非等向性微滴之散射特性及其應用在含液晶滴聚合物薄膜穿透特性之研究

Abstract

本論文研究液晶微滴在電場調制下之光散射特性並據以探討含液晶滴聚合物薄膜之光穿透性質。 我們對含正介電係數各向異性之線狀液晶圓球微滴做探討。 在圓球表面上則分別考慮了液晶指向矢與界面呈垂直或平行排列的兩種邊界條件。 我們首先以差分疊代數值計算法求解外加電場下三維空間中的液晶指向矢分佈的穩定解。 其計算法為用變分方法對張量型式液晶自由能密表示式求解自由能最小值。 無外加電場時，在垂直及平行排列邊界條件下，我們得到的穩定解分別是軸向型(axial)及雙極型(bipolar)的液晶指向矢分佈。 在外加電場調制過程中，我們觀察到液晶指向矢分佈有磁滯(hysteresis)現象與最近實驗上的報導相吻合。 從計算結果並發現該液晶指向矢分佈之遲滯現象強度可藉由降低液晶之介電係數各向異性對彈性係數比來減低。 我們以全散射截面來探討線狀液晶圓球微滴之電控散射特性。 其計算是採用不規折繞射近似(anomalous-diffraction approach) 散射理論。 我們分別討論了球滴大小、液晶之介電係數各向異性及彈性係數與電控散射特性的關係。 研究中我們發現由於半徑較大之液晶微滴其散射強度隨外加電場增強而有振盪現象，因此並非每個液晶微滴之最強散射都是發生在無外加電場時。 並且矢液晶微滴產生最強散射作用的外加電場強度是隨液晶微滴增大而降低。 此外，我們也証實液晶指向矢分佈在外加電場下之雙穩態亦使得液晶微滴之電控光散射特性具有磁滯現象。 最後，我們以一簡單模型考慮了多個液晶圓球微滴的集體散射行為來計算含液晶滴聚合物薄膜之光穿透特性。 由此計算我們證實了液晶微滴中液晶指向矢分佈之磁滯現象是導致含液晶滴聚合物薄膜光穿透有磁滯現象的原因。並且這光穿透之磁滯現象可介由降低液晶之介電係數各向異性對彈性係數比來減低。計算中我們也得到了含液晶滴聚合物薄膜之起始電壓與飽合電壓與液晶參數的關係。

The subject of this thesis is to investigate the electrically controllable light scattering properties of nematic droplets in a polymer-dispersed liquid crystal (PDLC). The problem of light scattering from a liquid crystal droplet is quite complex because of the irregular liquid crystal director configurations, the nonuniform optical axis distributions inside the droplet make the droplet an optically inhomogeneous anisotropic scatter. In this research, we first used the finite difference and the relaxation methods to simulate the molecular director configurations in a spherical nematic droplet with the presence of an applied electric field. The simulation was performed in three dimensions using the equal elastic constant approximation and hard anchoring condition. We examined nematic droplets with normal and tangential anchoring boundary conditions. The deformation free energy of the nematic droplet was described in terms of tensor representation. The axial and bipolar structured nematic droplets are derived as the stable configuration for normal and tangential boundary conditions, respectively. When an external field is applied on the cell, the field is set back to zero, the initial director configuration can be retrieved as have been observed in many experimental works. The hysteresis phenomenon of the change of director configurations is observed under an increasing-then-decreasing external field sequence as recently reported in experimental observation. In addition, we found that the hysteresis can be reduced by lowering the values of dielectric anisotropy to elastic constant ratio of liquid crystal. The total scattering cross section was calculated to investigate the electrically controlled scattering properties of nematic droplets. The scattering properties of the nematic droplets are calculated using the anomalous-diffraction light scattering theory. The electrooptical properties of the nematic droplet are examined with respect to the size of nematic droplet, the dielectric anisotropy and the elastic constant of the nematic liquid crystals. Our numerical results showed that there exists an optimum size of a nematic droplet for maximum scattering. However, the maximum scattering does not always occur in the absence of external field because oscillation is found in the voltage-dependent scattering properties of large nematic droplets. Some large nematic droplets could have maximum scattering effects at nonzero bias field and the bias fields are found to be a decrease function of droplet size. Furthermore, we used a simple model for collecting the light scattering effects of individual droplets to estimate the transmission of a PDLC film. We showed that the hysteresis of voltage-dependent transmission of a PDLC film is caused by the bistability of director orientations. Besides, the hysteresis of voltage-dependent transmission was found to be reduced by using the liquid crystal with low values of dielectric anisotropy to elastic constant ratio. The dependences of threshold and saturation voltage of a PDLC film on the dielectric anisotropy and elasticity of liquid crystals were also examined. A simple relation between these parameters is obtained. Besides, the PDLC films with axial nematic droplets could have smaller threshold voltage, saturation voltage and transmission hysteresis compared with the PDLC films with bipolar nematic droplets, all other things being equal. Moreover, our experimental data testified our simulation prediction that the PDLC film with suitable size of nematic droplets could has low operation voltage and sufficient scattering power.