Modeling Molecular Weight and Degree of Branching Distribution of Low-Density Polyethylene

Iedema, Piet D.; Wulkow, Michael; Hoefsloot, Huub C. J.

doi:10.1021/ma991711o

Cited by 102 publications

(173 citation statements)

References 25 publications

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“…When the scission reaction is involved together with long-chain branching, the time sequence of branching and scission must be properly accounted for. This kind of reaction system cannot be fully represented by a simple set of population balance differential equations [3][4][5][6][7]. On the other hand, by application of Monte Carlo (MC) method, based on the random sampling technique [8,9], history-dependence of branching and scission can be fully accounted for [7,[10][11][12].…”

Section: Open Accessmentioning

confidence: 99%

Model-Based Reactor Design in Free-Radical Polymerization with Simultaneous Long-Chain Branching and Scission

Tobita

2015

Processes

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Polymers are the products of processes and their microstructure can be changed significantly by the reactor systems employed, especially for nonlinear polymers. The Monte Carlo simulation technique, based on the random sampling technique, is used to explore the effect of reactor types on the branched polymer structure, formed through free-radical polymerization with simultaneous long-chain branching and scission, as in the case of low-density polyethylene synthesis. As a simplified model for a tower-type multi-zone reactor, a series of continuous stirred-tank reactors, consisting of one big tank and the same N-1 small tanks is considered theoretically. By simply changing the tank arrangement, various types of branched polymers, from star-like globular structure to a more randomly branched structure, can be obtained, while keeping the following properties of the final products, the monomer conversion to polymer, the average branching and scission densities, and the relationship between the mean-square radius of gyration and molecular weight.

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Section: Open Accessmentioning

confidence: 99%

Model-Based Reactor Design in Free-Radical Polymerization with Simultaneous Long-Chain Branching and Scission

Tobita

2015

Processes

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“…Indeed, commercial code PREDICI, using this principle, can only compute one-dimensional distributions. Nevertheless, with some adaptations [21] (remembering Teymour's ''numerical fractionating'' approach [16,22] ) it could be used for modeling ethylene free radical polymerization.…”

Section: Discussionmentioning

confidence: 99%

Prediction of Sol Fraction and Average Molecular Weights after Gelation for Non‐Linear Free Radical Polymerizations Using a Kinetic Approach

Costa

Dias

2003

Macro Theory & Simulations

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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.magnified imageComparison between predicted number‐average and weight‐average degrees of polymerization of sol in batch non‐linear free radical polymerizations of model system III.

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“…In fact, our approach (5.8)-(5.9) is closely related to a corresponding model reduction approach proposed in [18,19] for the Fokker-Planck equation, and to similar techniques in the context of polymerization kinetics (cf. [31]). …”

Section: Model Reduction Based On Conditional Expectations (Mrce) Thmentioning

confidence: 99%

On Reduced Models for the Chemical Master Equation

Jahnke¹

2011

Multiscale Model. Simul.

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Abstract. The chemical master equation plays a fundamental role for the understanding of gene regulatory networks and other discrete stochastic reaction systems. Solving this equation numerically, however, is usually extremely expensive or even impossible due to the huge size of the state space. Thus, the chemical master equation must often be replaced by a reduced model which operates with a considerably smaller number of degrees of freedom but hopefully still provides the essential information about the dynamics of the full system. We prove error bounds for two reduced models which have previously been proposed in the literature. Based on the error analysis, an alternative model reduction approach for the chemical master equation is introduced and discussed, and its advantage is illustrated by numerical examples.Key words. Chemical master equation, model reduction, hybrid models, error bounds AMS subject classifications. 34K60, 65C20, 60J27, 92D251. Introduction. Many processes in nature can be considered as reaction systems in which d ∈ N different species interact via r ∈ N reaction channels. The time evolution of such a system is usually modeled by the traditional reaction-rate equations, a set of d coupled ordinary differential equations which indicate how the concentrations of the d species change in time. This approach is simple and computationally cheap, but fails in situations where the influence of inherent stochastic noise cannot be ignored, and where certain species have to be described in terms of integer particle numbers instead of real-valued, continuous concentrations. This is the case in gene regulatory networks, viral kinetics with few infectious individuals, and many other biological systems.The chemical master equation (CME) respects the discreteness and randomness of the problem and thus provides a more accurate model. The system is considered as a random variable Z(t) which evolves according to a Markov jump process on N

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Modeling Molecular Weight and Degree of Branching Distribution of Low-Density Polyethylene

Cited by 102 publications

References 25 publications

Model-Based Reactor Design in Free-Radical Polymerization with Simultaneous Long-Chain Branching and Scission

Model-Based Reactor Design in Free-Radical Polymerization with Simultaneous Long-Chain Branching and Scission

Prediction of Sol Fraction and Average Molecular Weights after Gelation for Non‐Linear Free Radical Polymerizations Using a Kinetic Approach

On Reduced Models for the Chemical Master Equation

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