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.     

从统计力学推导流体状态方程(Ⅱ)——非球形多方阱势硬粒子微扰理论

本文从考虑真实分子的形状与势能出发,引进一新的用级数表示的径向分布函数形式,导出了任意形状硬粒子流体的级数状态方程.用此方程描述参考体系,用多方阱势来近似真实分子的势能曲线,采用Barker与Henderson的方法近似高级微扰项,导出了非球形多方阱势硬粒子微扰理论的通用表达式,以作为进一步导出实用状态方程的基础.     

共聚高分子体系的分子热力学模型

以共聚硬球链流体的分子热力学模型为基础，通过引入链节间方阱位能相互作用的贡献。建立了实际共聚高分子系统的分子热力学模型，对纯共聚高分子ＰＶＴ的关系结果，平均相对误差为０．２２％－０．８０％。     

Development of the semi-empirical equation of state for square-well chain fluid based on the Statistical Associating Fluid Theory (SAFT)

A semi-empirical equation of state for the freely jointed square-well chain fluid is developed. This equation of state is based on Wertheim’s thermodynamic perturbation theory (TPT) and the statistical associating fluid theory (SAFT). The compressibility factor and radial distribution function of square-well monomer are obtained from Monte Carlo simulations. These results are correlated using density expansion. In developing the equation of state the exact analytical expressions are adopted for the second and third virial coefficients for the compressibility factor and the first two terms of the radial distribution function, while the higher order coefficients are determined from regression using the simulation data. In the limit of infinite temperature, the present equation of state and the expression for the radial distribution function are represented by the Carnahan-Starling equation of state. This semi-empirical equation of state gives at least comparable accuracy with other empirical equation of state for the square-well monomer fluid. With the new SAFT equation of state from the accurate expressions for the monomer reference and covalent terms, we compare the prediction of the equation of state to the simulation results for the compressibility factor and radial distribution function of the square-well monomer and chain fluids. The predicted compressibility factors for square well chains are found to be in a good agreement with simulation data. The high accuracy of the present equation of state is ascribed to the fact that rigorous simulation results for the reference fluid are used, especially at low temperatures and low densities. This paper was presented at the 8th APCChE (Asia Pacific Confederation of Chemical Engineering) Congress held at Seoul between August 16 and 19, 1999.     

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     

基团贡献状态方程的开发与热力学模型参数的理论预测

热力学模型是研究流体相行为和热力学性质的重要工具。理论模型的有效应用离不开模型参数的确定。为赋予热力学模型的预测功能，目前的策略一是建立基团贡献(GC)状态方程(EOS)，二是探索热力学模型参数的理论预测方法。围绕先前开发的变阱宽方阱链流体状态方程(SWCF-VR)，采用基团贡献法思路获得了不同基团对模型参数的贡献值，建立了GC-SWCF方程，证实GC-SWCF方程能满意预测纯物质的密度。进一步将似导体屏蔽模型(COSMO)与SWCF结合，基于COSMO方法获得了192种有机化合物的SWCF方程的模型参数，这是一种不依赖实验数据确定模型参数的理论方法。发现COSMO+SWCF能较好地预测纯物质的密度。引入一个与温度无关的二元交互作用可调参数后，GC-SWCF与COSMO+SWCF都可应用于二元混合物密度与气液相平衡的计算中。     

Fiber length distribution and thermal,mechanical and morphological properties of thermally conductive polycarbonate/chopped carbon fiber composites

Chopped carbon fibers (CCFs) coated by poly(ethylene terephthalate) (PET) were treated using 3‐aminopropyltriethoxysilane (Si), and then used for fabricating thermally conductive polycarbonate/CCF (PC/(Si + PET)@CCFi) composites with various filler contents. Optical microscopy measurements indicated that CCF fillers in the composites had a wide length distribution and, with CCF content increasing, the mean fiber length and mean fiber aspect ratio steadily decreased. Compared to PC/(Si + PET)@CCF0, the molten flowability of composites declined. Thermogravimetric analysis and pyrolysis–gas chromatography–mass spectrometry characterizations showed that introducing CCFs could enhance the thermal stability of the composites and restrict the pyrolytic degradation of the polymer matrix. Moreover, both in‐plane and through‐thickness thermal conductivities increased with increasing CCF content. These conductivities at 50% CCF content reached 2.45 and 0.59 W m^?1 K^?1, and were improved by 11.25 and 1.95, respectively. Furthermore, the tensile and flexural properties of the composites continuously enhanced, accompanying decreased impact strength and elongation at break. Fractography revealed that fillers dispersed in matrix uniformly and a great many fiber cross‐sections and circular cavities coexisted in fracture surface, besides a clear interface and reduced long fibers. And the fracture behavior was mainly the breaking and peeling of fibers from matrix. © 2018 Society of Chemical Industry     

Investigations of polymer chains in oriented fluid phases with deuterium nuclear magnetic resonance

Deuterium nuclear magnetic resonance (D n.m.r.) is a potentially powerful technique for exploring molecular structural and dynamical properties of polymer chains in bulk fluids and concentrated solutions. A variety of systems can be investigated (the solid state, elastomeric networks, sheared polymer fluids, chain solutes in liquid crystal solvents, and polymeric liquid crystals), over a wide range of dimensions (local chain properties, rotational isomeric state parameters, behaviour between network junctions or entanglements, evolution of tube distributions, and domain sizes of homogeneous chain alignment). A coarse comparison of low molar mass liquid crystals with condensed phases of entangled polymer fluids and elastomeric networks illustrates the key features of the D n.m.r. technique and establishes a common framework for interpreting experiments.     

从统计力学推导流体状态方程(Ⅲ)——关于马丁-侯状态方程等的统计力学证明与解释

本文从多方阱非球形势硬粒子微扰理论出发,通过适当的近似与化简,导出了马丁-侯状态方程,从而使这个由经验提出的状态方程得到了统计力学的证明与解释.从多方阱非球形势硬粒子微扰理论出发,通过更粗略的近似也能得到范德华状态方程以及Barner与Adler改进的(?)offie状态方程.由理论分析,马丁-侯方程较为全面,不仅有高级微扰项,保留了多级密度展开式,同时取用了较精确的多级参考流体状态方程.     

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.     

RHEOLOGICAL BEHAVIOR OF POLYMER MELTS (I) UNIFIED MOLECULAR THEORY OF NON-LINEAR ISCOELASTICITY WITH CONSTRAINTS OF GAUSSIAN CHAIN ENTANGLEMENT FOR POLYMER MELTS

An approach with statistical mechanics and a unified molecular theory of non-linearviscoelasticity with constraints of Gaussian chain entanglement for polymer melts were proposed.Amultimode model structure for a single polymer chain with tail segments and N reversibleentanglement sites on the test polymer chain was developed.The probability distribution function ofthe end-to-end vector for a single polymer chain at entangled state and the viscoelastic free energyof deformation for polymer melts were calculated.Four types of stress-strain relationship and mem-ory function were derived from this theory.The above theoretical relationships were verified by experi-mental data of PS(polystyrene)and LDPE(low density polyethylene)melts.     

A GENERALIZED EQUATION OF STATE FOR POLAR AND NON-POLAR FLUIDS BASED ON FOUR-PARAMETER CORRESPONDING STATES THEOREM

A new generalized equation of state for polar and non-polar fluids based on the corresponding states theorem is developed, f n addition to two critical parameters, four parameters are required; two for the calculation of volumetric properties and two for the calculation of pressure and departure functions. Parameteres for more than 100 polar and non-polar fluids are given. Comparison with the existing generalized state equations showed that the new method, in general, shows a better agreement with the experimental data. The absolute average deviation is 0.48% for the vapor pressure and 0.32% for the saturated liquid volume.     

自由旋转珠杆链分子模型的Brown动力学模拟

利用聚合物分子理论,推导了自由旋转珠杆链分子模型在广义坐标下的伊藤型随机微分方程(朗之万方程),构造了相应的Brown动力学模拟算法,首次研究了该模型在定常剪切流和拉伸流中的动力学行为及其流变性质,并在微机上利用MATHE-MATICA软件实现了流动中高分子微观结构形态演变的动态显示.     

自由旋转珠杆链分子模型的Brown动力学模拟

利用聚合物分子理论,推导了自由旋转珠杆链分子模型在广义坐标下的伊藤型随机微分方程(朗之万方程),构造了相应的Brown动力学模拟算法,首次研究了该模型在定常剪切流和拉伸流中的动力学行为及其流变性质,并在微机上利用MATHE-MATICA软件实现了流动中高分子微观结构形态演变的动态显示.     

Calculation of surface tensions for liquid mixtures using the SWCF-VR EOS and Butler-type method

A generalized surface tension model for various types of liquid mixtures by coupling the equation of state for square-well chain fluids with variable ranges and Butler type method was presented. Transferable molecular parameters fitted from experimental pVT of pure fluids were used. The reliability of this model were tested with liquid mixtures including 87 conventional fluid mixtures, 20 aqueous alcohol-amine solutions, 12 ionic liquid solutions, 7 polymer solutions, and 4 liquid alloys. The overall average absolute deviations in correlations with one parameter for all binary mixtures, in predictions for all conventional binary mixtures except aqueous solutions and for all ternary mixtures are 1.94%, 1.82%, and 2.69%, respectively. The potential application of the model in simultaneously describing the phase equilibrium and surface tensions was partially verified. The results demonstrate that this model has an overall robustness and reliability in calculations of surface tensions for various liquid mixtures.     

变阱宽方阱链流体状态方程模拟制冷剂的汽液平衡

应用作者先前基于二阶微扰理论和PY2近似积分方程建立的可变阱宽方阱链流体状态方程模拟了纯制冷剂及其混合体系的汽液平衡。通过关联不同温度下制冷剂的饱和蒸气压和液体体积得到了18种纯制冷剂的分子参数,新方程计算的饱和蒸气压和液体体积总的平均偏差分别为1.11％和0.92％。结合简单混合规则,将此方程扩展到混合体系。研究发现,建立的方程可满意预测制冷剂二元混合体系除临界区附近外的汽液平衡,对两个三元体系汽液平衡的预测也取得了满意的效果,当引入一个与温度无关的可调参数时,关联精度大为提高,预示着新的方程可模拟制冷剂的汽液平衡。     

A new equation of state (hsft) based on fractal theory

This paper describes the molecular distribution of fluids by some fractal characteristics based on the current understandings of microstructures in fluids. The coordination relation was derived according to this fractal model, and the molecular mean potential function for simple square-well fluids was proposed. By applying this new mean potential function, a new equation of state (EOS) named HSFT was derived from statistical mechanics. Vapor pressures and saturated liquid densities of about 200 pure substances were correlated by the proposed model. Resulting equation parameters were further generalized by acentric factor ω and critical compressibility factor Zc. Saturated properties for 180 substances and enthalpies of vaporization for 115 substances, including compounds with strong polarity, were calculated by the generalized HSFT equation. Compared with several other equations of state, satisfactory results computed by HSFT equation imply that the generalized HSFT equation possesses better adaptability and reliability.     

A NEW EQUATION OF STATE (HSFT) BASED ON FRACTAL THEORY

This paper describes the molecular distribution of fluids by some fractal characteristics based on the current understandings of microstructures in fluids. The coordination relation was derived according to this fractal model, and the molecular mean potential function for simple square-well fluids was proposed. By applying this new mean potential function, a new equation of state (EOS) named HSFT was derived from statistical mechanics. Vapor pressures and saturated liquid densities of about 200 pure substances were correlated by the proposed model. Resulting equation parameters were further generalized by acentric factor ω and critical compressibility factor Zc. Saturated properties for 180 substances and enthalpies of vaporization for 115 substances, including compounds with strong polarity, were calculated by the generalized HSFT equation. Compared with several other equations of state, satisfactory results computed by HSFT equation imply that the generalized HSFT equation possesses better adaptability and reliability.     

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。