Three different long‐chain branch (LCB) formation mechanisms for ethylene polymerization with metallocenes in solution polymerization semi‐batch and continuous stirred‐tank reactors are modeled to predict the microstructure of the resulting polymer. The three mechanisms are terminal branching, C–H bond activation, and intramolecular random incorporation. Selected polymerization parameters are varied to observe how each mechanism affects polymer microstructure. Increasing the ethylene concentration during semi‐batch polymerization reduces the LCB frequency of polymers made with the terminal branching and intramolecular mechanisms, but has no effect on those made with the C–H bond activation mechanism, which disagrees with most previous data published in the literature. The intramolecular mechanism predicts that LCB frequencies hardly depend on polymerization time or ethylene conversion, which also disagrees with the published experimental data for these systems. For continuous polymerization reactors, experimental data relating polydispersity to LCB frequency can be well described with the terminal branching mechanism, but both C–H bond activation and intramolecular models fail to describe this experimental relationship. Therefore, detailed simulations confirm that the terminal branching mechanism is indeed the most likely mechanism for LCB formation when ethylene is polymerized with single‐site coordination catalysts such as metallocenes in solution polymerization reactors. 相似文献
The present contribution provides an overview of actual applications in modeling free‐radical polymerizations. Topics of interest are the simulation of pulsed laser polymerization experiments with subsequent analysis of the formed product by size exclusion chromatography (PLP‐SEC), single pulse laser experiments, experimental techniques for determining rate coefficients of elementary reactions that control polymer properties, and technical applications. Aspects being investigated are model validation and testing predictive potential in polymerization models using well‐defined experiments as well as developing and testing experimental strategies for deriving rate coefficients of elementary reactions that exist (especially when dealing with copolymerizations) within a network of complex coupled reactions. In any of these fields remarkable success in modeling can be achieved. This demonstrates the great potential that can grow from combining modern mathematical methods, computational power and detailed kinetic insights into the mechanism of polymerization. It is the wide scope of applications, e. g. ranging from modeling kinetics to the investigation of termination processes being dependent on the chain‐length of the macroradical (as an example of pure fundamental research) to modeling of technical reactors, that provides attractiveness and defines challenges. Especially, the success in transforming results directly from laboratory experiments into technical applications justifies laborious efforts in determining highly precise rate coefficients and proves the concept breaking down a complex process into elementary subparts. A necessary boundary condition for this is keeping in mind the demands along the whole scope of applications and avoiding simplifications that are only applicable for part of them. Although at a first glance this may appear to hinder fast progress in one discipline, it is the essential requirement for final success. 相似文献
Summary: A nonisothermal plug‐flow reactor for ethylene polymerization is reexamined so as to illustrate the principle and effect of a refined, semi‐microscopic modeling. The novel feature of the current simulation is the application of a Monte Carlo scheme to exactly solve the free‐radical polymerization involved, whereas a reptation‐based molecular theory is introduced in a self‐consistent manner to simulate more accurately the reactant fluid viscosity during polymerization. The simulation is shown to capture some in‐depth consequences of reaction‐transport coupling that cannot be revealed by a traditional, macroscopic type of modeling. The principle of a future extension for dealing with more complex flow reactors is briefly discussed.
Comparison of the predicted temperature profile between Monte Carlo‐based simulation and the ones using moment equations together with two different weight distributions is shown with experimental data for LDPE. 相似文献
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
The effect of micromixing on the dynamic behavior of continuous solution copolymerization tank reactors is evaluated both experimentally and theoretically. For this purpose, copolymerization reactions of styrene and divinylbenzene are carried out in a lab‐scale polymerization system, composed of two tank reactors in series, to provide experimental data of conversion and molar masses for analysis of micromixing effects. Besides, a detailed micromixing model, based on a dynamic population balance approach, is developed and solved with the method of characteristics, to investigate the micromixing effects on the dynamic behavior of conversion and molar masses in copolymerization reactions. Particularly, results show for the first time that micromixing effects can be important to explain the dynamic behavior of polymerization reactions performed in bulk, but are not sufficient to explain the whole set of available experimental data, which are much more sensitive to modification of residence time distributions and macromixing. 相似文献
This work is focused on the development and validation of a model accounting for the impact of the reactor residence time distribution in well‐stirred slurry‐phase catalytic polymerization of ethylene. Particle growth and morphology are described through the Multigrain model, adopting a two‐site model for the catalyst and a conventional kinetic scheme. Particle size distribution and polymer properties (average molecular weights and polydispersity) are computed as a function of particle size through a segregated model, assuming that neither breakage nor aggregation occur. Reactors are modeled by means of fundamental mass conservation equations. The model is applied to a system constituted by a series of two ideal continuous stirred tank reactors, where the synthesis of polyethylene with bimodal molecular weight distribution is performed, employing the initial catalyst size distribution as the only adjustable parameter. The model provides insights at the single particle scale for each specific size, thus highlighting the inhomogeneity which arises from the synergic effects of chemical kinetics and residence time distributions in both reactors. The satisfactory agreement between model results and experimental data, in terms of particle size distribution and average molecular weights, confirmed the suitability of the model and underlying assumptions. 相似文献
An improved kinetic model for the radical polymerization of N‐vinyl‐pyrrolidone (NVP) in aqueous medium is developed. Quantum chemical simulations reveal that the transfer to polymer is of minor importance whereas the transfer to monomer by hydrogen abstraction in 3‐position of the pyrrolidone ring leads to a radical with a double bond which initiates a new chain bearing a terminal double bond (TDB). The resulting dead chains with one, two, or more TDB are the main source for a strong increase of molar mass in batch reactors at high conversion due to long chain branching and crosslinking. This can be a source for gel formation and fouling in continuous reactors. 相似文献
In this paper, we developed two types of programs in order to simulate the polymerization reaction of a fully deuterated crystal of diacetylene 2,4‐hexadiynylene bis(p‐toluenesulfonate) (pTS‐D). The first simulation is based on a modification of Baughman's model, a classical model for simulating the polymerization of diacetylene crystals. The agreement between the simulated and experimental results concerning the reaction kinetics is satisfactory. With this simulation algorithm, we take into account the experimental observation that the polymerization of pTS‐H and pTS‐D crystals is really a random process of formation of polymer chains along the crystallographic axis b . The second simulation is based on the Monte Carlo method, which permits not only to simulate the kinetics of the reaction, but also the chain‐length distribution in the hydrogenated and deuterated compounds. These two types of simulations were already developed for the hydrogenated crystal of diacetylene, named pTS‐H. Two main modifications are applied in the case of pTS‐D for taking into account experimental results: in the first the rate constants of chain‐terminating microscopic processes are different in pTS‐H and pTS‐D which must be considered. The second modification concerns the evolution of the lattice deformation during the course of polymerization. The experimental variation of the b parameter as a function of polymer content X in pTS‐D is different from that in pTS‐H; this result is important to consider when calculating the activation energy of the initiation and propagation microscopic processes. 相似文献
Summary: The deconvolution of molecular weight distributions (MWDs) may be useful for obtaining information about the polymerization kinetics and properties of catalytic systems. However, deconvolution techniques are normally based on steady‐state assumptions and very little has been reported about the use of non‐stationary approaches for the deconvolution of MWDs. In spite of this, polymerization reactions are often performed in batch or semi‐batch modes. For this reason, dynamic solutions are proposed here for simple kinetic models and are then used for deconvolution of actual MWD data. Deconvolution results obtained with dynamic models are compared to deconvolution results obtained with the standard stationary Flory‐Schulz distributions. For coordination polymerizations, results show that dynamic MWD models are able to describe experimental data with fewer catalytic sites, which indicates that the proper interpretation of the reaction dynamics may be of fundamental importance for kinetic characterization. On the other hand, reaction dynamics induced by modification of chain transfer agent concentration seem to play a minor role in the shape of the MWD in free‐radical polymerizations.
This Figure illustrates that MWDs obtained at unsteady conditions should not be deconvoluted with standard steady‐state Flory‐Schulz distributions. 相似文献
We present terminal deoxynucleotidyl transferase‐catalyzed enzymatic polymerization (TcEP) for the template‐free synthesis of high‐molecular‐weight, single‐stranded DNA (ssDNA) and demonstrate that it proceeds by a living chain‐growth polycondensation mechanism. We show that the molecular weight of the reaction products is nearly monodisperse, and can be manipulated by the feed ratio of nucleotide (monomer) to oligonucleotide (initiator), as typically observed for living polymerization reactions. Understanding the synthesis mechanism and the reaction kinetics enables the rational, template‐free synthesis of ssDNA that can be used for a range of biomedical and nanotechnology applications. 相似文献