The importance of the three-particle correlation function in the theory of monatomic classical liquids like argon

The present study was motivated by the work of Fortov et al. (2008) on the use of experimental methods of analysis of spatial correlation of dust particles in plasma. Here, we therefore focus on the importance of the three-particle correlation function g ₃ in the theory of monatomic classical liquids like argon, in the framework of two-body central forces. We cover (i) the asymptotic relation of g ₃ to the Ornstein–Zernike direct correlation function c(r); (ii) the use of g ₃ to determine the specific heat difference c _P ? c _V ; and (iii) g ₃ related to the pressure dependence of the pair correlation function.     

Applications of self-consistent field theory in polymer systems

1Introduction Owing to the specificity of the long chain,polymers present complexity and versatility.These molecules in the system can be various in their topological struc-tures,such as linear,star,comb or circle structures;meanwhile they can be polymeri…     

Hierarchy of equations in the generalized density functional theory

Functional relations and equations of hierarchy in the generalized density functional theory (DFT) are derived from coordinate scaling and adiabatic connection. Local and nonlocal solutions for the noninteracting kinetic energy, exchange energy, correlation energy, and the kinetic energy correction functionals are presented. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Semiclassical self-consistent field perturbation theory for the hydrogen atom in a magnetic field

A recently developed perturbation theory for solving self-consistent field equations is applied to the hydrogen atom in a strong magnetic field. This system has been extensively studied using other methods and is therefore a good test case for the new method. The perturbation theory yields summable large-order expansions. The accuracy of the self-consistent field approximation varies according to field strength and quantum state but is often higher than the accuracy from adiabatic approximations. A new derivation is presented for the asymptotic adiabatic approximation, the most useful of the adiabatic approaches. This derivation uses semiclassical perturbation theory without invoking an adiabatic hypothesis. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 183–192, 1998     

Optimizing the electrochemical performance of imidazolium‐based polymeric ionic liquids by varying tethering groups

We report the synthesis and characterization of a series of novel imidazolium cation and bis(trifluoromethane)sulfonimide anion (TFSI^?)‐based ionic liquid (IL) model compounds and their corresponding polymeric ionic liquids (PILs) with various tethering groups. Ethylene oxide repeating units were attached as tethering groups to an imidazolium cation to optimize the glass transition temperatures (T_g) and ionic conductivities of the PILs. The novel PILs exhibit excellent conductivity values of around 8 × 10^?4 S/cm at room temperature. The thermophysical and electrochemical properties of ILs, including thermal transition, ionic conductivity, and rheological behavior, were characterized to investigate the effect of tethering groups. We conclude that the length of poly(ethylene oxide) tethering group has a tremendous effect on both physical property and electrochemical behavior and that charge carrier density is dominant in defining ionic conductivity with free ILs, whereas ion mobility plays a more important role after polymerization. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1339–1350     

Investigation of the structure of concentrated aqueous solution of LiCl at low temperatures by the method of integral equations

Peculiarities of the formation of the structure of aqueous LiCl solution (at a salt: water molar ratio of 1:5.3) in the temperature range 298-138 K were studied by the method of integral equations. Analysis of the results obtained suggests that transition of the system into the supercooled and glassy state is accompanied by an increase in the tetrahedral ordering of solvent molecules and a decrease in the number of interactions between the water molecules in unbound solvent. Lowering the temperature leads to an increase in the degree of structurization of water molecules surrounding the cation. Preferable formation of hydrogen bonds with the anion under extreme conditions was established. The glassy state of the solution is characterized by the absence of direct anion-cation correlations and increased (compared to standard conditions) probability of the formation of ion-water chains. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1881–1886, October, 1999.     

Description of the pVT behavior of ionic liquids and the solubility of gases in ionic liquids using an equation of state

A molecular thermodynamic model developed previously for fluids of chain-like molecules has been extended to correlate the pVT behavior of ionic liquids and the solubilities of gases such as CO₂, C₃H₆, C₃H₈, C₄H₁₀ in various ionic liquids. The relative deviation between the calculated molar volume and experimental data is less than 0.2%. It is shown that this equation of state can be used to correlate the solubility of CO₂ in ionic liquids with only one temperature-independent adjustable interaction parameter, and the accuracy of the correlation can be further improved using two temperature-independent adjustable parameters. The water content of ionic liquids has a large influence on the calculated results. For systems with water content lower than 0.1%, the average relative deviations of bubble point pressure are 3.14 and 4.90% using two parameters and one parameter, respectively. For systems containing C₃H₆, C₃H₈ and C₄H₁₀ two temperature dependent adjustable parameters are needed to obtain a good fit, and the corresponding deviation of the gas solubility is less than 2%, except for C₃H₈.     

Theoretical analysis on the preparation of gradient‐index polymeric rods by a centrifugal field

A theoretical analysis was conducted on the preparation of gradient‐index (GI) polymeric rods by a centrifugal field. Two kinds of materials system were used in this study: a polymer/monomer mixture and a polymer/dopant mixture. The predicted refractive index distribution (RID) was in good agreement with the experimental data reported in the literature. The effects of the essential parameters, including the molecular weight of the polymer, the composition and component properties (refractive index and density) of the mixture, the rotating speed, and the diameter of the GI rod on the RID were investigated. The results of a numerical simulation reveal that the essential parameters have significant effects on the RID. A materials property requirement was established theoretically for obtaining a rod RID with the refractive index decreasing from the center to the periphery. That is, the order of the density between the polymer and monomer (or dopant) needs to be the reverse of the refractive index. The enhancement of the polymer molecular weight, rotating speed, and rod radius increases the refractive index difference between the rod center and the periphery (Δn). However, the optimization of these parameters is required to obtain a suitable RID for practical applications. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1764–1772, 2000     

On the theory of thermal density fluctuations in the glassy state: Application to poly(vinyl acetate)

A theory of the liquid state, suitably modified for the glass, contains a characteristic structure functionh, which represents a free volume fraction. As shown previously by means of experimental pressure-volume-temperature studies,h retains finite, nonvanishing temperature and pressure coefficients upon passing through the glass transition. These results are now employed to compute the mean-square thermal density fluctuations in poly(vinyl acetate). AboveT _g , the result attests again to the satisfactory quantitative performance of the equilibrium theory. BelowT _g , two glasses formed at low and elevated pressures, respectively, are considered under quasi-equilibrium conditions. The results show the anticipated initial accord with the approximation proposed by Fischer and Wendorff, involving the isothermal compressibility of the liquid atT _g . The theory delineates the increasing departures with decreasing temperature observed in the literature. We comment finally on the trend of the fluctuations on approaching absolute zero. Explicit low temperature calculations remain to be undertaken.Dedicated to Professor Dr. F. H. Müller.     

Application of the group function theory to infinite systems

We consider application of the group function theory to an arbitrary infinite system consisting of weakly overlapping structural elements which may be atoms, ions, molecules, bonds, etc. We demonstrate that the arrow diagram (AD) expansion developed previously is ill‐defined for such a system resulting in divergences in any physical quantity associated with the entire system such as, for example, the energy and charge density. A “linked‐AD” theorem is then formulated and proven, which results in a diagrammatic expansion that scales correctly with the system size. Coulomb systems with long‐range interactions between structure elements are also considered and the diagrammatic expansion is rearranged in such a way as to also give the correct (linear) scaling. We give an explicit expression for the total energy up to the third order with respect to overlap. Finally, we discuss the problem of choosing structure elements (SE) in a general insulating system and propose a variational method based on a configuration interaction (CI) type expansion within the Fock subspace associated with every SE. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 511–534, 2000     

Partial summation of various subsets of low-temperature terms to all orders in the direct correlation function based thermodynamic perturbation theory of simple liquids

Various subsets of a new thermodynamic perturbation expansion for simple liquids [PHYSICAL REVIEW E 83, 021203 (2011)] is summed up by a new method to all orders which yield explicit formulas for the structure and thermodynamic of simple fluids. The formulas then have been tested successfully against computer simulations results for hard-core Yukawa potential.     

离子液体谱学性质和热力学数据关联的新进展

离子液体的性质是其微观结构和相互作用的外在表现,与其应用密切相关.谱学手段能从分子水平上探测离子液体的微观环境和相互作用,近年来在定量关联或预测离子液体宏观性质方面发挥着越来越重要的作用.本文着重概述了红外光谱(IR)、拉曼光谱(Raman)、核磁共振波谱(NMR)和电子顺磁波谱(ESR)等常见谱学手段在定量关联离子液体及其溶液体系宏观性质方面的研究进展以及发展方向.     

Modelling the volumetric properties of ionic liquids using a modified perturbed hard-sphere-chain equation of state

In this paper, a modified perturbed hard-sphere-chain equation of state (EOS) by Eslami [H. Eslami, Fluid Phase Equilib. 216 (2004) 21–26], is applied for modelling the thermodynamic properties of some ionic liquids (ILs). Two reliable scaling constants are used to determine two temperature-dependent parameters in the proposed EOS. The unique adjustable parameter that is reflecting the number of segments per molecule, r, compensates the uncertainties in the calculated temperature-dependent parameters. The reliability of the proposed EOS has been checked by comparing the results with 1561 experimental data points for 18 ILs over a broad range of pressures and temperatures. The overall average absolute deviation is 0.35%. A comparison of the predicted results, using the present EOS with the results of some previous models, indicates that the determined results of this EOS are in more accordance with experimental data than those.     

Statistical theory for hydrogen bonding fluid system of AaDd type (Ⅲ): Equation of state and fluctuations

The equation of the state of the hydrogen bonding fluid system of AaDd type is studied by the principle of statistical mechanics. The influences of hydrogen bonds on the equation of state of the system are obtained based on the change in volume due to hydrogen bonds. Moreover, the number density fluctuations of both molecules and hydrogen bonds as well as their spatial correlation property are investigated. Furthermore, an equation describing relation between the number density correlation function of "molecules-hydrogen bonds" and that of molecules and hydrogen bonds is derived. As application,taking the van der Waals hydrogen bonding fluid as an example, we considered the effect of hydrogen bonds on its relevant statistical properties.     

A simple method for evaluation of the self-consistency of the radial distribution functions and the orientation of water molecules in the first coordination sphere from the results of molecular dynamics calculations

A simple method for determination of the angular orientation of water molecules in the first coordination sphere from the radial distribution functions is proposed. A comparative analysis of the ability of the model potentials of pair interaction to take into account the effects of manybody interactions (MBI) was performed. The responses of the model pair potentials to the MBI effects in the first and second coordination spheres were found to be poorly correlated with each other. It was concluded that it is necessary to derive a new analytical type of potential functions of pair interaction. Published inIzvestiya Akademii Nauk. Seriya Khimicheskaya. No. 11, pp. 1842–1846. November. 2000.     

Transfer-matrix theory of the crystal–columnar transition in polymeric liquid crystals

The statistical–mechanical problem of the transition between crystalline and columnar phases in a main-chain liquid–crystalline polymer is treated in a simple model in which only longitudinal motions of the polymer chains are permitted. A mean-field approximation for the interchain potential is used to obtain a self-consistent equation for the crystalcolumnar transition temperature. When applied to typical homopolymers this theory correctly predicts transition temperatures above the degradation temperature; when applied to a crude model of a random copolymer a temperature in the observed range is predicted.     

Statistical theory for hydrogen bonding fluid system of AaDd type (Ⅲ): Equation of state and fluctuations

The equation of the state of the hydrogen bonding fluid system of A_aD_d type is studied by the principle of statistical mechanics. The influences of hydrogen bonds on the equation of state of the system are obtained based on the change in volume due to hydrogen bonds. Moreover, the number density fluctuations of both molecules and hydrogen bonds as well as their spatial correlation property are investigated. Furthermore, an equation describing relation between the number density correlation function of “molecules-hydrogen bonds” and that of molecules and hydrogen bonds is derived. As application, taking the van der Waals hydrogen bonding fluid as an example, we considered the effect of hydrogen bonds on its relevant statistical properties. Supported by the National Natural Science Foundation of China (Grant Nos. 20303006 and 20574016), the Natural Science Foundation of Hebei Province (Grant Nos. B2006000959 and B2004000093) and the Natural Science Foundation of Education Committee of Hebei Province (Grant No. 2003101)