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L. Blum - One of the best experts on this subject based on the ideXlab platform.
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Analytical solution of the Yukawa closure of the Ornstein—Zernike Equation III: the one-component case
Molecular Physics, 1999Co-Authors: L. Blum, J. N. HerreraAbstract:In previous work we have studied the solution of the Ornstein-Zernike Equation with a general multiyukawa closure. Here the direct correlation function is expressed by a rapidly converging sum of M (complex) exponentials. For a simple fluid the mathematical problem of solving the Ornstein-Zernike Equation is equivalent to finding the solution of a linear algebraic Equation of order M. The solution for the arbitrary case is given in terms of a scaling matrix Γ. For only one component this matrix is diagonal and the general solution using the properties of M-dimensional SOM Lie group is given. In the Mean Spherical Approximation (MSA) the excess entropy is obtained and expressed as a sum of 1-dimensional integrals of algebraic functions. We remark that the general solution of the M exponents-1 component case was found in our early work (Blum, L., and Hoye, J. S.,1978, J. stat. Phys., 19, 317) in implicit form. The present explicit solution agrees completely with the early one. Other thermodynamic properties...
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analytical solution of the yukawa closure of the Ornstein Zernike Equation iii the one component case
Molecular Physics, 1999Co-Authors: L. Blum, J. N. HerreraAbstract:In previous work we have studied the solution of the Ornstein-Zernike Equation with a general multiyukawa closure. Here the direct correlation function is expressed by a rapidly converging sum of M (complex) exponentials. For a simple fluid the mathematical problem of solving the Ornstein-Zernike Equation is equivalent to finding the solution of a linear algebraic Equation of order M. The solution for the arbitrary case is given in terms of a scaling matrix Γ. For only one component this matrix is diagonal and the general solution using the properties of M-dimensional SOM Lie group is given. In the Mean Spherical Approximation (MSA) the excess entropy is obtained and expressed as a sum of 1-dimensional integrals of algebraic functions. We remark that the general solution of the M exponents-1 component case was found in our early work (Blum, L., and Hoye, J. S.,1978, J. stat. Phys., 19, 317) in implicit form. The present explicit solution agrees completely with the early one. Other thermodynamic properties...
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Analytical solution of the Yukawa closure of the Ornstein—Zernike Equation. II. The full solution
Molecular Physics, 1998Co-Authors: L. Blum, J. N. HerreraAbstract:New and simpler forms are presented of the closure of the analytical solution of the Ornstein—Zernike Equation for the general case consisting of a sum of M Yukawa exponentials with factorizable coefficients in terms of an M × M scaling matrix γ (Blum, L., Vericat, F., and Herrera, J. N., 1992, J. statist. Phys., 66, 249) are presented. The general solution is given in terms of M(M—1) symmetry relations and M boundary conditions. The general form for the multicomponent case is obtained. For only one component the closure for n = 1, …, M is
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analytical solution of the yukawa closure of the Ornstein Zernike Equation ii the full solution
Molecular Physics, 1998Co-Authors: L. Blum, J. N. HerreraAbstract:New and simpler forms are presented of the closure of the analytical solution of the Ornstein—Zernike Equation for the general case consisting of a sum of M Yukawa exponentials with factorizable coefficients in terms of an M × M scaling matrix γ (Blum, L., Vericat, F., and Herrera, J. N., 1992, J. statist. Phys., 66, 249) are presented. The general solution is given in terms of M(M—1) symmetry relations and M boundary conditions. The general form for the multicomponent case is obtained. For only one component the closure for n = 1, …, M is
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Thermodynamic properties of an asymmetric fluid mixture with Yukawa interaction in the mean spherical approximation
The Journal of Chemical Physics, 1996Co-Authors: J. N. Herrera, L. Blum, E. García‐llanosAbstract:The analytical solution of mean spherical approximation of the Ornstein–Zernike Equation for a Yukawa fluid with factorizable coefficients is used to obtain a simple form of the Equation of state for the mixture. These results are an extension of Ginoza’s work.
G. A. Martynov - One of the best experts on this subject based on the ideXlab platform.
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The asymptotics of correlation functions and liquid–vapor phase transitions
High Temperature, 2017Co-Authors: G. A. MartynovAbstract:Power-law and exponential asymptotics of distribution functions are analyzed based on the Ornstein–Zernike Equation. The correlation length at the critical point is shown to remain finite and, therefore, the partition function has no singularity at this point.
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Two solutions for the Ornstein-Zernike Equation and critical phenomena in liquids
Russian Journal of Physical Chemistry A, 2012Co-Authors: G. A. MartynovAbstract:It is shown that the Ornstein-Zernike Equation, the equivalent of the Gibbs distribution, has two simultaneous solutions: analytical and nonanalytical. The analytical solution disappears at a critical point and only the nonanalytical solution remains (which, however, is not zero as we move away from the critical point). It is found that pressure and isothermal compressibility also have two components away from critical point: analytical and nonanalytical.
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Mechanism for creation of critical phenomena in liquids
Russian Journal of Mathematical Physics, 2011Co-Authors: G. A. MartynovAbstract:In the present paper, we study general methods of solving the Ornstein-Zernike Equation to find out what refinements are to be introduced into these Equations for them to describe properties of liquids not only in the regular domain of the phase diagram but also in a neighborhood of the critical point. This approach enabled us to obtain, by using the Ornstein-Zernike Equation, practically all known results of scaling theory and to establish some specific features of critical phenomena that were not known earlier.
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An asymptotic closure to the Ornstein-Zernike Equation and the problem of phase transitions
Russian Journal of Physical Chemistry A, 2004Co-Authors: G. A. Martynov, I. Odvarkova, A. MalijevskyAbstract:The asymptotic behavior of the Ornstein-Zernike Equation and its behavior at zero were analyzed. The results were used to construct a closure to the Ornstein-Zernike Equation that not only very accurately described numerical experiment data over the whole phase plane but also determined the crystallization curve of a liquid with an error no more than 1%.
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New insight on an old approach to the theory of critical phenomena
Theoretical and Mathematical Physics, 1999Co-Authors: G. A. MartynovAbstract:The theory of critical phenomena in liquids is constructed on the base of the Ornstein-Zernike Equation. Numerous previously unknown details of critical phenomena are found.
A. G. Vompe - One of the best experts on this subject based on the ideXlab platform.
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New closure for the Ornstein–Zernike Equation
The Journal of Chemical Physics, 1999Co-Authors: G. A. Martynov, G. N. Sarkisov, A. G. VompeAbstract:A closure for the Ornstein–Zernike Equation was proposed on the basis of an analysis of the properties of bridge functionals. The closure allows one to calculate the two-particle distribution function g(r) of the Lennard-Jones fluid with a relative error that does not exceed 1%–2% at all densities and temperatures. At the same time, the thermodynamic parameters of fluid in the same approximation are calculated with larger error. It has been shown that these facts are due to those additional errors that are entered by the formulas establishing the linkage between g(r) and thermodynamic parameters.
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new closure for the Ornstein Zernike Equation
Journal of Chemical Physics, 1999Co-Authors: G. A. Martynov, G. N. Sarkisov, A. G. VompeAbstract:A closure for the Ornstein–Zernike Equation was proposed on the basis of an analysis of the properties of bridge functionals. The closure allows one to calculate the two-particle distribution function g(r) of the Lennard-Jones fluid with a relative error that does not exceed 1%–2% at all densities and temperatures. At the same time, the thermodynamic parameters of fluid in the same approximation are calculated with larger error. It has been shown that these facts are due to those additional errors that are entered by the formulas establishing the linkage between g(r) and thermodynamic parameters.
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the bridge function expansion and the self consistency problem of the Ornstein Zernike Equation solution
Journal of Chemical Physics, 1994Co-Authors: A. G. Vompe, G. A. MartynovAbstract:We propose self‐consistent solutions to the Ornstein–Zernike Equation where the approximate closure is replaced by a bridge function expansion, whose main advantage is the improvement of correlation functions. Unknown coefficients of this expansion are found from the principle of total thermodynamic consistency. The latter includes not only the conventional pressure–compressibility Equation but also the relation between internal energy and pressure. We show that utilizing only the first Equation one may face a nonunique partially consistent solution conditioned by noncomplete formulation of the consistency problem. At the same time the suggested set of Equations is sufficient to determine a true and unique physical solution regardless of the number of unknown coefficients. In this paper we expand the bridge function in powers of potential of mean force and perform the example of building the approximate self‐consistent closure. Moreover, the approach via total thermodynamic consistency introduces the valu...
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The bridge function expansion and the self‐consistency problem of the Ornstein–Zernike Equation solution
The Journal of Chemical Physics, 1994Co-Authors: A. G. Vompe, G. A. MartynovAbstract:We propose self‐consistent solutions to the Ornstein–Zernike Equation where the approximate closure is replaced by a bridge function expansion, whose main advantage is the improvement of correlation functions. Unknown coefficients of this expansion are found from the principle of total thermodynamic consistency. The latter includes not only the conventional pressure–compressibility Equation but also the relation between internal energy and pressure. We show that utilizing only the first Equation one may face a nonunique partially consistent solution conditioned by noncomplete formulation of the consistency problem. At the same time the suggested set of Equations is sufficient to determine a true and unique physical solution regardless of the number of unknown coefficients. In this paper we expand the bridge function in powers of potential of mean force and perform the example of building the approximate self‐consistent closure. Moreover, the approach via total thermodynamic consistency introduces the valu...
J. N. Herrera - One of the best experts on this subject based on the ideXlab platform.
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Analytical solution of the Yukawa closure of the Ornstein—Zernike Equation III: the one-component case
Molecular Physics, 1999Co-Authors: L. Blum, J. N. HerreraAbstract:In previous work we have studied the solution of the Ornstein-Zernike Equation with a general multiyukawa closure. Here the direct correlation function is expressed by a rapidly converging sum of M (complex) exponentials. For a simple fluid the mathematical problem of solving the Ornstein-Zernike Equation is equivalent to finding the solution of a linear algebraic Equation of order M. The solution for the arbitrary case is given in terms of a scaling matrix Γ. For only one component this matrix is diagonal and the general solution using the properties of M-dimensional SOM Lie group is given. In the Mean Spherical Approximation (MSA) the excess entropy is obtained and expressed as a sum of 1-dimensional integrals of algebraic functions. We remark that the general solution of the M exponents-1 component case was found in our early work (Blum, L., and Hoye, J. S.,1978, J. stat. Phys., 19, 317) in implicit form. The present explicit solution agrees completely with the early one. Other thermodynamic properties...
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analytical solution of the yukawa closure of the Ornstein Zernike Equation iii the one component case
Molecular Physics, 1999Co-Authors: L. Blum, J. N. HerreraAbstract:In previous work we have studied the solution of the Ornstein-Zernike Equation with a general multiyukawa closure. Here the direct correlation function is expressed by a rapidly converging sum of M (complex) exponentials. For a simple fluid the mathematical problem of solving the Ornstein-Zernike Equation is equivalent to finding the solution of a linear algebraic Equation of order M. The solution for the arbitrary case is given in terms of a scaling matrix Γ. For only one component this matrix is diagonal and the general solution using the properties of M-dimensional SOM Lie group is given. In the Mean Spherical Approximation (MSA) the excess entropy is obtained and expressed as a sum of 1-dimensional integrals of algebraic functions. We remark that the general solution of the M exponents-1 component case was found in our early work (Blum, L., and Hoye, J. S.,1978, J. stat. Phys., 19, 317) in implicit form. The present explicit solution agrees completely with the early one. Other thermodynamic properties...
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Analytical solution of the Yukawa closure of the Ornstein—Zernike Equation. II. The full solution
Molecular Physics, 1998Co-Authors: L. Blum, J. N. HerreraAbstract:New and simpler forms are presented of the closure of the analytical solution of the Ornstein—Zernike Equation for the general case consisting of a sum of M Yukawa exponentials with factorizable coefficients in terms of an M × M scaling matrix γ (Blum, L., Vericat, F., and Herrera, J. N., 1992, J. statist. Phys., 66, 249) are presented. The general solution is given in terms of M(M—1) symmetry relations and M boundary conditions. The general form for the multicomponent case is obtained. For only one component the closure for n = 1, …, M is
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analytical solution of the yukawa closure of the Ornstein Zernike Equation ii the full solution
Molecular Physics, 1998Co-Authors: L. Blum, J. N. HerreraAbstract:New and simpler forms are presented of the closure of the analytical solution of the Ornstein—Zernike Equation for the general case consisting of a sum of M Yukawa exponentials with factorizable coefficients in terms of an M × M scaling matrix γ (Blum, L., Vericat, F., and Herrera, J. N., 1992, J. statist. Phys., 66, 249) are presented. The general solution is given in terms of M(M—1) symmetry relations and M boundary conditions. The general form for the multicomponent case is obtained. For only one component the closure for n = 1, …, M is
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Thermodynamic properties of an asymmetric fluid mixture with Yukawa interaction in the mean spherical approximation
The Journal of Chemical Physics, 1996Co-Authors: J. N. Herrera, L. Blum, E. García‐llanosAbstract:The analytical solution of mean spherical approximation of the Ornstein–Zernike Equation for a Yukawa fluid with factorizable coefficients is used to obtain a simple form of the Equation of state for the mixture. These results are an extension of Ginoza’s work.
F. Vericat - One of the best experts on this subject based on the ideXlab platform.
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solution of the Ornstein Zernike Equation for spheres with octupolar surface adhesion toward a simple model of water
The Journal of Physical Chemistry, 1996Co-Authors: L. Blum, F. VericatAbstract:An analytic solution of the molecular Ornstein−Zernike Equation for spheres with octupolar sticky potentials is given explicitly. In its most general form the closure of the direct correlation function is of the form of the mean spherical approximation for arbitrary multipolar interactions, and the total correlation function contains terms that arise in the Percus−Yevick approximation for spheres with anisotropic surface adhesion. In addition to generalizing several earlier analyses of special cases of this closure, the solution presented here contains new simplifying insights that reduce the complexity of the resulting algebraic Equations. The tetrahedral octupole case can be explicitly solved in terms of the inverses of two 3 by 3 matrices. We give explicit solution for a model that has the nearest-neighbor geometry of water and show that the atom−atom pair correlation functions are in rather fair agreement with the neutron scattering experiments, considering the shortcomings of the sticky potential.
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Solution of the Ornstein−Zernike Equation for Spheres with Octupolar Surface Adhesion: Toward a Simple Model of Water†
The Journal of Physical Chemistry, 1996Co-Authors: L. Blum, F. VericatAbstract:An analytic solution of the molecular Ornstein−Zernike Equation for spheres with octupolar sticky potentials is given explicitly. In its most general form the closure of the direct correlation function is of the form of the mean spherical approximation for arbitrary multipolar interactions, and the total correlation function contains terms that arise in the Percus−Yevick approximation for spheres with anisotropic surface adhesion. In addition to generalizing several earlier analyses of special cases of this closure, the solution presented here contains new simplifying insights that reduce the complexity of the resulting algebraic Equations. The tetrahedral octupole case can be explicitly solved in terms of the inverses of two 3 by 3 matrices. We give explicit solution for a model that has the nearest-neighbor geometry of water and show that the atom−atom pair correlation functions are in rather fair agreement with the neutron scattering experiments, considering the shortcomings of the sticky potential.