Yang Guo-Chen

Surface anchoring energy and the first order Fréedericksz transition of a NLC cell

Many authors have suggested new forms to describe the surface anchoring energy of the liquid crystal-wall interface, replacing the Rapini-Papoular (RP) formula g s = (1/2) A sin2 theta. If the RP function is considered as the primary approximation, and a lowest order modification is included, then the surface anchoring energy can be represented by g s = (1/2) A sin2 theta(1 + zeta sin2 theta). zeta characterizes the modification to the RP formula and varies for the different energy forms. It is well known that the RP formula predicts a second order Freedericksz transition. This paper points out that the transition can be first order if the modification is taken into account, in which case at the threshold point the tilt angle of the director at the middle layer of the cell, thetam, is finite. The conditions for the existence of the first order transition are obtained; zeta < 0 is required for a first order transition. The approximate expression of the threshold field is also given.

The first order Freedericksz transition at saturation point for weak anchoring NLC cells

On the basis of the modified Rapini-Papoular expression for the anchoring energy, the properties of the transition at saturation point for weak anchoring NLC cells has been studied analytically. We find that this transition may be of second order, as is usually predicted by many authors; however, it may also be first order. Whether it is first or second order is determined by the material, anchoring energy and thickness of the cell. The conditions for first order transition are deduced by an analytical method, and the results of calculation are shown by graph for κ (= K 11 / K 33 ) values 0.8, 0.6 and 0.4. The saturation field strengths for the first order transition case are calculated and shown in the table.

Multiple discrete energy levels and the bistable state of weak anchoring NLC cells

The weak anchoring nematic liquid crystal (NLC) cell is investigated with regard to energy. Because the Gibbs free energy of liquid crystal system used in theory does not include temperature and entropy, and because the equations and boundary conditions for δG=0 are also the mechanical equilibrium conditions of the continuum, the Gibbs free energy G is equivalent to the energy E of the liquid crystal continuum. There are multiple solutions which satisfy these equations and boundary conditions, each solution corresponding to a certain energy value. We call these discrete energy values and energy levels. Adopting a simple liquid crystal cell model, the energy levels are calculated in detail by means of analytical and numerical methods. The results show that there are three energy levels (or more in certain cases). The values and sequence of the energy levels are related to the external field and anchoring parameters. The relationships between the energy level structure and the bistable. Fréedericksz transition are disussed, together with their influence on the response time. The physical condition for the existence of more than three energy levels is also given.

The bistable state of a twisted nematic liquid crystal cell with weak anchoring boundary

On the basis of the modified general Rapini–Papoular expression for the anchoring energy, a twisted nematic liquid crystal cell has been studied analytically. In this paper, a new variable is introduced and is suitable for the calculation of the threshold point and the saturation point. The free energy being smallest in the equilibrium state, we find that bistable states can be formed from the uniform twisted state plus the disturbed state, the disturbed state plus the saturation state, and the uniform twisted state plus the saturation state.

The influences of surface polarization on NLC cells

The influence of the surface polarization, Ps , on a nematic liquid crystal (NLC) cell is investigated analytically. Flexoelectric polarization is considered, but selective ion absorption is ignored. The differential equations are derived for tilt angle, θ, of director n and the corresponding boundary conditions based on Gibbs free energy, and their solutions discussed. Equations for the reduced threshold voltage, uth , and the reduced saturation voltage, usat , are deduced and the relationships between uth , usat and reduced strength of surface polarization, p, derived.

Variational calculations of neutral bound excitons in GaAs quantum-well wires

The binding energy of an exciton bound to a neutral donor (D-0,X) in GaAs quantum-well wires is calculated variationally as a function of the wire width for different positions of the impurity inside the wire by using a two-parameter wavefunction. There is no artificial parameter added in our calculation. The results we have obtained show that the binding energies are closely correlated to the sizes of the wire, the impurity position, and also that their magnitudes are greater than those in the two-dimensional quantum wells compared. In addition, we also calculate the average interparticle distance as a function of the wire width. The results are discussed in detail.

First-order Fréedericksz transition at the threshold point for weak anchoring nematic liquid crystal cell under external electric and magnetic fields

Based on the modified formula of Rapini-Papoular, the equilibrium equation and boundary condition of the director have been obtained and the behaviour of the Freedericksz transition at the threshold point has been studied for weak-anchoring nematic liquid crystal cells under external electric and magnetic fields with the methods of analytical derivation and numerical calculation. The results show that, except for the usual second-order transition, the first-order Freedericksz transition can also be induced by a suitable surface anchoring technique for the liquid crystal cell given in the paper. The conditions for the existence of the first-order Freedericksz transition are obtained. They are related to the material elastic coefficient k11, k33 the thickness of the liquid crystal cell, the external electric field and the strength of surface anchoring, etc.

Binding Energy of Positively and Negatively Charged Excitons in GaAs/AlxGa1-xAs Quantum Wells

Using a simple two-parameter wavefunction, we calculate variationally the binding energy of positively and negatively charged excitons in GaAs/AlxGa1-xAs quantum wells for well widths from 10 to 300Angstrom. We consider the effect of effective mass, dielectric constant mismatch in the two materials, and the whole correlation among the particles. The results are discussed and compared in detail with previous experimental and theoretical results, which show fair agreement with them.

Threshold property of a nematic liquid crystal cell with two grating surface substrates

A grating surface can drive the liquid crystal molecules to orientate along the direction parallel or vertical to the projected plane of the grating surface. The nematic liquid crystal (NLC) cell manufactured with two pre-treated grating surface substrates may realize the vertical display, parallel display and twist display. In this paper, the threshold property of this NLC cell is investigated systematically. With the Frank elastic theory and the equivalent anchoring energy formula of grating surface substrate, the analytic expressions of the threshold voltage related to three displays are obtained, which are dependent on their geometrical parameters such as amplitude δ and pitch λ of the grating surface substrate. For a certain anchoring strength, the threshold voltage increases or decreases with the increase of the value δ/λ of the different displays.

Equivalent anchoring energy formula of a NLC on a grating surface and VCT effect

The voltage‐controlled twist (VCT) effect shows that a grating surface, with its particular anchoring properties, has the potential to become a new surface anchoring for liquid crystal devices. In order to describe these properties an equivalent anchoring energy is introduced. The alignment of a nematic liquid crystal (NLC) on such a grating originates from two mechanisms, so each produces a term in the equivalent anchoring energy. One is the interaction potential between NLC molecules and the molecules on the substrate surface, from which we derive the expression of the corresponding term. The other is the increased elastic strain energy, for which we adopt the result of Berreman. The equivalent anchoring energy obtained is a function of pitch λ and amplitude δ of the grating surface. Both the corresponding strength parameter and the easy direction are functions of λ and δ. The hybrid aligned nematic cell proposed by. Bryan‐Brown et al. is studied by the use of our formula, and the distribution of the director, the saturation state and the saturation voltage are calculated in detail. The results are consistent with experimental data, especially the values of λ and δ. The VCT effect can therefore be explained.