高分子材料微观结构及性质的积分方程理论研究
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摘要
近年来，积分方程理论(IET)成为国际上研究高分子体系结构和热力学性质的主要理论方法之一，是物理学界、高分子学界和化工界的一个热门研究领域。本工作采用高分子参考作用点模型理论(PRISM理论)研究了高分子及高分子纳米复合材料的结构和热力学性质，填补了国内用积分方程理论研究高分子材料的空白，为今后国内研究高分子体系开辟了一个新的方向。主要成果为：
详细介绍了高分子参考作用点模型理论的基本理论框架和模型构建，讨论了各种计算高分子链分子内结构因子的方法和PRISM理论中常用的几种闭合条件，并对这些方法和闭合条件进行了比较和评价。详细介绍了用离散Fourier变换和快速Fourier变换求解PRISM积分方程的两种数值计算方法。
结合PRISM理论、MD分子模拟和变分法，得到了可以描述聚苯乙烯熔体的单点半柔性链模型，提出了一个研究实际聚合物体系的有效方法。该模型能够抓住复杂的无规聚苯乙烯熔体的主要结构信息，可以半定量的描述各种条件下无规聚苯乙烯熔体的分子间相关函数、分子内相关函数、溶解度参数和x-光散射强度等结构和热力学性质，并得到了MD数据和实验数据的支持。
结合PRISM理论和MD模拟，提出了一个8-链节模型来研究无规聚苯乙烯熔体的各种性质，PRISM理论计算需要的分子内结构因子由MD模拟提供。用PRISM理论成功预测了无规聚苯乙烯熔体的各种微观的相关函数和结构因子，预测结果与MD模拟数据定量一致。此外，还用PRISM理论预测了无规聚苯乙烯熔体的溶解度参数和x-光散射强度等宏观性质，计算结果与实验数据定量一致。
采用PRISM理论研究了链状高分子纳米复合材料的结构和等效相互作用。用MD模拟数据验证了PRISM理论描述高分子纳米复合材料的可靠性。首次用PRISM理论预测了在非零的纳米颗粒体积分率下链状高分子纳米复合材料的结构和等效相互作用，系统的考察了纳米颗粒的体积分率、链状高分子的聚合度以及纳米颗粒-单体粒径比对体系各种性质的影响。
首次采用PRISM理论研究了星型高分子纳米复合材料的结构和等效相互作用。系统的研究了纳米颗粒-单体吸引力、纳米颗粒的体积分率、星型高分子的臂数、臂长以及纳米颗粒-单体粒径比等各种因素的影响。发现了星型高分子纳米复合材料的两种不同的凝聚方式：直接凝聚和桥接凝聚。详细讨论了高分子的整体构型和高分子-纳米颗粒的吸引力之间的相互作用对体系中纳米颗粒和星型高分子堆积状态的影响。
Integral equation theory (IET) has been employed recently to study the structure and thermodynamics properties of polymer systems. It is a very attractive field in physics, polymer science and chemical engineering. In this work, the polymer reference interaction site model theory (PRISM) is used to investigate the structure and thermodynamics properties in polymer and polymer nanocomposites, which is the first time in China to use integral equation theory to study the polymer systems. The main results obtained are:
The PRISM theory is introduced in detail. Different kinds of computationally convenient methods for determining the intramolecular structure factors are discussed and evaluated extensively, together with the usual closure approximations used in PRISM theory. The two numerical methods to solve PRISM integral equations are introduced based on the Discrete Fourier Transformation and Fast Fourier Transformation.
Combining PRISM theory, MD simulation and Variational method, a single-site semi flexible model is proposed to describe atactic polystyrene (aPS) melt. This is a reasonable method to investigate real polymer systems. The semiflexible model can capture the main features of aPS, and can semi-quantitatively describe the intermolecular correlation function, intramolecular correlation function, solubility parameters and x-ray scattering intensity for real aPS melt. Good agreement between theory and MD simulation is obtained.
An eight-site model is proposed to further describe aPS melt, where the intramolecular structure factors needed in PRISM calculations are obtained from MD simulations. The PRISM theory successfully predicts various microscopic information such as correlation functions and structure factors, and macroscopic properties such as solubility parameters and x-ray scattering intensity of real aPS melt. Quantitative agreements among theory, MD simulation and experiments are obtained.
The PRISM theory is used to study chain polymer nanocomposite melts. The theory is reliable to describe the structure and effective interactions in chain polymer nanocomposite melts which agree quantitatively with the MD simulations. Then the PRISM theory is firstly employed to predict the properties of the polymer nanocomposites where the particle volume fractions are nonzero. The roles of the particle volume fraction, degree of polymerization, and nanoparticle-monomer size ratio are systematically investigated.
The PRISM theory is used to study the structure and effective interactions in star polymer nanocomposite melts. The influences of thenanoparticle-monomer attraction strength, particle volume fraction, arm number, arm length, and nanoparticle-monomer size ratio are systematically studied. Two types of aggregation are observed in star polymer nanocomposite melts: the contact aggregation and the bridging aggregation. The different stable states of organization between nanoparticles are extensively discussed according to the interplay between the star architecture and the nanoparticle-monomer attractive interactions.
详细介绍了高分子参考作用点模型理论的基本理论框架和模型构建，讨论了各种计算高分子链分子内结构因子的方法和PRISM理论中常用的几种闭合条件，并对这些方法和闭合条件进行了比较和评价。详细介绍了用离散Fourier变换和快速Fourier变换求解PRISM积分方程的两种数值计算方法。
结合PRISM理论、MD分子模拟和变分法，得到了可以描述聚苯乙烯熔体的单点半柔性链模型，提出了一个研究实际聚合物体系的有效方法。该模型能够抓住复杂的无规聚苯乙烯熔体的主要结构信息，可以半定量的描述各种条件下无规聚苯乙烯熔体的分子间相关函数、分子内相关函数、溶解度参数和x-光散射强度等结构和热力学性质，并得到了MD数据和实验数据的支持。
结合PRISM理论和MD模拟，提出了一个8-链节模型来研究无规聚苯乙烯熔体的各种性质，PRISM理论计算需要的分子内结构因子由MD模拟提供。用PRISM理论成功预测了无规聚苯乙烯熔体的各种微观的相关函数和结构因子，预测结果与MD模拟数据定量一致。此外，还用PRISM理论预测了无规聚苯乙烯熔体的溶解度参数和x-光散射强度等宏观性质，计算结果与实验数据定量一致。
采用PRISM理论研究了链状高分子纳米复合材料的结构和等效相互作用。用MD模拟数据验证了PRISM理论描述高分子纳米复合材料的可靠性。首次用PRISM理论预测了在非零的纳米颗粒体积分率下链状高分子纳米复合材料的结构和等效相互作用，系统的考察了纳米颗粒的体积分率、链状高分子的聚合度以及纳米颗粒-单体粒径比对体系各种性质的影响。
首次采用PRISM理论研究了星型高分子纳米复合材料的结构和等效相互作用。系统的研究了纳米颗粒-单体吸引力、纳米颗粒的体积分率、星型高分子的臂数、臂长以及纳米颗粒-单体粒径比等各种因素的影响。发现了星型高分子纳米复合材料的两种不同的凝聚方式：直接凝聚和桥接凝聚。详细讨论了高分子的整体构型和高分子-纳米颗粒的吸引力之间的相互作用对体系中纳米颗粒和星型高分子堆积状态的影响。
Integral equation theory (IET) has been employed recently to study the structure and thermodynamics properties of polymer systems. It is a very attractive field in physics, polymer science and chemical engineering. In this work, the polymer reference interaction site model theory (PRISM) is used to investigate the structure and thermodynamics properties in polymer and polymer nanocomposites, which is the first time in China to use integral equation theory to study the polymer systems. The main results obtained are:
The PRISM theory is introduced in detail. Different kinds of computationally convenient methods for determining the intramolecular structure factors are discussed and evaluated extensively, together with the usual closure approximations used in PRISM theory. The two numerical methods to solve PRISM integral equations are introduced based on the Discrete Fourier Transformation and Fast Fourier Transformation.
Combining PRISM theory, MD simulation and Variational method, a single-site semi flexible model is proposed to describe atactic polystyrene (aPS) melt. This is a reasonable method to investigate real polymer systems. The semiflexible model can capture the main features of aPS, and can semi-quantitatively describe the intermolecular correlation function, intramolecular correlation function, solubility parameters and x-ray scattering intensity for real aPS melt. Good agreement between theory and MD simulation is obtained.
An eight-site model is proposed to further describe aPS melt, where the intramolecular structure factors needed in PRISM calculations are obtained from MD simulations. The PRISM theory successfully predicts various microscopic information such as correlation functions and structure factors, and macroscopic properties such as solubility parameters and x-ray scattering intensity of real aPS melt. Quantitative agreements among theory, MD simulation and experiments are obtained.
The PRISM theory is used to study chain polymer nanocomposite melts. The theory is reliable to describe the structure and effective interactions in chain polymer nanocomposite melts which agree quantitatively with the MD simulations. Then the PRISM theory is firstly employed to predict the properties of the polymer nanocomposites where the particle volume fractions are nonzero. The roles of the particle volume fraction, degree of polymerization, and nanoparticle-monomer size ratio are systematically investigated.
The PRISM theory is used to study the structure and effective interactions in star polymer nanocomposite melts. The influences of thenanoparticle-monomer attraction strength, particle volume fraction, arm number, arm length, and nanoparticle-monomer size ratio are systematically studied. Two types of aggregation are observed in star polymer nanocomposite melts: the contact aggregation and the bridging aggregation. The different stable states of organization between nanoparticles are extensively discussed according to the interplay between the star architecture and the nanoparticle-monomer attractive interactions.
引文
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