Measurement of the twist elastic constant by pha retardation technique
A. Nych, M. Voronin, V. Pergamenshchik,
Yu. Kolomzarov*, V. Sorokin* and V. Nazarenko1
Institute of Physics, 46 Nauki ave., Kyiv, 03039, Ukraine
*Institute of Semiconductor Physics, 45 Nauki ave., Kyiv, 03028, Ukraine
We have extended the experimental approach, ud by Yu. A. Nastyshyn et al. [J. Appl. Phys. 86, 4199 (1999)] for measuring polar anchoring strength, to measure the twist elastic constant in nematic liquid crystal. The method implies measurements of pha retardation changes in liquid crystal under the action of magnetic field. The obtained experimental data were fitted with the predictions of elastic theory. We found
K, is in good agreement with tho that the value of the measured elastic constant,
22
described in literature.
Keywords: liquid crystal, elastic constant, pha retardation.
Introduction
The elastic constants of nematic liquid crystals have attracted considerable interest for many years and for numerous rearchers [1–12]. This interest largely comes from the fact that elastic constants appreciably influence important display properties such as the threshold voltage, steepness of the electro-optical characteristic and so on. The demand to fabricate low power consumption, wide operation temperature range, high 1*****************.ua
contrast and fast switching time LCDs provides the rationale for the preci knowledge of elastic constant values as well as their temperature dependence. The reason why many reports are still concerned with the elastic constants is that the measurements are far from to be trivial.
The elastic constants of nematic liquid crystals are usually measured by the using Freedericksz transition induced by magnetic or electric field [1–6]. The experiments concern the investigation of direct measurement of the elastic torque exerted from a nematic sample on a glass plate were performed in [7, 10]. Other methods have been also propod in [9] and in [11]. However, the most reliable values of elastic constants have been obtained from measurement of the Freedericksz transi
tion in thin nematic layer. In most of the experiments the magnetic or electric field is applied perpendicular to the director. The director distortion occurs when the field exceeds a threshold value, C H . By assuming the strong anchoring of the director at the interface of the nematic layer one obtains a龙虾尾的做法
ii C K d H χπ=, where d is the thickness of layer, a χ is anisotropy of magnetic susceptibility and ii K is an elastic constant (1=i – splay, 2=i – twist, 3=i – bend). The accuracy of the described method strongly depends on the director orientation at the interface. Even small deviation of the director results in sufficient shift of the threshold field.
In the current paper we suggest an experimental technique to measure the twist elastic constant from the dependence of pha retardation of liquid crystal layer on the applied magnetic field. For a certain range of directions of the applied magnetic field the pha retardation demonstrates changes monotonically with the magnetic induction. 22K is determined from a simple fit of experimental curve.
Experiment
Experiments were performed for the cells with alignment induced by coating of two glass substrates
with the rubbed polyimide layer. The polyimide we ud, LARC-CP1, provides almost planar orientation, the deviation of the angle between the substrate and director is less than o 1 [13]. The cells were filled with the nematic liquid crystal 5CB, purchad from EM Industries and ud without any additional purification, with the parameters as following: extraordinary refractive index 708.1=e n
[1], ordinary refractive index 530.1=o n [1], (both at wavelength nm 8.632=λ), anisotropy of magnetic susceptibility 3112105.113m kg a −−×=χ [5]. The optical pha retardation of the liquid crystal cell was determined by the Senarmont technique (e, for example [14, 15]). Schematically this tup is shown on Fig. 1. The light source was He-Ne lar (nm 633=λ). The linear polarized light entering the sample emerges elliptically polarized. Setting the optical axis of the quarter-wave plate parallel to the polarizer transforms the elliptically polarized light pasd through the cell into linear polarized light. The measurement of the azimuth of this linear polarized light using the analyzer allows for determination of the pha retardation of the sample.
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Results and discussion
A common nematic liquid crystal is uniaxial crystal, meaning that one crystal axis is different from the other two. The single crystal axis that is unique is often called the "extraordinary" axis and its associa
ted refractive index is labeled e n , while the other two axes are "ordinary" axes with index o n [14]. The amount of pha retardation that
罗非鱼的功效与作用monochromatic wave acquires from traveling trough a nematic liquid crystal is related to a refractive index, n , wavelength, λ, and the path length inside the crystal, L , as nL λπ=Φ2 (1) An input beam that is normally incident on the liquid crystal layer will be resolved into ordinary and extraordinary axis components, each with a different refractive index. The beam that emerges has a pha delay difference or retardation between the axes. Applied magnetic field results in reorientation of liquid crystal molecules along the direction of the field. Since the distortion starts in the middle of the cell the resultant structure consists of twist deformation with maximum amplitude in the center of the cell and the director coincides this rubbing directions at the interfaces. However, for normal incidence the polarization of light transmitted through the liquid crystal layer is not distinguishing from that transmitted through twisted nematic layer. There is no detectable retardation, since the polarization of light follows director deformation so the polarization of emerging light always corresponds to the director orientation at the interface. The light is "ignorant" of the deformation inside liquid crystal layer. But, when the cell is tilted toward or away from the light beam, the amount of retardation depends on the degree of tilt and has an angular nsitivity to director twist.
Let us consider a homogeneously aligned nematic layer placed in magnetic field as it shown in Fig. 2. Input light, that is linearly polarized, makes a certain angle β with the cell. In the initial position the rubbing direction of the nematic cell was aligned along magnetic field. Then cell was rotated on an angle α around the normal to the cell in so manner that magnetic field induce only twist deformation of the director. In this geometry the effective extraordinary refractive index, eff n , of the LC becomes
γ⋅+γ⋅⋅=2222
cos sin e o o
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f n n n n n , (2)
where γ is the angle between the director and input light beam. γ can be determined from defined angles β and α as follow ()ϕ−α⋅β−=γsin sin cos , where ϕ is the angle between director and rubbing direction. The angular dependent pha retardation of the liquid crystal layer is expresd as ∫−∆λπ=Φ222d d eff dz n , (3)
where d is the thickness of liquid crystal layer and −γ⋅+γ⋅⋅β−=∆o e o o e i i eff n n n n n n n n 2
22222cos sin sin . (4)
The first factor, β−22sin i i
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n n , in eq. (4) originates from the incread optical path
length and it takes into account a light refraction at the liquid crystal/glass interface. Just after passing an isotropic glass layer, ordinary and extraordinary beams will posss a different refraction indexes and thus they will propagate parately. To simplify our calculations we assume that both beams refract together with index of refraction, that equals to isotropic refractive index of the nematic liquid crystal, ()32e o i n n n +=.
In the prence of the magnetic field, the Frank free energy density corresponding to the twist deformation is given by
学习的革命()202222121B n ⋅µχ− ∂ϕ∂=a d z K F (5)
