Rigorous calculation of pixel and inter-electrode capacitances of thin-film transistor liquid crystal displays using three-dimensional simulation

We have rigorously calculated for the first time all the inter-electrode and pixel capacitances of Thin-Film Transistor Liquid Crystal Displays using the electrical energy distribution inside a liquid crystal cell. The energy distribution is obtained from the three-dimensional profiles of potential distribution and molecular director. The dynamic equation of continuum theory for liquid crystals is described in a tensorial form in order to maintain the equivalence of n and -n . The effects of lateral fields generated by multiple electrodes of finite sizes are taken into account in the simulation. As a numerical technique, we used a finite difference method which is suitable for the highly non-linear equations. As a result, we confirmed that the pixel capacitance for our pixel structure is about 40% larger than that of the conventional approach. It is also revealed that the gate-common and gate-data inter-electrode capacitances are not negligible.     

Modelling of addressing schemes in surface stabilized ferroelectric liquid crystal cells using a three variable model in one dimension

The 'Three-Variable Model in One Dimension' has been successfully used to model the domain switching process for simple monopolar and bipolar pulses. In this paper, we discuss the development of this model to describe the switching process due to more complicated addressing waveforms. We have taken two contrasting addressing schemes: the Seiko scheme which is a simple example of a low voltage addressing scheme, and the Joers Alvey scheme, a high voltage addressing scheme which utilizes the high biaxiality properties of a ferroelectric liquid crystal (FLC) material. We experimentally simulate the voltage sequence 'seen' by a pixel subject to these addressing schemes, and take into consideration the worst case combinations of voltages that could cause switching and non-switching conditions. We show that the 'Three Variable Model in One Dimension' is in excellent agreement with experimental data for the Seiko addressing scheme, and can be used to predict the operating regime for the Joers Alvey addressing scheme.     

Continuum modelling of hybrid-aligned nematic liquid crystal cells: optical response and flexoelectricity-induced voltage shift

A continuum model is employed to study systematically the optical response of hybrid-aligned nematic (HAN) liquid crystal cells under the application of an external electric field. The influence of the flexoelectric effect is discussed for a large range of anchoring strengths at the homeotropic alignment layer. It is shown that the optical response of HAN cells is governed by a complicated interplay between the flexoelectric coefficient and homeotropic anchoring strength. In particular, the calculations reveal that, for weak homeotropic anchoring, the flexoelectric effect leads to a non-linear voltage shift of the optical transmittance as a function of flexoelectric coefficient, and gives rise to an asymmetry in the transmittance–voltage curve. Finally, a comparison of the continuum-model simulations with recent experimental observations indicates that both the flexoelectric coefficient and the anchoring strength of the nematic liquid crystal MBBA on a homeotropic polyimide alignment layer are significantly lower than previously reported.     

Continuum modelling of hybrid-aligned nematic liquid crystal cells: optical response and flexoelectricity-induced voltage shift

A continuum model is employed to study systematically the optical response of hybrid-aligned nematic (HAN) liquid crystal cells under the application of an external electric field. The influence of the flexoelectric effect is discussed for a large range of anchoring strengths at the homeotropic alignment layer. It is shown that the optical response of HAN cells is governed by a complicated interplay between the flexoelectric coefficient and homeotropic anchoring strength. In particular, the calculations reveal that, for weak homeotropic anchoring, the flexoelectric effect leads to a non-linear voltage shift of the optical transmittance as a function of flexoelectric coefficient, and gives rise to an asymmetry in the transmittance-voltage curve. Finally, a comparison of the continuum-model simulations with recent experimental observations indicates that both the flexoelectric coefficient and the anchoring strength of the nematic liquid crystal MBBA on a homeotropic polyimide alignment layer are significantly lower than previously reported.     

Liquid crystals: a chemical physicist's view

This paper has allowed me the rare opportunity and pleasure of acknowledging those who have played important roles in my scientific career. It has also enabled me to report work in the field of liquid crystals which has gone unpublished. The particular topics have been selected because they illustrate the areas of liquid crystal science with which I have been especially concerned. The predicted phase diagram of mixtures of rods and spheres is both intricate and interesting. The ability to test these predictions experimentally has required the use of quasi-spherical solutes such as tetraethyltin. The reasons for the failure of the experiments to conform to theory are investigated and explained in terms of the orientational order of this flexible molecule, determined using deuterium NMR spectroscopy. The tetrapodes are more exotic tetrahedral structures in which four mesogenic groups are linked to a central atom or group. The massive flexibility of such molecules poses a severe problem for the prediction of their liquid crystal behaviour. Here a solution to this problem is presented and used to predict the dependence of the transitional properties of the tetrapodes on the spacer length and the mode of its attachment to the mesogenic group. The same molecular field approach has been employed to predict the variation of the transitional properties of liquid crystal dimers with the length of the spacer. It is found that for spacers containing about 12 or more atoms the odd-even effect predicted for the transitional properties varies significantly depending on the model used to describe the spacer conformation. That is, whether the torsional angles defining the conformations are taken to be discrete or continuous. Cyanobiphenyl dimers with spacers containing up to 24 atoms have been synthesized to test these predictions. The Gay-Berne potential has proved to be an important model with which to study liquid crystal behaviour using simulation techniques. By joining two Gay-Berne particles together with a flexible ethane link we have constructed a Gay-Berne dimer and have been able to explore the properties of this mesogen. In particular its phase behaviour, the novel structure of the smectic A phase and how the conformational distribution alters with the phase have been studied. Despite its attractive features there are relatively simple systems for which the Gay-Berne potential is not suitable. These include molecules with a spherocylindrical shape and those with a sphere embedded at the centre of such a structure. In fact the shapes of many mesogenic molecules approximate to the former, and certain metallomesogenic molecules have shapes like the latter. The novel Corner S-function potential provides a valuable way to represent such cylindrically symmetric shapes and we use this to simulate the behaviour of these systems. It is found that the sphere has a major influence on the phase behaviour as well as on the crystal structure.     

The influence of lateral and terminal substitution on the structure of a liquid crystal dendrimer in nematic solution: A computer simulation study

The choice of lateral and terminal substitution can have a major influence on the structure of a liquid crystalline supermolecule, which in turn can induce radically different phase behaviour. In this study we use molecular dynamics simulations to investigate the shape of a liquid crystal dendrimer within a liquid crystalline solvent. A coarse-grained (CG) simulation model is employed to represent a third generation dendrimer in which 32 mesogenic groups are bonded to chains at the end of each branch of the dendrimer. In this CG-model the liquid crystal groups can be appended either terminally or laterally. This bonding option is used to generate the structure of four separate systems: (a) a dendrimer with 32 terminal mesogens, (b) a dendrimer with 32 laterally appended mesogens, (c) and (d) dendrimers with 16 lateral and 16 terminal groups represented with laterally bonded sites on one side of the molecule, model (c) or next to terminally bonded sites, model (d). The simulations show that the dendrimer is able to change shape in response to molecular environment and that the molecular shape adopted depends critically on the nature of the lateral/terminal susbstitution.     

The influence of lateral and terminal substitution on the structure of a liquid crystal dendrimer in nematic solution: A computer simulation study

The choice of lateral and terminal substitution can have a major influence on the structure of a liquid crystalline supermolecule, which in turn can induce radically different phase behaviour. In this study we use molecular dynamics simulations to investigate the shape of a liquid crystal dendrimer within a liquid crystalline solvent. A coarse‐grained (CG) simulation model is employed to represent a third generation dendrimer in which 32 mesogenic groups are bonded to chains at the end of each branch of the dendrimer. In this CG‐model the liquid crystal groups can be appended either terminally or laterally. This bonding option is used to generate the structure of four separate systems: (a) a dendrimer with 32 terminal mesogens, (b) a dendrimer with 32 laterally appended mesogens, (c) and (d) dendrimers with 16 lateral and 16 terminal groups represented with laterally bonded sites on one side of the molecule, model (c) or next to terminally bonded sites, model (d). The simulations show that the dendrimer is able to change shape in response to molecular environment and that the molecular shape adopted depends critically on the nature of the lateral/terminal susbstitution.     

On the observation of micellar structures by dielectric spectroscopy

Many cationic surfactants form, in the presence of certain organic acids, large supramolecular micellar structures in water. The dielectric response of one such system (cetyl trimethyl ammonium bromide-salicylic acid, CTMAS) has been studied as a function of frequency, concentration and temperature. The results are compared with dynamic mechanical data on the same system, which has been published in the literature.The dielectric response shows that the micelles form a rigid, open network structure, which does not impede ionic transport in the bulk liquid. However, the response also shows the presence of a frequency dispersive barrier capacitance. From the variation of the properties of this capacitance with CTMAS concentration and applied voltage over a range of frequencies, it is deduced that the barrier originates in an ordered micelle structure at each electrode.     

Optical response of a nematic liquid crystal cell at the splay – bend transition: a model and dynamic simulation

We study the dynamical optical response of a nematic liquid crystal cell that undergoes the splay–bend transition after applying a voltage across the cell. We formulate a simplified model that takes into account both the flexoelectric coupling and the surface rotational viscosity. The dynamic equations of the model are solved numerically to calculate the temporal evolution of the director profile and of the transmittance. We evaluate the response time as a function of a number of parameters, such as dielectric and elastic anisotropies, asymmetry of the surface pretilt angles, anchoring energy, surface rotational viscosity and flexoelectricity.     

Optical response of a nematic liquid crystal cell at the splay - bend transition: a model and dynamic simulation

We study the dynamical optical response of a nematic liquid crystal cell that undergoes the splay-bend transition after applying a voltage across the cell. We formulate a simplified model that takes into account both the flexoelectric coupling and the surface rotational viscosity. The dynamic equations of the model are solved numerically to calculate the temporal evolution of the director profile and of the transmittance. We evaluate the response time as a function of a number of parameters, such as dielectric and elastic anisotropies, asymmetry of the surface pretilt angles, anchoring energy, surface rotational viscosity and flexoelectricity.     

The optical response of liquid crystal cells to a low frequency driving voltage

This study investigates the optical response of liquid crystal cells to a low frequency square wave voltage of 0.1 Hz. It is found that there are three physical phenomena that dominate the overall properties of the device. The first is the discharging effect whereby the effective voltage over the liquid crystal layer decreases as a function of time; this occurs due to mobile ions being present within the liquid crystal material. The second is the charging-up of the cell where the effective voltage increases with time; this is attributed to charge separation taking place within the polyimide layer upon application of the d.c. voltage component. The third effect is cell asymmetry whereby the effective voltage depends upon the polarity of the externally applied field; this is the result of a locked-in d.c. holding voltage being present within the cell layers. These three effects are analysed in some detail with the view of developing a liquid crystal cell capable of being driven with a low frequency square wave voltage. A model of a liquid crystal cell in which the liquid crystal material can dissolve impurity ions from the alignment layers and in which the ions can then become re-adsorbed into the polyimide layer is deduced.     

Double layer in ionic liquids: The nature of the camel shape of capacitance

Monte Carlo simulations of a model ionic liquid show that if ions have charged heads and neutral counterparts, the latter give rise to the camel shape of the voltage dependence of the double layer capacitance. Neutral ‘tails’ of ions play the role of latent voids that can be replaced by charged groups via rotations and translations of ions. This provides extra degrees of freedom for the field-induced charge rearrangements in the double layer which results in the peculiar double-hump capacitance profile.     

The one-dimensional Coulomb lattice fluid capacitor

The one-dimensional Coulomb lattice fluid in a capacitor configuration is studied. The model is formally exactly soluble via a transfer operator method within a field theoretic representation of the model. The only interactions present in the model are the one-dimensional Coulomb interaction between cations and anions and the steric interaction imposed by restricting the maximal occupancy at any lattice site to one particle. Despite the simplicity of the model, a wide range of intriguing physical phenomena arise, some of which are strongly reminiscent of those seen in experiments and numerical simulations of three-dimensional ionic liquid based capacitors. Notably, we find regimes where over-screening and density oscillations are seen near the capacitor plates. The capacitance is also shown to exhibit strong oscillations as a function of applied voltage. It is also shown that the corresponding mean-field theory misses most of these effects. The analytical results are confirmed by extensive numerical simulations.     

Ferroelectric polymer nanocomposite alignment layer in twisted nematic liquid crystal devices for reducing switching voltage

Twisted nematic liquid crystal device (TNLCD) was fabricated using a ferroelectric zinc oxide (ZnO)-doped polyimide alignment layer. The ferroelectric nanoparticle can produce a local electric field, which can trigger the orientation of liquid crystal molecule and reduces the switching voltage. The uniform dispersion of ferroelectric ZnO nanoparticles in the alignment layer was studied using field emission scanning electron microscopy and atomic force microscopy. The ferroelectric property of ZnO-doped polyimide was investigated using dynamic contact electrostatic force microscopy. An increased local electric field due to the presence of nano ZnO was confirmed with the help of scanning tunnelling microscopy. An augmentation of capacitance was observed with an increase in concentration, which substantiates the reduction of switching voltage of TNLCD with the modification of ferroelectric nanoparticle-doped alignment layer.     

Shear aligned polymer dispersed ferroelectric liquid crystal devices

Fast switching liquid crystal devices can be produced by forming a dispersion of ferroelectric liquid crystal droplets in a polymer film. Such PDFLCs have been fabricated using a polymerization-induced phase separation technique involving ultraviolet photopolymerization, during which the film was sheared to obtain a uniform orientation of the liquid crystal medium. These birefringence devices show fast response times (sub-millisecond), optimum tilt angle (22.5°), and good contrast (∼ 30:1) at room temperature, using ferroelectric switching. We studied the tilt angles, response times and contrast ratio as a function of voltage and temperature to determine the effects of the preparation parameters on the electro-optic behaviour of these devices. Using a ferroelectric liquid crystal with long helical pitch, such devices appear to be bistable.     

A new anisotropic soft-core model for the simulation of liquid crystal mesophases

A new anisotropic soft-core model is presented, which is suitable for the rapid simulation of liquid crystal mesophases. The potential is based on a soft spherocylinder, which can be easily tuned to favor different liquid crystal mesophases. The soft-core nature of the potential makes it suitable for long-time step molecular dynamics or dissipative particle dynamics simulations, particularly as a reference model for mesogens or as an anisotropic solvent for use in combination with atomistic models. Results are presented for two variants of the new potential, which show different mesophase behaviors. Variants of the potential can also be linked together to produce more complicated molecular structures. Here, as an example, results are provided for a model multipedal liquid crystal, which has eight liquid crystalline groups linked to a central core via semiflexible chains. Here, despite the complexity of molecular structure, the model succeeds in showing the spontaneous formation of a liquid crystal phase. The results also demonstrate that there is a very strong coupling between the internal structure of the multipedal mesogen and the molecular order of the phase, with the mesogen spontaneously undergoing major structural rearrangement at the transition to the liquid crystal phase.     

A superionic state in nano-porous double-layer capacitors: insights from Monte Carlo simulations

Recently observed anomalous properties of ionic-liquid-based nanoporous supercapacitors [C. Largot et al., J. Am. Chem. Soc., 2008, 130, 2730-2731] have attracted much attention. Here we present Monte Carlo simulations of a model ionic liquid in slit-like metallic nanopores. We show that exponential screening of the electrostatic interactions of ions inside a pore, as well as the image-charge attraction of ions to the pore surface, lead to the 'anomalous' increase of the capacitance with decreasing the pore width. The simulation results are in good agreement with the experimental data. The capacitance as a function of voltage is almost constant for low voltages and vanishes above a certain threshold voltage. For very narrow pores, these two regions are separated by a peak. With increase of the pore size the peak turns into a bump and disappears for wide pores. This effect, related to a specific character of the voltage-induced filling of nanopores with counterions at high densities, is yet to be verified experimentally.     

Kerr effect investigations in a liquid crystal

Measurements are reported for the d.c. Kerr response and the pretransitional behaviour of a new liquid crystal, 4-cyanophenyl 4-pentylbenzoate at and above the nematic-isotropic phase transition temperature. The real parts of the third order nonlinear susceptibilities chi⁽³⁾ at and above the nematic-isotropic transition temperatures are determined for the new liquid crystal from the electro-optic Kerr effect (EOKE) experiments. The variation of the Kerr constant with temperature is discussed on the basis of the Landau-de Gennes model of the nematic-isotropic phase transition. The susceptibility values are also compared with that of the well known liquid crystal 4'-pentyl-4-cyanobiphenyl (5CB). The effect of the linking group of the liquid crystal on the suceptibility value is also discussed.     

Computer simulations of interactions between liquid crystal molecules and polymer surfaces II. Alignment of smectic C-forming mesogens

Computer simulations have been performed to examine the behaviour of the liquid crystalline molecule 4-n-heptyl-2-fluoro-phenyl 4-n-octyloxybiphenyl-4-carboxylate (MBF) when in contact with crystalline polymer surfaces. The simulations form part of a study of the alignment interactions that are found in liquid crystal displays. MBF forms several smectic phases including a chiral smectic C* phase when suitably doped. In this paper we examine the way that layers of MBF molecules interact with the structure of the crystalline polymer surface, with the aim of understanding how molecular level interactions give rise to macroscopic phenomena such as the cone angle in ferroelectric liquid crystal devices. Molecular dynamics simulations consisting of a fixed crystalline polymer surface in contact with either a single MBF molecule or up to two layers of them (48 molecules) have been performed. A variety of simple polymer surfaces have been examined and the simulations show that the cone angle is highly dependent on the geometry of both the liquid crystal molecule and the polymer substrate. For molecules of MBF on polyethylene substrates, a cone angle of 20 is predicted, in line with experimental findings.     

Chiral symmetry-breaking dynamics in the phase transformation of nematic droplets

Dynamic simulations of the isotropic–nematic phase transformation of liquid crystal droplets with homeotropic surface anchoring are found to predict chiral symmetry-breaking dynamics. These observations occur when using material parameters for pentyl-cyanobiphenyl (5CB) but not with the single elastic constant approximation for this material, which is frequently used in simulations. The twisting dynamic process occurs during the relaxation of the domain from an unstable radial texture to a stable uniform texture and involves simultaneous defect loop motion and twisting of the bulk nematic texture.