中文摘要：

针对被称为＂第一代聚羧酸高性能减水剂＂（以下简称为MPEG-type PCE）的甲基丙烯酸（MAA）/烯酸甲酯（MAA-MPEG）梳状共聚物分子,从高分子物理基础理论出发,构建等效自由连接链模型,结合前人的理论结果和实验数据,得到了MPEG-type PCE分子的回转半径、流体力学半径及其相应的支化参数的数学表达式.在此基础上,报道了以下三方面的工作：首先,将计算结果与文献中的实验结果进行比较,检验模型的合理性;其次,利用所建立的数学模型考察主链分子量、侧链分子量和侧链接枝密度对PCE分子的回转半径和流体力学半径的影响;最后,结合近年来发展的体积排除色谱分离理论,对PCE分子的真实分子量与其常规体积排除色谱＂表观分子量＂（又被称为GPC分子量）两者之间的差异进行了分析.本文所提出的计算模型和数学表达式没有不确定的指前因子,可用来估算MPEG-type PCE分子在稀水溶液中的尺寸以及根据其GPC分子量估算真实分子量.

英文摘要：

A simple ＂equivalent freely-jointed chain＂ model, parameterized with literature data on the persistence length of linear poly（methacrylic acid）（PMA） and poly（ethylene oxide）（PEO）, and the molecular weight dependence of the radius of gyration of linear PEO in aqueous solution, is developed for the so-called MPEG-type comb-shaped polycarboxylate ester-or ether-based superplasticizers（PCEs）. The model yields analytical expressions of the radius of gyration, the hydrodynamic radius, as well as their respective branching parameters and the characteristic size ratio of the radius of gyration to the hydrodynamic radius as a function of backbone molecular weight, side chain molecular weight, and the number of side chains, assumed to be evenly distributed along the polymer backbone, in the continuum limit. Our calculations and experimental results in the literature showed a fairly good agreement, especially when a correction factor of magnitude 1.1 for the radius of gyration and of 1.4 for the hydrodynamic radius were taken into account. After model validation, more predictions were made based on this simple model. Results of the radius of gyration and the hydrodynamic radius were presented as a function of the molecular weight of the PMA backbone, the molecular weight of the PEO side chains, and the molar ratio of methacrylic acid to polyalkyleneglycol methacrylate（known as the C/E ratio）. It was found that the ratio of the radius of gyration to the hydrodynamic radius of PCEs fell mostly in the range of 0.85 to 1.0, notably less than those commonly found for linear polymers. To further facilitate applications of our theoretical model in practice, predictions were made to the ratio of the apparent molecular weight measured in aqueous size exclusion chromatography by conventional column calibration using linear poly（ethylene oxide） polymer standards to the true molecular weight measured by e.g., light scattering, by assuming that polymers having the same retention volume had approximately t