Bulk Crosslinking Copolymerization: Comparison of Different Modeling Approaches (original) (raw)
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Modeling Crosslinking Polymerization in Batch and Continuous Reactors
Macromolecular Reaction Engineering, 2013
A new pseudo-distribution approach is applied to the modeling of crosslinking copolymerization of vinyl and divinyl monomer and compared to Monte Carlo (MC) simulations. With the number of free pending double bonds as the main distribution variable, a rigorous solution of the three leading moments of the molecular size distribution becomes possible. Validation takes place with data of methyl methacrylate with ethylene glycol dimethacrylate. Well within the sol regime perfect agreement is found, but near the gelpoint larger discrepancies do appear. This is probably due to the existence of multiradicals that are not taken into account in the population balance approaches.
Polymer, 2015
The effect of intramolecular crosslinking (IC) (cyclization) on gelation was studied using Monte Carlo simulations. The consumption of crosslinker in the IC process is proposed as one of the main reasons of significant overestimation of the gel point by Flory-Stockmayer theory. The system under study is atom transfer radical polymerization (ATRP) of a monomer and bifunctional (e.g. divinyl) crosslinker. The simulation method is based on dynamic lattice liquid algorithm (DLL) and reproduces changes of the system dynamics during polymerization. The effect of cyclization on gel point for various reagents ratios and dilutions was investigated. It is shown that intramolecular crosslinking does not change significantly the gel point in condensed systems (no solvent or below 10%). By contrast, it significantly increases gel points in diluted systems (40e90% of the solvent).
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.
Kinetic Gelation Modeling: Structural Inhomogeneity during Cross-Linking Polymerization
Macromolecules, 2003
Kinetic gelation models simulate free-radical polymerization on fixed lattices, where propagation and termination reactions are restricted to occur only between nearest neighbors. Here such a model is used with bifunctional sites and with kinetics recast as a Markov process through a stochastic approach. The reaction time is calculated by employing the probability density function and associated Monte Carlo method devised originally by Gillespie. As polymerization proceeds, the evolution of structure is characterized by pair correlation functions of three typessof reacted sites, of doubly reacted sites, and of monomers. These show that as polymerization proceeds, reacted sites and doubly reacted sites come to be distributed more uniformly in space; monomers come to be distributed less uniformly. A higher initiation rate constant, a higher initiator concentration, and a lower propagation rate constant lead to more uniform distribution of reacted sites, of doubly reacted sites, and of monomers. These factors also lead to lower average connectivity between reacted sites. These trends are strongest at low conversions. In contrast, an enhanced primary cyclization leads to less uniform distribution of reacted sites but to more uniform distribution of monomers. It also leads to higher connectivity between reacted sites that are close together but to lower connectivity between reacted sites that are far apart. Finally, at high conversions it leads to a more uniform distribution of doubly reacted sites.
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, 2018
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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%.
Estimation of copolymerization kinetic parameters by maximum likelihood method
AIChE Journal, 2004
A kinetic study of free-radical solution copolymerization of isobutyl methacrylate and lauryl methacrylate in benzene, initiated with 2,2-azoisobutyronitrile (AIBN) was performed at different monomer feed compositions, at low conversion level. To avoid the complications of copolymerization kinetics, the compositional-averaged rate constant method was applied to dead-end polymerization in constant and variable volume polymerization systems. A conditional probability approach, with "maximum likelihood function" (MLF), was used for estimating the kinetic parameters from experimental data. This method provides point estimates as well as joint probability regions. The validity of this method was approved for the statistically justified and best estimation of the rate parameters in copolymerization systems. Statistical analysis indicated that, although copolymer composition is well described by the terminal unit model (TUM), the rate data are not. Like many other systems recently examined, the data were well represented by the implicit penultimate unit effect (IPUE) model of Fukuda and coworkers. It was found that the coupled rate parameter k p /k t 0.5 is greater than the TUM predictions, whereas most of the previous systems studied have coupled rate parameters lower than those predicted by the TUM. An interactive computer simulator for parameter estimation was developed, which is run in two modes of estimation and prediction and is capable of receiving input data from both keyboard and databank.