液晶物理-9月28日-2

n = n0S S = 1 T/Tc= 0.25 S：order parameter n0：birefringence when S = 1 連續彈性體理論連續彈性體理論 通常在液晶中之導軸 n 是隨位置而變化的。此變化在微觀尺度上十分微 小，而液晶無論是受到表面配向或外加力場之作用而導致液晶分子排列 方式的任何形變，均可以如下之三種基本形變來探討其物理現象。每一 種形變都可分解為此三種形變的組合，如空間座標的三個基底。 11 Splay, KBend, K 33 Twist, K22 其中: K11、K22、K33分別為Splay、Twist、Bend形變之彈性係數(elastic constant) 液晶之連續彈性體理論，僅對彈性能量考量及假設所有秩序參數S為常 數。此假設於方向或位置秩序有缺陷(defect)之區域即不成立。 Elastic Constants K11：K22：K33 1：1：( z / x )2 x y：width of LC z：length of LC in general, K33 K11 K22Kii S2, C3H7F F C3H7F F F Upon application of an external perturbation field, a nematic liquid crystal will undergo deformation just as any solid. The free energy densities associated with these deformations are given by Free Energy Densities Splay：F1=K11(n)2 1 2 Twist：F2=K22(nn)2 1 2 Bend：F3=K33(n(n)2 1 2 Total free energy density F = F1+ F2+ F3 Freedericksz Transition 外加電場E造成的力矩 = -dUE/d = ( /8 )E2sin2 = 0, /2，= 0，液晶不會轉動 導軸 n 的方向為統計平均值，每一液晶的長軸與 n 之 間有一擾動 加至臨界電壓 Vth時，液晶開始轉動 Vth= (Kii/ 0 )1/2 UE= -DE = -E2-(nE)2 1 8 8 8 = -E2-(Ecos )2 8 8 彈彈 性性 係係 數數 之之 測測 定定 Vth= (Kii/ 0 )1/2 E Spray Kii= K11 E Bend Kii= K33 E Twist Vth=K11+(K33-2K22)/41/2/( 0 )1/2 an internal resistance to flow, arising from the intermolecular forces in the fluid the viscosity increases at low temperature as a result of lower molecular kinetic energy rotational viscosity provides a resistance to the rotational motion of the LC molecules Viscosity Rotational Viscosity Viscosity, especially rotational viscosity 1, plays a crucial role in the LCD response time. The switching time of a nematic LC device is approximately proportional to 1d2, where d represents the cell spacing. It is known experimentally that molecules with a higher number of rings or longer alkyl chains are characterized by an increasing viscosity. LCs with high values of usually exhibit higher viscosities due to the sronger polar interaction between the molecules. Response time rise 1d2 K- 1 V Vth 2 decay 1d2 K Homogeneous cell：K11 Homeotropic cell：K33 t T 10% 90% Rise timeDecay time Vth= (Kii/ 0 )1/2 , but Vth, as Kii Rotational viscosity is a complicated function of molecular shape, moment of inertia, activation energy and temperature. Several theories have been developed in an attempt to account for the origin of LC viscosity. A general form for 1 is expressed as Several variations have been employed to fit experimental data. 1 = ( 0 + 1S+ 2S2)exp ESm K(T Tmelting) de Jeu Model 1 = 1Sexp(E/kT) 1 : proportional constant E : activation energy of diffusion k : Boltzmann constant S : order parameter Viscosity unit : 1Pa-s (pascal-second) = 1N-s/m2in SI (MKSA) units = 10 poise (1posie=1dyn-s/cm2in cgs unit) 1 , as T S = (1-) T Tc The simuated rotational viscosity using 1 = 1Sexp(E/kT) for E=400 (circles), 380 (squares) and 360 meV (triangles) assuming Tc=100 and =0.25 Resistivity the bulk resistivity (電阻係數) of a LC mixture depends on the purity of the individual components and what polar groups are employed impurity ions tend to accumulate near the alignment layer interfaces resistivity affects the voltage holding ratio (VHR) and power consumption 某一灰階電壓V, 經過一個 frame time 後,電壓降為V , V /V 稱為VHR low VHR causes the voltage of a pixel image to decay with time and gives rise to undesirable image flickering for active-matrix LCDs the LC cell resistivity reduces rapidly as the temperature increases P = V2/R 許多影響LCD性能之物理參數與秩序參數S間有著密切 之相關性，如下所示: Example: 當TN cell之溫度上升時，其臨界電壓Vth如何變化? NomenclatureParameter() Elastic ConstantKiiS2 Birefringence nS Dielectric Anisotropy S