Integrated Kinetic Monte Carlo–Structure–Rheology Model for Solution Copolymerization of Ethylene and α-Olefins (original) (raw)
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AIChE Journal, 1990
A dynamic kinetic model describing gas-phase olefin copolymerization using a multiple active site Ziegler-Natta catalyst is presented. This model is capable of predicting production rate, molecular weight, and copolymer composition changes observed in an industrial reactor. The model also explains how broad molecular weight distributions and bimodal copolymer compositions can occur as has been observed for commercial linear polyethylenes.
Polymer, 2011
The effect of dilution on random living copolymerization of vinyl-and divinyl monomers with fast initiation and slow propagation was simulated and compared with the experiments. Two Monte Carlo simulation methods have been used: one, purely statistical, based on the FloryeStockmayer (FS) theory and the second using the dynamic lattice liquid model (DLL). The results were compared with experiments using atom transfer radical polymerization (ATRP), one of controlled/living radical polymerization methods. Molecular weights, polydispersities and the crosslinking/cyclization of macromolecules were analyzed as a function of conversion and time for various solvent concentrations and initiator crosslinker/monomer ratios. The results obtained by the DLL method are in good agreement with the experiment, showing an increase of conversion and time at gel point with dilution, i.e., with the increase of solvent concentration. The FS theory was found to be unable to reproduce even qualitatively the dilution effect on gelation. It is shown that intrachain crosslinking becomes more and more important with increasing solvent concentration, preventing macroscopic gelation at high dilutions, even if the number of crosslinks per primary chain is much greater than one (Flory criterion).
Macromolecules, 1994
DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
Bulk Crosslinking Copolymerization: Comparison of Different Modeling Approaches
Macromolecular Reaction Engineering, 2014
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.
Thermodynamics of copolymerization
Progress in Polymer Science, 1992
CONTENTS 1. Introduction 2. Equilibrium in copolymerization. General outlook 3. Analysis of copolymerization thermodynamics. Previous results 4. Dyad model copolymerization 4.1. Application of equations to real systems 4.2. Recent analogous treatments of other authors 5. Triad model copolymerization 5.1. Application of equations to real systems 6. Chain-ring equilibria in equilibrium copolymerization systems 7. Copolymerization equilibrium in systems with physical interactions 8. Homopolymerizations which can be regarded as copolymerizations References 917 919 921 926 929 929 933 937 938 940 944 950
A general kinetic analysis of non-linear irreversible copolymerizations
Chemical Engineering Science, 1994
non-linear wpolymerizations with arbitrarily wt numbers of ~OIIOIXI~TS are described specifying the stoichiorncrric so&cients of the reactions involving end-groups. Rate equations for chc voctatial generating function or discrete transform of the distribution ot end-groups and repeating unita and ifa derivatives with respea to logarithms of hplace pnmmeters can thus be written. Similar rate equations CBII be written for the discrete transforms ol the distributions of descendants of each linking group with respect to their numlxrs of end-groups. This allows the prediction of et properties. such as the concentration of dastically active network chains and mass fraction or pendant material. Mars balance equations using these rate laws are non-linear partial diExential equations sdlvable by the TIWII~~ of characteristic Numerical methods arc developed for computidg m&cular weight distributions and average malceular weights Wore and after gelation, BS well a$ the weight fraction of sol and gel properties relati IO its elasticity behaviour. The curing ol B tetraepoxide with a primary diamine is taken ti a cam study and r~ults are mmpared with predictions by the theory of branching ~~c-Gcw%.
Macromolecular Reaction Engineering, 2009
A simplified kinetic scheme of eythylene/a-olefin copolymerization has been developed by adding reactions responsible for the unusual kinetic behavior to a general mechanism. The estimation of rate constants has been simplified by making physically meaningful initial guesses. Rate constants affecting yield, MWD and comonomer content have been estimated separately. Experiments were designed to investigate the effects of each rate constant independently. The obtained rate constants show that the sites which are responsible for formation of short chains with higher 1-butene content are more active at the beginning of polymerization, while the sites which are responsible for formation of longer chains with lower 1-butene units are more active at the final stages of polymerization.
2010
The random living copolymerization of vinyl and divinyl monomers with fast initiation and slow propagation was simulated using two Monte Carlo methods: one, purely statistical, corresponding to the mean-field FloryeStockmayer (FS) theory and the dynamic lattice liquid model (DLL). The results were compared with experiments in which atom transfer radical polymerization (ATRP) method was used. Molecular weights, polydispersities and the cross-linking/cyclization of macromolecules were modeled as a function of conversion for various cross-linker concentrations. The results obtained by the DLL and FS methods and experiments are presented and the sources of discrepancies are discussed. The DLL method yields gel points, molecular weight distributions and critical exponents closer to experimental values and gives an insight into cross-linking processes near the gel point (leading to gelation). More realistic gel structure is obtained due to an appropriate modeling of intra-chain cyclization and diffusion effects, especially close to and above the gel point.
1997
DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement: