Diagrammatic analysis of correlations in polymer fluids: Cluster diagrams via Edwards’ field theory

Edwards’ functional integral approach to the statistical mechanics of polymer liquids is amenable to a diagrammatic analysis in which free energies and correlation functions are expanded as infinite sums of Feynman diagrams. This analysis is shown to lead naturally to a perturbative cluster expansion that is closely related to the Mayer cluster expansion developed for molecular liquids by Chandler and co-workers. Expansion of the functional integral representation of the grand-canonical partition function yields a perturbation theory in which all quantities of interest are expressed as functionals of a monomer-monomer pair potential, as functionals of intramolecular correlation functions of non-interacting molecules, and as functions of molecular activities. In different variants of the theory, the pair potential may be either a bare or a screened potential. A series of topological reductions yields a renormalized diagrammatic expansion in which collective correlation functions are instead expressed diagrammatically as functionals of the true single-molecule correlation functions in the interacting fluid, and as functions of molecular number density. Similar renormalized expansions are also obtained for a collective Ornstein-Zernicke direct correlation function, and for intramolecular correlation functions. A concise discussion is given of the corresponding Mayer cluster expansion, and of the relationship between the Mayer and perturbative cluster expansions for liquids of flexible molecules. The application of the perturbative cluster expansion to coarse-grained models of dense multi-component polymer liquids is discussed, and a justification is given for the use of a loop expansion. As an example, the formalism is used to derive a new expression for the wave-number dependent direct correlation function and recover known expressions for the intramolecular two-point correlation function to first-order in a renormalized loop expansion for coarse-grained models of binary homopolymer blends and diblock copolymer melts.     

The partial distribution functions and effective pair potentials of some H-bonded liquids from diffraction data

The partial structures and distribution functions are directly linked to structural model of molecular liquids. The comparative study of partial distribution function of different hydrogen-bonded liquids gives the information that hydrogen-bonding is stronger in alcohols than in water and ammonia. The effective pair potential is directly related to the pair correlation function. The comparative study of such potentials for different hydrogen-bonded liquids gives some characteristic features.     

Rotational velocity correlation functions from the pseudo-lattice far infra-red profiles of molecular liquids

The observation of absorption peaks in the far infra-red power absorption profiles of molecular liquids is analysed with the rotational velocity correlation function. These are oscillatory and much longer lived than their equivalents from “conventional” broad band data for molecular liquids in the far infra red.     

Viscosity, shear waves, and atomic-level stress-stress correlations

The Green-Kubo equation relates the macroscopic stress-stress correlation function to a liquid's viscosity. The concept of the atomic-level stresses allows the macroscopic stress-stress correlation function in the equation to be expressed in terms of the space-time correlations among the atomic-level stresses. Molecular dynamics studies show surprisingly long spatial extension of stress-stress correlations and also longitudinal and transverse waves propagating in liquids over ranges which could exceed the system size. The results reveal that the range of propagation of shear waves corresponds to the range of distances relevant for viscosity. Thus our results show that viscosity is a fundamentally nonlocal quantity. We also show that the periodic boundary conditions play a nontrivial role in molecular dynamics simulations, effectively masking the long-range nature of viscosity.     

Molecular simulation study of the glass transition in a soft primitive model for ionic liquids

In this paper, we present a molecular dynamics study of the glass transition for a soft-core primitive model for ionic liquids, in which cations are fully flexible chains of tangent soft spherical monomers, being the positively charged monomer at one of the ends of the chain, and anions as charged soft spheres. We have monitored transport coefficients such as the self-diffusion coefficients and the shear viscosity, as well as correlation functions such as the mean-square displacement, the self-intermediate scattering function, and probes of heterogeneous dynamics such as the van Hove distribution function and the four-points susceptibility. The analysis of these properties indicates that, for a given pressure, the glass transition shows a weak temperature dependence on the cation length, occurring first for short-chain than for long-chain ionic liquids.     

The corrected Enskog theory and the transport properties of molecular liquids

Analytical expressions for the transport coefficients of liquids based on the corrected Enskog theory have been used in order to determine the self-diffusion coefficient (D) for molecular liquids as a function of density and temperature. The liquids considered are those composed of linear molecules and NH₃. The calculated D values agree with the experimental ones for those molecular liquids for which experimental self-diffusion data are available. The translational part of the thermal conductivity (λ_trans) has also been calculated and compared with the experimental thermal conductivity (λ). It turns out that λ_trans for diatomic molecular liquids practically represents the whole of λ in a substantial fraction of the liquid range, indicating that the internal degrees of freedom hardly contribute to the thermal conductivity in these dense liquids. A comparison is made with recently published results based on the modified Enskog theory.     

基于Weiss分子场理论对极性液体中静态介电常数随温度变化及其相应取向关联的研究

迄今为止,并没有被普遍接受的液体静态介电常数的微观理论模型, 主要原因是对属于强关联系统的液体中分子之间的取向关联特征仍不十分清楚. 本文基于Weiss分子场理论(WMFT), 对水(water, H₂O)、甲醇(methanol, CH₄O)、乙醇(ethanol, C₂H₆O)和正丙醇(1-propanol, C₃H₈O)等4种极性液体中静态介电常数, 具体为Curie-Weiss常数、Curie温度和Weiss分子场因子随温度变化规律进行分析研究, 得出上述液体中: 1)铁电关联(ferroelectric correlation, FC)和反铁电关联(anti-ferroelectric correlation, AFC)共存, 且FC比AFC强得多, 以及随温度降低FC减弱和/或AFC增强; 2)结构均匀的WMFT不能定量描述上述液体中足够低的温度下反常大的静态介电常数. 可以想象FC和较弱AFC的共存必然导致极性液体中关联序的空间不均匀, 由此作者提出了空间不均匀关联序的粗粒近似的Weiss分子场理论, 并用此理论对上述液体中静态介电常数随温度快速变化的行为进行了解释. 上述结果对深入认知液体物理学, 包括玻璃化转变机制的探索, 无疑是有价值的.     

氯铝酸离子液体的酸性及其催化烷基化反应研究

分别采用吡啶探针和乙腈探针红外光谱法研究了氯铝酸离子液体的酸性,结合固体酸表征方法,研究了离子液体的酸性对吡啶探针各振动模式的影响。发现当氯铝酸离子液体AlCl₃的摩尔分数x为0.4～0.5时,离子液体显弱Lewis酸性,强碱性吡啶探针分子能很好地表征离子液体的酸性,而弱碱性乙腈探针分子只适用于表征酸性较强的离子液体。考察了氯铝酸离子液体酸强度对苯与长链烯烃烷基化反应的影响,结果发现,AlCl₃的摩尔分数x≤ 0.5时,离子液体没有催化活性;x>0.55时,随着离子液体酸性的增强,烯烃转化率升高,但2位烷基苯选择性下降。结合离子液体的酸强度对烷基化反应机理进行初步分析认为具有催化活性的物质是强Lewis酸Al₂Cl-₇。     

Simulation studies of shear viscosity time correlation functions in liquid CS2

The Green—Kubo time correlation function for the shear viscosity in liquid CS₂ has been simulated by molecular dynamics at several thermodynamic state points. The breakdown of this function into its kinetic and potential contributions as well as the cross-term between the two has been performed. Intermolecular interactions were obtained from a three-centre atom—atom (12/6) Lennard-Jones potential model. The time correlation functions for the potential part of the shear viscosity contain component two-, three- and four-body terms that were explicitly evaluated to show that they partially cancel each other at short times but at long times, they exhibit approximately exponential decays with magnitude ratios corresponding to nearly perfect cancellation. In this respect, the correlation functions for CS₂ resemble those of liquid argon. In addition, the microscopic stress tensor was separated into the portions arising from the repulsive and attractive branches of the Lennard-Jones model. This split gives rise to positive autocorrelation functions involving the repulsive and the attractive forces plus a negative cross-correlation function between the two that partially cancels the contributions of the autocorrelation functions. It is argued that the breakdown of the potential part of the shear viscosity into its component parts is helpful in elucidating the role of molecular re-orientation in determining the separate short and long time behaviours of this time correlation function for liquids such as CS₂.     

Theory of inelastic neutron scattering from molecular fluids

The time-dependent angular pair correlation function is discussed and its use in the analysis of inelastic neutron scattering experiments from polyatomic fluids is described, including both the coherent and incoherent spectra. The set of formal results given here permits a systematic interpretation of neutron inelastic scattering spectra on simple molecular liquids. Neutron spectra second moments are reviewed, and a new result for the fourth moment is given for the incoherent spectrum. Numerical results for the moments are obtained. The fourth moment depends on the mean squared torque and the mean squared force acting on a molecule in the fluid, and may provide a means for studying intermolecular forces in dense fluids. In addition, a method of calculating the correlation function for weak anisotropic forces is outlined.     

Dynamical current correlations in simple liquids

Expressions for the longitudinal and transverse current correlation functions of simple liquids are obtained using Mori's formalism. These involve unknown damping functions. The use of damping functions for a free gas gives results which are in complete disagreement with experiments. The results obtained on the basis of a renormalized free particle memory function in which the collisional damping of collective excitations is incorporated show remarkable improvement over earlier results and are in reasonable agreement with the molecular dynamics data of Rahman. Therefore, the choice of the memory function is as important as the satisfaction of lower order moments.     

液体理论中的Kirkwood变分方法的推广

本文克服了Cohen理论的缺点,对液体理论中Kirkwood变分方法作了推广。经过这样推广,格胞模型理论就可以系统地考虑分子运动关联性的任何级近似。把所得结果应用到一维情形,得到的自由能是严格正确的。应用到三维情形,最低级近似得LJD结果,一级近似得Taylor结果。     

Surface effects and dipolar correlations of confined and constrained liquids investigated by NMR relaxation experiments and computer simulations.

Local order and molecular dynamics of liquids near surfaces strongly deviate from the behavior in the bulk. This in particular refers to liquid crystals above the bulk isotropization temperature. Transverse relaxation data of 5CB examined in porous glasses with different pore sizes are reported. A strong pore size effect was found. For the interpretation, a simple diffusion-adsorption computer simulation was carried out. Molecules can diffuse from the isotropic bulk part of the pore fluid to the ordered surface layer and vice versa. The residual dipolar correlation function is characterized by a slowly decaying tail owing to repeated returns of molecules to the surface. At each return the molecular orientation correlation is recovered as far as the surface sites visited have orientations correlated to the initial site. That is, molecular orientation is controlled by the "reorientation mediated by translational displacement" process considered in previous papers.     

流体静态和动态平衡性质的分子动力学模拟

基于LJ势能模型和soft-sphere势能模型对不同状态下氩流体的径向分布函数、速度相关函数、横向粒子流相 关函数和中间散射函数进行模拟,重点讨论了LJ势能分子间吸引力和软心势能“软度”对流体静态和动态平衡性质的影 响,结果发现软心势能的影响比分子间吸引力的影响更显著,而且动态平衡性质中出现的振荡现象也是由软心势能所致。     

Shear induced anisotropy in two-dimensional liquids

The behavior of a dense two-dimensional soft disc liquid under shear is studied via nonequilibrium molecular dynamics. The structure factor for the liquid at a given shear rate is evaluated directly by plotting the particle positions, taken at random from the NEMD simulation at that shear, onto photographic film and using light scattering to obtain a diffraction pattern. The pair correlation function of this system is also extracted directly by histogramming the particle positions with respect to a given central particle as a function of separation and angle. The pair correlation function is compared to that approximated by a Fourier series expansion to rank ten. Results are reported as a function of shear rate from a shear rate of 0.1 (when the fluid is essentially Newtonian) to 10 (when the fluid can display a string phase). The appearance of the string phase is discussed and shown to be a consequence of the definition of temperature in the simulation algorithm. A modification of the algorithm is proposed. Comparisons between this work and previous work with three-dimensional liquids are given. The two-dimensional structure factor is compared with that obtained from a real colloidal suspension via light scattering.     

Ionic liquids in external electric and electromagnetic fields: a molecular dynamics study

The non-thermal effects of external electric and electromagnetic fields in the microwave to far-infrared frequency range and at (r.m.s.) electric field intensities of 10^?3 to 0.25?V/Å_r.m.s. on neat salts of 1,3-dimethyl-imidazolium hexafluorophosphate ([dmim][PF₆]) and 1-butyl-3-methyl-imidazolium hexafluorophosphate ([bmim][PF₆]) have been investigated by means of non-equilibrium molecular dynamics simulation. Significant alterations in molecular mobility were found vis-à-vis zero-field conditions. Using Green–Kubo and transient time correlation function analysis, the electrical conductivity of these ionic liquids has been estimated. The results indicate that ionic liquids respond most significantly to frequencies much lower than those of smaller polar solvents such as water, although the mechanism of the field response is almost exclusively translational.     

Uniform-sign cross-peak double-quantum-filtered correlation spectroscopy

We detail the uniform-sign cross-peak double-quantum-filtered correlation spectroscopy (UC2QF COSY) experiment, a new through-bond correlation method for disordered solids. This experiment is a refocused version of the popular double-quantum-filtered correlation spectroscopy experiment in liquids. Its key feature is that it provides in-phase and doubly absorptive line shapes, which renders it robust for chemical shift correlation in solids. Both theory and experiment point to distinct advantages of this protocol, which are illustrated by several experiments under challenging conditions, including fast magic-angle spinning (30kHz), anisotropic molecular motion, and (13)C correlation spectroscopy at the natural abundance isotope level.