Both a free volume approach for Helmholtz free energy and a theoretically-based fitted formula for radial distribution function (rdf) of hard sphere solid are employed to describe the Helmholtz free energy of Lennard-...Both a free volume approach for Helmholtz free energy and a theoretically-based fitted formula for radial distribution function (rdf) of hard sphere solid are employed to describe the Helmholtz free energy of Lennard-Jones solid in the framework of the first order thermodynamic perturbation theory, which also is employed for the uniform LennardJones fluid. The dividing of the Lennard-Jones potential follows from the WCA prescription, but the specification of the equivalent hard sphere diameter is determined by a simple iteration procedure devised originally for liquid state, but extended to solid state in the present study. Two hundred sheiks are used in the rdf to get an accurate perturbation term.The present approach is very accurate for the description of excess Helmholtz free energy of LJ solid, but shows some deviation from the simulation for excess Helmholtz free energy of uniform LJ fluid when the reduced temperature kT/ε is higher then 5. The present approach is satisfactory for description of solid-liquid phase transition of the Lennard-Jones model.展开更多
A new bridge functional as a function of indirect correlation function was proposed, which was basedon analysis on the asymptotic behavior of the Ornstein-Zernike (OZ) equation system and a series expansion whoserenor...A new bridge functional as a function of indirect correlation function was proposed, which was basedon analysis on the asymptotic behavior of the Ornstein-Zernike (OZ) equation system and a series expansion whoserenormalization resulted in an adjustable parameter determined by the thermodynamics consistency condition. Theproposed bridge functional was tested by applying it to bulk hard sphere and hard core Yukawa fluid for the predictionof structure and thermodynamics properties based on the OZ equation. As an application, the present bridge functionalwas employed for non-uniform fluid of the above two kinds by means of the density functional theory methodology, theresulting density distribution profiles were in good agreement with the available computer simulation data.展开更多
One recently proposed self-consistent hard sphere bridge functional was combined with an exponential function exp(-cr) and a re-normalized indirect correlation function to construct the bridge function for fluid with ...One recently proposed self-consistent hard sphere bridge functional was combined with an exponential function exp(-cr) and a re-normalized indirect correlation function to construct the bridge function for fluid with hard core and interaction tail. In the present approach, the adjustable parameter α was determined by the thermodynamic consistency realized on the compressibility modulus, the re-normalization of the indirect correlation function was realized by a modified Mayer function with the interaction potential replaced by the perturbative part of the interaction potential. As an example, the present bridge function was combined with the Ornstein-Zernike (OZ) equation to predict structure and thermodynamics properties in very good agreement with the simulation data available for Lennard-Jones (L J). Based on the universality principle of the free energy density functional and the test particle trick, the numerical solution of the OZ equation was employed to construct the first order direct correlation function of the non-uniform fluid as a functional of the density distribution by means of the indirect correlation function. In the framework of the density functional theory, the numerically obtained functional predicted the density distribution of LJ fluid confined in two planar hard walls that is in good agreement with the simulation data.展开更多
A statistical mechanics method is proposed for calculation of potential ofmean force (PMF). In the case of solvophobic or solvophilic macroparticles immersed in solvent bathof soft sphere or Lennard-Jones particles, p...A statistical mechanics method is proposed for calculation of potential ofmean force (PMF). In the case of solvophobic or solvophilic macroparticles immersed in solvent bathof soft sphere or Lennard-Jones particles, prediction accuracy for the PMF and MF from the simplestimplementation of the proposed method, where hypernetted chain approximation is adopted forcorrelation of the macroparticle-macroparticle at infinitely dilute limit, is comparable to that ofa recent more sophisticated approach based on mixture Ornstein—Zernike integral equation / bridgefunction from fundamental measure functional. Adaptation of the present method for general complexQuids is discussed, and method for improving the accuracy is suggested. Differences and relativemerits of the present recipe compared with that based on potential distribution theory is discussed.展开更多
The Ornstein-Zernike equation is solved with the Rogers-Young approximation for bull, hard sphere fluid and Lennard-Jones fluid for several state points. Then the resulted bulk fluid radial distribution function combi...The Ornstein-Zernike equation is solved with the Rogers-Young approximation for bull, hard sphere fluid and Lennard-Jones fluid for several state points. Then the resulted bulk fluid radial distribution function combined with the test particle method is employed to determine numerically the function relationship of bridge functional as a function of indirect correlation function. It is found that all of the calculated points from different phase space state points for a same type of fluid collapse onto a same smooth curve. Then the numerically obtained curve is used to substitute the analytic expression of the bridge functional as a function of indirect correlation function required in the methodology [J. Chem. Phys. 112 (2000) 8079] to determine the density distribution of non-uniform hard sphere fluid and Lennard-Jones fluid. The good agreement of theoretical predictions with the computer simulation data is obtained. The present numerical procedure incorporates the knowledge of bulk fluid radial distribution function into the constructing of the density functional approximation and makes the original methodology more accurate and more flexible for various interaction potential fluid.展开更多
A systematic methodology is proposed to deal with the weighted density approximation version of clas-sical density functional theory by employing the knowledge of radial distribution function of bulk fluid. The presen...A systematic methodology is proposed to deal with the weighted density approximation version of clas-sical density functional theory by employing the knowledge of radial distribution function of bulk fluid. The presentmethodology results from the concept of universality of the free energy density functional combined with the test particlemethod. It is shown that the new method is very accurate for the predictions of density distribution ofa hard sphere fluidat different confining geometries. The physical foundation of the present methodology is also applied to the quantumdensity functional theory.展开更多
文摘Both a free volume approach for Helmholtz free energy and a theoretically-based fitted formula for radial distribution function (rdf) of hard sphere solid are employed to describe the Helmholtz free energy of Lennard-Jones solid in the framework of the first order thermodynamic perturbation theory, which also is employed for the uniform LennardJones fluid. The dividing of the Lennard-Jones potential follows from the WCA prescription, but the specification of the equivalent hard sphere diameter is determined by a simple iteration procedure devised originally for liquid state, but extended to solid state in the present study. Two hundred sheiks are used in the rdf to get an accurate perturbation term.The present approach is very accurate for the description of excess Helmholtz free energy of LJ solid, but shows some deviation from the simulation for excess Helmholtz free energy of uniform LJ fluid when the reduced temperature kT/ε is higher then 5. The present approach is satisfactory for description of solid-liquid phase transition of the Lennard-Jones model.
基金国家自然科学基金，Scientific Research Fund of EducationDepartment of Hunan Province of China
文摘A new bridge functional as a function of indirect correlation function was proposed, which was basedon analysis on the asymptotic behavior of the Ornstein-Zernike (OZ) equation system and a series expansion whoserenormalization resulted in an adjustable parameter determined by the thermodynamics consistency condition. Theproposed bridge functional was tested by applying it to bulk hard sphere and hard core Yukawa fluid for the predictionof structure and thermodynamics properties based on the OZ equation. As an application, the present bridge functionalwas employed for non-uniform fluid of the above two kinds by means of the density functional theory methodology, theresulting density distribution profiles were in good agreement with the available computer simulation data.
基金国家自然科学基金，Scientific Research Fund of Educational Department of Hunan Province of China
文摘One recently proposed self-consistent hard sphere bridge functional was combined with an exponential function exp(-cr) and a re-normalized indirect correlation function to construct the bridge function for fluid with hard core and interaction tail. In the present approach, the adjustable parameter α was determined by the thermodynamic consistency realized on the compressibility modulus, the re-normalization of the indirect correlation function was realized by a modified Mayer function with the interaction potential replaced by the perturbative part of the interaction potential. As an example, the present bridge function was combined with the Ornstein-Zernike (OZ) equation to predict structure and thermodynamics properties in very good agreement with the simulation data available for Lennard-Jones (L J). Based on the universality principle of the free energy density functional and the test particle trick, the numerical solution of the OZ equation was employed to construct the first order direct correlation function of the non-uniform fluid as a functional of the density distribution by means of the indirect correlation function. In the framework of the density functional theory, the numerically obtained functional predicted the density distribution of LJ fluid confined in two planar hard walls that is in good agreement with the simulation data.
文摘A statistical mechanics method is proposed for calculation of potential ofmean force (PMF). In the case of solvophobic or solvophilic macroparticles immersed in solvent bathof soft sphere or Lennard-Jones particles, prediction accuracy for the PMF and MF from the simplestimplementation of the proposed method, where hypernetted chain approximation is adopted forcorrelation of the macroparticle-macroparticle at infinitely dilute limit, is comparable to that ofa recent more sophisticated approach based on mixture Ornstein—Zernike integral equation / bridgefunction from fundamental measure functional. Adaptation of the present method for general complexQuids is discussed, and method for improving the accuracy is suggested. Differences and relativemerits of the present recipe compared with that based on potential distribution theory is discussed.
文摘The Ornstein-Zernike equation is solved with the Rogers-Young approximation for bull, hard sphere fluid and Lennard-Jones fluid for several state points. Then the resulted bulk fluid radial distribution function combined with the test particle method is employed to determine numerically the function relationship of bridge functional as a function of indirect correlation function. It is found that all of the calculated points from different phase space state points for a same type of fluid collapse onto a same smooth curve. Then the numerically obtained curve is used to substitute the analytic expression of the bridge functional as a function of indirect correlation function required in the methodology [J. Chem. Phys. 112 (2000) 8079] to determine the density distribution of non-uniform hard sphere fluid and Lennard-Jones fluid. The good agreement of theoretical predictions with the computer simulation data is obtained. The present numerical procedure incorporates the knowledge of bulk fluid radial distribution function into the constructing of the density functional approximation and makes the original methodology more accurate and more flexible for various interaction potential fluid.
文摘A systematic methodology is proposed to deal with the weighted density approximation version of clas-sical density functional theory by employing the knowledge of radial distribution function of bulk fluid. The presentmethodology results from the concept of universality of the free energy density functional combined with the test particlemethod. It is shown that the new method is very accurate for the predictions of density distribution ofa hard sphere fluidat different confining geometries. The physical foundation of the present methodology is also applied to the quantumdensity functional theory.
