Introduction of reactive functionality by the incorporation of divinylbiphenyl in ethylene copolymerization with styrene or 1‐hexene using aryloxo‐modified half‐titanocenes and MAO catalysts

An efficient introduction of vinyl group into poly (ethylene‐co‐styrene) or poly(ethylene‐co?1‐hexene) has been achieved by the incorporation of 3,3′‐divinylbiphenyl (DVBP) in terpolymerization of ethylene, styrene, or 1‐hexene with DVBP using aryloxo‐modified half‐titanocenes, Cp′TiCl₂(O?2,6‐ⁱPr₂C₆H₃) [Cp′ = Cp*, ^tBuC₅H₄, 1,2,4‐Me₃C₅H₂], in the presence of MAO cocatalyst, affording high‐molecular‐weight polymers with unimodal distributions. Efficient comonomer incorporations have been achieved by these catalysts, and the content of each comonomer could be varied by its initial concentration charged. The postpolymerization of styrene was initiated from the vinyl group remained in the side chain by treatment with n‐BuLi. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 2581–2587     

Olefin polymerization with Me4Cp–Amido complexes with electron‐withdrawing groups

A series of Me₄Cp–amido complexes {[η⁵:η¹‐(Me₄C₅)SiMe₂NR]TiCl₂; R = t‐Bu, 1 ; C₆H₅, 2 ; C₆F₅, 3 ; SO₂Ph, 4 ; or SO₂Me, 5 } were prepared and investigated for olefin polymerization in the presence of methylaluminoxane (MAO). X‐ray crystallography of complexes 3 and 4 revealed very long Ti N bonds relative to the bonds of 1 . These complexes were employed for ethylene–styrene copolymerizations, styrene homopolymerizations, and propylene homopolymerizations in the presence of MAO. The productivities of the catalysts derived from 3 – 5 were much lower than the productivity of the catalyst derived from 1 for the propylene polymerizations and ethylene–styrene copolymerizations, whereas the styrene polymerization activities were much higher for the catalysts derived from 3 – 5 than for the catalyst derived from 1 . The polymerization behavior of the catalysts derived from the metallocenes 3 – 5 were more reminiscent of monocyclopentadienyl titanocene Cp′TiX₃/MAO catalysts than of CpATiX₂/MAO catalysts such as 1 containing alkylamido ligands. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 4649–4660, 2000     

Olefin polymerization and copolymerization with soluble transition‐metal complex catalysts

Olefin polymerizations catalyzed by Cp′TiCl₂(O‐2,6‐ⁱPr₂C₆H₃) ( 1 – 5 ; Cp′ = cyclopentadienyl group), RuCl₂(ethylene)(pybox) { 7 ; pybox = 2,6‐bis[(4S)‐4‐isopropyl‐2‐oxazolin‐2‐yl]pyridine}, and FeCl₂(pybox) ( 8 ) were investigated in the presence of a cocatalyst. The Cp*TiCl₂(O‐2,6‐ⁱPr₂C₆H₃) ( 5 )–methylaluminoxane (MAO) catalyst exhibited remarkable catalytic activity for both ethylene and 1‐hexene polymerizations, and the effect of the substituents on the cyclopentadienyl group was an important factor for the catalytic activity. A high level of 1‐hexene incorporation and a lower r_E · r_H value with 5 than with [Me₂Si(C₅Me₄)(N^tBu)]TiCl₂ ( 6 ) were obtained, despite the rather wide bond angle of Cp Ti O (120.5°) of 5 compared with the bond angle of Cp Ti N of 6 (107.6°). The 7 –MAO catalyst exhibited moderate catalytic activity for ethylene homopolymerization and ethylene/1‐hexene copolymerization, and the resultant copolymer incorporated 1‐hexene. The 8 –MAO catalyst also exhibited activity for ethylene polymerization, and an attempted ethylene/1‐hexene copolymerization gave linear polyethylene. The efficient polymerization of a norbornene macromonomer bearing a ring‐opened poly(norbornene) substituent was accomplished by ringopening metathesis polymerization with the well‐defined Mo(CHCMe₂Ph)(N‐2,6‐ⁱPr₂C₆H₃)[OCMe(CF₃)₂]₂ ( 10 ). The key step for the macromonomer synthesis was the exclusive end‐capping of the ring‐opened poly(norbornene) with p‐Me₃SiOC₆H₄CHO, and the use of 10 was effective for this polymerization proceeding with complete conversion. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 4613–4626, 2000     

Stereospecific styrene polymerization and ethylene–styrene copolymerization with titanocenes containing a pendant amine donor

A series of monocyclopentadienyl titanium complexes containing a pendant amine donor on a Cp group ( A = CpTiCl₃, B = Cp^NTiCl₃, C = Cp^NTiCl₂TEMPO, for Cp = C₅H₅, Cp^N = C₅H₄CH₂CH₂N(CH₃)₂, and TEMPO = 2,2,6,6‐tetramethylpiperidine‐N‐oxyl) are investigated for styrene homopolymerization and ethylene–styrene (ES) copolymerization. When activated by methylaluminoxane at 70 °C, complexes with the amine group ( B and C ) are active for styrene homopolymerization and afford syndiotactic polystyrene (sPS). The copolymerizations of ethylene and styrene with B and C yield high‐molecular weight ES copolymer, whereas complex A yields mixtures of sPS and polyethylene, revealing the critical role that the pendant amine has on the polymerization behavior of the complexes. Fractionation, NMR, and DSC analyses of the ES copolymers generated from B and C suggest that they contain sPS. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1579–1585, 2010     

Efficient introduction of aromatic vinyl group by incorporation of divinylbiphenyl,p‐divinylbenzene in syndiospecific styrene polymerization using aryloxo‐modified half‐titanocene catalysts

An efficient introduction of aromatic vinyl group into syndiotactic polystyrene has been achieved by incorporation of 3,3′‐divinylbiphenyl, p‐divinylbenzene (DVB) in syndiospecific styrene polymerization using aryloxo‐modified half‐titanocenes, Cp′TiCl₂(O‐2,6‐ⁱPr₂C₆H₃) (Cp′ = ^tBuC₅H₄, 1,2,4‐Me₃C₅H₂), in the presence of MAO. The resultant polymers possessed high molecular weights with uniform molecular weight distributions, and the DVB contents could be varied by the initial feed molar ratios (6–23 mol %) without decrease in the M_n values. The syndiotactic stereo‐regularity and presence of the vinyl groups were confirmed by NMR spectra. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 1902–1907     

Efficient terpolymerization of ethylene and styrene with α‐olefins by aryloxo‐modified half‐titanocene‐based catalysts and cocatalyst systems

Aryloxo‐modified half‐titanocenes, Cp′TiCl₂(O‐2,6‐ⁱPr₂C₆H₃) [Cp′ = Cp* ( 1 ), ^tBuC₅H₄ ( 2 )], catalyze terpolymerization of ethylene and styrene with α‐olefin (1‐hexene and 1‐decene) efficiently in the presence of cocatalyst, affording high‐molecular‐weight polymers with unimodal distributions (compositions). Efficient comonomer incorporations have been achieved by these catalysts. The content of each comonomer (α‐olefin, styrene, etc.) could be controlled by varying the comonomer concentration charged, and resonances ascribed to styrene and α‐olefin repeated insertion were negligible. The terpolymerization with p‐methylstyrene (p‐MS) in place of styrene also proceeded in the presence of [PhN(H)Me₂][B(C₆F₅)₄] and AlⁱBu₃ cocatalyst, and p‐MS was incorporated in an efficient matter, affording high‐molecular‐weight polymers with uniform molecular weight distributions. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 2565–2574     

Efficient ethylene/norbornene copolymerization by half‐titanocenes containing imidazolin‐2‐iminato ligands and MAO catalyst systems

Ethylene copolymerizations with norbornene (NBE) using half‐titanocenes containing imidazolin‐2‐iminato ligands, Cp′TiCl₂[1,3‐R₂(CHN)₂C?N] [Cp′ = Cp ( 1 ), ^tBuC₅H₄ ( 2 ); R = ^tBu ( a ), 2,6‐ⁱPr₂C₆H₃ ( b )], have been explored in the presence of methylaluminoxane (MAO) cocatalyst. Complex 1a exhibited remarkable catalytic activity with better NBE incorporation, affording high‐molecular‐weight copolymers with uniform molecular weight distributions, whereas the tert‐BuC₅H₄ analog ( 2a ) showed low activity, and the resultant polymer prepared by the Cp‐2,6‐diisopropylphenyl analog ( 1b ) possessed broad molecular weight distribution. The microstructure analysis of the poly(ethylene‐co‐NBE)s prepared by 1a suggests the formation of random copolymers including two and three NBE repeating units. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 2575–2580     

Effect of Cocatalyst in Ethylene/Styrene Copolymerization by Aryloxo‐Modified Half‐Titanocene–Cocatalyst Systems for Exclusive Synthesis of Copolymers at High Styrene Concentrations

Factors affecting the product distributions in ethylene/styrene copolymerizations catalyzed by Cp*TiCl₂(O‐2,6‐ⁱPr₂C₆H₃) are explored in the presence of various cocatalysts at high styrene/ethylene feed ratios (at 40 and 55 °C). Ethylene/styrene copolymers were the sole product when the reactions were conducted in the presence of [PhN(H)Me₂][B(C₆F₅)₄] and AlⁱBu₃/Al(octyl)₃ even at 55 and 70 °C, whereas syndiotactic polystyrene was by‐produced when the polymerizations were performed at >40 °C in the presence of MAO; the ratios of the copolymer/SPS were affected by the reaction temperature as well as Al cocatalyst employed.

     

Insertions‐ und Substitutionsreaktion von Ameisensäuremethylester mit [Cp′2ZrCl(PHTipp)] – Molekülstruktur von meso‐trans‐[Cp′2ZrCl{OCH(PHTipp)2}] (Cp′ = η5‐C5MeH4, Tipp = 2,4,6‐Pri3C6H2)

Insertion and Substitution Reaction of Methyl Formate with [Cp′₂ZrCl(PHTipp)] – Molecular Structure of meso‐trans ‐[Cp′₂ZrCl{OCH(PHTipp)₂}] (Cp′ = η⁵‐C₅MeH₄, Tipp = 2,4,6‐Prⁱ₃C₆H₂) [Cp′₂ZrCl(PHTipp)] ( 1 ) (Cp′ = η⁵‐C₅MeH₄, Tipp = 2,4,6‐Prⁱ₃C₆H₂) reacts with methyl formate with insertion and substitution to give [Cp′₂ZrCl{OCH(PHTipp)₂}] ( 2 ). 2 was characterized spectroscopically (¹H, ³¹P NMR, IR, MS) and by X‐ray structure determination. Only the meso‐trans isomer is present in the solid state.     

Catalytic Trimerization of Ethylene with Highly Active Half-sandwich Titanium Complexes Bearing Pendant p-Fluorophenyl Groups

Two new complexes[η~5-C_5H_4CMe_2-(p-fluorophenyl)]TiCl_3(1)and[μ~5-C_5H_4C(cyclo-C_5H_(10))-(p-fluoro-phenyl)]TiCl_3(2)were synthesized and characterized.Their activities and selectivities for trimerization of ethylenewere investigated.The introduction of fluorine atom greatly weakened the arene coordination,but this disadvanta-geous factor can be eliminated by introduction of a bulky substituent,such as cyclo-C_5H_(10),to the bridging carbonlinked to the Cp ring.The combinative effect of the fluorine substitute and the bridging unit can make complex 2 asa highly active and selective catalyst for ethylene trimerization.Its productivity and selectivity for 1-hexene canreach 1024.0 kg·mol~(-1)·h(-1) and 99.3% respectively.     

Copolymerization of styrene and conjugated dienes with half‐sandwich titanium(IV) catalysts: The effect of the ligand structure on the monomer reactivity,monomer sequence distribution,and insertion mode of dienes

The copolymerization of styrene and 1,3‐butadiene (Bd) or isoprene (Ip) was carried out with half‐sandwich titanium(IV) Cp′TiCl₃ catalysts (where Cp′ is cyclopentadienyl 1 , indenyl 2 , or pentamethylcyclopentadienyl 3 ) with methylaluminoxane as a cocatalyst. For the copolymerization with Bd, catalyst 3 gave the copolymers containing the highest amount of Bd among the catalysts used. The resulting copolymers were composed of a styrene–Bd multiblock sequence. High melting points were observed in the copolymers prepared with catalyst 1 . The structures of hydrogenated poly(styrene‐co‐Bd) were studied by ¹³C NMR spectroscopy, and the long styrene sequence length was detected in the copolymers prepared with catalyst 1 . For styrene/Ip copolymerization, random copolymers were obtained. Among the used catalysts, catalyst 1 gave the copolymers containing the highest amount of Ip. The copolymers prepared with catalyst 1 showed a steep melting point depression with increasing Ip content because of the high ratio of 1,4‐inserted Ip units and/or the low molecular weights of the copolymers. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 939–946, 2003     

Selective Insertion in Copolymerization of Ethylene and Styrene Catalyzed by Half‐Titanocene System Bearing Ketimide Ligand: A Theoretical Study

The copolymerization of ethylene and styrene can be efficiently carried out by using Cp*TiCl₂ (N = C^t Bu₂)/MAO (Cp*=η ⁵‐C₅Me₅ ) system, yielding the poly(ethylene‐co ‐styrene)s with isolated styrene units. In order to investigate the reasons for formation of the structure, the mechanism of copolymerization, especially the selective insertion of ethylene and styrene, is studied in detail by density functional theory (DFT ) method. At the initiation stage, insertion of ethylene is kinetically more favorable than insertion of styrene, and insertion of styrene kinetically and thermodynamically prefers 2,1‐insertion. That is different from the conventional half‐titanocene system, in which the 1,2‐insertion is favorable. At chain propagation stage, the computational results suggest that the continuous insertion of styrene is hard to occur at room temperature due to the high free energy barriers (28.90 and 35.04 kcal/mol for 1,2‐insertion, and 29.15 and 34.00 kcal/mol for 2,1‐insertion) and thermodynamically unfavorable factors in two different conditions. That is mainly attributed to the steric hindrance between the coming styrene and chain‐end styrene or ketimide ligand. The computational results are in good agreement with the experimental data.     

A Tandem Catalytic System for the Synthesis of Ethylene–Hex‐1‐ene Copolymers from Ethylene Stock

Summary: A tandem catalytic system, composed of (η⁵‐C₅H₄CMe₂C₆H₅)TiCl₃ ( 1 )/MMAO (modified methyl aluminoxane) and [(η⁵‐C₅Me₄)SiMe₂(tBuN)]TiCl₂ ( 2 )/MMAO, was applied for the synthesis of ethylene–hex‐1‐ene copolymers with ethylene as the only monomer stock. During the reaction, 1 /MMAO trimerized ethylene to hex‐1‐ene, while 2 /MMAO copolymerized ethylene with the in situ produced hex‐1‐ene to poly(ethylene–hex‐1‐ene). By changing the catalyst ratio and reaction conditions, a series of copolymer grades with different hex‐1‐ene fractions at high purity were effectively produced.

The overall strategy of the tandem 1 / 2 /MMAO catalytic system.     

Direct synthesis of linear low‐density polyethylene of ethylene/1‐hexene from ethylene with a tandem catalytic system in a single reactor

Tandem catalysis offers a promising synthetic route to the production of linear low‐density polyethylene. This article reports the use of homogeneous tandem catalytic systems for the synthesis of ethylene/1‐hexene copolymers from ethylene stock as the sole monomer. The reported catalytic systems employ the tandem action between an ethylene trimerization catalyst, (η⁵‐C₅H₄CMe₂C₆H₅)TiCl₃ ( 1 )/modified methylaluminoxane (MMAO), and a copolymerization metallocene catalyst, [(η⁵‐C₅Me₄)SiMe₂(^tBuN)]TiCl₂ ( 2 )/MMAO or rac‐Me₂Si(2‐MeBenz[e]Ind)₂ZrCl₂ ( 3 )/MMAO. During the reaction, 1 /MMAO in situ generates 1‐hexene with high activity and high selectivity, and simultaneously 2 /MMAO or 3 /MMAO copolymerizes ethylene with the produced 1‐hexene to generate butyl‐branched polyethylene. We have demonstrated that, by the simple manipulation of the catalyst molar ratio and polymerization conditions, a series of branched polyethylenes with melting temperatures of 60–128 °C, crystallinities of 5.4–53%, and hexene percentages of 0.3–14.2 can be efficiently produced. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4327–4336, 2004     

The Effect of SiMe3 and SiEt3 Para Substituents for High Activity and Introduction of a Hydroxy Group in Ethylene Copolymerization Catalyzed by Phenoxide-Modified Half-Titanocenes

Remarkable effects of SiMe₃ and SiEt₃ para-substituents in the phenoxide-modified half-titanocenes, Cp*TiCl₂(O-2,6-ⁱPr₂-4-R-C₆H₂) [R=SiMe₃ ( 6 ), SiEt₃ ( 7 )], toward the catalytic activities in ethylene copolymerizations with 2-methyl-1-pentene, 1-decene, 1-dodecene and with 9-decen-1-ol (DC-OH) have been demonstrated. The activities by 6 , 7 at 50 °C showed higher than those conducted at 25 °C in all cases in the presence of MAO cocatalyst. Efficient synthesis of high-molecular-weight (HMW) ethylene copolymers incorporating DC-OH (or 5-hexen-1-ol, HX-OH) has been attained in the copolymerization by 7 , which showed better DC-OH (HX-OH) incorporation at 50 °C to afford the HMW copolymers, poly(ethylene-co-DC-OH)s, with high activities (activity 1.21–3.81×10⁵ kg-polymer mol⁻¹-Ti h, M_n=6.55–10.0×10⁴, DC-OH 2.3–3.6 mol %).     

Copolymerization of 2‐butene and ethylene with catalysts based on titanium and zirconium complexes

The polymerization of 2‐butene and its copolymerization with ethylene have been investigated using four kinds of dichlorobis(β‐diketonato)titanium complexes, [ArN(CH₂)₃NAr]TiCl₂ (Ar = 2,6‐ⁱPr₂C₆H₃) and typical metallocene catalysts. The obtained copolymers display lower melting points than those produced of homopolyethylene under the same polymerization conditions. ¹³C NMR analysis indicates that 9.3 mol‐% of 2‐butene units were incorporated into the polymer chains with Ti(BFA)₂Cl₂‐MAO as the catalyst system. With the trans‐2‐butene a higher copolymerization rate was observed than with cis‐2‐butene. A highly regioselective catalyst system for propene polymerization, [ArN(CH₂)₃NAr]TiCl₂ complex using a mixture of triisobutylaluminium and Ph₃CB(C₆F₅)₄ as cocatalyst, was found to copolymerize a mixture of 1‐butene and trans‐2‐butene with ethylene up to 3.1 mol‐%. Monomer isomerization‐polymerization proceeds with typical metallocene catalysts to produce copolymers consisting of ethylene and 1‐butene.     

Pentafulvenkomplexe des Titans — Synthese,Struktur und Fluktuierendes Verhalten von Cp′Ti{η6‐C5H4=C(p‐Tol)2}Cl (Cp′ = Cp*, Cp)

Complexes of Titanium — Synthesis, Structure, and Fluxional Behaviour of CpTi{η⁶‐C₅H₄=C(p‐Tol)₂}Cl (Cp′ = Cp*, Cp) The reaction of Cp′TiCl₃ (C′ = Cp* or Cp) with magnesium and 6, 6‐di‐para‐tolylpentafulvene generates good yields of pentafulvene complexes Cp*Ti{η⁶‐C₅H₄=C(p‐Tol)₂}Cl ( 4 ) and CpTi{η⁶‐C₅H₄=C(p‐Tol)₂}Cl ( 5 ), respectively. The crystal and molecular structure of 4 have been determined from X‐ray data and exhibits compared to known η⁶‐pentafulvene complexes an unusual large Ti—C(p‐Tol)₂ (Fv)‐distance (2.535(5)Å) evoked by the bulky substituents at the exocyclic carbon. Dynamic ¹H‐NMR and spin saturation transfer experiments point out a rotation of the fulvene ligand around the Ti—Ct2 axis (Ct2 = centroid of the fulvene ring carbon atoms) with an activation barrier ΔG^≠_C = 60.6 ± 0.5 kJ mol⁻¹ (T_C = 314 ± 2 K). For 5 this barrier is significantly larger. Analogous dynamic behaviour is well known for diene complexes, but to our knowledge, it is here first‐time described for a pentafulvene complex.     

An experimental and computational evaluation of ethylene/styrene copolymerization with a homogeneous single‐site titanium(IV)‐constrained geometry catalyst

Styrene was copolymerized with ethylene using the geometry constrained Me₂Si(Me₄Cp)(N‐tert‐butyl)TiCl₂ Dow catalyst activated with methylaluminoxane. Increasing the styrene/ethylene ratio in the reactor feed had the effects of reducing both the activity of the catalyst and the molecular weight of the copolymers produced. However, the higher the styrene/ethylene ratio used, the greater the amount of styrene that became incorporated in the copolymer. We discuss these experimental findings within the framework of a computational analysis of ethylene/styrene copolymerization performed through hybrid density functional theory (B3LYP). In general, there was good agreement between the experimental and theoretical results. Our findings point to the suitability of combining experimental and theoretical data for clarifying the copolymerization mechanisms that take place in α‐olefin‐organometallic systems. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 711–725, 2005     

Copolymerization of ethylene and 1-hexene with TiCl4/MgCl2 catalysts modified by 2,6-diisopropylphenol

A supported TiCl4/MgCl2 catalyst without internal electron donor (O-cat) was prepared firstly. Then it was modified by 2,6-diisopropylphenol to make a novel modified catalyst (M-cat). These two catalysts were used to catalyze ethylene/1-hexene copolymerization and 1-hexene homopolymerization. The influence of cocatalyst and hydrogen on the catalytic behavior of these two catalysts was investigated. In ethylene/1-hexene copolymerization, the introduction of 2,6-iPr2C6H3O-groups did not deactivate the supported TiCl4/MgCl2 catalyst. Although the 1-hexene incorporation in ethylene/1-hexene copolymer prepared by M-cat was lower than that prepared by O-cat, the composition distribution of the former was narrower than that of the latter. Methylaluminoxane (MAO) was a more effective activator for M-cat than triisobutyl-aluminium (TIBA). MAO led to higher yield and more uniform chain structure. In 1-hexene homopolymerization, the presence of 2,6-iPr2C6H3O-groups lowered the propagation rate constants. Two types of active centers with a chemically bonded 2,6-iPr2C6H3O-group were proposed to explain the observed phenomena in M-cat.     

Monomer-isomerization polymerization. XI. Monomer-isomerization copolymerizations of 2-butene with 2-pentene and 2-hexene with Ziegler-Natta catalyst

2-Pentene and 2-hexene were found to undergo monomer-isomerization copolymerizations with 2-butene by Al(C₂H₅)₃–VCl₃ and Al(C₂H₅)₃–TiCl₃ catalysts in the presence of nickel dimethylglyoxime or transition metal acetylacetonates to yield copolymers consisting of the respective 1-olefin units. For comparison, the copolymerizations of 1-pentene with 1-butene and 1-hexene with 1-butene by Al(C₂H₅)₃–VCl₃ catalyst were also attempted. The compositions of the copolymers obtained from these copolymerizations were determined by using the calibration curves between the compositions of the respective homopolymer mixtures and the values of D₇₆₆/D₁₃₈₀ in the infrared spectra. The monomer reactivity ratios for the monomer-isomerization copolymerizations of 2-butene (M₁) with 2-pentene and 2-hexene, in which the concentrations of both 1-olefins calculated from the observed isomer distribution were used as those in the monomer feed mixture, and for the ordinary copolymerizations of 1-butene (M₁) with 1-pentene and 1-hexene by Al(C₂H₅)₃-VCl₃ catalyst were determined as follows: 2-butene (M₁)/2-pentene (M₂): r₁ = 0.14, r₂ = 0.99; 1-butene (M₁)/1-pentene (M₂): r₁ = 0.30, r₂ = 0.74; 2-butene (M₁)/2-hexene (M₂): r₁ = 0.11, r₂ = 0.62; 1-butene (M₁)/1-hexene (M₂): r₁ = 0.13, r₂ = 0.90.