液晶自由能的简单推导

描述液晶向列相和胆甾相弹性性质的自由能密度,其形式为其中n(r)为空间r处之指向(director),代表分子的平均取向,｜n｜=1.2π/q0为胆甾相的螺距.在向列相中,q0=0.K1—K3为弹性常数.有关这些物理量的进一步讨论,参看文献[1-4]. 这个简单的自由能的具体形式(从1933年起Oseen[1]和 Zocher[2]初步考虑,其后1958年Frank[3]比较完备的处理,以至后人的进一步工作)经过漫长三十多年的时间,才以(1)式的通用形式固定下来.目前常用的推导方法,除了Frank本人所提出的方案外,还有de Gennes在他《液晶物理》这本经典著作里的一个方法[4]以及Nehring和S…     

液晶在电场和剪切耦合作用下的流变学行为

本文通过理论和实验对液晶 5CB在剪切和电场耦合作用下流变行为进行了研究. 采用液晶连续理论, 建立了包括界面锚定能, 弹性自由能, 介电自由能和流动能在内的系统 Gibbs自由能公式, 通过最小化系统自由能的方法求解液晶在剪切和电场耦合作用下的取向分布及其黏度变化, 从分子基础模型上揭示了液晶在耦合作用下的流变行为、微观机理及其影响规律, 并通过流变测试对此进行验证. 对比分析了理论和试验结果的误差和原因, 发现界面锚定效应对于液晶分子的取向和黏度具有重要影响. 理论和试验结果均表明, 液晶在电场作用下具有明显的电黏效应, 表现出非牛顿流变行为, 其黏度值由剪切和电场的竞争和耦合作用共同决定. 在外电场作用下液晶的黏度可以增加到初始值的 4倍左右, 液晶这种其自身黏度可随着外场 (例如运动速度) 改变的特性在一定的条件下可以自适应地满足不同工况对黏度的要求, 这对实现智能摩擦润滑具有重要的意义. 关键词： 液晶 流变行为 电黏效应 耦合作用     

空间各向异性两体势向列相液晶形变研究

基于分子两体势研究向列相液晶的形变.该两体势是空间各向异性的并且依赖于液晶的弹性常数.理论处理中假定具有理想向列序，这意味着分子长轴取向方向与液晶指向矢是重合的，而总自由能等于总相互作用能.以解析形式研究了三种基本的Fréedericksz 转变并对混合排列向列相液晶盒中的指向矢分布进行了数值计算.检查了文献中最近提出的两种从弹性能到两体作用势的映射方案，发现只有一种方案给出的结果与连续体理论一致. 关键词： 空间各向异性两体势 理想向列序 液晶形变 Fréedericksz 转变     

全漏光导波技术确定液晶材料的挠曲电系数

利用全漏光导波技术,测量负性向列相液晶材料MS-N01300-000的展曲和弯曲挠曲电系数之和.根据液晶弹性和多层光学理论得到同一电压下不同挠曲电系数的反射率随内角(入射到液晶层角度)的理论变化曲线.实验中,将液晶材料灌注到混合排列向列相液晶盒中,在液晶盒上分别加交流电和直流电,采用全漏光导波技术得到反映液晶指向矢分布的液晶波导反射率随内角变化曲线.实验发现,由于液晶挠曲电作用,同一电压值下反射率随内角变化曲线发生微小移动.对比理论与实验曲线,由曲线移动距离得到MS-N01300-000液晶材料展曲和弯曲挠曲电系数之和为2.5×10-11 C/m.     

基于修正的Gruhn-Hess两体势模型研究弯曲形变向列相液晶盒

使用修正的Gruhn-Hess空间各向异性两体势模型研究弯曲形变向列相液晶盒.为了易与弹性理论的结果进行比较,做单一弹性常数近似.在理想有序条件下,对模型进行连续化处理,截断到形变的二阶项,给出的自由能密度公式与含k₁₃项的弹性理论公式一致.使用模型直接研究强锚泊弯曲形变向列相盒,没有出现弹性理论给出的边界处不连续.通过Monte Carlo模拟研究发现,两体势中的k₁₃项将加剧弯曲盒中间层的涨落.     

向列液晶预倾角与其弹性常量的相关性研究

向列液晶分子在基片上形成预倾角是液晶分子进行重新排列取向的过程,预倾角的大小会影响与取向相关的向列液晶的弹性变形行为.本文通过设置不同的预倾角,在不同的温度下用激光散射技术测量向列液晶的弛豫系数,从而获得液晶的弹性常量,并研究弹性常量随预倾角的变化规律.研究结果表明,当预倾角小于某一角度,由于向列液晶分子内部排列不规整而无法体现其整体的弹性变形特征;当预倾角达到一定的角度,向列液晶就表现出最大的弹性常量值,液晶特有的弹性变形行为得以充分的体现.     

聚合物网络稳定铁电液晶中的条纹织构的研究

对聚合物网络稳定的铁电液晶体系进行了研究.实验表明,在聚合物网络单体聚合过程中施加低频交变电场，在偏光显微镜下观察到均匀的液晶分子排列出现一新的条纹织构.从体系自由能的角度对条纹织构给出合理的解释. 关键词：     

Monte Carlo模拟空间各向异性势向列相液晶微滴

基于分子两体势,用Monte Carlo方法计算向列相液晶微滴.两体势基于格点模型,是空间各向异性的且依赖于液晶的弹性常数.假定向列相液晶微滴具有自由表面,引入切向内禀强度定量描写表面引发的分子内禀易取向的强弱.通过各向异性势的两种方案,在低温下计算切向内禀强度和二阶序参数在微滴内不同区域的变化,与Lebwohl-Lasher模型作对比分析.结果表明:只有一种方案在微滴表面产生内禀易取向,且内禀强度值的大小与K₃₃/K₁₁值有关;空间不完整的向列相液晶使得微滴由内层到外层有序度越来越低.     

Gruhn-Hess两体势修正模型向列相液晶微滴的Monte Carlo模拟

基于Gruhn-Hess两体势修正模型,用Monte Carlo方法模拟向列相液晶微滴.Gruhn-Hess两体势是空间各向异性的,修正模型的势参数依赖于液晶的弹性常数K₁₁、K₂₂、K₃₃及表面弹性常数K₁₃.假设向列相液晶微滴具有自由表面,在低温下计算分子二阶序参数和切向内禀强度在微滴内不同区域的变化,并与Gruhn-Hess两体势模型一作对比分析.结果表明:附加K₁₃项的修正模型在微滴表面产生内禀锚定,其大小决定了内禀易取向方向及内禀锚定强度的大小,且内禀强度的大小与K₃₃/K₁₁值有关;空间不完整的向列相液晶微滴由内层到外层有序度逐渐降低.     

基于液晶空间光调制器的光栅衍射效率

基于Jones矩阵理论和液晶弹性自由能理论，分析计算了扭曲向列型液晶空间光调制器（TN-LCSLM）的复振幅调制特性.以显示一维矩形光栅为例，详细计算了不同输入输出偏振器配置下的一级衍射效率.数值计算结果和分析表明，在加输出偏振器和不加输出偏振器两种情况下都存在一个具有最大一级衍射效率的取向配置.     

Elastic properties of nematoid arrangements formed by amoeboid cells

In culture migrating and interacting amoeboid cells can form nematoid arrangements in analogy to a nematic liquid crystal phase. A nematoid arrangement is formed if the interaction has an apolar symmetry. Different cell types like human melanocytes (= pigment cells of the skin), human fibroblasts (= connective tissue cells), human osteoblasts (= bone cells), human adipocytes (= fat cells) etc., form a nematoid structure. Our hypothesis is that elastic properties of these nematoid structures can be described in analogy to that of classical nematic liquid crystals. The orientational elastic energy is derived and the orientational defects (disclination) of nematoid arrangements are investigated. The existence of half-numbered disclinations shows that the nematoid structure has an apolar symmetry. The density- and order parameter dependence of the orientational elastic constants and their absolute values are estimated. From the defect structure, one finds that the splay elastic constant is smaller than the bend elastic constant (melanocytes). The core of a disclination is either a cell free space or occupied by non oriented cells (isotropic state), by a cell with a different symmetry, or by another cell type. Received 3 May 1999 and Received in final form 29 September 1999     

Nematic order in small systems: measuring the elastic and wall-anchoring constants in vibrofluidized granular rods

We investigate nematic order in vibrated granular rods confined to a small quasi-2D container less than 10 rod lengths in diameter. As rod density ρ increases, patterning shifts from bipolar to uniform alignment. We find that a continuum liquid crystal free energy functional captures key patterning features down to almost the particle size. By fitting theory to experiments, we estimate the relative values of bend and splay elastic constants and wall anchoring. We find that splay is softer than bend for all ρ and rod lengths tested, while the ratio of the average elastic constant to wall anchoring increases with ρ.     

Anomalous temperature dependence of elastic constants in the nematic phase of binary mixtures made of rodlike and bent-core molecules

We report on two anomalous trends in the temperature dependences of the splay (K11) and bend (K33) elastic constants in the nematic (N) phase of mixtures of compounds with rodlike (R) and bent-core (BC) molecules: As the sample is cooled from the isotropic to N transition point, (i) K33 increases, attains a maximum value and then decreases, and (ii) close to the N to smectic A (SmA) transition point, K11 decreases sharply. At higher temperatures the bow axes of BC molecules are aligned along the director n, strongly favoring a bend distortion of n as the orientational order parameter is increased. Close to the N-SmA transition point the smecticlike short-range order builds up, and the arrow axes of BC molecules are aligned along n, facilitating a splay distortion of n. A simple model calculation brings out the anomalous trend in K33.     

弹性形变对丝状相液晶相变的影响

应用Saupe形式的弹性自由能,研究了简单的扭曲,展曲和弯曲形变对相变的影响.结果表明,弹性形变可以产生从各向同性相至双轴丝状相的一级相变,对螺状相液晶,当系统手征性增加并超过某一临界值时,一级相变可过渡到二级相变. 关键词：     

On spatial variations of nematic ordering

We present a theory of orientational order in nematic liquid crystals which interpolates between several distinct approaches based on the director field (Oseen and Frank), order parameter tensor (Landau and de Gennes), and orientation probability density function (Onsager). As in density-functional theories, the suggested free energy is a functional of spatially-dependent orientation distribution, however, the nonlocal effects are taken into account via phenomenological elastic terms rather than by means of a direct pair-correlation function. In illustration of this approach we consider a simplified model with orientation parameter on a circle and reveal its relation to the complex Ginzburg-Landau theory.     

Electrostatic origin of the Frank elastic energy and anisotropic line tension of the domains in monolayers at the air-water interface

The free energy of condensed phase domains in monolayers at the air-water interface has been analyzed by taking into account the surface pressure, line tension, and electrostatic energy due to the normal and in-plane spontaneous polarization. We found that this free energy was reduced to the sum of the Frank elastic energy and anisotropic line tension, which were used to reproduce the shapes of domains in fatty acid monolayers, in the limit of small orientational deformation. Domains in monolayers are interesting systems as a meeting point between the physics of liquid crystals and electrostatics.     

c-director relaxation around a vortex of strength +1 in free-standing smectic-C films

The relaxation of director fields in freely suspended smectic films is studied experimentally by means of polarizing microscopy, and analyzed by solving the torque balance equation under appropriate initial and boundary conditions. We consider in particular the role of anchoring conditions of the c-director at particles and defects in the film. The structure of regular relaxation patterns allows to determine the elastic anisotropy of smectic materials. The splay elastic constant can exceed the bend constant by a factor of two and more. A remarkable consequence of this anisotropy is the stick-slip-like relaxation around a central defect of topological strength s = + 1.     

Flexoelastic properties of polar liquid crystals

Structural properties of liquid crystals, such as the order parameters and the orientational, radial, and direct correlation distribution functions of polar liquid crystals 4-n-heptyloxy-4′-n-cyanobiphenyl (7OCB) and 4-n-hexyloxy-benzylidene-4′-n-aminobenzonitrile (HBAB) have been calculated using a combination of numerical simulation and statistical mechanics methods. It has been shown that the calculated values of both the Frank elastic coefficients K _i (i = 1, 2, 3) corresponding to the splay, twist, and bend deformations and the flexoelectric coefficients e _i (i = 1, 3) agree with the experimental data for 7OCB. The calculated values of the same coefficients for HBAB have been published for the first time.     

Electron beam irradiation induced changes in the dielectric and electro-optical properties of a room temperature nematic display material 4-(trans-4′-n-hexylcyclohexyl) isothiocyanatobenzoate (6CHBT)

Dielectric and electro-optical studies of a pure and electron beam irradiated liquid crystalline compound 4-(trans-4′-n-hexylcyclohexyl) isothiocyanatobenzoate have been carried out. Dielectric anisotropy, relaxation frequency, activation energy and distribution parameter of an observed non-collective mode corresponding to the molecular rotation about the short axes have been determined as a function of temperature and irradiation dose whereas threshold and switching voltages, splay elastic constant are determined as a function of irradiation dose. The relaxation frequencies initially decrease up to an irradiation dose of 40 kGy but thereafter increase due to irradiation. The activation energies are increased up to irradiation dose of 40 kGy but around 60 kGy dose of irradiation, we found decrease in the activation energy. Electro-optical measurements show the lowering of the threshold voltage with sufficient improvement in the steepness of the transmission voltage curves due to irradiation. The observed changes in the dielectric and electro-optical properties are related with the cis–trans isomerization due to electron beam irradiation.     

Structure and elastic properties of a nematic liquid crystal: A theoretical treatment and molecular dynamics simulation

The Frank elasticity constants which describe splay (K ₁), twist (K ₂), and bend (K ₃) distortion modes are investigated for 4-n-pentyl-4'-cyanobiphenyl (5CB) in the nematic liquid crystal. The calculations rest on statistical-mechanical approaches where the absolute values of K _i (i=1,2,3) are dependent on the direct correlation function (DCF) of the corresponding nematic state. The DCF was determined using the pair correlation function by solving the Ornstein-Zernike equation. The pair correlation function, in turn, was obtained from molecular dynamics (MD) trajectory. Three different approaches for calculations of the elasticity constants were employed based on different level of approximation about the orientational order and molecular correlations. The best agreement with experimental values of elasticity constants was obtained in a model where the full orientational distribution function was used. In addition we have investigated the approximation about spherical distribution of the intermolecular vectors in the nematic phase, often used in derivation of various mean-field theories and employed here for the construction of the DCF. We found that this assumption is not strictly valid, in particular a strong deviation from the isotropic distribution is observed for short intermolecular distances. Received 22 March 2000 and Received in final form 9 June 2000