Monte Carlo simulation and integral equation study of Hertzian spheres in the low-temperature regime

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.

Data-driven approximations to the bridge function yield improved closures for the Ornstein-Zernike equation

A key challenge for soft materials design and coarse-graining simulations is determining interaction potentials between components that give rise to desired condensed-phase structures. In theory, the Ornstein-Zernike equation provides an elegant framework for solving this inverse problem. Pioneering work in liquid state theory derived analytical closures for the framework. However, these analytical closures are approximations, valid only for specific classes of interaction potentials. In this work, we combine the physics of liquid state theory with machine learning to infer a closure directly from simulation data. The resulting closure is more accurate than commonly used closures across a broad range of interaction potentials.

Structure of the simple harmonic-repulsive system in liquid and glassy states studied by the triple correlation function

An efficient description of the structures of liquids and, in particular, the structural changes that happen with liquids on supercooling remains to be a challenge. The systems composed of soft particles are especially interesting in this context because they often demonstrate non-trivial local orders that do not allow to introduce the concept of the nearest-neighbor shell. For this reason, the use of some methods, developed for the structure analysis of atomic liquids, is questionable for the soft-particle systems. Here we report about our investigations of the structure of the simple harmonic-repulsive liquid in 3D using the triple correlation function (TCF), i.e., the method that does not rely on the nearest neighbor concept. The liquid is considered at reduced pressure (P = 1.8) at which it exhibits remarkable stability against crystallization on cooling. It is demonstrated that the TCF allows addressing the development of the orientational correlations in the structures that do not allow drawing definite conclusions from the studies of the bond-orientational order parameters. Our results demonstrate that the orientational correlations, if measured by the heights of the peaks in the TCF, significantly increase on cooling. This rise in the orientational ordering is not captured properly by the Kirkwood's superposition approximation. Detailed considerations of the peaks' shapes in the TCF suggest the existence of a link between the orientational ordering and the slowdown of the system's dynamics. Our findings support the view that the development of the orientational correlations in liquids may play a significant role in the liquids' dynamics and that the considerations of the pair distribution function may not be sufficient to understand intuitively all the structural changes that happen with liquids on supercooling. In general, our results demonstrate that the considerations of the TCF are useful in the discussions of the liquid's structures beyond the pair density function and interpreting the results obtained with the bond-orientational order parameters.

Evidence of Structural Inhomogeneities in Hard-Soft Dimeric Particles without Attractive Interactions

We perform Monte Carlo simulations of a simple hard-soft dimeric model constituted by two tangent spheres experiencing different interactions. Specifically, two hard spheres belonging to different dimers interact via a bare hard-core repulsion, whereas two soft spheres experience a softly repulsive Hertzian interaction. The cross correlations are soft as well. By exploring a wide range of temperatures and densities we investigate the capability of this model to document the existence of structural inhomogeneities indicating the possible onset of aggregates, even if no attraction is set. The fluid phase behavior is studied by analyzing structural and thermodynamical properties of the observed structures, in particular by computing radial distribution functions, structure factors and cluster size distributions. The numerical results are supported by integral equation theories of molecular liquids which allow for a finer and faster spanning of the temperature-density diagram. Our results may serve as a framework for a more systematic investigation of self-assembled structures of functionalized hard-soft dimers able to aggregate in a variety of structures widely oberved in colloidal dispersion.