Branching and Crosslinking in Coordination Terpolymerizations

Abstract

A general kinetic method, based upon population balances of generating functions, is applied to the prediction of the microstructure and molecular size of non‐linear terpolymers obtained through the coordination polymerization of two monovinyl monomers and a non‐conjugated diene. A rather complex kinetic scheme involving crosslinking and long‐chain branching is considered. It is shown that even in these conditions it is possible to carry out the prediction of molecular size and mass distributions, sequence size distributions, and z‐average mean‐square radius of gyration of the polymers. The influence of some kinetic parameters on the properties of the products is studied, considering a homogeneous operation in a semi‐batch reactor. The used simulation method is able to predict these properties before and after gelation whenever it occurs.magnified image

Simple model to predict gel formation in olefin‐diene copolymerizations catalyzed by constrained‐geometry complexes

“…Previous modeling studies of olefin‐diene copolymerizations have typically focused on semi‐batch systems, and they have used finite element10 or generating functions11 to address the numerical complexities encountered in rigorous non‐linear polymerization modeling. Here, we have made several simplifications to derive a simple analytical relation suitable for process control of industrial reactors.…”

Gel Formation in Aqueous Suspension Nitroxide‐Mediated Radical Co‐Polymerization of Styrene/Divinylbenzene

“…Recent modeling studies based on the use of the method of moments and the Flory–Stockmayer theory of gelation26, 27 showed that NMRP seems to lead to more homogeneous polymer networks, but this effect is less important when the initial content of crosslinker is increased. Combination of the new experimental results presented here with a general kinetic modeling approach based on generating functions75–81, 84 will hopefully improve this discussion.…”

“…Especially important in this field were the developments obtained by Dušek 24, 74. Experimental researches have been accompanied by the development of different theories aiming at the description of the crosslinking process and gel formation 75–81…”

Controlled Synthesis, Characterization, and Flow Properties of Ethylene–Diene Copolymers

“…In particular, the weight‐averaged molar mass diverges as a power‐law function of the reduced distance to the gel point. A number of existing synthesis and modeling studies focus on this semibatch reaction of α‐olefin (ethylene or propylene) with non‐conjugated dienes.…”

“…At a certain diene concentration, the solution of the approximated equations fails to predict a real root for the weight averaged molar mass and is identified as the gel point. Many of the subsequent theoretical studies retained the closure approximation, while introducing more complexity in the description of the reaction steps. In a recent publication, we used Monte Carlo simulations to show that the exponential distribution of residence times of the molecules synthesized in a CSTR and the residence time dependence of the probability for branch formation at the pendant dienes lead to molar mass distributions with power‐law tails with the power‐law exponent demanding finite values of the first three moments of the molar mass at gelation.…”