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.     

Evaluation of translational friction coefficients of micro-sized spherical probes in nematic liquid crystals

We study the translational friction coefficients of a spherical micrometric probe moving in nematic liquid crystalline fluids, by solving numerically the constitutive hydrodynamic equations of uncompressible isothermal nematic fluids (Leslie–Ericksen equations). The nematic medium is described by a vector field, which specifies the director orientation at each point and by the velocity vector field. Simulations of director dynamics surrounding the moving probe are presented, and the dependence of translational diffusion upon liquid crystal viscoelastic parameters is discussed. The time evolution of director field is studied in the presence of an orienting magnetic field in two characteristic situations, i.e. direction of motion parallel and perpendicular to field. In particular, a detailed analysis is given for the case of a spherical probe in rectilinear motion in nematic MBBA (4-methoxibenzylidene-4′-n-butylaniline), together with a comparison with other nematogens.     

Simulation of reorientation dynamics in bipolar nematic droplets

A two-dimensional model composed of a synthesis of the Leslie-Ericksen continuumtheory of nematics and the Euler-Lagrange equation for surface director motion is used to study the magnetic-induced director reorientation dynamics confined in spherical bipolar droplets with viscoelastic surfaces. The magnetic field is restricted to the droplet axis of symmetry direction. The numerical results indicate that the surface viscosity and anchoring strength must be taken into account to describe accurately director reorientation dynamics in droplets. In addition, the numerical results replicate frequently reported experimental observations on the performance of polymer dispersed liquid crystal films. These observations include the familiar 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, this model is able to predict precisely the relationships between the rise and decay times and the external applied field strength, and the fact that the switching field strength is inversely proportional to droplet size.     

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.     

Linear analysis of pattern formation in nematics in oblique magnetic fields

The dynamics of nematic director field reorientation in non-Freedericksz geometries, after a magnetic field H is applied at an oblique angle relatively to the initial homogeneous director n 0 ( H not normal to n 0), is studied considering a magnetic reorientation driven by hydrodynamic instabilities (with backflow). This study is carried out for bounded samples between two parallel plates with planar boundary conditions and with rigid anchoring. Linear stability and wave vector selection analysis predict that, when the angle of the magnetic to the initial director field is increased, for a given magnetic field intensity, two transitions from a homogeneous to a transient distorted director field reorientation can occur: a transition at a first critical angle to an aperiodic distorted director field and a transition at a second critical angle to a periodic distorted director field. It is shown that the periodic mode is cut off at a higher reduced field when the magnetic field acts away from the normal direction.     

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.     

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.     

The transient dynamics leading to spin turbulence in high-field solution magnetic resonance: a numerical study

The dynamics under the joint action of radiation damping and the distant dipolar field in high-field solution magnetic resonance are investigated. Different dynamical regimes during the evolution are identified and their individual features are discussed. In the steady state, the dynamics can be associated with a strange attractor in phase space on which the motion is chaotic. The possibility of the observed chaotic motion being spatiotemporal is examined.     

Proton NMR investigation of a hydrogen-bonded liquid crystal gel

Proton NMR is employed to determine director distributions in a hydrogen-bonded liquid crystal gel in the presence of a magnetic field. The samples consist of the mesogen 8CB mixed with small percentages of gelator, which forms a hydrogen-bonded network when the sample is cooled below the gelation point in the isotropic liquid. Since the gelation occurs above the clearing point, a non-oriented random director configuration is frozen in. The configuration of the hydrogen-bonded network is found to be isotropic. It fixes a preferential random local orientation of the nematic director, even in the presence of an external magnetic field of a few Tesla. The NMR spectra of the samples give information on orientation and order in such systems. A simple model for the director field is provided.     

Proton NMR investigation of a hydrogen-bonded liquid crystal gel

Proton NMR is employed to determine director distributions in a hydrogen-bonded liquid crystal gel in the presence of a magnetic field. The samples consist of the mesogen 8CB mixed with small percentages of gelator, which forms a hydrogen-bonded network when the sample is cooled below the gelation point in the isotropic liquid. Since the gelation occurs above the clearing point, a non-oriented random director configuration is frozen in. The configuration of the hydrogen-bonded network is found to be isotropic. It fixes a preferential random local orientation of the nematic director, even in the presence of an external magnetic field of a few Tesla. The NMR spectra of the samples give information on orientation and order in such systems. A simple model for the director field is provided.     

Magnetic field controlled optical phase retardation in a hybrid nematic cell

We have studied the phase retardation of linearly polarized light in a hybrid nematic liquid crystal cell. For a certain range of directions of the applied magnetic field the phase retardation is found to change non-monotonically with the magnetic induction. The observed behaviour is described rather well by the standard Frank elastic theory. The corrections resulting from subsurface deformations, which are characteristic both for second order elasticity approach and for surface field theory, are also considered. The analysis of the experimental data suggests that the presence of distortions in the zero-field director configuration is the necessary condition for the non-monotonic phase retardation, which implies that such an experiment could be used for the detection of misalignment of the effective pretilts in a nematic cell.     

Computer simulation of elongated bipolar nematic droplets 1. External field aligned parallel to the droplet axis of symmetry

The magnetically-induced transient nematic director reorientation dynamics, confined in elongated bipolar droplets, is studied in this paper. Numerical results are obtained by solving the Leslie-Ericksen continuum theory in ellipses. The aspect ratio is varied to determine the effect of droplet shape on director reorientation dynamics. The magnetic field is restricted to the droplet axis of symmetry direction, which has not yet been studied but is fundamentally important in polymer dispersed liquid crystal (PDLC) film operation. The numerical results replicate frequently-reported experimental observations on the performance of PDLC films. These observations include the familiar exponential increases 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. In addition, the experimental observation that switching field strength increases while decay time decreases as the droplet becomes more elongated, are also exhibited by the numerical results.     

Computer simulation of elongated bipolar nematic droplets 1. External field aligned parallel to the droplet axis of symmetry

The magnetically-induced transient nematic director reorientation dynamics, confined in elongated bipolar droplets, is studied in this paper. Numerical results are obtained by solving the Leslie-Ericksen continuum theory in ellipses. The aspect ratio is varied to determine the effect of droplet shape on director reorientation dynamics. The magnetic field is restricted to the droplet axis of symmetry direction, which has not yet been studied but is fundamentally important in polymer dispersed liquid crystal (PDLC) film operation. The numerical results replicate frequently-reported experimental observations on the performance of PDLC films. These observations include the familiar exponential increases 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. In addition, the experimental observation that switching field strength increases while decay time decreases as the droplet becomes more elongated, are also exhibited by the numerical results.     

Field quenching of director fluctuations in thin films of nematic liquid crystals

The continuum theory of director fluctuations in nematic liquid crystals is extended to take account of finite sample size which more accurately describes experiments on thin films. The effect of external fields on director fluctuations is considered for two cell geometries: (i) the field parallel to the director for materials of positive susceptibility anisotropy, and (ii) the field perpendicular to the director for materials of negative susceptibility anisotropy. In the latter geometry, quenching of fluctuations leads to induced biaxiality. Comparison with experimental results shows that even allowing for the finite size of the sample, there is still a significant disagreement between theory and experiment, especially from thin samples.     

Anisotropy of non-mesogenic polymer networks dispersed in a liquid crystal matrix

We report here original results characterizing in situ the interactions between a smectic liquid crystal phase and a polymer network dispersed in it. These results have been obtained by neutron scattering on smectic liquid crystal (8CB) samples containing a physical network of 1.5wt% polymer. The samples were polymerized in the isotropic, or in the smectic A phases. For the first time it is experimentally proved that the polymerization of non-mesogenic monomers in an aligned smectic A matrix induces anisotropy in the resulting network. The network becomes elongated along the liquid crystal director. When the polymerization is carried out in the isotropic phase the polymer network has an isotropic distribution even if a magnetic field, which orients the liquid crystal director, is later applied. On the other hand, studies show that after several thermal cycles, the liquid crystal orientational order still remained. Without other external constraints, the polymer network freezes the alignment of the liquid crystal. It is probably imposed by pendant reticulates on the diffuse liquid crystal-polymer interfaces.     

Magnetic alignment study of rare-earth-containing liquid crystals

The liquid-crystalline rare-earth complexes of the type [Ln(LH)3(DOS)3]-where Ln is Tb, Dy, Ho, Er, Tm, or Yb; LH is the Schiff base N-octadecyl-4-tetradecyloxysalicylaldimine; and DOS is dodecylsulfate-exhibit a smectic A phase. Because of the presence of rare-earth ions with a large magnetic anisotropy, the smectic A phase of these liquid crystals can be easier aligned in an external magnetic field than smectic A phases of conventional liquid crystals. The magnetic anisotropy of the [Ln(LH)3(DOS)3] complexes was determined by measurement of the temperature-dependence of the magnetic susceptibility using a Faraday balance. The highest value for the magnetic anisotropy was found for the dysprosium(III) complex. The magnetic alignment of these liquid crystals was studied by time-resolved synchrotron small-angle X-ray scattering experiments. Depending on the sign of the magnetic anisotropy, the director of the liquid-crystalline molecules was aligned parallel or perpendicular to the magnetic field lines. A positive value of the magnetic anisotropy (and parallel alignment) was found for the thulium(III) and the ytterbium(III) complexes, whereas a negative value of the magnetic anisotropy (and perpendicular alignment) was observed for the terbium(III) and dysprosium(III) complexes.     

Orientational Behaviour of the Nematic Director upon Macroscopic Rotation at the Magic Angle

The ¹⁹F N.M.R. spectrum of 1,2,2,2-tetrachloro-l,l-difluoroethane has been studied in the nematic liquid crystal ZLI1167 (Merck) upon rotation at the magic angle. The director of the liquid crystal is oriented perpendicular to the spinning axis when the angle between the rotation axis and the magnetic field is less than the magic angle and parallel when this angle is more than the magic angle. It is shown that exactly at the magic angle the spectrum corresponds to a frequency modulated powder pattern. This powder pattern leads to an understanding of the orientational behaviour of the director when a nematic is spun at the magic angle.     

Effects of a transverse electric field in nematics: Induced biaxiality and the bend Fréedericksz transition

We have studied the effects of a transverse electric field on director fluctuations in the nematic liquid crystal 5CB (4-n-pentyl-4′-cyanobiphenyl) in the bend Fréedericksz geometry. The sample was homeotropically aligned by surface treatment of the glass cell walls and an additional magnetic field was applied perpendicular to the walls. An electric field was then applied parallel to the walls; below the bend Fréedericksz transition, director fluctuations parallel to the electric field are enhanced. This field-induced biaxiality was observed and studied by monitoring the intensity of light transmitted by the sample placed between crossed polarizers. Landau theory for 5CB predicts the electric field induced bend transition to be first order. Our observations of the transmitted intensity are consistent with this prediction. We have also observed that this transition is to a modulated rather than to a uniform phase.     

Structure and internal dynamics of a side chain liquid crystalline polymer in various phases by molecular dynamics simulations: a step towards coarse graining

Side chain liquid crystalline polymer with relatively long spacer was modeled on a semiatomistic level and studied in different liquid crystalline phases with the aid of molecular dynamics simulations. Well equilibrated isotropic, polydomain smectic and monodomain smectic phases were studied for their structural and dynamic properties. Particular emphasis was given to the analysis on a coarse-grained level, where backbones, side chains, and mesogens were considered in terms of their equivalent ellipsoids. The authors found that the liquid crystalline phase had a minor influence on the metrics of these objects but affected essentially their translational and orientational order. In the monodomain smectic phase, mesogens, backbones, and side chains are confined spatially. Their diffusion and shape dynamics are frozen along the mesogen director (the one-dimensional solidification) and the reorientation times increase by one to one-and-half orders of magnitude. In this phase, besides obvious orientational order of mesogens and side chains, a stable detectable order of the backbones was also observed. The backbone director is confined in the plane perpendicular to the mesogen director and constantly changes its orientation within this plane. The backbone diffusion in these planes is of the same range as in the polydomain smectic phase at the same temperature. A detailed analysis of the process of field-induced growth of the smectic phase was performed. The study revealed properties of liquid crystalline polymers that may enable their future fully coarse-grained modeling.     

Addressing non-idealities in NMR experiments on rotating liquid crystals

Unequivocal evidence for a biaxial nematic phase in low-molar-mass calamitic thermotropic liquid crystals has been challenging to generate. Recently we provided NMR evidence that nonlinear calamitic mesogens based on the oxadiazole heterocycle exhibit a biaxial nematic phase (Phys. Rev. Lett., 2004, 92, 145505). Herein we probe the robustness of that claim by exploring potential variations of the director distribution from the ideal one that would apply to nematics rotated about an axis perpendicular to the spectrometer magnetic field. Moreover, we demonstrate that our methodology, when applied to the high temperature uniaxial nematic TBBA, yields a biaxial order parameter η = 0.0, thereby confirming the validity of our procedures. Our findings suggest that the original claim of biaxial order (η∼0.1) as reflected by probe molecule studies of oxadiazole mesogens is still valid.