用密度泛函理论研究非极性混合流体表面性质

应用密度泛函理论研究了二元非极性混合流体的表面性质.分子作为球形链处理,不同分子内的两链节相互作用以硬核Yukawa势能表示.为了避免计算中势能作用数值积分截断导致的误差,采用了合理的长程校正方法.根据微扰理论建立了流体的状态方程以计算汽液相平衡.从纯流体汽液相平衡数据回归得分子的链节作用参数ε/k、d和m_s,这些参数预测纯流体表面张力时可获得较好结果.继而引入混合参数k_ij表示不同分子链节作用情况,计算了6种非极性混合流体的汽液相平衡、表面张力、表面密度剖面.结果表明,本方法应用于二元非极性流体混合物时汽液表面张力计算值与实验值符合良好,同时显示某些二元混合流体表面区可能出现组分的相对富集现象.     

链状流体的分子热力学模型(Ⅰ)──纯物质

实际链状流体的分子热力学模型表示为参考流体（硬球链流体）的贡献与一微扰项之和.作者先前建立的硬球链流体的状态方程用于计算参考流体的性质,用Alder等人对方阱流体的计算机模拟结果计算微扰项的贡献,从而建立了实际链状纯流体的分子热力学模型.该模型具有非常简单的形式,用三个与温度无关的分子参数（分子的链数,链节的直径和链节间的方阱位能阱深）可以较好地关联从球形小分子到链状高分子、分子间没有氢键作用的流体的饱和蒸汽压、饱和液体体积和pVT关系     

链状流体的分子热力学模型(Ⅰ)──纯物质

实际链状流体的分子热力学模型表示为参考流体（硬球链流体）的贡献与一微扰项之和.作者先前建立的硬球链流体的状态方程用于计算参考流体的性质，用Alder等人对方阱流体的计算机模拟结果计算微扰项的贡献，从而建立了实际链状纯流体的分子热力学模型.该模型具有非常简单的形式，用三个与温度无关的分子参数（分子的链数，链节的直径和链节间的方阱位能阱深）可以较好地关联从球形小分子到链状高分子、分子间没有氢键作用的流体的饱和蒸汽压、饱和液体体积和pVT关系     

用改进的密度泛函理论预测三元硬球混合物的结构

在Ronsenfeld的权重函数的基础上,在计算流体自由能密度时利用硬球混合物流体的Boublik—Mansoori—Canahan-Starling-Leland状态方程来代替硬球的定标粒子理论,从而得到了改进的密度泛函理论。结合测试粒子法,对不同组成的三元硬球混合物流体的径向分布函数进行了计算：与分子模拟数据比较结果表明,使用合适的密度泛函理论,测试粒子法能够成功地计算多元硬球混合物流体的结构性质。本研究为使用统计力学理论计算其它复杂流体的热力学性质提供了一种方法。     

缔合型链式硬球自扩散系数方程

将链式硬球模型自扩散系数方程与统计缔合流体理论（SAFT）相结合起来。实际非球状的缔合分子以有缔合点的硬球链来模拟。缔合流体中自扩散系数被认为是由非缔合贡献和氢键缔合贡献两部分组成：链式硬球自扩散系数方程用以计算非缔合流体的自扩散系数，而统计缔合流体理论描述了氢键数与密度和温度的关系，从而得到缔合对自扩散系数的影响，对于水（包括超临界水），醇类和HF等流体在宽广的压力和温度范围内，使用实验数据对本方程进行检验，其自扩散系数的相对平均偏差在7．5％左右。     

环状和支链硬球链流体的状态方程

以单体缔合的统计力学理论为基础，建立了链状分子亥氏孙数和状态方程和空们相关函数的关系，并应用于环 状和支链硬球链流体。对这两类流体压缩因子的预测结果与计算机模型值相吻合。     

用微扰理论、平均球近似结合统计缔合流体理论建立纯流体的状态方程

分别采用微扰理论和平均球近似（MSA）处理实际流体偶极──偶极间的相互作用,结合统计缔合流体理论（SAFT）处理氢键缔合相互作用,建立了一个纯缔合流体的状态方程．用分子链节微观参数分别关联了37种纯缔合流体（水、醇、酸和胺）的饱和液相密度和饱和蒸汽压．结果表明：采用微扰理论处理偶极──偶极相互作用的关联结果明显优于平均球近似,与分子模拟数据比较,结论一致．     

粒子在溶液中吸附聚电解质行为及粒子间的相互作用(Ⅰ)模型建立

以自洽场 (CSF)理论为基础 ,综合粒子、溶剂分子和聚合物链节之间的相互作用及聚合物分子链电荷的作用对粒子在溶液中吸附聚合物的影响 ,采用前末端链节决定随机行走模型 (PRDWM)建立了粒子在聚合物溶液中吸附平衡后的粒子表面的链节密度分布的数学模型———链节密度分布函数 ,并通过吸附前后粒子表面自由能的变化建立了吸附聚合物分子链的粒子间的相互作用势能模型     

含临界点的统计缔合流体理论研究(Ⅰ)非极性流体

从适合于临界点的计算出发 ,对统计缔合流体理论方程进行改进 :(1)对链状分子的每个链节考虑其非球形度 ;(2 )提出必须考虑链节成链时对色散作用的影响 .建立了扩展的统计缔合流体理论状态方程 ,对于正构烷烃和异构烷烃的计算表明 ,该方程计算温度范围大 ,从低温区到临界区 ,特别是在临界点附近精度有明显提高 ,临界点的计算值和实验值基本符合 .扩展了理论状态方程的适用性 ,可望用于各种含临界区域流体体系的热力学计算     

链状流体的分子热力学模型(Ⅱ)──混合物汽液平衡

实际链状流体混合物的亥氏函数表示为参考流体（硬球链流体混合物）的贡献和由于链节间的方阱位能相互作用的贡献之和．前者直接用作者先前建立的硬球链流体混合物的分子热力学模型计算,不含混合规则;后者采用Alder等人的结果,用vanderWaals单流体理论计算混合物的能量参数.对于不含氢键作用的二元混合物,有一可调相互作用参数,需由实验数据拟合得到．本模型可以满意地关联小分子混合物和高分子溶液的汽液平衡。     

硬球链流体在狭缝中密度分布的Monte Carlo模拟

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 configurationai-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 configurationai 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 eauations of state of HSCFs by different authors.     

A simplified expression for the hard-sphere dimer fluid radial distribution function

Recently, in our laboratory a closed form expression for the correlation function of the hard-sphere dimer fluid obtained from Wertheims multidensity Ornstein-Zernike integral equation theory with Percus-Yevick approximation was presented by Kim et al. [2001]. However, it is difficult to apply its expression to perturbation theory and vapor-liquid equilibria calculations, since it is of very complex form. In this work, we present a simplified expression for the first shell of the radial distribution function (RDF) of the hard-sphere dimer fluid using a series expansion of the analytical expression. The expansion is carried out in terms of both the packing fraction and the radial distance. Expressions are also obtained for the coordination number and its first and second derivatives as functions of radial distance and packing fraction. These expressions, which are useful in perturbation theory, are simpler to use than those obtained from the starting equation, while giving good agreement with the original expression results. Then we present an simplified equation of state for the square-well dimer fluid of variable well width (λ) based on Barker-Henderson perturbation theory using its expression for the radial distribution function of the hard-sphere dimer fluid, and test its expression with NVT and Gibbs ensemble Monte Carlo simulation data [Kim et al., 2001].     

电化学界面处离子分布、静电势和ξ势的研究

Density functional theory is applied to predicting the structures and electrostatic potentials of planar electrochemical surfaces within the framework of the restricted primitive model where small ions are represented by charged hard spheres of equal diameter and the solvent is assumed to be a continuous dielectric medium. The hard-sphere contribution to the excess Helmholtz energy functional is evaluated using the modified fundamentalmeasure theory and the electrostatic contribution is obtained from the quadratic functional Taylor expansion using the second-order direct correlation function from the mean-spherical approximation. Numerical results for the ionic density profiles and the mean electrostatic potentials near a planar surface of various charge densities are in excellent agreement with molecular simulations. In contrast to the modified Gouy-Chapman theory, the present density functional theory correctly predicts the second layer formation and charge inversion of charged surfaces as observed in simulations and in experiments. The theory has also been tested with the zeta potentials of positively charged polystyrene particles in aqueous solutions of KBr. Good agreement is achieved between the calculated and experimental results.     

电化学界面处离子分布、静电势和ζ势的研究

Density functional theory is applied to predicting the structures and electrostatic potentials of planar electrochemical surfaces within the framework of the restricted primitive model where small ions are represented by charged hard spheres of equal diameter and the solvent is assumed to be a continuous dielectric medium. The hard-sphere contribution to the excess Helmholtz energy functional is evaluated using the modified fundamental-measure theory and the electrostatic contribution is obtained from the quadratic functional Taylor expansion using the second-order direct correlation function from the mean-spherical approximation. Numerical results for the ionic density profiles and the mean electrostatic potentials near a planar surface of various charge densities are in excellent     

甲烷在单壁碳纳米管中的吸附的密度泛函研究

纳米微孔材料的出现使得有可能在中低压下微孔介质中吸附存储天然气 .由于天然气的主要成分是甲烷 ,其吸附存储为研究者所关注 .碳纳米管由单层或几层纯碳同轴圆柱状结构层组成 ,每个管状层由碳六边形构成 ,与石墨内结构相似 .单壁的碳纳米管称为单壁碳纳米管 (ＳｉｎｇｌｅＷａｌｌｅｄＣａｒｂｏｎＮａｎｏｔｕｂｅ ,ＳＷＮＴ) .它作为一种吸附材料在实验和理论研究中受到高度重视 .在ＳＷＮＴ中吸附的密度泛函理论 (ＤＦＴ)研究与计算机模拟相比较少 .文献中只有Ｇｏｒｄｏｎ等[1] 在 1999年采用密度泛函的方法和过分简化的氢分子势能函…     

Thermodynamic and structural properties of hard-sphere fluids confined within a spherical hard-wall pore

The grand canonical ensemble Monte Carlo simulations have been carried out to investigate the thermodynamic and structural properties of hard-sphere fluids confined within a spherical hard-wall pore. Equilibrium partition coefficients and pore density profiles are computed over a wide range of particle-to-pore size ratios and concentrations distributing between an external bulk phase and a pore phase. The simulation data for equilibrium partitioning are used to assess the limitations and applicabilitiec of theoretical approximations including the virial expansion equation and the extended two-state prediction. The Monte Carlo results obtained in these studies, in conjunction with the theoretical models, provide the basis for a discussion on the steric effects in size-exclusion partitioning of such systems.     

SIMPLIFIED HARD-SPHERE AND HARD-SPHERE CHAIN EQUATIONS OF STATE FOR ENGINEERING APPLICATIONS

A simple hard-sphere equation of state is proposed. This hard-sphere equation is a ratio of second-order polynomials that meets the ideal gas and close-packed density limits. It predicts the compressibility of hard-sphere fluids at low and medium densities to within a degree of quality similar to the widely used Carnahan-Starling equation. In addition, the proposed equation performs better at high densities, particularly near the close-packed density. An expression is also derived to relate the site-site correlation function at contact for hard dimers with the site-site correlation function at contact for hard spheres. With this relationship, the thermodynamic perturbation-dimer theory (TPT-D) of hard-sphere chains is simplified. The new theory performs comparably with the TPT-D when the compressibility factors of hard-sphere chain fluids containing up to 201-mer are predicted, however, it has the advantages of both simplicity and accuracy. From a practical perspective, this theory can be used to construct equations of state for polymer solutions or fluid systems containing short- and long-chain molecules.     

SIMPLIFIED HARD-SPHERE AND HARD-SPHERE CHAIN EQUATIONS OF STATE FOR ENGINEERING APPLICATIONS

A simple hard-sphere equation of state is proposed. This hard-sphere equation is a ratio of second-order polynomials that meets the ideal gas and close-packed density limits. It predicts the compressibility of hard-sphere fluids at low and medium densities to within a degree of quality similar to the widely used Carnahan-Starling equation. In addition, the proposed equation performs better at high densities, particularly near the close-packed density. An expression is also derived to relate the site-site correlation function at contact for hard dimers with the site-site correlation function at contact for hard spheres. With this relationship, the thermodynamic perturbation-dimer theory (TPT-D) of hard-sphere chains is simplified. The new theory performs comparably with the TPT-D when the compressibility factors of hard-sphere chain fluids containing up to 201-mer are predicted, however, it has the advantages of both simplicity and accuracy. From a practical perspective, this theory can be used to construct equations of state for polymer solutions or fluid systems containing short- and long-chain molecules.     

流体相平衡模拟计算的一种新方法——等概率扰动法

根据统计力学的等概率假设,本文提出一种新的扰动分子的方法——等概率扰动法,以产生Monte Carlo模拟中的Markov链.新方法可以在1个盒子里同时模拟包括界面区域在内的流体相平衡,并且对纯流体,模拟只需在正则系综里进行即可.应用该方法,模拟计算了纯方阱流体在不同温度下的汽液共存密度、沿高度方向上的密度分布图及化学位等.研究表明,传统的Metropolis位移技术不适于模拟此类非均相体系.