LIQUID-CRYSTALS WITH VARIABLE DEGREE OF ORIENTATION
LIQUID-CRYSTALS WITH VARIABLE DEGREE OF ORIENTATION
复制标题
DOI：
10.1007/bf00380413
复制
发表时间：
1991-01-01
影响因子：
2.5
通讯作者：
ERICKSEN, JL
中科院分区：
文献类型：
--
作者：
ERICKSEN, JL
对于显示器件中常用的小分子液晶，CHANDRASE~ ZHAR [1]所称的Oseen-Zcher-Frank方程（以下简称OZF方程）在描述许多静态现象方面已相当成功。对于涉及流动的现象，他称之为埃里克森-莱斯利方程的方程已经被相当成功地使用：它们简化为静力学的OZF方程。许多工人接受他所谓的帕罗迪关系，昂萨格关系。据我所知，还没有进行过仔细的实验测试。CURRIE [2]指出，它确实具有某种稳定性条件的地位。Kuzuu和DoI [3]注意到，他们所考虑的分子理论的类型确实暗示了这种关系。我遵循DE GENNES [4]的说法，将所得方程称为EL或ELP理论，这取决于是否假定Parodi关系成立。首先，我很想看到一个数学上合理的缺陷理论的发展，这个理论可能是静止的，也可能是运动的。以OZF方程为基础的点缺陷静态理论现在已经发展得相当完善，正如ERICKSEN [5]和KINDERLEHRER [6]在调查中所讨论的那样。我相信EL和ELP理论能够描述动点缺陷。然而，尽管作出了一些认真的努力，但在进行相关分析方面没有取得真实的进展。对于某些观察到的向错（线缺陷），会遇到更严重的困难。根据前面提到的理论，这些更剧烈的奇点会导致能量积分等，分歧在处理相当具体的情况时，工作者们通过排除小半径的管，赋予它有限的”核心能量”来修补理论，我只是不相信人们可以用这样的思想作为发展令人满意的数学理论的基础，特别是对于运动缺陷。这种现象对于双折射和双折射液晶都是有意义的。在后者中，它们与CLADIS [7]和SETHNA [8]讨论的有趣的“蓝相”有关。在修补相当有效的理论时，存在着这样一种危险，即在修补一个缺陷时，人们会发现其他好的预测受到了不利的影响。慢慢地，我认为这个风险值得冒。有生理上的原因-
For the small-molecule nematic liquid crystals commonly used in display devices, what CHANDRASE~ ZHAR [1] calls the Oseen-Z6cher-Frank equations, hereafter referred to as the OZF equations, have been quite successful in describing many static phenomena. For phenomena involving flow, what he calls the Ericksen-Leslie equations have been used rather successfully: they reduce to the OZF equations for statics. Many workers accept what he calls Parodi's relation, an Onsager relation. Careful experimental tests of this have not been made, as far as I know. CURRIE [2] points out that it does have some status as a stability condition. Kuzuu & DoI [3] note that the type of molecular theory which they consider does imply this relation. I follow DE GENNES [4] in referring to the resulting equations as the EL or ELP theory, depending on whether Parodi's relation is presumed to hold.Two things have motivated me to consider modifying the equations. For one thing, I am interested in seeing the development of a mathematically sound theory of defects which might be at rest, or moving. The static theory of point defects, based on the OZF equations, is now rather well developed, as is discussed in surveys by ERICKSEN [5] and KINDERLEHRER [6]. I believe that the EL and ELP theories are capable of describing moving point defects. However, no real progress has been made in developing pertinent analyses, despite some serious efforts. More serious difficulties are encountered with some observed kinds of disclinations (line defects). According to the aforementioned theories, these more violent singularities cause energy integrals, etc., to diverge. In dealing with rather specific situations, workers have patched up the theory by excluding a tube of small radius, assigning a finite" core energy" to it. I just do not believe that one can use such ideas as a basis for developing satisfactory mathematical theory, particularly for moving defects. Such phenomena are of interest for both nematic and cholesteric liquid crystals. In the latter, they are associated with the interesting" blue phases" discussed by CLADIS [7] and SETHNA [8], among other things. In tinkering with theories which work rather well, there is some danger that, in fixing one flaw, one will find other good predictions affected adversely. Slowly, I have come to the view that the risk is worth taking. There is a physically reason-