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The canonical $\,NLT\,$ partition function of a quasi-one dimensional (q1D) one-file system of equal hard disks [J. Chem Phys. \textbf{153}, 144111 (2020)] provides an analytical description of the thermodynamics and ordering in this system (a pore) as a function of linear density $\,Nd/L\,$ where $\,d\,$ is the disk diameter. We derive the analytical formulae for the distance dependence of the translational pair distribution function and the distribution function of distances between next neighbor disks, and then demonstrate their use by calculating the translational order in the pore. In all cases, the order is found to be of a short range and to exponentially decay with the disks' separation. The correlation length presented for different pore widths and densities shows a non-monotonic dependence with a maximum at $\,Nd/L = 1\,$ and tends to the 1D value for a vanishing pore width. The results indicate a special role of this density when the pore length $\,L\,$ is equal exactly to $N$ disk diameters. A comparison between the theoretical results for an infinite system and the results of a molecular dynamics simulation for a finite system with periodic boundary conditions is presented and discussed., Comment: published in Journal of Molecular Liquids. arXiv admin note: substantial text overlap with arXiv:2206.05980

The analytical canonical NLT partition function of a quasi-one dimensional (q1D) system of hard disks [J. Chem Phys. v.153, 144111 (2020)] provides a direct analytical description of the thermodynamics and ordering in this system (a pore) as a function of the linear density N/L both for finite and infinite systems. It is alternative to the well-developed transfer matrix method based on the isobaric NPT ensemble. We derive the analytical formulae for the actual distance dependence of the translational pair distribution function (PDF) and the DF of distances between next neighbor disks, and then demonstrate their use by calculating the translational order in the pore. In all cases, the order is found to be of a short range and to exponentially decay with the disks' separation. The correlation length presented for the whole range of the q1D pore widths and different densities shows a non-monotonic dependence with a maximum at the density N/L=1 and tends to the 1D value for a vanishing pore width. The results indicate a special role of this density when the pore length L is equal exactly to N disk diameters. We introduce an orientational order parameter that accounts for the local quality of the crystalline zigzag formed by disks and is related to its structural element. This parameter is maximum in the densely packed state and vanishes for a very low density. Due to specific quasi-one dimensional geometry, this macroscopic order parameter is constant along the pore so that the macroscopic orientational order is of a liquid crystalline type., Comment: 29 pages, 4 figures

Molecular dynamics computer simulations of collective excitations in a system of hard disks confined to a narrow channel of the specific width, that resembles 2D triangular lattice at disk close packing, are performed. We found that transverse excitations, which for hard-disk system are absent in the limit of 1D and are of acoustic nature in the limit of 2D, in the case of q1D hard-disk system emerge in the form of transverse optical excitations and could be considered as a tool to detect the structural transition to a zigzag ordering. By analyzing density evolution of longitudinal static structure factor and pair distribution function we have shown that driving force of zigzag ordering is caging phenomenon that in the case of hard-disk system is governed by excluded volume interaction with first and second neighbors and is of entropic origin., Comment: 5 pages, 4 figures

The freezing mechanism suggested for a fluid composed of hard disks [Huerta et al., Phys. Rev. E, 2006, 74, 061106] is used here to probe the fluid-to-solid transition in a hard-dumbbell fluid composed of overlapping hard disks with a variable length between disk centers. Analyzing the trends in the shape of second maximum of the radial distribution function of the planar hard-dumbbell fluid it has been found that the type of transition could be sensitive to the length of hard-dumbbell molecules. From the ${NpT}$ Monte Carlo simulations data we show that if a hard-dumbbell length does not exceed 15% of the disk diameter, the fluid-to-solid transition scenario follows the case of a hard-disk fluid, i.e., the isotropic hard-dumbbell fluid experiences freezing. However, for a hard-dumbbell length larger than 15% of disk diameter, there is evidence that fluid-to-solid transition may change to continuous transition, i.e., such an isotropic hard-dumbbell fluid will avoid freezing., Comment: 9 pages, 7 figures

We argue that recently proposed [Melnyk et al., Fluid Phase Equilibr., 2009, Vol. 279, 1] a criterion to split the pair interaction energy into two parts, one of which is forced to be responsible the most accurate as possible for excluded volume energy in the system, results in expressions for the virial coefficients that improve the performance of the virial equation of state in general, and at subcritical temperatures, in particular. As an example, application to the Lennard-Jones-like hard-core attractive Yukawa fluid is discussed., Comment: 12 pages, 6 figures

We discuss the photograph procured from the archives of the V. Stefanyk Lviv National Scientific Library of Ukraine dated by 1904 which shows Marian Smoluchowski together with professors and graduate students of the Philosophy department of the Lviv University. The personalia includes both the professors and the graduates depicted on the photograph with the emphasis on the graduates as being much less known and studied. The photograph originates from the collection of the Shevchenko Scientific Society, therefore a brief historical background on the activities of physicists in this society around that period of time is provided as well., Comment: 8 pages, 1 photograph

The freezing mechanism, recently suggested for a monodisperse hard-disk fluid [Huerta et al., Phys. Rev. E, 2006, 74, 061106] is extended here to an equimolar binary hard-disk mixtures. We are showing that for diameter ratios, smaller than 1.15 the global orientational order parameter of the binary mixture behaves like in the case of a monodisperse fluid. Namely, by increasing the disk number density there is a tendency to form a crystalline-like phase. However, for diameter ratios larger than 1.15 the binary mixtures behave like a disordered fluid. We use some of the structural and thermodynamic properties to compare and discuss the behavior as a function of diameter ratio and packing fraction., Comment: 9 pages, 4 figures

Exponential approximation based on the first order mean spherical approximation (FMSA) is applied to the study of the structure and thermodynamics of hard-core repulsive Yukawa fluids. The proposed theory utilizes an exponential enhancement of the analytical solution of the FMSA due to Tang and Lu [J. Chem. Phys., 1993, 99, 9828] for the radial distribution function. From comparison with computer simulation data we have shown that at low density and low temperature conditions, where original FMSA theory fails, the FMSA-based exponential theory predicts a significant improvement., Comment: 14 pages, 6 figures

A perturbation approach based on the first-order mean spherical approximation (FMSA) is proposed. It consists in adopting a hard-sphere plus short-range attractive Yukawa fluid as the novel reference system, over which the perturbative solution of the Ornstein-Zernike equation is performed. A choice of the optimal range of the reference attraction is discussed. The results are compared against conventional FMSA/HS theory and Monte-Carlo simulation data for compressibility factor and vapor-liquid phase diagrams of the medium-ranged Yukawa fluid. Proposed theory keeps the same level of simplicity and transparency, as the conventional FMSA/HS approach does, but shows to be more accurate., Comment: 8 pages, 3 figures

Monte Carlo simulation studies are performed for the Lennard-Jones like two Yukawa (LJ2Y) potential to show how properties of this model fluid depend on the replacement of the soft repulsion by the hard-core repulsion. Different distances for the positioning of hard core have been explored. We have found, that for temperatures that are slightly lower and slightly higher of the critical point temperature for the Lennard-Jones fluid, placing the hard core at distances that are shorter than zero-potential energy is well justified by thermodynamic properties that are practically the same as in original LJ2Y model without hard core. However, going to extreme conditions with the high temperature one should be careful since presence of the hard core provokes changes in the properties of the system. The later is extremely important when the mean spherical approximation (MSA) theory is applied to treat the Lennard-Jones-like fluid., Comment: 11 pages, 13 figures

Virial coefficients $B_2$ through $B_4$ and the vapor-liquid equilibria for the EXP6 and 2-Yukawa (2Y) fluids have been determined using numerical integrations and Gibbs ensemble simulations, respectively. The chosen 2Y models have been recently determined as an appropriate reference fluid for the considered EXP6 models., Comment: 8 pages, 1 figure

An analytical expression for square-well fluid direct correlation function (DCF) obtained recently by Tang (Y.Tang, J. Chem. Phys. 127, 164504 (2007)) in the first-order mean spherical approximation is extended for wider well widths (2