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There is indeed a finite-size issue in computer simulations of the correlation decay in a quasi-one-dimensional system of hard disks. The correlation function obtained from the exact canonical $NVT$ partition function shows a decay which is much slower and more complex than the exponential one, presented in the Comment.

We consider application to the hard sphere (HS) model of the mapped-averaging framework for generating alternative ensemble averages for thermodynamic properties. Specifically, we develop a...

We present the results of molecular dynamic studies of collective dynamics in a system of hard disks confined to a narrow quasi-one-dimensional (quasi-1D) channel. The computer simulations have been performed for the specific channel width of 3/2 of disk diameter in which the disk arrangement at close packing resembles zigzag ordering characteristic of a vertically oriented two-dimensional (2D) triangular lattice. In such a quasi-1D system, which is intermediate between 1D and 2D arrays of hard disks, the transverse excitations obey very specific dispersion law typical of the usual optical transverse modes. This is in a sharp contrast both to the 1D case, where transverse excitations are not possible, and to the 2D case, where the regular shear waves with a propagation gap were observed. Other peculiarities of the dispersion of collective excitations as well as some results of disk structuring and thermodynamics of the quasi-1D hard disk system are presented and discussed for a range of hard disk densities typical for fluid and distorted crystal states.

The authors show that a densely packed solid zigzag develops windowlike defects through which disks move across the pore and gain entropy as it approaches its fluid phase.

Наведено короткий історичний огляд про внесок двох всесвітньо відомих львівських наукових дослідників — Маріана Смолуховського та Станіслава Улама — у розвиток сучасних галузей фізичної науки, таких як молекулярне моделювання, комп’ютерний експеримент та молекулярна інженерія, висвітлено їх зв’язок із останніми дослідженнями, проведеними у львівських університетах та науково-дослідних установах. A brief historical overview towards the contribution of two famous Lviv scholars – Marian Smoluchowski and Stanis law Ulam – to the development of modern physical science fields such as molecular modeling and computer simulations is presented and discussed in connection with recent studies carried out in Lviv universities and research institutions.

Microscopic equations for the coefficients of the effective Landau-Ginzburg-Wilson (LGW) fluid Hamiltonian are presented in the case of the reference system that consists of hard spheres with a short-range Yukawa attraction. The mean-field level analysis of the critical parameters of the Sutherland fluid, based on the effective LGW fluid Hamiltonian with two different reference systems, namely, widely used pure hard spheres and hard spheres with the short-range Yukawa attraction, is performed. From the comparison with computer simulation data, the superiority of the reference system that incorporates the short-range attraction is shown.

Analytical solution of the first-order Ornstein–Zernike equation known as the first-order mean spherical approximation (FMSA) theory due to Tang and Lu [J. Chem. Phys. 99, 9828 (1993)] is used to write down a closed equation for the static structure factor of the hard-sphere fluid with a short-range Yukawa attraction. Calculations are performed for a Yukawa decay exponent that corresponds to a range of attraction that does not exceed the first coordination shell of Lennard-Jones-like simple fluids. By comparison with Monte Carlo simulation data it is shown that the analytical FMSA equation for the static structure factor is of the same or even of superior accuracy as that within the seminumerical mean spherical approximation theory.

The papers in this special issue of ``Condensed Matter Physics'' have been submitted with the dedication to Professor Dr. Yuriy Kalyuzhnyi on the occasion of his 70th birthday.

Collective excitations in hard-sphere fluids were studied in a wide range of wave numbers and packing fractions η by means of molecular dynamics simulations. We report the observation of non-hydrodynamic transverse excitations for packing fractions η≥0.395 in the shape of transverse current spectral functions. Dispersion of longitudinal excitations in the whole range of packing fractions shows a negative deviation from the linear hydrodynamic law with increasing wave numbers even for dense hard-sphere fluids where the transverse excitations were observed. These results do not support a recent proposal within the "Frenkel line" approach that the positive sound dispersion in liquids is defined by transverse excitations. We report calculations of the cutoff "Frenkel frequencies" for transverse excitations in hard-sphere fluids and discuss their consistency with the estimated dispersions of shear waves.

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., 12 pages, 6 figures

Analytic expressions for the Laplace transform of the interaction energy and force between two exceedingly large hard spheres at infinite dilution in a polydisperse hard-sphere suspending fluid are presented. The equations are based on the Percus–Yevick approximation for the many-component suspending fluid, supplemented by the hypernetted chain approximation for the correlation function of the suspended spheres. By applying the Derjaguin approximation, the energy and force results for two spheres are related to the energy per unit area and the disjoining pressure between two flat walls suspended in a polydisperse fluid. Numerical results for the representative Schultz distributions of the diameters of the species comprising the suspending fluid are presented and discussed.

The analytic solution of the Poisson equation for a system of two identical charges near a uniformly charged plane is used to understand the phenomenon of an attraction between a pair of charged particles next to an oppositely charged surface that has been observed recently. We found that there is no direct attractive interaction between like charges. We have shown that what is observed experimentally could be interpreted as the ‘apparent attraction’ resulting from the extra force experienced by each charge being in the non-zero plane parallel electric field due to the charged surface. This surface-induced electric field and force are directed to the center of the surface and can oppose the direct Coulomb repulsion between like charges. Both the field and force can be obtained naturally within the framework of classical electrodynamics if the effects of the finite size of a charged surface are taken into account.

A non-traditional approach to the computer simulation study of a class of quasi-two-dimensional Coulomb systems (charged particles confined to a layer near a charged planar surface) is presented. The essence of the approach lies in exploiting the fact that the charged confinement is of finite dimensions. The main consequence of such a finiteness is a non-zero potential gradient along the finite charged area that includes a non-zero tangential component of the electric field. A system of like-charged spherical particles confined by the planar surface that includes an oppositely charged squared area is considered as an example. We find that the like-charged particles, independent of their concentration, all become confined on the oppositely charged area, if the surface charge balances the total charge carried by the particles, and if the electrostatic coupling is sufficiently large. The local density of the particles above the charged area is not homogeneous; near the boundaries of the charged square a clea...

The structure of a starlike molecule (SLM) fluid with four arms of different length is studied by applying the associative Percus–Yevick integral equation (IE) theory and canonical Monte Carlo (MC) simulations. In the IE study the SLM fluid is modelled by a fluid of hard spheres with four associative sites on each sphere while the MC has been performed for a freely-joined tangent hard sphere fluid. The total radial distribution functions have been calculated in both approaches for different volume fraction regimes and different arm lengths. It is shown that the associative IE theory predicts the structure of SLM fluid best for relatively long arms and at high densities. Additionally, the dependence of the SLM centre–centre correlations on the functionality and fluid particle density has been analysed using the MC results.

Two models have been used in these Monte Carlo simulations: the original model with an angular-dependent associative interaction and a model with an angular-averaged potential, which is better suited for simulation and computationaly more efficient. We show that in the homogeneous case under the same conditions, both models yield a nearly identical interparticle structure, but with a slightly different degree of dimerization. This causes differences between these models in the local density distribution of monomers and dimers when an inhomogeneity is present, though the resulting local total density distribution is found to be the same. The theoretical predictions based on Wertheim's theory of association are always closer to the simulation data for the model with the angular-averaged potential.

The Born–Green–Yvon (BGY) equation with Fischer–Methfessel (FM) approximation is used to calculate the density profiles of the planar liquid–vapor interface of Lennard-Jones fluid in a hard-sphere disordered rigid matrix. The density profiles are compared with the results of canonical ensemble Monte Carlo simulations. Both theory and simulation show that the thickness of the interface increases in the presence of disordered media. The phase diagrams for two different matrix densities have been evaluated and compared with the predictions of mean field and optimized cluster theories. Comparison with Monte Carlo data for low matrix densities indicates that the BGY-FM theory works reasonably well. Possible extensions of the theory are also discussed.

A dimerizing model of Lennard-Jones particles near a hard wall is studied using the inhomogeneous or second order Wertheim Ornstein-Zernike equation and the inhomogeneous associative Percus-Yevick closure. We investigate the influence of the degree of dimerization on the shape of the density profiles and on inhomogeneous pair correlation functions.

Canonical ensemble Monte Carlo simulations and the non-uniform Percus–Yevick (NPY) equation for the local density are used to study the influence of surface mediated thirdorder interactions on the adsorption of associating hard spheres on a hard wall. A comparison of the NPY density profiles with the computer simulations data indicates that this approximation predicts the fluid structure reasonably well.

The associative replica Ornstein-Zernike equations, supplemented by the associative hypernetted chain approximation are used to describe the Smith-Nezbeda model for an associating fluid adsorbed in a disordered hard sphere matrix. These equations have been developed by combining the replica Ornstein-Zernike equations with the Wertheim theory of association in fluids. The pair distribution functions and fraction of unbonded species are calculated. Also investigated is the influence of the association on the equation of state and the chemical potential of the absorbed fluid.

The inhomogeneous OZ equation, together with the LMBW equation for the density profile, with the bulk associating fluid taken as a reference system, is solved. Wertheim's description of the reference fluid, which provides an adequate description of chemical association far from the surface, is used. In the vicinity of the surface, the reference inhomogeneous PY closure is formulated and applied. The theory of Wertheim for bulk association is combined, for what we believe is the first time, with a pair level theory for inhomogeneous fluids. A few preliminary results for this reference approach are reported.

We performed Monte-Carlo computer simulations of a fluid of chemically reacting, or overlapping, hard spheres near a hard wall. The model of the interparticle potential is that introduced by Cummings and Stell. This investigation is directed to the determination of the structure of the fluid at the wall, and the orientation of the dimers in particular. In addition, we applied the singlet Percus–Yevick, hypernetted chain and Born–Green–Yvon equations to calculate the total density profiles of the particles. A comparison with the Monte-Carlo data indicates that the singlet Percus–Yevick theory is superior and leads to results that are in reasonable agreement with simulations for all the parameters investigated. We also calculated the average numbers of dimers formed in the bulk part of the system and the results are compared with different theoretical predictions.

An investigation is begun into the structure of a chemically reacting or associating hard core Yukawa fluid near a hard wall by using Monte Carlo simulations. The model of the interparticle potential is an extension of that introduced by Cummings and Stell for an overlappping hard sphere fluid. This investigation studies the changes in the structure of this chemically reacting fluid at the wall, introduced by the presence of long-range attractive forces acting between atoms. The long-range attractive forces cause a lowering of the total number of particles in the vicinity of the wall and weaken the orientational ordering of the dimers formed by the effect of the chemical interactions. Also the singlet integral equation approach is applied to calculate the density profiles. A comparison of the theoretical predictions with the Monte Carlo data indicates that, in contrast to systems without long-range attractive forces, the singlet theory is insufficient, especially when the chemical interactions increase.

A nonlocal density functional theory, developed by Zhou and Stell [J. Chem. Phys. 92 (1990) 5533] for simple nonuniform fluids is used to describe the local density of overlapping particles near a hard wall. A comparison of the results of this theory and those obtained from the singlet level approach with computer simulations is presented. This comparison shows that the density functional theory gives quite satisfactory results.

The adsorption of associating hard spheres on a hard wall by using the nonuniform Percus–Yevick equation for the local density and the pair correlation functions is studied. A comparison of the density profiles with computer simulation data indicates that this approximation predicts the fluid structure significantly better than the singlet Percus–Yevick and hypernetted chain approximations.

The direct correlation function of the complex discrete potential model fluids is obtained as a linear combination of the first-order mean spherical approximation (FMSA) solution for the simple square well model that has been reported recently [Hlushak et al., J. Chem. Phys. 130, 234511 (2009)]. The theory is employed to evaluate the structure and thermodynamics of complex fluids based on the square well-barrier and square well-barrier-well discrete potential models. Obtained results are compared with theoretical predictions of the hybrid mean spherical approximation, already reported in the literature [Guillen-Escamilla et al., J. Phys.: Condens. Matter 19, 086224 (2007)], and with computer simulation data of this study. The compressibility route to thermodynamics is then used to check whether the FMSA theory is able to predict multiple fluid–fluid transitions for the square barrier-well model fluids.

The Laplace transform is obtained for the pair distribution function between a pair of ions, an ion and a macroion, and a pair of macroions in an ion-dipole fluid. This fluid is a simplified model of an electrolyte with a discrete model of solvent (hard spheres with embedded point dipoles). From these results, an expression for the solvation force between macroions is obtained. This result consists of the classical DLVO result plus a series of corrections.

The linear response theory is applied to the interaction site model for the evaluation of static dielectric properties of a flexible water model. The atom–atom radial distribution functions derived from hybridization of the computer simulations and optimized cluster theory [A. D. Trokhymchuk, M. F. Holovko, E. Spohr, and K. Heinzinger, Mol. Phys. 77, 903 (1992)] are employed for the calculation of the polarization structure factor and the moments of the polarization correlation function. The color charge version of the dipolar hard sphere model [F. O. Raineri, H. Resat, and H. L. Friedman, J. Chem. Phys. 96, 3068 (1992)] proved to be helpful for the understanding of the effects of intramolecular charge distribution and flexibility on the dielectric properties of the interaction site model. The dielectric constant for the flexible BJH water model is calculated and the region of negative values of the static dielectric function is obtained. The possibility of a subdivision of this region into two parts at k...

On August 7, 2004, the Henderson Symposium on Basic and Applied Statistical Mechanics of Condensed Matter was held at Brigham Young University in Provo, Utah. This Festschrift grew out of that occasion and includes some of the articles presented on that occasion, at which we also celebrated his 70th birthday.

A model for the formation of diatomic molecules from the association of spherically symmetric atoms is reported. The model incorporates a flexible intracore chemical bond mimicked by Gaussian potential and Lennard-Jones interatomic interactions. To calculate the correlation functions necessary to describe the chemical equilibrium and phase diagrams, the second-order Percus-Yevick approximation is applied. Some structural properties of the model are discussed in terms of binary and triplet distribution functions.

The possibility of the existence of a pre-preak in the structure factor of water at 0.6 ů1 is discussed on the basis of the combination of computer simulation and integral equation theory techniques. It indicates spatial correlations in water at distances of the order of 10 Å.