Q-Tensor models of defect dynamics in pure and doped liquid crystals

纯液晶和掺杂液晶中缺陷动力学的 Q 张量模型

• 批准号: EP/J006920/1
• 负责人: Giampaolo D'Alessandro
• 金额: $ 35.94万
• 依托单位: University of Southampton
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2012
• 资助国家: 英国
• 起止时间: 2012 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FJ006920%2F1
• 关键词: Tensor; models; defect; dynamics; pure

Liquid crystals are best known for their applications in modern flat screens, but other technologically important applications include colour-sensitive thermometers, temperature-sensitive paints, optoelectronic equipment such as shutters and sensors, materials such as ultra-light body armour, as well as very recently in microfluidic devices-on-a-chip. They are also materials of great fundamental interest because they exhibit some liquid-like properties (they flow) and some solid-like properties (their properties depend on direction). Despite intense theoretical work over the last forty years, it is still the case that new applications require a more fundamental mathematical understanding of liquid crystalline models in order that rapid device prediction can be made. A major headache in liquid crystal theory is the so-called "defect" problem. Liquid crystals usually exhibit a preferred direction, but this preferred direction can change from place to place. The defects are lines or points near which the preferred direction dissolves. An analogy can be seen when one combs one's hair: it is impossible to comb hair uniformly over a sphere; there will always be some holes in the pattern. Cosmologists have also use the liquid crystal defects as models of the early universe. The internal patterns of the defects also provide the dramatic and beautiful characteristic optical signatures for individual types of liquid crystal. Describing them has caused much difficulty in mathematical theories of liquid crystals. The standard theory (due to the Scottish mathematician Frank Leslie) just omits them, while alternative approaches ("the Q-tensor" theory) often are computationally inefficient in regions in which the preferred direction changes only slowly. In the latter case, even when there is a computational model for the liquid crystal properties, it may be difficult to provide a physical picture. The end result is that properties of new devices cannot be predicted reliably and quickly. Our project will provide a more sophisticated model of the motion of defected nematic liquid crystals. We shall build on a new mathematical approximation which we have recently developed. This approach, which we have labelled the Defect-free Q-tensor approximation (DFQTA), uses the best features of the Leslie and Q-tensor approaches. In non-defected liquid crystals, this approach has led to dramatic improvements (of the order of a factor of 100) in the computational time required to solve some benchmark problems, without any loss of accuracy. Our new model will treat defect motion by patching together solutions in the defect-free and defected regions. The defect-free region will be treated using DFQTA. The defect itself will be cut out of the problem, and treated separately using a range of approximations made possible by the fact, amongst others, that the regions that contains them are small. The two regions will be matched using asymptotic analysis. Our approach will combine the algorithmic requirements of engineers (who often downplay the necessity for mathematical analysis), with sophisticated mathematical approximation tools to obtain an accurate and computationally efficient model. One particular engineering application concerns nanoparticles suspended in liquid crystal solutions. Nanoparticles are of micron size or smaller, and even at very low concentrations (much less than 1% by volume), they can change the properties of the solvent significantly. These particles are being used in a new generation of devices, both in liquid crystals and elsewhere. But in liquid crystals the nanoparticles are attracted to defects. Both the motion and the optical signature of the nanoparticles seem to be governed by defects which trap them. Our new theory will enable such systems to be treated successfully on computationally accessible time-scales.

液晶以其在现代平板屏幕中的应用而闻名，但其他重要的技术应用包括颜色敏感温度计、温度敏感涂料、光电子设备(如快门和传感器)、材料(如超轻型防弹衣)以及最近在微流控芯片设备中的应用。它们也是非常重要的基本材料，因为它们表现出一些类似液体的性质(它们是流动的)和一些类似固体的性质(它们的性质取决于方向)。尽管在过去的四十年里进行了大量的理论工作，但新的应用仍然需要对液晶模型有更基本的数学理解，以便能够快速地进行器件预测。液晶理论中一个令人头疼的问题就是所谓的“缺陷”问题。液晶通常表现出一个优先的方向，但这个优先的方向可能会因地而异。缺陷是首选方向在其附近溶解的线或点。当一个人梳理头发时，可以看到一个类比：不可能在一个球体上均匀地梳理头发；图案上总是会有一些洞。宇宙学家还使用液晶缺陷作为早期宇宙的模型。缺陷的内部图案还为各种类型的液晶提供了戏剧性和美丽的特征光学特征。描述它们在液晶的数学理论中造成了很大的困难。标准理论(由于苏格兰数学家弗兰克·莱斯利)只是忽略了它们，而替代方法(Q张量理论)在首选方向变化缓慢的地区往往计算效率低下。在后一种情况下，即使存在液晶性质的计算模型，也可能难以提供物理图像。最终的结果是，新设备的性能无法可靠和快速地预测。我们的项目将为缺陷向列相液晶的运动提供一个更复杂的模型。我们将建立在我们最近开发的一种新的数学近似的基础上。这种方法，我们称之为无缺陷Q张量近似(DFQTA)，它利用了Leslie和Q张量方法的最佳特征。在没有缺陷的液晶中，这种方法在解决一些基准问题所需的计算时间方面有了显著的改进(提高了100倍)，而精度没有任何损失。我们的新模型将通过将无缺陷和有缺陷区域的解决方案拼接在一起来处理缺陷运动。无缺陷区域将使用DFQTA进行处理。缺陷本身将被从问题中剔除，并使用一系列近似值单独处理，这一范围的近似值是由于包含它们的区域很小等事实而可能的。这两个区域将使用渐近分析进行匹配。我们的方法将结合工程师的算法要求(他们经常淡化数学分析的必要性)，以及复杂的数学近似工具，以获得准确和计算高效的模型。一个特殊的工程应用涉及悬浮在液晶溶液中的纳米颗粒。纳米粒子的尺寸为微米或更小，即使在非常低的浓度下(体积分数远低于1%)，它们也可以显著改变溶剂的性质。这些粒子正被用于新一代设备，无论是液晶还是其他地方。但在液晶中，纳米颗粒会被缺陷所吸引。纳米粒子的运动和光学特征似乎都受到捕获它们的缺陷的控制。我们的新理论将使我们能够在可计算的时间尺度上成功地处理这样的系统。

项目成果

Thermal optical non-linearity of nematic mesophase enhanced by gold nanoparticles--an experimental and numerical investigation.

• DOI: 10.1039/c6cp00116e
• 发表时间: 2016-04
• 期刊: Physical chemistry chemical physics : PCCP
• 作者: O. Kurochkin;Y. Murugesan;Thomas P. Bennett;G. D’Alessandro;Yuri Reznikov;Baijia J. Tang;G. Mehl;Malgosia Kaczmarek

Inter-continental school of geometry and topology in soft matter, optics and biological systems: I-CAMP'14's review

软物质、光学和生物系统中的几何和拓扑学的洲际学派：I-CAMP14 的评论

• DOI: 10.1080/1358314x.2014.973262
• 发表时间: 2014
• 期刊: Liquid Crystals Today
• 影响因子: 3.1
• 作者: Alimagham F