimental values of epsilon(j) and epsilon(j)(omega) for 5CB is obtained. The bulk Frank elastic constants K(i) (i=1,2,3), for splay, twist, and bend distortion modes, as well as their ratios K(3)/K(1) and K(2)/K(1) are also obtained.

Molecular dynamics study of mesophase formation using a transverse quadrupolar Gay-Berne model

The effect of the transverse electric quadrupole moment on the formation of liquid-crystal mesophases was investigated by means of a computer-simulation study. A simple model of the molecular interaction employed the addition of a transverse, point quadrupole to a Gay-Berne potential. The transverse quadrupole was seen to raise the temperature of onset of the smectic phase. A large magnitude quadrupole stabilized the smectic-A phase over the temperature range studied compared to a Gay-Berne reference fluid. The presence of a large quadrupole stabilized cubic smectic phases rather than the more usual hexagonal smectic-B phases.

Mean-field theory of acentric order of dipolar chromophores in polymeric electro-optic materials

A mean-field theory of macroscopic order of dipolar chromophores in a polymer matrix in the presence of an external electric field is developed. The theory is applied to characterize the electro-optic coefficient of the Pockel effect that forms the basis for a variety of polymeric nonlinear electro-optic materials. The coefficient is studied as a function of chromophore concentration, polymer properties, and manufacturing conditions, including temperature, strength of the applied electric field, and macroscopic shape of the sample. The model reproduces the observed behavior of the electro-optic coefficient and explains the nonlinear concentration dependence of the coefficient at high chromophore concentrations. Specific recommendations for system design are suggested from the analysis of the obtained data.

Statistical-mechanical study of the pair correlations for the dipolar Gay-Berne model

A statistical-mechanical theory based upon the method of conditional distribution function has been applied to calculations of the nearest-neighbor (NN) and next NN correlators as well as order parameters. The method takes into account translational and orientational correlations as well as their coupling. Using the dipolar Gay-Berne interaction potential, calculations have been carried out for temperatures and densities corresponding to a nematic phase. The results in orientational distribution functions indicate a significant effect of the dipole-dipole interactions on the orientational order of the liquid crystal. It was found that NN particles tend to be mutually antiparallel, whereas a reversed tendency is observed for next NN particles. These results are in agreement with computer simulations and with interpretations of experimental data.