Transition into the gel regime for crosslinking radical polymerisation in a continuously stirred tank reactor (original) (raw)
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Transition into the gel regime for free radical crosslinking polymerisation in a batch reactor
Polymer, 2014
Crosslinking polymerization 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, for the first time and to a full extent resolves the crosslinking problem as formulated by Zhu et al.[1]and 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 model has been validated with data from an experimental crosslinking polymerization, Methyl Methacrylate with Ethylene Glycol Dimethacrylate. Non-trivial patterns in the time evolution of average quantities like crosslink densities, partly observed in prior studies [2, 3, 4], are naturally emerging from the model by computing marginals of the four-dimensional distribution possessing an interesting multimodal structure.
Continuous free radical polymerization in disperse systems
Makromolekulare Chemie. Macromolecular Symposia, 1987
Continuous free radical polymerization in disperse systems was performed in a laminar stirred tubular reactor which is a novel reactor type with narrow residence time distribution in the laminar flow regime. The residence time distribution of such a reactor can be modelled by very simple dimensionless equations containing the axial and radial Reynolds numbers of the reactor a t operating conditions. In such a reactor of pilot plant scale the continuous free radical polymerization of acrylamide in emulsion and of vinyl acetate in suspension was studied with respect to conversion and performance of reactor. For modelling the conversion of polymerization t h e segregation and the dispersion model were used and the results compared with experimental data. Both are suitable models for modelling the upper and lower limit of conversion of micro or macro mixed polymerizations. The vinyl acetate polymerization was also investigated with respect to the breadth of the molecular weight distribution of the polymer formed in batch, continuous segregated, and continuous micro mixed reactors. Models were developed employing a complex kinetic scheme including transfer reaction to polymer and terminal double bond polymerization. Simulation results showed that the molecular weight distribution order in the different reactor types is not fixed, but a function of reactant concentrations and importance of chain branching. The simulations are compared with experimental data.
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.
Network Formation by Free Radical Polymerization in Isothermal Continuous Flow Stirred Reactors
Macromolecular Reaction Engineering, 2016
The authors apply the method of moments to the study of network formation in continuous flow stirred reactors when chain transfer to polymer and coupling are present in the reac tion scheme. This approach leads to analytical solutions for the various moments involved. The authors start by assuming that the rate of coupling is proportional to the length of dead chains, which allow them to review and extend previous work in this area. This is followed by similar derivations when a coupling agent is present and the rate of coupling is proportional to the number of coupling groups that such agent leaves in dead polymer molecules, demonstrating that higher values of second order moments can be reached at lower levels of unreacted coupling agent.
Macromolecules, 1992
A new theoretical framework is proposed for modeling diffusion-controlled free-radical polymerization reactions. Termination and propagation rate constants as well as initiator efficiency are expressed in terms of a reaction-limited term and a diffusion-limited one. The latter is shown to depend on the diffusion coefficient of the corresponding species (i.e., polymer, monomer, primary radicals) and an effective reaction radius. All parameters appearing in the diffusion-limited part of the kinetic rate constants have a clear physical meaning and can be evaluated in terms of the physical and transport properties of the reacting species. It is shown that the proposed approach for modeling diffusion-controlled reactions does not require the introduction of critical break points to mark the onset of various diffusional effects (Le., gel effect, glass effect). The ability of the present model to elucidate the mechanism of diffusion-controlled reactions is demonstrated by analyzing the free-radical polymerizations of styrene and methyl methacrylate initiated by the thermal decomposition of AIBN, AIBME, AVN, and LPO chemical initiators. It is shown that, at high conversions, initiator efficiency strongly depends on the size of initiator molecules. The present model predictions are in excellent agreement with experimental data on monomer conversion, total radical concentration, and average molecular weights measured in different laboratories by ODriscoll and Huang42 and Zhu et al.l0
Radical initiated polymerization in a bi-functional mixture by a computer simulation model
APS, 2004
Computer simulations are performed to study the polymerization behavior in a mixture of bifunctional groups such as olefins ͑A͒ and acrylates ͑B͒ in an effective solvent ͑a coarse description for vegetable oil derived macromonomers ͑VOMMs͒ in solution͒ on a cubic lattice. A set of interactions between these units and solvent ͑S͒ constituents and their relative concentrations (p A , p B , and p S) are considered. Samples are equilibrated with Metropolis algorithm to model the perceived behavior of VOMMs. The covalent bonding between monomeric units is then implemented via reaction pathways initiated by stochastic motion of free radicals ͑a very small fraction͒. The rate of reaction shows decay patterns with the time steps ͑t͒ with power laws ͑i.e., R ab ␣t Ϫr , rХ0.4-0.8), exponential decays ͑i.e., R ab ␣e Ϫ0.001t), and their combination. Growth of A-B bonding is studied as a function of polymer concentration pϭp A ϩ p B for four different model systems appropriate for VOMMs. The data from the free radical initiated simulations are compared to the original simulations with homopolymerization. While most of the data are consistent with experimental observations, the variations are found to be model dependent.
Radical initiated polymerization in a bifunctional mixture via computer simulation
The Journal of Chemical Physics, 2004
Computer simulations are performed to study the polymerization behavior in a mixture of bifunctional groups such as olefins (A) and acrylates (B) in an effective solvent (a coarse description for vegetable oil derived macromonomers (VOMMs) in solution) on a cubic lattice. A set of interactions between these units and solvent (S) constituents and their relative concentrations (pA, pB, and pS) are considered. Samples are equilibrated with Metropolis algorithm to model the perceived behavior of VOMMs. The covalent bonding between monomeric units is then implemented via reaction pathways initiated by stochastic motion of free radicals (a very small fraction). The rate of reaction shows decay patterns with the time steps (t) with power laws (i.e., Rabαt−r, r≅0.4–0.8), exponential decays (i.e., Rabαe−0.001t), and their combination. Growth of A–B bonding is studied as a function of polymer concentration p=pA+pB for four different model systems appropriate for VOMMs. The data from the free ...