V. M. Sysoev

Equation of state for liquid nitrogen in the high-density limit

Equations of state are proposed for describing the isothermal compression of liquid argon. These equations are derived by the method of integral equations in the statistical theory of the condensed state of matter. The thermophysical data are analyzed for calculating the isotherms and parameters of molecular interaction potential.

Divergence of activity expansions: Is it actually a problem?

For realistic interaction models, which include both molecular attraction and repulsion (e.g., Lennard-Jones, modified Lennard-Jones, Morse, and square-well potentials), the asymptotic behavior of the virial expansions for pressure and density in powers of activity has been studied taking power terms of high orders into account on the basis of the known finite-order irreducible integrals as well as the recent approximations of infinite irreducible series. Even in the divergence region (at subcritical temperatures), this behavior stays thermodynamically adequate (in contrast to the behavior of the virial equation of state with the same set of irreducible integrals) and corresponds to the beginning of the first-order phase transition: the divergence yields the jump (discontinuity) in density at constant pressure and chemical potential. In general, it provides a statistical explanation of the condensation phenomenon, but for liquid or solid states, the physically proper description (which can turn the infinite discontinuity into a finite jump of density) still needs further study of high-order cluster integrals and, especially, their real dependence on the system volume (density).

Evaluation of the curvature-correction term from the equation of state of nuclear matter

Based on the nuclear equation of state, the curvature correction term to the surface tension coeffi- cient is calculated. Tolmanscorrection is shown to be sensitive to the Skyrme force parametriza- tion. The temperature dependence of the Tolman length, important in heavy ion collisions experi- ments, is derived. In suggested approach the curvature term is related to the bulk properties of the nuclear matter through the equation of state. The obtained results are compared with the existing theoretical calculations based on the Gibbs-Tolman formalism and with the theoretical predictions concerning its dependence on the interparticle distance.

Equation of state for all regimes of a fluid: From gas to liquid

The study of Mayers cluster expansion (CE) for the partition function demonstrates a possible way to resolve the problem of the CE non-physical behavior at condensed states of fluids. In particular, a general equation of state is derived for finite closed systems of interacting particles, where the pressure is expressed directly in terms of the density (or system volume) and temperature-volume dependent reducible cluster integrals. Although its accuracy is now greatly affected by the limited character of the existing data on the reducible cluster integrals and, especially, the absence of any information on their density dependence, a number of simple approximations indicate the qualitative adequacy of this equation in various regimes of a fluid: from gaseous to liquid states (including the transition region).

Calculating the chemical potential of components of a binary solution in a plane-parallel pore

The chemical potential of components of a binary solution is calculated using the expansion of the external field potential in a Taylor series. An expansion of the chemical potential in terms of concentration-concentration direct correlation functions of all orders is obtained. For a plane-parallel pore with an exponential near-wall potential, a solution to the obtained differential equation is constructed in the smooth-inhomogeneity approximation.

Influence of the drops size on the coefficient of surface tension in a wide range of pressures and temperatures along the coexistence curve

Abstract The new method for estimation of Tolman δ-corrections for liquid droplets is proposed on the basis of equation of state. It is revealed that Tait equation of state for such evaluations can be used. The set of estimates was established for δ-correction in the case of H 2 O and Ar in a wide temperature range. Both cases give δ δ ∼ | τ | − a) gives a = 0.5 (here τ= T c −T T c ). Studying of Tolman δ-corrections behavior within the framework of the mean-field theory is resulted in δ=− 1σ 0 16p c by using Van der Waals equations of state. Here σ 0 is an amplitude factor of the surface tension for the flat surface σ ∞ = σ 0 τ 3 2 . The analysis of experimental data for a set of fluids demonstrates the satisfactory fit of the obtained result with experiment. Using the scaling theory for description of an equation of state of the coexistence curve and surface tension give such δ ∼ τ β − ν , where β and ν are critical exponents. Thus, δ-correction has singular character as critical point approaches.

Size dependence of the surface tension of a free surface of an isotropic fluid

We report on the size dependence of the surface tension of a free surface of an isotropic fluid. The size dependence of the surface tension is evaluated based on the Gibbs-Tolman-Koenig-Buff equation for positive and negative values of curvatures and the Tolman lengths. For all combinations of positive and negative signs of curvature and the Tolman length, we succeed to have a continuous function, avoiding the existing discontinuity at zero curvature (flat interfaces). As an example, a water droplet in the thermodynamical equilibrium with the vapor is analyzed in detail. The size dependence of the surface tension and the Tolman length are evaluated with the use of experimental data of the International Association for the Properties of Water and Steam. The evaluated Tolman length of our approach is in good agreement with molecular dynamics and experimental data.

Curvature correction term as a constraint for the Skyrme interaction

The curvature correction term to the surface tension is used as a criterion for the efficiency of the Skyrme interaction in describing surface properties. Based on the nuclear equation of state, the curvature correction term to the surface tension coefficient is calculated for 97 standard Skyrme interaction parameter sets in the vicinity of nuclear saturation density at zero temperature. The main idea is to find those parametrizations that give the Tolman

The influence of fluctuation inhomogeneity in a volume phase on one-layer adsorption

\ensuremath{\delta}

Virial and high-density expansions for the Lee-Yang lattice gas.

correction close to the available theoretical predictions from the statistical theory. Only 59 out of 97 models give satisfactory results. Comparison of the obtained results with the results of the implementation of different macroscopic and microscopic constraints to Skyrme parametrizations available in the literature allows us to select four models that satisfy all the constraints.