Modelling of ring-free crosslinking chain (co)polymerization

Dušek, Karel; Šomvársky, Ján

doi:10.1002/(sici)1097-0126(199711)44:3<225::aid-pi870>3.0.co;2-c

Cited by 25 publications

(25 citation statements)

References 3 publications

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“…[see definitions (32) and (40)]. The effective functionality (the average number of bonds with infinite continuation) of EACs, f e , is Each bond with infinite continuation issued by an EAC contributes by 1 / 2 to the number of EANCs, and thus the molar concentration of EANCs, ν e , is given by if the GF F n chain (Z, z) is normalized to the total concentration of primary chains, c 0 , (F n chain (1, 1) ) c 0 ).…”

Section: Figure 3 States Of Cross-linked Structural Units Distinguismentioning

confidence: 99%

“…This description is based on a generalization of the TBP, 28,29 where separate sets of variables for structural units and links are introduced in generating functions (this approach has already been used for description of network formation by stepwise polyaddition reaction 6,[30][31][32] neighbors and guarantees possibility to obtain the number distribution of size and composition of sol molecules (not always possible in existing theories). The model allows one to describe, in dependence on the conversion of the cross-linking reaction, not only the amount and composition of sol and gel, but also substructures in sol and gel.…”

Section: Introductionmentioning

confidence: 99%

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Polyfunctional Cross-Linking of Existing Polymer Chains

2000

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Polyfunctional cross-linking of polydisperse copolymer primary chains is described theoretically, and dependences of structural parameters on conversion (R) before and after the gel point are derived. In particular, concentrations and average molecular weights of the sol, the elastically active network chains and their backbone chains, and dangling chains are given as functions of R. The theory can be used for chemical as well as physical gelation processes. A generalized theory of branching processes (TBP) is used, in which two sets of variables are introduced, for units and for links.

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Section: Figure 3 States Of Cross-linked Structural Units Distinguismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Polyfunctional Cross-Linking of Existing Polymer Chains

2000

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“…Within the mathematical modeling framework, many tools for crosslinking copolymerization are available, such as generating functions, numerical fractionation and balance of sequences . Despite this diversity of available methods, modeling approaches for styrene–DMA copolymerization are scarce, and are generally focused on the prediction of copolymer composition .…”

Section: Introductionmentioning

confidence: 99%

Styrene–dimethacrylate copolymerization kinetic modeling

Aguiar

2015

Polymer International

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A model for the copolymerization of styrene with dimethacrylate including the post‐gelation period, diffusion effects and cyclization reactions was developed. The numerical fractionation method, balance of sequences and pseudo‐homopolymerization hypothesis were used for such a purpose. Diffusion effects were taken into account through an exponential correlation between the termination rate coefficient and the monomer conversion. Average rate coefficients of cyclization and crosslinking reactions were fitted. The model was validated through literature data for the copolymerizations of styrene with ethylene glycol dimethacrylate and styrene with tetraethylene glycol dimethacrylate. The predictions were satisfactory in the range 1–20% of dimethacrylate and temperature at 95 °C. © 2015 Society of Chemical Industry

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“…Crosslinked copolymers are materials of great interest in a large variety of application fields . Besides a very intensive experimental research, modeling tools have been developed throughout the years, in order to predict product properties and deepen the understanding of such complex systems . Notably, the models employed in free‐radical bulk crosslinking copolymerization need to deal not only with chain length distribution (CLD), which naturally arises in any type of polymerization, but also with complex molecular architectures, whose detailed structure determines the end use properties.…”

Section: Introductionmentioning

confidence: 99%

Bulk Crosslinking Copolymerization: Comparison of Different Modeling Approaches

Lazzari

Hamzehlou

Reyes

et al. 2014

Macromol. React. Eng.

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The predictions of four different models of crosslinking copolymerization,Kinetic Monte Carlo (KMC), statistic/kinetic Flory/Tobita (FT) model, and two kinetic approaches based on population balance equations (PBE) (solved with generating functions (GF) and numerical fractionation (MRNF), respectively), were compared. The approaches underlying more restrictive assumptions but asking for less computational effort, FT and MRNF, lead to very satisfactory predictions in terms of average properties (sol and gel fractions, degrees of polymerizations, crosslinking densities). On the other hand, fully detailed models (KMC) as well as more computationally demanding numerical solutions of the detailed PBE (GF) become necessary when the chain length distributions are required.

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Modelling of ring-free crosslinking chain (co)polymerization

Cited by 25 publications

References 3 publications

Polyfunctional Cross-Linking of Existing Polymer Chains

Polyfunctional Cross-Linking of Existing Polymer Chains

Styrene–dimethacrylate copolymerization kinetic modeling

Bulk Crosslinking Copolymerization: Comparison of Different Modeling Approaches

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