Computer simulation study of a nematogenic lattice model based on an elastic energy mapping of the pair potential

Director configurations in a nematic liquid crystal can be determined by minimizing its total elastic free energy, for given elastic constants and specific boundary conditions. In some cases, these configurations have been obtained by numerical procedures where the elastic free energy density plays the same role as the overall potential energy in a standard Metropolis Monte Carlo simulation. The interaction energies or potentials used in these studies are short ranged but, in general, not pairwise additive, unless the three elastic constants are set to a common value, thus reducing the potential to that in the well-known Lebwohl-Lasher lattice model. On the other hand, we can construct, in different ways, a lattice model with pairwise additive interactions, which approximately reproduces the elastic free energy density, where the parameters defining the pair potential are expressed as linear combinations of elastic constants. An anisotropic nematogenic pair interaction of this kind, originally proposed by Gruhn and Hess (T. Gruhn and S. Hess, Z. Naturforsch. A51, 1 (1996)), has recently been investigated by one of us, using a Monte Carlo simulation (S. Romano, Int. J. Mod. Phys. B 12, 2305 (1998)). Here we propose another approximate procedure for the mapping, and study the resulting pair potential model with the aid of Monte Carlo simulations. The behaviour of the nematic phases formed by the two models is compared together with the predictions of molecular field theory and the properties of the Lebwohl-Lasher model.     

Structure of liquid crystal droplets with chiral propeller texture

We experimentally studied a nematic liquid crystal whose molecules form twisted head-to-head H-bonded dimers. We observed that when the material transformed from the isotropic to nematic phase, it formed droplets with chiral propeller textures. We carried out a computer simulation to investigate the liquid crystal director configuration inside the droplets and to study the effects of elastic constants and chirality on the droplet texture. Results of our study show it is likely that the material in the droplets had nonzero chirality due to spontaneous chiral phase separation.     

Orientation and anchoring effects in stretched polymer dispersed nematic liquid crystals

The induction of liquid crystal orientation through mechanical stretching was investigated for polymer dispersed liquid crystals (PDLCs) by means of infrared dichroism. Using a nematic liquid crystal BL006 and polyacrylic acid as the polymer matrix, it was possible to stretch the PDLC films with BL006 in either the isotropic or the nematic phase. After cooling the films under strain to room temperature, the molecular orientation of BL006 was found to be much higher for films that contained isotropic liquid droplets of BL006 at the time of stretching than for films that had nematic droplets. Stretching PDLC films with isotropic droplets results in no molecular orientation, but the orientation is induced during the subsequent cooling when BL006 goes through the isotropic-to-nematic phase transition. Interestingly for PAA/BL006, the nematic director orients along the long axes of the elongated droplets despite liquid crystal anchoring perpendicular to the polymer interface.     

Orientation and anchoring effects in stretched polymer dispersed nematic liquid crystals

The induction of liquid crystal orientation through mechanical stretching was investigated for polymer dispersed liquid crystals (PDLCs) by means of infrared dichroism. Using a nematic liquid crystal BL006 and polyacrylic acid as the polymer matrix, it was possible to stretch the PDLC films with BL006 in either the isotropic or the nematic phase. After cooling the films under strain to room temperature, the molecular orientation of BL006 was found to be much higher for films that contained isotropic liquid droplets of BL006 at the time of stretching than for films that had nematic droplets. Stretching PDLC films with isotropic droplets results in no molecular orientation, but the orientation is induced during the subsequent cooling when BL006 goes through the isotropic-to-nematic phase transition. Interestingly for PAA/BL006, the nematic director orients along the long axes of the elongated droplets despite liquid crystal anchoring perpendicular to the polymer interface.     

Optical properties of stretched polymer dispersed liquid crystal films

The basic mechanisms determining the formation of optical anisotropy in stretched, thin polymer dispersed liquid crystal (PDLC) films with micron sized nematic droplets have been studied experimentally and the results analysed in terms of a proposed theoretical model. The experiments were performed on PDLC films with the bipolar nematic director configuration in the droplets, where the film transmittance, microscopic structure, and birefringence of the polymer matrix were studied. It is shown that the orientational ordering of bipolar nematic droplets, introducing the main contribution to the ability of stretched PDLC film to polarize the transmitted light, is strongly dependent upon initial droplet shape and the elastic properties of the polymer matrix. The 'anomalous' nematic director orientation is also observed in a portion of elongated droplets where the axes of bipolar configurations do not coincide with the major axes of the droplet cavities due to the presence of inclusions at the cavity walls. The effect of alternation of droplet size and shape upon stretching and the influence of optical anisotropy of the polymer matrix on film transmittance are analysed. On the basis of the results obtained, simple criteria for optimization of main PDLC polarizer performance are formulated.     

Computer simulation of a real liquid crystal

We carried out a computer simulation study of a liquid crystal using semi-empirical atom-atom potentials (the Lennard-Jones 6-12 modification) with nematic 4-ethoxybenzylidene-4-n-butylaniline as an example. The two stages of the calculations were (1) simulation of the structure of an isolated molecule and (2) Monte Carlo simulation of liquid crystal phase. The energy of the system was calculated as the sum over all atomic pair interactions. The molecular structure preferred in the nematic phase is discussed.     

Computer simulation of elongated bipolar nematic droplets II. External field aligned normal to the droplet axis of symmetry

Numerical results from the modelling and computer simulation of the magnetic-induced director reorientation dynamics in elongated bipolar nematic droplets are presented in this paper. The magnetic field is applied normally to the droplet axis-of-symmetry direction, which is one possible scenario found in applications of polymer dispersed liquid crystal (PDLC) films. This case has not yet been studied numerically, and its understanding is far from complete. The model is composed of the Leslie-Ericksen and Frank continuum theories and is solved in two dimensions since bipolar nematic droplets exhibit mirror symmetry in certain planes. The numerical results replicate frequently reported experimental observations on the performance of PDLC films. These observations include the ubiquitous exponential increase followed by saturation in light transmittance as the external applied field increases, and the exponential increase (decrease) followed by saturation as time increases in the on (off)-state. Furthermore, in contrast to current understanding for both the on- and off-states, the model predicts that the directors in the centre (surface) region of the droplet exhibit a dead time (no dead time) before reorientation. The numerical results presented in this paper provide a better understanding of the director reorientation dynamics in elongated bipolar nematic droplets; this can be used to optimize the design and performance of devices using PDLC films.     

Computer simulation of elongated bipolar nematic droplets II. External field aligned normal to the droplet axis of symmetry

Numerical results from the modelling and computer simulation of the magnetic-induced director reorientation dynamics in elongated bipolar nematic droplets are presented in this paper. The magnetic field is applied normally to the droplet axis-of-symmetry direction, which is one possible scenario found in applications of polymer dispersed liquid crystal (PDLC) films. This case has not yet been studied numerically, and its understanding is far from complete. The model is composed of the Leslie-Ericksen and Frank continuum theories and is solved in two dimensions since bipolar nematic droplets exhibit mirror symmetry in certain planes. The numerical results replicate frequently reported experimental observations on the performance of PDLC films. These observations include the ubiquitous exponential increase followed by saturation in light transmittance as the external applied field increases, and the exponential increase (decrease) followed by saturation as time increases in the on (off)-state. Furthermore, in contrast to current understanding for both the on- and off-states, the model predicts that the directors in the centre (surface) region of the droplet exhibit a dead time (no dead time) before reorientation. The numerical results presented in this paper provide a better understanding of the director reorientation dynamics in elongated bipolar nematic droplets; this can be used to optimize the design and performance of devices using PDLC films.     

A novel orientation-dependent potential model for prolate mesogens

An intermolecular potential is introduced for the study of molecular mesogenic fluids. The model combines distinct features of the well-known Gay-Berne and Kihara potentials by incorporating dispersive interactions dependent on the relative pair orientation to a spherocylinder molecular core. Results of a Monte Carlo simulation study focused on the liquid crystal phases exhibited by the model fluid are presented. For the chosen potential parameters, molecular aspect ratio L*=5 and temperatures T*=2, 3, and 5, isotropic, nematic, smectic-A, and hexatic phases are found. The location of the phase boundaries as well as the equation of state of the fluid and further thermodynamical and structural parameters are discussed and contrasted to the Kihara fluid. In comparison to this latter fluid, the model induces the formation of ordered liquid crystalline phases at lower packing fractions and it favors, in particular, the appearance of layered hexatic ordering as a consequence of the greater attractive interaction assigned to the parallel side-to-side molecular pair configurations. The results contribute to the evaluation of the role of specific interaction energies in the mesogenic behavior of prolate molecular liquids in dense environments.     

Droplet shape and reorientation fields in nematic droplet/polymer films

Polymer films containing droplets of nematic liquid crystal form an important class of new electro-optic light valves and displays. While previous work has shown that the nematic droplet size is an important factor in the electro-optic properties of these films, here we report that the droplet shape is equally important in determing the electro-optics of the film. Electron micrographs show that for films using polyvinyl alcohol as the polymeric binder the cavities formed by the polymer matrix are oblate in nature, and aligned with the minor axis perpendicular to the film plane. In oblate cavities the elastic-deformation free energy is minimized when the director field in the droplet is aligned along a major axis of the spheroid; the electric field performs work on the nematic in reorienting the nematic into a higher-energy state, equal to the elastic-free-energy difference between the two configurations. Calculations and experiment are used to estimate the elastic and electric field free-energy-density changes that occur upon reorientation of the nematic droplet. The general agreement between these two values is used to indicate that droplet shape anisotropy is a major factor in determining the electrooptic properties of these films.     

Droplet shape and reorientation fields in nematic droplet/polymer films

Polymer films containing droplets of nematic liquid crystal form an important class of new electro-optic light valves and displays. While previous work has shown that the nematic droplet size is an important factor in the electro-optic properties of these films, here we report that the droplet shape is equally important in determing the electro-optics of the film. Electron micrographs show that for films using polyvinyl alcohol as the polymeric binder the cavities formed by the polymer matrix are oblate in nature, and aligned with the minor axis perpendicular to the film plane. In oblate cavities the elastic-deformation free energy is minimized when the director field in the droplet is aligned along a major axis of the spheroid; the electric field performs work on the nematic in reorienting the nematic into a higher-energy state, equal to the elastic-free-energy difference between the two configurations. Calculations and experiment are used to estimate the elastic and electric field free-energy-density changes that occur upon reorientation of the nematic droplet. The general agreement between these two values is used to indicate that droplet shape anisotropy is a major factor in determining the electrooptic properties of these films.     

Molecular modelling of liquid crystal systems: An internal coordinate Monte Carlo approach

A Monte Carlo scheme is presented which is designed to provide a convenient mechanism to model accurately the internal molecular structure of liquid crystalline molecules. The technique stores atomic positions in terms of bond lengths, bond angles and dihedral angles within a Z-matrix, and the Monte Carlo scheme involves generating trial configurations from changes to the Z-matrix using the MM2 molecular mechanics potential to describe energy changes between different molecular conformations. The technique is applied to the liquid crystal molecule 4-n-pentyl-4'-cyanobiphenyl (5CB), and results are presented for the conformational populations and dihedral angle distributions of 5CB in the gas phase at 300 K. The effect of a nematic mean field on the distribution of molecular conformations is also examined via the addition of a conformation-dependent potential of mean torque to the internal energy.     

Monte Carlo simulations on mesophase formation using dipolar Gay-Berne model

We report the results of a Monte Carlo simulation of polar particles interacting via the Gay-Berne potential combining dipole-dipole interactions. Simulations were carried out on a system of 256 particles with either a zero dipole moment or longitudinal dipole moment located at the centre of the molecule. The system was found to spontaneously form nematic, smectic and crystal phases from an isotropic phase with a random configuration as temperature was decreased, irrespective of values of the dipole moment. The results do not give any indication of a net polarization even in the system with a strong dipole moment (μ* = 2.00). The transition temperature from the isotropic to nematic phase is not sensitive to the value of the dipole moment within the limits of statistical error, while the transition from the nematic to smectic phase depends on the strength of dipole moment. At lower temperatures forming the smectic or the crystal phase, the translational order along the director increases with increasing dipole moment. The dipolar interactions contribute to the long range ordering.     

Dynamic response of super-twisted nematic liquid crystal displays

The dynamics of super-twisted nematic (STN) liquid crystal displays was studied by detailed computer simulation. The time evolution of director configuration and velocity of flow as obtained by solving Ericksen-Leslie hydrodynamic equations. The influence of d/p value and pretilt angle on the dynamic response was also studied. A comparison was also made between twisted nematic and STN liquid crystal displays.     

Computer simulations of nematic droplets

Abstract

Nematic droplets are intimately connected with disclinations, because in nematic droplets, point and line-shaped defects, as well as surface defects, are not generated at random, but inevitably by topological constraints. Thus, droplets provide a good means for investigating nematic defects. There is a growing interest in both topics due to the applications in polymer dispersed liquid crystal devices [1–3], but also in classical display modelling, where nematic defects are to be avoided. Various types of droplets are investigated theoretically with the aid of a previously developed numerical algorithm [4,5], which is based on a dynamic equation for the alignment tensor a _μv. The rotational diffusion, the influence of an orienting external field, and the Frank elasticity (in the one-coefficient approximation) are taken into account, but flow processes are neglected. For the application to nematic droplets, a new type of boundary conditions had to be used, which I have called ‘true planar anchoring’. I simulate the relaxation of the director field of nematic droplets from the isotropic state and vice versa for various types of anchoring and cavity shapes. Contrast pictures, as if viewed under crossed Nicols, are computed and compared to experiment. The results obtained elucidate the nature of the surface disclinations of strength one (boojums). In particular, it is found that their occurrence can be understood as a consequence of the planar anchoring, without any further assumptions. Moreover, a phase transition-like transformation of the director configuration is predicted which is temperature controlled and occurs, as the blue phases do, close to the nematic-isotropic transition temperature T_c.     

Fluctuating Interfaces in Liquid Crystals

Summary: We review and compare recent work on the properties of fluctuating interfaces between isotropic and nematic liquid-crystalline phases. Molecular dynamics and Monte Carlo simulations have been carried out for systems of ellipsoids and hard rods with aspect ratio 15:1, and the fluctuation spectrum of interface positions (the capillary wave spectrum) has been analyzed. In addition, the capillary wave spectrum has been calculated analytically within the Landau-de Gennes theory. The theory predicts that the interfacial fluctuations can be described in terms of a wave vector dependent interfacial tension, which is anisotropic at small wavelengths (stiff director regime) and becomes isotropic at large wavelengths (flexible director regime). After determining the elastic constants in the nematic phase, theory and simulation can be compared quantitatively. We obtain good agreement for the stiff director regime. The crossover to the flexible director regime is expected at wavelengths of the order of several thousand particle diameters, which was not accessible to our simulations.     

Dynamic response of super-twisted nematic liquid crystal displays

The dynamics of super-twisted nematic (STN) liquid crystal displays was studied by detailed computer simulation. The time evolution of director configuration and velocity of flow as obtained by solving Ericksen-Leslie hydrodynamic equations. The influence of d/p value and pretilt angle on the dynamic response was also studied. A comparison was also made between twisted nematic and STN liquid crystal displays.     

Critical behaviour of nematic liquid crystals in oblique magnetic fields

The static critical behaviour of a bulk nematic liquid crystal sample in an oblique magnetic field is analysed. When a magnetic field is applied at a suitable angle alpha with respect to the initially homogeneous nematic director, a spatially inhomogeneous director pattern can be formed. The transition to the deformed state and the formation of walls between the domains resulting from the two equally stable configurations above the transition are studied. The width of the walls is found to diverge at the transition. The critical exponents corresponding to the transition and wall formation are shown to be characteristic of a mean field second order phase transition.     

Molecular dynamics simulation of the nematic liquid crystal phase in the presence of an intense magnetic field

The influence of an intense external field on the dynamics of the nematic liquid crystal phase is investigated using a molecular dynamics simulation for the Gay-Berne nematogen under isobaric-isothermal conditions. The molecular dynamics as a function of the second-rank orientational order parameter P<2> for a system consisting of a nematic liquid crystal in the presence of an intense magnetic field is compared with that of a similar system without the field. The translational motion of molecules is determined as a function of the translational diffusion coefficient tensor and the anisotropy and compared with the values predicted theoretically. The rotational dynamics of molecules is analyzed using the first- and the second-rank orientational time correlation functions. The translational diffusion coefficient parallel with respect to the director is constrained by the intense field, although the perpendicular one is decreased as the P<2> is increased, just as it is in the system without the field. However, no essential effect of the strong magnetic field is observed in the rotational molecular dynamics. Further, the rotational diffusion coefficient parallel with respect to the director obtained from the first-rank orientational time correlation function in the simulation is qualitatively in agreement with that in the real nematic liquid crystalline molecules. The P<2> dependence of the rotational diffusion coefficient for the system with the intense magnetic field shows a tendency similar to that for the system without the field.     

Electric field studies of liquid crystal droplet suspensions

The responses of freely-suspended micron-sized liquid crystal droplets subjected to an alternating electric field are presented. By examining droplets of isotropic, nematic bipolar, and nematic radial configurations, we test the effect of anchoring on the droplet response. Specifically, using birefringence and scattering dichroism we measure the relaxation of electric field-induced orientation following a field pulse. Results indicate that bipolar and radial droplets in suspension orient in the field through very different mechanisms. Bipolar droplets are observed to rotate their defect axes in the field while radial droplets orient through a nematic distortion. By varying the field pulse, we observe that droplets also respond differently to the field depending on their relative sizes. In radial droplet suspensions we quantitatively measure time scales associated with the reorientation and restructuring of the defect region.