arXiv subjects

A. Trokhymchuk

Publications and source records attributed to A. Trokhymchuk.

13 recordsLinked to original sources

arXiv2026

An elastic model of confined hydrogel particles with competing entropic and energetic networks

This work presents an elastic model to study the interplay between entropic and energetic networks in confined hydrogel particles. We consider a quasi-two-dimensional system composed of spherical hydrogel beads confined in a circular container, where particle growth occurs through hydration. Based on experimental observations, an elastic potential is introduced to model interactions between particles and between particles and the confining wall. Computational simulations based on energy minimization identify the lowest-energy configurations adopted during growth. Analysis of the resulting energy landscapes reveals emergent self-organization, adaptability, and cooperativity arising from the competition between entropic and energetic networks.

cond-mat.soft↗

arXiv2026

Excluded volume and molecular field in the Lennard-Jones fluid: a modified first-order perturbation theory

The equation of state and, more generally, the thermodynamics of the Lennard-Jones fluid have long served as a benchmark problem in the statistical theory of fluids. Among available theoretical approaches, first-order perturbation theory occupies a special position: only at this level does the correction to the Helmholtz free energy admit an exact statistical-mechanical expression. In this work, we present a systematic, simulation-based assessment of a non-classical first-order perturbation theory in which the reference system incorporates the entire short-range part of the interaction, while the perturbation is confined to the remaining long-range tail. We show that this range-based decomposition transforms the perturbation contribution into a small, smoothly varying, near-mean-field quantity over a broad supercritical thermodynamic domain. When its density and temperature derivatives are consistently retained, the resulting equation of state reproduces high-accuracy reference data with excellent fidelity. The results demonstrate that the success of first-order perturbation theory is governed primarily by the physical content of the reference system and by the consistent treatment of its state dependence, rather than by the formal truncation order of the expansion.

cond-mat.dis-nn↗

arXiv2026

Canonical partition function and distance dependent correlation functions of a quasi-one-dimensional system of hard disks

The canonical NLT partition function of a quasi-one dimensional (q1D) one-file system of equal hard disks [J. Chem Phys. 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.

cond-mat.dis-nn↗

arXiv2025

Bimodality of local structural ordering in extremely confined hard disks

By combining computer simulations and a unit cell model approach, we study the apparent bimodality of local structural ordering in a system of confined hard disks. It is shown that a two-dimensional (2D) array of hard disks confined laterally within a quasi-1D hard wall channel of the width commensurate with the bulk 2D triangular lattice at disk close packing, possesses a bimodal probability distribution for the distance between disks' left and right nearest neighbors. The observed feature aligns with the concept of locally favored structures intensively exploited in the studies of anomalous thermodynamic and kinetic behavior of hydrogen-bonding fluids, except that the reported case is driven by entropic bonding only. The bimodality is observed in a range of densities associated with the vicinity of freezing transition in bulk 2D hard disks, indicating a crossover from the "gas-like" to "liquid-like" state in confined quasi-1D hard disks. Such a phenomenon was not reported for bulk 2D hard disks and is physically unexpected for confined q1D hard disks.

cond-mat.soft↗

arXiv2016

Frustration of freezing in a two dimensional hard-core fluid due to particle shape anisotropy

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.

cond-mat.soft↗

arXiv2015

Virial expansions and augmented van der Waals approach: Application to Lennard-Jones-like Yukawa fluid

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.

cond-mat.soft↗

arXiv2012

Towards frustration of freezing transition in a binary hard-disk mixture

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.

cond-mat.soft↗

arXiv2012

Marian Smoluchowski: A story behind one photograph

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.

physics.hist-ph↗

arXiv2012

Simplified exponential approximation for thermodynamics of a hard-core repulsive Yukawa fluid

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.

cond-mat.soft↗

arXiv2012

Improved first order mean spherical approximation for simple fluids

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.

cond-mat.soft↗

arXiv2012

Mean spherical approximation for the Lennard-Jones-like two Yukawa model: Comparison against Monte Carlo data

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.

cond-mat.soft↗

arXiv2011

Virial coefficients and vapor-liquid equilibria of the EXP6 and 2-Yukawa fluids

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.

cond-mat.soft↗

arXiv2009

Direct correlation function of square well fluid with wide well: First order mean spherical approximation

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<lambda<3). Theoretically obtained direct correlation functions and radial distribution functions for square-well fluid with lambda=2.1 and lambda=2.5 are compared with corresponding results of Monte-Carlo simulation.

cond-mat.stat-mech↗