Extension of Huron-Vidal-type Mixing Rule to Three-parameter Harmens-Knapp Cubic Equation of State

In this paper was extended the HV-type mixing rules to Harmens-Knapp cubic equation state (HK CEOS). The new HV-type mixing rule with HK CEOS was tested for Vapor-liquid equilibrium(VLE) of different polar and nonpolar systems. The tested results are in good agreement with existing experimental data within a wide range of temperatures and pressures. In comparison with the VDW mixing rule, the new mixing rule gives much better predictions for the VLE of nonpolar and polar systems.     

用状态方程预测极性溶剂中多种气体的亨利常数

应用立方型链转子状态方程预测不同温度和压力下多种超临界气体在亚临界极性液体中的亨利常数,得到良好的结果.并从理论上加以分析和讨论.     

Modelling the Vapor–Liquid Equilibrium of Polymer Solutions Using a Cubic Equation of State

This work presents the vapor–liquid equilibrium calculations in an isothermal flash, applied to polymer solutions, using the Peng–Robinson cubic equation of state modified by Stryjek–Vera, and the mixing rule introduced by Wong–Sandler. This rule allows combining the rigid lattice thermodynamic model of Flory–Huggins to the Peng–Robinson–Stryjek–Vera equation of state. As the Gibbs free energy must be minimum in the equilibrium state, a stochastic optimization method, the simulated annealing algorithm, was used to find out the extreme of this thermodynamic potential.     

Applying the concepts of density functional theory to simple systems

Equations are derived for the chemical potential and local hardness of the ground states of helium and the related two electron ions. With these properties it is possible to correct the energies of the simple single‐zeta wave functions to the nearly exact values. The calculations are simple for these simple systems. In principle, it is possible to extend this method to all atoms and molecules. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Improvement on the Carnahan-Starling Equation of State for Hard-sphere Fluids

Making use ofWeierstrass's theorem and Chebyshev's theorem and referring to the equations of state of the scaled-particle theory and the Percus-Yevick integration equation, we demon-strate that there exists a sequence of polynomials such that the equation of state is given by the limit of the sequence of polynomials. The polynomials of the best approximation from the third order up to the eighth order are obtained so that the Carnahan-Starling equation can be improved successively. The resulting equations of state are in good agreement with the simulation results on the stable fluid branch and on the metastable fluid branch.     

Cubic and Columnar Supramolecular Architectures of Rod–Coil Molecules in the Melt State

The liquid crystalline behavior of compounds 1 (n = 7, 12, 15) differs significantly from that exhibited for conventional rodlike molecules. They organize into layered smectic, bicontinuous cubic or hexagonal columnar mesophases depending on the temperature or the volume fraction of coil segments.     

The second virial coefficient of 3-centerLennard-Jones molecules and its relation to 1- and 2- center molecules

The second virial coefficients of homonuclear three-centerLennard-Jones molecules are calculated with various parameters of the isosceles triangle connecting the three sites. A special effort is made to establish the reducedBoyle temperaturesT _B and the values of the second virial coefficients atT/T _B=0.3 for the sake of comparison with one- and two-centerLennard-Jones molecules. It is shown that it is possible to find parameter values of the interaction potential of one- and two-centerLennard-Jones molecules which give very similar values of second virial coefficients forT/T _B0.3, and the equivalence conditions are established. These conditions might not only give a basis for a microscopic scaling of state variables, but also some restrictions for the validity of the group contribution concept.Presented in part at the DFG-Colloquium at Paderborn, 19th April 1982, and at the 5th Conference on Mixtures of Nonelectrolytes and Intermolecular Interactions, April 18–22, 1983, at Halle (GDR).     

Evaluation of the parameters of the Bender equation of state for low acentric factor fluids and carbon dioxide

Volumetric properties of several low acentric factor fluids (Ar, CH₄, C₂H₆, Kr, N₂, Ne, O₂, Xe) as well as CO₂ are modeled using the Bender equation of state. This equation is a linear function of 19 adjustable parameters, which are evaluated from properties data, using a linear numerical procedure. The validity of the EOS is tested by calculating the Joule-Thomson inversion curve. A simple model is in particular used to correlate the inversion properties predicted by the Bender equation, expressed in term of reduced pressure as a function of reduced temperatures ranging from 0.8 to 6. The simple correlation reproduces accurately the used data. We employ data on state behaviour ρ(P,T) of homogeneous fluid phases, vapour-liquid equilibrium, second virial coefficient and the coordinates of the critical point.     

The viscosity of triethylamine vapor at low densities and in the saturated vapor phase

For the first time, results of high-precision measurements of the viscosity coefficient of triethylamine vapor at low densities are reported. The relative measurements with an all-quartz oscillating-disk viscometer were carried out along seven isochores at densities from 0.002 to 0.009 mol m⁻³ in the temperature range between 298 and 498 K. The uncertainty is estimated to be ±$\pm$0.2% at ambient temperature, increasing up to ±$\pm$0.3% at higher temperatures. First isothermal values were recalculated from the original experimental data and then evaluated with a first-order expansion for the viscosity, in terms of density. In addition, viscosity values of the saturated vapor were determined at low temperatures. The results are utilized to model the viscosity coefficient of triethylamine vapor at moderately low densities. A so-called individual correlation on the basis of the extended theorem of corresponding states was employed to describe the zero-density viscosity coefficient, whereas the Rainwater–Friend theory was used to represent the initial density dependence expressed as second viscosity virial coefficient.     

从Bragg方程的Ewald图建立倒易点阵概念

倒易点阵是化学、物理、地质学、矿物学、材料学等专业相关课程中重要的教学内容,也是通识化本科教学过程中的难点之一。目前,大多数本科教材仅给出了其中的教学内容点,各部分间缺乏逻辑关系,这给教师课堂教学以及学生自学带来了困难。从Bragg方程的Ewald图解法入手,建立倒易点阵概念,给出了构建时的2个关键问题,倒易基矢如何定义和倒易矢量结点指数如何确定,并用数理推导证明如果大小为1/d（hkl）的倒易矢量g垂直于对应正空间中一组晶面间距为d（hkl）、密勒指数为（hkl）的平行晶面,则它在倒易点阵中的结点指数为hkl,该倒易矢量可记为ghkl。从Ewald图解法构建倒易点阵概念的思路,将使倒易点阵更形象化、具体化及逻辑化,为师生理解和深化倒易点阵概念提供了一条新途径。     

PSRK: A Group Contribution Equation of State Based on UNIFAC

A group contribution equation of state called PSRK (Predictive Soave-Redlich-Kwong) which is based on the Soave-Redlich-Kwong equation (Soave, 1972) has been developed. It uses the UNIFAC method to calculate the mixture parameter a and includes all already existing UNIFAC parameters. This concept makes use of recent developments by Michelsen (1990b) and has the main advantage, that vapor-uquid-equilibria (VLB) can be predicted for a large number of systems without introducing new model parameters that must be fitted to experimental VLB-data. The PSRK equation of state can be used for VLB-predictions over a much larger temperature and pressure range than the UNIFAC γ--approach and is easily extended to mixtures containing supercritical compounds. Additional PSRK parameters, which allow the calculation of gas/gas and gas/alkane phase equilibria, are given in this paper. In addition to those mixtures covered by UNIFAC, phase equilibrium calculations may also include gases like CH₄ C₂H₆, C₃H₆, c₄H₁₀, CO₂, N₂, H₂ and CO.     

Prediction of the thermodynamic properties of {ammonia + water} using cubic equations of state with the SOF cohesion function

The SOF cohesion function for cubic equations of state is based on the behavior of the residual energy of pure fluids. It contains two adjustable parameters for each component, which have been obtained for over 800 substances by regression of pure-fluid saturation pressures, and correlated in terms of a four-parameter corresponding states principle. In the present work, we compare the performance of this function and of the original Soave cohesion function with the Redlich-Kwong and Peng-Robinson equations of state in the prediction of vapor-liquid equilibria and enthalpy-composition diagrams for the polar system {ammonia + water}. We use simple van der Waals one-fluid mixing rules, linear for the covolume and quadratic for the cohesion parameter with one (symmetric) and two (asymmetric) binary interaction parameters. The non-linear least squares minimization algorithm lsqnonlin, in Matlab^®, is used to adjust the interaction parameters to phase equilibrium and enthalpy data taken from the IAPWS fundamental formulation. Upper and lower bounds of the optimized interaction parameters are obtained using Matlab^®bootstrap with 95% confidence of a normal distribution sampling. The validity of the parameters as functions of temperature is between the triple point of water and the critical point of ammonia. At lower temperatures, a rapid increase of statistical uncertainties is observed that can be attributed to the scarcity of phase equilibrium data.The two-parameter SOF cohesion function and the cubic equations of state are shown to give accurate predictions of the VLE and enthalpies of {ammonia + water}. Both equations of state give very similar results. Statistical analysis of the interaction parameters shows that their values (within the range of validity mentioned above) are effectively the same for both cohesion functions. At higher temperatures, however, extrapolation of the two cohesion functions gives different results, and correspondingly requires different interaction parameters.     

A Theoretical Study of the Hard-Sphere Fluid-Solid Interface II. Test of an Alternative Variational Form

Abstract

We examine the hard-sphere fluid-solid interface using a form for the inhomogeneous density that differs significantly from those in our previous paper. As before, our approach avoids the square-gradient approximation. We present results for the [111] interface which qualitatively support our earlier findings. While the new density profile closely resembles those observed in computer simulations of Lennard-Jones systems, the surface free energy calculated from this an satz is almost 2.5 times as large as the earlier estimates.     

用积分方程方法决定胶粒之间的空耗势

Binary components Ornstein-Zernike integral equation with the concentration of large particle component being set to zero was employed to study the depletion potential behavior between two large neutral colloid particles （modeled as hard spheres）immersed in a sea of small neutral solvent particles. The prediction for the depletion potential behavior compared well with simulation data and experimental data available in the literature. It is found that the Hansen-Verlet one phase criterion,based on the effective one component system with the present depletion potential,for the freezing transition is completely not suitable for the real binary components system. It is disclosed that the unsuitability is due to the volume term of the solid phase and liquid phase which can not be treated selfconsistently in the Hansen-Verlet one phase criterion.     

六配位与八配位Oh对称晶场中Mn2+光谱及基态立方零场分裂研究

CaF₂晶体掺入Mn²⁺后,Mn²⁺取代了Ca²⁺,受到8个邻近的F^-所产生的八配位立方O_h对称晶场作用,Mckeever等计锋了Mn²⁺的吸收谱,其基态立方零场分裂参量α已有实验观测值。     

Computation of some thermodynamic properties of nitrogen using a new intermolecular potential from molecular dynamics simulation

A new pair-potential energy function of nitrogen has been determined via the inversion of reduced viscosity collision integrals and fitted to obtain an analytical potential form. The pair-potential reproduces the second virial coefficient, viscosity, thermal conductivity, self-diffusion coefficient, and thermal diffusion factor of nitrogen in a good accordance with experimental data over wide ranges of temperatures and densities. We have also performed the molecular dynamics simulation to obtain pressure, internal energy, heat capacity at constant volume, and self-diffusion coefficient of nitrogen at different temperatures and densities using our calculated pair-potential and some other potentials. The molecular dynamics of the nitrogen molecules has been also used to determine nitrogen equation of state in two (low and high) pressure ranges. Our results are in a good agreement with experiment and literature values.     

A simple statistical mechanical theory for the mutual solubility of fluid mixtures of water and organic solvents under high pressure

A simple statistical mechanical theory is presented to explain phase diagrams of fluid mixtures with both a lower critical solution temperature and an upper critical solution temperature under pressure. By postulating a temperature dependence for the interaction free energy parameter of the constituent molecules and a pressure dependence for the excess volume, phase diagrams with both lower critical solution temperature, and upper critical solution temperature and their pressure dependence can be reproduced by quadratic surfaces in temperature-concentration-pressure space. The topological aspects of the observed phase diagrams in this space have been related to our theoretical model, and the thermodynamical meaning of the topologies has been interpreted based on our model. Experimental data for the mutual solubility of water and 2-butanol under pressure and that of water and 3-methylpyridine with added salts have been analyzed quantitatively and theoretical parameters are determined.     

聚合物-溶剂-非溶剂三元相图的计算

改进了Pouchly提出的Flory-Huggins半经验展开式,详细推导了相应的计算三元相图中双结点溶解度曲线(Binodal线)和亚稳均相极限线(Spinodal线)的方程;计算了非溶剂和溶剂的相互作用参数g₁₂、溶剂和醋酸纤维素的相互作用参数g₂₃同时依浓度变化的三元相图。结果表明:新的Flory-Huggins方程更具有普适性。