Statistics of random macromolecular networks, 1. Stepwise polymerization of polyfunctional monomers bearing identical reactive groups

Durand, Dominique; Bruneau, Claude‐Marcel

doi:10.1002/macp.1982.021830424

Cited by 43 publications

(18 citation statements)

References 19 publications

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“…Statistical derivation -Special case with / 3 = 0 a general formula given by Eq. (5). In this particular case, Eq.…”

Section: Concept Of the Molecular Weight Distribution On The Number Amentioning

confidence: 84%

Statistical derivation of kinetic molecular weight development equations in nonlinear free‐radical polymerization

Tobita

1997

Macro Theory & Simulations

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SUMMARY:We propose a statistical method to derive the differential equations that describe the weight-average molecular weight development during nonlinear free-radical polymerizations, by using the random sampling technique. We consider two types of nonlinear freeradical polymerization schemes, free-radical polymerization with chain transfer to polymer and free-radical crosslinking (co)polymerization. The obtained equations fully agree with those obtained through the kinetic approach using the method of moments. The physical meaning of each term in the differential equations as well as the implication of the functional form is discussed from the point of view of the statistical derivation.

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“…Statistical derivation -Special case with / 3 = 0 a general formula given by Eq. (5). In this particular case, Eq.…”

Section: Concept Of the Molecular Weight Distribution On The Number Amentioning

confidence: 84%

Statistical derivation of kinetic molecular weight development equations in nonlinear free‐radical polymerization

Tobita

1997

Macro Theory & Simulations

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“…Therefore, accurate models for the prediction of network formation and structure are of great importance. 64) , and Durand and Bruneau 65) . These equations give satisfactory predictions for condensation polymerization reactions, but are generally not suitable for predicting network formation in free-radical copolymerizations.…”

Section: Gelationmentioning

confidence: 97%

Modeling and semi-batch control of cross-link density distribution in the free-radical copolymerization of vinyl/divinyl monomers

Enright

Zhu²

2000

Macromol. Theory Simul.

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A general model has been developed to describe the cross‐link density development during the free radical copolymerization of vinyl/divinyl monomers. The conventional copolymerization theory based on the terminal model is applied to the cross‐linking system in a novel way. The cross‐link density profile is illustrated for both batch and standard semi‐batch processes. A new semi‐batch feed procedure is proposed that results in a uniform cross‐link density throughout the reaction.

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“…Such a system – conveniently denoted “Afi” by a.o. Durand and Bruneau1–consists initially of monomers bearing one (functionality f = 1), two ( f = 2), three ( f = 3), or more ( f ≥ 4) functional groups, denoted as A groups. When two A groups react, they form a bond, linking the two monomeric units to which the groups are attached.…”

Section: Introductionmentioning

confidence: 99%

A Fast Method to Compute the MSD and MWD of Polymer Populations Formed by Step‐Growth Polymerization of Polyfunctional Monomers With Identical Reactive Groups

Hillegers

Blokhuis

Slot

2012

Macro Theory & Simulations

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A fast method is presented for the calculation of the MSD and the MWD of polymers obtained via step‐growth polymerization of polyfunctional monomers bearing identical reactive groups (i.e., systems of type “Afi”). Using this method, the complete distribution can be calculated rapidly, not just the statistical averages of the polymer population such as $\overline {M} _{{\rm n}} $ or $\overline {M} _{{\rm w}} $. The computed MSD and MWD give more insight than these averages and can be compared to similar data measured on actual polymer systems. The low‐ and intermediate molecular size/weight part of the distribution curves are calculated using a recurrence scheme, while the high‐molecular tail (large and very large polymers) of the distributions is derived from an asymptotic approximation of the associated generating functions.

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Statistics of random macromolecular networks, 1. Stepwise polymerization of polyfunctional monomers bearing identical reactive groups

Cited by 43 publications

References 19 publications

Statistical derivation of kinetic molecular weight development equations in nonlinear free‐radical polymerization

Statistical derivation of kinetic molecular weight development equations in nonlinear free‐radical polymerization

Modeling and semi-batch control of cross-link density distribution in the free-radical copolymerization of vinyl/divinyl monomers

A Fast Method to Compute the MSD and MWD of Polymer Populations Formed by Step‐Growth Polymerization of Polyfunctional Monomers With Identical Reactive Groups

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