Proton N.M.R. lineshape in nematic microdroplets

The dependence of the proton N.M.R. absorption spectrum on nematic director configuration and molecular self-diffusion in nematic submicrondroplets is analysed. The lineshape is evaluated numerically for radial and bipolar director configuration. The motional averaging is taken into account by means of a numerical simulation of the molecular diffusion which induces slow molecular reorientations due to non-uniform orientational ordering in the droplet. This diffusion process strongly affects the absorption spectra of the radial configuration, whereas spectra of the bipolar configuration are only slightly influenced. The possibility of determinating the submicrometre nematic droplet structures using the proton N.M.R. lineshape is discussed.     

On the Influence of Elastic Modes on the N.M.R. Lineshapes of Polymer Liquid Crystals

We have studied the influence of thermally excited orientational fluctuations on the N.M.R. lineshape of a nematic monodomain. The influence is characterized by a static order parameter S_stat whose theoretical expression in terms of viscoelastic parameters is derived. This model is applied to the proton N.M.R. spectrum of a thermotropic main chain polymer. The values of S_stat are deduced from the study of the changes of the N.M.R. lineshape as a function of the angle between the static magnetic field and the nematic director. Good agreement is obtained with theoretical values calculated using estimated values of the Leslie viscosity coefficients and the Frank elastic constants. The importance of an accurate knowledge of S_stat for a number of problems is stressed.     

On the Influence of Elastic Modes on the N.M.R. Lineshapes of Polymer Liquid Crystals

Abstract

We have studied the influence of thermally excited orientational fluctuations on the N.M.R. lineshape of a nematic monodomain. The influence is characterized by a static order parameter S _stat whose theoretical expression in terms of viscoelastic parameters is derived. This model is applied to the proton N.M.R. spectrum of a thermotropic main chain polymer. The values of S _stat are deduced from the study of the changes of the N.M.R. lineshape as a function of the angle between the static magnetic field and the nematic director. Good agreement is obtained with theoretical values calculated using estimated values of the Leslie viscosity coefficients and the Frank elastic constants. The importance of an accurate knowledge of S _stat for a number of problems is stressed.     

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.     

Numerical analysis of the radial-axial structure transition with an applied field in a nematic droplet

In this paper the director configurations and the free energies of a nematic droplet with a surface normal anchoring condition are calculated numerically. For this surface anchoring, a transition occurs between the radial and axial structures with respect to an applied field. In the calculation of the director configurations, the position of a disclination has been fixed. Comparing the free energies for different disclinations, the stable position which gives the minimum free energy is found. In calculating the free energy of a droplet, it is assumed that the free energy density of the nematic phase does not exceed the isotropic free energy density, so that the large distortion in the vicinity of the disclination causes a nematic-isotropic transition and the free energy density of the disclination core becomes equal to the isotropic free energy density. The director configuration in a droplet is calculated as a function of an applied field for different isotropic free energy densities, elastic constant ratios and droplet shapes. The relation between the radial-axial structure transition and these factors are clarified.     

Numerical analysis for a nematic droplet in polymer dispersed liquid crystals

Starting from the Landau-de Gennes free energy expression, the author has numerically analysed the director pattern in a nematic droplet of polymer dispersed liquid crystals. The nematic director has been understood as the eigenvector, which corresponds to the largest eigenvalue of the tensor order parameter. To investigate the droplet structure influence, all equations have been treated on the curvilinear coordinate system which is generated along the droplet boundary. In the case of spherical and spheroidal droplets with normal strong anchoring, the director exhibits an axial configuration and a disclination ring. The ring radius and the capactiance of the system change without hysteresis with the applied voltage.     

Confinement of a liquid crystal to small droplets and its effect on nuclear magnetic relaxation

Abstract

The spatial dependence of the orientation of the molecular director and of the nematic order parameter is obtained by minimization of the Landau–de Gennes free energy of the nematic liquid crystal confined in a spherical droplet. Special attention is given to the vicinity of the nematic–isotropic transition. The influence of the resulting nematic structure, large liquid crystal–polymer interface and restricted molecular diffusion on the nuclear magnetic relaxation is analysed. The translationally-induced molecular reorientation and the liquid crystal–polymer cross relaxation are discussed in particular. The possibility of an indirect study of the molecular anchoring on the polymer surface is demonstrated.     

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.     

Study of internal ring rotation and molecular reorientation in the liquid crystal 5O.7 by deuterium N.M.R. spectroscopy

The spectral densities of motion were determined by deuterium N.M.R. relaxation measurements in the nematic, smectic A and smectic C phases of 4-n-pentyloxybenzylidene-d₁-4'-heptylaniline and 4-n-pentyloxybenzylidene-4'-heptylaniline-2,3,5,6-d₄. By examining two atomic sites on a 5O.7 molecule, we were able to gain information on the reorientation motion and internal rotation of the aniline ring. It was also found that director fluctuations make some contribution to the spectral density J₁ (ω). We use the superimposed rotations model to account for the internal ring motion and the small step rotational diffusion model for the molecular reorientation. The derived rotational diffusion constants for the spinning and tumbling motions appear to give physically plausible activation energies in the mesophases of 5O.7.     

Some N.M.R. experiments using lyotropic nematic liquid crystals

A series of lyotropic nematic liquid crystals based on aniso-dimensional micelles can be subdivided according to micelle shape and diamagnetic susceptibility anisotropy. The proton magnetic resonance spectra of benzene dissolved in dilute solution in several of these phases have been analysed. The signs of the partially averaged dipole-dipole coupling give information about the relative alignment of the six-fold symmetry axis of benzene, the director and the magnetic field. The system caesium perfluorooctanoate/water is unusual in two respects. The system forms a nematic phase with only a binary mixture and the disk micelles align in a perpendicular plane to the magnetic field. As a result the binary system has been studied previously in some detail (see N. Boden, S. A. Come and K. W. Jolley, 1987, J. phys. Chem.91, 4092). New measurements on the interesting phase diagram have been accomplished using caesium-133 and deuterium magnetic resonance measurements at various temperatures. Some dilatometric measurements have been made to complement the N.M.R. studies.     

Orientational ordering of 4-substituted phenylcyclohexanes studied by carbon-13 two-dimensional N.M.R.

An N.M.R. method combining the techniques of separated local field spectroscopy (SLF) and variable angle spinning (VAS) is valuable in the investigtion of nematic liquid crystals. Rapid sample spinning causes the nematic director to align along the spinning axis, resulting in narrow peaks in the C-13 N.M.R. spectrum. SLF is a two-dimensional N.M.R. method which produces a first order splitting pattern for each carbon signal from which C-H dipolar coupling constants can be determined. The order parameters for all segments of the liquid crystal molecule can then be calculated. Results for three 4'-cyanophenylcyclohexanes are considered here. These compounds are trans-substituted at the 4 position of cyclohexane ring with n-pentane (PCH5), 1-pentene (3d₁CP) and 3-pentene (1d₃CP), respectively.     

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.     

The influence of director fluctuations on molecular reorientation of a small probe molecule in a liquid-crystalline environment

The influence of director fluctuations on a probe molecule dissolved in a nematic liquid crystal is calculated to all orders using the gaussian properties of the director field. Consequences for the N.M.R. spectrum and relaxation through quadrupolar interaction of the probe molecule are indicated. It is found that the equilibrium distribution of molecular orientations, and consequently quadrupolar spectral splittings are virtually unchanged by fluctuations in the director field. The spectral densities are also obtained and it is shown that in addition to J₀₁ also J₀₀ and J₀₂ become frequency dependent in the N.M.R. frequency range. The frequency dependence of J₀₀ and J₀₂ has a logarithmic contribution; the magnitude of the frequency dependent contribution to J₀₂ is, however, insufficient to explain experimental results.     

Orientational ordering of 4-substituted phenylcyclohexanes studied by carbon-13 two-dimensional N.M.R.

Abstract

An N.M.R. method combining the techniques of separated local field spectroscopy (SLF) and variable angle spinning (VAS) is valuable in the investigtion of nematic liquid crystals. Rapid sample spinning causes the nematic director to align along the spinning axis, resulting in narrow peaks in the C-13 N.M.R. spectrum. SLF is a two-dimensional N.M.R. method which produces a first order splitting pattern for each carbon signal from which C–H dipolar coupling constants can be determined. The order parameters for all segments of the liquid crystal molecule can then be calculated. Results for three 4′-cyanophenylcyclohexanes are considered here. These compounds are trans-substituted at the 4 position of cyclohexane ring with n-pentane (PCH5), 1-pentene (3d ₁CP) and 3-pentene (1d ₃CP), respectively.     

Some N.M.R. experiments using lyotropic nematic liquid crystals

Abstract

A series of lyotropic nematic liquid crystals based on aniso-dimensional micelles can be subdivided according to micelle shape and diamagnetic susceptibility anisotropy. The proton magnetic resonance spectra of benzene dissolved in dilute solution in several of these phases have been analysed. The signs of the partially averaged dipole–dipole coupling give information about the relative alignment of the six-fold symmetry axis of benzene, the director and the magnetic field. The system caesium perfluorooctanoate/water is unusual in two respects. The system forms a nematic phase with only a binary mixture and the disk micelles align in a perpendicular plane to the magnetic field. As a result the binary system has been studied previously in some detail (see N. Boden, S. A. Come and K. W. Jolley, 1987, J. phys. Chem. 91, 4092). New measurements on the interesting phase diagram have been accomplished using caesium-133 and deuterium magnetic resonance measurements at various temperatures. Some dilatometric measurements have been made to complement the N.M.R. studies.     

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.     

Control of liquid crystal droplet configuration in polymer dispersed liquid crystal with macro-iniferter polystyrene

A polystyrene macro-iniferter was applied to control the alignment of liquid crystal molecules at the droplet wall of polymer dispersed liquid crystal (PDLC) films. The aspects of the alignment were monitored by observing the droplet in the PDLC film. With increasing the macro-iniferter polystyrene in the composition, the configuration of LC droplets changes from bipolar to radial. This is because the high concentration of the macro-iniferter polystyrene results in a small surface interaction between the LC and the polymer matrix, which favours the formation of radial configuration. The radial configuration was stable under our conditions. However, increasing the LC and the initiator concentrations resulted in the change from radial to bipolar.     

Study of internal ring rotation and molecular reorientation in the liquid crystal 5O.7 by deuterium N.M.R. spectroscopy

Abstract

The spectral densities of motion were determined by deuterium N.M.R. relaxation measurements in the nematic, smectic A and smectic C phases of 4-n-pentyloxybenzylidene-d ₁-4′-heptylaniline and 4-n-pentyloxybenzylidene-4′-heptylaniline-2,3,5,6-d ₄. By examining two atomic sites on a 5O.7 molecule, we were able to gain information on the reorientation motion and internal rotation of the aniline ring. It was also found that director fluctuations make some contribution to the spectral density J ₁ (ω). We use the superimposed rotations model to account for the internal ring motion and the small step rotational diffusion model for the molecular reorientation. The derived rotational diffusion constants for the spinning and tumbling motions appear to give physically plausible activation energies in the mesophases of 5O.7.