An Equation for the Correlation of Viscosities of Binary Mixtures

Knowledge of the viscosity of binary mixtures is of great importance in many industrial processes. Rarely can the viscosity of mixtures be obtained from the sum of the viscosities of the pure components. The theoretical study of the viscosity of mixtures is generally complicated. Numerous empirical correlation models have been proposed. The present study proposes a new empirical correlation equation, based on lineal behavior. The equation can easily be used with one, two or three parameters, and in many cases it improves upon the models that are commonly used. Likewise, the excess viscosity calculated with the proposed equation generally yield more satisfactory results than those obtained with the polynomial equation of Redlich-Kister.     

An interaction site model integral equation study of molecular fluids explicitly considering the molecular orientation

We implemented an interaction site model integral equation for rigid molecules based on a density-functional theory where the molecular orientation is explicitly considered. In this implementation of the integral equation, multiple integral of the degree of freedom of the molecular orientation is performed using efficient quadrature methods, so that the site-site pair correlation functions are evaluated exactly in the limit of low density. We apply this method to Cl(2), HCl, and H(2)O molecular fluids that have been investigated by several integral equation studies using various models. The site-site pair correlation functions obtained from the integral equation are in good agreement with the one from a simulation of these molecules. Rotational invariant coefficients, which characterize the microscopic structure of molecular fluids, are determined from the integral equation and the simulation in order to investigate the accuracy of the integral equation.     

Transcorrelated calculations of homogeneous electron gases

We have constructed the complete transcorrelated equation for homogeneous electron gases and investigated this equation on two- and three-dimensional systems. Correct asymptotic behaviours of the correlation factors can be easily obtained from the transcorrelated equation, both the long-range RPA type decay and the short-range spin dependent cusp conditions. The complete transcorrelated equation is solved numerically and the outcome correlation energies agree very well with variational quantum Monte Carlo results. Possible simplifications of the transcorrelated calculations are discussed, where we find that the RPA equation for the correlation factor can be considerably improved by adding one more term in the equation.     

Surface tension and density of binary mixtures of monoalcohols,water and acetonitrile: equation of correlation of the surface tension

Measurements of the surface tension (σ) and density (ρ) of binary mixtures of monoalcohols, water and acetonitrile at 298.15 K and at atmospheric pressure, as a function of mole fraction (x) have been made. The experimental values of the deviation of surface tension and the excess of molar volume (Δσ, V ^E) have been correlated by the Redlich–Kister equation. An empirical correlation equation is presented for the study of the surface tension of these mixtures, and comparisons are made of the experimental values of surface tension versus those obtained with the correlation equation and with other models of correlation. Finally, with the purpose of corroborating the validity of the correlation equation, the latter is applied to other reference binary mixtures.     

Theoretical study on the sound absorption of electrolytic solutions. I. Theoretical formulation

A theory is formulated that describes the sound absorption of electrolytic solutions due to the relative motion of ions, including the formation of ion pairs. The theory is based on the Kubo-Green formula for the bulk viscosity. The time correlation function of the pressure is projected onto the bilinear product of the density modes of ions. The time development of the product of density modes is described by the diffusive limit of the generalized Langevin equation, and approximate expressions for the three- and four-body correlation functions required are given with the hypernetted-chain integral equation theory. Calculations on the aqueous solutions of model electrolytes are performed. It is demonstrated that the theory describes both the activated barrier crossing between contact and solvent-separated ion pairs and the Coulombic correlation between ions.     

Compensation effect and isokinetic temperature in thermal dissociation reactions of the type Asolid ⇌ Bsolid + Cgas

It is shown that the Zawadzki — Bretsznajder rule, compensation effect, and isokinetic temperature are simple consequences of interpretation of the Arrhenius equation as a projection correlation. It is established that such an interpretation of the Arrhenius equation allows the discrimination of the deviation factors which impart a definite (although not always simple and recognized) physical sense, to the known empirical correlation. A possibility of deriving new correlation relationships by this method of reasoning is presented.     

A quantitative evaluation of the electrostatic theory for ion pair chromatography

Summary A quantitative model for ion pair chromatography based on the electrostatic theory is described. The model is based on the solution of the linearised Poisson-Boltzmann equation in a cylinder. The obtained equations are compared with experimental data from a number of different systems. The agreement between theory and experiments is satisfactorily. Systematic deviations due to the use of the linearised equation and ion correlation effects are discussed.     

The application of the Dubinin-Astakhov equation to the characterization of microporous carbons

A study is made of the adsorption of carbon dioxide at 195 K on a series of microporous carbons. The adsorption data are analysed using the Dubinin-Astakhov equation. It is found that the adsorption isotherms obey the Dubinin-Astakhov equation over the pressure range studied.The characteristic energy of adsorption calculated from the slope of the Dubinin-Astakhov plot is shown to be in correlation with the mean value of the adsorption potential. The microporosity of carbons is interpreted in terms of the characteristic parameters of the adsorption pontential distribution, determined by means of the Dubinin-Astakhov equation. It is found good agreement between these parameters and the micropore size distribution.     

An integral equation theory for inhomogeneous molecular fluids: the reference interaction site model approach

An integral equation theory which is applicable to inhomogeneous molecular liquids is proposed. The "inhomogeneous reference interaction site model (RISM)" equation derived here is a natural extension of the RISM equation to inhomogeneous systems. This theory makes it possible to calculate the pair correlation function between two molecules which are located at different density regions. We also propose approximations concerning the closure relation and the intramolecular susceptibility of inhomogeneous molecular liquids. As a preliminary application of the theory, the hydration structure around an ion is investigated. Lithium, sodium, and potassium cations are chosen as the solute. Using the Percus trick, the local density of solvent around an ion is expressed in terms of the solute-solvent pair correlation function calculated from the RISM theory. We then analyze the hydration structure around an ion through the triplet correlation function which is defined with the inhomogeneous pair correlation function and the local density of the solvent. The results of the triplet correlation functions for cations indicate that the thermal fluctuation of the hydration shell is closely related to the size of the solute ion. The triplet correlation function from the present theory is also compared with that from the Kirkwood superposition approximation, which substitutes the inhomogeneous pair correlation by the homogeneous one. For the lithium ion, the behavior of the triplet correlation functions from the present theory shows marked differences from the one calculated within the Kirkwood approximation.     

The perturbation theory of the extended Hartree–Fock approximation for two-electron atoms

The first-order 1/Z perturbation theory of the extended Hartree–Fock approximation for two-electron atoms is described. A number of unexpected features emerge: (a) it is proved that the orbitals must be expanded in powers of Z^?1/2, rather than in Z^?1 as expected; (b) it is shown that the restricted Hartree–Fock and correlation parts of the orbitals can be uncoupled to first order, so that second-order energies are additive; (c) the equation describing the first-order correlation orbital has an infinite number of solutions of all angular symmetries in general, rather than only one of a single symmetry as expected; (d) the first-order correlation equation is a homogeneous linear eigenvalue-type equation with a non-local potential. It involves a parameter μ and an eigenvalue ω(μ) which may be interpreted as the probability amplitude and energy of a virtual correlation state. The second-order correlation energy is 2μ²ω. Numerical solutions for the first-order correlation orbitals, obtained variationally, are presented. The approximate second-order correlation energy is nearly 90% of the exact value. The first-order 1/Z perturbation theory of the natural-orbital expansion is described, and the coupled first-order integro-differential perturbation equations are obtained. The close relationship between the first-order extended Hartree–Fock correlation orbitals and the first-order natural correlation orbitals is discussed. A comparison of the numerical results with those of Kutzelnigg confirms the similarity.     

The modified Hartree–Fock self-consistent field equation

A one-electron correlation operator is introduced into the Hartree–Fock self-consistent field equation. The correlation operator is derived from the second-order perturbation theory. Energies of atomic and molecular systems calculated from this modified Hartree–Fock equation are equal to that from second-order perturbation of Hartree–Fock equation. The modified equation can also be solved self-consistently by the LCAO approximation. We also presented the modified expressions for other operators.     

Analyses of the electronic collective motions by means of a nonlinear dynamical equation

A nonlinear dynamical equation for the electronic collective motion is presented by employing the traditional time-dependent procedure. The equation is applied to the model π-electron system of ethylene, and the effects of nonlinear interactions are investigated using its several states as reference states. It is shown that the nonlinear correlation plays an important role in describing the change of the lower excited states.     

Quantum Chemistry Investigation into the Distribution Properties of 2-Formamido-phenylacrylates in n-Octanol/Water System

1INTRODUCTION Quantitative structure-activity relationship(QSAR)is one of the necessary tools that could be employed to evaluate the hazards of organic chemicals.QSAR equation could be utilized to forecast the biological activity of unknown organic compounds,which is significant for initial screening and evaluation of toxic compounds[1].2-Formamido-phenylacrylates and their derivates are important intermediates for the synthesis of spice,pesticide and medicine.Wei et al.estimated the s…     

Thermally activated escape rate for the Brownian motion of a fixed axis rotator in a double well potential for all values of the dissipation

The extension of the Kramers theory of the escape rate of a Brownian particle from a potential well to the entire range of damping proposed by Mel'nikov and Meshkov [J. Chem, Phys. 85, 1018 (1986)] is applied to the rotational Brownian motion of fixed axis rotators in a double well cosine potential. The procedure yields an expression for the Kramers escape rate valid for all values of the dissipation including the very low damping (VLD), very high damping (VHD), and crossover regimes. This equation provides a good asymptotic estimate of the correlation time tau per pendicular of the longitudinal dipole moment correlation function calculated by solving the underlying Langevin equation using the matrix-continued fraction method. Moreover, for low barriers, where the Mel'nikov and Meshkov approach is not applicable, analytic equations for tau in the VLD and VHD limits are derived and a simple extrapolating equation that is valid for all values of the damping is proposed.     

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 critical review on the stability constants of the fluoride complexes of actinides in aqueous solution and their correlation with fundamental properties of the ions

Literature data on the stability constants of the fluoride complexes of the actinides in different oxidation states have been compiled. In order to have a reasonable inter-comparison, the stability constant (β₁) values obtained in diverse ionic strength media are converted to so called thermodynamic stability constants, β ₁ ⁰ using the DAVIES equation (a modification of Debye-Huckel equation). A correlation of the β ₁ ⁰ values with the fundamental properties of the actinide ions using various models available in the literature has been attempted. Using the values of inonic radii and best available values of the stability constants of a large number of metal ions from recent compilations a comparative study of the various models or relations available in the literature has been tried. For metal ions in general, the semi-empirical relation recently developed by BROWN, SYLVA and ELLIS (BSE equation)_gives the best correlation. In an attempt to accommodate the unusual trend in the stability constants of the tetravalent actinides a modification in a parameter of the BSE equation has been proposed. Good agreement between the theoretically calculated and experimentally determined values for actinides in different oxidation states is obtained in most of the cases. Further improvements in theoretical relation as well as experimental data are required for better correlation.     

Liquid-vapor equilibrium in the dimethyl sulfoxide-methanol system

The liquid-vapor phase equilibrium in the dimethyl sulfoxide-methanol binary system was studied with the use of a statistical method. Partial pressures of dimethyl sulfoxide and methanol were calculated by integrating the Gibbs-Duhem equation. Molar excess Gibbs energies were described by the Redlich-Kister equation, and correlation parameters were calculated. It was found that molar excess Gibbs energies are negative, and the deviation from ideality increases as temperature increases.     

Analytic solution of the mean spherical approximation for a multi-component plasma

The mean spherical approximation for a mixture of charged hard spheres in a uniform neutralizing background is solved analytically. The factor correlation functions and the excess thermodynamic properties are explicitly expressed through a single parameter, which can be obtained by solving an algebraic equation.     

Calculating Density of Molecular Liquids Using Agrawal-Thodos Equation

The correlation between the parameters of the Agrawal-Thodos equation, the fundamentalconstants of a substance are established. A modified equation is proposed, in which the minimum set of easily measurable properties of the substance is used as input data.