When Mayo falls short (Ctr ≫ 1): the use of cumulative chain length distribution data in the determination of chain transfer constants (Ctr) for radical polymerizations

2020 ◽  
Vol 11 (26) ◽  
pp. 4281-4289
Author(s):  
Matt K. Donald ◽  
Stefan A. F. Bon
Keyword(s):  
Molecular Weight ◽  
Free Radical ◽  
Chain Length ◽  
Weight Distribution ◽  
Chain Transfer ◽  
Length Distribution ◽  
Distribution Data ◽  
Chain Length Distribution ◽  
Radical Polymerizations

A method to determine chain transfer constants in free radical polymerizations that are >1 using molecular weight distribution data.

scholarly journals Correction: When Mayo falls short (Ctr ≫ 1): the use of cumulative chain length distribution data in the determination of chain transfer constants (Ctr) for radical polymerizations

2021 ◽  
Vol 12 (6) ◽  
pp. 947-947
Author(s):  
Matt K. Donald ◽  
Stefan A. F. Bon
Keyword(s):  
Chain Length ◽  
Chain Transfer ◽  
Length Distribution ◽  
Distribution Data ◽  
Chain Length Distribution ◽  
Radical Polymerizations

Correction for ‘When Mayo falls short (Ctr ≫ 1): the use of cumulative chain length distribution data in the determination of chain transfer constants (Ctr) for radical polymerizations’ by Matt K. Donald and Stefan A. F. Bon, Polym. Chem., 2020, 11, 4281–4289, DOI: 10.1039/D0PY00348D.

scholarly journals The molecular-weight distribution of glycosaminoglycans

1973 ◽  
Vol 135 (4) ◽  
pp. 631-637 ◽  
Author(s):  
John J. Hopwood ◽  
H. Clem Robinson
Keyword(s):  
Molecular Weight ◽  
Molecular Weight Distribution ◽  
Weight Distribution ◽  
Chondroitin Sulphate ◽  
Average Molecular Weight ◽  
Length Distribution ◽  
Accurate Estimation ◽  
Distribution Data ◽  
Gel Chromatography ◽  
Chain Length Distribution

1. A rapid and sensitive method for the accurate estimation of the molecular-weight distribution of keratan sulphate and chondroitin sulphate isolated from adult bovine nasal septum and intervertebral disc is described. The method utilizes gel chromatography of reductively labelled glycosaminoglycan and end-group estimation of number-average molecular weight for each fraction across the peak of eluted glycosaminoglycan. 2. Chain-length distribution data obtained by this procedure are used to evaluate mechanisms of chondroitin sulphate biosynthesis.

Modelling the Complete Molecular Weight Distribution in Chain Growth Polymerizations

2016 ◽  
Vol 1819 ◽  
Author(s):  
Ramiro Infante-Martínez ◽  
Enrique Saldívar-Guerra ◽  
Odilia Pérez-Camacho ◽  
Maricela García-Zamora ◽  
Víctor Comparán-Padilla
Keyword(s):  
Molecular Weight ◽  
Free Radical ◽  
Radical Polymerization ◽  
Molecular Weight Distribution ◽  
Weight Distribution ◽  
Chain Transfer ◽  
Free Radical Polymerization ◽  
Experimental Program ◽  
Chain Growth ◽  
Coordination Polymerization

ABSTRACTThis work shows the development of several models for chain-growth polymerizations that admit the direct calculation of the complete molecular weight distribution of the polymer. The direct and complete calculation implies that no statistical mean values are employed as in the moments method neither numerical approximations like in the minimum-squared based methods. The free radical polymerization of ethylene (LDPE) and the coordination via metallocenes polymerization of ethylene (HDPE) are taken as examples for analysis.In the free radical polymerization case, the conventional scheme for chain-growth polymerization is adopted, with steps for initiation, propagation, chain transfer to small species and the additional step of chain transfer to dead chains [1]. The kinetic parameter are obtained from the open literature. Two kind of reactors were modelled: batch and continuous stirred tank reactor. For this last case, a simulation strategy was considered in which the run started from an initial known population of dead chains. Results show that typical non-linear polymerization profiles for the molecular weight distribution are obtained. For the coordination polymerization of ethylene via metalocenes, the standard coordination model was employed [2]. A two-site catalyst was considered and kinetic parameters reported in the open literature were used. For this study an experimental program in a lab-scale reactor was undertaken in order to obtain modelling data [3]. Results show that the standard model adequately reproduces the experimental data in the kinetic and molecular attributes of the polymer.

scholarly journals Method of Moments Applied to Most-Likely High-Temperature Free-Radical Polymerization Reactions

Processes ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 656 ◽  
Author(s):  
Hossein Riazi ◽  
Ahmad Arabi Shamsabadi ◽  
Michael Grady ◽  
Andrew Rappe ◽  
Masoud Soroush
Keyword(s):  
High Temperature ◽  
Free Radical ◽  
Radical Polymerization ◽  
Chain Length ◽  
Method Of Moments ◽  
Length Distribution ◽  
Free Radical Polymerization ◽  
Polymer Chains ◽  
Rate Equations ◽  
Chain Length Distribution

Many widely-used polymers are made via free-radical polymerization. Mathematical models of polymerization reactors have many applications such as reactor design, operation, and intensification. The method of moments has been utilized extensively for many decades to derive rate equations needed to predict polymer bulk properties. In this article, for a comprehensive list consisting of more than 40 different reactions that are most likely to occur in high-temperature free-radical homopolymerization, moment rate equations are derived methodically. Three types of radicals—secondary radicals, tertiary radicals formed through backbiting reactions, and tertiary radicals produced by intermolecular chain transfer to polymer reactions—are accounted for. The former tertiary radicals generate short-chain branches, while the latter ones produce long-chain branches. In addition, two types of dead polymer chains, saturated and unsaturated, are considered. Using a step-by-step approach based on the method of moments, this article guides the reader to determine the contributions of each reaction to the production or consumption of each species as well as to the zeroth, first and second moments of chain-length distributions of live and dead polymer chains, in order to derive the overall rate equation for each species, and to derive the rate equations for the leading moments of different chain-length distributions. The closure problems that arise are addressed by assuming chain-length distribution models. As a case study, β-scission and backbiting rate coefficients of methyl acrylate are estimated using the model, and the model is then applied to batch spontaneous thermal polymerization to predict polymer average molecular weights and monomer conversion. These predictions are compared with experimental measurements.

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