从硬球微扰理论推导马丁-侯状态方程

从Ｂａｒｈｅｒ－Ｈｅｎｄｅｒｓｏｎ的硬球微扰理论出发，运用幂级数形式的径向分布函数和分段的势能函数导出马丁－侯状态方程，推导过程中导出了一种理论式，计算Ｐ－Ｖ－Ｔ性质的精确度与马丁－侯原式相当，理论式的常数与分子微观参数有确定的函数关系。     

基于化学缔合统计理论的链状流体状态方程

基于化学缔合统计理论的链状流体状态方程(EOS)能够反映实际分子的形状、链节成链、缔合等具体信息,在实际流体热力学性质计算中有着广泛应用.一般的链状流体EOS仅考虑相邻链节间的相关性,我们则借助统计力学和计算机模拟结果在模型中纳入了相间链节间的相关性,获得的硬球链流体(HSCF)模型能够更好地预测模型流体的压缩因子和第二维里系数.以HSCF为参考,引入方阱色散微扰项获得了实际方阱链流体(SWCF)EOS;结合根据黏滞球模型导得的缔合项,进一步构建了缔合流体EOS.最近,我们根据微扰理论和积分方程方法又开发了一新的变阱宽方阱链流体(SWCF-VR)模型.SWCF和SWCF-VREOSs可很好地用于计算小分子、聚合物、离子液体等纯流体及混合物的相行为、热焓、表面张力、黏度等热力学及传递性质,显示了模型良好的工程应用价值.本文就本课题组多年来在自由空间范畴内基于化学缔合统计理论开发链状流体EOS及其实际应用作系统的总结.     

基于格子的链状流体分子热力学模型

格子模型是高分子溶液理论最常采用的流体模型,在此基础上建立的分子热力学模型在流体混合物的热力学性质、相平衡行为的计算等方面有广泛的应用．最近,我们对基于格子的混合亥氏函数模型重新进行了审视,采用统计力学理论推导与计算机模拟相结合的现代分子热力学研究方法建立了新的分子热力学模型,可以反映高分子链枝化、配位数、链刚性、共聚物链组成、氢键、压力等的影响,对小分子系统和高分子溶液的热力学性质和相平衡关系的计算不仅与Monte Carlo模拟结果吻合,比现有其他理论预测效果更好,对高分子溶液、离子液体混合物等实际系统的相平衡计算也取得令人满意的结果,显示出模型优越的工程应用价值．本文对上述工作进行了系统总结．     

一个新的方阱流体状态方程

将方阱势能函数视为硬球势和一个短程均匀负势的叠加,并由统计力学方法导出了相应的状态方程,这个方程包含两个定标的径向分布函数.利用已知的压缩因子分子动力学模拟数据,回归得到了这两个径向分布函数,从而建立了一个新的方阱流体状态方程.它的吸引项要比Alder等人回归得到的简单得多,与方阱流体压缩因子的MD数据一致性也更好,特别是在高密度区域.     

马丁-侯状态方程的理论式

从Barker Henderson的硬球微扰理论出发导出了一个新的状态方程 ,其形式与马丁 侯状态方程十分相似 ,其全部常数可以按马丁 侯方程的方法求出 ,只需要临界点与一个蒸气压点的数据便可较精确地预测流体的P V T性质 .利用其特性常数与分子微观参数的关系可以求出流体分子的微观参数     

分子拓扑指数与链烷烃热力学性质的关系

碳原子个数N和路径数P3是表征链烷烃分子的大小、支化度和形状等结构特征的重要参数,引入烷烃所含甲基数的1.5次方M1和3次方M2表征取代基效应,运用多元线性模型研究了链烷烃标准生成焓、标准摩尔熵、标准生成吉布斯自由能等三种热力学性质与N,P3,M1和M2之间的定量关系,相关系数分别达到0.9993,0.9989和0.9972,标准偏差分别是2.2809kJ/mol,5.9093J/(mol·K),2.0585kJ/mol,其计算值与实验值非常接近.     

甲氰菊酯的热容及热力学性质的研究

采用精密自动绝热量热测量了自已合成并提纯到0.9916(摩尔分数)的甲氰菊酯在80~400K温区的热容.在此温区发现一固液熔化相变.其熔化温度、摩尔熔化焓、摩尔熔化熵分别为:(322.476^+~-0.012)K,(18.57^+~-0.29)kj.mol^-^1,(57.59^+~-1.01)J.K^-^1.mol^-^1.报道了该物质每隔5K的热力学函数值,用热重法研究了该化合物的热分解,对试样的化学纯度进行了量热研究。     

流体混合物热力学性质的分子模拟研究-逐级取样法

本文对三个Lennard-Jonese二元混合物进行了逐级取样模拟, 获得各体系的超额Helmholtz自由能, 超额内能及超额压力等性质, 所得结果与Nakanishi通过伞形取样法的结果一致, 表明本文方法能够有效地对混合物各类超额性质进行研究。     

6个聚合物胞腔理论状态方程的分子参数比较

利用Ｚｏｌｌｅｒ提供的ＰＢＤ和ＰＩ两种聚合物系列样品的Ｐ－Ｖ－Ｔ数据，对Ｃｅｌｌ、Ｆｌｏｒｙ、ＳＳ、ＳＨＴ、ＳＨＴＦ和ＯＣＭ６个状态方程的分子参数及其随链结构变化的规律作了比较，得到了一些有益的结论。     

电解质模型流体的MonteCarlo分子模拟

采用正则系综Monte Carlo分子模拟方法，模拟得到了一系列状态条件下1：1 价和2：2价对称电解质模型流体的径向分布函数、构型能和压缩因子的“机器实验 数据”，这些数据对构筑电解质溶液的新参考流体具有重要意义。模拟过程中，电 解质溶液被简化为硬球离子和硬球点偶扳子的混合物，离子—离子、离子—偶极和 偶极—偶极长程位能计算采用了Ewald求和方法。最后，对离子—偶极子混合物的 结构和热力学性质与体系温度、密度和浓度的关系进行了分析和讨论。     

改进压缩性近似并导出新的硬球微扰理论表达式

提出在Barker与Henderson的压缩性近似推导中,相邻壳层之间的分子数应该相关,导出了相关系数和改进的二级微扰项,提高了高级微扰项在较高密度区的准确性。对二级以上的高级微扰项采用Barker与Henderson的近似方法,得到一个简单的微扰理论表达式,以硬球势为参考势,方阱势为微扰势,用一新的级数形式的径向分布函数导出了自由能、内能、比热、压缩因子的级数表达式。其四项截断式的计算结果与MC、MD计算机模拟值符合较好。     

Modeling the amorphous phase of comb‐like polymers

In this work, we apply a methodology recently developed by us to perform atomistic simulations of the amorphous phase of poly(α‐octadecyl β‐aspartate) and poly‐ (octadecyl acrylate). The simulation method, which is denoted SuSi/CB, combines the strength of an algorithm specially designed to generate atomistic models of dense amorphous polymers and the Configurational Bias Monte Carlo procedure. Modeling results reveal that poly(octadecyl acrylate) presents a tendency to adopt backbone helical conformations, while no trace of helicity was detected in the amorphous phase poly(α‐octadecyl β‐aspartate). Regarding the side chain organization, the paraffinic pool formed by the octadecyl side chains is slightly greater for the poly(acrylate) than for the poly(β‐aspartate). According to these features, it can be concluded that the small chemical differences between the two investigated polymers are enough to provide some distinctive structural features. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 953–966, 2006     

A Thermodynamic Model for Square-well Chain Fluid: Theory and Monte Carlo Simulation

A thermodynamic model for the freely jointed square-well chain fluids was developed based on the thermodynamic perturbation theory of Barker-Henderson, Zhang and Wertheim. In this derivation Zhang's expressions for square-well monomers improved from Barker-Henderson compressibility approximation were adopted as the reference fluid, and Wertheim's polymerization method was used to obtain the free energy term due to the bond connectivity. An analytic expression for the Helmholtz free energy of the square-well chain fluids was obtained. The expression without adjustable parameters leads to the thermodynamic consistent predictions of the compressibility factors, residual internal energy and constant-volume heat capacity for dimer, 4-mer, 8-mer and 16-mer square-well fluids. The results are in good agreement with the Monte Carlo simulation. To obtain the MC data of residual internal energy and the constant-volume heat capacity needed, NVT MC simulations were performed for these square-well chain fluids.     

分子体积及表面积的Monte Carlo模拟计算

建立了用Ｍｏｎｔｅ Ｃａｒｌｏ方法模拟计算ｖａｎ ｄｅｒ ｗａａｌｓ分子体积和表面积的算法，在一定的置信度条件下，可获得在指定置信限内的期望值，与Ｂｏｄｅｒ算法比较，此算法有更优的精度。     

Excess energy and equation of state of fluids with hard-core potential models from a second-order Monte Carlo perturbation theory

Monte Carlo simulations in the NVT ensemble of the reference hard-sphere fluid have been performed to obtain the “exact” first- and second-order terms in the inverse temperature expansion of the free energy of fluids with hard-core potentials. The results have been used to obtain parametrizations of the free energy of fluids with Sutherland potentials with variable range as well as for a fluid with a hard-core Lennard–Jones potential. The results for the excess energy and the equation of state are compared with simulation data available in the literature for these fluids.     

Asymptotic Functional Form Preservation Method for the Perturbation Theory: Application to Anharmonic Oscillators

The asymptotic functional form preservation method is developed for the perturbation theory to obtain the energy eigenvalues of anharmonic oscillators. The conventional energy perturbative series expansion for the anharmonic oscillator is strongly divergent even if the anharmonicity is small. Employing a transformation containing an unphysical parameter, we analytically continue this series expansion into a new series expansion applicable to all the range of the perturbation parameter. The unphysical parameter is determined by the principle of minimal sensitivity. This new series expansion is reduced to the conventional energy perturbative series expansion for small anharmonicity, and it preserves the correct asymptotic functional form when the perturbation parameter tends to infinity. Then, we use the full‐range energy series expansion to calculate the energy eigenvalues of the anharmonic oscillator. In addition to excellent energy eigenvalues obtained for the oscillator with small and strong anharmonicity, accurate energy eigenvalues can be obtained using the full‐range energy series expansion when the perturbation parameter tends to infinity.     

Perturbation Theory of Polymer Chains Revisited, 2—Intermolecular Excluded Volume of Random and Self‐Avoiding Walks

The intermolecular compatibility of 10⁷–10⁸ independent pair configurations of linear chains (chain length 64 ≤ N ≤ 8192) with and without intramolecular interaction on various lattices is checked and the intermolecular excluded volume u evaluated. From the (average) number of possible i‐tuples of overlaps in the pair configurations the parameters C_k of the perturbation theory are calculated. Differences between the various lattice types at finite N vanish completely for N → ∞. While the theoretical values of C₁ and C₂ were recovered within very narrow limits for chains without intramolecular interaction, markedly higher figures apply to self‐avoiding walks. The excluded volume u itself and higher C_k parameters are called upon to test several classical and renormalized perturbation theories.

     

Studies on the Adsorption of Asymmetrical Triblock Copolymers by Scheutjens-Fleer Theory and Monte Carlo Simulation

The adsorption of asymmetrical triblock copolymers from a non-selective solvent on solid surface has been studied by using Scheutjens-Fleer mean-field theory and Monte Carlo simulation method on lattice model. The main aim of this paper is to provide detailed computer simulation data, taking A8-kB20Ak as a key example, to study the influence of the structure of copolymer on adsorption behavior and make a comparison between MC and SF results. The simulated results show that the size distribution of various configurations and density-profile are dependent on molecular structure and adsorption energy. The molecular structure will lead to diversity of adsorption behavior. This discrepancy between different structures would be enlarged for the surface coverage and adsorption amount with increasing of the adsorption energy. The surface coverage and the adsorption amount as well as the bound fraction will become larger as symmetry of the molecular structure becomes gradually worse. The adsorption layer becomes thicker with increasing of symmetry of the molecule when adsorption energy is smaller but it becomes thinner when adsorption energy is higher. It is shown that SF theory can reproduce the adsorption behavior of asymmetrical triblock copolymers. However, systematic discrepancy between the theory and simulation still exists.The approximations inherited in the mean-filed theory such as random mixing and the allowance of direct back folding may be responsible for those deviations.     

Numerical Interchain Mean-Field Theory for the Specific Heat of the Bimetallic Ferromagnetically Coupled Chain Compound MnNi(NO2)4(en)2 (en = Ethylenediamine)

We present a detailed study of the field-dependent specific heat of the bimetallic ferromagnetically coupled chain compound MnNi(NO2)4(en)2, en = ethylenediamine. For this material, which in zero field orders antiferromagnetically below TN=2.45 K, small fields suppress magnetic order. Instead, in such fields, a double-peak-like structure in the temperature dependence of the specific heat is observed. We attribute this behavior to the existence of an acoustic and an optical mode in the spin-wave dispersion as a result of the existence of two different spins per unit cell. We compare our experimental data to numerical results for the specific heat obtained by exact diagonalization and Quantum Monte Carlo simulations for the alternating spin-chain model, using parameters that have been derived from the high-temperature behavior of the magnetic susceptibility. The interchain coupling is included in the numerical treatment at the mean-field level. We observe remarkable agreement between experiment and theory, including the ordering transition, using previously determined parameters. Furthermore, the observed strong effect of an applied magnetic field on the ordered state of MnNi(NO2)4(en)2 promises interesting magnetocaloric properties.     

用重整化群理论研究胶体模型体系的相行为

用yukawa势能函数表达胶体颗粒之间的吸引作用。用Duh-Mier-Y-Teran状态方 程表达液相Helmholtz自由能。用一阶微扰理论、固体硬球径向分布函数解析式和 改进的胞腔模型建立固相状态方程，结合建立的状态方程和重整化群理论。研究了 胶体模型体系的液-液相平衡和液-固相平衡。研究表明，颗粒之间色散作用量程参 数的变化对胶休到本世纪末茶杯 系的相行为有特殊需要影响。所得结果与分子模 拟数据吻合良好。