Order parameter and its critical exponent for some binary mixtures showing induced nematic phase

Refractive index measurements as a function of temperature have been performed for an induced nematic binary system by means of thin prism technique. The temperature dependence of the birefringence (Δn) has been assessed from the measured refractive index data. A direct extrapolation method has been employed to determine the orientational order parameter for the investigated mixtures and the order parameter so obtained has also been compared with the mean field values. The Haller type fitting expression results in a relatively lower value of the order parameter critical exponent (β) compared to the theoretically predicted values. Therefore, a four-parameter power law expression, consistent with the mean field theory as well as the first-order character of the nematic–isotropic (N-I) phase transition have been used to explore the critical behavior of the order parameter near the N-I transition.     

Fluctuations-Inclusive Approach to Phase Transitions in Binary Mixtures

The hierarchical reference theory of fluids (HRT) is applied to the study of the phase diagram of binary mixtures of simple fluids. This approach implements the renormalization group machinery into a liquid-state theory in order to systematically deal with the effect of long-range correlations which play a crucial role in the onset of criticality and phase separation. The effect of fluctuations is embodied in a partial differential equation (PDE) for the free energy of the mixture. Recently, a robust numerical algorithm has been developed which enabled us to integrate this PDE on a substantial density mesh even at low temperature, when the coexistence region spreads over most of the density– concentration plane.We have considered a model mixture of spherical particles interacting via a hard-core plus attractive tail potential, and adjusted the particle diameters ₁, ₂ and the strengths of the attractive interactions ₁₁, ₂₂, ₁₂ so as to mimic mixtures of simple fluids such as argon–krypton or neon–krypton. In the latter case the theory reproduces the occurrence of a minimum in the critical temperature (the so-called critical double point) and of immiscibility at high pressure. We have also studied the phase diagram of a symmetric mixture such that ₁= ₂ and ₁₁= ₂₂ as the ratio = ₁₂/ ₁₁ is varied. In particular, we find that, in agreement with the mean-field picture, by decreasing , a critical endpoint occurring at equal species concentration is turned into a tricritical point. An interesting feature of the HRT is that, whenever phase coexistence occurs, the conditions of phase equilibria are implemented by the theory itself, without any need of enforcing them a posteriori. This allows one to straightforwardly map the phase diagram and the critical lines of the mixture.     

Demixing in Isotropic Binary Mixtures of Rodlike Macromolecules

A binary mixture of long rigid rods of diameters D _i and lengths L _i (i=1, 2) may demix into two isotropic phases, and we give necessary conditions on the molecular size parameters for this transition to exist. These conditions imply that the two diameters must be sufficiently unequal, D ₂/D ₁>( + )², or D ₂/D ₁<( + )², while the length ratio is limited to an interval f _–(D ₂/D ₁)<L ₂/L ₁<f ₊(D ₂/D ₁). The functions f _± are given explicitly.     

Localization and Screening Enhancement in Asymmetric Binary Ionic Mixtures

The equation of state of binary ionic mixtures of similar ions, such as nitrogen, oxygen and carbon, has been extensively studied. The study of dense asymmetric mixtures, where Z₂ >> Z₁, has primarily focused on mixtures of hydrogen and iron at solar conditions. Using molecular dynamics simulations, we examine the behavior of highly asymmetric binary ionic mixtures, where the coupling of the high‐Z species may be orders of magnitude higher than the coupling of the low‐Z species. For the conditions we have studied, we find that strong correlations and signatures of solidification occur in the high‐Z species, while the low‐Z species exists as a freely flowing fluid within the high‐Z solid matrix. Solidification of the low‐Z species is correlated with the coupling between the two components. Using the Widom expansion method, we compute the plasma screening enhancement of the nuclear reaction rates for Z = 1 in a high‐Z matrix. We also provide some estimates of the coefficient of binary diffusion in the mixture. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Critical Analyses of Order Parameter and Phase Transitions at High Density in Gross-Neveu Model

By critical analyses of the order parameter of symmetry breaking, we have researched the phase transitionsat high density in D = 2 and D = 3 Gross-Neveu (GN) model and shown that the gap equation obeyed by the dynamicalfermion mass has the same effectivenesss as the effective potentials for such analyses of all the second order and somespecial first order phase transitions. In the meantime we also further ironed out a theoretical divergence and proventhat in D = 3 GN model a first order phase transition does occur in the case of zero temperature and finite chemicalpotential.     

Critical Analyses of Order Parameter and Phase Transitions at High Density in Gross－Neveu Model

By critical analyses of the order parameter of symmetry breaking, we have researched the phase transitions at high density in D = 2 and D = 3 Gross-Neveu (GN) model and shown that the gap equation obeyed by the dynamical fermion mass has the same effectivenesss as the effective potentials for such analyses of all the second order and some specJal first order phase transitions. In the meantime we also further ironed out a theoretical divergence and proven that in D = 3 GN model a first order phase transition does occur in the case of zero temperature and finite chemical potential.     

Studies on the Chiral Order Parameter in the Schwinger Model

Based on an analytical technique using a unitary transformation and the variational method, we study the chiral order parameter in the Schwinger model in the lattice formalism with Kogut-Susskind fermions. The fermion condensate (ψψ)fo r any coupling constant and fermion mass are calculated. Chiral symmetry is shown to be broken in the massless limit and good scaling behavior is obtained.     

The Order Parameter of the Chiral Potts Model

An outstanding problem in statistical mechanics is the order parameter of the chiral Potts model. An elegant conjecture for this was made in 1983. It has since been successfully tested against series expansions, but there is as yet no proof of the conjecture. Here we show that if one makes a certain analyticity assumption similar to that used to derive the free energy, then one can indeed verify the conjecture. The method is based on the ‘‘broken rapidity line’’ approach pioneered by Jimbo et al. (J. Phys. A 26:2199--2210 (1993).).     

Binary nonadditive hard-sphere mixtures at high dimension

At high spatial dimension, a suitably scaled classical system of interacting particles truncates at second virial terms. A binary mixture of nonadditive hard spheres with sufficiently repulsive interaction between unlike particles decomposes at sufficiently high density into two coexisting phases. The region around the critical density behaves classically.     

Ground-State Properties and Phase Separation of Binary Mixtures in Mesoscopic Ring Lattices

We investigated the spatial phase separation of the two components forming a bosonic mixture distributed in a four-well lattice with a ring geometry. We studied the ground state of this system, described by means of a binary Bose–Hubbard Hamiltonian, by implementing a well-known coherent-state picture which allowed us to find the semi-classical equations determining the distribution of boson components in the ring lattice. Their fully analytic solutions, in the limit of large boson numbers, provide the boson populations at each well as a function of the interspecies interaction and of other significant model parameters, while allowing to reconstruct the non-trivial architecture of the ground-state four-well phase diagram. The comparison with the L-well (L=2,3) phase diagrams highlights how increasing the number of wells considerably modifies the phase diagram structure and the transition mechanism from the full-mixing to the full-demixing phase controlled by the interspecies interaction. Despite the fact that the phase diagrams for L=2,3,4 share various general properties, we show that, unlike attractive binary mixtures, repulsive mixtures do not feature a transition mechanism which can be extended to an arbitrary lattice of size L.     

描述混合物固液相变的两个近似模型

 提出了描述混合物固液相变的两个近似模型：混合相模型和等效物质模型。通过对304钢的计算和比较表明，由两个模型计算得到的结果与直接利用304钢的材料参数计算得到的结果相符合。     

拉曼峰强作为分子晶体相变的有序度

本文介绍以拉曼峰强为分子晶体相变有序度的概念，并以ＫＨ＿（１－ｘ）Ｄ＿（ｘ）Ｆ＿２和Ｋ＿（１－ｘ）Ｎａ＿（ｘ）Ｆ＿２为例说明晶格振动模在相变过程中的临界性质可以因此得到。晶格振动模的临界性质反映着掺杂体系的丰富信息。     

Nonradiative Relaxation of Thiacarbocyanine Dyes in Binary Mixtures

It was found that preferential solvation of cyanine dyes in binary mixtures can strongly affect both their isomerization and aggregation; the comparison of absorption and fluorescence excitation spectra might be a useful tool for studying these nonradiative processes.     

极化聚合物薄膜取向有序度及极化寿命的表征

研究了极化聚事物薄膜波导的退极化过程,提出了表征极化聚合物薄膜取向有序度和极化寿命的集成光学方法。采用集成光学中的棱镜耦合技术,测量极化前后聚合物薄膜光波导的各向异性有效折射率。通过求解各向异性介质光波导的模式本征方程,得到波导极化前后寻常光和非寻常光折射率的变化及其随时间衰减,进而得到取向有序度随时间的变化曲线。采用复合指数函数模型进行最小二乘曲线拟合,进而推测其极化寿命。实验中以键合型ＤＡＮＳ     

On the Statistical Mechanics and Surface Tensions of Binary Mixtures

Within a lattice model describing a binary mixture with fixed concentrations of the species we discuss the relationship between the surface tension of the mixture and the concentrations.     

Phase diagram involving the mesomorphic behavior of binary mixture of sodium oleate and orthophosphoric acid

The present investigation deals with the binary mixture of two non-mesogenic compounds, viz. sodium oleate (Naol) and orthophosphoric acid (H₃PO₄) which exhibits very interesting liquid crystalline smectic phases at large range of concentrations and temperature. The mixtures with concentrations ranging from 10% to 90% Naol in H₃PO₄ exhibit SmA, SmC, SmE and SmB phases, sequentially when the specimen is cooled from its isotropic phase. Physical properties, such as ultrasonic velocity, adiabatic compressibility and molar compressibility, show anomalous behavior at the isotropic to mesosphase transition.     

高斯噪声诱导二元混合物/粒子系统有序结构的形成

采用蒙特卡罗方法研究高斯噪声场对添加硬球粒子的二元混合物系统自组装的驱动作用.发现硬球粒子与组分之间的相互作用决定硬球粒子在畴中存在的区域.当硬球粒子与组分之间的相互作用较大,硬球粒子浓度n≤0.05时,对于足够强的高斯噪声场,存在一个最佳噪声作用概率区域(p=0.005~0.02),其间高斯噪声已完全消除硬球粒子的钉扎效应,使体系快速生长并形成取向性很好的条状畴结构.     

Regular Binary Thermal Lattice-Gases

We analyze the power spectrum of a regular binary thermal lattice gas in two dimensions and derive a Landau–Placzek formula, describing the power spectrum in the long-wavelength, low frequency domain, for both the full mixture and a single component in the binary mixture. The theoretical results are compared with simulations performed on this model and show a perfect agreement. The power spectrums are found to be similar in structure as the ones obtained for the continuous theory, in which the central peak is a complicated superposition of entropy and concentration contributions, due to the coupling of the fluctuations in these quantities. Spectra based on the relative difference between both components have in general additional Brillouin peaks as a consequence of the equipartition failure.     

H-Point Standard Addition Method (HPSAM) in Simultaneous Spectrophotometric Determination of Binary Mixtures: An Overview

Abstract

The H-point standard addition method (HPSAM) is a modification of the standard addition method that transforms the incorrigible error resulting from the presence of a direct interferent in the determination of an analyte into a constant systematic error. This error can then be evaluated and eliminated. The method was established for resolving strongly overlapping spectra of two analytes and permits both proportional and constant errors produced by the matrix of the sample to be corrected directly. The technique is based on the principle of dual-wavelength spectrophotometry and the standard addition method. The application of the method requires only two wavelengths, and the analytical signal caused by one of the species should be constant and that of the other should differ as much as possible. This overview discusses both the theoretical and practical aspects of HPSAM applications.     

在高密度下核物质的色超导性

建立了相变热力学理论和场论的关系. 强调在量子场论中必须引进序参量场， 则相变的讨论就类似于Goldstone bosons 的产生. 如果只讨论一级相变， Goldstone bosons场就足够了; 如果要讨论二级相变， 则必须讨论一系列的场， 这些场构成一个对称群的表示. 另外, 也将这一思想用到色超导中. In this paper we built a relation between the thermodynamical theory of the phase transition and field theory. We emphasized that in the quantum field theory we have to introduce the order parameter fields. Then the discussion of the phase transition is closed to the creation of the Goldstone bosons. If we only discuss the first order transition, the Goldstone bosons fields are sufficient. If we want to discuss the second order transition, we have to discuss a set of fields that constructs a representation of a symmetry group. We also apply this concept to color superconductivity.