Excess thermodynamic quantities in binary systems of non electrolytes.: Different ways of calculating excess compressibilities.

Recent work involved the evaluation of ideal and excess quantities for a wide-ranging set of thermodynamic variables. A literature search revealed that unjustifiable assumptions are frequently made in establishing the expressions of ideal mixing laws, giving rise to erroneous values of corresponding quantities.A large number of such approximate laws have been proposed to estimate “excess” isothermal and isentropic compressibility. The knowledge of rigorous ideal mixing laws allows the difference between pseudo-excess and exact excess compressibility to be evaluated. This provides us with an excellent tool for recalculating exact excess quantities from erroneous data likely to be found in the literature. The amplitude of the various differences has been illustrated using examples taken from among the properties of the water—acetonitrile system.     

Molecular Interactions in Binary Mixtures of Benzene with 1-Alkanols(C5,C7,C8) at 35℃:An Ultrasonic Study

Densities and ultrasonic speeds have been measured in binary mixtures of benzene with 1‐pentanol, 1‐heptanol and 1‐octanol, and in the pure components, as a function of composition at 35 °C. The isentropic compressibility, intermolecular free length, relative association, acoustic impedance, isothermal compressibility, thermal expansion coefficient, deviations in isentropic compressibility, excess free length, excess volume, deviations in ultrasonic speed, excess acoustic impedance, apparent molar compressibility, apparent molar volume, partial molar volume of 1‐alkanol in benzene have been calculated from the experimental data of densities and ultrasonic speeds. The variation of these parameters with composition indicates weak interaction between the component molecules and this interaction decreases in the order: 1‐pentanol > l‐heptanol> 1‐octanol. Further, theoretical values of ultrasonic speeds were evaluated using free length theory, collision factor theory, Nomoto's relation and Van Dæl‐Vangeel ideal mixing relation. The relative merits of these theories and relations were discussed for these systems.     

Structure factor and thermodynamics of rigid dendrimers in solution

The "polymer reference interaction site model" (PRISM) integral equation theory is used to determine the structure factor of rigid dendrimers in solution. The theory is quite successful in reproducing experimental structure factors for various dendrimer concentrations. In addition, the structure factor at vanishing scattering vector is calculated via the compressibility equation using scaled particle theory and fundamental measure theory. The results as predicted by both theories are systematically smaller than the experimental and PRISM data for platelike dendrimers.     

Studies on mechanical and swelling behavior of polymer networks on the basis of the scaling concept. 3. The osmotic compressibility of gels

The osmotic compressibility of chemically crosslinked poly(vinyl acetate) (PVAc) gels in equilibrium with pure diluent has been determined by the method of decreasing equilibrium swelling in different swelling agents. The concentration dependence of the osmotic compressibility has been found to follow a scaling law with an exponent which was greater than that predicted by the mean-field theory. A comparison has been made between the elastic moduli determined by unidirectional deformation measurements and the compressional moduli obtained from the osmotic compressibility data.     

Analysis of dielectric relaxations of w/o emulsions in the light of theories of interfacial polarization

An attempt is made to apply dielectric theories of interfacial polarization to observations of dielectric relaxations for W/O emulsions. Approximate formulas for disperse systems in a W/O type were derived from the two theories: one proposed by Maxwell and Wagner for dilute disperse systems of spherical particles, and the other developed by Hanai for concentrated disperse systems. Dielectric measurements were carried out on concentrated W/O emulsions prepared from kerosene and distilled water or KCl aqueous solutions by minimal use of emulsifiers. Marked dielectric relaxations were observed with the emulsions, the dielectric parameters having been determined to characterize the relaxation data. Phase parameters such as relative permittivity, electric conductivity and volume fraction of the disperse phase were evaluated from the dielectric parameters by use of the approximate formulas of the respective theories. The phase parameters evaluated and the frequency dependence of complex permittivity of the W/O emulsions deduced from the theory for concentrated disperse systems are in excellent agreement with the observed data in comparison to that for dilute disperse systems. It is concluded that the dielectric relaxations due to the interfacial polarization of disperse systems of spheres are explained satisfactorily by the theory for concentrated disperse systems.     

Comparative vibrational spectroscopic study of 1,3-diacetylbenzene and 2,6-diacetylpyridine aided with density functional calculation

Comparative studies of the Raman and infrared spectra of 1,3-diacetylbenzene and 2,6-diacetylpyridine have been made. The spectra are interpreted with the aid of normal mode analysis following full structure optimization based on the density functional method using different levels of theories and various basis sets combination. The unscaled DFT LSDA frequencies approximate the experimental ones in much more uniform fashion than B3LYP or B3PW91 theories do. Nevertheless the use of overall scale factor leads to further significant improvement with less than 2% error. The scaled B3PW91 6-31G result is best, even though LSDA 6-311G frequencies are superior to the B3PW91 ones before scaling. While making complete assignments of vibrational wavenumbers on the basis of potential energy distribution, some interesting observation in the vibrational spectra of these two molecules have been noticed. Instances of Fermi resonances between fundamentals and some combination modes of vibration have also been ascertained. Following the quantum chemical calculation optimized geometries of the both molecules are predicted. The theoretical global minimum energy calculation helps to find the structural symmetries of the molecules.     

Liquid Structural Theories Related via a Force Correlation Function

Abstract

Four approximate theories of dense liquid structure are cast into directly comparable form using a force correlation function. Numerical comparisons via computer simulation data are proposed as a result.     

Generalized density-functional theory: Conquering the N -representability problem with exact functionals for the electron pair density and the second-order reduced density matrix

Using the constrained search and Legendre-transform formalisms, one can derive “generalized” density-functional theories, in which the fundamental variable is either the electron pair density or the second-order reduced density matrix. In both approaches, theN-representability problem is solved by the functional, and the variational principle is with respect to all pair densities (density matrices) that are nonnegative and appropriately normalized. The Legendre-transform formulation provides a lower bound on the constrained-search functional. Noting that experience in density-functional and density-matrix theories suggests that it is easier to approximate functionals than it is to approximate the set ofN-representable densities sheds some light on the significance of this work.     

Convergence of approximate two-component Hamiltonians: how far is the Dirac limit

A systematic elimination of the off-diagonal parts of the Dirac Hamiltonian is carried out in the spirit of the Douglas-Kroll [Ann. Phys. 82, 87 1974] approach and the recently proposed infinite-order two-component method. The present approach leads to a series of approximate two-component Hamiltonians which are exact through a certain order in the external potential. These Hamiltonians are used to study the convergence pattern of approximate two-component theories. It is shown that to achieve an acceptably high accuracy for low-lying one-electron levels in heavy and superheavy systems one needs to use approximate Hamiltonians of prohibitively high order in the external potential. One can conclude that the finite-order two-component Hamiltonians are of limited usefulness in accurate relativistic calculations for heavy and superheavy systems.     

Compressibility of polymers

The compressibility of polyisobutylene and polystyrene above their glass transition temperature is treated as the sum of two parts; a free-volume compressibility and, as originally suggested by Bridgman, a compressibility of the molecules themselves. Two different models are used to treat the free-volume compressibility, and as a result values for the molecular compressibility are estimated. These are in reasonable agreement with other values in the literature. The magnitude of this “molecular compressibility” is then considered in relation to some existing treatments of intermolecular forces. These suggest that intermolecular contacts are more compressible than covalent bonds, and on this basis the observed levels of molecular compressibility can be explained.     

Ultrasonic and Volumetric Studies of Molecular Interactions in Acetonitrile + 1‐Alkanol (C6, C8, C10) Binary Liquid Mixtures at Different Temperatures

The densities, ρ, and ultrasonic speeds, u, have been measured in the binary liquid mixtures of acetonitrile (ACN) with 1‐hexanol, 1‐octanol and 1‐decanol, and in the pure components, as a function of composition at 25, 30, 35, 40 and 45 °C. The deviations in isentropic compressibility, Δκ_s, excess molar volume, V^E, deviations in ultrasonic speed, Δu, apparent molar compressibility, K_?2, apparent molar volume, V_?2, partial molar compressibility, $ {\rm \bar K}^\circ _{\phi,2} $, and partial molar volume, $ {\rm \bar V}^\circ _2 $, of 1‐alkanols in ACN have been calculated from the experimental data of densities and ultrasonic speeds. The variations of these parameters with composition of the mixtures indicate that the structure‐breaking effect dominates over that of the hydrogen‐bonding effect between unlike molecules, suggesting that ACN‐alkanol interaction is weaker than ACN‐ACN and alkanol‐alkanol interactions, and that the interaction (ACN‐alkanol) follows the order: 1‐hexanol > 1‐octanol > 1‐decanol. The excess molar volume data have been analysed by using Flory and Prigogine‐Flory‐Patterson theories. Further, the ultrasonic speeds in these mixtures were theoretically calculated with the help of several theories and empirical relations using the pure component data. The validity and relative merits of these theories and relations have been discussed.     

Improvement on macroscopic compressibility approximation and beyond

A numerical procedure is proposed to extend the thermodynamic perturbation expansion (TPE) to a higher order. It is shown that the present second order term is superior to that due to a macroscopic compressibility approximation (MCA), a local compressibility approximation, and a superposition approximation by Barker and Henderson [Rev. Mod. Phys. 48, 587 (1976)]. Extensive model calculation and comparison with simulation data available in literature and supplied in the present report indicate that the present third order TPE is superior to a previous second order TPE based on the MCA, two previous perturbation theories, which are respectively based on an analytical mean spherical approximation for an Ornstein-Zernike equation, and an assumed explicit functional form for the Laplace transform of radial distribution function multiplied by radial distance, and a recent generalized van der Waals theory. The present critical temperature for a hard core attractive Yukawa fluid of varying range is in very good agreement with that due to a hierarchical reference theory. The present third order TPE is computationally far more modest than the self-consistent integral equation theory, and therefore is a viable alternative to use of the latter.     

Computation of the equation of state of the quantum hard-sphere fluid utilizing several path-integral strategies

The compressibility factor of the quantum hard-sphere fluid within the region (rho(N) (*)相似文献   

Excess compressibility in binary liquid mixtures

Brillouin scattering experiments have been carried out on some mixtures of molecular liquids. From the measurement of the hypersonic velocities we have evaluated the adiabatic compressibility as a function of the volume fraction. We show how the quadratic form of the excess compressibility dependence on the solute volume fraction can be derived by simple statistical effects and does not imply any interaction among the components of the system other than excluded volume effects. This idea is supported by the comparison of the experimental results with a well-established prototype model, consisting of a binary mixture of hard spheres with a nonadditive interaction potential. This naive model turns out to be able to produce a very wide spectrum of structural and thermodynamic features depending on values of its parameters. An attempt has made to understand what kind of structural information can be gained through the analysis of the volume fraction dependence of the compressibility.     

Generation of potential energy curves for the X1Sigma(+)g, B1Delta(+)g, and B'1Sigma(+)g states of C2 using the effective valence shell Hamiltonian method

Calculations of the ground and excited state potential energy curves of C2 using the third-order effective valence Hamiltonian (Hv3rd) method are benchmarked against full configuration interaction and other correlated single-reference perturbative and nonperturbative theories. The large nonparallelity errors (NPEs) exhibited even by state-of-art coupled cluster calculations through perturbative triples indicate a serious deficiency of these single-reference theories. The Hv method, on the other hand, produces a much reduced NPE, rendering it a viable approximate many-body method for accurately determining global ground and excited state potential energy curvessurfaces.     

Ultrasound velocity and density studies in some refined and unrefined edible oils

Density and ultrasonic velocity at a frequency of 3?MHz and in the temperature range 298–333?K are measured in some of the refined and unrefined edible oils, namely coconut oil, castor oil, sunflower oil, kardi (safflower oil) and groundnut oil, which are predominantly used in south India. Velocity has been observed to be decreasing with temperature nonlinearly in some oils in the temperature range studied. This is in agreement with others' observations made in different oils and fats. Velocity change with temperature is attributed to change in intermolecular distance with temperature and the nature of variation depends on the internal molecular dynamics. Density of all the oils has been found to be decreasing with temperature. Various physical parameters such as specific volume, molar sound velocity, adiabatic compressibility, molar compressibility and intermolecular free length have been estimated using measured data on velocity and density.     

Density Functional Theory and the Capillary Evaporation of a Liquid in a Slit

Density functional theory is applied to a Lennard-Jones fluid near a single hard wall and in a slit formed by two walls. We use some simplified versions of the Weeks-Chandler-Andersen (WCA) and the Barker-Henderson (BH) theories. Only the most crude mean field version of the WCA theory, in which the hard-sphere correlation function is set equal to unity for all distances, seems useful. Use of the full WCA approximation is impractical because the effective hard-sphere diameter is density dependent. Generally, the best results are obtained using the BH macroscopic compressibility approximation. Our earlier study of "evaporation" of Lennard-Jones molecules in a slit is extended to other densities using the mean field theory. Copyright 2000 Academic Press.     

Ultrasonic measurements and other allied parameters of praseodymium and neodymium palmitates in mixed organic solvents

Ultrasonic measurements on praseodymium and neodymium palmitates were made in a mixture of 60% benzene and 40% dimethyl sulfoxide (V/V), to determine the critical micelle concentration (CMC), soap-solvent interaction, and various acoustic and thermodynamic parameters. The values of the CMC increase with the increase in the size of the cation in the soap molecules. The ultrasonic velocity, specific acoustic impedance, apparent molar compressibility, apparent molar volume and relative association increase while the adiabatic compressibility, intermolecular free length, solvation number, molar sound velocity and available volume decrease with increasing soap concentration.     

Evaluation of unperturbed and thermodynamic parameters of polymer solutions from viscometric data

The existing approximate theories of polymer solutions are generalized by a simple equation. It is combined with the Kirkwood- Riseman perturbation treatment of viscosity together with the Kuhn model of random coil dimensions to produce two expressions for the unperturbed and thermodynamic parameters of polymers in solvents. A test of these equations on a large variety of polymer systems yields results which are comparable with the experimental values.