Nematic-isotropic interfaces under shear: a molecular-dynamics simulation

We present a large-scale molecular-dynamics study of nematic-paranematic interfaces under shear. We use a model of soft repulsive ellipsoidal particles with well-known equilibrium properties, and consider interfaces which are oriented normal to the direction of the shear gradient (common stress case). The director at the interface is oriented parallel to the interface (planar). A fixed average shear rate is imposed with moving periodic boundary conditions, and the heat is dissipated with a profile-unbiased thermostat. First, we study the properties of the interface at one particular shear rate in detail. The local interfacial profiles and the capillary wave fluctuations of the interfaces are calculated and compared with those of the corresponding equilibrium interface. Under shear, the interfacial width broadens and the capillary wave amplitudes at large wavelengths increase. The strain is distributed inhomogeneously in the system (shear banding), the local shear rate in the nematic region being distinctly higher than in the paranematic region. Surprisingly, we also observe (symmetry-breaking) flow in the vorticity direction, with opposite direction in the nematic and the paranematic state. Finally, we investigate the stability of the interface for other shear rates and construct a nonequilibrium phase diagram.     

Computational modelling of nematic phase ordering by film and droplet growth over heterogeneous substrates

This paper presents a computational study of defect nucleation associated with the kinetics of the isotropic‐to‐nematic phase ordering transition over heterogeneous substrates, as it occurs in new liquid crystal biosensor devices, based on the Landau–de Gennes model for rod‐like thermotropic nematic liquid crystals. Two regimes are identified due to interfacial tension inequalities: (i) nematic surface film nucleation and growth normal to the heterogeneous substrate, and (ii) nematic surface droplet nucleation and growth. The former, known as wetting regime, leads to interfacial defect shedding at the moving nematic‐isotropic interface. The latter droplet regime, involves a moving contact line, and exhibits two texturing mechanisms that also lead to interfacial defect shedding: (a) small and large contact angles of drops spreading over a heterogeneous substrate, and (b) small drops with large curvature growing over homogeneous patches of the substrate. The numerical results are consistent with qualitative defect nucleation models based on the kinematics of the isotropic–nematic interface and the substrate–nematic–isotropic contact line. The results extend current understanding of phase ordering over heterogeneous substrates by elucidating generic defect nucleation processes at moving interfaces and moving contact lines.     

Density functional theory study of the nematic-isotropic transition in an hybrid cell

We have employed the density functional theory formalism to investigate the nematic-isotropic capillary transitions of a nematogen confined by walls that favor antagonist orientations to the liquid crystal molecules (hybrid cell). We analyze the behavior of the capillary transition as a function of the fluid-substrate interactions and the pore width. In addition to the usual capillary transition between isotropiclike to nematiclike states, we find that this transition can be suppressed when one substrate is wet by the isotropic phase and the other by the nematic phase. Under this condition the system presents interfacelike states which allow us to continuously transform the nematiclike phase to the isotropiclike phase without undergoing a sharp phase transition. Two different mechanisms for the disappearance of the capillary transition are identified. When the director of the nematiclike state is homogeneously planar-anchored with respect to the substrates, the capillary transition ends up in a critical point. This scenario is analogous to the observed in Ising models when confined in slit pores with opposing surface fields which have critical wetting transitions. When the nematiclike state has a linearly distorted director field, the capillary transition continuously transforms in a transition between two nematiclike states.     

Theory of solvation in polar nematics

We develop a linear response theory of solvation of ionic and dipolar solutes in anisotropic, axially symmetric polar solvents. The theory is applied to solvation in polar nematic liquid crystals. The formal theory constructs the solvation response function from projections of the solvent dipolar susceptibility on rotational invariants. These projections are obtained from Monte Carlo simulations of a fluid of dipolar spherocylinders which can exist both in the isotropic and nematic phases. Based on the properties of the solvent susceptibility from simulations and the formal solution, we have obtained a formula for the solvation free energy which incorporates the experimentally available properties of nematics and the length of correlation between the dipoles in the liquid crystal. The theory provides a quantitative framework for analyzing the steady-state and time-resolved optical spectra and makes several experimentally testable predictions. The equilibrium free energy of solvation, anisotropic in the nematic phase, is given by a quadratic function of cosine of the angle between the solute dipole and the solvent nematic director. The sign of solvation anisotropy is determined by the sign of dielectric anisotropy of the solvent: solvation anisotropy is negative in solvents with positive dielectric anisotropy and vice versa. The solvation free energy is discontinuous at the point of isotropic-nematic phase transition. The amplitude of this discontinuity is strongly affected by the size of the solute becoming less pronounced for larger solutes. The discontinuity itself and the magnitude of the splitting of the solvation free energy in the nematic phase are mostly affected by microscopic dipolar correlations in the nematic solvent. Illustrative calculations are presented for the equilibrium Stokes shift and the Stokes shift time correlation function of coumarin-153 in 4-n-pentyl-4'-cyanobiphenyl and 4,4-n-heptyl-cyanopiphenyl solvents as a function of temperature in both the nematic and isotropic phases.     

Viscoelastic theory for nematic polymer interfaces

A macroscopic theory for the dynamics of compressible nematic polymer‐viscous fluid interfaces is developed from first principles. The theory is used to define and characterize the basic interfacial viscoelastic material properties of the ordered interfaces. The theory is based on a decomposition of the kinematic fields and nematic tensor order parameter that takes into account the symmetry breaking of the interface. The interfacial rate of entropy production used to identify the interfacial viscoelastic modes is given in terms of surface rate of deformation tensor and the surface Jaumann derivative of the tangential component nematic tensor order parameter. The derived surface viscous stress tensor is asymmetric and thus describes surface flow‐induced changes in the tensor order parameter. Consistency with the Boussinesq surface fluid appropriate for Newtonian interfaces is established. The interfacial material functions are identified as the dynamic surface tension, the interfacial dilational viscosities, and the interfacial shear viscosities. The interfacial material functions depend on the surface tensor order parameter and as a consequence anisotropy is their characteristic feature. Two characteristic interfacial tensions and two dilational viscosities are predicted depending on the director orientation. In addition six interfacial shear viscosities arise as the directors sample the velocity, velocity gradient, and vorticity directions. Finally the theory provides for the necessary theoretical tools needed to describe the interfacial dynamics of nematic polymer interfaces, such as capillary instabilities, Marangoni flows, and wetting phenomena.     

Nematic-isotropic interfacial tension anisotropy of a calamitic lyotropic liquid crystal

In a planar oriented sample of a calamitic nematic lyotropic system (mixture of sodium lauryl sulphate/water/decanol), isotropic pretransitional domains appear at the nematic to isotropic transition. The domains are oblong in shape with the long axis along the orientational direction. We show experimental evidence that this oblong shape is determined by the nematic-isotropic interfacial tension anisotropy. Two uniparametric models of simple angular dependences for the interfacial tension are tested. Using the differential system obtained from the Young-Laplace condition at the nematic-isotropic interface, the domain shape can be numerically calculated for each value of the interfacial tension anisotropy. By processing the values of the transmitted light through both an isolated isotropic domain and its surrounding nematic zone, we obtain the anisotropy of the interfacial tension as the main fitting parameter. An estimation of the ratio of the extreme values for the interfacial tension is given.     

Polymer blends containing liquid crystal polymers

Polymer blends can be either composed of mixtures of flexible components, of a stiff chain and a flexible macromolecule, or of two stiff-chain polymers. All three cases may be dealt with in terms of the Flory lattice model. Special attention is paid to the influence of liquid crystalline order on the miscibility of the two polymers. For isotropic mixtures all three cases may be described in terms of the usual Flory–Huggins approximation. If a nematic phase is formed the miscibility of blends of rigid rods with flexible macromolecules (molecular composites) is strongly reduced because of entropic reasons. Highly ordered mixture of two stiff-chain polymers in melt can be described in terms of the regular solution theory leading to the same miscibility criterion as is valid for two flexible polymers. All deductions are compared to recent experimental work.     

Slow dynamics of banana-shaped molecules: a theoretical approach to analyze 2H-NMR T2 relaxation times

In the present work, we analyze pulsed deuterium NMR experiments performed on the isotropic and nematic phases of the banana-shaped liquid-crystalline mesogen 4-chloro-1,3-phenylene bis{4-4'-(11-undecenyloxy) benzoyloxy} benzoate (ClPbis11BB) selectively deuterated on the central ring. Starting from a previous evidence of unusual slow dynamics in the isotropic phase (Domenici V. et al., J. Phys. Chem. B 2005, 109, 769), a quantitative and model-supported analysis of the deuterium NMR data is performed here by accounting for slow-motional modulation of the magnetic anisotropies through the full solution of the stochastic Liouville equation. Focusing on the quadrupolar echo experiments performed in the nematic phase, the analysis of the transverse relaxation rate has been carried out by considering single-molecule motions and fluctuations of the local director. The main conclusions are: (a) director fluctuations are not relevant on driving the signal relaxation; (b) molecular reorientations about transverse axes control the dynamic regime of the signal relaxation and impose a full slow-motional treatment; (c) the small amplitude tumbling of the molecule within the wells of orientational potential occurs with characteristic times up to the microsecond. The outcome of our analysis has to be taken as indicative of very slow dynamics concerning out-of-plane motions of the molecules. Besides the specific application, this paper also offers the methodological tools to treat the pulsed deuterium NMR experiment in the slow-motional regime of reorientational motions and provides a detailed comparison with the usually employed fast-motional approximation.     

The director distribution in a spinning nematic mesophase subject to a statis magnetic field

We have determined the probability distribution function for the director in a spinning nematic mesophase subject to a static magnetic field using electrons resonance spectroscopy. For low spinning speeds the director is found to be inclined to the magnetic field as predicted by a continum theory analysis of the system; there is however a small spread in the angle made by the director with the field. This is inhomogeneity in the director alignment increases smoothly as the angular velocity of the mesophase is increased until at high speeds the director adopts an isotropic distribution mesophase which account for the dispersion in the director produced by sample rotation.     

Topologically non-equivalent textures generated by the nematic electrohydrodynamics

Some classes of nematic liquid crystals can be driven through turbulent regimes when forced by an external electric field. In contrast to isotropic fluids, a turbulent nematic exhibits a transition to a stochastic regime that is characterised by a network of topological defects. We study the deformations arising after the electric field has been switched-off. In contrast to the turbulent regime, the relaxation of this topological-defect regime involves the annihilation of an interlacement of defect lines. We show that these defect lines separate regions of the nematic having topologically non-equivalent textures.     

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.     

Molecular theory of dielectric relaxation in nematic dimers

This paper reports a theory for the dielectric relaxation of dimeric mesogenic molecules in a nematic liquid crystal phase. Liquid crystal dimers consist of two mesogenic groups linked by a flexible chain. Recent experimental studies [D. A. Dunmur, G. R. Luckhurst, M. R. de la Fuente, S. Diez, and M. A. Perez Jubindo, J. Chem. Phys. 115, 8681 (2001)] of the dielectric properties of polar liquid crystal dimers have found unexpected results for both the static (low frequency) and variable frequency dielectric response of these materials. The theory developed in this paper provides a quantitative model with which to understand the observed experimental results. The mean-square dipole moments of alpha,omega-bis[(4-cyanobiphenyl-4'-yl]alkanes in a nematic phase have been calculated using both the rotational isomeric state model and a full torsional potential for the carbon-carbon bonds of the flexible chain. The orienting effect of the nematic phase is taken into account by a parametrized potential of mean torque acting on the mesogenic groups and the segments in the flexible chain. Results of calculations using the full torsional potential are in excellent agreement with experimental results for comparable systems. The probability density p(eq)(beta(A),beta(B)) for the orientation of the mesogenic groups (A,B) along the nematic director is also calculated. The resultant potential of mean torque is a surface characterized by four deep energy wells or sites equivalent to alignment of the terminal groups A and B approximately parallel and antiparallel to the director; of course, the reversal of the director leads to equivalent sites. This potential energy surface provides the basis for a kinetic model of dielectric relaxation in nematic dimers. Solution of the Fokker-Planck equation corresponding to this four-site model gives the time dependence of the site populations, and hence the time-correlation functions for the total dipole moment along the director. In this model the end-over-end rotation of the molecule, corresponding to simultaneous reversal of both mesogenic groups, is excluded because the activation energy is too large. Results are presented for a number of cases, in which a dipole is located on one or both of the mesogenic groups, and additionally where the groups differ in size. For the latter, under particular conditions, the correlation function exhibits a biexponential decay, which corresponds to two low frequency absorptions in the dielectric spectrum. This is exactly what has been observed for nonsymmetric nematic dimers having different groups terminating a flexible chain. Experimental results over a range of temperature for the nonsymmetric dimer alpha-[(4-cyanobiphenyl)-4'-yloxy]-omega-(4-decylanilinebenzylidene-4'-oxy)nonane can be fitted precisely to the theory, which provides new insight into the orientational and conformational dynamics of molecules in ordered liquid crystalline phases.     

Dynamic behaviour at a nematic liquid crystal-rubbednylon interface using evanescent wave photon correlation spectroscopy

Photon correlation spectroscopy of light scattered by director fluctuations from an evanescent optical wave propagating in the nematic liquid crystal 5CB is used to study the interfacial dynamic behaviour of the liquid crystal. The intensity correlation function of light scattered by interfacial orientation fluctuations is measured by illuminating to give a short optical penetration depth within the nematic. These surface scattering correlation functions strongly differ from the bulk correlation function and are interpreted in terms of a nematic surface orientation mode arising from the coupling between the director field and the fluid velocity. It is shown that the analysis of the surface mode gives a method for measuring anchoring energies in liquid crystals. The anchoring energy obtained for rotation of the director away from the rubbing direction about an axis normal to the surface for 5CB at a rubbed nylon surface is 7.14±0.7 × 10-² ergcm-².     

Capillary waves in a colloid-polymer interface

The structure and the statistical fluctuations of interfaces between coexisting phases in the Asakura-Oosawa model [J. Chem. Phys. 22, 1255 (1954)] for a colloid-polymer mixture are analyzed by extensive Monte Carlo simulations. We make use of a recently developed grand canonical cluster move with an additional constraint stabilizing the existence of two interfaces in the (rectangular) box that is simulated. Choosing very large systems, of size L x L x D with L=60 and D=120, measured in units of the colloid radius, the spectrum of capillary wave-type interfacial excitations is analyzed in detail. The local position of the interface is defined in terms of a (local) Gibbs surface concept. For small wave vectors capillary wave theory is verified quantitatively, while for larger wave vectors pronounced deviations show up. When one analyzes the data in terms of the concept of a wave vector-dependent interfacial tension, a monotonous decrease of this quantity with increasing wave vector is found. Limitations of our analysis are critically discussed.     

Molecular dynamics study of the n-hexane-water interface: towards a better understanding of the liquid-liquid interfacial broadening

By molecular dynamics simulations, we have studied the hydrophilic-hydrophobic interface between water and n-hexane liquid phases. For all temperatures studied our computed interfacial tension agrees very well with the experimental value. However, the interfacial width calculated from capillary wave theory systematically overestimates the width obtained from fitting either the total density or composition profile. We rationalize the applicability of capillary wave theory for our system by reconsidering the usual value taken for the correlation length. This is motivated by the presence of order at the interface. Possible implications for recent experimental studies on the structure of model alkane-water interfaces are discussed, including the significance of the intrinsic width parameter.     

Density functional theory of freezing of a system of conjugated oligomers parameterised via Gay–Berne potential

Density functional theory (DFT) of freezing is used to study the isotropic–nematic, isotropic–smectic A and nematic–smectic A phase transitions in a system of large, semi-flexible conjugated oligomers parameterised within Gay–Berne (GB) potential. The pair correlation functions of the isotropic fluid, used as structural inputs in the DFT, are calculated by solving the Percus–Yevick integral equation theory. Large number of spherical harmonic coefficients of each orientation-dependent functions has been considered to ensure the numerical accuracy at different densities and temperatures for the system of these model GB ellipsoids having large aspect ratio (length-to-breadth ratio). We found that the system of GB ellipsoids parameterised for conjugated oligomers shows stable isotropic, nematic and smectic A phases. At low temperatures, on increasing the density, isotropic fluid makes a direct transition to smectic A phase. Nematic phase get stabilised in between the isotropic and smectic A phases on increasing the temperature. Using the transition parameter obtained through the DFT, we have plotted the temperature–density and pressure–temperature phase diagrams which are found to be qualitatively similar to the one obtained in simulations for the systems with low aspect ratio GB particles.     

Dielectric spectroscopy of liquid crystalline dispersions

We describe dielectric spectroscopy measurements on dispersions of two thermotropic liquid crystals (5CB and 8CB) in a poly(dimethylsiloxane) matrix. 5CB exhibits nematic and isotropic phases, while 8CB exhibits smectic, nematic, and isotropic phases. The spectra of the dispersions exhibit a temperature-dependent dielectric relaxation in the interval from 100 to 1000 Hz, with relaxation times that depend strongly on whether the dispersed phase is isotropic, nematic, or smectic. The dielectric relaxation times also depend on the viscosity of the matrix fluid. These results suggest a coupling between the electric field and the mechanics of the interface that affects the spectrum of the dispersed phase and shifts the Maxwell-Wagner interfacial polarization peak.     

Non-linear liquid crystal waveguides

Abstract

We consider a cylindrical nematic liquid crystal waveguide with an infinite homogeneous isotropic cladding, and study the propagation of TM and TE modes. The dielectric tensor of the liquid crystal core which governs wave propagation is determined by the configuration of the nematic director. For TM modes, propagating optical fields alter the director configuration, and thus change the dielectric tensor. For both TM and TE modes, we consider the effects of the propagating fields on the order parameter tensor. We use an iterative numerical scheme to determine the propagation constant as a function of optical power. For the TM modes, the propagation constant increases continuously with the power. For the TE modes, an abrupt increase is found.     

Morphology of microphase separated domains in rod-coil copolymer melts

We investigate the morphology of microphase separated domains in diblock copolymers where each chain consists of a stiff rod block and a flexible coil block. A simplified phenomenological model system is introduced, which is coarse-grained in terms of the local concentration difference between the two blocks and the local director field of the rod part. Computer simulations of this set of time-evolution equations in two dimensions show in the weak segregation regime that the elastic energy in the rod-block rich domains affects drastically the structures of microphase separated domains. A coil-to-rod transition is incorporated into the model system to examine the elastic and anisotropic effects. The effects of the external electric field are also investigated to control the domain morphology.