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Dynamics of Polymeric Fluids：Part Ⅱ The Molecular Theory of Die Swell： Correlation of Ultimate Die Swelling Effect to the Molecular Parameters and the Operational Variables

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Journal of Materials Science & Technology 2006年第5期22卷 664-676页

作者： mingshi song Qiang XU Guixian HU Sizhu WU Key Laboratory of Science and Technology of Controlled Chemical Reactions Beijing University of Chemical TechnologyBeijing 100029 China

A general expression for the correlation of the simple shear （tanφ） to the molecular parameters and the shear rate （·↑γ） was deduced. It shows that the simple shear （tanφ） may be resolved into free recoil （recoverable strain） and viscous heating （unrecoverable strain）. The magnitudes of the simple shears for recoil （tanφE） and （tanφv） for viscous heating not only depended on the molecular parameters and the operational variables, but also on the exponential fractions of the recoverable （1--↑W·↑γ） and unrecoverable （-↑W·↑γ） conformations for recoil and viscous heating. Therefore the magnitudes of the simple shears （tanφE） for recoil and （tanφv） for viscous heating are, respectively, expressed as the partition function to the （1--↑W·↑γ）th power and the partition function to the （-↑W·↑γ）th power. Thus correlations of the total recoil and the ultimately recoverable strains to the molecular parameters [n′, α, η0, GN^0 and （1--↑W·↑γ）] and the operational variables （·↑γ, （L/D） and tr） were deduced respectively, which show that at very different shear rates （0≤·↑γ≤∞） the polymeric liquids may exhibit a very different viscoelastic behaviors. After introducing the uniform two-dimensional extension, the definition of swelling ratio and the ratio of L to D [De=（L/D）], two expressions for the ultimate die swelling effect and the ultimate extrudate swelling ratio BEVT5 to the molecular parameters [n′, α, η0, GN^0 and （1--↑W·↑γ）] and the operational variables （·↑γ, （L/D） and tr） were obtained. The two correlation expressions were verified by the experimental data of high-density polyethylene （HDPE） which shows that the two correlation expressions can be used to predict the correlations of the ultimate extrudate swelling behaviors of polymeric liquids to the molecular parameters and the operational variables.

关键词： Die swell Viscoelastic recoil Entanglement

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Dynamics of Polymeric Fluids 1. The Molecular Theory of Die Swell:A Set of Equation on Swelling Ratio in Extrudates

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Journal of Materials Science & Technology 2006年第1期22卷 93-107页

作者： mingshi song Guixian HU Zhihong YANG Qiang xu Sizhu WU Key Laboratory of Science and Technology of Controlled Chemical Reactions Beijing University of Chemical TechnologyBeijing 100029 China

The structural model of the multiple-transient networks and the mechanism of the multiple-reptation entangled chains due to the dynamic reorganization in the entangled sites were extensively applied on the die swell of polymeric liquids in the steady simple shear flow. The total （recoverable and unrecoverable） viscoelastic free energy of deformation and flow, the constitutive equation and the expression of the simple shear （tanψ） were deduced from the conformational probability distribution function of the entangled polymer chains. It found that：（1） the magnitudes of simple shear （tanψ） depended not only on the free recoil （or recoverable strain） but also on the viscous heating （or unrecoverable strain）; （2） the total recoil may be resolved into the instantaneous and delayed recoil. Based on these facts, the functions of the partition and two experiential fractions of the recoverable （1-Wγ） and the unrecoverable （Wγ） conformations for the recoil and viscous heating of polymeric liquids were defined correspondingly. Then the correlation of the instantaneously and ultimately （or total） recoverable strains to the （N1/T12）w and the fraction of trans-form conformation was obtained. After introducing the condition of uniform two-dimensional extension （αx=αy=α, αz=α^-2） and the swell ratio （B=α）, two sets of equations on the instantaneous and ultimate swelling ratios （BE, BEVT） were obtained, and a method to determine the fraction of the recoverable transform conformation were proposed, The equations of BE and BE5 were verified by the experimental data of HDPE （high denisity polyethylene） at two different high temperatures. It shows that the molecular theory of die swell can be used to predict the correlation of the swelling to the （NI/TI2）w and the fraction of trans-form conformation.

关键词： Die swell Entanglement Viscoelastic recoil

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Correlation of cooperatively localized rearrangement on the "fluidized domain" in glass substances (or polymers) to their fragility Ⅲ:Theory of dynamic fragility at isochoric state

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Science China(Physics,Mechanics & Astronomy) 2011年第3期54卷 420-436页

作者： JIN Yan song mingshi HU GuiXian WU DaMing School of Materials Science and Engineering Beijing University of Chemical Technology Beijing 100029 China School of Mechanical and Electrical Engineering Beijing University of Chemical Technology Beijing 100029 China

A set of universal equations on the reduced stress relaxation modulus with K-W-W stretched exponential function has been derived from the dynamics of α and β structural relaxation processes. In the present work, the K-W-W decay function is used to define the three types of relaxations (single α, single β relaxation and α-β co-relaxation), then their average times of relaxation are theoretically calculated from the reduced shear stress relaxation modulus and the relaxation time spectrum function H(τ). When the average time of co-relaxation, the reference temperatures (ficitive Tf and glass transition Tg) and the isostructural parameter achieved from the conditions of isostructural glass state are introduced into the reduced shear stress relaxation modulus (GT) under the equilibrium state, a set of correlations between isochoric fragility index (mvα, mvβ and mvαβ) and the coupling strength (α and β) under the reference temperatures are derived from the exact definition of isochoric fragility. So the theory of dynamic fragility for glass substances at isochoric state is developed. The theory can predict the following main features of structural relaxations and behavior of isochoric fragility: the temperature dependence of peak relaxation frequency exhibits a bifurcation with a pair of single α and single β relaxations; the temperature dependence of Stickel equation on 1/T exhibits two crossovers with VFTH(1) and VFTH(2) at the temperatures of Tf and Tg regime; there are two linear correlations between isochoric fragility index (mvα and mvβ) and the coupling strength. Fine agreements between the theoretical calculation and experimental results are obtained.

关键词： isochoric fragility fluidized domain constituent chains &alpha and &beta relaxation dynamics of structural relaxation reduced stress relaxation modulus

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Rheological Behaviour for Polymer Melts and Concentrated SolutionsPart Ⅱ: Material Function with Nagai Chain Constraints and Determination of Their Parameters from Flow Curves

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Journal of Materials Science & Technology 1995年第2期11卷 141-152页

作者： mingshi song Sizhu WU and Xiuyun DU(Research Institute of Polymeric Materials, Beijing University of Chemical Technology, Beijing, 100029, China) Beijing Univ of Chemical Technology Beijing China

An integral constitutive equation and a set of material functions for describing the strain history of polymer melts were formulated in terms of the Cauchy-Green and Finger tensors. A simple memory function and the dependence of ηo and τt on M3.4 were derived from the theory of non-linear viscoelasticity with constraints of entanglements for polymer melts and substituted into the Oldroye-Walters-Fredickson constitutive equation. An integral constitutive equation for polymer melts was consequently obtained. Some material functions of the constitutive equation related to certain 'test flow' are examined as follows : (1) simple steady shear flow; (2) steady elongation flow; (3) small-amplitude oscillatory shear flow; (4) stress growth upon the inception of steady shear elongation flow; (5) stress relaxation (modulus and compllance). These theoretical relations for simple steady shear flow were compared with experimental data from our laboratory and references for various polymer melts and concentrated solutions. A good agreement between the theory and experiment was achieved.

关键词： LDPE Material Function with Nagai Chain Constraints and Determination of Their Parameters from Flow Curves Rheological Behaviour for Polymer Melts and Concentrated SolutionsPart Flow GR

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Rheological Behavior for Polymer Melts and Concentrated Solutions——Part Ⅶ: A Quantitative Verification for the Molecular Theory of Non-linear Viscoelasticity with Entanglement Constraints in Polymer Melts

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Journal of Materials Science & Technology 2001年第3期17卷 375-382页

作者： mingshi song, Chen ZHANG and Guixian HU Research Institute of Polymeric Materials, Beijing University of Chemical Technology, Beijing 100029, China E-mail: wangzhchen@*** Res. Inst. of Polymeric Mat. Beijing Univ. of Chem. Technol. Beijing 100029 China

Based on the molecular theory of non-linear viscoelasticity with constrained entanglements in polymer melts, the material functions in simple shear flow were formulated, the theoretical relations between. eta((gamma) over dot), psi (10)((gamma) over dot) and shear rate ((gamma) over dot), and topologically constrained dimension number n ' and a were derived. Linear viscoelastic parameters (eta (0) and G(N)(0)) and topologically constrained dimension number (n ' a and )over bar>) as a function of the primary molecular weight (M-n), molecular weight between entanglements (M-C) and the entanglement sites sequence distribution in polymer chain were determined. A new method for determination of viscoelastic parameters (eta (0), psi (10), G(N)(0) and J(e)(0)), topologically constrained dimension number (n ', a and v) and molecular weight (M-n, M-c and M-e) from the shear flow measurements was proposed. It was used to determine those parameters and structures of HDPE, making a good agreement between these values and those obtained by other methods. The agreement affords a quantitative verification for the molecular theory of nonlinear viscoelasticity with constrained entanglement in polymer melts.

关键词： Rheological Behavior for Polymer Melts and Concentrated Solutions A Quantitative Verification for the Molecular Theory of Non-linear Viscoelasticity with Entanglement Constraints in Polymer Melts Part

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Rheological Behaviour for Polymer Melts and Concentrated Solutions Part Ⅰ:A New Multiple Reptation Model to Predict the Nonlinear Visco-elasticity with Nagai Chain Constraints in Entangled Polymer Melts

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Journal of Materials Science & Technology 1995年第1期11卷 15-30页

作者： mingshi song and Sizhu WU(Dept. of Polymer Science, Beijing University of Chemical Technology Beijing, 100029, China)

An approach of stochastically statistical mechanics and a unified molecular theory of nonlinear viscoelasticity with constraints of Nagai chain entanglement for polymer melts have been proposed. A multimode model structure for a single polymer chain with n tail segments and N reversible entanglement sites on the test polymer chain is developed. Based on the above model structure and the mechanism of molecular flow by the dynamical reorganization of entanglement sites, the probability distribution function of the end-to-end vectr for a single polymer chain at entangled state and the viscoelastic free energy of deformation for polymer melts are calculated by using the method of the stochastically statistical mechanics. The four types of stress-strain relation and the memory function are derived from this thery. The above theoretical relations are verified by the experimentaf data for various polymer melts. These relations are found to be in good agreement with the experimental results

关键词： Rheological Behaviour for Polymer Melts and Concentrated Solutions Part A New Multiple Reptation Model to Predict the Nonlinear Visco-elasticity with Nagai Chain Constraints in Entangled Polymer Melts

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均聚物结晶与熔融化转变的稳态和亚稳态统计理论 III. 分子分凝统计结晶动力学~熔体内结晶增长速率的一般化表征和它们对生长机制的依赖性

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Chinese Journal of Chemical Physics 2005年第5期18卷 197-210页

作者：宋名实胡桂贤王海侨李效玉北京化工大学可控化学反应科学与技术基础教育部重点实验室北京100029

首先对微晶粒尺寸增长速率的表征进行总结.从微晶核和粒—高分子链组网络结构特点(高分子链组是微晶核和微晶粒同连接链段的复合体)同增长速率间的三个相关性的特征: ①晶核和晶粒加大同连接链段缩短的并存性; ②微晶核和粒表面上连接... 详细信息

首先对微晶粒尺寸增长速率的表征进行总结.从微晶核和粒—高分子链组网络结构特点(高分子链组是微晶核和微晶粒同连接链段的复合体)同增长速率间的三个相关性的特征: ①晶核和晶粒加大同连接链段缩短的并存性; ②微晶核和粒表面上连接链段的缩短机制存有简并性; ③微晶粒内和粒表面上stem的反顺式构象共存性出发.建议了一种评估和计算微晶粒尺寸增长速率的新方法和原则,基于该种计算方法和原则用统计力学和动力学相结合法推导出了高分子熔体内几种不同结晶生长机制(近邻折叠、近邻伸直分凝和近邻折叠同近邻伸直分凝并存等生长方式)下微晶粒—高分子链组中微晶粒数增长速率和微晶粒尺寸增长速率动力学方程.

关键词：结晶生长机制结晶生长动力学晶粒数增长速率晶粒尺寸增长速率

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Rheological Behaviour for Polymer Melts and Concentrated Solutions Part Ⅲ: A New Multiple Entanglement Model to Predict the Dependence of Linear Viscoelastic Function (η_0, Ψ_(10)~0,η_(ext)~0) on the Ranges of Primary Molecular Weights and the Species of Polymers

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Journal of Materials Science & Technology 1995年第3期11卷 197-208页

作者： mingshi song and Jincai YANG (Research Institute of Polymeric Materials, Beijing University of Chemical Technology, Beijing, 100029, China)Yiding SHEN(North West Institute of Light Industry, Shanxi Xianyang, 712087, China)

It is shown theoretically that the viscoelasticity of polymer melts is determined by three combining factorst they are the primary molecular weight and its distribution, the number of entanglement sites on polymer chain and the sequence distribution of constituent chains in entanglement spacings. A unified quantity for the three combing factors is the average constrained dimensional number of constituent chains in the long entanglement spacings (v). A new relation of v to the primary molecular weight and the number of testing polymers were derived from the multiple entanglement and reptation model, and a new method for determining v was proposed. The dependences of linear viscoelastic functions on the primary molecular weight and its distribution were derived by the statistical method. When Mn=6Me to 18 Me, the values of (v) can range from 3.33 to 3.70. Their values are in a good agreement with the experiment data, and it can slightjy vary with the different species of polymers and the different ranges of molecular weight of polymers

关键词： exp ext A New Multiple Entanglement Model to Predict the Dependence of Linear Viscoelastic Function Rheological Behaviour for Polymer Melts and Concentrated Solutions Part

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浅析摔跤运动员的战术意识及临场运用

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哈尔滨体育学院学报 2005年第3期23卷 118-119,123页

作者：宋明仕大庆体育运动学校黑龙江大庆163311

摔跤运动是一项徒手对抗运动,竞争激烈、身体对抗性强。一名优秀的运动员,要做到有勇有谋,具体情况具体安排制胜的战术,灵活运用,力胜智取。以国内12名优秀摔跤运动员为研究对象,采用文献研究、现场观察与统计的研究方法,针对运动员的... 详细信息

摔跤运动是一项徒手对抗运动,竞争激烈、身体对抗性强。一名优秀的运动员,要做到有勇有谋,具体情况具体安排制胜的战术,灵活运用,力胜智取。以国内12名优秀摔跤运动员为研究对象,采用文献研究、现场观察与统计的研究方法,针对运动员的战术意识及临场运用的重要作用作了论迷。为提高我国摔跤运动员的战术意识及临场运用水平作以参考。

关键词：摔跤运动员战术意识临场运用

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前置屏幕式光学前轮定位仪结构分析及性能评定

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汽车技术 1988年第5期 14-23页

作者：李明石宋魁武湖北汽车工业学院武汉汽车测试设备研究所

推算了前置屏幕式光学前轮定位仪的特性方程,给出了台架验证结果,认定这类定位仪的设计存在原则性错误。

关键词：前轮定位一置仪结构误差

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