### 物理代写|光学代写Optics代考|UNITS 24

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|光学代写Optics代考|MOLECULAR STRUCTURES AND CHEMICAL COMPOSITIONS

With few exceptions, liquid crystals are composed of organic substances with a typical structure, as depicted in Figure 1.1. They are aromatic and, if they contain benzene rings, they are often referred to as benzene derivatives. In general, aromatic liquid crystal molecules such as those shown in Figure $1.1$ comprise a side chain $\mathrm{R}$, two or more aromatic rings $A$ and $A^{\prime}$, connected by linkage groups $X$ and $Y$, and at the other end connected to a terminal group $\mathrm{R}^{\prime}$.

Examples of side chain and terminal groups are alkyl $\left(\mathrm{C}{n} \mathrm{H}{2 n+1}\right)$, alkoxy $\left(\mathrm{C}{n} \mathrm{H}{2 n+1} \mathrm{O}\right)$, and others such as acyloxyl, alkyl carbonate, alkoxy carbonyl, and the nitro and cyano groups. The Xs of the linkage groups are simple bonds or groups such as stilbene $(-\mathrm{CH}==\mathrm{CH}-)$, ester $\left(-|_{\mathrm{C}}^{\mathrm{O}} \mathrm{O}-\right)$, tolane $(-\mathrm{C} \equiv \equiv \mathrm{C}-)$, azoxy $(-\mathrm{N}==\mathrm{N}-)$, Schiff base $(-\mathrm{CH}==\mathrm{N}-)$, acetylene $(-\mathrm{C} \equiv \equiv \mathrm{C}-)$, and diacetylene $(-\mathrm{C} \equiv \equiv \mathrm{C}-\mathrm{C} \equiv \equiv \mathrm{C}-)$. The names of liquid crystals are often fashioned after the linkage group (e.g. Schiff-base liquid crystal). There are quite a number of aromatic rings. These include saturated cyclohexane or unsaturated phenyl, biphenyl, and terphenyl in various combinations.

The majority of liquid crystals are benzene derivatives; the rest include heterocyclics, organometallics, sterols, and some organic salts or fatty acids. Their typical structures are shown in Figures 1.2-1.4. Heterocyclic liquid crystals are similar in structure to benzene derivatives, with one or more of the benzene rings replaced by a pyridine, pyrimidine, or another similar group. Cholesterol derivatives are the most common chemical compounds that exhibit the cholesteric (or chiral nematic) phase of liquid crystals. Organometallic compounds are special in that they contain metallic atoms and possess interesting dynamical and magneto-optical properties.

## 物理代写|光学代写Optics代考|Electronic Optical Transitions and UV Absorption

Since liquid crystal constituent molecules are quite large, their energy level structures are rather complex. In essence, the basic quantum mechanical theory is similar to the one described in Chapter 10 for a multilevel molecule. Generally, the energy levels are referred to as orbitals: $\pi, n$, and $\sigma$ orbitals for the ground and low-lying levels and $\pi^{}, n^{}$, and $\sigma^{}$ for their excited counterparts. Since most liquid crystals are aromatic compounds, containing one or more aromatic rings, the energy levels or orbitals of aromatic rings play a major role. In particular, the $\pi \rightarrow \pi^{}$ transitions in a benzene molecule have been extensively studied. Figure $1.6$ shows three possible $\pi \rightarrow \pi^{*}$ transitions in a benzene molecule.

In general, these transitions correspond to the absorption of light in the near-UV spectral region $(\leq 200 \mathrm{~nm})$ [2]. These results for a benzene molecule can also be used for interpreting the absorption of liquid crystals containing phenyl rings. On the other hand, in a saturated cyclohexane ring or band, usually only $\sigma$ electrons are involved. The $\sigma \rightarrow \sigma^{}$ transitions correspond to absorption of light of shorter wavelength $(\leq 180 \mathrm{~nm})$ in comparison to the $\pi \rightarrow \pi^{}$ transition mentioned previously.
These optical properties are also related to the presence or absence of conjugation (i.e. alternations of single and double bonds, as in the case of a benzene ring). In such conjugated molecules, the $\pi$ electron’s wave function is delocalized along the conjugation length, resulting in absorption of light in a longer wavelength region compared to, for example, that associated with the $\sigma$ electron in compounds that do not possess conjugation. Absorption data and spectral dependence for a variety of molecular constituents, including phenyl rings, biphenyls, terphenyls, tolanes, and diphenyl-diacetylenes, may be found in [2].

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。