TY - JOUR

T1 - On the Сhoice of the Equation of State for a System of Hard Spheres in Calculations of Density Profiles and Surface Tension of Droplets and Bubbles

AU - Shchekin, A. K.

AU - Tatyanenko, D. V.

AU - Gosteva, L. A.

AU - Apitsin, K. D.

N1 - A.K. Shchekin, D.V. Tatyanenko, L.A. Gosteva, and K.D. Apitsin, On the Сhoice of the Equation of State for a System of Hard Spheres in Calculations of Density Profiles and Surface Tension of Droplets and Bubbles // Russ. J. Gen. Chem. 2022. V. 92. No. 4. P. 629–640.

PY - 2022/4

Y1 - 2022/4

N2 - Abstract: The dependences of the pressure, the chemical potential and the free-energy density on the number density of particles for a homogeneous system of hard spheres have been compared using the Carnahan–Starling equation of state, the Rusanov equations of state and the 18-coefficient virial expansion. The full and a narrower ranges of the number density of hard spheres have been considered. It is shown that in general the 6th-order Rusanov equations agree better with the virial expansion over the full range of the number density, but this is due to the high-density region. In the low- and medium-density regions, the Carnahan–Starling equation shows slightly better agreement with the 18-coefficient virial expansion. Using the dependences of the chemical potential and the free-energy density on the local number density of particles obtained from the Carnahan–Starling equation of state, the truncated 6th-order Rusanov equation, and the 18-coefficient virial expansion within an integral density functional theory, we have calculated the molecular density profiles in radially nonuniform spherical small droplets and bubbles of an argon-like substance and plotted the surface tension of small droplets and bubbles vs the curvature of their equimolecular surface. It is shown that the choice of the equation of state affects the values of quantities characterizing the two-phase equilibrium,e.g., the value of the chemical potential or the surface tension at a flat interface, and can shift the droplet or bubble size.

AB - Abstract: The dependences of the pressure, the chemical potential and the free-energy density on the number density of particles for a homogeneous system of hard spheres have been compared using the Carnahan–Starling equation of state, the Rusanov equations of state and the 18-coefficient virial expansion. The full and a narrower ranges of the number density of hard spheres have been considered. It is shown that in general the 6th-order Rusanov equations agree better with the virial expansion over the full range of the number density, but this is due to the high-density region. In the low- and medium-density regions, the Carnahan–Starling equation shows slightly better agreement with the 18-coefficient virial expansion. Using the dependences of the chemical potential and the free-energy density on the local number density of particles obtained from the Carnahan–Starling equation of state, the truncated 6th-order Rusanov equation, and the 18-coefficient virial expansion within an integral density functional theory, we have calculated the molecular density profiles in radially nonuniform spherical small droplets and bubbles of an argon-like substance and plotted the surface tension of small droplets and bubbles vs the curvature of their equimolecular surface. It is shown that the choice of the equation of state affects the values of quantities characterizing the two-phase equilibrium,e.g., the value of the chemical potential or the surface tension at a flat interface, and can shift the droplet or bubble size.

KW - chemical potential

KW - density functional theory

KW - equation of state for system of hard spheres

KW - free-energy density

KW - structure of fluid interfaces

KW - surface tension of droplets and bubbles

KW - virial coefficients

UR - http://www.scopus.com/inward/record.url?scp=85131003559&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/0c955fa2-d2cb-3e1e-a0f2-f75a70cede5c/

U2 - 10.1134/s1070363222040041

DO - 10.1134/s1070363222040041

M3 - Article

AN - SCOPUS:85131003559

VL - 92

SP - 629

EP - 640

JO - Russian Journal of General Chemistry

JF - Russian Journal of General Chemistry

SN - 1070-3632

IS - 4

ER -