Molecular dynamics simulation of thermomechanical coupling in cholesteric liquid crystals

The lack of a centre of inversion in a cholesteric liquid crystal allows linear cross-couplings between thermodynamic forces and fluxes that are polar vectors and pseudo vectors respectively. This makes it possible for a temperature gradient parallel to the cholesteric axis to induce a torque which rotates the director. This phenomenon is known as the Lehmann effect. The converse is also possible: one can drive a heat current by rotating the director. In this work a recently developed non-equilibrium molecular dynamics simulation algorithm is applied to calculate the cross-coupling coefficient between the temperature gradient and the torque for a molecular model system based on the Gay-Berne fluid. According to the Onsager reciprocity relations this cross-coupling coefficient is equal to the coupling between the director angular velocity and the heat current. The cross-coupling coefficients are found to be very small but non-zero and the Onsager reciprocity relations are satisfied within the statistical uncertainty.     

Permeative flows in cholesteric liquid crystals

We use lattice Boltzmann simulations to solve the Beris-Edwards equations of motion for a cholesteric liquid crystal subjected to Poiseuille flow along the direction of the helical axis (permeative flow). The results allow us to clarify and extend the approximate analytic treatments currently available. We find that if the cholesteric helix is pinned at the boundaries there is an enormous viscosity increase. If, instead, the helix is free the velocity profile is flattened, but the viscosity is essentially unchanged. We highlight the importance of secondary flows, and, for higher flow velocities, we identify a flow-induced double twist structure in the director field--reminiscent of the texture characteristic of blue phases.     

Untwisting of a cholesteric elastomer by a mechanical field

A mechanical strain field applied to a monodomain cholesteric elastomer will unwind the helical director distribution. There are similarities with the classical problem of an electric field applied to a cholesteric liquid crystal but also differences. Frank elasticity is of minor importance unless the gel is very weak. The interplay is between the director being helically anchored to the rubber elastic matrix and the external mechanical field. Stretching perpendicular to the helix axis induces the uniform unwound state via the elimination of sharp, pinned twist walls above a critical strain. Unwinding through conical director states occurs when the elastomer is stretched along the helical axis.     

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.     

Green–Kubo relations for dynamic interfacial excess properties

In this paper we analyze the fluctuations of the in-plane interfacial excess fluxes in multiphase systems, in the context of the extended irreversible thermodynamics formalism. We derive expressions for the time correlation functions of the surface extra stress tensor, the surface mass flux vector, and the surface energy flux vector, and use these expressions to derive Green–Kubo relations for the surface shear viscosity, the surface dilatational viscosity, the surface diffusion coefficient, and the surface thermal conductivity. These Green-Kubo relations can be used to compute these excess transport coefficients using for example molecular dynamics simulations.     

光栅扭矩动态测量系统设计及实现

机械主轴在各种载荷和工作环境下的扭矩测量，国内外一直没有比较好的解决方案。针对这一现状，提出通过在主轴2端安装圆光栅及指示光栅，采用对光栅莫尔条纹计数及细分的方法实现主轴扭矩非接触式动态直接测量。其方法是在将莫尔条纹进行光电转换后，采用集成可编程模拟器件对信号进行放大、滤波和比较，然后利用软核微处理器实现数据采集、处理和控制，从而取代FPGA＋MCU的方式。实验中，测量系统采用1200条刻线的圆光栅，在主轴转速为0～1500r/min的范围内测量其扭矩，扭转角精度小于0.001°。实验结果表明，采用圆光栅莫尔条纹可以达到主轴扭矩高精度测量的要求，为机械主轴测量提供了一种新的非接触式测量方法。     

Rotational viscosity of uniaxial molecules

Non-equilibrium molecular dynamics (NEMD) are used to calculate the vortex or rotational viscosity of fluids composed of uniaxial molecules. It is shown that the NEMD homogeneous spin flow algorithm proposed by Edberg, R., Evans, D. J., and Moriss, G. P., 1987, Molec. Phys., 62, 1357 considerably underestimates the vortex viscosity. A modified version of this algorithm is proposed and applied to liquid chlorine and nitrogen. The results are in good agreement with previous work using equilibrium or other NEMD methods, and also show that at high spin rates the vortex viscosity decreases with increase in magnitude of the external torque used to drive the spin flow.     

基于分子动力学模拟流体输运性质的稳定性分析

利用线性响应理论对Ar流体输运参数进行了分子动力学模拟,结果发现:导热系数和黏度会随着自相关积分函数积分时间的增加而产生剧烈波动,而扩散系数却相对稳定. 针对积分稳定性这一问题,对导热系数和黏度中的热流密度和应力张量进行了分解分析,发现含分子间作用力项是影响稳定性的最大因素. 从牛顿力学出发对作用力项的影响机理进行了分析,指明减小这种影响的最主要方法是使在体系进行统计输运参数前达到稳定平衡状态,即最小的预平衡步数应该满足使体系达到该状态下熵最大或者能量最低,并尽量减小温度对体系的影响. 同时,还对模拟盒尺寸、统计步长等因素对积分稳定性的影响进行了分析,给出了保持稳定性的建议. 关键词： 分子动力学 输运性质 自相关函数 稳定性     

Magnetic rotation and chiral symmetry breaking

The deformed mean field of nuclei exhibits various geometrical and dynamical symmetries which manifest themselves as various types of rotational and decay patterns. Most of the symmetry operations considered so far have been defined for a situation wherein the angular momentum coincides with one of the principal axes and the principal axis cranking may be invoked. New possibilities arise with the observation of rotational features in weakly deformed nuclei and now interpreted as magnetic rotational bands. More than 120 MR bands have now been identified by filtering the existing data. We present a brief overview of these bands. The total angular momentum vector in such bands is tilted away from the principal axes. Such a situation gives rise to several new possibilities including breaking of chiral symmetry as discussed recently by Frauendorf. We present the outcome of such symmetries and their possible experimental verification. Some possible examples of chiral bands are presented.     

On the possibility of the violation of the Curie-Neumann principle in anisotropic media with dissymmetry

The dynamics of defects and their mutual transformation and annihilation in drops of a nematic-cholesteric mixture in the presence of quasistatic electric fields has been investigated by the birefringence method. Three basic independent configurations of the director distribution—static and dynamic with the right and left-handed twists of cholesteric layers around the axis parallel to the field—are formed above the threshold field. The possible mechanisms of the observed processes have been discussed. It has been shown that a certain symmetry of the causes (the nematic-cholesteric liquid crystal and field) does not necessarily lead to the corresponding symmetry of the induced structures and mechanical processes. An anisotropic distribution of the orientation of rotating spiral structures with respect to the normal to the nematic-cholesteric liquid crystal layer has been revealed.     

Role of interfaces in higher order angular terms of magnetic anisotropies: ultrathin film structures

The role of interface inhomogeneities on macroscopic magnetic anisotropy terms was investigated using simple mathematical modeling. It is shown that the intrinsic anisotropies caused by the spin–orbit interaction in the presence of lateral inhomogeneities can create additional magnetic anisotropies with higher order angular terms. The lateral inhomogeneous distribution of the uniaxial anisotropy can result in the presence of a fourth order angular term. These anisotropies decrease the total energy, and their strength is affected by the exchange averaging effect. Large atomic terraces allow the local magnetic moment to deviate from the mean orientation resulting in negative higher order angular terms in magnetic anisotropies satisfying the sample symmetry. The negative sign results in the magnetic easy axes being oriented 45° with respect to the intrinsic uniaxial axis. It is shown that the additional higher order terms do not always have to satisfy the time inversion symmetry. Odd powers in directional cosines can arise when the exchange restoring torque becomes comparable to or weaker than torques from the internal fields. The additional higher order angular terms in magnetic anisotropies decrease usually more rapidly with the sample thickness than the intrinsic interface anisotropies. Their rapid decrease in strength with an increasing sample thickness allows one to distinguish them from the intrinsic interface anisotropies. It will be shown that the magnetic anisotropies originating in interface inhomogeneities can play an important role in the magnetic phase transitions of ultrathin film structures.     

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.     

Steady low shear rate cholesteric flow normal to the helical axis

Steady cholesteric flow at low shear rate normal to the helical axis is studied analytically for shear flow and plane Poiseuille flow on the basis of Leslie’s continuum theory. For general asymmetric solutions the angle made by the director at the sample centre with the primary flow is found to profoundly affect the oscillations of the apparent viscosity with pitch for pitches of the order of the sample thickness. The velocity and orientation profiles are also found to change drastically. These considerations may be important in flow experiments on long pitch cholesterics.     

Double-helix chiral fibers

A polarization-selective photonic stop band is demonstrated in a new chiral fiber structure with double-helix symmetry. The stop band exists for only circularly polarized radiation with the same handedness as the structure and is centered at a wavelength in the fiber equal to the fiber pitch. When one part of the chiral fiber is twisted about its axis, a localized mode is produced, which can be tuned across the gap by changing the twist angle. Observations in single-mode fibers are in good agreement with one-dimensional simulations of a dispersive cholesteric material. At higher frequencies, however, we find a sharp onset of a broad polarization-selective scattering band, which is not present in one-dimensional simulations.     

Deformation of cholesteric elastomers by uniaxial stress along the helix axis

The deformation of cholesteric elastomers by mechanical stress applied parallel to the helix axis is studied by calculation of the free-energy density. The Frank-elasticity contribution is taken into account. A chiral solvent, present at cross-linking time, is in general considered to be replaced after cross-linking by a solvent with different chirality. Two special cases considered are zero and unchanged solvent chirality, the first known as that of imprinted cholesteric elastomers, the latter equivalent to intrinsic cholesteric elastomers with chemically attached chiral groups. Depending on material parameters and imposed strain, the director can show a tilt towards the helix axis up to the maximum tilt, corresponding to a nematic state. In case of intrinsic elastomers with low conformation anisotropy, direct transitions from untilted to nematic states can be induced by straining. The helix structure of the director field is coarsened with an average wave number different to that of the information inscribed in the network at cross-linking time, if this lowers the average free-energy density. Switching between different states can be achieved with electric fields of reasonable values applied parallel to the helix axis. Spectra of the reflection of polarized light are calculated.     

Bistable surface anchoring and hysteresis of pitch jumps in a planar cholesteric liquid crystal

The relationship between bistable surface anchoring and the pitch jump process is examined for a planar cholesteric liquid crystal. Introducing a high-order, azimuthal surface anchoring potential into a simple model to describe a cholesteric, we derive an expression for the director twist as the natural pitch of the liquid crystal is allowed to vary. Writing the energy in terms of the surface twist, we are able to determine the twists which minimize the total energy of the system. We demonstrate how a pitch jump is related to an energy exchange from one branch of metastable states to another. We then discuss how the co-existence of energy minima and their associated solution branches may help explain the thermal hysteresis observed experimentally in cholesterics in the neighbourhood of a pitch jump. The presence of a higher-order surface energy term can expand the range of anchoring strengths in which pitch jumps are possible. We also investigate the influence of bidirectional surface anchoring on the behaviour of the total energy. Intermediate quarter-turn pitch jumps can occur, depending on the relative strength of the high-order anchoring term, and these can have a significant effect on the system hysteresis.     

Soliton-like molecular deformations in a nematic liquid crystal film

We study the nature of molecular deformations in a nematic liquid crystal film with elastic energy under homeotropic boundary conditions. The deformation in terms of splay, twist and bend fields of the director axis is found to be governed by the completely integrable Davey-Stewartson-I (DS-I) equation in (2+1) dimensions. Using the line soliton and breather solutions of the DS-I equation, the director axis is constructed, the components of which exhibit damped spatial oscillations. However, the splay and bend fields of the director axis exhibit localized structures of deformation.     

Neoclassical toroidal plasma viscosity torque in collisionless regimes in tokamaks

Bumpiness in a magnetic field enhances the magnitude of the plasma viscosity and increases the rate of the plasma flow damping. A general solution of the neoclassical toroidal plasma viscosity (NTV) torque induced by nonaxisymmetric magnetic perturbation (NAMP) in the collisionless regimes in tokamaks is obtained in this Letter. The plasma angular momentum can be strongly changed, when there is a small deviation of the toroidal symmetry caused by a NAMP of the order of 0.1% of the toroidal field strength.     

Equilibrium structures of planar nematic and cholesteric films in electric fields

Liquid crystal layers subjected to an electric or a magnetic field can have several types of instabilities. This paper reviews recent theoretical studies concerning equilibrium structures of planar layers.

Using the Oseen-Frank elasticity theory, the Freedericksz transition and the transition to static periodic domains of planar nematic and cholesteric films are reconsidered. A perturbation treatment of nonlinear torque balance equations for the director is suitable to derive amplitude equations for the film distortions under the action of a field and to predict the topological features of phase diagrams for equilibrium states. The competition between the Freedericksz effect and the formation of periodic distortions is studied varying material and geometrical parameters. Some results are useful to optimize cholesteric mixtures for application in display devices in such a manner, that the occurrence of periodic domains is avoided.     

How to improve the accuracy of equilibrium molecular dynamics for computation of thermal conductivity?

Equilibrium molecular dynamics (EMD) simulations through Green-Kubo formula (GKF) have been widely used in the study of thermal conductivity of various materials. However, there exist controversial simulation results which have huge discrepancies with experimental ones in literatures. In this Letter, we demonstrate that the fluctuation in calculated thermal conductivity is due to the uncertainty in determination of the truncation time, which is related to the ensemble and size dependent phonon relaxation time. We thus propose a new scheme in the direct integration of heat current autocorrelation function (HCACF) and a nonzero correction in the double-exponential-fitting of HCACF to describe correctly the contribution to thermal conductivity from low frequency phonons. By using crystalline Silicon (Si) and Germanium (Ge) as examples, we demonstrate that our method can give rise to the values of thermal conductivity in an excellent agreement with experimental ones.