典型超支化高分子体系的统计热力学及其应用  

Statistical mechanics and thermodynamics for typical hyperbranched polymerization systems

作　　者：顾芳[1] 赵昨非 洪晓钟[3] 王海军[1] Fang Gu;Zuo-Fei Zhao;Xiao-Zhong Hong;Hai-Jun Wang(College of Chemistry and Environmental Science,Hebei University,Baoding 071002,China;College of Science,Langfang Normal University,Langfang 065000,China;College of Physical Science and Technology,Hebei University,Baoding071002,China)

机构地区：[1]河北大学化学与环境科学学院,保定071002 [2]廊坊师范学院理学院,廊坊065000 [3]河北大学物理科学与技术学院,保定071002

出　　处：《中国科学：化学》2021年第9期1168-1190,共23页SCIENTIA SINICA Chimica

基　　金：国家自然科学基金的长期支持。

摘　　要：以典型的超支化聚合反应体系为例概述了体系的热力学和统计力学性质,重点集中在平均分子量、均方回转半径及支化点密度等特征与热力学量间的关联,以期阐明超支化高分子空间结构与物理性质的调控机制.从空间关联的角度赋予重均聚合度以相应的物理解释,建立其与等温压缩系数的直接关系.通过子链分布导出均方回转半径和流体力学半径的解析形式,并利用高分子的邻接矩阵进行具体计算.在此基础上,从相变与临界现象的角度出发,解释了体系中相关物理量的标度行为,给出相应的广义标度律.为了优化超支化高分子的工业生产流程,引入生成函数方法系统地探讨了分批投料过程中的相关参数对平均高分子量的影响.此外,提出了基于生长代数的Monte Carlo模拟方案,用以辅助研究高分子结构与特征的对应关系.作为应用,揭示了环化效应、溶剂效应及非等活性等因素对聚合反应的影响.We summarize statistical thermodynamics of two typical polymerization systems to relate thermodynamic quantities to the properties of hyperbranched polymers(HBPs)such as average degree of polymerization(DP),radius of gyration,and branching density.An attempt is made to obtain the regulation mechanism of structure and properties of HBPs.Starting from the physical viewpoint,the isothermal compressibility has been associated with the weight average DP of polymers that is interpreted as the spatial correlation of monomers due to polymerization.The subchain is employed to derive the mean square radius of gyration and hydrodynamics radius,and a calculation is implemented in terms of the adjacent matrix of an HBP.Furthermore,the scaling behavior of the system is studied to give the generalized scaling law.The average properties of HBPs under the semi-batch mode are also presented by means of the generation function method.In addition,a Monte Carlo simulation method based on the growth generation is proposed,by which the spatial structure of an HBP can be easily analyzed in detail.As an application,the effect of cyclization,nonequal reactivity,and solvent quality on the polymerization is also carried out.

关 键 词：超支化高分子 统计热力学 平均聚合度 回转半径 广义标度律 

分 类 号：TQ317[化学工程—高聚物工业]