2ZrCl2 Catalyst Active-Center Distribution on ... - ACS Publications

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Effects of Supported (nBuCp)2ZrCl2 Catalyst Active-Center Distribution on Ethylene−1-Hexene Copolymer Backbone Heterogeneity and Thermal Behaviors Muhammad Atiqullah,*,†,‡ Siripon Anantawaraskul,§ Abdul-Hamid M. Emwas,∥ Mamdouh A. Al-Harthi,⊥ Ikram Hussain,† Anwar Ul-Hamid,# and Anwar Hossaen† †

Center for Refining and Petrochemicals, Research Institute, ‡Center of Research Excellence in Petroleum Refining and Petrochemicals, ⊥Department of Chemical Engineering, and #Center for Engineering Research, Research Institute, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia § Department of Chemical Engineering, Kasetsart University, Jatujak, Bangkok 10900, Thailand ∥ NMR Core Laboratory, King Abdullah University of Science & Technology, Thuwal 23955-6900, Saudi Arabia ABSTRACT: Two catalysts, denoted as catalyst 1 [silica/MAO/(nBuCp)2ZrCl2] and catalyst 2 [silica/nBuSnCl3/MAO/ (nBuCp)2ZrCl2] were synthesized and subsequently used to prepare, without separate feeding of methylaluminoxane (MAO), ethylene homopolymer 1 and homopolymer 2, respectively, and ethylene−1-hexene copolymer 1 and copolymer 2, respectively. Gel permeation chromatography (GPC), Crystaf, differential scanning calorimetry (DSC) [conventional and successive selfnucleation and annealing (SSA)], and 13C nuclear magnetic resonance (NMR) polymer characterization results were used, as appropriate, to model the catalyst active-center distribution, ethylene sequence (equilibrium crystal) distribution, and lamellar thickness distribution (both continuous and discrete). Five different types of active centers were predicted in each catalyst, as corroborated by the SSA experiments and complemented by an extended X-ray absorption fine structure (EXAFS) report published in the literature. 13C NMR spectroscopy also supported this active-center multiplicity. Models combined with experiments effectively illustrated how and why the active-center distribution and the variance in the design of the supported MAO anion, having different electronic and steric effects and coordination environments, influence the concerned copolymerization mechanism and polymer properties, including inter- and intrachain compositional heterogeneity and thermal behaviors. Copolymerization occurred according to the first-order Markovian terminal model, producing fairly random copolymers with minor skewedness toward blocky character. For each copolymer, the theoretical most probable ethylene sequences, nE MPDSC‑GT and nE MPNMR‑Flory, as well as the weight-average lamellar thicknesses, Lwav DSC−GT and Lwav SSA DSC, were found to be comparable. To the best of our knowledge, such a match has not previously been reported. The percentage crystallinities of the homo- and copolymers increased linearly as a function of LMPDSC‑GT. This indicates that the homo- and copolymer chains folded excluding the butyl branch. The results of the present study will contribute to developing future supported metallocene catalysts that will be useful in the synthesis of new grades of ethylene−α-olefin linear low-density polyethylenes (LLDPEs).

1. INTRODUCTION

pertinent literature, in the context of the present study, is reviewed. First, the relation of the copolymer composition distribution (CCD) to the thermal properties is considered. Several studies1,2 determined the CCD only qualitatively without correlating it to the thermal properties, whereas Paredes et al.3,4 observed that the peak melting temperature and percentage crystallinity decreased with increasing 1-hexene mole percentage in the copolymer. The CCD of ethylene−1-hexene copolymers, synthesized by supported metallocenes, varied from monomodal to bimodal, depending on the support and metallocene types, support modification, amount of 1-hexene fed, and so on.1−4 Note that none of the cited reports studied the alternate melting and crystallization behaviors of the

Metallocenes, because of their ability to undergo remarkable structural variations, can regulate the comonomer-introduced branch distribution, intrachain microstructures, and structural/ enchainment defects of ethylene−α-olefin copolymers [called linear low-density polyethylenes (LLDPEs)] in a highly versatile fashion. The density, crystallinity, melting, and processing characteristics and thermal, rheological, and mechanical properties of LLDPE differ significantly from those of low-density polyethylene (LDPE) and high-density polyethylene (HDPE). Consequently, LLDPE has a series of applications superior to those of LDPE and HDPE. During processing, LLDPEs melt as well as crystallize. Therefore, it is important to investigate their thermal behaviors. In this study, our focus was ethylene−1-hexene copolymer, particularly synthesized using supported metallocenes. Note that supported catalysts are a prerequisite for industrial plants to attain the desired polymer particulate morphology. Next , the © 2013 American Chemical Society

Received: Revised: Accepted: Published: 9359

February 16, 2013 June 8, 2013 June 12, 2013 June 12, 2013 dx.doi.org/10.1021/ie4005139 | Ind. Eng. Chem. Res. 2013, 52, 9359−9373

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experimental copolymers nor did they address these findings from the viewpoints of (i) the catalyst active-center distribution, (ii) the variance in the design of the supported cocatalyst anion (having different electronic and steric effects and coordination environments), (iii) the copolymer intrachain heterogeneity (monomer sequence distributions and the associated microstructural parameters), and (iv) the ethylene sequence (equilibrium crystal) length distribution. Second, the ethylene−1-hexene copolymer intrachain microstructure and its effects on polymer melting behaviors are summarized. Hung et al.5 synthesized a series of ethylene−1hexene copolymers with ethylene contents of 49−85 mol % and average reactivity ratio products (⟨rErH⟩) of 1.8−2.2, using a mixed-π-ligand nonbridged metallocene. The samples were aged for 36 h. The ranges of melting span, peak melting temperature, and heat of fusion were found to be 28−106 °C, 36−94 °C, and 0.9−23.2 J/g, respectively. These findings were qualitatively attributed to the comonomer sequence distribution and long crystallizable ethylene sequence. Unfortunately, no values were reported for the sequence distributions and average ethylene sequence lengths nE, nor was the CCD determined. Based on the fact that ⟨rErH⟩ was greater than unity, the copolymers were concluded to be blocky. This conclusion was not further evaluated by determining the random parameter χR6 and the sequence length distribution. Chaichana et al.7 noted that the high incorporation of 1-hexene by [SiMe2(tBuN)(Flu)]TiMe2 synthesized alternating ethylene−1-hexene copolymers without any peak melting temperature (1-hexene = 31.6−77.0 mol %, ⟨rErH⟩ = 0.487−0.737). This result was ascribed to fairly high values of content of the EHH (E = ethylene, H = 1-hexene) triad sequence (0.144− 0.424) and varying ethylene and 1-hexene sequence lengths (nE = 1.533−3.530, nH = 2.104−1.300). Park et al.8 synthesized two ethylene−1-hexene copolymers using Et(Ind)2ZrCl2 and Et(Ind)2ZrCl2/TiCl4 impregnated on a methylaluminoxane(MAO-) treated silica−magnesium hybrid support. They studied the copolymer melting behavior by determining the lamellar thickness distribution (LTD). The LTD of the former was found to be wider than that of the latter. This was correlated to the difference in average sequence length and EEH content (for the former copolymer, nE = 20.5 and [EEH] = 9.20; for the latter copolymer, nE = 46.1 and [EEH] = 4.21). These studies1−5,7,8 did not address the melting behaviors of ethylene−1-hexene copolymer from the perspective of the multiplicity of active centers of the supported catalyst, which really affects the copolymer compositional heterogeneity (CCD and intrachain sequence distributions). Metallocenes can be generally supported using several immobilization procedures, as discussed by Severn and Chadwick.9 It turns out that silica/methylaluminoxane (MAO) cocatalyst/zirconocene, in general, offers higher catalyst activity than the remaining routes. However, MAO gels and degrades during cocatalyst feeding. Hence, in this study, two supported catalysts, namely, silica/MAO/ (nBuCp)2ZrCl2 (catalyst 1) and silica/nBuSnCl3/MAO/ (nBuCp)2ZrCl2 (catalyst 2), were synthesized, and polymerization trials were conducted without separately feeding MAO. Silica was used as the support because of its stability at high temperatures; availability with varying pore sizes, volumes, and surface areas; low price; and very large-volume usage by industry.10 (nBuCp)2ZrCl2 was chosen because of its stability, commercial availability at a reasonable price, capability of polymerizing ethylene with high activity in solution, and

considerable application in the synthesis of supported metallocene catalysts.3,4,11−16 In the embodiment of the proposed supported catalysts, silica is heterogeneous. It comprises tetrahedral SiO4 units, siloxane bridges (Si−O−Si)n, and silanols RSi−OH (as surface terminations). Siloxane bridges can typically be 6−10membered rings, whereas silanols can be geminal, vicinal, and isolated.17,18 On the other hand, MAO, represented by the formula (AlOMe)n·(AlMe3)m with n = 6−13 and m = 1−4, maintains cage structures having dynamic equilibrium between trimethylaluminum (TMA) and oligomers of methylaluminoxane (−CH3OAl−)n.19−25 Therefore, silica and MAO are the potential sources of catalyst active-center distribution. To assess the effects of this catalytic characteristic, particularly on the copolymerization mechanism, comonomer composition distribution, and structural microstructures, and the resulting copolymer melting behaviors is, therefore, worth investigating. This will eventually add new insight to this subject and broaden our comprehension. In view of the previous discussions, this study was organized as follows: We first assessed the occurrence of heterogeneous catalysis by the proposed supported catalysts in the absence of the separate feeding of the MAO cocatalyst. This is a prerequisite for studying the subsequent objectives. We then elucidated the catalyst active-center distribution by simultaneously deconvoluting the measured molecular weight and copolymer composition distributions and addressed the model prediction experimentally as well as from the perspective of MAO structural heterogeneity. Finally, we evaluated how the catalyst active-center distribution affects the ethylene−1-hexene copolymer compositional heterogeneity, copolymerization mechanism, and resulting copolymer thermal behaviors.

2. EXPERIMENTAL SECTION 2.1. Materials. Silica PQ 3030 having a surface area of 322 m2/g, an average pore volume of 3.00 cm3/g, and a pore size of 374 Å was used as the catalyst support. (nBuCp)2ZrCl2 and MAO (30 wt % in toluene) was obtained from Chemtura (Bergkamen, Germany), and analytical-grade toluene, n-hexane (both 99.999% pure), molecular sieves, 0.05% (w/v) 2,6-di-tert-butyl-4-methyl phenol (BHT), 1,2,4trichlorobenzene (TCB) (analytical-grade and deuterated), and triisobutylaluminum (TIBA) were all purchased from Aldrich. n BuSnCl3 was obtained from Gelest Chemicals (Morrisville, PA), and ethylene (99.999% pure) was purchased from Abdullah Hashim (a local vendor). An oxygen trap (OT-4SS) and moisture absorber (500CC 316-SS) were obtained from Agilent and Parker, respectively. United Petrochemicals, an affiliate of Saudi Basic Industries Corporation (SABIC), gave us the 1-hexene as a gift. 2.2. Synthesis of Supported Catalysts. We synthesized catalyst 1 [silica/MAO/(nBuCp) 2ZrCl2 ] and catalyst 2 [silica/nBuSnCl3/MAO/(nBuCp)2ZrCl2] as follows. All manipulations were performed under argon using standard Schlenk technique. The required amount of silica was dehydroxylated at 250 °C for 4 h using a Thermocraft furnace equipped with a vertical quartz glass tube, a digital temperature indicator and controller, a gas flow meter, and a vacuum pump. The silica was continuously fluidized during dehydroxylation using nitrogen. Upon completion of dehydroxylation, it was stored in an inert glovebox. 9360

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The average particle size and the span of particle size distribution of each catalyst are reported in Table 1. 2.4. Polymerization Trials and Determination of Polymer Particulate Morphology. Ethylene was homoand copolymerized using a computer-interfaced, AP Miniplant laboratory-scale reactor setup. It consisted of a fixed top head and a 1-L jacketed Büchi glass autoclave. The glass reactor was baked for 2 h at 120 °C. Then, it was purged with nitrogen four times at the same temperature. The reactor was cooled from 120 to 40 °C. About 200 mL of dried n-hexane was transferred to the reactor. Then, 1.0 mL of 1.0 M triisobutylaluminum (TIBA) was added to scavenge the impurities that could poison the catalyst, and the mixture was stirred for 10 min. n-Hexane was dried by contacting it with 4A molecular sieves at room temperature overnight, which decreased the moisture level to less than 10 ppm. The molecular sieve was activated at 230 °C. At this stage, for the copolymerization, 10 mL of 1-hexene was added. The resulting mixture was stirred at 50 rpm for 10 min. For the homopolymerization, no 1-hexene was added. The experimental catalyst was slurried in 50 mL of n-hexane. The whole volume was siphoned into the reactor under mild argon flow. Ethylene was polymerized by passing it through oxygen- and moisture-removing columns and finally feeding it into the reactor at 5 bar. The polymerization temperature and stirrer speed were set at 50 °C and 750 rpm, respectively, and the trial was continued for 1 h. The polymerization was quenched by stopping the ethylene flow and venting the postpolymerization ethylene (in the reactor) to the atmosphere. Then, the data acquisition was stopped, the stirrer speed was reduced to about 100 rpm, and the reactor was gradually cooled to room temperature. Upon completion of the polymerization trials as described, the reactor was opened; the resulting polymer was dried under ambient conditions in a hood, and the dried polymer was weighed to obtain the yield. The polymer yield was subsequently used to determine the corresponding catalyst activity (reported in Table 1). Using each catalyst, one homoand one copolymer were synthesized, the morphologies of which were evaluated as described next. The bulk density was measured using a graduated measuring cylinder. A preweighed mass of the polymer particles was introduced into it. The volume was measured after properly stirring the cylinder. Polymer bulk densities are summarized in Table 2. The average polymer particle size was measured in the same way as for the catalyst. 2.5. Catalyst and Polymer Particulate Surface Morphologies. The catalyst and the experimental polyethylene samples were first coated with a layer of carbon to increase the surface conductivity. These coated samples were characterized using a scanning electron microscope equipped with an energydispersive X-ray spectrometer. The particulate morphology was evaluated by operating the electron microscope in the backscattered electron imaging (BEI) mode. 2.6. Molecular Weights and Polydispersity Indices. The synthesized polymers were characterized in terms of molecular properties [weight-average molecular weight (Mw) and polydispersity index (PDI)] using gel permeation chromatography (GPC) (Polymer Laboratories GPC 220, Shropshire, U.K.). The GPC operating conditions and procedure detailed in one of our earlier publications were followed. 28 The instrument was calibrated using nine polystyrene standards whose peak molecular weights ranged from 2608000 to 1530. The polystyrene calibration curve was

The solvents were dried using 4A molecular sieve. Catalyst 1 was prepared by mixing the dehydroxylated silica in a slurry with dried toluene in a specially designed Schlenck flask. MAO was added to this slurry drop by drop under argon using constant stirring at room temperature. Then, this mixture was heated for several hours. Finally, (nBuCp)2ZrCl2, dissolved in dried toluene, was reacted with this mixture for a defined period of time. The synthesized catalyst was dried under a vacuum. The catalyst, upon drying, turned free-flowing, and it was saved in a glovebox. To prepare catalyst 2, the dehydroxylated silica was first functionalized using nBuSnCl3 as follows: The required amount of silica was placed in a specially designed Schlenk flask under argon. Then, it was mixed in a slurry using dried toluene under magnetic stirring. Next, nBuSnCl3 was injected into the silica− toluene slurry. The resulting mixture was refluxed to tether n BuSnCl3 to silica. The functionalized silica was dried to freeflowing particles under a vacuum and saved it in a glovebox. The remaining catalyst synthesis work followed that of catalyst 1. 2.3. Elemental Composition and Particulate Properties of Supported Catalysts. The elemental compositions of the synthesized catalysts were determined in terms of Si, Al, Sn, and Zr using inductively coupled plasma (ICP) spectrometry (ICP Spectro Ciros Vision, FVE 12-Axial). The procedure summarized in an earlier publication was followed.26 Table 1 lists the concentrations of these metals measured in the synthesized catalysts. Table 1. Elemental Composition and Particulate Properties of the Synthesized Catalystsa catalyst 1b

catalyst 2c

wt % wt % wt % wt % − 102 kg of PE (g of catalyst)−1 h−1 μm

28.43 67.78 0 3.70 61.89 52.5

19.08 73.49 3.76 3.66 67.83 27.0

47.545

56.283

−

1.812

1.662

property catalyst composition silicon (Si) aluminum (Al) tin (Sn) zirconium (Zr) Al/Zr molar ratio copolymerization activity volume-weighted mean particle size span of particle size distribution

units

a Polymerization conditions: polymerization medium, 240.0 mL of nhexane; 1-hexene content, 10.0 mL; scavenger, 1.0 mL of 1.0 M TIBA; temperature, 50 °C; mode of polymerization trial, continuous feeding of ethylene (g) at 5 bar. bCatalyst 1: silica/MAO/(nBuCp)2ZrCl2. c Catalyst 2: silica/nBuSnCl3/MAO/(nBuCp)2ZrCl2.

The particle size distributions of the catalyst samples were measured using a computer-interfaced Mastersizer 2000 particle size analyzer (Malvern Instruments, Malvern, U.K.). First, the liquid feeder was cleaned using deionized water; then the background signal of water in the dispersant tank was measured. Next, about 0.5 g of catalyst sample that showed an obscursion limit of ∼5.0% in deionized water was dispersed. The optical properties of the samples were selected from the library of materials available in the provided software. Each sample was analyzed using five cycles having various stirrer speeds and different intensities of ultrasound. The particle size distribution and its average were calculated using Mie theory. 9361



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crystallized at a cooling rate of 0.2 °C/min from 95 to 35 °C. The qualitative differential composition distribution (dw/dT versus T) was obtained by numerical differentiation of the integral analogue. Finally, this was converted into a quantitative version using a calibration curve developed in our laboratory. 2.9. Copolymer Microstructure and Sequence Length Distribution. The microstructural parameters, including average short-chain branch content and 1-hexene mole percentage in the synthesized copolymers, were determined using 13C nuclear magnetic resonance (NMR) spectroscopy. For this purpose, a Bruker 600 MHz AVANAC III spectrometer (Bruker BioSpin, Rheinstetten, Germany) was used. The details of this instrument and the NMR operating conditions and procedure are available in one of our earlier publications.26 The spectra were recorded using a DEPT (distortionless enhancement by polarization transfer) 135 pulse sequence, and they were analyzed using Bruker Topspin 2.1 software (Bruker BioSpin, Rheinstetten, Germany). The receiver gain was set at 203. Exponential line broadening of 1 Hz was applied before Fourier transformation. DEPT was used because of its prioritized advantages that include enhanced 13C signal sensitivity; superior spectral editing; and capability to distinguish methyl CH3, methylene CH2, and methine CH sites, and identify branches. The 1-hexene mole percentage was calculated in the synthesized copolymers by quantifying the butyl branch, following the published literature.30,40,41 The copolymer microstructural parameters were calculated following the well-known publications of Hsieh and Randall42 and Seger and Maciel.43 In this matter, the calculation of the triad sequences in the 13C NMR spectrum forms the basis, which we accomplished by applying the peak assignment procedures reported earlier. First, the various triad mole fractions were determined using the Seger−Maciel algorithm and the associated collective peak assignment regions. Because the concentration of a given triad is proportional to the algebraic expression of the concerned peak areas, this algorithm does not require signal calibration. Seger and Maciel highlighted the advantages of this approach. Table 3 lists the triad mole fractions of copolymers 1 and 2. Next, the monad and diad mole fractions and the copolymer microstructural parameters of our interest were calculated using the relations reported in refs 5 and 43. Table 4 reports the copolymer microstructural parameters.

Table 2. Properties of the Synthesized Ethylene Homo- and Copolymers units

copolymer 1 copolymer 2

volume-weighted mean particle size

itemized polymer properties

μm

span of particle size distribution

−

particle bulk density

g/mL

polymer material density, dpolymb

g/mL

weight-average molecular weight, Mw

g/mol

polydispersity index, PDI

−

peak melting point, Tpm

°C

peak crystallization point, Tpc

°C

crystallinity, Xc

%

most probable lamellar thickness, LMPDSC‑GT weight-average lamellar thickness, Lwav DSC−GT weight-average lamellar thickness, Lwav SSA DSC width of DSC-GT lamellar thickness distribution, Lσ DSC−GT width of SSA DSC lamellar thickness distribution, Lσ SSA DSC breadth of Crystaf composition distribution, Tσ

nm nm

189.029,a 225.354 1.417,a 1.615 0.272,a 0.290 0.951,a 0.918 166678,a 74435 5.496,a 3.8152 133.30,a 118.07 116.01,a 105.24 79.60,a 43.69 18.96,a 10.81 18.56,a 9.29

nm

9.63

113.514,a 226.188 1.247,a 1.657 0.300,a 0.299 0.951,a 0.926 370126,a 80342 6.2424,a 3.5789 133.32,a 121.62 118.82,a 110.60 68.98,a 52.94 14.68,a 12.75 13.25,a 11.21 11.40

nm

6.76,a 3.15

3.72,a 3.77

nm

2.03

2.30

°C

9.23

5.69

a

Value for the corresponding homopolymer. bCalculated using the semiempirical relation dpolym (material density) = (Tpm + 306)/462.27

converted into the corresponding polyethylene calibration curve using the Mark−Houwink constants of both polymers.29 The Cirrus single detector software was used to calculate the average molecular weights and the polydispersity indices, which are reported in Table 2. 2.7. Thermal Properties and Thermal Melt Fractionation. The thermal properties of the experimental resins and films in terms of peak melting point (Tpm) and percentage crystallinity were measured by differential scanning calorimetry (DSC; DSC Q2000, TA Instruments, New Castle, DE). The instrument was calibrated using indium. The experimental procedure reported in the literature was followed.30,31 The data were acquired for each cycle and handled using the TA Explorer software. Tpm was used to calculate the material density, dpolym.27 Table 2 reports these thermal properties of the as-synthesized polyethylenes. The synthesized copolymers were thermally fractionated using the DSC instrument according to the successive selfnucleation and annealing (SSA) experimental procedure reported in the literature.32−37 Seven annealing steps (160, 125, 119, 114, 111, 107, and 103 °C) were applied. Details are available in ref 33. 2.8. Copolymer Composition Distribution. The composition distributions of copolymer 1 and copolymer 2 were determined using a Polymer Char CRYSTAF 100 instrument. The fractionation principle of this technique has already been published in the literature.38−40 A sample solution of concentration 0.1% (w/w) was prepared in 1,2,4-trichlorobenzene (TCB) at 160 °C under stirring for 60 min. The solution was equilibrated at 95 °C for 45 min and was subsequently

Table 3. Average Copolymer Composition and Triad Sequence Mole Fractionsa catalyst 1b copolymer 1 [E] [H] [EEE] [EEH] [HEH] [EHE] [EHH] [HHH]

Average Copolymer Mole Fraction 0.962 0.038 Triad Mole Fractiond 0.915 0.047 0.000 0.028 0.010 0.000

catalyst 2c copolymer 2 0.982 0.018 0.953 0.029 0.000 0.014 0.004 0.000

E = ethylene, H = 1-hexene. HEE ⇔ EEH; EHH ⇔ HHE. bCatalyst 1: silica/MAO/(nBuCp)2ZrCl2. cCatalyst 2: silica/nBuSnCl3/MAO/ (nBuCp)2ZrCl2. dCalculated using the collective peak assignment algorithm of Seger and Maciel.43 a

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Table 4. Comparison of Microstructural Parameters for Copolymer 1 and Copolymer 2 parameter run number average sequence length nE NMR nH NMR nE MPNMR‑Flory nE MPDSC‑GT persistence ratio, ρ random parameter, χR cluster index ΩE ΩH rE rH first-order Markov reactivity ratio product, rErHb average reactivity ratio product, ⟨rErH⟩b

value for a Bernoullian ethylene−1hexene copolymer

value for a first-order Markovian ethylene−1hexene copolymer

copolymer 1

copolymer 2

2.355

1.448 67.821 1.117 55.000 50.197 1.097 0.912 58.416 0.997 ∞ 162.256 0.043 6.973 6.986

1

any

10 1 1

1 1

1a

1a

40.853 1.146 40.000 42.559 1.103 0.907 34.311 0.987 ∞ 76.928 0.054 4.110

1a

1a

4.152

a Holds for a single-site catalyst; for a multisite catalyst, rErH or ⟨rErH⟩ ≫ 1. bEstimated by applying the relationships listed in refs 5 and 43. E = ethylene, H = 1-hexene. nE MPNMR‑Flory and nE MPDSC‑GT were determined from Figures 7 and 8, respectively.

Figure 1. SEM images of representative (a) catalyst 1 and copolymer 1 particles and (b) catalyst 2 and copolymer 2 particles.

of the sequence of n ethylene units, according to Flory model, is related to the ethylene perpetuation probability p by44,45

The ethylene sequence (equilibrium crystal) length distribution was modeled as follows. The normalized weight fraction wn 9363


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4.2. Copolymer Composition Distribution. Figure 2 shows how the composition distribution of copolymer 1,

(1)

For a statistical copolymer with very long chains, p is related to the experimental reactivity ratio product, ⟨rErH⟩, and ethylene mole fraction, XE, by45 p=1−

1 − [1 − 4(1 − ⟨rErH⟩)XE(1 − XE)]1/2 ; 2(1 − ⟨rErH⟩)XE

⟨rErH⟩ ≠ 1

p = XA = XE ; ⟨rErH⟩ = 1

(2) (3)

3. THEORETICAL BACKGROUND 3.1. Modeling of Catalyst Active-Center Distribution. The catalytic synthesis of ethylene homo- and copolymers (with an α-olefin) is implicitly a statistical process. Consequently, the polymer backbones consist of a mixture of chains that can be represented by various single-site molecular weight distributions (MWDs) and copolymer composition distributions (CCDs). Therefore, the deconvolution of the measured MWDs and CCDsan inverse computational techniquecan determine the number of types of active catalyst sites, that is, the catalyst active-center distribution, and model the corresponding backbone microstructures (MWD and CCD). The mathematical development of the aforementioned deconvolution model and the associated computational algorithm are detailed in the literature.46−59 3.2. Modeling of Lamellar Thickness Distribution. The lamellar thickness distribution was modeled using the traditional Gibbs−Thomson equation,60−63 the Flory model,45,64−67 the cycle 3 DSC melting phase transformation endotherm, and the concept of a continuous distribution.68

Figure 2. Crystaf-determined composition distributions of copolymer 1 and copolymer 2, synthesized by catalyst 1 and catalyst 2, respectively.

determined by Crystaf, differed qualitatively from that of copolymer 2. Copolymer 1 had a bimodal composition distribution. On the other hand, copolymer 2 had an apparently unimodal composition distribution. This observed difference in composition distribution can be expressed by quantitatively reporting the root-mean-square crystallization temperature Tσ (see Table 2). Note that Tσ, which is already defined in the literature,38−40 measures the width of the distribution. The root-mean-square crystallization temperatures for copolymer 1 and copolymer 2 were found to be 9.23 and 5.69 °C, respectively. This means that the incorporation of 1-hexene per polyethylene backbone length (which generates the butyl sidechain branch) was more uniform in copolymer 2 than in copolymer 1. This is explained by considering the difference in catalyst composition and active-site surface chemistry. In catalyst 1, MAO was tethered on silica having isolated −OH Brönsted acid groups; then (nBuCp)2ZrCl2 was impregnated on this structure. In catalyst 2, the isolated −OH Brönsted acid groups were first converted into the corresponding Lewis acid moieties by functionalization with nBuSnCl3 before MAO and (nBuCp)2ZrCl2 were loaded. This transformation of silica surface acidity (Brönsted → Lewis) and the subsequent interaction with MAO in catalyst 2 made the resulting surface chemistry (electronic versus steric effects) of the active-site types and coordination environments differ from those of catalyst 1. Consequently, the Crystaf traces and the corresponding composition distributions of these two copolymers differed. Next, the catalyst active-center distribution, which was modeled using independent deconvolution of the MWD of a homopolymer as well as the simultaneous deconvolution of the MWD and CCD of the corresponding copolymer, is discussed. 4.3. Catalyst Active-Center Distribution. Figure 3 presents the model-predicted Schulz−Flory MWDs of homopolymer 1 and homopolymer 2. On the other hand, Figure 4 shows the Schulz−Flory and Stockmayer MWD and CCD for copolymer 1. For copolymer 2, Figure 5 displays the analogous results. Table 5 reports the estimated model parameters of each catalyst site type in catalyst 1 and catalyst 2. The active-site types were numbered in increasing order of the number-average molecular weight of the Schulz−Flory and Stockmayer components.

4. RESULTS AND DISCUSSION 4.1. Catalyst versus Copolymer Particulate Morphology. In the absence of separate feeding of MAO cocatalyst, no reactor fouling was observed. Free-flowing polyethylene particles with an average bulk density of 0.30 g/mL were obtained (see Table 2). The scanning electron microscopy (SEM) images in Figure 1 show that the polymer particle replicated the corresponding supported catalysts. Because of fragmentation of the original catalyst particles and growth of polymer around these fragments, the polymer particle size increased. The absence of reactor fouling, the achievement of free-flowing polymer particles with good bulk density, and the manifestation of the replication phenomenon establish the occurrence of heterogeneous catalysis in our study. This finding is explained as follows: Without any separate feeding of MAO, a polymer film presumably forms instantaneously around the catalyst particles (due to polymerization) by the active centers available on the surface of the as-synthesized supported catalysts. This film coats the catalyst constituents with a surrounding shell and prevents leaching. This phenomenon is somewhat similar to the conventional prepolymerization that is practiced to feed supported olefin polymerization catalysts into an industrial plant. The work of Smit et al.,68,69 who also polymerized ethylene without separately feeding the MAO cocatalyst, supports our proposed explanation. By taking the SEM cross-sectional image of the dynamic growth of the polyethylene particles, they confirmed that the polymer grew on the fragmenting catalyst particles, not in the polymerization medium/solution. 9364



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Figure 3. Model-predicted Schulz−Flory MWD of homopolymer 1 and homopolymer 2, generated by catalyst 1 and catalyst 2 active-site types, respectively. Excellent agreement is noted between model and experiment.

Figure 4. Model-predicted Schulz−Flory and Stockmayer MWD and CCD of copolymer 1 with catalyst 1 active-site types. Excellent agreement is noted between model and experiment.

Figure 5. Model-predicted Schulz−Flory and Stockmayer MWD and CCD of copolymer 2 with catalyst 2 active-site types. Excellent agreement is noted between model and experiment.

The following observations are common. For each homopolymer, the model-predicted MWD matched the corresponding experimental distribution very well. The same is true for the model-predicted MWD and CCD for each copolymer. It should especially be noted that, in both catalysts having particularly low Al/Zr ratios (62 and 68), five active-site types were predicted by the modeling of the distributions of both homo- and copolymers. This finding conforms to the SSA thermal fractionation results of both copolymers, which also show five melting peaks (see Figure 6). Note that this number of melting peaks differs from the number of annealing steps used (seven) in the SSA experiment. The implications of Figure 6 for copolymer thermal behaviors are detailed in section 4.5.

In the current context of catalyst active-center multiplicity, the study published by Mäkelä-Vaarne et al.70 is of particular relevance. They characterized an as-synthesized silica/MAO/ (nBuCp)2HfCl2 catalyst using extended X-ray absorption fine structure (EXAFS) spectroscopy, which showed several peaks that indicated multiple catalytic species (see Figure 2 (sample 4) of Mäkelä-Vaarne et al.70). Therefore, our work related to catalyst 1 [silica/MAO/(nBuCp)2ZrCl2] agrees with that study. Note that the electron structures of zirconium ([Kr]4d25s2) and hafnium ([Xe]4f145d26s2) are almost identical. According to the already mentioned model predictions and SSA results, the modification of the silica surface by nBuSnCl3 did not change the number of active-site types. Each SSA peak melting temperature represents copolymer backbones with 9365



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Table 5. Catalyst Site Types and Estimated Deconvolution Model Parameters model parameters active catalyst site type 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

χ2 × 103

mi

Catalyst 1, Homopolymer 1 2.83 0.0377 0.1638 0.3346 0.3602 0.1038 Catalyst 1, Copolymer 1 7.05 0.0760 0.2312 0.3329 0.0900 0.2699 Catalyst 2, Homopolymer 2 1.36 0.0477 0.0835 0.3602 0.3550 0.1535 Catalyst 2, Copolymer 2 4.96 0.0792 0.1820 0.4698 0.1422 0.1269

Mni (g/mol) 12583 59668 178504 445576 1283822 3088 17707 42097 51375 109525 3202 11836 40512 99875 212946 5028 13661 32266 69007 106663

Figure 6. Successive self-nucleation and annealing (SSA) thermal fractionations of (a) homopolymer 1 and copolymer 1 and (b) homopolymer 2 and copolymer 2. The copolymer peak melting temperatures conform to the model-predicted catalyst active-center types, as well as qualitatively indicate the structural/enchainment defect introduced through the incorporation of 1-hexene.

practically the same side-chain branching (SCB)/chain imperfection but different mass fractions (see Table 6 and Figure 7). The SCB was calculated using the correlation available in the literature65 (Tpm = −1.69 × SCB + 133) and the related mass fraction applying the J-integral DSC data. Considering the drop in SSA Tpm and Mni values in each copolymer (due to the incorporation of 1-hexene, which works as a chain-transfer agent) with respect to the corresponding homopolymer, the SSA Tpm values were correlated to the related Schulz−Flory and Stockmayer catalyst site types (Table 6). The predicted five active catalyst site types in both catalysts can be attributed as follows. Based on published reports,20−24,71−73 it is speculated that the experimental MAO consists of a mixture of five different three-dimensional cage structures that feature the following: (i) Each MAO structure comprises n methylaluminoxane −(AlOMe) n − repeat units.20−24,71−73 The proposed five MAO structures can be denoted by five different values of n. Figure 3.4 of ref 22 can be consulted for a facile schematic visualization. (ii) Each of the five proposed MAO structures has preferably one type of defined strong active Lewis acid catalyst site that can be ascribed to the −AlO2Me− environment. This is stated based on an electron paramagnetic resonance (EPR) spin-probe study of Lewis acid sites of MAO reported by Talsi et al.72 Accordingly, five different active ion pairs [Zr]+[MAOsupported]n− are likely to prevail in each supported catalyst.20−24,71−73 4.4. Copolymer Microstructure and Copolymerization Mechanism. Here, the effects of the supported catalyst type on the copolymer intrachain microstructure and the related copolymerization mechanism are discussed. The copolymer microstructure is defined in terms of the triad mole fractions

Table 6. Effect of SSA DSC-Fractionated Peak Melting Temperatures on Side-Chain Branching and Lamellar Thickness copolymer 1

copolymer 2

peak melting temperaturea (°C)

SCB

lamellar thickness (nm)

123.0 (CST 1)

5.92

13.56

117.5 (CST 2) 114.0 (CST 3) 109.5 (CST 4) 105.0 (CST 5) a

9.17 11.24 13.91 16.57

10.52 9.20 7.92 6.96

peak melting temperature (°C) 123.0 (CST 117.5 (CST 113.5 (CST 109.0 (CST 104.5 (CST

SCB

lamellar thickness (nm)

5.92

13.56

9.17

10.52

11.54

9.04

14.20

7.81

16.86

6.87

1) 2) 3) 4) 5)

CST = Schulz−Flory and Stockmayer catalyst site type.

and the associated microstructural parameters, as well as the theoretical ethylene sequence length distribution and its most probable value, nE MPNMR‑Flory (peak of the distribution). Table 3 reports that the contents of HEH and HHH in both copolymers are zero. The literature supports this finding.7,42,74−76 The remaining triad mole fractions of copolymer 1 differ from those of copolymer 2. Table 4 compares the microstructural parameters of the two copolymers. The following observations can be made: (i) For type A, the average 1-hexene sequence length nH NMR, persistence ratio ρ, 9366



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7, respectively. The corresponding random parameter χR equals 0.91 (see Table 4). In the literature,6,77 either ⟨rErH⟩ (rErH|first‑order Markov) or χR has been used to identify the copolymer type. However, these are lumped kinetic parameters. Hence, it can be proposed that the modeled (theoretical) ethylene sequence length distribution of the experimental copolymer should also be compared against that of the corresponding ideal random copolymer having ⟨rErH⟩ = 1. See Figure 8, which shows the extents to which copolymer 1

Figure 7. Comparison of discrete SCB distributions of copolymer 1 and copolymer 2, determined using the SSA DSC technique. CST = Schulz−Flory and Stockmayer catalyst site type.

random parameter χR, ΩE value, first-order Markovian reactivity ratio product rErH, and average experimental reactivity ratio product ⟨rErH⟩ of copolymer 1 and copolymer 2 are mutually comparable. (ii) For type B, the run number of copolymer 1 is greater than that of copolymer 2. (iii) For type C, the average ethylene sequence length, nE NMR, and cluster index of copolymer 1 are less than those of copolymer 2. From the preceding analysis, it can be remarked that the catalyst active-site distribution and the variance in the design of the supported MAO anion, characterized by different electronic and steric effects (due to nBuSnCl3) and coordination environments, affected the copolymer microstructural parameters of only types B and C. The eventual consequences of this finding on thermal behaviors are discussed in the next section. Now, the reactivity ratios of ethylene (rE) and 1-hexene (rH) and their product (⟨rErH⟩) for both catalysts and copolymers are addressed. For catalyst 1 (copolymer 1), rE = 76.928, and rH = 0.054, whereas for catalyst 1 (copolymer 2), rE = 162.256, and rH = 0.043. rE and rH are defined by rE = kEE/kEH and rH = kHH/kHE, where kEE and kHH are the ethylene and 1-hexene terminal model homopropagation rate constants, respectively, and kEH and kHE are the cross-propagation rate constants. Therefore, rE and rH indicate the activities of the catalyst toward insertion of ethylene and 1-hexene, respectively. One can note that rE|catalyst 2/rE|catalyst 1 = 2:1 and rH|catalyst 2/rE|catalyst 1 = 0.8:1. Hence, copolymer 2 has a longer ethylene sequence, nE NMR, than copolymer 1 (see Table 4). The variance in rE and rH in copolymer 1 and copolymer 2 results from the difference in catalyst surface chemistry (electronic versus steric effects) of the active-site types and coordination environments. Next, ⟨rErH⟩ is addressed. In the literature,5 based on experimental data, ethylene−αolefin copolymers have been classified as follows: (i) ⟨rErα‑olefin⟩ = 1, random; (ii) ⟨rErα‑olefin⟩ = 0.2−1.0, slightly alternating to random; (iii) ⟨rErα‑olefin⟩ = 0.005−0.01, highly alternating; and (iv) ⟨rErα‑olefin⟩ = 2.0−4.0, blocky character. For ethylene−1hexene copolymers, ⟨rErH⟩ was independently calculated using the published triad mole fractions, and the results were compiled. It can be noted that unsupported metallocenes mostly synthesize slightly alternating to approximately random ethylene−1-hexene copolymers (⟨rErH⟩ = 0.186−1.300) according to the first-order Markovian statistical/terminal copolymerization model.7,42,43,73−76 However, in this study it was observed that catalyst 1 and catalyst 2 synthesized copolymer 1 with ⟨rErH⟩ ≈ 4 and copolymer 2 with ⟨rErH⟩ ≈

Figure 8. Comparison of theoretical ethylene sequence (equilibrium crystal) length distributions of copolymer 1 and copolymer 2, calculated using the Flory model.

and copolymer 2, from a distributive perspective, differ from the corresponding perfectly random analogues. Based on the three mentioned criteria (⟨rErH⟩, χR, and the Figure 8 prediction), it is concluded that catalyst 1 and catalyst 2 synthesized fairly random copolymers with minor skewedness toward blocky character ([EHH] = 0.004 and 0.010, Table 3). This random feature enabled us to thermally fractionate the copolymers using the SSA DSC technique; see Figure 6. Now, the heterogeneous copolymerization mechanism is addressed. Table 4 shows that ⟨rErH⟩ for each copolymer matches the corresponding first-order Markovian value. Hence, both supported catalysts copolymerized ethylene with 1-hexene following the terminal statistical copolymerization mechanism. ΩE ≈ 1 additionally supports this conclusion. The catalyst active-center distribution and the variant design of the supported MAO anion did not affect this kinetic feature. However, rErH|first‑order Markov or ⟨rErH⟩ ≫ 1 (significant deviation from unity) has important catalytic implications. This means that both catalyst 1 and catalyst 2 have multiple active catalyst sites.43,78 Therefore, the microstructural characterization of the synthesized copolymers by 13C NMR spectroscopy further supported the deconvolution model predictions and the SSA DSC experimental results that were already reported earlier. Figure 8 shows that the theoretical ethylene sequence length distribution (SLD) of copolymer 1 significantly differed from that of copolymer 2. Therefore, SLD, similarly to MWD and CCD, can also be used to reflect the effects of the supported catalyst active-site distribution and the variance in the design of the supported MAO anion (having different electronic and steric effects and coordination environments) on the copolymer backbone heterogeneity. 9367



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4.5. Copolymer Thermal Behaviors. This section considers the copolymer thermal behaviors in terms of peak melting and crystallization temperatures (Tpm and Tpc), percentage crystallinity, SSA-induced fractionation temperatures (multiple alternate melting and crystallization behavior), and lamellar thickness distribution (LTD). These properties are discussed them from the viewpoint of the copolymer composition distribution (CCD), intrachain microstructure heterogeneity [monomer sequence distributions (that is, defect concentration and its distribution) and the associated microstructural parameters], and theoretical ethylene sequence (equilibrium crystal) length distribution and its most probable value, all of which are dictated by catalyst type. In both copolymers, the incorporation of 1-hexene, with reference to the corresponding homopolymers, decreased the peak melting and crystallization temperatures (Tpm and Tpc), as well as the percentage crystallinity (see Table 2). This behavior is attributed to the structural/enchainment defect (shown in Figures 3 and 6) and the eventual partial disruption of the crystal package of the polyethylene chains31 that resulted from (i) the incorporation of 1-hexene; (ii) the monomer sequence distributions, the effect of which is quantified by the average ethylene sequence length nE NMR, cluster index, and run number, all of which are determined by 13C NMR spectroscopy; and (iii) the theoretical ethylene sequence (equilibrium crystal) length distribution (see Figure 8; calculated using the Flory model), the influence of which is assessed by its most probable ethylene sequence nE MPNMR‑Flory. Copolymer 2 showed a higher percentage crystallinity than copolymer 1 (52.94% versus 43.69%). This can be correlated with the higher average ethylene sequence length nE NMR, cluster index, and most probable ethylene sequence nE MPNMR‑Flory of copolymer 2 relative to copolymer 1. The opposite relation holds for run number. Therefore, these particular microstructural parameters can be grouped to evaluate the intrinsic crystallizability of the ethylene−1-hexene copolymer backbones. These parameters originate statistically from the concerned addition copolymerization. Physically, this means that, in copolymer 2, 1-hexene shortened the average ethylene sequence length less; consequently, the chains, on average, were less frequently interrupted from folding than copolymer 1. The depression in peak melting temperature [ΔTpm = (Tpm|homopolymer − Tpm|copolymer)] and peak crystallization temperature [ΔTpc = (Tpc|homopolymer − Tpc|copolymer)] appeared to be inversely related to ethylene sequence length nE NMR, cluster index, and most probable ethylene sequence nE MPNMR‑Flory. Crystallization was discussed earlier from the perspective of microstructural parameters, determined using 13C NMR spectroscopy. Now, this subject is addressed in terms of melting properties such as lamellar thickness distribution and the corresponding most probable and average values, determined using DSC. Figure 9 mutually compares the lamellar thickness distributions of homopolymer 1, copolymer 1, homopolymer 2, and copolymer 2, which were calculated using expressions available in the literature45,61−67 and the DSC data, as well as the corresponding most probable lamellar thickness LMPDSC‑GT from the peak of each distribution. In this calculation, T0m = 145.5 °C, ΔH0f = 290 J cm−3, and σssfe = 90 mJ m−2 were used. They have been reported in the literature61 to be the best values to be used. However, T0m,copolym was estimated as described in the literature.45,64−67 LMPDSC‑GT was next converted into the most probable ethylene sequence

Figure 9. Comparison of lamellar thickness distributions of homopolymer 1, copolymer 1, homopolymer 2, and copolymer 2, calculated using the Gibbs−Thompson equation and conventional DSC.

nE MPDSC‑GT by dividing it by the length of an ethylene repeat unit (0.254 nm). We summarize below the findings of Figure 9 as follows: (i) LMPDSC‑GT decreased in the order homopolymer 1 > homopolymer 2 > copolymer 2 > copolymer 1 (see Table 2). Note that homopolymer 1 and homopolymer 2 have neither interchain composition distribution nor intrachain microstructural heterogeneity. On the other hand, copolymer 2 and copolymer 1 have such differences, which influenced the corresponding LMPDSC‑GT values. This is another reflection of the effect of the supported catalyst active-site distribution and the variance in the design of the supported MAO anion on polyethylene melting behavior. (ii) nE MPDSC‑GT for each copolymer, compared very well with the corresponding value of nE MPNMR‑Flory that we calculated using the Flory model and 13C NMR spectroscopy (see Table 6). To the best of our knowledge, such a match has not previously been reported in the literature. (iii) ΔTpm and ΔTpc appeared to be inversely correlated with the most probable lamellar thickness LMPDSC‑GT and the ethylene sequence length nE MPDSC‑GT. (iv) The DSC-GT lamellar thickness distributions of copolymer 1 and copolymer 2 resembled the corresponding CCDs (see Figure 2). Figure 10 shows that the percentage crystallinity, inclusive of the homopolymers, increased linearly as a function of

Figure 10. Variation of percentage crystallinity as a function of the most probable lamellar thickness LMPDSC‑GT, calculated using the Gibbs−Thompson equation and conventional DSC. 9368



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LMPDSC‑GT, which is directly related to nE MPDSC‑GT and nE MPNMR‑Flory. This finding has important physical significance. This linear relation indicates that the homopolymers and copolymers undergo similar chain folding behaviors. The copolymer ethylene backbone sequences were subjected to an increase in repulsive energy generated between the backbone and the butyl branch (that results from the incorporation of 1hexene). Consequently, the butyl branch is excluded from chain folding. This means that the structural/enchainment defect due to 1-hexene is excepted from the crystal lattice, forming a pure polyethylene phase. Note that the formation of such a phase influences the copolymer mechanical properties and various end-use properties. The literature supports this conclusion.45,79−83 Now, the multiple alternate melting and crystallization behavior of copolymer 1 and copolymer 2 is discussed. Both copolymers showed similar successive self-nucleation and annealing (SSA) thermal fractionation results, that is, five distinct melting peaks (at 105.40, 109.76, 114.01, 117.71, and 123.00 °C for copolymer 1 and at 105.19, 109.56, 113.83, 117.73, and 123.30 °C for copolymer 2; see Figure 6). These peak temperatures and the corresponding lamellar thicknesses (Table 6) are mutually comparable. Hence, the two copolymers have similar crystallizable lengths of PE sequences; however, their weight fractions differ (Figure 11). Unlike the copolymers,

(SCB)], crystallinity, and lamellar thickness. SCB is inversely connected to the latter two, which are directly related. Therefore, the branch content decreased, and the lamellar thickness increased with increasing peak melting temperatures. The lamellar thickness was calculated using expressions reported in the literature;45,67 Table 6 lists these values. The SSA traces of ethylene−1-hexene copolymers, synthesized using supported metallocenes such as MgCl2(THF)2/MAO/ Cp2ZrCl2/MAO and SiO2(MAO)/Me2Si(Ind)2ZrCl2, have been reported in the literature.32,84 They also showed multiple melting peaks; hence, the literature supports our findings. Note that, in SSA fractionation, the polymer undergoes multiple alternate melting and crystallization processes (without physical separation of the chains) as the temperature decreases. Therefore, it is sensitive to linear and uninterrupted chain sequences, hence, to both intra- and interchain defects.32−37 Our 13C NMR results, reported earlier, complement this remark. Figure 11 shows that the discrete SSA DSC lamellar thickness distribution of copolymer 1 significantly differs from that of copolymer 2. Because of the relationship between the SSA DSC peak melting temperature and the catalyst active-site type (which was already reported earlier), this figure directly reflects the effects of catalyst active-site distribution and the variance in the design of the supported MAO anion on the corresponding copolymer discrete LTD. Also, recall Figures 3−7 in this context. However, we note that, interestingly, the widths of these distributions and the following weight-average lamellar thicknesses, Lwav DSC−GT and Lwav SSA DSC, were found to be mutually comparable (see Table 2). These thermal properties were calculated using mathematical expressions available in the literature.65 Finally, we discuss how catalyst 1 and catalyst 2 affect the melting point Tmp and crystallinity Xc of the synthesized polymers (see Table 2). One can note that the Tmp value of homopolymer 1 (133.30 °C) equals that of homopolymer 2 (133.32 °C). However, the Xc value of homopolymer 1 (79.60%) is greater than that of homopolymer 2 (68.98%). This shows that the experimental supported catalyst type affected only the Xc values of the homopolymers but not their Tmp values. The variation in Xc can be attributed to the variation in lamellar thickness distribution and its most probable or weight-average value (see Figure 9). The lamellar thickness distribution of homopolymer 2 is well shifted to the left of that of homopolymer 1. Also, the LMP DSC‑GT and Lwav DSC‑GT values of homopolymer 2 are much less than those of homopolymer 1. Hence, it is concluded that the crystallizable length of PE sequences produced by catalyst 2 is much less than that of catalyst 1, which is eventually reflected in the crystallinity values. Next, the influence of catalyst 1 and catalyst 2 on Tmp and Xc of the corresponding copolymers is addressed. The Tmp value of copolymer 1 (118.07 °C) is close to that of copolymer 2 (121.62 °C), which aligns with what was stated earlier for the homopolymers. However, the Xc value of copolymer 1 (43.69%) is less than that of copolymer 2 (52.94%). This finding can be correlated with the melting characteristics such as LMP DSC‑GT and Lwav DSC‑GT, as well as the interchain compositional heterogeneity index (i.e., the Crystaf CCD width σCrystaf) and the intrachain microstructural parameters such as the average ethylene sequence length, represented by nE NMR, nE MP‑Flory, and nE DSC‑GT. The aforementioned melting parameter(s) and average ethylene sequence length of copolymer 1 are less than those of

Figure 11. Comparison of discrete lamellar thickness distributions of copolymer 1 and copolymer 2, determined using the SSA DSC technique. CST = Schulz−Flory and Stockmayer catalyst site type.

the homopolymers, being linear, did not demonstrate any multiplicity of melting peaks. Based on this finding and the exclusion of the butyl group from chain folding (Figure 10), one can remark that the SSA trace of each copolymer also indicates the structural defect resulting from 1-hexeneintroduced butyl branches, which was in essence also measured using Crystaf. This provides a probable clue to why the number of active-site types, determined by the deconvolution of the Crystaf CCD, matches the number of SSA fractionation temperatures. SSA DSC showed better resolution than Crystaf. This made the intra- and intercopolymer backbone heterogeneity comparable, although this was not clearly revealed by the Crystaf traces (monomodal versus bimodal). However, the corresponding homopolymer, in each case, consisted of fairly straight chain backbones. Each SSA peak signifies a population of backbones that have the same branch content [side-chain branching 9369



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copolymer 2. However, the opposite trend holds for σCrystaf. This explains the difference in crystallinity between copolymer 1 and copolymer 2, which results from the varying capabilities of catalyst 1 and catalyst 2 to insert 1-hexene into the growing copolymer backbone according to 1,2 and 2,1 insertion mechanisms. This is again affected by the supported zirconocene+−MAO− ion pairs having different electronic and steric effects and coordination environments.

each catalyst. This result complements the deconvolution model predictions and SSA DSC experimental results that we reported earlier. (iii) The average ethylene sequence length n E NMR , theoretical most probable ethylene sequence (nE MPDSC‑GT and nE MPNMR‑Flory), cluster index, and most probable lamellar thickness LMPDSC‑GT of copolymer 1 were less than those of copolymer 2. These results align with the corresponding copolymer reactivity ratios rE and rH and explain why the percentage crystallinity varied accordingly. Therefore, these particular microstructural parameters can be grouped to evaluate the intrinsic crystallizability of ethylene−1-hexene copolymer backbones. (iv) For each copolymer, both nE MPDSC‑GT and nE MPNMR‑Flory and the weight-average lamellar thicknesses Lwav DSC−GT and Lwav SSA DSC were found to be mutually comparable. To the best of our knowledge, such a match has not previously been reported. (v) The percentage crystallinity of the homo- and copolymers increased linearly as a function of LMPDSC‑GT. This linear relation indicates that the homopolymer and copolymer chains folded in a similar fashion. This means that the butyl branch (that results from the incorporation of 1hexene) was excluded from chain folding. (vi) This study coherently addressed heterogeneous metallocene catalysis (applied to ethylene homo- and copolymerization), the modeling of catalyst active-center types, copolymer compositional heterogeneity, the copolymerization mechanism, and the resulting copolymer thermal behaviors, which, to the best of our knowledge, have not previously been reported. Such a treatment of this subject will assist in the design and synthesis of future supported metallocene catalysts, capable of better regulating the copolymer backbone compositional variations and the resulting polymer thermal behaviors.

5. CONCLUSIONS Metallocenes are an important family of polyolefin catalysts. Therefore, in this study, two supported metallocene catalysts, namely, silica/MAO/(nBuCp)2ZrCl2 (catalyst 1) and silica/nBuSnCl3/MAO/(nBuCp)2ZrCl2 (catalyst 2) were synthesized. Using these catalysts, two ethylene homopolymers (homopolymer 1 and homopolymer 2) and the corresponding ethylene−1-hexene copolymers (copolymer 1 and copolymer 2) were prepared under the same polymerization conditions without separate feeding of MAO. There was no reactor fouling during polymerization. Both copolymers were free-flowing particles, showed good morphology (bulk density ≈ 0.30 g/ mL), and replicated the particle size distribution of the corresponding supported catalyst. The synthesized polymers were characterized using GPC, Crystaf, DSC (conventional and SSA), and 13C NMR spectroscopy, and the results were applied, as appropriate, to model the catalyst active-center distribution, MWD, CCD, ethylene sequence (equilibrium crystal) length distribution, and lamellar thickness distribution (both continuous and discrete). Various model parameters were calculated using these model predictions. This combination of models with experiments effectively illustrated how and why the active-center distribution and variance in the design of the supported MAO anion, having different electronic and steric effects and coordination environments, influence the concerned copolymerization mechanism and polymer properties, including inter- and intrachain compositional heterogeneity and thermal behaviors. The results of the present study will contribute to developing future supported metallocene catalysts that will be useful for synthesizing new grades of ethylene−α-olefin linear low-density polyethylenes (LLDPEs). The major conclusions are as follows: (i) Five active-center types were predicted in each catalyst, as corroborated by our SSA DSC experiments, as well as by EXAFS work published in the literature.70 An excellent match was noted between the experimental results and model predictions. Hence, metallocenes impregnated particularly on an MAO-pretreated support can be rightly envisioned to comprise an ensemble of isolated single sites that have varying coordination environments. This finding can be attributed to the presence of five different MAO cage structures, each having variable aluminoxane −(AlOMe)− repeat units. (ii) Catalyst 1 and catalyst 2 synthesized copolymers having experimental reactivity product ratios, ⟨rErH⟩, of ∼4 and ∼7, respectively. These values match the first-order Markovian statistical model predictions; hence, terminal model copolymerization occurred in each case. The theoretical ethylene sequence distribution of copolymer 1 significantly differed from that of copolymer 2. However, the corresponding random parameter χR equaled 0.91. Accordingly, both copolymers were rated as fairly random with minor skewedness toward blocky character. The SSA DSC experiments also support this conclusion. The ⟨rErH⟩ values, being significantly different from unity, also indicate the existence of multiple active sites in

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the financial support provided by King Abdulaziz City for Science and Technology (KACST) via the Science & Technology Unit at King Fahd University of Petroleum & Minerals (KFUPM) through Project 08-PET90-4 as part of the National Science and Technology Innovation Plan. The technical assistance provided by the Center of Refining & Petrochemicals (CRP), the Center for Engineering Research at Research Institute, the Center of Research Excellence in Petroleum Refining & Petrochemicals (CoREPRP), and the Department of Chemical Engineering, KFUPM, Dhahran, Saudi Arabia; the NMR Core Laboratory, King Abdullah University of Science & Technology (KAUST), Thuwal, Saudi Arabia; and the Department of Chemical Engineering, Kasetsart University, Bangkok, Thailand, is also gratefully acknowledged. The technical assistance of Mr. Sagir Adamu is also appreciated.

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