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William Franco
William Franco

Polymerization Process Modeling Dotson Download Pdf


Polymer components are shaped mostly out of the molten state. As in the case of semi-crystalline polymers, crystallization can be suppressed by shock cooling, thermal process design allows to influence the solid bodies properties. A simulation approach that enables to predict these properties based on a forecast of crystallinity is presented in this paper. The main effects to consider and possibilities of modeling and simulation are discussed. A detailed description of how to create an experimental foundation using dynamic scanning calorimetry (DSC) and a rheometer is provided. Suppression of crystallization is modeled by a novel phenomenological approach, based on data over a large band of cooling rates. Special focus is put on parameter identification and extension of insufficient DSC data. The mechanical behavior is modeled using a weighted approach based on a nonlinear-thermoviscoelastic model for the molten state and a highly viscous Newtonian model for the solid state. Parameterization of both models is highlighted. An implementation in OpenFOAM is documented, emphasizing specific methods that were applied. Results of simulations for a simplified profile extrusion and injection molding case are presented. Basic relationships are forecasted correctly by the method, and important findings are presented for both processes.




polymerization process modeling dotson download pdf



The underlying mechanism is that, during non-isothermal crystallization, the applied cooling rate influences crystal growth. In the case of low cooling rates, large crystals develop, leading to high crystallinity. For high cooling rates, many small crystals can be found, resulting in a large count of impingements that reduce crystallinity, see, e.g., [6]. Furthermore, it is possible to completely suppress crystallization for even higher cooling rates. The standard procedure for investigating these effects is to perform DSC [7] scans. Only recently, commercial equipment that allows to investigate the latter effect at such high cooling rates was made available, see [8] and [9]. This makes possible a new way to formulate phenomenological crystallization models. In combination with modeling the influence of crystallization on a flow process, this represents the core of this paper.


Considering the peaks in this plot, it shows that, e.g., for 2.5 K min\(^-1\), the sample melts at around 165 \(^\circ \)C and crystallizes at 130 \(^\circ \)C. From this, an approximate discrepancy of 35 K results, which is detectable for all cooling rates presented in Fig. 1. This finding means, just crystallized regions will not melt because of a small rise in temperature. Regarding crystallization processes in technical devices that are designed particularly for cooling, this means crystallization can be considered to be an irreversible process, as such devices do not allow the temperature to increase. It is a valuable effect for modeling considering that this demands a model formulation allowing only progress of crystallization. In order to investigate the crystallization behavior further, a greater range of cooling rates was investigated. However, since only the latent heat signal \(\dotq(\theta ,\dot\theta )\) is of interest, the caloric signal is subtracted based on a polynomial fit. This leads to graphs shown in Fig. 2, already allowing to determine general dependencies for crystallization.


The present work addresses the modeling and simulation of the addition of copolymerizations of styrene and methyl methacrylate in batch mode, and the formation of tailored vinyl acetate/acrylic acid copolymers is evaluated through stochastic optimization procedures based on the Monte Carlo method. A kinetic model of the free-radical reaction was proposed in order to predict the behavior of the reaction system taking into consideration the presence of the penultimate unit effect. The profiles of conversion and copolymer composition were also evaluated considering the effect of the medium viscosity (kinetic phenomena related to gel and glass effects) on the reaction performance. It was shown that the proposed model for chain-growth copolymerization is able to describe strong nonlinear behaviors such as autoacceleration of the polymerization and drift of copolymer composition. It was also shown that copolymers with homogeneous composition can be successfully synthesized through manipulation of the monomer feed flow rate based on a stochastic optimization procedure.


In spite of the popularity of the terminal model, it is generally agreed that the existence of the penultimate unit effect in important chain-growth polymerization systems seems to be general rather than an exception, which clearly indicates that this polymerization kinetic based on the terminal model oversimplifies actual polymerization reaction processes [8, 14]. Initial studies on the influence of the penultimate unit effect in free-radical copolymerizations date from 1940s. Among then, the pioneering works of Merz et al. [2], Barb [30], and Ham [33] must be highlighted.


According to the proposed kinetic mechanism and assuming that the long-chain and quasi-steady-state hypotheses are valid for the polymer radicals and admitting that the propagation terms are much larger than the initiation, chain transfer, and termination terms, it is possible to write the following set of mass balance equations for the copolymerization process:wherewhere is the reactivity ratio monomers and , is the radical reactivity ratios for growing polymer chain , is the cross-termination constant between polymer radicals and , and is the moles of monomer incorporated into polymer chains.


A uniform polymer (often referred to as a monodisperse polymer) is composed of molecules of the same mass.[5] Nearly all natural polymers are uniform.[6] Synthetic near-uniform polymer chains can be made by processes such as anionic polymerization, a method using an anionic catalyst to produce chains that are similar in length. This technique is also known as living polymerization. It is used commercially for the production of block copolymers. Uniform collections can be easily created through the use of template-based synthesis, a common method of synthesis in nanotechnology.[citation needed]


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