依据硬球流体的高阶维里系数性质,结合硬球流体物态方程的最新进展SK方程(Schultz A J,Kofk D A,2014),给出了一个新的硬球流体的物态方程.通过误差分析发现,新方程相对于SK方程,在低密度稳定区和高密度非稳定区对压缩因子的描述的误差...依据硬球流体的高阶维里系数性质,结合硬球流体物态方程的最新进展SK方程(Schultz A J,Kofk D A,2014),给出了一个新的硬球流体的物态方程.通过误差分析发现,新方程相对于SK方程,在低密度稳定区和高密度非稳定区对压缩因子的描述的误差明显降低,精度明显提高.与其它高精度的物态方程比较,在低密度稳态区域新方程的精度仅次于KLM方程;在高密度亚稳态区域新方程的精度仅次于TGM方程;在全密度区间内新方程的精度仅次于TGM方程.展开更多
Making use of Weierstrass＇s theorem and Chebyshev＇s theorem and referring to the equations of state of the scaled-particle theory and the Pereus-Yevick integration equation, we demonstrate that there exists a sequen...Making use of Weierstrass＇s theorem and Chebyshev＇s theorem and referring to the equations of state of the scaled-particle theory and the Pereus-Yevick integration equation, we demonstrate that there exists a sequence of polynomials such that the equation of state is given by the limit of the sequence of polynomials. The polynomials of the best approximation from the third order up to the eighth order are obtained so that the Carnahan-Starling equation can be improved successively. The resulting equations of state are in good agreement with the simulation results on the stable fluid branch and on the metastable fluid branch.展开更多
Covering a wide range of bulk densities, density profiles for hard-sphere chain fluids (HSCFs) with chain length of 3,4,8,20,32 and 64 confined between two surfaces were obtained by Monte Carlo simulations using exten...Covering a wide range of bulk densities, density profiles for hard-sphere chain fluids (HSCFs) with chain length of 3,4,8,20,32 and 64 confined between two surfaces were obtained by Monte Carlo simulations using extended continuum configurational-bias (ECCB) method. It is shown that the enrichment of beads near surfaces is happened at high densities due to the bulk packing effect, on the contrary, the depletion is revealed at low densities owing to the configurational entropic contribution. Comparisons with those calculated by density functional theory presented by Cai et al. indicate that the agreement between simulations and predictions is good. Compressibility factors of bulk HSCFs calculated using volume fractions at surfaces were also used to test the reliability of various equations of state of HSCFs by different authors.展开更多
A theoretical method was proposed to extend a bridge density functional approximation （BDFA） for the non-uniform hard sphere fluid to the non-uniform Lennard-Jones （LJ） fluid. The DFT approach for LJ fluid is simp...A theoretical method was proposed to extend a bridge density functional approximation （BDFA） for the non-uniform hard sphere fluid to the non-uniform Lennard-Jones （LJ） fluid. The DFT approach for LJ fluid is simple, quantitatively accurate in a wide range of coexistence phase and external field parameters. Especially, the DFT approach only needs a second order direct correlation function （DCF） of the coexistence bulk fluid as input, and is therefore applicable to the subcritical temperature region. The present theoretical method can be regarded as a non-uniform counterpart of the thermodynamic perturbation theory, in which it is not at the level of the free energy but at the level of the second order DCF.the National Natural Science Foundation of China （No. 20546004） and the Natural Science Foundation of Education Department of Hunan Province （No.04C711）.展开更多
An enhanced KR-fundamental measure functional （FMF） is elaborated and employed to investigate binary and ternary hard sphere fluids near a planar hard wall or confined within two planar hard walls separated by certa...An enhanced KR-fundamental measure functional （FMF） is elaborated and employed to investigate binary and ternary hard sphere fluids near a planar hard wall or confined within two planar hard walls separated by certain interval. The present enhanced KR-FMF incorporates respectively, for aim of comparison, a recent 3rd-order expansion equation of state （EOS） and a Boublfk＇s extension of Kolafa＇s EOS for HS mixtures. It is indicated that the two versions of the EOS lead to, in the framework of the enhanced KR-FMF, similar density profiles, but the 3rd-order EOS is more consistent with an exact scaled particle theory （SPT） relation than the BK EOS. Extensive comparison between the enhanced KR-FMF-3rd-order EOS predictions and corresponding density profiles produced in different periods indicates the excellent performance of the present enhanced KR-FMF-3rd-order EOS in comparison with other available density functional approximations （DFAs）. There are two anomalous situations from whose density profiles all DFAs studied deviate significantly; however, subsequent new computer simulation results for state conditions similar to the two anomalous situations are in very excellent agreement with the present enhanced KR-FMF-3rd-order EOS. The present paper indicates that （i） the validity of the ＂naive＂ substitution elaborated in the present paper and peculiar to the original KR-FMF is still in operation even if inhomogeneoas mixtures are being dealt with; （ii） the high accuracy and self-consistency of the third order EOS seem to allow for application of the KR-FMF-third order EOS to more severe state conditions; and （iii） the ＂naive＂ substitution enables very easy the combination of the original KR-FMF with future＇s more accurate but potentially more complicated EOS of hard sphere mixtures.展开更多
From point of view of weighted density procedure, it is guessed that a Percus-Yevick （PY） compressibility excess free energy density, appearing in the Kierlik Rosinberg type fundamental measure functional （KR-FMF）...From point of view of weighted density procedure, it is guessed that a Percus-Yevick （PY） compressibility excess free energy density, appearing in the Kierlik Rosinberg type fundamental measure functional （KR-FMF） and expressed in terms of scaled particle variables, can be substituted by a corresponding expression dictated by a more accurate Mansoori Carnahan-Starling Leland （MCSL） equation of state, while retaining the original weighting functions; it is numerically indicated that the resultant undesirable non-self-consistency between the PY type weighting function and MCSL type excess free energy density had no bad effect on the performance of the resultant augmented KR-ffMF which, on the one hand, preserves the exact low-density limit of the original KR-FMF and holds a high degree of pressure self-consistency, on the other hand, improves significantly, as expected, the predictions of density profile of hard sphere fluid at single hard wall contact location and its vicinity, and of the bulk hard sphere second order direct correlation function （DCF）, obtained from functional differentiation. The FMF is made applicable to inhomogeneous non-hard sphere fluids by supplementing a functional perturbation expansion approximation truncated at the lowest order with summation of higher order terms beyond the lowest term calculated by the FMF for an effective hard sphere fluid; the resultant extended FMF only needs second order DCF and pressure of the fluid considered at coexistence state as inputs, consequently is applicable whether the considered temperature is above critical point or below critical point. The extended MCSL-augmented KR-FMF is found to be endowed with an excellent performance for predictions of density profile and surface tension by comparing the present predictions of these two quantities with available computer simulation data for inhomogeneous hard core attractive Yukawa fluid and Lennard-3ones fluid.展开更多
文摘依据硬球流体的高阶维里系数性质,结合硬球流体物态方程的最新进展SK方程(Schultz A J,Kofk D A,2014),给出了一个新的硬球流体的物态方程.通过误差分析发现,新方程相对于SK方程,在低密度稳定区和高密度非稳定区对压缩因子的描述的误差明显降低,精度明显提高.与其它高精度的物态方程比较,在低密度稳态区域新方程的精度仅次于KLM方程;在高密度亚稳态区域新方程的精度仅次于TGM方程;在全密度区间内新方程的精度仅次于TGM方程.
文摘Making use of Weierstrass＇s theorem and Chebyshev＇s theorem and referring to the equations of state of the scaled-particle theory and the Pereus-Yevick integration equation, we demonstrate that there exists a sequence of polynomials such that the equation of state is given by the limit of the sequence of polynomials. The polynomials of the best approximation from the third order up to the eighth order are obtained so that the Carnahan-Starling equation can be improved successively. The resulting equations of state are in good agreement with the simulation results on the stable fluid branch and on the metastable fluid branch.
基金Supported by the National Science Foundation of China (No. 29736170, No. 20025618) and the Doctoral Research Foundation by Ministry of Education of China (No. 1999025103). Additional support provided by the Visiting Researcher Foundation of University La
文摘Covering a wide range of bulk densities, density profiles for hard-sphere chain fluids (HSCFs) with chain length of 3,4,8,20,32 and 64 confined between two surfaces were obtained by Monte Carlo simulations using extended continuum configurational-bias (ECCB) method. It is shown that the enrichment of beads near surfaces is happened at high densities due to the bulk packing effect, on the contrary, the depletion is revealed at low densities owing to the configurational entropic contribution. Comparisons with those calculated by density functional theory presented by Cai et al. indicate that the agreement between simulations and predictions is good. Compressibility factors of bulk HSCFs calculated using volume fractions at surfaces were also used to test the reliability of various equations of state of HSCFs by different authors.
文摘A theoretical method was proposed to extend a bridge density functional approximation （BDFA） for the non-uniform hard sphere fluid to the non-uniform Lennard-Jones （LJ） fluid. The DFT approach for LJ fluid is simple, quantitatively accurate in a wide range of coexistence phase and external field parameters. Especially, the DFT approach only needs a second order direct correlation function （DCF） of the coexistence bulk fluid as input, and is therefore applicable to the subcritical temperature region. The present theoretical method can be regarded as a non-uniform counterpart of the thermodynamic perturbation theory, in which it is not at the level of the free energy but at the level of the second order DCF.the National Natural Science Foundation of China （No. 20546004） and the Natural Science Foundation of Education Department of Hunan Province （No.04C711）.
基金Supported by the National Natural Science Foundation of China under Grant No.20973202
文摘An enhanced KR-fundamental measure functional （FMF） is elaborated and employed to investigate binary and ternary hard sphere fluids near a planar hard wall or confined within two planar hard walls separated by certain interval. The present enhanced KR-FMF incorporates respectively, for aim of comparison, a recent 3rd-order expansion equation of state （EOS） and a Boublfk＇s extension of Kolafa＇s EOS for HS mixtures. It is indicated that the two versions of the EOS lead to, in the framework of the enhanced KR-FMF, similar density profiles, but the 3rd-order EOS is more consistent with an exact scaled particle theory （SPT） relation than the BK EOS. Extensive comparison between the enhanced KR-FMF-3rd-order EOS predictions and corresponding density profiles produced in different periods indicates the excellent performance of the present enhanced KR-FMF-3rd-order EOS in comparison with other available density functional approximations （DFAs）. There are two anomalous situations from whose density profiles all DFAs studied deviate significantly; however, subsequent new computer simulation results for state conditions similar to the two anomalous situations are in very excellent agreement with the present enhanced KR-FMF-3rd-order EOS. The present paper indicates that （i） the validity of the ＂naive＂ substitution elaborated in the present paper and peculiar to the original KR-FMF is still in operation even if inhomogeneoas mixtures are being dealt with; （ii） the high accuracy and self-consistency of the third order EOS seem to allow for application of the KR-FMF-third order EOS to more severe state conditions; and （iii） the ＂naive＂ substitution enables very easy the combination of the original KR-FMF with future＇s more accurate but potentially more complicated EOS of hard sphere mixtures.
基金Supported by the National Natural Science Foundation of China under Grant No.20973202
文摘From point of view of weighted density procedure, it is guessed that a Percus-Yevick （PY） compressibility excess free energy density, appearing in the Kierlik Rosinberg type fundamental measure functional （KR-FMF） and expressed in terms of scaled particle variables, can be substituted by a corresponding expression dictated by a more accurate Mansoori Carnahan-Starling Leland （MCSL） equation of state, while retaining the original weighting functions; it is numerically indicated that the resultant undesirable non-self-consistency between the PY type weighting function and MCSL type excess free energy density had no bad effect on the performance of the resultant augmented KR-ffMF which, on the one hand, preserves the exact low-density limit of the original KR-FMF and holds a high degree of pressure self-consistency, on the other hand, improves significantly, as expected, the predictions of density profile of hard sphere fluid at single hard wall contact location and its vicinity, and of the bulk hard sphere second order direct correlation function （DCF）, obtained from functional differentiation. The FMF is made applicable to inhomogeneous non-hard sphere fluids by supplementing a functional perturbation expansion approximation truncated at the lowest order with summation of higher order terms beyond the lowest term calculated by the FMF for an effective hard sphere fluid; the resultant extended FMF only needs second order DCF and pressure of the fluid considered at coexistence state as inputs, consequently is applicable whether the considered temperature is above critical point or below critical point. The extended MCSL-augmented KR-FMF is found to be endowed with an excellent performance for predictions of density profile and surface tension by comparing the present predictions of these two quantities with available computer simulation data for inhomogeneous hard core attractive Yukawa fluid and Lennard-3ones fluid.
