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 reaction 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.
An overview of a systematic investigation of a tetrafunctional peroxide initiator's behaviour is presented. The study focuses on three main areas of research: kinetic experiments, polymer characterization and modelling efforts. The kinetic investigation compared the behaviour of the tetrafunctional initiator (JWEB50) to that of a monofunctional counterpart (TBEC) for a variety of monomers. Although higher rates of polymerization were generated with JWEB50 for all monomers investigated, switching from a mono‐ to a tetrafunctional initiator actually decreased the polymer molecular weight for methyl methacrylate. While chromatographic characterization methods were able to detect branching in polystyrene samples produced with JWEB50, this was not the case for poly(methyl methacrylate). However, evidence of branching was clearly observed for both polystyrene and PMMA when rheological methods were employed. In order to explain the experimental results, a mathematical model was developed. Through its use, the concentration and chain length of various polymer structures (i.e., linear, star or coupled stars) was found to depend upon monomer type and reaction conditions.
This is the first of a series of works aiming at developing a tool for designing “living” free radical polymerization processes in tubular reactors, in order to achieve tailor‐made MWDs. A mathematical model of the nitroxide‐mediated controlled free radical polymerization is built and implemented to predict the complete MWD. It is shown that this objective may be achieved accurately and efficiently by means of the probability generating function (pgf) transformation. Comparison with experimental data is good. The potential of the resulting model for optimization activities involving the complete MWD is also shown.
Several unit operations are combined in series to form an integrated, continuous polymerization process; namely inline degassing of monomer stock solution prior to reaction, polymerization using the RAFT approach and precipitation after reaction to form a solid polymeric product. The polymerization is conducted at 70–80 °C with reaction times of 30–90 min in a stainless steel tubular flow reactor, yielding poly(acrylamide) at high conversion (typically >90%) and with a low polydispersity of 1.14–1.23. The axial dispersion occurring inside the tubular flow reactor during polymerization is characterized by reaction profiling using a series of NMR samples. The process can be scaled up to a total output of 1.36 kg of polymer per day on this laboratory‐scale reactor.
The gel effect in the reactive extrusion process for free radical polymerization in a closely intermeshing co‐rotating twin screw extruder was investigated. First the reaction kinetic model was constructed mainly on the basis of entanglement theory. Next, numerical calculation expressions for the initiator and monomer concentrations, monomer conversion, average molecular weight and apparent viscosity were deduced. Finally, the evolution of the above variables were shown and discussed for the example of butyl methacrylate. The simulated results of the monomer conversion are in good agreement with experimental results.
Full chain‐length distribution (CLD) modelling applying the Galerkin finite‐element method[1] (FEM) to polymerization reactors featuring a certain degree of gel formation is confronted with extremely long computation times. The paper describes a new method to predict CLDs for systems where gel formation may occur. The new concept is to model a part of the CLD up to a cut‐off length L, while satisfying the full set of population balances. With transfer to polymer as the mechanism responsible for gelation, this gives rise to a closure problem, which has been solved by assuming the dead CLD beyond L to be represented by a part of a Flory distribution. The method could be proved to work by performing simulations and comparing cut‐off CLDs to full CLDs for non‐gelling systems and comparing results for different L for systems with gelation. The model is demonstrated for polymerization reactors, the batch reactor and the continuous stirred‐tank reactor (CSTR), with either disproportionation or recombination termination. Reliable results are obtained for systems with moderate gel formation. Comparing these results to those from moment models including balance equations up to the fourth moment, a number of interesting differences have been found. 相似文献
Mass balance equations in terms of the moment generating function of the distribution of mole concentrations of polymer species for free radical copolymerizations of mono/divinyl monomers could be numerically solved after gel point using open source code ACDC, needed for extremely stiff two‐point boundary value problems. For the first time, it became possible to compare the error of earlier well‐known approximated estimation methods for the weight fraction of sol and average molecular weights to this accurate mathematical solution. It turns out that predictions by the pseudo‐kinetic method are reasonable only when equal reactivity of double bonds prevails, causing early gelation in the batch reactor. Otherwise the discrepancies between the exact and approximate solutions are quite important.
Comparison between predicted number‐average and weight‐average degrees of polymerization of sol in batch non‐linear free radical polymerizations of model system III. 相似文献
Summary: Procedures are developed to estimate kinetic rate coefficients from available rate data for the free radical solution polymerization of butyl acrylate at 50 °C. The analysis is based upon a complete mechanistic set that includes the formation of mid‐chain radicals through backbiting and their subsequent reaction, and contains no assumptions on how the rate coefficient for cross‐termination of mid‐chain and end‐chain radicals is related to the two homo‐termination rate coefficients. After a thorough statistical analysis, the results of the fitting are combined with other recent literature data to provide a complete set of individual rate coefficients for the butyl acrylate system. Monomer addition to a mid‐chain radical is estimated to be slower than addition to a chain‐end radical by a factor of more than 400. The termination of two mid‐chain radicals is estimated to be two orders of magnitude slower than termination of two end‐chain radicals, with the cross‐termination rate coefficient close to the geometric mean.
Formation of a mid‐chain radical by intramolecular chain transfer to polymer by a chain‐end radical. 相似文献
Summary: A detailed investigation of chain transfer to polymer during free radical ring‐opening polymerization of the eight‐membered disulfide monomer 2‐methyl‐7‐methylene‐1,5‐dithiacyclooctane (MDTO) is presented. It has been shown that extensive chain transfer to polymer occurs involving both poly(MDTO) radicals and cyanoisopropyl radicals. Significant decreases in molecular weight were observed when cyanoisopropyl radicals were generated in the presence of poly(MDTO) in the absence of monomer. The molecular weight distribution (MWD) obtained from polymerization of MDTO in the presence of pre‐added poly(MDTO) was markedly different from that obtained without pre‐added polymer. A kinetic model was constructed in an attempt to quantitatively describe the chain transfer to polymer process based on the addition fragmentation chain transfer mechanism. It was found however that the simulated MWDs were considerably broader than the experimental MWDs, which were similar to the Schulz‐Flory distribution.
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