An analytical expression for the direct correlation function of a hard-sphere liquid derived from the extended scaled particle theory

Morse potential specific bond volume: a simple formula with applications to dimers and soft-hard slab slider

Morse potential interaction is an important type of the vibrational potentials, especially, in the quantum mechanics which is used for the describing of general vibrational cases rather than the harmonic one. Morse potential has three fitting parameters, the depth of the Morse interaction, the distance of equilibrium bond and the range parameter which determines the range of the well. The Morse interaction specific bond volume is a three dimensional image of the bond length in its molar case, and this specific volume is the generalisation in three dimensions. In this study, the integral equation theory of the simple fluids has been applied for deriving a novel formula of the specific bond volume for Morse potential based on one of the approaches in the theory and based on the boundary conditions. We find that the specific bond volume of Morse potential depends on the absolute temperature via logarithmic function and square root function, besides, the specific bond volume of Morse potential decreases when the temperature decreases for different values of the molar volume and for different values of the depth of Morse well. In addition to that, the specific bond volume of Morse potential increases when the depth of the well decreases for different temperature values. Also, it is found from the formula which we derive that the specific bond volume of Morse potential increases via linear function with the molar volume of the system for different values of temperatures. We apply the formula of the specific bond volume of Morse potential for finding this specific volume for two molecules of the hydrogen halogens, which are the hydrogen chloride, and hydrogen fluoride. We find that the specific bond volume of the hydrogen chloride is greater than the one of the hydrogen fluoride. Also, we apply the formula for the two simple molecules gases which are the hydrogen molecules, and the nitrogen molecules. Besides, we apply the formula for the slab-slider system in two cases: hard and soft materials, and we concluded that the changes of the specific bond volume of the soft materials is faster than the hard materials. We believe that the formula which is found of the specific bond volume of Morse potential is general and can be applied for multiple materials.

Morse oscillator equation of state: An integral equation theory based with virial expansion and compressibility terms

A number of interaction energy types are employed in the vibrations studies, especially in the spectroscopic analysis, such as the harmonic oscillator and Morse oscillator. In this research, a derivation of an analytical formula of equation of state of Morse oscillator is considered by employing the approximations used in the simple fluids theory. The compressibility formula of the pressure and the virial expansion formula of the pressure using the solutions of the main equation of the simple fluids theory with one of the approximations of the theory are employed for the purpose of the derivation. The virial coefficients of the total Morse oscillator pressure (the first order one, and the second order one) are found for Morse oscillator with respect to the fractional volume of the components, where we conclude that the first order term is proportional to the absolute temperature directly and depends on the diameter of the particles, while we concluded that the second order coefficient term is more complicated than the first order one with temperature, and also, depends on the three Morse oscillator parameters and the diameter of the particles. Besides, we conclude that the total pressure of Morse oscillator, generally, depends on the minimum energy of the well of Morse oscillator, the width parameter of Morse oscillator, and the equilibrium bond distance of the oscillator, in addition to their dependence on the absolute temperature of the components, and the diameter of the particles. The formula of the Morse oscillator equation of state which is found in this research can be applied to multiple materials described using Morse oscillator such as lots of dimers in the vibrations spectroscopy.

Structural properties of additive binary hard-sphere mixtures. III. Direct correlation functions

An analysis of the direct correlation functions c_{ij}(r) of binary additive hard-sphere mixtures of diameters σ_{s} and σ_{b} (where the subscripts s and b refer to the "small" and "big" spheres, respectively), as obtained with the rational-function approximation method and the WM scheme introduced in previous work [S. Pieprzyk et al., Phys. Rev. E 101, 012117 (2020)2470-004510.1103/PhysRevE.101.012117], is performed. The results indicate that the functions c_{ss}(r<σ_{s}) and c_{bb}(r<σ_{b}) in both approaches are monotonic and can be well represented by a low-order polynomial, while the function c_{sb}(r<1/2(σ_{b}+σ_{s})) is not monotonic and exhibits a well-defined minimum near r=1/2(σ_{b}-σ_{s}), whose properties are studied in detail. Additionally, we show that the second derivative c_{sb}^{''}(r) presents a jump discontinuity at r=1/2(σ_{b}-σ_{s}) whose magnitude satisfies the same relationship with the contact values of the radial distribution function as in the Percus-Yevick theory.

Representation of the direct correlation function of the hard-sphere fluid

An accurate representation of the structural pair correlation functions of the hard sphere (HS) fluid up to the freezing density is proposed which combines the pole expression for the total correlation function h(r), the Ornstein-Zernike equation, and molecular dynamics (MD) computer simulation data. In the scheme, h(r) is expressed in terms of a set of pole parameters, which reveals how the tail of the Fourier transform of h(r) contains information on the discontinuities in the derivatives of the direct correlation function (DCF). This formulation leads to a DCF expressed as the sum of a numerically obtainable part and an analytic part which consists of elementary integral terms, some of which are found to give rise to the discontinuities. An exact formula for the magnitude of these discontinuities is derived, which indicates that there is a particular density (ρ≅0.133) below which the magnitude of the discontinuities decreases with increasing order of the derivative. With the accurate MD simulation data the set of parameters that specifies h(r) was determined. These can be used to obtain the different structural functions of the HS fluid, and following the calculation stages of the pole structure scheme the DCF is obtained. From this route to the DCF the second pole of the HS fluid can be determined and the non-negligible role of the "out of core" part of the DCF at high densities is revealed. The density-dependent separation range where the two pole approximation represents well the h(r) has been determined.