Radius of Gyration of Comb-shaped Copolymers by the Wormlike Chain Model:Theory and Its Applications to MPEG-type Polycarboxylate-type Superplasticizers

Yan-wei Wang; Hong-xia Zhao; Xin Shu; Yong Yang; Qian-ping Ran

doi:10.11777/j.issn1000-3304.2017.16363

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Radius of Gyration of Comb-shaped Copolymers by the Wormlike Chain Model:Theory and Its Applications to MPEG-type Polycarboxylate-type Superplasticizers

Research Article | 更新时间：2021-01-26

- Radius of Gyration of Comb-shaped Copolymers by the Wormlike Chain Model:Theory and Its Applications to MPEG-type Polycarboxylate-type Superplasticizers
- Acta Polymerica Sinica Issue 11, Pages: 1816-1831(2017)
- 作者机构：
  
  高性能土木工程材料国家重点实验室江苏苏博特新材料股份有限公司南京 211103
- 作者简介：
- 基金信息：
- DOI：10.11777/j.issn1000-3304.2017.16363
  CLC：
- Published：20 November 2017，
  
  Received：23 January 2017，
  
  Revised：4 March 2017，
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Yan-wei Wang, Hong-xia Zhao, Xin Shu, Yong Yang, Qian-ping Ran. Radius of Gyration of Comb-shaped Copolymers by the Wormlike Chain Model:Theory and Its Applications to MPEG-type Polycarboxylate-type Superplasticizers. [J]. Acta Polymerica Sinica (11):1816-1831(2017)
DOI：

Yan-wei Wang, Hong-xia Zhao, Xin Shu, Yong Yang, Qian-ping Ran. Radius of Gyration of Comb-shaped Copolymers by the Wormlike Chain Model:Theory and Its Applications to MPEG-type Polycarboxylate-type Superplasticizers. [J]. Acta Polymerica Sinica (11):1816-1831(2017) DOI： 10.11777/j.issn1000-3304.2017.16363.

摘要

利用蠕虫状链模型对梳状共聚物分子的均方回转半径进行了理论分析，建立了回转半径与主链轮廓长度、主链持久长度、侧链轮廓长度、侧链持久长度、侧链数目以及侧链沿主链的分布情况（均匀分布和梯度分布）之间的定量数学关系.在此基础上，以被称为"第一代聚羧酸系高性能减水剂"（以下简称为MPEG-type PCE）的甲基丙烯酸（MAA）/烯酸甲酯（MAA-MPEG）梳状共聚物分子为研究对象，结合实验数据，对其聚电解质主链的持久长度进行了分析，并考察了主侧链长度、刚柔性、侧链分布、接枝密度等分子结构参数对PCE回转半径的影响，最后对模型的局限性作简要说明.梳状共聚物分子的蠕虫状链模型物理图像简洁，参数意义明确，应用于PCE分子体系时较之前所报道的柔性链模型要更为合理，能够为分析PCE的分子结构与溶液构象和吸附构象之间的关系提供更科学的视角.

Abstract

The expression obtained by Nakamura

et al

. on the radius of gyration of regular comb-shaped copolymers

where both the backbone and the side chains are described by the wormlike chain (WLC) model

was reformulated. It was demonstrated that in certain limiting cases their result conforms to classical expressions of the radius of gyration for a linear WLC (the Benoit-Doty equation)

a symmetric star-shaped polymer with WLC arms (the Mansfield-Stockmayer equation)

and the branching parameters for symmetric star and regular comb-shaped

derived by Zimm

Stockmayer and Berry

Orofino

respectively

under the assumption of ideal Gaussian chain statistics. Depending on the synthesis method and monomer reactivity

comb-shaped copolymers often possess a non-even distribution of side chains along the polymer backbone. To understand the effects of side-chain distribution on the radius of gyration of comb-shaped copolymers

the method by Nakamura

et al

. was extended to the case where the side chains were not regularly distributed

but followed a gradient-type distribution

modelled using geometric progressions. On the application side

the afore-derived WLC theory was applied to comb-shaped copolymers made of a negatively charged poly(methacrylate acid) (PMAA) backbone

partially grafted with poly(ethylene glycol) (PEG) side chains

referred to as polycarboxylate-based superplasticizers

or MPEG-type PCEs

in cement and concrete research. Particular focus was placed on rational choices of model parameters

which is an essential step in applying theory to practice. Based on data in the literature and model fitting

methods and recommended parameter values were developed for converting experimental characteristics of MPEG-type PCEs to their corresponding WLC model parameters. Furthermore

effects of backbone stiffness

side-chain distribution

side-chain persistence length

and grafting density on the unperturbed radius of gyration were explored in detail in the relevant range of parameter values of MPEG-type PCEs. The present work may shed light on how to arrive at a compromise between a mathematically tractable theory and its application to complicated industrial polymeric products. Although the present model is still rather idealized in the sense that it does not take into account of detailed monomer-monomer

monomer-solvent interactions such as the often discussed excluded volume and electrostatic interactions

it can serve as an important reference for assessing the contributions of those complicated interactions in further studies.

关键词

梳状共聚物蠕虫状链模型回转半径持久长度聚羧酸减水剂

Keywords

Comb-shaped copolymerWormlike chainRadius of gyrationPersistence lengthPolycarboxylate-type superplasticizers

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