Transition into the gel regime for free radical crosslinking polymerisation in a batch reactor (original) (raw)
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Chemical Engineering Science, 2015
Crosslinking radical polymerisation in a continuously stirred tank reactor has been studied by means of a four-dimensional population balance model accounting for chain length, free pending double bonds, crosslinks, and multiradicals as dimensions. The model covers both pre-gel and gel regimes in a straightforward manner. Approximations on radial basis functions have been employed to reduce the size of the system with minimal information loss. The comparison with Monte Carlo simulations shows interesting and unexpected features.
Qualitative percolation study of free-radical cross-linking polymerization
Polymer Bulletin, 1984
Simulations of a conceptually simple model for free-radical cross-linking polymerization have been performed in relation to experimental indications for (temporary) microgel particles. Many qualitative features ascribed to microgels show up in the simulation. In particular this model yields qualitative agreement with experiments on the conversion dependence of the number of pendant double bonds.
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.
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.
Critical properties for gelation in free-radical crosslinking copolymerization
Macromolecular Theory and Simulations, 1995
A kinetic model was used to predict the molecular weight developments and the critical properties in free-radical crosslinking copolymerization. The predictions of the model were compared to the experimental data reported previously. Agreement of the kinetic model with experiments is satisfactory for both low and high crosslinker contents. The model parameters indicate increasing extent of shielding of pendant vinyl groups as the reaction proceeds due to the increasing number of multiple crosslinkages. The calculation results indicate that the real critical exponents can only be observed in the region E < 10-2-10-3 where experimental studies are very difficult. Outside of this region, the apparent critical exponent y describing the divergence of the weight-average molecular weight was found to deviate from the classical value due to the conversion dependent kinetics of free-radical crosslinking copolymerization.
2001
A kinetic gelation model that incorporates the kinetics of free radical homopolymerization is implemented to determine the effects of kinetics on polymerization statistics and microstructures. The simulation is performed on a simple cubic lattice that has 100 sites in each direction. A new algorithm for random selecting of the next step in a self-avoiding random walk and very efficient mechanisms of mobility of components are introduced to improve the generality of the predictions by removing commonly occurring deficiencies due to early trapping of radicals. A first order kinetics is considered for decomposition of initiator that enables us to consider the effect of temperature on polymerization reaction. Better understanding of microstructural evolution during polymerization and providing a framework to produce a realistic system of highly packed random chains within polymer network are among the benefits of model.
Journal of Applied Polymer Science, 1997
In free radical polymerization diffusion-controlled processes take place simultaneously to the normal chemical reactions. Despite extensive efforts to model such processes a consistent model for the design of a polymerization reactor has not yet been established. In this article a semiempirical model describing the conversion, polymerization degree, and molecular weight distribution (MWD) for the free radical polymerization is developed for the entire course of the reaction. The model includes the change of termination, propagation, transfer, and initiation rate. By simultaneous parameter estimation from the conversion and degrees of polymerization data the model parameters have been determined for isothermal polymerizations of methyl methacrylate (MMA) and styrene (ST). The simulation results for the conversion, degrees of polymerization, and MWD are in good accordance with experimental data for suspension and bulk polymerization of MMA and ST up to very high conversions. The influence of diffusion on the propagation rate in case of polymerization of MMA is negligible compared to the influence of the cage effect on the radical efficiency; in case of ST polymerization both effects must be included in the kinetic model. The model presented is also tested for polymerizations conducted in the presence of solvent and / or chain transfer agents.
Chemical Engineering Science, 2004
A dynamic model for continuous ethylene-propylene-diene terpolymerization reactors in which crosslinking and gel formation are attributable to reactions between the pendant double bonds of diene units has been developed. The model is applicable to other types of crosslinking reactions such as those due to aging, polymer blending, and vulcanization. The polymer properties at the gel point and in the post-gel region are computed using the numerical fractionation method. Direct application of this method to the prediction of terpolymer properties in the gel or post-gel region can lead to severe numerical problems, due to large di erences in order of magnitude of various moments across the generations. These problems are overcome by applying a pseudo-kinetic rate constant method, i.e., by constructing a moment model for a pseudo-homopolymer that approximates the behavior of the actual terpolymer under the long chain and quasi-steady state assumptions. The pseudo-homopolymer model is then used as the basis for application of the numerical fractionation method. We show that the proposed dynamic model is capable of predicting realistic polydispersities and molecular weight distributions even near the gel point with as few as 11 generations, and in the post-gel region with as few as ÿve generations. The largest steady-state polydispersities of the soluble polymer are obtained when the crosslinking rate just exceeds the critical value for gelation. The steady-state polydispersity decreases exponentially in the post-gel region at higher values of the rate constant, while the sol fraction decreases in a more linear fashion. The overall molecular weight distribution (MWD) of the sol is constructed assuming a Schulz two parameter distribution for each generation. For the industrial case of a small number of crosslinks, the ÿrst two generations contribute the most to the MWD, which is unimodal. The tail of the MWD is longest near the initial gelation time; the tail is shortened in the post-gel region as higher generations are consumed. ?
Chemical Product and Process Modeling, 2000
An efficient Monte Carlo (MC) algorithm and a two-dimensional fixed pivot technique (2-D FPT) are described for the calculation of the average and distributed molecular properties of polymers in batch free-radical polymerization and copolymerization reactors. Simulations are carried out, under different reactor conditions, to calculate the individual monomer conversions, the leading moments of the 'live' and 'dead' polymer chain length distributions as well as the dynamic evolution of the distributed molecular properties (i.e., molecular weight distribution (MWD), long chain branching distribution (LCBD), copolymer composition distribution (CCD), joint LCB-MW and CC-MW distributions, etc.). The validity of the numerical calculations is examined via a direct comparison of the simulation results, obtained by the two numerical methods, with experimental data on the styrene-methyl methacrylate and vinyl acetate batch free-radical polymerization systems. Additional comparisons between the MC and the 2-D FPT methods are carried out for both polymerization systems, under different polymerization conditions. It is clearly shown that both numerical methods are capable of predicting the distributed molecular, branching and copolymer properties, with high accuracy, up to very high monomer conversions.
Structural development during nonlinear free-radical polymerizations
Macromolecules, 1988
Relationships have been derived which describe structural development in nonlinear free-radical polymerizations as a function of conversion. The recursive analysis is based on the assumptions of ideal network formation and those assumptions standard in the kinetic analysis of linear free-radical polymerizations. Significant is the fact that changes in average primary chain length (e.g., due to drift or Trommsdorff effect), which in linear systems give rise to large polydispersities, can be accounted for in these relationships. While it is shown that for many systems such rigor is unnecessary in the pregel regime, it is also shown that neglect of such effects in the postgel regime may lead to serious errors. For the case in which monomer depletion is the only source of a changing kinetic chain length, the gel point is observed to be delayed and the network observed to be looser in comparison with the case in which monomer depletion is neglected.