Mathematical modeling of crystallization analysis fractionation of ethylene/1‐hexene copolymers

Abstract

Crystallization analysis fractionation (Crystaf) is a polymer characterization technique for estimating the chemical composition distributions of semicrystalline copolymers. Although Crystaf has been widely used during the recent years, it is still a relatively new polymer characterization technique. More quantitative understanding of its fractionation mechanism is essential for further developments. In this work, three ethylene/ 1-hexene copolymers with different 1-hexene fractions, but similar number-average molecular weights, were analyzed by Crystaf at several cooling rates. A mathematical model was proposed to describe the effect of comonomer fraction and cooling rate on Crystaf fractionation from a fundamental point of view. The model describes the experimental Crystaf profiles of ethylene/1-hexene copolymers with different 1-hexene fractions measured at distinct cooling rates very well.

Ethylene/1‐Butene Copolymerization over Heterogeneous Metallocene Catalyst

“…All the samples present unimodal composition distributions but a significant reduction of crystallization temperature is observed when increasing 1-butene fraction. These results are in agreement with others previously reported, [26,27] confirming the decrease of copolymers crystallinity with the comonomer incorporation. It is remarkable that low 1-butene contents in the copolymer (test 9 and 10) leads to CRYS-TAF profiles slightly narrower than that corresponding to the homopolymer, suggesting that copolymers with very homogeneous distributions of 1-butene along polyethylene chains can be obtained when using this heterogeneous metallocene catalysts under the experimental conditions used.…”

Effect of Operating Conditions on Dynamic Crystallization of Ethylene/1‐Octene Copolymers

“…[ 15 ] Similar trends also observed in both CRYSTAF and TREF models. [10][11][12][13][14] The parameter n was also found to be constant at 4.5, which is close to the Avrami exponent in CRYSTAF and TREF models ( n ≈ 4.49) as well. The values of parameter k were strongly infl uenced by the cooling rate, the k value increases with an increase in the cooling rate; this has also been observed in CRYSTAF and TREF models.…”

“…[10][11][12][13][14][15] The modeling approach based on crystallization kinetics and the concept of population balances was fi rst introduced to describe CRYSTAF. [10][11][12][13] Although TREF differs from CRYSTAF, the concept of population balances can be adapted to TREF by discretizing the TREF columns in a series of small control volumes. A TREF model based on crystallization/dissolution kinetics and population balances was successfully used to describe the TREF analysis of ethylene/1-olefi ns with various chain microstructures at a wide range of operating conditions.…”

“…The mass fraction of polymer chains crystallized at a specifi c column location and time is calculated as the product between the mass crystallization fraction obtained from Equation 17 and the mass dispersion profi les obtained from Equation 11 :…”

Recent Advances in High-Temperature Fractionation of Polyolefins

“…Therefore, the authors argue that CRYSTAF (or equivalently TREF) is an essential analysis tool to characterize copolymers made with coordination catalysts, even when they are expected to behave as single-site catalysts. Soares et al [60] investigated three different ethylene/1-hexene copolymers with different 1-hexene contents but similar number average molar masses at several cooling rates for CRYSTAF analysis. They proposed a mathematical model to describe the effect of comonomer fraction and cooling rate on CRYSTAF fractionation.…”