Anatol Malijevský | Institute of Chemical Technology Prague (original) (raw)

Papers by Anatol Malijevský

Research paper thumbnail of Introduction to the Thermodynamics of Hard Spheres and Related Systems

Research paper thumbnail of On extrapolation of virial coefficients of hard spheres

Condensed Matter Physics, 2012

Several methods of extrapolating the virial coefficients, including those proposed in this work, ... more Several methods of extrapolating the virial coefficients, including those proposed in this work, are discussed. The methods are demonstrated on predicting higher virial coefficients of one-component hard spheres. Estimated values of the eleventh to fifteenth virial coefficients are suggested. It has been speculated that the virial coefficients, B n , beyond B 14 may decrease with increasing n, and may reach negative values at large n. The extrapolation techniques may be utilized in other fields of science where the art of extrapolation plays a role.

Research paper thumbnail of 0Statistical Thermodynamics

This chapter deals with the statistical thermodynamics (statistical mechanics) a modern alternati... more This chapter deals with the statistical thermodynamics (statistical mechanics) a modern alternative of the classical (phenomenological) thermodynamics. Its aim is to determine thermodynamic properties of matter from forces acting among molecules. Roots of the discipline are in kinetic theory of gases and are connected with the names Maxwelland

Research paper thumbnail of Correlation of heat capacities of liquids as a function of temperature

Fluid Phase Equilibria, 1992

Five different equations for the correlation of heat capacities of liquids have been examined and... more Five different equations for the correlation of heat capacities of liquids have been examined and tested. The following criteria have been considered in selecting a suitable correlation equation: (1) the ability to fit experimental data precisely; (2) meaningful behavior of the relationship when used for extrapolation beyond the temperature liits of the experimental data; (3) the possibility to integrate the equation analytically in order to calculate enthalpy and entropy differences. A polynomial seems to be the most dependable form for an equation in describing heat capacity as a function of temperature. The drawback of the polynomial equation of degree higher than four is that it has poor extrapolation characteristics and the possibility of oscillations, To correlate experimental data that cover a wide temperature range, a large number of terms in a polynomial equation would be necessary. In such cases, cubic splines with up to tive knots have been used to fit the data within the assumed error of measurement. A new correlation equation has been proposed which provides a reasonable extrapolation, especially in the region towards the critical point.

Research paper thumbnail of The fifth virial coefficients of fused hard sphere fluids

Czechoslovak Journal of Physics, 1988

The virial coefficients up to B 5 of 34 fused hard sphere models have been computed using about (... more The virial coefficients up to B 5 of 34 fused hard sphere models have been computed using about (4-10) • 10 s trial configurations of a modified Monte Carlo integration method. The principle of the conformal behaviour of hard particle systems is tested against these data. It is found that while for the fourth coefficient the principle is satisfied in all the cases, the fifth coefficients exhibit more complicated behaviour and do not conform, in general, to this principle.

Research paper thumbnail of Integral equation study of additive two-component mixtures of hard spheres

Molecular Physics, 1996

The Ornstein-Zernike equation for additive hard sphere mixtures is solved numerically by using th... more The Ornstein-Zernike equation for additive hard sphere mixtures is solved numerically by using the Martynov-Sarkisov (MS) closure and a recent modification of the Verlet (MV) closure. A comparison of the predictions for the equation of state and, to a lesser extent, the contact values of the radial distribution function, shows both theories to give similar, reasonably accurate, results in most

Research paper thumbnail of An accurate integral equation for molecular fluids

Molecular Physics, 1991

Percus-Yevick (PY), hypernetted chain (HNC) and modified Verlet (VM) integral equation theories a... more Percus-Yevick (PY), hypernetted chain (HNC) and modified Verlet (VM) integral equation theories are used to study the structure and thermodynamic properties of hard prolate ellipsoids of revolution in the isotropic fluid region. Results for the spherical harmonic coefficients of the pair distribution function and for the compressibility factors are compared with new Monte Carlo results reported in this work for length-to-breadth ratios a/b= 2, 3, and 5. For a/b= 2 and 3, the VM harmonic coefficients are in good agreement with the ...

Research paper thumbnail of Computer simulation of the chemical potentials of fused hard sphere diatomic fluids

Chemical Physics Letters, 1995

An efficient method for calculating the chemical potential of hard sphere fluids up to high densi... more An efficient method for calculating the chemical potential of hard sphere fluids up to high densities by computer simulation is extended to the case of fluids of hard homonuclear and heteronuclear diatomics. The chemical potentials have been simulated at packing fractions up to 7/= 0.45 and used to test the results of several equations of state. To our knowledge, this Letter gives the first direct calculation of the chemical potentials of these molecular fluids using computer simulation techniques.

Research paper thumbnail of The Ornstein-Zernike equation for hard spheres near a hard wall

Molecular Physics, 1991

Hard-sphere-hard-wall density profiles are studied using the Henderson-Abraham-Barker (HAB) formu... more Hard-sphere-hard-wall density profiles are studied using the Henderson-Abraham-Barker (HAB) formulation of the Ornstein-Zernike (OZ) equation. A new method of numerically solving this equation is proposed that consists of a combination of Newton-Raphson and Picard iteration approaches. The new method is rapidly convergent and insensitive to the initial estimate. A new reference hypernetted chain (RHNC) theory for the OZ equation is proposed that uses the bridge function of a bulk fluid hard sphere reference system, and ...

Research paper thumbnail of Direct method for determining parameters in intermolecular pair potentials from PVT data and from thermodynamic properties of dilute gases. I. Calculation of parameters from PVT data

Collection of Czechoslovak Chemical Communications, 1973

Research paper thumbnail of Low-temperature and high-temperature approximations for penetrable-sphere fluids: Comparison with Monte Carlo simulations and integral equation theories

Physical Review E, 2007

The two-body interaction in dilute solutions of polymer chains in good solvents can be modeled by... more The two-body interaction in dilute solutions of polymer chains in good solvents can be modeled by means of effective bounded potentials, the simplest of which being that of penetrable spheres (PSs). In this paper we construct two simple analytical theories for the structural properties of PS fluids: a low-temperature (LT) approximation, that can be seen as an extension to PSs of the well-known solution of the Percus-Yevick (PY) equation for hard spheres, and a high-temperature (HT) approximation based on the exact asymptotic behavior in the limit of infinite temperature. Monte Carlo simulations for a wide range of temperatures and densities are performed to assess the validity of both theories. It is found that, despite their simplicity, the HT and LT approximations exhibit a fair agreement with the simulation data within their respective domains of applicability, so that they complement each other. A comparison with numerical solutions of the PY and the hypernetted-chain approximations is also carried out, the latter showing a very good performance, except inside the core at low temperatures.

Research paper thumbnail of A comparison of the correlation functions of the Lennard–Jones fluid for the first-order Duh–Haymet–Henderson closure with molecular simulations

Research paper thumbnail of A rapidly convergent method of solving the OZ equation

Http Dx Doi Org 10 1080 00268978500102651, Aug 22, 2006

ABSTRACT A new method is proposed for solving numerically the Ornstein-Zernike equation for syste... more ABSTRACT A new method is proposed for solving numerically the Ornstein-Zernike equation for systems with a spherically symmetrical pair-potential. The method is based on expansion of the function Gamma(r)=r[h(r) - c(r)] in suitable basis functions and on a combination of Newton-Raphson and direct iterations. Tests on the PY and HNC approximations for hard spheres and Lennard-Jones fluid have shown that the proposed method is three to nine times as rapid as the related and so far the most efficient method of Gillan. Other advantages besides the speed are low sensitivity to the choice of initial estimate and a relatively simple computational scheme.

Research paper thumbnail of Monte Carlo simulations of thermodynamic properties of argon, krypton and xenon in liquid and gas state using new ab initio pair potentials

Http Dx Doi Org 10 1080 00268970310001638808, Nov 18, 2009

Research paper thumbnail of An integral equation and Monte Carlo study of homo- and hetero- nuclear square-well diatomic fluids

Http Dx Doi Org 10 1080 00268970009483406, Sep 1, 2009

Squa re-well homo-nu clear and hetero-nuclear diatomic uids are studied using the Ornstein-Zernik... more Squa re-well homo-nu clear and hetero-nuclear diatomic uids are studied using the Ornstein-Zernike equation and the recently proposed R H N C-VM closure. M onte Carlo canonical simulations have been performed to complete recent literature simulation data. The integral equation thermodyna mic and structural results are compared with these and literature simulation data at three elongations over a large range of densities and temperatures. The R H NC-VM theory agrees excellently with the simulation thermodyna mic and structural results. Its accuracy revealed slight errors in simulation data in work by Lṍsal and Nezbeda [1999, M olec. Phys., 96, 335]. The data have been re-simulated.

Research paper thumbnail of Accurate equation of state of the hard sphere fluid in stable and metastable regions

Physical Chemistry Chemical Physics, 2004

New accurate data on the compressibility factor of the hard sphere fluid are obtained by highly o... more New accurate data on the compressibility factor of the hard sphere fluid are obtained by highly optimized molecular dynamics calculations in the range of reduced densities 0.20-1.03. The relative inaccuracy at the 95% confidence level is better than 0.00004 for all densities but the last deeply metastable point. This accuracy requires careful examination of finite size effects and other possible sources of errors and applying corrections. The data are fitted to a power series in y/(1 À y), where y is the packing fraction; the coefficients are determined so that virial coefficients B 2 to B 6 are reproduced. To do this, values of B 5 and B 6 are accurately recalculated. Virial coefficients up to B 11 are then estimated from the equation of state.

Research paper thumbnail of Critical consolute point in hard-sphere binary mixtures: Effect of the value of the eighth and higher virial coefficients on its location

Collection of Czechoslovak Chemical Communications, 2010

ABSTRACT Various truncations for the virial series of a binary fluid mixture of additive hard sph... more ABSTRACT Various truncations for the virial series of a binary fluid mixture of additive hard spheres are used to analyze the location of the critical consolute point of this system for different size asymmetries. The effect of uncertainties in the values of the eighth virial coefficients on the resulting critical constants is assessed. It is also shown that a replacement of the exact virial coefficients in lieu of the corresponding coefficients in the virial expansion of the analytical Boublík–Mansoori–Carnahan–Starling–Leland equation of state, which still leads to an analytical equation of state, may lead to a critical consolute point in the system.

Research paper thumbnail of Chapter 19. The Estimation of Heat Capacities of Pure Liquids

Research paper thumbnail of An Accurate Analytical Representation of the Bridge Function of Hard Spheres and a Question of Existence of a General Closure to the Ornstein-Zernike Equation

Collection of Czechoslovak Chemical Communications, 2011

The bridge function of hard spheres is accurately calculated from computer simulation data on the... more The bridge function of hard spheres is accurately calculated from computer simulation data on the pair distribution function via the inverted Ornstein–Zernike equation at reduced densities ρ* ≡ Nσ3/V ranging from 0.2 to 1.02, i.e. from low densities through densities in a vicinity of the phase transition to crystal to densities of metastable fluid region. The data are used to propose an analytical representation of the bridge function as a function of the interparticle distance and density. They are further used to construct the so-called Duh– Haymet plot. It is demonstrated that a “general closure” to the Ornstein–Zernike equation in the form B(r) = f[γ(r)], where γ is the indirect (or series) correlation function, does not match the data. Nor does an extended closure B(r) = f[γ(r),ρ*] even in the simplest case of the one component hard sphere fluid. A relative success of literature closures to the Ornstein–Zernike equation is discussed.

Research paper thumbnail of Structure of ternary additive hard-sphere fluid mixtures

Physical Review E, 2002

Monte Carlo simulations on the structural properties of ternary fluid mixtures of additive hard s... more Monte Carlo simulations on the structural properties of ternary fluid mixtures of additive hard spheres are reported. The results are compared with those obtained from a recent analytical approximation [S. B. Yuste, A. Santos, and M. López de Haro, J. Chem. Phys. 108, 3683 (1998)] to the radial distribution functions of hard-sphere mixtures and with the results derived from the solution of the Ornstein-Zernike integral equation with both the Martynov-Sarkisov and the Percus-Yevick closures. Very good agreement between the results of the first two approaches and simulation is observed, with a noticeable improvement over the Percus-Yevick predictions especially near contact.

Research paper thumbnail of Introduction to the Thermodynamics of Hard Spheres and Related Systems

Research paper thumbnail of On extrapolation of virial coefficients of hard spheres

Condensed Matter Physics, 2012

Several methods of extrapolating the virial coefficients, including those proposed in this work, ... more Several methods of extrapolating the virial coefficients, including those proposed in this work, are discussed. The methods are demonstrated on predicting higher virial coefficients of one-component hard spheres. Estimated values of the eleventh to fifteenth virial coefficients are suggested. It has been speculated that the virial coefficients, B n , beyond B 14 may decrease with increasing n, and may reach negative values at large n. The extrapolation techniques may be utilized in other fields of science where the art of extrapolation plays a role.

Research paper thumbnail of 0Statistical Thermodynamics

This chapter deals with the statistical thermodynamics (statistical mechanics) a modern alternati... more This chapter deals with the statistical thermodynamics (statistical mechanics) a modern alternative of the classical (phenomenological) thermodynamics. Its aim is to determine thermodynamic properties of matter from forces acting among molecules. Roots of the discipline are in kinetic theory of gases and are connected with the names Maxwelland

Research paper thumbnail of Correlation of heat capacities of liquids as a function of temperature

Fluid Phase Equilibria, 1992

Five different equations for the correlation of heat capacities of liquids have been examined and... more Five different equations for the correlation of heat capacities of liquids have been examined and tested. The following criteria have been considered in selecting a suitable correlation equation: (1) the ability to fit experimental data precisely; (2) meaningful behavior of the relationship when used for extrapolation beyond the temperature liits of the experimental data; (3) the possibility to integrate the equation analytically in order to calculate enthalpy and entropy differences. A polynomial seems to be the most dependable form for an equation in describing heat capacity as a function of temperature. The drawback of the polynomial equation of degree higher than four is that it has poor extrapolation characteristics and the possibility of oscillations, To correlate experimental data that cover a wide temperature range, a large number of terms in a polynomial equation would be necessary. In such cases, cubic splines with up to tive knots have been used to fit the data within the assumed error of measurement. A new correlation equation has been proposed which provides a reasonable extrapolation, especially in the region towards the critical point.

Research paper thumbnail of The fifth virial coefficients of fused hard sphere fluids

Czechoslovak Journal of Physics, 1988

The virial coefficients up to B 5 of 34 fused hard sphere models have been computed using about (... more The virial coefficients up to B 5 of 34 fused hard sphere models have been computed using about (4-10) • 10 s trial configurations of a modified Monte Carlo integration method. The principle of the conformal behaviour of hard particle systems is tested against these data. It is found that while for the fourth coefficient the principle is satisfied in all the cases, the fifth coefficients exhibit more complicated behaviour and do not conform, in general, to this principle.

Research paper thumbnail of Integral equation study of additive two-component mixtures of hard spheres

Molecular Physics, 1996

The Ornstein-Zernike equation for additive hard sphere mixtures is solved numerically by using th... more The Ornstein-Zernike equation for additive hard sphere mixtures is solved numerically by using the Martynov-Sarkisov (MS) closure and a recent modification of the Verlet (MV) closure. A comparison of the predictions for the equation of state and, to a lesser extent, the contact values of the radial distribution function, shows both theories to give similar, reasonably accurate, results in most

Research paper thumbnail of An accurate integral equation for molecular fluids

Molecular Physics, 1991

Percus-Yevick (PY), hypernetted chain (HNC) and modified Verlet (VM) integral equation theories a... more Percus-Yevick (PY), hypernetted chain (HNC) and modified Verlet (VM) integral equation theories are used to study the structure and thermodynamic properties of hard prolate ellipsoids of revolution in the isotropic fluid region. Results for the spherical harmonic coefficients of the pair distribution function and for the compressibility factors are compared with new Monte Carlo results reported in this work for length-to-breadth ratios a/b= 2, 3, and 5. For a/b= 2 and 3, the VM harmonic coefficients are in good agreement with the ...

Research paper thumbnail of Computer simulation of the chemical potentials of fused hard sphere diatomic fluids

Chemical Physics Letters, 1995

An efficient method for calculating the chemical potential of hard sphere fluids up to high densi... more An efficient method for calculating the chemical potential of hard sphere fluids up to high densities by computer simulation is extended to the case of fluids of hard homonuclear and heteronuclear diatomics. The chemical potentials have been simulated at packing fractions up to 7/= 0.45 and used to test the results of several equations of state. To our knowledge, this Letter gives the first direct calculation of the chemical potentials of these molecular fluids using computer simulation techniques.

Research paper thumbnail of The Ornstein-Zernike equation for hard spheres near a hard wall

Molecular Physics, 1991

Hard-sphere-hard-wall density profiles are studied using the Henderson-Abraham-Barker (HAB) formu... more Hard-sphere-hard-wall density profiles are studied using the Henderson-Abraham-Barker (HAB) formulation of the Ornstein-Zernike (OZ) equation. A new method of numerically solving this equation is proposed that consists of a combination of Newton-Raphson and Picard iteration approaches. The new method is rapidly convergent and insensitive to the initial estimate. A new reference hypernetted chain (RHNC) theory for the OZ equation is proposed that uses the bridge function of a bulk fluid hard sphere reference system, and ...

Research paper thumbnail of Direct method for determining parameters in intermolecular pair potentials from PVT data and from thermodynamic properties of dilute gases. I. Calculation of parameters from PVT data

Collection of Czechoslovak Chemical Communications, 1973

Research paper thumbnail of Low-temperature and high-temperature approximations for penetrable-sphere fluids: Comparison with Monte Carlo simulations and integral equation theories

Physical Review E, 2007

The two-body interaction in dilute solutions of polymer chains in good solvents can be modeled by... more The two-body interaction in dilute solutions of polymer chains in good solvents can be modeled by means of effective bounded potentials, the simplest of which being that of penetrable spheres (PSs). In this paper we construct two simple analytical theories for the structural properties of PS fluids: a low-temperature (LT) approximation, that can be seen as an extension to PSs of the well-known solution of the Percus-Yevick (PY) equation for hard spheres, and a high-temperature (HT) approximation based on the exact asymptotic behavior in the limit of infinite temperature. Monte Carlo simulations for a wide range of temperatures and densities are performed to assess the validity of both theories. It is found that, despite their simplicity, the HT and LT approximations exhibit a fair agreement with the simulation data within their respective domains of applicability, so that they complement each other. A comparison with numerical solutions of the PY and the hypernetted-chain approximations is also carried out, the latter showing a very good performance, except inside the core at low temperatures.

Research paper thumbnail of A comparison of the correlation functions of the Lennard–Jones fluid for the first-order Duh–Haymet–Henderson closure with molecular simulations

Research paper thumbnail of A rapidly convergent method of solving the OZ equation

Http Dx Doi Org 10 1080 00268978500102651, Aug 22, 2006

ABSTRACT A new method is proposed for solving numerically the Ornstein-Zernike equation for syste... more ABSTRACT A new method is proposed for solving numerically the Ornstein-Zernike equation for systems with a spherically symmetrical pair-potential. The method is based on expansion of the function Gamma(r)=r[h(r) - c(r)] in suitable basis functions and on a combination of Newton-Raphson and direct iterations. Tests on the PY and HNC approximations for hard spheres and Lennard-Jones fluid have shown that the proposed method is three to nine times as rapid as the related and so far the most efficient method of Gillan. Other advantages besides the speed are low sensitivity to the choice of initial estimate and a relatively simple computational scheme.

Research paper thumbnail of Monte Carlo simulations of thermodynamic properties of argon, krypton and xenon in liquid and gas state using new ab initio pair potentials

Http Dx Doi Org 10 1080 00268970310001638808, Nov 18, 2009

Research paper thumbnail of An integral equation and Monte Carlo study of homo- and hetero- nuclear square-well diatomic fluids

Http Dx Doi Org 10 1080 00268970009483406, Sep 1, 2009

Squa re-well homo-nu clear and hetero-nuclear diatomic uids are studied using the Ornstein-Zernik... more Squa re-well homo-nu clear and hetero-nuclear diatomic uids are studied using the Ornstein-Zernike equation and the recently proposed R H N C-VM closure. M onte Carlo canonical simulations have been performed to complete recent literature simulation data. The integral equation thermodyna mic and structural results are compared with these and literature simulation data at three elongations over a large range of densities and temperatures. The R H NC-VM theory agrees excellently with the simulation thermodyna mic and structural results. Its accuracy revealed slight errors in simulation data in work by Lṍsal and Nezbeda [1999, M olec. Phys., 96, 335]. The data have been re-simulated.

Research paper thumbnail of Accurate equation of state of the hard sphere fluid in stable and metastable regions

Physical Chemistry Chemical Physics, 2004

New accurate data on the compressibility factor of the hard sphere fluid are obtained by highly o... more New accurate data on the compressibility factor of the hard sphere fluid are obtained by highly optimized molecular dynamics calculations in the range of reduced densities 0.20-1.03. The relative inaccuracy at the 95% confidence level is better than 0.00004 for all densities but the last deeply metastable point. This accuracy requires careful examination of finite size effects and other possible sources of errors and applying corrections. The data are fitted to a power series in y/(1 À y), where y is the packing fraction; the coefficients are determined so that virial coefficients B 2 to B 6 are reproduced. To do this, values of B 5 and B 6 are accurately recalculated. Virial coefficients up to B 11 are then estimated from the equation of state.

Research paper thumbnail of Critical consolute point in hard-sphere binary mixtures: Effect of the value of the eighth and higher virial coefficients on its location

Collection of Czechoslovak Chemical Communications, 2010

ABSTRACT Various truncations for the virial series of a binary fluid mixture of additive hard sph... more ABSTRACT Various truncations for the virial series of a binary fluid mixture of additive hard spheres are used to analyze the location of the critical consolute point of this system for different size asymmetries. The effect of uncertainties in the values of the eighth virial coefficients on the resulting critical constants is assessed. It is also shown that a replacement of the exact virial coefficients in lieu of the corresponding coefficients in the virial expansion of the analytical Boublík–Mansoori–Carnahan–Starling–Leland equation of state, which still leads to an analytical equation of state, may lead to a critical consolute point in the system.

Research paper thumbnail of Chapter 19. The Estimation of Heat Capacities of Pure Liquids

Research paper thumbnail of An Accurate Analytical Representation of the Bridge Function of Hard Spheres and a Question of Existence of a General Closure to the Ornstein-Zernike Equation

Collection of Czechoslovak Chemical Communications, 2011

The bridge function of hard spheres is accurately calculated from computer simulation data on the... more The bridge function of hard spheres is accurately calculated from computer simulation data on the pair distribution function via the inverted Ornstein–Zernike equation at reduced densities ρ* ≡ Nσ3/V ranging from 0.2 to 1.02, i.e. from low densities through densities in a vicinity of the phase transition to crystal to densities of metastable fluid region. The data are used to propose an analytical representation of the bridge function as a function of the interparticle distance and density. They are further used to construct the so-called Duh– Haymet plot. It is demonstrated that a “general closure” to the Ornstein–Zernike equation in the form B(r) = f[γ(r)], where γ is the indirect (or series) correlation function, does not match the data. Nor does an extended closure B(r) = f[γ(r),ρ*] even in the simplest case of the one component hard sphere fluid. A relative success of literature closures to the Ornstein–Zernike equation is discussed.

Research paper thumbnail of Structure of ternary additive hard-sphere fluid mixtures

Physical Review E, 2002

Monte Carlo simulations on the structural properties of ternary fluid mixtures of additive hard s... more Monte Carlo simulations on the structural properties of ternary fluid mixtures of additive hard spheres are reported. The results are compared with those obtained from a recent analytical approximation [S. B. Yuste, A. Santos, and M. López de Haro, J. Chem. Phys. 108, 3683 (1998)] to the radial distribution functions of hard-sphere mixtures and with the results derived from the solution of the Ornstein-Zernike integral equation with both the Martynov-Sarkisov and the Percus-Yevick closures. Very good agreement between the results of the first two approaches and simulation is observed, with a noticeable improvement over the Percus-Yevick predictions especially near contact.