Chiral electrostatic interaction and cholesteric liquid crystals of DNA

Explicit expressions for electrostatic interaction between stiff DNA duplexes of finite length are obtained. These expressions allow for the helical symmetry of charge distribution on DNA molecules and reveal chiral and non-chiral interaction terms. Asymptotic expressions at small twist angles are applied to evaluate the cholesteric pitch and the twist elastic constant and their dependence on the length of DNA fragments. These estimates suggest an explanation for the large value of the cholesteric pitch and its nonmonotonic variation with the density of the liquid crystal. An analysis of biaxial correlations rationalizes the driving force of the transition from the cholesteric to hexagonal phase upon dehydration.     

Symmetry of electrostatic interaction between pyrophosphate DNA molecules

We study chiral electrostatic interaction between artificial ideal homopolymer DNA-like molecules in which a number of phosphate groups of the sugar-phosphate backbone are exchanged for the pyrophosphate ones. We employ a model in which the DNA is considered as a one-dimensional lattice of dipoles and charges corresponding to base pairs and (pyro)phosphate groups, respectively. The interaction between molecules of the DNA is described by a pair potential U of electrostatic forces between the two sets of dipoles and charges belonging to respective lattices describing the molecules. Minima of the potential U indicate orientational ordering of the molecules and thus liquid crystalline phases of the DNA. We use numerical methods for finding the set of minima in conjunction with symmetries verified by the potential U . The symmetries form a non-commutative group of 8th order, S . Using the group S we suggest a classification of liquid crystalline phases of the DNA, which allows several cholesteric phases, that is polymorphism. Pyrophosphate forms of the DNA could clarify the role played by charges in their liquid crystalline phases, and open experimental research, important for nano-technological and bio-medical applications.     

High resolution off-magic-angle spinning NMR for cholesteric liquid crystals

High resolution NMR of cholesteric liquid crystals is realized by off-magic-angle spinning (OMAS). Using the average potential theory, it is shown that the pitch axes of a cholesteric liquid crystal with a positive (negative) magnetic susceptibility anisotropy are aligned along the spinning axis with an OMAS angle larger (smaller) than the magic angle without any distortion of the helical structure, which is untwisted or distorted by the static magnetic field in some static samples. Hence, the line broadening due to the anisotropies of chemical shifts and/or quadrupole couplings is removed, while information of the anisotropies in cholesteric alignments can be obtained from the line positions. A detailed theoretical analysis of effects of spinning frequency and molecular diffusion along the pitch axis on the linewidth is given, predicting that the resolution is improved greatly at a spinning frequency much higher than the rotational diffusion coefficient. These theoretical results are verified by ¹³C OMAS experiments on a cholesteric liquid crystal of p-ethoxybenzyl-p-[(S)-2- methylbutyl]aniline (EBMBA) and cholesteric mixtures of p-methoxybenzylidene-p-n-butylaniline (MBBA) and cholesteryl chloride (CC).     

Interaction of nucleic acid segments as a result of modification of the network of hydrogen bonds of the solvent

It is shown that experimental results on the influence of various factors in the formation efficiency and structure of cholesteric liquid-crystal dispersions of nucleic acids cannot be consistently described using conventional theories of liquid crystal formation. A new model is proposed for the interaction of nucleic acid segments which allows for a change in the particular structure of the solvent hydrogen bonds in the presence of nucleic acid molecules. The conclusions of the model agree with existing spectroscopic and structural investigations of DNA dispersions. According to our model, interaction between nucleic acid molecules and solvent modifies proton tunneling processes in the latter, leading to effective interaction between the nucleic acids. A theoretical analysis of the model is made using a pseudospin formalism in which the effective interaction potential of the nucleic acid segments is calculated. It is shown that this potential may lead to nematic ordering for small distances between the nucleic acid molecules (R ≤ 30 Å) and cholesteric ordering for large distances.     

Twist in chiral interaction between biological helices

Using an exact solution for the pair interaction potential, we show that long, rigid, chiral molecules with helical surface charge patterns have a preferential interaxial angle approximately sqrt[RH]/L, where L is the length of the molecules, R is the closest distance between their axes, and H is the helical pitch. Estimates based on this formula suggest a solution for the puzzle of small interaxial angles in alpha-helix bundles and in cholesteric phases of DNA.     

液晶胆甾相的形成机制

采用量子理论的方法研究了胆甾相液晶的形成机制.证明了通常采用的手性作用势确实能够导致胆甾相的形成，并给出螺距的表示式. 关键词： 液晶 量子理论 螺距     

Symmetries of electrostatic interaction between DNA molecules

A model for pair interaction U of DNA molecules generated by the discrete dipole moments of base-pairs and the charges of phosphate groups is studied. A noncommutative group of eighth order ℒ of symmetries that leave U invariant is found. The minima are classified with the use of group ℒ and numerical methods are employed for finding them. The minima may correspond to several cholesteric phases, as well as to phases formed by crosslike conformations of molecules at an angle close to 90°—the “snowflake phase.” The results depend on the effective charge Q of the phosphate group, which can be modified by the polycations or the ions of metals. The snowflake phase could exist for Q above the threshold Q _C. Below Q _C, there could be several cholesteric phases. Close to Q _C, the snowflake phase could change into the cholesteric one at constant distance between adjacent molecules. The text was submitted by the authors in English.     

横向电场对平面织构胆甾相液晶螺距及反射特性的影响

阐述一种理论模型,讨论共面转换（IPS）模式下横向电场对平面织构胆甾相液晶螺距及扭曲角的影响．利用琼斯矩阵法计算了光正入射情况下未加电场时胆甾相液晶的反射谱．在上述模型基础上,计算了施加电场后胆甾相液晶的反射峰值波长以及反射带宽随场强的变化关系．探讨了忽略锚定与强锚定两种边界条件下横向电场对平面织构胆甾相液晶螺距及反射特性的影响．所得结论在理论上证实：共面转换模式下电场可以调谐胆甾相液晶的反射光颜色,从而为基于电控螺距原理的胆甾相液晶反射式彩色显示方案提供了理论上的依据． 关键词： 胆甾相液晶 电控螺距 共面转换 琼斯矩阵法     

A comparison of orientational order measurements in cholesteric and nematic liquid crystals

We present a quantitative comparison of orientation order parameter measurements at constant pressure and constant density in cholesteric and nematic liquid crystals. The two phases show great similarity. In addition, the volume dependence of the mean-field potential is estimated for this cholesteric, and found to differ from measurements in nematics.     

Piezoelectric effect in liquid crystals

A piezoelectric effect has been observed in a cholesteric liquid crystal layer (an electric field effect type, a mixture of cholesteryl oleyl carbonate, cholesteryl chloride and cholesteryl nonanoate) [1]. The layer, subjected to shear vibration, generates an alternating electric potential of the same frequency as the exciting vibration. In the present paper an extension of these investigations is reported to cases with various mixing ratios and also to one of smectic liquid crystals (lecithin with water). For a cholesteric liquid crystal of a particular mixing ratio, the strength of the electric generation is found to reach as high as 450 mV(p-p) for a vibratory shear displacement of 1 μm(p-p) under a certain molecular orientation preparation. Small electric generation is also observed for the above smectic liquid crystal but not for the nematic liquid crystals (MBBA and EBBA). A simple continuum elasticity model can qualitatively explain the behaviour of this electric potential generation.     

Optical filter with tunable wavelength and bandwidth based on cholesteric liquid crystals

An optical filter with tunable wavelength and bandwidth has been demonstrated using two cholesteric liquid crystals configured in a reflection mode, in which the incident light is first reflected by one cholesteric liquid crystal and then by the other one. The central wavelength can be tuned from 527 nm to 574 nm and the bandwidth can be changed from 10 nm to 80 nm. It has potential applications in many fields, especially in optical communications and multispectral and hyperspectral imaging systems.     

The microscopic theory for BPI and BPII of the blue phase

A statistical theory of the blue phase of chiral liquid crystal is proposed. The form of the interaction potential between molecules is assumed to be the same as that used in the theory for cholesteric phase. Using the cell model of the liquid statistical theory, we deduced the distribution function of single molecule. The free energy of the system obtained has the same form as that of the Ginzberg－Landau phenomenology theory. The order-parameter tensors of BPI and BPII phases we calculated can be compared with the experimental results.     

复合周期的介质-液晶光子晶体研究

本文研究了掺入各向同性周期性介质层缺陷的一维复合周期胆甾型液晶光子晶体的禁带特性.发现同一般的胆甾型液晶不同,复合介质-液晶周期结构对左旋偏振入射光和右旋入射光都会出现共同禁带.当各向同性介质层占一个周期的厚度比例越小,左旋偏振光的禁带效应逐渐消失,而右旋偏振光的禁带则逐渐合并变大;且各向同性介质的折射率越大,则两种偏振光的禁带效应越明显,更容易出现共同禁带;通过调整厚度比,可以在可见光范围内出现对应红、绿、蓝色波长的禁带,从而可以用于液晶显示的反射式彩色滤光片. 关键词： 胆甾型液晶 光子晶体 禁带 缺陷     

Polymer-stabilized cholesteric liquid crystals as switchable photonic broad bandgaps

A cholesteric liquid crystal can be considered as a one-dimensional photonic crystal with a refractive index that is regularly modulated along the helix axis because of the particular arrangement of the molecules. The result is that the propagation of light is suppressed for a particular range of wavelengths (bandgap). A polymer-stabilized cholesteric liquid crystal (PSCLC), which is obtained by in situ photopolymerization of reactive liquid-crystal molecules in the presence of non-reactive liquid-crystal molecules in an oriented Bragg planar texture, is elaborated by combining the UV-curing with a thermally induced pitch variation. As a consequence, it is shown here that memory effects are introduced into the characteristics of the reflection band of the material at room temperature. In the visible spectrum, the reflection bandwidth can be tuned in agreement with the thermal ramp and broadened. In addition, the bandgap filters can be switched between broadband reflective, scattering and transparent states by subjecting them to an electric field. Related application fields of these functional materials are switchable smart windows for the control of the solar-light spectrum and white-or-black polarizer-free reflective displays.     

Novel approach to study liquid crystal phase transitions using Legendre moments

A novel approach is proposed to investigate the phase transitions of cholesteric liquid crystals using the Legendre moments. The textures of cholesteric liquid crystals (cholesteryl butyrate, cholesteryl n-valerate, cholesteryl decanoate, and cholesteryl myristate) are captured as a function of temperature using high-resolution camera attached to the arthroscopic mode of polarizing optical microscope with hot stage. A recurrence formula is used to compute the Legendre moments of the liquid crystal textures based on the Legendre polynomial using MATLAB software. The abrupt change in the values of Legendre moments as a function of temperature gives the phase transitions of liquid crystals. The investigated transition temperatures of cholesteric liquid crystals are compared with other techniques.     

The synthesis of the chiral non-mesogenic d-seco estrone derivatives and their influence on the phase transitions of cholesteric liquid crystals

The synthesis of new chiral seco-estrone derivatives is presented, as well as their influence on the phase transition of binary mixtures of cholesteryc liquid crystals. The new chiral derivatives do not posses any liquid crystalline phases and were synthesized in several synthetic steps, starting from estrone. We have studied the mixtures of cholesteryl non-anoate (40%) with cholesteryl myristate (40%) and addition of new chiral derivatives 3 4, or 5 (20%). It was concluded that the addition of chiral derivative 3 to the binary mixture stabilizes smectic A and cholesteric phase and shifts the phase transition temperature with respect to pure binary mixture for about 5°C towards lower temperatures. The extension of the temperature range of the cholesteric phase from 5°C to 15°C was established in the case when the derivatives 3 and 4 are added to the binary mixture of cholesteryl nonanoate with cholesteryl myristate. The phase diagrams of investigated compounds are formed on the basis of data obtained by the optical microscopy. Using X-ray diffraction on the crystalline powder of unoriented samples we have determined the molecular parameters: the thickness of smectic and cholesteric layers and average distance between the long axes of neighboring molecules.     

液晶胆甾相中的分子短程关联

向列相液晶的二粒子集团理论被推广应用于研究胆甾相二维模型.手征性分子固定在三维简单立方晶格的格点上,而分子取向限制在二维.理论结果表明,平衡态螺旋波矢依赖于温度的变化,且存在胆甾相到向列相相变.通过考虑分子间短程关联,二粒子集团理论的数值结果较平均场理论更接近Monte Carlo模拟结果.     

Effect of dipole forces on the structure of the liquid phases of DNA

The dipole-dipole contribution to the energy of the pair interaction between DNA molecules has been calculated and analyzed. Rigid fragments of DNA, i.e., of a length of about the persistent length, which have discrete dipole moments of base pairs, are considered. For a given distance between the centers of mass of molecules, the energy of the dipole-dipole interaction is a function of three angular variables; the angles ?₁ and ?₂ between the central dipoles of both molecules and the z axis passing through the centers of the molecules, as well as the angle ξ between long axes of the molecules, are taken as these variables. It is shown that the dipole energy has minima when the mutual orientation of the molecules satisfies one of the following conditions: (i) ?₁ = ?₂ = 0 or (ii) ?₁ = ?₂ = π. The cholesteric twist angle ξ can be both positive and negative in dependence on the type of the minimum. For realistic cholesteric dispersion parameters, the dipole energy is only slightly lower than the experimentally known binding energy of the molecules in dispersion. The results allow the assumption that the dipole forces significantly affect the structure and other properties of DNA suspensions; in particular, they can lead to nontrivial texture phenomena, biaxial correlation, and multistability.