Statistical Theory Of Liquids Research Articles

Nonclassical critical indices in the statistical theory of liquids and equations of state with regular and scaling components

Nonclassical critical indices γ = 9/8 and β = 3/8 obtained in works using the statistical theory of liquids are used to approximate data on the isothermal compressibility of 4He and SF6 on critical isochores and binodals, and on the shape of a binodal. The ratio of asymptotic compressibility coefficients Γ0+/Γ0− on critical isochores and binodals is determined from experiments using statistical theory and it is shown that Γ0+/Γ0− coincides with the magnitude of this ratio for linear scaling model with γ = 9/8 and β = 3/8 indices. Highly accurate P-ρ-T data on 4He and SF6 are approximated at these values of the indices using new combined equations of state that include regular and scaling components. The advantage of describing of P-ρ-T data in this manner, compared to describing them with the same equations of state using the critical indices of the three-dimensional Ising model, is demonstrated.

Analytic and nonanalytic components of pressure in liquids and gases

The investigation of the fundamental equations of the statistical theory of liquids shows that in any system, along with the pressure determined by the distribution of density of the particles inside the correlation sphere (the virial pressure), there is a thermostat pressure determined by the behavior of the matter at infinite distance from the correlation sphere. By definition, the first pressure is a function of the interaction potential, whereas the other does not depend on the potential, and hence is universal. Experimental data confirm the existence of a universal component of the pressure.

The thermoelastic properties and structural relaxation of magnetic liquids

The kinetic equations for one-and two-particle distribution functions were used to study the thermoelastic properties of magnetic liquids in the presence of an external not uniform magnetic field. Dynamic equations for the heat conductivity coefficient λ(ω) and thermal elastic modulus Z(ω) over a wide reduced frequency range were obtained. The asymptotic behavior of λ(ω) and Z(ω) was studied at low and high frequencies; the results were in agreement with those obtained for classic liquids by the method of molecular dynamics. The λ(ω) and Z(ω) values were calculated for a magnetic liquid based on kerosene and Fe3O4 magnetic particles. The numerical data on transfer coefficients and elastic properties of magnetic liquids were on the whole in agreement with the general conclusions of the statistical theory of liquids.

Methods of statistical physics in heavy nucleus collision theory.

A method to calculate heavy nucleus collision cross sections based on the analogy between the Glauber-Sitenko multiple scattering theory and statistical theory of liquids is suggested. Extensive use is made of the scaled particle method in the Rowlison-Widom model to calculate the free energy and the partition function.

Thermodynamic properties of metastable liquefied inert gases

Abstract The paper gives the results of measuring the speed of ultrasound in stable and metastable liquid krypton and xenon. The experiments have been carried out in the temperature range from 160 to 193 K (Kr) and from 220 to 270 K (Xe). The highest pressure was 4.0 MPa. The maximum pressure extended into the metastable region for liquid xenon amounted to 1.7 MPa. The insensitivity of superheated liquid to infinitely small adiabatic perturbations of the state variables has been considered. In the framework of the classical thermodynamic perturbation theory wer have shown that in the p, T-variables the spinodal is the envelope of the lines of constant value of the ultrasonic speed. A possibility of describing metastable states in the statistical theory of liquids is discussed. The sound speed at the line of the attainable superheat of liquefied inert gases has been estimated by the thermodynamic perturbation theory, the multistructural theory and the elementary hole theory.

Application of methods of the scattering theory in the statistical theory of liquids

This paper is devoted to the application of the projection methods of the nonrelativistic quantum theory of scattering (the method of Petrov-Bubnov-Galerkin (PBG) and the Bubnov-Galerkin (BG) method) in the statistical theory of liquids. By means of the projection PBG method we have found a new family of equations both for the correlation functions and for the radial distribution function (RDF). In the generalized equation for the RDF we have obtained new terms which are linear and quadratic in the density and the latter are absent in all the previous theories. By means of the projection BG principle the approximate eigenfunctions of the Liouville operator in a liquid were obtained as a linear combination of the Kihara functions. It was shown that the spectrum of the collective excitations is determined by the complex Fourier transformation of the force acting on an arbitrary particle in a liquid.

Метод интегральных уравнений в статистической теории жидкостей

Метод интегральных уравнений в статистической теории жидкостей

Statistical Theory of Liquids.

Statistical Theory of Liquids.

A Statistical Theory of Liquids. III

In the present paper the author incorporates the dissipative processes of heat conduction and viscosity into his theory. In order to do that, he generalizes first the procedures of statistical mechanics in such a way that they might describe processes involving molecular flow. This is achieved in close analogy to Boltzmann's treatment for gases: Boltzmann's integro-differential equation is replaced by Gibbs' principle of "conservation of density-in-phase," and the solution is sought in form of a power series which modifies (slightly) the canonical ensemble. Finally the anisotropic distribution function in real space is obtained by integrating the multidimensional distribution function with regard to all coordinates and moments except those of one particle.Section I gives the introduction and Section II the general outline of the theory. In Section III heat conduction is treated in form of the linear problem. The potential is smoothed out by making it dependent on the position of the center of mass only. With this simplification an asymptotic solution can be found which yields the time-dependent temperature gradient and heat current, and thereby the coefficient of heat conduction. In Section IV viscosity is treated in a similar way, and Section V treats the averaging processes involved in the evaluation of physical quantities. Finally, in Section VI, the coefficients of heat conduction and viscosity are calculated numerically for ten liquids from the potentials previously determined. The agreement is (with a few exceptions) about as good as might be anticipated from such a rigorous test. Thus, the same potentials, with their four available constants, have served now to calculate ten independent physical constants with a fair accuracy.

A Statistical Theory of Liquids. II

In continuation of Part I, vapor pressure, surface tension, and the neighborhood of the critical point are discussed. Section IX deals with the vapor pressure law. A comparison with experimental data shows that the experimental values of the heat of vaporization are, on the average, 55 percent higher than the calculated values for the ten liquids studied. This suggests association in the liquid phase. However, even for the noble gases and mono-atomic metal vapors there remains a discrepancy, though of less degree. In Section X the previously established expression for the surface tension is developed. The "number of molecules per sq. cm of surface" can be defined by the aid of integrals involving the potential of molecular interaction. If, then, a "molar surface ${S}^{*}$," is defined as a surface containing one mole of the liquid, the equation of state for the surface phase assumes the form $\ensuremath{\gamma}{S}^{*}=RT$. The value for mercury can be calculated quantitatively from the potential as established in Part I. In the case of the other nine liquids the potential has to be "cut off" at a distance of the order ${\ensuremath{\sigma}}_{1}$. E\"otv\"os' law follows as a limiting law for sufficiently high temperatures.---In Section XI the potential in the surface layer is supplemented for the case that the density in the vapor phase becomes comparable with that in the liquid phase. Then the proof of the coexistence of the two phases (Section IV) is extended to the neighborhood of the critical point. For that neighborhood the rule of Cailletet and Mathias is deduced. Finally the Kamerlingh Onnes constant is deduced from the special form of potential introduced in Section VII. It comes out 25 to 33 percent too low.

A Statistical Theory of Liquids. I

A theory is developed which deduces the elastic and thermal properties of a liquid from the expression of the mutual potential between two molecules, these being considered as centers of force. The two-phase system consisting of liquid and vapor is treated as a statistical unit and thus dynamical expressions for the vapor pressure and the surface tension are obtained. The characteristic parameter of the theory is the mean distance between nearest neighbors, $\ensuremath{\sigma}$. Its dependence on molecular density and temperature is determined by combining Boltzmann's theorem with a geometrical formula due to P. Hertz. The agreement with experimental data (after introduction of a specialized form of the potential) is satisfactory and will be further investigated in subsequent papers. The Introduction (Section I) exposes the general scope of the theory. In Section II the expression for the potential energy is established and suitably simplified by integration. In Section III the partition function for the two-phase system is formed without further neglections. In Section IV the co-existence of the two phases is shown to be possible only if surface tension is taken into account. Section V contains the determination of $\ensuremath{\sigma}$ as sketched above. In Section VI the general formulae for the liquid state are established. Section VII introduces a special form for the intermolecular forces and in Section VIII comparison with experimental data, covering heat of vaporization, compressibility, expansion, and specific heat, is carried through for ten liquids widely different in character.