Nematic Fluid Research Articles

Nematic fluid structure in wall-field geometry

We describe an integral equation method for obtaining the distribution of a nematic fluid near a wall and interacting with a uniform orienting field. Complete density-orientational profiles are calculated for a model nematic with different wall-particle interactions and different orientations of the wall with respect to the field. For orienting walls we identify particular long-range correlations that are responsible for reorientation of the bulk nematic at zero external field. These correlations become stronger as the wall-particle interaction is increased in range; they become longer ranged as the orienting field is weakened. Special attention is focused on systems where the wall-particle interaction favors orientations perpendicular to the surface. The local director orientation can vary discontinuously with the distance from the surface when the orienting influences of the field and the wall are antagonistic. At high densities smectic-like structures appear. Adsorption phenomena are also discussed. For inert hard walls, the ordered fluid avoids the surface, and a surface layer where the particles tend to orient perpendicular to the bulk director appears. Experimentally, this might be seen as wetting of the wall by a less-ordered fluid.

Colloidal hard-rod fluids near geometrically structured substrates.

Density functional theory is used to study colloidal hard-rod fluids near an individual right-angled wedge or edge as well as near a hard wall, which is periodically patterned with rectangular barriers. The Zwanzig model, in which the orientations of the rods are restricted to three orthogonal orientations but their positions can vary continuously, is analyzed by numerical minimization of the grand potential. Density and orientational order profiles, excess adsorptions, as well as surface and line tensions are determined. The calculations exhibit an enrichment [depletion] of rods lying parallel and close to the corner of the wedge (edge). For the fluid near the geometrically patterned wall, complete wetting of the wall-isotropic liquid interface by a nematic film occurs as a two-stage process in which first the nematic phase fills the space between the barriers until an almost planar isotropic-nematic liquid interface has formed separating the higher-density nematic fluid in the space between the barriers from the lower-density isotropic bulk fluid. In the second stage, a nematic film of diverging film thickness develops upon approaching bulk-isotropic-nematic coexistence.

Nematic liquid crystals and ordered micropolar fluids

We re-examine the dynamics of uniaxial nematic liquid crystals using the polar fluid model. This modelling approach was investigated by Eringen, but his description of rotational elasticity is significantly less tractable than that proposed by Ossen and Frank who represented the microstructure by a unit vector, known as the director. In this paper we combine the Ossen–Frank elastic energy with the polar fluid model and establish the differences of the resulting polar nematic fluid model with the classical Eriksen–Leslie equations of nematodynamics. Although the polar fluid framework seems quite different from the Eriksen–Leslie model, the non-dissipative contributions in the final equations appear to be closely related, while the dissipative contributions differ slightly.

Thermodynamics of soft anisotropic interfaces

The Gibbs-Duhem equation for interfaces between nematic liquid crystals and isotropic fluids is formulated and shown to be a generic equation for soft anisotropic surfaces. The one-to-one correspondence between the nematic and crystalline surface Gibbs-Duhem equations is established. Consistency between the surface Gibbs-Duhem equation and the classical equations of interfacial nematostatics is shown. Using a phase space that takes into account thermodynamics, liquid crystalline order, and geometric variables, the generalized nematic surface Gibbs-Duhem equation reveals the presence of couplings between shape, adsorption, temperature, and average molecular orientation. Merging the thermodynamic analysis with nematostatics results in a model for morphactancy, that is, adsorption-induced interfacial shape selection. The specific roles of gradient bulk Frank elasticity, interfacial tension, and anchoring energy are elucidated by analyzing particular paths in the thermodynamic-geometric phase space.

Phase Behaviour of Uncured and UV-cured (2-ethylhexylacrylate-1,6-hexanedioldiacrylate)/E7 Mixtures

The equilibrium phase diagram of UV-cured (2-ethylhexylacrylate-1,6-hexanedioldiacrylate) and the multicomponent nematic fluid E7 is established by polarized optical microscopy and differential scanning calorimetry. The enthalpy changes at the nematic-isotropic transition for both uncured and UV-cured samples are used to determine the liquid crystal (LC) solubility limit in the acrylate rich phase and to estimate the fractional amount of phase separated LC.

Duality in 2 + 1D quantum elasticity: superconductivity and quantum nematic order

Superfluidity and superconductivity are traditionally understood in terms of an adiabatic continuation from the Bose-gas limit. Here we demonstrate that at least in a 2 + 1D Bose system, superfluidity can arise in a strict quantum field-theoretic setting. Taking the theory of quantum elasticity (describing phonons) as a literal quantum field theory with a bosonic statistic, superfluidity and superconductivity (in the EM charged case) emerge automatically when the shear rigidity of the elastic state is destroyed by the proliferation of topological defects (quantum dislocations). Off-diagonal long range order in terms of the field operators of the constituent particles is not required. This is one of the outcomes of the broader pursuit presented in this paper. In essence, it amounts to the generalization of the well known theory of crystal melting in two dimensions by Nelson et al. [Phys. Rev. B 19 (1979) 2457; Phys. Rev. B 19 (1979) 1855], to the dynamical theory of bosonic states exhibiting quantum liquid-crystalline orders in 2 + 1 dimensions. We strongly rest on the field-theoretic formalism developed by Kleinert [Gauge fields in Condensed Matter, vol. II: Stresses and Defects, Differential Geometry, Crystal Defects, World Scientific, Singapore, 1989] for classical melting in 3D. Within this framework, the disordered states correspond to Bose condensates of the topological excitations, coupled to gauge fields describing the capacity of the elastic medium to propagate stresses. Our focus is primarily on the nematic states, corresponding with condensates of dislocations, under the topological condition that disclinations remain massive. The dislocations carry Burgers vectors as topological charges. Conventional nematic order, i.e., the breaking of space-rotations, corresponds in this field-theoretic duality framework with an ordering of the Burgers vectors. However, we also demonstrate that the Burgers vectors can quantum disorder despite the massive character of the disclinations. We identify the physical nature of the ‘Coulomb nematic’ suggested by Lammert et al. [Phys. Rev. Lett. 70 (1993) 1650; Phys. Rev. E 52 (1995) 1778] on gauge-theoretical grounds. The 2 + 1D quantum liquid crystals differ in fundamental regards from their 3D classical counterparts due to the presence of a dynamical constraint. This constraint is the glide principle, well known from metallurgy, which states that dislocations can only propagate in the direction of their Burgers vector. In the present framework this principle plays a central role. This constraint is necessary to decouple compression rigidity from the dislocation condensate. The shear rigidity is not protected, and as a result the shear modes acquire a Higgs mass in the dual condensate. This is the way the dictum that translational symmetry breaking goes hand in hand with shear rigidity emerges in the field theory. However, because of the glide principle compression stays massless, and the fluids are characterized by an isolated massless compression mode and are therefore superfluids. Glide also causes the shear Higgs mass to vanish at orientations perpendicular to the director in the ordered nematic, and the resulting state can be viewed as a quantum smectic of a novel kind. Our most spectacular result is a new hydrodynamical way of understanding the conventional electromagnetic Meissner state (superconducting state). Generalizing to the electromagnetically charged elastic medium (‘Wigner Crystal’) we find that the Higgs mass of the shear gauge fields, becoming finite in the nematic quantum fluids, automatically causes a Higgs mass in the electromagnetic sector by a novel mechanism.

PH as a trigger of peptide beta-sheet self-assembly and reversible switching between nematic and isotropic phases.

The hierarchical self-assembly of rationally designed synthetic peptides into beta-sheet tapes, ribbons, fibrils, and fibers opens up potentially useful routes to soft-solidlike materials such as hydrogels, organogels, or liquid crystals. Here, it is shown how incorporation of Glu (-CH(2)CH(2)COOH) or Orn (-CH(2)CH(2)CH(2)NH(2)) into the primary structure of an 11 amino acid peptide enables self-assembly to be rapidly (seconds) and reversibly controlled by simply changing pH. Solutions of monomeric peptide, typically at concentrations in excess of 0.003 v/v, can be switched within seconds to, for example, nematic gel states comprised of interconnected orientationally ordered arrays of fibrils or vice versa. This is to be compared with the lyophilized peptide dissolution route to nematic fluids and gels which is impracticably long, taking many hours or even days. An important design principle, that stabilization of fibrillar dispersions requires of the order of one unit of net positive or negative charge per peptide molecule, is first demonstrated and then used to design an 11 amino acid peptide P(11)-3 (CH(3)CO-Gln-Gln-Arg-Phe-Gln-Trp-Gln-Phe-Gln-Gln-Gln-NH(2)) whose self-assembly behavior is independent of pH (1 < pH < 10). pH control is then incorporated by appropriately positioning Glu or Orn side chains so that the peptide-peptide free energy of interaction in the tapelike substructure is strongly influenced by direct electrostatic forces between gamma-COO(-) in Glu(-) or delta-NH(3)(+) in Orn(+), respectively. This design principle is illustrated by the behavior of two peptides: P(11)-4 (CH(3)CO-Gln-Gln-Arg-Phe-Glu-Trp-Glu-Phe-Glu-Gln-Gln-NH(2)) which can be switched from its nematic to its isotropic fluid state by increasing pH and P(11)-5 (CH(3)CO-Gln-Gln-Orn-Phe-Orn-Trp-Orn-Phe-Gln-Gln-Gln-NH(2)) designed to exhibit the converse behavior. Acid-base titrations of fibrillar dispersions reveal deprotonation of the gamma-COOH of Glu or of the delta-NH(3)(+) of Orn(+) occurs over wide bands of up to 5 pH units, a feature of polyelectrolytes. The values of the energy parameters controlling self-assembly can therefore be smoothly and continuously varied by changing pH. This enables isotropic fluid-to-nematic transitions to be triggered by relatively small additions of acid or base, typically 1 part in 10(3) by volume of 1 M HCl or NaOH.

Local structure in nematic and isotropic liquid crystals

By computer simulations of systems of ellipsoids, we study the influence of the isotropic/nematic phase transition on the direct correlation functions (DCF) in anisotropic fluids. The DCF is determined from the pair distribution function by solving the full Ornstein–Zernike equation, without any approximations. Using a suitable molecular-fixed reference frame, we can distinguish between two qualitatively different contributions to the DCF: One which preserves rotational invariance, and one which breaks it and vanishes in the isotropic phase. We find that the symmetry preserving contribution is barely affected by the phase transition. However, symmetry breaking contributions emerge in the nematic phase and may become quite substantial. Thus the DCF in a nematic fluid is not rotationally invariant. In the isotropic fluid, the DCF is in good agreement with the prediction of the Percus–Yevick theory.

Generalized lattice Boltzmann algorithm for the flow of a nematic liquid crystal with variable order parameter

A lattice Boltzmann (LB) scheme is described, which recovers the equations developed by Qian-Sheng for the hydrodynamics of a nematic liquid crystal with a tensor order parameter. The standard mesoscopic LB scalar density is generalized to a tensor quantity and the macroscopic momentum, density, and tensor order parameter are recovered from appropriate moments of this mesoscopic density. A single lattice Boltzmann equation is used with a direction dependent Bhatnagar, Gross, and Krook (BGK) collision term, with additional forcing terms to recover the antisymmetric terms in the stress tensor. A Chapman-Enskog analysis is presented, which demonstrates that the Qian-Sheng scheme is recovered, provided a lattice with sixth-order isotropy is used. The method is validated against analytical results for a number of cases including flow alignment of the order tensor and the Miesowicz viscosities in the presence of an aligning magnetic field. The algorithm accurately recovers the predicted changes in the order parameter in the presence of aligning flow, and magnetic, fields. Preliminary results are given for an extension of the method to model the interface between isotropic and nematic fluids.

Small-Angle Neutron Scattering from Peptide Nematic Fluids and Hydrogels under Shear

Small-angle neutron scattering has been used to study the mesoscopic structure responsible for the nonlinear rheology of aqueous dispersions of self-assembling peptide fibrils (nematic-fluid states) and fibrillar networks (nematic hydrogels). The orientation of the nematic director has been studied as a function of the shear rate (0−500 s-1) in both gel and fluid phases. The powder-averaged scattering data from the fluid nematic phase has been modeled using a Kratky−Porod wormlike chain and the cross-sectional area (a stack of 8−10 tapes) of the self-assembled fibrils measured under flow in the direction of the velocity gradient. A separate observation of the aggregate structure in both the fluid and the gel states was possible in the tangential-velocity direction. An apparent increase in the diameter of the fibrils upon gelation is, in view of the electron micrographs, attributed to fiber formation by the entwining of pairs of fibrils: it is estimated that approximately 10% of the total contour length of the fibrils participates in these fiberlike junctions. The stress-controlled nonlinear rheology has also been studied, and the nematic fluids were found to display Type I shear thinning behavior, typical of liquid-crystalline polymers. Stress relaxation in the form of a loss of orientation only occurred at high concentrations (6 mM) in nematic gels. Furthermore, the gels were observed to display Lozenge shaped scattering at intermediate shear rates, indicative of mobile oriented fibrils in an unoriented network.

Nematic Homopolymers: From Segmented to Wormlike Chains

We present a density functional approach to orientational ordering in homopolymeric systems. The polymers are modeled as chains of identical rodlike segments connected via a simple generic bending potential. The segments are impenetrable to each other, and it is their mutual excluded volume that drives the transition from the orientationally disordered isotropic phase to the orientationally ordered nematic fluid. These excluded volume effects are accounted for within the so‐called Onsager approximation at the chain–chain level and in an independent pairwise overlap approximation at the segment–segment level. The Khokhlov and Semenov formalism for nematic wormlike polymers is shown to be an exact limiting case of our treatment. The ordering transition is studied analytically by using a linear stability analysis of the isotropic phase yielding the properties of the system at the isotropic‐nematic (I–N) bifurcation point. Using a numerical scheme, the equilibrium distribution functions in the nematic phase are calculated, and the location of the thermodynamic I–N transition is determined. For stiff bending potentials, chains with a relatively small number of segments are found to behave like wormlike chains, and we determine the regime of model parameters for which this identification holds.

Surface anchoring on layers of grafted liquid-crystalline chain molecules: A computer simulation

By Monte Carlo simulations of a soft ellipsoid model for liquid crystals, we study whether a layer of grafted liquid-crystalline chain molecules can induce tilt in a nematic fluid. The chains are fairly short (four monomers) and made of the same particles as the solvent. They are attached to a substrate which favors parallel (planar) alignment. At low grafting densities, the substrate dominates and we observe planar alignment. On increasing the grafting density, we find a first order transition from planar to tilted alignment. Beyond the transition, the tilt angle with respect to the surface normal decreases continuously. The range of accessible anchoring angles is quite large.

A study of orientational ordering in a fluid of dipolar Gay–Berne molecules using density-functional theory

We present a density-functional approach to describe the orientational ordering of nonpolar and dipolar Gay–Berne fluids. The first-order perturbation theory developed by Velasco et al. [J. Chem. Phys. 102, 8107 (1995)] for a Gay–Berne fluid is simplified and tested for molecules with a length to breath ratio of κ=3 and energy anisotropies of κ′=1, 1.25, 2.5, and 5. The theory is found to be in fair agreement with existing simulation data for the location of the isotopic–nematic phase transition, but it overestimates the vapor–liquid critical point of the fluid due to a description of the free energy at the mean-field level. The effect on the phase behavior of including a central longitudinal point dipole within the Gay–Berne molecule is studied using a correct treatment of the long-range dipolar contribution at the level of a second-order virial theory [B. Groh and S. Dietrich, Phys. Rev. E 50, 3814 (1994)]. For a given energy anisotropy of κ′=5 and reduced dipole moment μ*=0.5 we search for a stable ferroelectric nematic phase by changing the length to breath ratio κ. We do not find any evidence of ferroelectric nematic ordering for κ&amp;gt;1.5; the system only exhibits vapor–liquid and isotropic–nematic phase transitions for these values of the aspect ratios. For a slightly elongated and oblate shaped potential (e.g., κ=0.5), regions of stable isotropic–ferroelectric nematic and nematic–ferroelectric nematic phase coexistences are observed. The results of the theory indicate that a ferroelectic nematic fluid phase may be stabilized with respect to the positional ordering in the fluid of oblate dipolar particles. Comparison are made, where appropriate, with the existing results of Monte Carlo simulations for dipolar Gay–Berne fluids (Rull and co-workers, Molec. Phys. 94, 439 (1998); J. Chem. Phys. 109, 9529 (1998)).

Surface anchoring on liquid crystalline polymer brushes

We present a Monte Carlo study of the surface anchoring of a nematic fluid on swollen layers of grafted liquid crystalline chain molecules. The liquid crystalline particles are modeled by soft repulsive ellipsoids, and the chains are made of the same particles. An appropriately modified version of the configurational bias Monte Carlo algorithm is introduced, which removes and redistributes chain bonds rather than whole monomers. With this algorithm, a wide range of grafting densities could be studied. The substrate is chosen such that it favors a planar orientation (parallel to the surface). Depending on the grafting density, we find three anchoring regimes: planar, tilted, and perpendicular alignment. At low grafting densities, the alignment is mainly driven by the substrate. At high grafting densities, the substrate gradually loses its influence and the alignment is determined by the structure of the interface between the brush and the pure solvent instead.

An anchoring transition at surfaces with grafted liquid-crystalline chain molecules

The anchoring of nematic liquid crystals on surfaces with grafted liquid crystalline chain molecules is studied by computer simulations and within a mean field approach. The computer simulations show that a swollen layer of collectively tilted chains may induce untilted homeotropic (perpendicular) alignment in the nematic fluid. The results can be understood within a simple theoretical model. The anchoring on a layer of mutually attractive chains is determined by the structure of the interface between the layer of chain molecules and the solvent. It is controlled by an interplay between the attractive chain interactions, the translational entropy of the solvent and its elasticity. A second order anchoring transition driven by the grafting density from tilted to homeotropic alignment is predicted.

The hard ellipsoid-of-revolution fluid I. Monte Carlo simulations

We present the results of Monte Carlo simulations on a system of hard ellipsoids of revolution with length-to-breadth ratios a/b = 3, 2.75, 2, 1.25 and b/a = 3, 2.75, 2, 1.25. We identify four distinct phases, viz. isotropic fluid, nematic fluid, ordered solid and plastic solid. The coexistence points of all first order phase transitions are located by performing absolute free energy computations for all coexisting phases. We find nematic phases only for a/b ≥ 2.75 and a/b ≤ 1/2.75. A plastic solid is only observed for 1.25 ≥ a/b ≥ 0.8. It is found that the phase diagram is surprisingly symmetric under interchange of the major and minor axes of the ellipsoids.

Quantum theory of a nematic Fermi fluid

We develop a microscopic theory of the electronic nematic phase proximate to an isotropic Fermi liquid in both two and three dimensions. Explicit expressions are obtained for the small amplitude collective excitations in the ordered state; remarkably, the nematic Goldstone mode (the directorwave) is overdamped except along special directions dictated by symmetry. At the quantum critical point we find a dynamical exponent of $z=3$, implying stability of the gaussian fixed point. The leading perturbative effect of the overdamped Goldstone modes leads to a breakdown of Fermi liquid theory in the nematic phase and to strongly angle dependent electronic self energies around the Fermi surface. Other metallic liquid crystal phases, {\it e. g.} a quantum hexatic, behave analogously.

Novel Glass-Forming Liquid Crystals. 6. High-Temperature Glassy Nematics

To furnish new insight into structure−property relationships governing glassy nematic liquid crystals, novel material systems were synthesized and characterized. Highly ordered, solid films were also prepared via spin-coating for the determination of optical birefringence. It was found that a linear nematogen, such as the cyanoterphenyl group, contributes to an elevated glass transition temperature and a wide nematic fluid temperature range with a mixed or an extended core structure. However, an angular nematogen, such as the cyanophenylnaphthyl group, is more versatile in inducing glass formation with a broader range of core structures. Morphologically stable, glassy nematics with a Tg close to 130 °C, a Tc close to 350 °C, a nematic fluid temperature range of 265 °C, and an optical birefringence of 0.44 accomplished in this study represent significant improvements over existing materials. A stereochemical modification of the bicyclooctene ring from an exo-, exo- to an endo-, and exo-configuration, fluor...

Structure and rheology of model side-chain liquid crystalline polymers with varying mesogen length

We probed the structural transitions and rheological properties of norbornene-based polymeric liquid crystals with attached side mesogenic groups of varying length. Whereas the short side chain liquid crystals (C5) formed a nematic mesophase, the long ones (C9) formed a smectic-A solid. The degree of polymerization of the main backbone affected the isotropic-mesophase transition temperatures, but did not influence the change of the mesophase dynamics from the isotropic to the anisotropic state. The temperature dependence of the shift factors obtained from the time-temperature superposition were divided into three regions, namely isotropic, mesophase, and transition, all exhibiting Arrhenius behavior except for the nematic fluid, which followed a WLF dependence. A remarkable strain hardening observed in both nematic and smectic samples was attributed to the dynamic coupling of the main chain and the mesogenic side groups. By applying large amplitude oscillatory shear, macroscopic alignment was achieved; the long recovery times upon flow cessation suggested a very slow structural reorganization, which was much longer in the smectics compared to the nematics, possibly due to the involvement of smaller length scales in the former case.

Ferroelectric Nematic and Smectic Liquid Crystals from Tapered Molecules

Nematic fluids with polar order could be most useful new molecular materials. However, such ferroelectric liquid crystals have not been observed as yet. This paper describes the first computer simulations of a ferroelectric nematic phase made from simple tapered particles as shown in the picture and gives some hints about the relevant molecular features.