Development of a Kinetic Model for Thermal Crosslinking of Rubbery Polymers

Abstract

Summary: A kinetic model for the thermal crosslinking of rubbery polymers is presented. The reaction mechanism used to develop the model includes thermal radical generation producing a polymeric radical and a primary radical, crosslinking from attack of a polymer radical to any inactive polymer molecule, bimolecular radical termination among chains of any degree of branching, and radical termination between a polymer radical and a primary radical from the thermal radical generation. The overall polymer population is divided into “generations”, which are defined in terms of the number of primary (linear) chains of original rubbery polymer attached to the polymer molecule. Mass balances for each generation are written down, and expressions to calculate fraction of branched molecules, gel fraction, and number and weight average chain lengths are derived. Model simulations, parameter sensitivity analyses and preliminary parameter estimation studies are presented, taking the thermal crosslinking of linear polybutadiene as a case study.Development of a kinetic model for thermal crosslinking of rubbery polymers: reaction mechanism, model equations and parameter sensitivity analyses.magnified imageDevelopment of a kinetic model for thermal crosslinking of rubbery polymers: reaction mechanism, model equations and parameter sensitivity analyses.

Multiscale Modeling and Characterization of Radical-Initiated Modification of Molten Polyolefins

“…Based on the above mechanism and kinetic rate information, a model can be constructed through which quantitative relationships between the product properties and the reaction conditions are established. In general, there are two approaches to modeling the complex reaction network for macromolecules, namely, the numerical population balance and the kinetic stochastic method. ,,,− Under a proper scheme of parameterization, both strategies are capable of calculating properties, such as molecular weight distribution (MWD) and gel content that closely match with experimental data. However, the implementation of the stochastic method does not require closure rules and the mono-radical approximation (that are commonly used in the population balance method ,,− ), and is therefore numerically easier to be adopted in this work.…”

Mechanism and Kinetics

“…A kinetic model incorporating many of the features discussed here has been implemented by Vivaldo -Lima et al and used to fi t experimental data with good success, as shown in Figure 3.1 [36] .…”

Sol MWD During Styrene, Vinyl Acetate, Methyl Methacrylate, and Butyl Acrylate Homopolymerization: A Numerical Study Using the NFT Approach

“…The NFT, either in its original form or in improved versions, has been used to model the emulsion polymerization of vinyl monomers with chain transfer to polymer (CTP) and termination by combination (TC), [26] and the copolymerization of vinyl/ divinyl monomers. [27][28][29] Vivaldo-Lima et al [30] developed a kinetic model to calculate the branching and crosslinking fractions, as well as number-and weight-average molecular weights in the thermal crosslinking of rubbery polymers. In the development of their model, Vivaldo-Lima et al [30] used some of the ideas of the NFT.…”

“…[27][28][29] Vivaldo-Lima et al [30] developed a kinetic model to calculate the branching and crosslinking fractions, as well as number-and weight-average molecular weights in the thermal crosslinking of rubbery polymers. In the development of their model, Vivaldo-Lima et al [30] used some of the ideas of the NFT. The group of Morbidelli has also been active in the study of gelation, particularly in water-dispersion polymerization processes.…”