《向列相液晶的连续体力学与空间各向异性优势格点模型的研究》由会员分享，可在线阅读，更多相关《向列相液晶的连续体力学与空间各向异性优势格点模型的研究（45页珍藏版）》请在金锄头文库上搜索。
1、河北工业大学硕士学位论文向列相液晶的连续体力学与空间各向异性优势格点模型的研究姓名：周璇申请学位级别：硕士专业：理论物理指导教师：张志东20091201河北工业大学硕士学位毕业论文 i向列相液晶的连续体力学与空间各向异性势 格点模型的研究 向列相液晶的连续体力学与空间各向异性势 格点模型的研究 摘摘 要要 关于液晶的理论可以分为两大基本类别：一类是连续介质理论，另一类是分子理论。这两种理论研究问题的思路大相径庭，但在解释有关液晶的现象中各有所长。 连续介质理论主要解释液晶在电场、磁场和力场等外场中的行为。本文第一部分以液晶连续体力学理论为基础，研究混合排列向列相（HAN）液晶的动力学行为。建立
2、了三种情形下的指向矢运动方程，即严格考虑引流效应，通过有效粘滞系数eff考虑引流效应和完全忽略引流效应。通过对加电压和撤电压过程的数值模拟，我们发现：通过有效粘滞系数eff考虑引流效应不会发生引流效应引起的指向矢过倾斜现象，但会影响液晶响应速度。 分子理论是从分子间相互作用出发研究液晶的宏观性质。由于液晶分子为有机大分子，通常只能通过两体势模型描写其相互作用。1996，Gruhn 和 Hess 基于向列相的宏观弹性自由能密度公式提出了一种空间各向异性两体作用势模型（Gruhn-Hess 模型） 。有两种从弹性能到势参数的映射方案，分别称为模型一和模型二。最近，作者将两体势理论与弹性理论相结合,
3、讨论了势参数与弹性常数13k 的关系,建立了新的模型修正 Gruhn-Hess 两体势模型。本文二、三部分基于该两体势模型研究弯曲形变向列相液晶盒和 TN 模式液晶盒。该两体势是空间各向异性的并且依赖于液晶的弹性常数。 第二部分利用单一弹性常数近似下的修正模型研究弯曲形变向列相液晶盒。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13k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，并不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13k 项将加剧弯曲盒中间层的涨落。第三部分利用模型一模拟研究 TN 模
4、式液晶盒。通过 Monte Carlo 模拟和琼通过分子动力学方法研究向列相液晶格点模型 ii 斯矩阵方法得到 TN 液晶盒的电光特性曲线和中间层指向矢分布。我们发现：电光特性曲线和中间层的极角分布曲线相似；1133kk取值会影响陡度因子的大小，1133kk取值越大，陡度因子越大。 关键词：关键词：空间各向异性两体势，引流效应，有效粘滞系数，表面弹性常数13k ，内禀锚定，陡度因子，Monte Carlo 模拟 河北工业大学硕士学位毕业论文 iiiSTUDY OF CONTINUUM MECHANICS AND SPATIALLY ANISOTROPIC PAIR POTENTIAL LATT
5、IC MODEL OF NEMATIC LIQUID CRYSTAL ABSTRACT There are two basic theories about liquid crystal：continuum medium theory and molecule theory，which are used to explain different phenomenon of liquid crystals. The continuum medium theory are used to explain the behavior of liquid crystal under electric f
6、ield, magnetic field and other outfields. The dynamic behavior of hybrid alignment nematic （HAN）liquid crystals is investigated based upon the dynamic theory of liquid crystals in the first section. The equations for the director are built in three different conditions; i. e. first，backflow effect i
7、s taken into account rigorously; second， the backflow is considered by the effective rotational viscosity eff; third， the backflow effect is neglected directly. Through computer simulation to the progress of switching up the voltage and switching off the voltage，we get the effect of the effective ro
8、tational viscosity eff on the director profiles and the effective refractive index of liquid crystal . Molecule theory is studying macroscopic properties of liquid crystal based on molecular interaction. The molecule of liquid crystal is organic macromolecule, so we usually describe the interaction
9、with pair potential model. In 1996, Gruhn and Hess proposed a spatially anisotropic pair potential, which approximately reproduced the elastic free energy density（Gruhn-Hess model）. There are two mapping schemes from the elastic energy to the pair potential models, called model I and model II. Recen
10、tly，the pair potential theory of liquid crystal is associated with the macroscopic elastic theory of liquid crystal and the relations of potential parameters and 通过分子动力学方法研究向列相液晶格点模型 iv the elastic constant 13kare discussed, a modified Gruhn-Hess pair potential model was established. In the second a
11、nd third section, the bend distortion and Twisted Nematic mode liquid crystals are studied based upon the molecular pair potential model which is spatially anisotropic and dependent on elastic constants of liquid crystals. In the second part, nematic liquid crystal cell with bend distortions is stud
12、ied based upon the modified model under one-constant approximation. In perfect order, we get the continuous form of the free energy density formula, neglecting the ranks after the second rank of distortions, which is consistent with the elastic theory. The study of strong anchoring nematic liquid cr
13、ystal cell with bend distortions based on the model doesnt present the surface discontinuities obtained by the elastic theory. By Monte Carlo simulation, we find that the 13k term in pair potential will increase the fluctuation in the middle cell. TN mode liquid crystal is studied based upon model I
14、 in the third part. By Monte Carlo simulations and Jones matrix method, we get the electro-optical curves of TN cells and the director profiles in the middle layer at different values of1133kk. It is shown that the curves of electro-optic characteristic are similar to that of the polar angle in the
15、middle cell; the magnitude of 1133kk will influence the steepness factor of TN cells, the bigger the value of 1133kk，the bigger the steepness factor . KEY WORDS: spatially anisotropic pair potential, backflow effect, the effective rotational viscosity, surface elastic term13k , intrinsic anchoring,
16、steepness factor, Monte Carlo simulation 原创性声明原创性声明 本人郑重声明：所呈交的学位论文，是本人在导师指导下，进行研究工作所取得的成果。除文中已经注明引用的内容外，本学位论文不包含任何他人或集体已经发表的作品内容，也不包含本人为获得其他学位而使用过的材料。对本论文所涉及的研究工作做出贡献的其他个人或集体，均已在文中以明确方式标明。本学位论文原创性声明的法律责任由本人承担。 学位论文作者签名： 日期： 关于学位论文版权使用授权的说明关于学位论文版权使用授权的说明 本人完全了解河北工业大学关于收集、保存、使用学位论文的以下规定：学校有权采用影印、缩印、扫描、数字化或其它手段保存论文；学校有权提供本学位论文全文或者部分内容的阅览服务；学校有权将学位论文的全部或部分内容编入有关数据库进行检索、交流；学校有权向国家有关部门或者机构送交论文的复印件和电子版。 （保密的学位论文在解密后适用本授权说明） 学位论文作者签名： 日期： 导师
