Graph Theory and Molecular Distribution. 2. Copolycondensation of A-Group Polyfunctional Monomers with B-Group Polyfunctional Monomers

Durand, Dominique; Bruneau, Claude‐Marcel

doi:10.1021/ma60072a040

Cited by 28 publications

(19 citation statements)

References 2 publications

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“…any molecular segment containing only caprolactam monomers (located between two extremities or functional groups A x B y different from A 1 B 1 ) can be described by a Flory distribution with the same average molecular weight M n,Strand , and (2) we know, a priori, that every chain extremity is of type 'A' (real or virtual). [29][30][31][32] In contrast to the actual polycondensation process and to usual Monte Carlo algorithms, the molecules are therefore not built from the different monomers (A 1 B 1 , B 2 , A 3 , . ), but directly from specic sub-chains which can be considered as building blocks of the molecules.…”

Section: Modelingmentioning

confidence: 99%

“…Some works have already been proposed in this direction for metallocene polyethylene [25][26][27] as well as for polydisperse polyamide samples. [28][29][30][31][32] In the latter case, it has been shown that classical Monte Carlo statistics lead to a good approximation of the sample, which is formed by a condensation reaction process. The objective here is to propose a simplied Monte Carlo approach, which takes advantage -while without losing accuracy -of the fact that we know a priori that every generation will be described by a Flory-type molecular weight distribution and that they will all have the same average molecular weight (whatever their seniority).…”

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confidence: 99%

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Structure and rheology of branched polyamide 6 polymers from their reaction recipe

et al. 2013

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Section: Modelingmentioning

confidence: 99%

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confidence: 99%

Structure and rheology of branched polyamide 6 polymers from their reaction recipe

et al. 2013

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“…There are statistical methods (for example Durand and Bruneau, [7] Fradet and Tessier [3] ) that give the averages and will serve for comparison. Figure 2 shows the molecular weight distributions of the studied recipes, of Table 1, at full amine conversion.…”

Section: Molecular Weight Distributionmentioning

confidence: 99%

Monte Carlo Simulation of Randomly Branched Step‐Growth Polymers: Generation and Analysis of Representative Molecular Ensembles

Hillegers¹,

Kapnistos

Nijenhuis

et al. 2011

Macro Theory & Simulations

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A Monte Carlo simulation procedure has been set up and applied to generate representative ensembles of randomly branched step‐growth polymers based on their reaction recipe. The molecular distributions thus obtained are consistent with those from statistical/analytical approaches. However, because the current method gives access to the complete ensemble of simulated molecules, a very detailed structural analysis is possible. Our procedures are applicable to any ‘AfBg’ system with f + g ≥ 1. We apply this approach to randomly branched polyamides in order to gain insight into their molecular structure and understand the effect of the reaction recipe on the final product.

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“…In a very different way, using graph theory, the formulas of Stockmayer have also been derived by Durand and Bruneau7 for system “Afi” and in 19798 for system “Afi + Bgj.”…”

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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Graph Theory and Molecular Distribution. 2. Copolycondensation of A-Group Polyfunctional Monomers with B-Group Polyfunctional Monomers

Cited by 28 publications

References 2 publications

Structure and rheology of branched polyamide 6 polymers from their reaction recipe

Structure and rheology of branched polyamide 6 polymers from their reaction recipe

Monte Carlo Simulation of Randomly Branched Step‐Growth Polymers: Generation and Analysis of Representative Molecular Ensembles

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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