Tension gradients and Marangoni flows in nematic interfaces

This brief report (i) presents equations that govern the balance of tangential forces in interfaces between isotropic viscous fluids and nematic liquid crystals, and (ii) establishes the physical origin of nematic Marangoni flows. It is shown that surface gradients in the orientation dependent surface free energy gives rise to tangential nematic Marangoni forces. Tangential nematic Marangoni forces are caused by surface gradients of the nematic tensor order parameter, and the kinetic coefficient characterizing this interfacial phenomenon is proportional to nematic elastic storage. Expressions of the Marangoni forces using a classical constitutive equation for the surface free energy are given for general and uniaxial nematic ordering states. Nematic Marangoni flows or nematocapillarity augments the class of Marangoni flows present in electrocapillarity, diffusocapillarity, and thermocapillarity.     

Effects of severe-strain-induced defects on the mechanical response of two kinds of high-angle grain boundaries

ABSTRACT

Grain boundaries of metallic materials subjected to severe plastic deformation exhibit significantly enhanced diffusivity and excess energy compared with their relaxed poly- or bi-crystalline counterparts even when the macroscopic degrees of freedom are the same in both types of grain boundaries. Boundaries of excess energy are/can be relaxed by annealing. As a first step in accounting for this experimentally observed high-energy state of general high-angle grain boundaries subjected to severe plastic deformation, a concept of localised basic shear units and the presence of localised extra free volume in these units situated in different locations in the grain boundaries, which was originally proposed to explain steady-state structural superplastic flow, is made use of. Using MD simulation, the mechanical response of these modified grain boundaries is compared with that of their relaxed state. The results are also compared with a case of a homogeneous distribution of extra free volume within the grain boundary. The localised shear units containing extra free volume introduced in the grain boundaries are found to alter their physical and mechanical features strongly, which, in turn, drastically affect, consistent with experimental results, the mechanical response of the heavily deformed material.     

Strongly anisotropic elastic moduli of nematic elastomers: Analytical expressions and nonlinear temperature dependence

Exact formulae for the elastic moduli of the nematic elastomers are obtained by the implicit function method based on somewhat general energy functions. The formulae indicate that both the moduli parallel and perpendicular to the director of the nematic elastomers are smaller than the modulus of the classical elastomers because of the mechanical-nematic coupling. Moreover, the moduli are generally anisotropic due to the biaxiality induced by stretching the nematic elastomers perpendicular to the director. Then we get the explicit analytical expressions of the parallel and perpendicular moduli by making use of the Landau-de Gennes free energy and the neo-classical elastic energy. Very different from the classical elastomers, they are both strongly nonlinear functions of the temperature in the nematic phase. Furthermore, their ratio, the degree of anisotropy, changes with the temperature as well. The results agree qualitatively with some experiments. Better quantitative agreement is obtained by some modifications of the constitutive relation of the elastic energy.     

Orientational coupling amplification in ferroelectric nematic colloids

We investigated the physical properties of low concentration ferroelectric nematic colloids, using calorimetry, optical methods, infrared spectroscopy, and capacitance studies. The resulting homogeneous colloids possess a significantly amplified nematic orientational coupling. We find that the nematic orientation coupling increases by approximately 10% for particle concentrations of 0.2%. A manifestation of the increased orientational order is that the clearing temperature of a nematic colloid increases by up to 40 degrees C compared to the pure liquid crystal host. A theoretical model is proposed in which the ferroelectric particles induce local dipoles whose effective interaction is proportional to the square of the orientational order parameter.     

Theory of excluded volume effects in nematic liquid crystals

An expression for the free energy of nematic liquid crystals is given by taking account of the excluded volume effects as well as dispersion forces. The dependence of nematic order on concentration and/or shape of molecules is discussed.     

Reexamining the phase diagram of the Gay—Berne fluid

This work reexamines and updates earlier investigations on the phase behaviour of the Gay-Berne liquid crystal model, concentrating on the effect of varying temperature. Constant volume and constant pressure Monte Carlo simulations are combined for systems consisting of N = 500 molecules along different isotherms over the reduced temperature range 0.60 ≤ T ≤ 1.25. As in previous simulation studies of the model, the study identifies nematic and smectic B phases on compressing the isotropic fluid, the particular phase sequence depending on temperature. The nematic phase is found to be stable with respect to the isotropic phase for reduced temperatures T ≥ 0.75. In the temperature range 0.75 ≤ T ≤ 1.25, the phase boundaries of the isotropic-nematic transition are obtained by computing the Helmholtz free energy of both phases from thermodynamic integration. From the simulation data, the relative volume change at the isotropic-nematic transition is about 2%, and this value appears to be rather insensitive to changes in temperature. On compressing the nematic phase, the Gay-Berne fluid undergoes a strong first-order transition to the smectic B phase. This transition is studied by using constant pressure simulation, and the coexistence properties are estimated from the limits of mechanical stability of the nematic phase. Larger relative volume changes are found at the transition than those suggested by previous studies, with typical values increasing up to 10.5% as the temperature is decreased. The results are consistent with the existence of strong coupling between nematic and smectic order parameters. For temperatures T ≤ 0.70 the nematic phase is no longer stable, and the phase sequence isotropic-smectic B is observed. Therefore, the Gay-Berne model exhibits an isotropic-nematic-smectic B triple point. Extrapolating the present simulation data, this triple point is located approximately at reduced temperature T_INB ? 0.70 and reduced pressure P_INB ? 1.825.     

Molecular field theory for nematic liquid crystal film with finite layers

The nematic liquid crystal film composed of n molecular layers is studied based upon a spatially anisotropic pair potential, which reproduces approximately the elastic free energy density. On condition that the system has perfect nematic order, as in the Lebwohl—Lasher model, the director in the film is isotropic. The effect of the temperature is investigated by means of molecular field theory. Some new results are obtained. Firstly, symmetry breaking takes place when taking account of the temperature, and the state with the director along the normal of the film has the lowest free energy. Secondly, the N—I phase transition temperature increases as an effect of finite sizes instead of decreasing as in the Lebwohl—Lasher model. Thirdly, the nematic order is induced in the layers near the surface in the isotropic phase.     

Mean-Field Limit and Phase Transitions for Nematic Liquid Crystals in the Continuum

We discuss thermotropic nematic liquid crystals in the mean-field regime. In the first part of this article, we rigorously carry out the mean-field limit of a system of N rod-like particles as \(N\rightarrow \infty \), which yields an effective ‘one-body’ free energy functional. In the second part, we focus on spatially homogeneous systems, for which we study the associated Euler–Lagrange equation, with a focus on phase transitions for general axisymmetric potentials. We prove that the system is isotropic at high temperature, while anisotropic distributions appear through a transcritical bifurcation as the temperature is lowered. Finally, as the temperature goes to zero we also prove, in the concrete case of the Maier–Saupe potential, that the system converges to perfect nematic order.     

Enhancement of Nematic Order and Global Phase Diagram of a Lattice Model for Coupled Nematic Systems

We use an infinite-range Maier–Saupe model, with two sets of local quadrupolar variables and restricted orientations, to investigate the global phase diagram of a coupled system of two nematic subsystems. The free energy and the equations of state are exactly calculated by standard techniques of statistical mechanics. The nematic–isotropic transition temperature of system A increases with both the interaction energy among mesogens of system B, and the two-subsystem coupling J. This enhancement of the nematic phase is manifested in a global phase diagram in terms of the interaction parameters and the temperature T. We make some comments on the connections of these results with experimental findings for a system of diluted ferroelectric nanoparticles embedded in a nematic liquid-crystalline environment.     

Lattice Boltzmann Simulation of 3D Nematic Liquid Crystal near Phase Transition

Phase transition between nematic and isotropic liquid crystal is a very weak first order phase transition.We avoid to use the normal Landau-de Gennes‘s free energy that reduces a strong first order transition,and set up a data base of free energy calculated by means of Tao-Sheng-Lin‘s extended molecular field theory that can explain the experiments of the equilibrium properties of nematic liquid crystal very well.Then we use the free energy method of lattice Boltzmann developed by Oxford group to study the phase decomposition,pattern formation in the flow of the liquid crystal near transition temperature.     

Coherent transmission and angular structure of light scattering by monolayer films of polymer dispersed liquid crystals with inhomogeneous boundary conditions

We consider monolayer polymer films with oriented droplets of a nematic liquid crystal (LC). Relations for the coherent transmission coefficients of a layer of oriented ellipsoidal droplets and for the intensity of light scattered by monolayers of spherical and spheroidal droplets have been obtained. The amplitude-phase screen model and the interference approximation of the theory of multiple wave scattering have been used. To describe light scattering by an individual ellipsoidal droplet with inhomogeneous surface binding, we have developed an anomalous diffraction approximation. For monolayers of spherical LC droplets, the coherent scattering coefficients and the angular scattering structure have been analyzed. The internal structure of nematic droplets have been calculated by the relaxation method based on the solution of the minimization problem of the free energy volume density. We have studied basic regular features of light scattering by a monolayer with homogeneous and inhomogeneous boundary conditions at the LC-polymer interface. We show that, for films that contain droplets with inhomogeneous boundary conditions of the tangentially normal type, the angular structure of the scattered light is asymmetric with respect to the polar scattering angle.     

Free energy of semiflexible polymers and structure of interfaces

The free energy of semiflexible polymers is calculated as a functional of the compositional scalar order parameter and the orientational order parameter of second-rank tensor S_ij on the basis of a microscopic model of wormlike chains with variable segment lengths. We use a density functional theory and a gradient expansion to evaluate the entropic part of the free energy, which is given in a power series of .The interaction term of the free energy is derived with a random phase approximation. For the rigid rod limit, the nematic-isotropic transition point is given by , N and w being the degree of polymerization and the anisotropic interaction parameter, respectively, and the degree of ordering at the transition point is 0.33448. We also find that the contour length of polymer chains becomes larger in a nematic phase than in an isotropic phase. Interface profiles are obtained numerically for some typical cases. In the neighborhood of isotropic-isotropic interfaces, polymer chains tend to align parallel to the interface on the polymer-rich side and perpendicular on the poor side. When an isotropic region and a nematic region coexist, orientational order parallel to the interface is preferred in the nematic region. Received: 28 May 1998 / Revised: 12 August 1998 / Accepted: 8 September 1998     

Simulations of nematic homopolymer melts using particle-based models with interactions expressed through collective variables

We develop a hybrid Monte Carlo approach for modelling nematic liquid crystals of homopolymer melts. The polymer architecture is described with a discrete worm-like chain model. A quadratic density functional accounts for the limited compressibility of the liquid, while an additional quadratic functional of the local orientation tensor of the segments captures the nematic ordering. The approach can efficiently address large systems parametrized according to volumetric and conformational properties, representative of real polymeric materials. The results of the simulations regarding the influence of the molecular weight on the isotropic-nematic transition are compared to predictions from a Landau-de Gennes free energy expansion. The formation of the nematic phase is addressed within Rouse-like dynamics, realized using the current model.     

Director deformation in a nematic liquid crystal with a ferromagnetic nanoparticle suspension

In view of the recent interest regarding nematic liquid crystals with a nanoparticle suspension, we investigate the director dynamics of a nematic matrix in the perspective of a soliton framework. The nematic liquid crystal is dispersed with ferromagnetic nanoparticles in order to enhance the director activity associated with the improved magnetization of the ferronematic matrix. The free energy density of the nematic matrix is deduced to be the Ginzburg–Landau (GL) equation for the director reorientation. We obtain a series of localized solutions for the GL equation, and also the dynamics is expressed in terms of the soliton evolution for the director by using the standard Hirota bilinearization procedure.     

A generic equation of state for liquid crystalline phases of hard-oblate particles

A generic equation of state (EoS) is developed for the hard cylindrical disc model to describe the isotropic phase of hard cut-sphere particles introducing a correction parameter to incorporate the negative contributions from higher-order virial coefficients. The isotropic–nematic–columnar phase diagram of hard cut-sphere fluids is investigated combining the new EoS with a scaled Onsager free energy for the nematic phase and an extended cell theory for columnar phase. By mapping the virial coefficients of an oblate spherocylinder on to those of the cylindrical disc (which are known algebraically), the new generic EoS is used to describe the isotropic and nematic phases of hard oblate spherocylinder particles. The predictions of the generic EoS are compared with available simulation data.     

Study of intrinsic anchoring in nematic liquid crystals based on modified Gruhn-Hess pair potential

A nematic liquid crystal slab composed of N molecular layers is investigated using a simple cubic lattice model, based upon the molecular pair potential which is spatially anisotropic and dependent on elastic constants of liquid crystals. A perfect nematic order is assumed in the theoretical treatment, which means the orientation of the molecular long axis coincides with the director of liquid crystal and the total free energy equals to the total interaction energy. We present a modified Gruhn-Hess model, which is relative to the splay-bend elastic constant K₁₃. Furthermore, we have studied the free nematic interfacial behavior (intrinsic anchoring) by this model in the assumption of the perfect nematic order. We find that the preferred orientation at the free interface and the intrinsic anchoring strength change with the value of modification, and that the director profile can be determined by the competition of the intrinsic anchoring with external forces present in the system. Also we simulate the intrinsic anchoring at different temperatures using Monte Carlo method and the simulation results show that the intrinsic anchoring favors planar alignment and the free interface is more disordered than the bulk.     

Ideal focusing in the theory of electrostatic spectrographs

The problem of synthesis of field structures, in which the spectrographic principle of separating charged particle flows is implemented and ideal angular focusing is simultaneously observed in the symmetry plane for each energy value, is formulated. The search for spectrographic media is effectively carried out with the help of inverse mechanical problems. Two approaches are proposed, one of which involves the reduction to the integral Abel equation and the other is based on the application of the Goursat theorem. The algorithms for the synthesis of spectrographic media with ideal focusing of flows are described in detail, and possible versions of solutions corresponding to representatives of two structural classes (with potentials homogeneous in the Euler sense and with homogeneous potentials with a logarithmic singularity) are indicated. The prospects of developing high-transmission spectrographs for energy analysis are outlined.     

Giant flexoelectricity of bent-core nematic liquid crystals

Flexoelectricity is a coupling between orientational deformation and electric polarization. We present a direct method for measuring the flexoelectric coefficients of nematic liquid crystals (NLCs) via the electric current produced by periodic mechanical flexing of the NLC's bounding surfaces. This method is suitable for measuring the response of bent-core liquid crystals, which are expected to demonstrate a much larger flexoelectric effect than traditional, calamitic liquid crystals. Our results reveal that not only is the bend flexoelectric coefficient of bent-core NLCs gigantic (more than 3 orders of magnitude larger than in calamitics) but also it is much larger than would be expected from microscopic models based on molecular geometry. Thus, bent-core nematic materials can form the basis of a technological breakthrough for conversion between mechanical and electrical energy.     

Threshold and saturation properties of the field-induced twist cell with two parameters weak anchoring boundaries

On the basis of two-parameter formula of weak surface coupling anchoring energy of nematic liquid crystals proposed by Zhao et al recently, the general torque equilibrium equation and boundary conditions of the director have been obtained and the threshold field as well as the saturation field of the field-induced twist cell have been analysed for three kinds of configurations, i.e. homogeneous, splay and Pi cells formed by different rubbing conditions and pretilt angles. The results indicated that the polar anchoring has no effect on the threshold field. It is determined only by the twist anchoring and pretilt angle. But, the polar anchoring and twist anchoring are coupling with each other and have a great influence on the saturation field. The formulae for calculating the threshold field and saturation field are given. These results will be very useful in understanding surface physics and the design of liquid crystal cells.