Multicenter nature of titanium‐based Ziegler–Natta catalysts: Comparison of ethylene and propylene polymerization reactions

This article discusses the similarities and differences between active centers in propylene and ethylene polymerization reactions over the same Ti‐based catalysts. These correlations were examined by comparing the polymerization kinetics of both monomers over two different Ti‐based catalyst systems, δ‐TiCl₃‐AlEt₃ and TiCl₄/DBP/MgCl₂‐AlEt₃/PhSi(OEt)₃, by comparing the molecular weight distributions of respective polymers, in consecutive ethylene/propylene and propylene/ethylene homopolymerization reactions, and by examining the IR spectra of “impact‐resistant” polypropylene (a mixture of isotactic polypropylene and an ethylene/propylene copolymer). The results of these experiments indicated that Ti‐based catalysts contain two families of active centers. The centers of the first family, which are relatively unstable kinetically, are capable of polymerizing and copolymerizing all olefins. This family includes from four to six populations of centers that differ in their stereospecificity, average molecular weights of polymer molecules they produce, and in the values of reactivity ratios in olefin copolymerization reactions. The centers of the second family (two populations of centers) efficiently polymerize only ethylene. They do not homopolymerize α‐olefins and, if used in ethylene/α‐olefin copolymerization reactions, incorporate α‐olefin molecules very poorly. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1745–1758, 2003     

Co-oligomerization of ethylene and higher linear alpha olefins. II. Olefin reactivities in various reaction steps of co-oligomerization with nickel ylide-based system

Part I described co-oligomerization reactions of ethylene and various linear α-olefins (propylene, 1-butene, 1-hexene, 1-heptene, 1-octene, and 1-decene) in the presence of the homogeneous catalyst consisting of sulfonated nickel ylide and diethylaluminum ethoxide. The present article analyzes olefin reactivities in various reaction steps of the co-oligomerization reactions as well as reactivities of various catalytic species. Chain propagation reactions (insertion into the Ni? C bonds) with participation of α-olefins exhibit poor regioselectivity, primary insertion being ca. 60% more probable than the secondary insertion. Ethylene is significantly more reactive in chain propagation reactions: 50–70 times compared to olefin primary insertion and 100–120 times compared to olefin secondary insertion. Reactivities of α-olefins in chain propagation reactions decrease slightly for higher olefin alkyl groups. Reactivities of Ni? C bonds in chain propagation and chain termination reactions strongly depend on the structure of the alkyl group attached to the nickel atom. The Ni? CHR? CH₂? R bond has very low reactivity in ethylene insertion reaction and usually decomposes in the α-hydrogen elimination process. Kinetic analysis of olefin co-oligomerization reactions provides numerous analogies with olefin copolymerization reactions in the presence of Ziegler–Natta catalysts.     

Ethylene polymerization reactions with Ziegler–Natta catalysts. II. Ethylene polymerization reactions in the presence of deuterium

Ethylene polymerization reactions with many Ziegler–Natta catalysts exhibit several features which differentiate them from polymerization reactions of α-olefins: a relatively low ethylene reactivity, higher polymerization rates in the presence of α-olefins, a high reaction order with respect to ethylene concentration, and strong reversible rate depression in the presence of hydrogen. A detailed kinetic analysis of ethylene polymerization reactions (see ref. 1 ) provided the basis for a new reaction scheme which explains all these features by postulating the equilibrium formation of a Ti C₂H₅ species with the H atom in the methyl group β-agostically coordinated to the Ti atom in an active center. This mechanism predicts that the β-agostically stabilized Ti C₂H₅ groups can decompose in the β-hydride elimination reaction with expulsion of ethylene and the formation of a Ti H bond even in the absence of hydrogen in the reaction medium. If D₂ is used as a chain transfer agent instead of H₂, the mechanism predicts the formation of deuterated ethylene molecules, which copolymerize with protioethylene. To prove this prediction, several ethylene homopolymerization reactions were carried out with a supported Ziegler–Natta titanium-based catalyst in the presence of large amounts of D₂. Analysis of gaseous reaction products and polymers confirmed the formation of several types of deuterated ethylene molecules and protio/deuterioethylene copolymers, respectively. In contrast, a metallocene catalyst, Cp₂ZrCl₂ MAO, does not exhibit these kinetic features. In the presence of deuterium, it produces only DCH₂ CH₂ (CH₂ CH₂)_x CH₂ CH₂D molecules. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 4273–4280, 1999     

Hydrogen effects in propylene polymerization reactions with titanium‐based Ziegler–Natta catalysts. I. Chemical mechanism of catalyst activation

The hydrogen activation effect in propylene polymerization reactions with Ti‐based Ziegler–Natta catalysts is usually explained by hydrogenolysis of dormant active centers formed after secondary insertion of a propylene molecule into the growing polymer chain. This article proposes a different mechanism for the hydrogen activation effect due to hydrogenolysis of the Ti? iso‐C₃H₇ group. This group can be formed in two reactions: (1) after secondary propylene insertion into the Ti? H bond (which is generated after β‐hydrogen elimination in the growing polymer chain or after chain transfer with hydrogen), and (2) in the chain transfer with propylene if a propylene molecule is coordinated to the Ti atom in the secondary orientation. The Ti? CH(CH₃)₂ species is relatively stable, possibly because of the β‐agostic interaction between the H atom of one of its CH₃ groups and the Ti atom. The validity of this mechanism was demonstrated in a gas chromatography study of oligomers formed in ethylene/α‐olefin copolymerization reactions with δ‐TiCl₃/AlEt₃ and TiCl₄/dibutyl phthalate/MgCl₂–AlEt₃ catalysts. A quantitative analysis of gas chromatography data for ethylene/propylene co‐oligomers showed that the probability of secondary propylene insertion into the Ti? H bond was only 3–4 times lower than the probability of primary insertion. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 1353–1365, 2002     

Homo-and copolymerization of vinylcyclohexane with α-olefins in the presence of heterogeneous and homogeneous catalytic systems

The polymerization and copolymerization of vinylcyclohexane with α-olefins in the presence of several heterogeneous and homogeneous catalytic systems were studied. It was shown that, with respect to activity in the polymerization of vinylcyclohexane, the tested catalysts can be arranged in the following order: α-TiCl₃ < titanium-magnesium catalyst < metallocene catalyst. Poly(vinylcyclohexane) prepared with heterogeneous catalytic systems is a solid semicrystalline polymer. The properties of polymers synthesized with homogeneous systems differ substantially depending on the type of the metallocene used. In the presence of metallocenes with a C ₂ symmetry, crystalline powderlike products arise, while in the case of metallocenes with C ₁ and C _s symmetries, polymerization yields amorphous viscous products. Molecular-mass distributions of poly(vinylcyclohexane) samples prepared using both heterogeneous titanium-magnesium catalysts and homogeneous metallocene complexes show a bimodal pattern, indicating the heterogeneity of active centers of these catalysts. Upon introduction of a comonomer (ethylene, propylene, and 1-hexene) into the reaction mixture, the activity of all studied catalytic systems increases. When Me₂C(3-Me-Cp)(Flu)ZrCl₂ and rac-Me₂SiInd₂ZrCl₂ are used as catalysts, the degree of crystallinity of the copolymers grows owing to the presence of ethylene or propylene units in poly(vinylcyclohexane) chains.     

Olefin polymerization catalyzed by amide vanadium(IV) complexes: The stereo‐ and regiochemistry of propylene insertion

The reaction of VCl₃(THF)₃ with 1 equiv of the lithium salt of ligand ArNH(Me₂SiCH₂CH₂SiMe₂)NHAr or ArNH(SiMe₃) (Ar = 2,6‐Me₂C₆H₃) afforded the corresponding V(IV) amide complexes, [1,2‐CH₂CH₂(Me₂SiNAr)₂]VCl₂ ( 3 ) and (Me₃SiNAr)₂VCl₂ ( 4 ). The activation of 3 and 4 with the alkyl aluminum compound Al₂Et₃Cl₃ or AlEt₂Cl produced active ethylene polymerization catalysts exhibiting productivity values among the highest reported for vanadium amide based catalysts. Moreover, syndiotactic specific propylene polymerization was successfully conducted at ?40 °C in the presence of 3 /Al₂Et₃Cl₃ and 4 /Al₂Et₃Cl₃. Syndiotactic polypropylenes with moderate stereoregularity ([rr] = 0.66) and a concentration of regioirregular propylene of 6.9 mol % were obtained. Monomodal molecular weight distributions and polydispersity indices lower than 2 were observed in the polymerization runs carried out in heptane solutions. Thus, ethylene–propylene copolymers with propylene concentrations up to 45 mol % were synthesized and characterized by ¹³C NMR and thermal analysis. Good alternation and random distribution of the two monomers were actually obtained. Samples with elevated concentrations of propylene were completely amorphous, with a glass‐transition temperature of ?50 °C. The properties and structure of the copolymers produced with amide vanadium catalysts 3 and 4 were similar to those reported for ethylene–propylenes produced with industrial vanadium‐based catalysts, suggesting the presence of the same active catalyst species. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3279–3289, 2006     

Recent data on the number of active centers and propagation rate constants in olefin polymerization with supported ZN catalysts

Data on the number of active centers (Cp) and propagation rate constants (Kp) have been obtained by means of polymerization quenching with ¹⁴CO of propylene and ethylene polymerization with supported titanium-magnesium catalysts (TMC) with different composition. In the case of propylene polymerization the Cp and Kp values have been measured separately for isospecific, aspecific and low stereospecific centers. Effects of MgCl₂ support, internal and external donors are discussed on the basis of data obtained. Data on the strong effect of diffusion limitation at ethylene polymerization with number of TMC have been obtained and a set of methods have been used to exclude this effect. Data on Cp and Kp values at ethylene polymerization with low stereospecific and highly stereospecific catalysts are presented.     

Studies on Ziegler-Natta catalysts. Part IV. Chemical nature of the active site

The determination of the number of sites active in the polymerization of ethylene on the surface of α-TiCl₃–Al(CH₃)₃ dry catalysts leads to the conclusion that this number is small in comparison to the total surface of the catalyst. Qualitatively this conclusion is also reached by two other independent methods. Infrared spectra of the catalyst before and after polymerization do not show a change in the type of bonds present in the surface. Electron microscopy proves that no active sites are formed on the basal plane of the α-TiCl₃ which constitutes 95% of the total surface. The results strongly favor the lateral faces of α-TiCl₃ as the preferred location of active centers. The lateral faces contain chlorine vacancies and incompletely coordinated titanium atoms. This must then be the essential conditions for the formation of active centers. The propagation of the polymer chain has been repeatedly shown to follow an insertion mechanism. The active site, therefore, necessarily contains a metal–carbon bond. The study of catalysts derived from TiCl₃CH₃ leads to the conclusion that a Ti? C bond on titanium of incomplete coordination is the active species in these cases. The alkylation of surface titanium atoms was proven to be an intermediate step in the catalyst formation from TiCl₃ and AlR₃. Survival of titanium–alkyl bonds on the lateral faces, where titanium atoms are incompletely coordinated explains best, in the light of our data, the activity of Ziegler-Natta catalysts. Coordination of aluminum alkyl compounds in or around the active center probably complicates the structure of the active centers.     

Co-oligomerization of ethylene and higher linear alpha olefins. I. Co-oligomerization with the sulfonated nickel ylide-based catalytic system

Co-oligomers of ethylene and a series of linear α-olefins (propylene, 1-butene, 1-hexene, 1-heptene, 1-octene, and 1-decene) were synthesized with a homogeneous catalyst consisting of sulfonated nickel ylide and diethylaluminum ethoxide at 90°C. GC analysis of the co-oligomerization products allowed complete structural identification of all reaction products, α-olefins with linear and branched chains, vinylidene olefins, and linear olefins with internal double bonds. The article describes the reaction scheme of ethylene–olefin co-oligomerization. The scheme includes chain initiation reactions (insertion of ethylene or an olefin into the Ni? H bond), chain propagation reactions, and chain termination reactions via β-hydride elimination. Primary and secondary inertions of α-olefins into the Ni? H bond in the initiation stage proceed with nearly equal probabilities. Higher olefins participate in the chain growth reactions (insertion into the Ni? C bond) also both in primary and secondary insertion modes. The primary insertion of an α-olefin molecule into the Ni? C bond produces the β-branched Ni? CH₂? CR₁R₂ group. This group is susceptible to β-hydride elimination with the formation of vinylidene olefins. However, the Ni? CH₂? CR₁R₂ groups can participate in further ethylene insertion reactions and thus form vinyl oligomerization products with branched alkyl groups. On the other hand, the secondary insertion of an α-olefin molecule into the Ni? C bond produces the α-branched Ni? CR₁R₂ bond which does not participate in further chain growth reactions and undergoes the β-hydride elimination reaction with the formation of linear reaction products with internal double bonds. Most co-oligomer molecules contain only one α-olefin fragment. However, the analysis of ethylene-propylene and ethylene-1-heptene co-oligomers allowed identification of products with two olefinic fragments which are also formed in the copolymerization reactions with small yields.     

Ethylene polymerization reactions with Ziegler–Natta catalysts. I. Ethylene polymerization kinetics and kinetic mechanism

Kinetics of ethylene homopolymerization reactions and ethylene/1-hexene copolymerization reactions using a supported Ziegler–Natta catalyst was carried out over a broad range of reaction conditions. The kinetic data were analyzed using a concept of multicenter catalysis with different centers that respond differently to changes in reaction parameters. The catalyst contains five types of active centers that differ in the molecular weights of material they produce and in their copolymerization ability. In ethylene homopolymerization reactions, each active center has a high reaction order with respect to ethylene concentration, close to the second order. In ethylene/α-olefin copolymerization reactions, the centers that have poor copolymerization ability retain this high reaction order, whereas the centers that have good copolymerization ability change the reaction order to the first order. Hydrogen depresses activity of each type of center in the homopolymerization reactions in a reversible manner; however, the centers that copolymerize ethylene and α-olefins well are not depressed if an α-olefin is present in the reaction medium. Introduction of an α-olefin significantly increases activity of those centers, which are effective in copolymerizing it with ethylene but does not affect the centers that copolymerize ethylene and α-olefins poorly. To explain these kinetic features, a new reaction scheme is proposed. It is based on a hypothesis that the Ti—C₂H₅ bond in active centers has low reactivity due to the equilibrium formation of a Ti—C₂H₅ species with the H atom in the methyl group β-agostically coordinated to the Ti atom in an active center. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 4255–4272, 1999     

Propylene polymerization with catalysts containing divalent titanium

The behavior in propylene polymerization of divalent titanium compounds of type [η⁶-areneTiAl₂Cl₈], both as such and supported on activated MgCl₂, has been studied and compared to that of the simple catalyst MgCl₂/TiCl₄. Triethylaluminium was used as cocatalyst. The Ti–arene complexes were active both in the presence and in the absence of hydrogen, in contrast to earlier reports that divalent titanium species are active for ethylene but not for propylene polymerization. ¹³C-NMR analysis of low molecular weight polymer fractions indicated that the hydrogen activation effect observed for the MgCl₂-supported catalysts should be ascribed to reactivation of 2,1-inserted (“dormant”) sites via chain transfer, rather than to (re)generation of active trivalent Ti via oxidative addition of hydrogen to divalent species. Decay in activity during polymerization was observed with both catalysts, indicating that for MgCl₂/TiCl₄ catalysts decay is not necessarily due to overreduction of Ti to the divalent state during polymerization. In ethylene polymerization both catalysts exhibited an acceleration rather than a decay profile. It is suggested that the observed decay in activity during propylene polymerization may be due to the formation of clustered species that are too hindered for propylene but that allow ethylene polymerization. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 2645–2652, 1997     

Mechanism and kinetics of polymerization of propylene in a microwave plasma

Flowing microwave plasma of propylene and propylene with argon was studied by mass spectrometry. Plasma composition was investigated as a function of external parameters such as pressure, argon/propylene ratio, and microwave-induced power. It was found that the propylene broke down to C₂H₂ and CH₄, or reacted further with propylene. Two main products, leading to the determination of three main chain reactions for the polymerization of propylene by ion-molecule interactions, were observed, namely, C₂H₂ and CH₄. These were the propylene, acetylene, and ethylene chain reactions. It was also found that the propylene disappeared in a pseudo-first-order reaction. Consequently an overall rate constant for the polymerization was determined (50 sec^–1 at 1 torr pressure for propylene plasma). This constant is found to be linearly dependent upon the propylene percent concentration, and nonlinearly dependent upon plasma pressure.Partly presented at the 157th meeting of the Electrochemical Society, St. Louis, Missouri, May 11–16, 1980.     

Polymerization with TMA-protected polar vinyl comonomers. I. Catalyzed by group 4 metal complexes with η5-type ligands

This paper describes the use of several kinds of group IV Cp based catalyst systems, in the synthesis of co- and terpolymers of ethylene, propylene and α-olefins endowed with OH and COOH functional groups. The hydroxy monomers used were 5-hexen-1-ol (4) and 10-undecen-1-ol (5) and the carboxy monomer was 10-undecen-1-oic acid (6). The three catalyst systems used were the C₂ symmetric ansa-zirconocene (1) the “in-site” titanium complex (2) and the non-rigid zirconocene (3), all activated by methylaluminoxane. Trimethylaluminium was used to protect the functional group of polar monomers. The first two catalyst systems suffer similar activity loss in the presence of polar monomer whereas the third one exhibited better tolerance toward the hydroxyolefins. NMR and FTIR spectroscopies were used to characterize the polymerization products. All three catalyst systems afforded functionalized co- and terpolymers by direct polymerization of ethylene/propylene/hydroxy-α-olefins but only the catalyst system (1)/MAO displays appreciable activities for direct polymerization of ethylene, propylene and carboxy-α-olefins. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 2457–2469, 1999     

Peculiarities of Ethylene Polymerization Reactions with Heterogeneous Ziegler–Natta Catalysts: Kinetic Analysis

The previously developed kinetic scheme for olefin polymerization reactions with heterogeneous Ziegler–Natta catalysts states that the catalysts have several types of active centers which have different activities, different stabilities, produce different types of polymer materials, and respond differently to reaction conditions. In the case of ethylene polymerization reactions, each type of center exhibits an unusual chemical feature: a growing polymer chain containing one ethylene unit, Ti—C₂H₅, is unusually stable and can decompose with the formation of the Ti—H bond. This paper examines quantitative kinetic ramifications of this chemical mechanism. Modeling of the complex kinetics scheme described in the Scheme demonstrates that it correctly and quantitatively predicts three most significant peculiarities of ethylene polymerization reactions, the high reaction order with respect to the ethylene concentration, reversible poisoning with hydrogen, and activation in the presence of α‐olefins.     

Experimental and Computational Approaches on the Isospecific Role of Monoester-Type Internal Electron Donor for TiCl4/MgCl2 Ziegler-Natta Catalysts

In this work, a combination of experimental and computational approaches on the isospecific role of monoester-type internal electron donors (ED) such as phenylpropionate (PhP), ethylheptanoate (EH), methylbenzoate (MB), ethylbenzoate (EB) for TiCl₄/ED/MgCl₂ Ziegler-Natta catalysts had been performed. The propylene polymerization results revealed that the isospecificity of catalysts increases in the following order: PhP < EH < MB < EB. The subsequent molecular modeling on the electronic properties of the donors and two kinds of cluster model catalysts: TiCl₄/ED/MgCl₂ and TiCl₄/ED/(MgCl₂)₄ based on density functional theory (DFT) method was carried out. Two kinds of ED coordination on MgCl₂ clusters through either O or  O within the monoester-type ED had been disclosed. A perfect correlation between the dipole moment of ED, the coordination bond length of O … Mg, the competitive coordination from  O with Mg ion and the isospecificity of the catalysts had been established.     

Polymerization of propylene catalyzed over highly active and stereospecific catalysts synthesized with Mg(OEt)2/benzoyl chloride/TiCl4

A series of monoester catalysts has been studied, each catalyst prepared by the reaction of magnesium diethoxide with benzoyl chloride [BzCOCl, to produce ethyl benzoate (EB) in situ] in the presence of excess titanium tetrachloride. Solid product and catalysts obtained by subsequent treatments with titanium tetrachloride were characterized by elemental analysis, IR spectroscopy, x-ray diffraction, BET measurement, and thermal gravimetric analysis. The catalysts yielded very high activity (above 20 kg polymer/g Ti h atm) for the polymerization of propylene in slurry reactions. From the results of polymerization as well as catalyst characterization, the effects of internal and external Lewis bases on the isospecificity and stability of catalysts are discussed in detail. © 1992 John Wiley & Sons, Inc.     

Ion pairs formed in metallocene-based systems by the “double activation” mechanism and their catalytic activity

The DFT method is used to study the interaction between metallocene catalyst precursors used in ethylene and propylene polymerization and two molecules of the Al-containing cocatalyst Al(C₆F₅)₃. The participation of two Al centers in metallocene activation accounts for the catalytic activity and other properties of the catalytic systems. Two energy parameters characterizing the number of active sites and the polymerization rate per site are calculated. Published in Russian in Kinetika i Kataliz, 2006, Vol. 47, No. 2, pp. 215–222. The article was translated by the authors.     

Mechanism of olefin polymerization on supported Ziegler-Natta catalysts based on data on the number of active centers and propagation rate constants

The number of active centers (C _g) and propagation rate constants (k _g) for the polymerization of propylene and ethylene on highly active titanium-magnesium catalysts (TMCs) of different compositions at 70°C were determined using the method of ¹⁴CO inhibition of polymerization. In the polymerization of propylene on the TiCl₄/D₁/MgCl₂-AlEt₃/D₂ system (D₁ is dibutyl phthalate or 2,2-diisobutyl-1,3-dimethoxypropane; D₂ is a silane), the effects of D₁ and D₂ donors on the values of C _g and k _g were studied. It was found that the donors decreased the values of k _g for nonstereospecific centers, had no effect on the values of k _g for stereospecific centers, and increased the fraction of stereospecific centers, as well as the fraction of sleeping centers regardless of their stereospecificity. The rate constants of isotactic-chain transfer with C₃H₆, AlEt₃, H₂,and ZnEt₂ were determined. In the polymerization of ethylene, a number of TMCs exhibited strong diffusion limitations, which manifested themselves in a dramatic decrease in the determined values of k _g. It was demonstrated that diffusion limitations can be removed by decreasing the particle size and the concentration of active centers and by performing prepolymerization with propylene. The values of k _g in ethylene polymerization were similar for stereospecific and nonstereospecific centers.__________Translated from Kinetika i Kataliz, Vol. 46, No. 2, 2005, pp. 180–190.Original Russian Text Copyright © 2005 by Bukatov, Zakharov, Barabanov.     

The mechanism of ethylene polymerization by nickel salicylaldiminato catalysts - Agostic interactions and their kinetic isotope effects

The ethylene polymerization reaction of a neutral nickel catalyst was studied by DFT calculations at the Becke3LYP/6-31G(d) level of theory. As in related cases a β-agostic bond stabilizes the nickel alkyl ground states. Transition states for the insertion of the olefin show a distinct α-agostic interaction, which has not been observed for late metal polymerization catalysts before. An ethylene-alkyl complex was identified as the resting state of the reaction. The overall barrier height of the reaction amounts to 17.54 kcal/mol, which slightly increases to 17.60 kcal/mol for the polymerization of deuterated ethylene. Therefore, a small positive kinetic isotope effect (k_H/k_D = 1.09) can be calculated, which is caused by the α-agostic interaction in the transition state. A comparison to other late metal based polymerization systems reveals that the ethylene coordination step of highly active catalysts is significantly lower in energy compared to catalysts which are only moderately active.     

用乙酰氯淬灭法测定Ziegler-Natta催化剂的活性中心数

The reactions of Solvay TiCl₃-AlR₃ (R=C₂H₅,i-C₄H₉) catalysts with acetyl chloride were studied. The main reaction, which is much faster than the reactions between A1R₃ and CH₃COC₁, is as follows:It is found that when CH₃COC₁ was introduced into 1-octene polymerization systems catalyzed by TiCl₃-AlR₃ for 5-15min, it reacted selectively and completely with the active centers to produce acetyl-ended polymer chains.With CH₃COC₁ as a quenching agent, the number of active centers in .these polymerization systems were determined by measuring the content of carbonyl in the polymer,and the results consist with those obtained by kinetics-molecular-weight method.