{"title":"稳态自由基聚合过程中分子量分布的解析表达式","authors":"Shenhua Jiao, Rui Liu, Xiaowen Lin, Xi Chen","doi":"10.1016/j.polymer.2025.128427","DOIUrl":null,"url":null,"abstract":"<div><div>The Flory distribution is well known for describing the chain length distribution (CLD) and the molecular weight distribution (MWD) of polymers. However, it cannot be used for many polymerizations with complex reaction mechanisms, such like bi-molecular termination and reversible reactions involved mechanisms. In this work, a more general formula is proposed to extend the Flory distribution. Analytical expressions for CLD and MWD are derived for various radical polymerization systems, including free radical polymerization (FRP), atom-transfer radical polymerization (ATRP), and reversible addition–fragmentation chain transfer (RAFT) polymerization. The results obtained using the derived analytical expressions are further validated by comparison with numerical solutions of other modeling methods, confirming the efficiency and accuracy of this derivation study.</div></div>","PeriodicalId":405,"journal":{"name":"Polymer","volume":"328 ","pages":"Article 128427"},"PeriodicalIF":4.1000,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analytical expressions for molecular weight distribution in steady-state radical polymerizations\",\"authors\":\"Shenhua Jiao, Rui Liu, Xiaowen Lin, Xi Chen\",\"doi\":\"10.1016/j.polymer.2025.128427\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The Flory distribution is well known for describing the chain length distribution (CLD) and the molecular weight distribution (MWD) of polymers. However, it cannot be used for many polymerizations with complex reaction mechanisms, such like bi-molecular termination and reversible reactions involved mechanisms. In this work, a more general formula is proposed to extend the Flory distribution. Analytical expressions for CLD and MWD are derived for various radical polymerization systems, including free radical polymerization (FRP), atom-transfer radical polymerization (ATRP), and reversible addition–fragmentation chain transfer (RAFT) polymerization. The results obtained using the derived analytical expressions are further validated by comparison with numerical solutions of other modeling methods, confirming the efficiency and accuracy of this derivation study.</div></div>\",\"PeriodicalId\":405,\"journal\":{\"name\":\"Polymer\",\"volume\":\"328 \",\"pages\":\"Article 128427\"},\"PeriodicalIF\":4.1000,\"publicationDate\":\"2025-04-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Polymer\",\"FirstCategoryId\":\"92\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0032386125004136\",\"RegionNum\":2,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"POLYMER SCIENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Polymer","FirstCategoryId":"92","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0032386125004136","RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"POLYMER SCIENCE","Score":null,"Total":0}
Analytical expressions for molecular weight distribution in steady-state radical polymerizations
The Flory distribution is well known for describing the chain length distribution (CLD) and the molecular weight distribution (MWD) of polymers. However, it cannot be used for many polymerizations with complex reaction mechanisms, such like bi-molecular termination and reversible reactions involved mechanisms. In this work, a more general formula is proposed to extend the Flory distribution. Analytical expressions for CLD and MWD are derived for various radical polymerization systems, including free radical polymerization (FRP), atom-transfer radical polymerization (ATRP), and reversible addition–fragmentation chain transfer (RAFT) polymerization. The results obtained using the derived analytical expressions are further validated by comparison with numerical solutions of other modeling methods, confirming the efficiency and accuracy of this derivation study.
期刊介绍:
Polymer is an interdisciplinary journal dedicated to publishing innovative and significant advances in Polymer Physics, Chemistry and Technology. We welcome submissions on polymer hybrids, nanocomposites, characterisation and self-assembly. Polymer also publishes work on the technological application of polymers in energy and optoelectronics.
The main scope is covered but not limited to the following core areas:
Polymer Materials
Nanocomposites and hybrid nanomaterials
Polymer blends, films, fibres, networks and porous materials
Physical Characterization
Characterisation, modelling and simulation* of molecular and materials properties in bulk, solution, and thin films
Polymer Engineering
Advanced multiscale processing methods
Polymer Synthesis, Modification and Self-assembly
Including designer polymer architectures, mechanisms and kinetics, and supramolecular polymerization
Technological Applications
Polymers for energy generation and storage
Polymer membranes for separation technology
Polymers for opto- and microelectronics.