Application Of Thermodynamic Perturbation Theory Research Articles

Thermodynamic perturbation theory of simple liquids. A hierarchy of equations for expansion coefficients

The properties of an expansion of the statistical sum of a simple liquid with respect to the potential in thermodynamic perturbation theory are analyzed. The coefficients of this expansion are determined by the unperturbed potential, depend on temperature and density, and can be calculated by means of mathematical modeling. It is shown here that the derivatives of these coefficients with respect to temperature and density are expressed through the higher expansion coefficient (these relations are usually called a hierarchy of equations). These coefficients determine the expansion of the Helmholtz free energy and RDF with respect to the perturbation potential. The thermodynamic characteristics of the system (entropy, internal energy, pressure) are expressed through both the differential relations for the Helmholtz free energy and the integral expressions containing RDF. It is found that the hierarchy of equations obtained in this work makes these different methods equivalent. This is important for the application of thermodynamic perturbation theory because it becomes unnecessary to model any other equilibrium properties of the system apart from the expansion coefficients.

The application of thermodynamic perturbation theory to the calculation of excess free energy of small systems: 1. The study of the dimensional dependence of specific free energy of small droplets

Fundamentals of the application of the method of thermodynamic perturbation theory to finding the excess free energy of small objects were analyzed. The size dependence of the specific surface free energy of small droplets of a simple Lennard-Jones fluid, water, and metal melts was studied in the first and second approximations of the perturbation theory. It was established that, for all studied systems, the size dependence of the surface tension was satisfactorily described by Tolman’s formula. At small particle radii, Rusanov’s formula was well fulfilled.

The application of thermodynamic perturbation theory to the calculation of excess free energy of small systems: 2. Excess free energy and disjoining pressure in the wetting layer of apolar liquid

Isotherms of disjoining pressure in the wetting film of apolar liquid on unmodified and modified solid surfaces were studied based on the thermodynamic perturbation theory. Specific calculations were performed for two systems: (1) the wetting film of decane on aluminum surface and (2) the wetting film of decane on aluminum surface modified by pentanol. It was shown that the results of calculation agree with experimental data.

On the gas–gas equilibria of second kind of nonpolar fluid binary mixtures from a hard-sphere EXP-6 molecular model

The phase behavior of a molecular-based model of nonpolar binary mixtures is investigated by the application of thermodynamic perturbation theory. The pair potential interaction model is represented as a reference system of equal size hard-spheres perturbed by the exponential-6 potential. It is found that the qualitative behavior of gas–gas immiscibility of second kind is very much sensitive to the hardness of the potential (ratio of the hard sphere diameter to the size parameter of the perturbation). Calculated theoretical phase diagrams are compared with results from Monte Carlo simulations in the Gibbs ensemble performed for this model mixture.

High-pressure phase equilibria study of the hydrogen-water fluid mixture

Abstract The phase behavior of aqueous fluid binary mixtures is investigated by the application of thermodynamic perturbation theory to the polarizable hard-sphere dipole model. Isotherms and isobars of the three-dimensional pressure-temperature-composition phase diagram are calculated for the H 2 -H 2 O fluid mixture. The isotherms and isobars investigated in this work are compared with the experimental data.

Gas–gas equilibria of aqueous fluid binary mixtures

In a previous work [Chem. Phys. Lett. 100, 378 (1983)], by the application of thermodynamic perturbation theory to the polarizable hard-spheres dipole model, we found that on the P–T diagram the critical curve for the Ar–H2O mixture exhibits a negative slope. The same behavior on the critical curve has been found in a recent experimental reinvestigation of this mixture. Here it is investigated whether the theoretical approach can also predict the gas–gas equilibria of type I of the aqueous fluid binary mixtures. Good agreement with the experimental data is found for He–H2O and H2–H2O binary mixtures.

First-order anharmonic correction to the free energy of a Coulomb crystal in periodic boundary conditions.

The free energy of the classical one-component plasma is calculated analytically in the crystalline phase for both fcc and bcc lattices to 0( T'), where T is the temperature. By application of thermodynamic perturbation theory, we explicitly evaluate the effect of three- and four-phonon interactions on the partition function. Periodic boundary conditions are applied to make contact with previous numerical work, in which the O(T ) term was assumed to be negligible. We find that it is much larger than previously thought. This increases the thermodynamic stability of the crystal phase over previous estimates.

On the gas–liquid critical curves of different size hard-spheres binary mixtures interacting via the Lennard-Jones potential

The critical behavior of binary mixtures represented by a potential model of different size hard spheres plus a Lennard-Jones interaction is studied by the application of thermodynamic perturbation theory. The Lennard-Jones potential function is the perturbing potential to the hard-sphere reference system. It is found that convexity of the critical curves of type I is sensitive to small changes of the unlike interaction parameter values. Results for Ar–Kr and CH4–Kr mixtures are in good agreement with experimental data.

Azeotropic states in the CO2–C2H6 mixture from the hard sphere Lennard-Jones quadrupolar molecular model

Azeotropic states and phase equilibria for the CO2–C2H6 mixture are studied by the application of thermodynamic perturbation theory to the hard sphere Lennard-Jones quadrupolar molecular model. It is shown that theory can predict both phase equilibria and the azeotropic qualitative behavior observed in the real mixture.

Application of thermodynamic perturbation theory to a hexadecapolar fluid

The formulae for the application of thermodynamic perturbation theory to an octahedral molecule whose first permanent electric multipole is a hexacapole have been developed. They are applied to the prediction of the thermodynamic properties of sulphur hexafluoride from a spherical (n - 6) reference potential. A comparison between experimental data and the predictions for sulphur hexa-fluoride show that the theory is of sufficient accuracy for many engineering purposes although it is unable to reproduce the entire set of experimental information within its estimated uncertainty.

Application of thermodynamic perturbation theory to multicentre Lennard—Jones molecules. Results for CF 4, CCl 4, neo-C 5H 12 and SF 6 as tetrahedral and octahedral models

Model fluids consisting of regular tetrahedral four- and five-centre and regular octahedral six- and seven-centre Lennard—Jones molecules are considered. The vapour—liquid equilibrium is determined by using perturbation theory on the liquid and virial expansion up to second virial coefficient on the gas side. Comparison is made with experimental data of CF 4, CCl 4, neo-C 5H 12 and SF 6.

A blip-function calculation of the structure of liquid binary alloys

The authors present an extension of the blip-function expansion of Weeks, Chandler and Andersen (WCA) (1971) to liquid binary alloys. It turns out that the fact that realistic interionic pair potentials tend to be non-additive for most alloys poses a serious problem. They propose to resolve this problem by modifying the separation of the pair potentials in repulsive short-range and long-range terms in such a way that the repulsive parts are always additive, the non-additivity being entirely absorbed in the long-range terms. They show that this results in a first important improvement of the structure of liquid alloys over a simple hard-sphere picture. However, we emphasise that this should only be considered as a first step towards a systematic application of thermodynamic perturbation theory to liquid alloys.

Equilibrium properties of simple molecular fluids

The application of thermodynamic perturbation theory in which all tensor interactions are taken as perturbation of the pair central potential to the computation of the equilibrium properties of uniform molecular fluids is considered. Comparisons with experiment are made for nitrogen, oxygen, carbon monoxide, carbon dioxide, and methane. Theoretical expressions are given and calculations made for Helmholtz free energy, configurational energy, entropy, and pressure, taking into account the influence of permanent electric multipole moments, induced dipole moments, anisotropic dispersion, and overlap forces. The influence of three-body nonadditive interaction arising from dispersion and classical electric induction interactions between asymmetric molecules on the thermodynamic properties is also considered. Excellent agreement with experiment is obtained for all systems.

Application of thermodynamic perturbation theory to polar and polarizable fluids

The results of Monte Carlo computations for the Stockmayer potential are used to assess the numerical accuracy of the perturbation scheme developed by Stell, Rasaiah and Narang (see abstr. A39024 of 1972) for the calculation of thermodynamic properties of polar fluids. The Stockmayer model consists of a Lennard-Jones potential plus a dipole-dipole interaction and the perturbation theory is based on an expansion of the Helmholtz free energy of the Stockmayer system about that of the Lennard-Jones fluid in powers of mu 2, where mu is the dipole moment.

Theory of the Thermodynamic Properties of Liquid Metals

Thermodynamic properties of the liquid metals Li, Na, K, and Al are calculated using a pseudopotential model together with an application of thermodynamic perturbation theory based on the Gibbs-Bogoliubov inequality. The theory is used to predict many properties associated with the melting phenomenon; for example, the melting temperature and density as a function of temperature, and the latent heat of fusion. It is found that the theory reproduces the trend in latent heats between the alkali metals, in contrast to previous work, although quantitative agreement with experiment is no better than has been obtained before. The theory is also applied to the prediction of thermodynamic properties on and away from the melting curve; in particular, the specific heat and velocity of sound of sodium are calculated over a wide range of temperature. Agreement with experiment is found to be good.

Thermodynamic perturbation theory for simple polar fluids, I

The application of thermodynamic perturbation theory to the computation of the properties of simple polar fluids is considered. The Helmholtz free energy of a fluid of molecules interacting via a Stockmayer potential v S is computed through fourth order in μ, where μ is the dipole moment. Numerical results are obtained on the basis of both the ‘exact’ Monte-Carlo computations for a Lennard-Jones system and the Verlet-Weis perturbation-theoretic computations for that system. The results obtained on the latter basis are then compared with results for a fluid of molecules interacting via a central-force potential v ES that is conformal with the Lennard-Jones 6–12 potential and equivalent to the Stockmayer potential through order μ4. To facilitate the comparison the v ES results are computed according to the Verlet-Weis method. The v ES results and the fourth-order (in μ) v S results constitute two different approximations to the thermodynamics of the Stockmayer potential; the compressibility factors as well as the free energies of the two approximations are compared. It is concluded that the thermodynamic contribution of the dipole term of v S is significant over the whole liquid region when μ2=εσ3, where ε and σ are the usual Lennard-Jones parameters. For this μ, the two approximations we consider give results in close agreement.

Impurity Scattering in Superconductors

The effect of impurity scattering on the free energy of a superconductor is calculated by means of a straightforward application of thermodynamic perturbation theory. It is shown that in the vicinity of the transition, it is necessary to take into account second-order terms in the impurity concentration, even in the very dilute limit. These corrections are calculated with the aid of a variational technique. The resulting modification in the transition temperature and thermodynamic properties are in agreement with those obtained using the Green's-function technique, provided the impurity concentration is sufficiently small.