Terminal and Penultimate Reactivity Ratios in Single‐Site Ethene/Propene Copolymerizations: Comparison of Kakugo and Direct Peak Methods

Abstract

Summary: The original, first‐order Kakugo method is extended to find second‐order reactivity ratios of homogeneous catalysts in ethene/propene copolymerizations based on triad fractions. Subsequently, the first‐ and second‐order reactivity ratios of eight Si‐bridged C2‐symmetric ansa‐zirconocenes or hafnocenes, as obtained by the Direct Peak method, are used to compare with the Kakugo methods. From the results it is clear that the second‐order methods give better descriptions than the first‐order methods. Only the results of the second‐order Direct Peak method are statistically justified, reflecting reliabilities >99.5%. Though the Direct Peak method in all cases gives the most reliable reactivity ratios, the second‐order Kakugo method turns out to be a practical tool to find estimates.Second‐order Kakugo method.imageSecond‐order Kakugo method.

Ethylene/propylene copolymerization over three conventional C2‐symmetric metallocene catalysts: Correlation between catalyst configuration and copolymer microstructure

“…In addition, we also found that in MBu system, propylene units in the copolymers, even in small amounts, tend to arrange in a consecutive way to form mini‐blocks within polymer chains, and there is a strong penultimate effect, which is widespread for many metallocenes and is reported by some authors 32–37. Losio et al33 consider the “penultimate effect” as the influence of penultimate unit on the insertion rate of a monomer.…”

“…According to the literature,2 the results afforded by statistical method are more reliable with respect to the Fineman‐Ross approach, which is based on the assumption of the validity of the ultimate effect. So the gap between the two sets of r E and r P indicates that there is a strong “penultimate effect” in the SiPh and MBu systems, which is referred by some authors for E/P copolymerizations 2, 23, 32–37. In this case, with respect to first‐order Markovian statistical model, the second‐order model allows a better fitting with experiment data.…”

“…In this case, with respect to first‐order Markovian statistical model, the second‐order model allows a better fitting with experiment data. On the basis of literature,32–37 model selection seems not to affect the interpretation of experimental data; therefore, the results from first‐order Markovian model are still analyzed in detail.…”

How the restriction of sliding diffusion of comonomers affects crystallization and melting of homogeneous copolymers

“…These copolymers have been synthesized by copolymerization of ethene/ethylene (denoted as '1') and propene/propylene (denoted as '2') with six comparable, but slightly different metallocene catalysts [7]. The copolymerization kinetics of these systems can be well described by penultimate or second-order Markovian reactivity ratios r ijk with i, j, k elements of {1,2} [8].…”

Molecular structure and driving force to metastable states: Janus faces in polymer crystallization

“…Both Ziegler–Natta and metallocene catalysts for the polymerization of ethylene‐based copolymers can be tackled. In principle the direct 13 C NMR peak method can be applied to all types of copolymers after some adjustments . It is even possible to describe copolymers made using a mixture of homogeneous catalysts facilitating work on heterogeneous catalysts having bimodal (co)monomer sequence length distributions, like in the case of LLDPE and VLDPE.…”