Mathematical modeling of the bivariate molecular weight—Long chain branching distribution of highly branched polymers.

Krallis, Apostolos; Kiparissides, Costas

doi:10.1016/j.ces.2007.03.035

Cited by 22 publications

(13 citation statements)

References 11 publications

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“…[7] While Pladis and Kiparissides include backbiting, they assume that it only produces short-chain branches, and do not consider the effects of short-chain branching on the polymer properties. Krallis and Kiparissides [8] use the fixed-pivot technique to model the bivariate molecular weight-long chain branching distribution, using population balance Equations for both live and dead chains. In this algorithm, the domains of chain length and branching level are discretized using a two-dimensional grid, and the population balance Equations are solved at specific grid points.…”

Section: Introductionmentioning

confidence: 99%

“…These authors also assume that all long-chain branches are formed via intermolecular chain transfer to polymer or terminal double bond polymerization. [8][9][10] 13 C nuclear magnetic resonance (NMR) spectroscopy provides a way to measure the total branching content, independent of the mechanical properties of the polymer. Solution-state NMR [3,4] and swollen-state NMR [1,11] are techniques commonly used to measure branching content in alkyl acrylates.…”

Section: Introductionmentioning

confidence: 99%

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Multiscale Modeling of Branch Length in Butyl Acrylate Solution Polymerization

Rawlston

Schork

Grover

2010

Macro Theory & Simulations

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Branch lengths resulting from both backbiting and intermolecular chain transfer to polymer are examined for the solution polymerization of butyl acrylate, using a rate‐equation model and ordinary differential equations. Backbiting is allowed to generate branches of varying length, according to a cumulative distribution function obtained from a lattice kinetic Monte Carlo simulation. About 8% of the branches produced by backbiting are 10 mers or longer. In contrast to common assumptions about the origins of short‐chain and long‐chain branches, the model indicates that nearly all of the long‐chain branches may be produced by backbiting, rather than intermolecular chain transfer to polymer.magnified image

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multiscale Modeling of Branch Length in Butyl Acrylate Solution Polymerization

Rawlston

Schork

Grover

2010

Macro Theory & Simulations

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“…However, batch polymerization of VAc could be described up to high monomer conversions without polyradicals, explaining why in the present work this assumption is followed also bearing in mind that statistically a dominant role of monoradicals is expected. 10,31,40,50,51 Only at very high monomer conversions, batch modeling studies indicated that large (poly)radical species with several double bonds could exist. 45 To validate the maximum number of double bonds considered in this work, simulations with up to 10 double bonds have been considered as well and as illustrated further, the maximum number of 2 is affordable.…”

Section: Kinetic Modelmentioning

confidence: 99%

Interplay of Head, Tail, and Mid-Chain Radicals in Bulk Free-Radical and Reversible Degenerative Addition Fragmentation Chain-Transfer Polymerizations of Vinyl Acetate

et al. 2019

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A detailed kinetic model for isothermal bulk free-radical and degenerative reversible addition−fragmentation chain-transfer (RAFT) polymerizations of vinyl acetate is presented up to monomer conversions of ca. 0.95, considering a distinction between head and tail end-chain radicals and primary and tertiary mid-chain radicals (MCRs). Diffusional limitations are taken into account for conventional initiation and termination, with a reduction of the gel-effect as chain transfer to the monomer lowers the apparent termination reactivities. The tail radicals are essential for the accurate description of backbiting and RAFT deactivation and the primary MCRs for chain transfer to the polymer. The model is based on the application of the method of moments with over 100 macrospecies types and thousands of reactions to obtain the temporal evolution of the monomer conversion, the number and mass average chain length, the number fraction of short-and long-chain branches, the number fraction of unsaturated chains, and the number fraction of chains with head-to-head defects. After a successful model validation of the experimental literature data, the model is applied to understand the complex interplay of the radical types involved and to highlight the control of the branching and unsaturation amounts under RAFT polymerization conditions. Headto-head defects can however not be avoided for realistic average chain lengths.

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“…Besides, the quasi steady state approximation was employed. Another reported approach is the fixed pivot technique, which has been employed for computing MW‐CCDs5 and MW‐LCBDs 6, 7. This is a sectional grid method in which the distribution domains are discretized in such a form that any two moments of the distribution in each dimension are exactly preserved 8.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of Bivariate Polymer Property Distributions Using 2D Probability Generating Functions, 1 – Numerical Inversion Methods

Asteasuain

Brandolin

2010

Macro Theory & Simulations

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This is the first of two papers presenting a new mathematical method for modeling bivariate distributions of polymer properties. It is based on the transformation of the infinite mass balances describing the evolution of a two‐dimensional distribution using 2D probability generating functions (pgf). A key step of this method is the inversion of the transforms. In this work, two numerical inversion methods of 2D pgfs are developed and carefully validated. The accuracy obtained with both methods was very satisfactory. The inversion formulas of both methods are simple and easy to implement. A simple copolymerization example is used to show the complete procedure from the derivation of the pgf balances to the recovery of the bivariate molecular weight distribution.magnified image

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Mathematical modeling of the bivariate molecular weight—Long chain branching distribution of highly branched polymers.

Cited by 22 publications

References 11 publications

Multiscale Modeling of Branch Length in Butyl Acrylate Solution Polymerization

Multiscale Modeling of Branch Length in Butyl Acrylate Solution Polymerization

Interplay of Head, Tail, and Mid-Chain Radicals in Bulk Free-Radical and Reversible Degenerative Addition Fragmentation Chain-Transfer Polymerizations of Vinyl Acetate

Mathematical Modeling of Bivariate Polymer Property Distributions Using 2D Probability Generating Functions, 1 – Numerical Inversion Methods

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