Full Paper 2096 Summary: Concurrent tandem catalysis systems have shown a significant advantage in the convenient synthesis of linear low-density polyethylene (LLDPE) from a sole ethylene monomer stock by uniquely coupling the tandem action between an ethylene oligomerization catalyst and an ethylene copolymerization catalyst in a single reactor. Recently, we have reported the successful synthesis of ethylene-hexene derived LLDPE using an effective concurrent tandem catalysis system comprising (Z5-C5H4CMe2C6H5)TiCl3 (1)/ MMAO and a CGC copolymerization catalyst, [(Z5C5Me4)SiMe2(tBuN)]TiCl2 (2)/MMAO. In this work, we report the results from an extensive study on the important rheological properties of LLDPE grades prepared with this tandem catalysis system. Two sets of LLDPE samples having different short-chain branching density (SCBD) were prepared with the tandem catalysis system under various catalyst concentrations and at temperatures of 25 and 45 8C. The melt rheological properties of these polymers were evaluated using small-amplitude dynamic oscillation measurements. These polymers have been found to possess typical rheological properties found in long-chain branched (LCB) polymers, such as enhanced zero-shear viscosity (Z0), improved shearthinning, elevated dynamic moduli, and thermorheological complexity, which indicate the presence of long-chain branching in the polymers. The long-chain branching density (LCBD) of the two respective sets of polymers were qualita- tively compared and correlated to the polymerization conditions including catalyst ratio and temperature. This work represents the first study on the rheological properties of LLDPE synthesized with concurrent tandem catalysis, and it discloses another appealing feature of this unique approach—its ability to produce LCB LLDPE from a single ethylene monomer stock. Synthesis of linear low-density polyethylene (LLDPE) from ethylene using ethylene oligomerization catalyst and an ethylene copolymerization catalyst. Long-Chain Branching and Rheological Properties of Ethylene-1-Hexene Copolymers Synthesized from Ethylene Stock by Concurrent Tandem Catalysis Zhibin Ye,*1 Fahad AlObaidi,2a Shiping Zhu,*2 Ramesh Subramanian1 1 School of Engineering, Laurentian University, Sudbury, Ontario, Canada P3E 2C6 E-mail: zye@laurentian.ca 2 Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada L8S 4L7 E-mail: zhuship@mcmaster.ca Received: June 11, 2005; Accepted: August 5, 2005; DOI: 10.1002/macp.200500248 Keywords: catalysis; concurrent tandem catalysis; linear low-density polyethylene (LLDPE); long-chain branching; rheological properties; structure Introduction As an important family of polyethylenes, linear low-density polyethylene (LLDPE), a copolymer of ethylene with a-olefins, has been extensively used for a broad range of a Current address: SABIC R&T, Polymer Research Department, Polyolefins Section, Riyadh, Saudi Arabia. Macromol. Chem. Phys. 2005, 206, 2096–2105 commodity applications, particularly for film applications. Compared to high-density polyethylene (HDPE), LLDPE possesses reduced melting point, crystallinity, and density attributed to the presence of short-chain branches with controlled length and frequency on the polymer backbone, which not only facilitates effective polymer processing but also introduces additional favorable material properties.[1] Commercial LLDPE is produced by ethylene DOI: 10.1002/macp.200500248 ß 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Long-Chain Branching and Rheological Properties of Ethylene-1-Hexene Copolymers Synthesized from Ethylene Stock . . . copolymerization with a-olefin comonomers, such as 1-butene, 1-hexene, and 1-octene, using classical multisite Ziegler-Natta catalysts. More recently metallocene catalysts, which have tremendously revolutionalized olefin polymerization in the past two decades, have been used in some commercial LLDPE processes. This new generation of homogeneous single-site catalysts has opened up a unique route to a novel series of LLDPE grades with unprecedented controlled chain structure and superior tailored properties.[2] Metallocene LLDPE exhibits some outstanding materials properties compared to Ziegler-Natta polymers like higher transparency and enhanced mechanical performance as a consequence of more uniform distribution of shortchain branching (SCB) and narrower molecular weight distribution (MWD).[2–4] More importantly, LLDPE prepared with a number of metallocene catalyst systems, such as the constrained geometry catalyst (CGC), has been shown to possess the most desired long-chain branching structure, a characteristic structure ubiquitous in LDPE from conventional radical polymerization processes.[4] Without compromising other excellent properties, the presence of a small amount of LCB in metallocene LLDPE dramatically improves the viscoelastic properties of the polymer, thereby making the polymer mimic the excellent processability and high melt strength typically found in long-chain branched (LCB) LDPE.[5] These excellent processing properties coupled with other superior properties make LCB metallocene LLDPE a perfect substitute for conventional LDPE in the market for a broad range of important applications.[2] The incorporation of in situ generated vinyl-ended macromonomers into growing polymer chains by the open-structured homogeneous catalysts during copolymerization has been believed to be the mechanism responsible for the formation of LCB in metallocene LLDPE.[6,7] Given their valuable features and tremendous technological advance, extensive research has been undertaken to synthesize, characterize, and study the viscoelastic properties of LCB metallocene LLDPE.[6–25] As an alternative to the conventional two-monomer (ethylene and a-olefin) approach for LLDPE production, recently a new synthetic approach, which utilizes concurrent tandem catalysis to produce LLDPE with ethylene as the sole monomer stock in a single reactor, has attracted a significant amount of research interest.[26,27] This novel approach employs the concurrent tandem action between two catalysts in the system: one catalyst (ethylene oligomerization catalyst) oligomerizes ethylene into 1-alkene, while the other catalyst (ethylene copolymerization catalyst) concurrently copolymerizes the in situ generated 1alkene with ethylene to produce LLDPE.[26,27] By selecting suitable catalyst combinations and adjusting catalyst concentration ratios, LLDPE with controlled SCB length and density can be effectively produced. Compared to the Macromol. Chem. Phys. 2005, 206, 2096–2105 www.mcp-journal.de conventional copolymerization approach, this tandem catalysis approach possesses an appealing advantage of using ethylene as the only monomer, which avoids the use of a-olefin and hence precludes the separate ethylene oligomerization process usually required in LLDPE production.[28,29] A number of versatile tandem catalysis systems,[28–42] particularly systems employing a combination of single-site homogeneous catalysts, have been successfully developed and summarized in recent review articles.[26,27] The concurrent tandem catalysis approach is conceptually elegant and virtually successful. It is aimed at a convenient synthesis of LLDPE. However, the properties of LLDPE prepared by this novel approach, particularly the viscoelastic properties critical to the processing and applications of the polymers, have never been investigated. From the application point of view, it is also highly desirable in this approach to introduce the valuable LCB structure into these polymers to enhance their processing properties. We speculate that LCB LLDPE can be produced by this approach as well if we select a unique copolymerization catalyst (such as CGC) in the tandem catalyst combination, which has the capability of in situ generation and incorporation of vinyl-ended macromonomers. Recently, we used a tandem catalyst system comprising of an ethylene trimerization catalyst, (Z5-C5H4CMe2C6H5)TiCl3 (1)/MMAO, and a CGC copolymerization catalyst, [(Z5C5Me4)SiMe2(tBuN)]TiCl2 (2)/MMAO, for the successful synthesis of LLDPE of n-butyl branches with ethylene as the only monomer stock.[28,29] In this work, we carried out a further investigation on the melt rheological properties of LLDPE prepared with this tandem catalysis system and the results reported here show convincingly the presence of a sparse level of LCB in these polymers. This work hence demonstrates that LCB LLDPE can be obtained from ethylene as the sole monomer using this unique tandem catalysis system that comprises a CGC catalyst having high macromonomer generation and incorporation ability. It represents another appealing feature of this concurrent tandem catalysis approach for LLDPE preparation. Experimental Part The detailed synthesis of n-butyl branched LLDPE utilizing the tandem catalysis system, comprising (Z5-C5H4CMe2C6H5)TiCl3 (1)/MMAO and [(Z5-C5Me4)SiMe2(tBuN)]TiCl2 (2)/ MMAO, has been reported in our previous articles.[28,29] The synthesis was carried out in a 500 mL glass reactor equipped with a magnetic stirrer under atmospheric pressure of ethylene. Typical synthesis procedure is as follows: Toluene and MMAO were introduced into the purged reactor under nitrogen protection. Subsequently, the reactor was evacuated, pressurized with ethylene, and then placed into an oil bath set at the operating temperature. After equilibrium for 10 min, stock solutions in toluene for both catalysts with ß 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 2097 2098 Z. Ye, F. AlObaidi, S. Zhu, R. Subramanian prescribed amounts were injected simultaneously to initiate the concurrent ethylene trimerization and copolymerization. The system temperature and ethylene pressure were kept constant throughout the reaction. The contents of the reactor were magnetically stirred. After 1 h, the reaction was quenched by injecting 20 mL methanol and venting the reactor. The synthesized polymer was collected, washed with an excessive amount of methanol, and then dried. The thermal properties of the polymer, including melting point (Tm), and melting enthalpy (DHm), were measured using a calibrated TA 2910 MDSC in the standard DSC mode. Ultra high-purity N2 gas at a flow rate of 30 mL
min1 was purged through the calorimeter. A refrigerated cooling system (RCS) with the cooling capacity to 220 K was attached to the DSC cell. The polymer sample (about 5 mg) was first heated to 180 8C at the rate of 10 8C
min1 in order to remove any thermal history. It was then cooled down to 20 8C at the rate of 10 8C
min1. A second heating cycle was applied to acquire a DSC thermogram at the scanning rate of 10 8C
min1. The peak temperature with the highest endotherm was chosen as the melting point. The molecular weight (MW) and MWD of the polymer samples were measured at 140 8C in 1,2,4trichlorobenzene using a Waters Alliance GPCV 2000 with DRI detector coupled with an in-line capillary viscometer. The polymer MWs were calculated according to a universal calibration curve based on 11 polystyrene standards with MWs ranging from 2.5  103 to 1.09  106 g
mol1. The 75.4 MHz 13 C NMR analyses were conducted using a Bruker AV300 Pulsed NMR spectrometer at 120 8C. The polymer samples were dissolved in 1,2,4-trichlorobenzene and deuterated o-dichlorobenzene mixture (weight ratio of 9/4) in 10 mm NMR tubes with a concentration about 20 wt.-%. Waltzsupercycle decoupling was used to remove 13C-1H couplings. At least 2 500 scans were applied for each acquisition to obtain a good signal-to-noise ratio. The polymer chemical shift assignments and calculations followed the ASTM D5017-91 method.[43] Rheological measurements of the polymer melts were carried out on an ATS RheoSystem STRESSTECH HR rheometer in the stress-controlled oscillation mode using 20 mm parallel plate geometry at a gap of about 1.0 mm. Before the measurements, the polymer samples were conditioned with 1 000 ppm Irganox 1 010 antioxidant supplied from CibaGeigy Canada. The fine polymer reactor powders were mixed with the antioxidant solution in acetone. The acetone was then evaporated overnight under vacuum at 75 8C. Subsequently, the antioxidant-conditioned polymer powders were pelletized using an ATLAS Laboratory Mixing Molder at 150 8C and further compression-molded in a carver press at 150 8C into small disks with 20 mm in diameter and 1.5 mm in thickness. The rheological measurements were conducted in the frequency range of 0.002–50 Hz. Strain sweeps were performed at 1 Hz before frequency sweeps in order to establish the linear viscoelastic region. The experiments were performed at regular intervals of 10 8C within temperature range from 140 to 200 8C. Temperature was maintained within 0.2 8C using an ETC-3 (elevated temperature control) temperature control system and the measurements were all conducted under N2 atmosphere. Results and Discussion Polymer Synthesis using Tandem Catalysis System and Structural Characterization Two sets of ethylene-1-hexene LLDPE polymers, PE1– PE4 and PE6–PE8 as shown in Table 1, were prepared from ethylene stock with the concurrent tandem catalysis system comprising of the ethylene trimerization catalyst, (Z5-C5H4CMe2C6H5)TiCl3 (1)/MMAO, which trimerizes ethylene into 1-hexene, and the copolymerization CGC catalyst, [(Z5-C5Me4)SiMe2(tBuN)]TiCl2 (2)/MMAO, which copolymerizes the in situ generated 1-hexene with Table 1. Synthesis conditions and properties of polymer samples investigated. Other conditions: solvent, toluene; total volume, 150 mL; Al/Ti ¼ 1 000; ethylene pressure, 1 atm. Polymer sample PE1 PE2 PE3 PE4 PE5 PE6 PE7 PE8 PE9 M w a) Trimerization CGC Temperature Polymerization catalyst (1) (2) time, t mmol mmol 8C h kg
mol1 30 15 10 5 0 50 25 7.5 0 15 15 15 15 15 25 25 25 25 25 25 25 25 25 45 45 45 45 1 1 1 1 1 1 1 1 1 99 118 160 100 386 40 41 75 147 PDIa) 3.2 2.8 4.3 3.3 11.9 2.6 2.9 3.7 6.7 Tmb) wb) Hexene percentagec) SCBD 8C % mol-% per 1 000 carbons 60.0, 127.3d) 80.8, 126.1d) 91.8 113.6 135.1 121.7 124.2 127.0 134.1 7.6 18.5 28.0 34.3 56.6 40.6 44.7 56.9 68.9 9.5 6.9 5.1 3.0 0 n.d.e) n.d. n.d. 0 40.0 30.3 23.1 14.2 0 n.d. n.d. n.d. 0 a) Determined by GPCV. Measured by DSC. Crystallinity was calculated based on the melting enthalpy of 290 J
g1 for a perfect PE crystal. c) 1-Hexene molar percentage in the copolymer, determined by 13C NMR. d) Higher melting peak is from a small amount of polymer byproduct produced by the trimerization catalyst. e) n.d.: not determined. b) Macromol. Chem. Phys. 2005, 206, 2096–2105 www.mcp-journal.de ß 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 2099 Long-Chain Branching and Rheological Properties of Ethylene-1-Hexene Copolymers Synthesized from Ethylene Stock . . . Complex Viscosity Curve A detailed investigation on the melt rheological properties of these polymers was carried out using small-amplitude dynamic oscillation measurements, and the presence of sparse LCB in these polymers was elucidated from the rheological results. The complex viscosity curves obtained at 190 8C for the set of LLDPE samples (PE1–PE4) and HDPE sample PE5 prepared at 25 8C are shown in Figure 1. It can be seen that the four LLDPE samples show very different complex viscosity curves despite possessing very similar M w and PDI, which are two important parameters that dramatically affect complex viscosity and shearthinning nature of the polymer. The Cross equation,[45] given by Equation (1), was applied to fit the complex viscosity curves. Z0 1 þ ðtoÞa Macromol. Chem. Phys. 2005, 206, 2096–2105 PE1 PE2 PE3 100000 PE4 PE5 10000 1000 0.01 0.1 1 10 100 Angular Frequency (rad/s) 1000 Figure 1. Polymer melt complex viscosity curve at 190 8C for samples PE1–PE5 prepared at 25 8C. where Z0 is zero-shear viscosity, t is a characteristic relaxation time, and a is a dimensionless exponent that is independent of temperature. The zero-shear viscosity for each polymer at 190 8C obtained by fitting the Cross model is listed in Table 2, and it qualitatively increases in the following order: PE1 < PE2 < PE3 < PE4. Typically comparing PE1 and PE4, which have almost the same M w and PDI, the zero-shear viscosity for PE4 is more than an order of magnitude higher than that of PE1. For linear HDPE, Raju et al.[46] proposed the following equation to correlate Z0 of HDPE at 190 8C to the weight average MW of the polymer: 3:6 Z0 ¼ 3:4  1015 M w ð2Þ This equation is independent of PDI and has been found to be valid for conventional linear Ziegler-Natta polyethylenes of PDI ranging from 3 to 35.[18,47,48] Studies have Rheological Properties and Elucidation of Long-Chain Branching Z*ðoÞ ¼ 1000000 Complex Viscosity (Pa s) ethylene. The trimerization catalyst has been shown to produce 1-hexene of high purity.[28,44] The CGC catalyst was adopted owing to its well-known outstanding capability in producing LCB polymers.[4,6,7] These polymers were prepared at two temperature levels (25 and 45 8C) and with different concentration ratios for the two catalysts under atmospheric pressure of ethylene to achieve different short-chain branching density (SCBD) and, therefore, different melting temperature (Tm) and crystallinity (w). Table 1 summarizes the polymerization conditions and the polymer properties, including weight average MW (M w ) and polydispersity index (PDI), Tm and w, and SCBD. For comparison purposes, two homo-polyethylene samples, PE5 and PE9, were also prepared at the two respective temperatures using the sole CGC catalyst under equivalent conditions. The synthesis and characterization of these polymers have been reported in our previous articles.[28,29] From Table 1, it can be seen that LLDPE samples prepared at the same temperature possess similar weight average MWs and PDIs, while their melting temperature, crystallinity, and SCBD decrease significantly with an increase in the concentration ratio of catalyst 1/catalyst 2 as expected. Compared to the set (PE1–PE4) prepared at 25 8C, the samples (PE6–PE8) prepared at 45 8C all have higher melting temperature and crystallinity, and hence lower SCBD owing to the pronounced deactivation of the trimerization catalyst 1 at elevated temperatures.[28,44] The two homo-polyethylene samples, PE5 and PE9, have much higher M w and possess broader MWD due to difficulty in monomer diffusion typically observed in the ethylene homopolymerization system. ð1Þ www.mcp-journal.de Table 2. 190 8C. Some rheological properties of polymers investigated at Polymer samples PE1 PE2 PE3 PE4 PE5 PE6 PE7 PE8 PE9 Z0a) Estimated Z0b) Pa
s Pa
s 1.4  104 8.4  104 1.1  105 2.3  105 1.8  106 2.0  103 3.7  102 4.4  103 4.8  104 3.3  103 6.2  103 1.8  104 3.4  103 4.4  105 1.3  102 1.4  102 1.2  103 1.4  104 nc) 0.82 0.71 0.68 0.62 0.33 0.82 0.88 0.79 0.71 a) Zero-shear viscosity obtained by fitting complex viscosity curve using Equation (1). b) Calculated zero-shear viscosity by using Equation (2). c) Power-law exponent obtained by fitting complex viscosity curve using Equation (3). ß 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 2100 Z. Ye, F. AlObaidi, S. Zhu, R. Subramanian also shown that Equation (2) can be applied to linear side chain branched LLDPE samples with SCBD ranging from zero to as high as 48.5/1 000 carbons.[18,19] However, this equation is not valid for LCB polyethylenes, which usually exhibit much higher Z0 than the value calculated with the equation.[10,11,18,19] The zero-shear viscosities for the four samples, PE1–PE4, were estimated using Equation (2) and listed in Table 2. These estimated values are far lower (almost an order of magnitude) than the zero-shear viscosities obtained from the Cross model equation, which suggests the presence of LCB structure in these four polymers. The power-law expression, given by Equation (3), was used to fit the complex viscosity curves in order to quantify and compare the shear-thinning behaviors of the four polymers. Z* ¼ mon1 ð3Þ where m is the consistency and n is the power-law exponent, which indicates the degree of shear-thinning. Improved shear-thinning, i.e., higher degree of non-Newtonian behavior and lower n value, is usually observed in LCB polymers and polymers of high PDI and it becomes more pronounced with the increase in long-chain branching density (LCBD) and PDI.[9,22] The power-law exponents for the four polymers at 190 8C are listed in Table 2, and they decreased in the following order: PE1 > PE2  PE3 > PE4. Since the four polymers have fairly similar M w and PDI, the different n value thus reflects the different LCBD in this set of polymers, which increases in the following manner: PE1 < PE2  PE3 < PE4. This suggests that LCBD tends to decrease with an increase in SCBD of the polymer, i.e., LCBD decreases with an increase in the concentration ratio of catalyst 1 to catalyst 2 during polymerization. For the set of LLDPE polymers prepared at 45 8C, PE6– PE8, Figure 2 compares their complex viscosity curves at 190 8C. The values of Z0 and n for these polymers listed in Complex Viscosity (Pa s) 100000 10000 1000 100 PE6 PE7 PE8 0.1 1 10 PE9 10 0.01 100 1000 Angular Frequency (rad/s) Figure 2. Polymer melt complex viscosity curve at 190 8C for samples PE6–PE9 prepared at 45 8C. Macromol. Chem. Phys. 2005, 206, 2096–2105 www.mcp-journal.de Table 2 were obtained using Equation (1) and (3), respectively. For each polymer, particularly PE6, the Z0 value is much higher than the estimated one calculated using Equation (2) based on the MW of the polymer M w, thus indicating a certain degree of LCB present in the polymers. Comparing samples PE6 and PE7 having very similar M w and PDI, PE6 exhibits a much higher Z0 (2.0  103 Pa
s for PE6 and 3.7  102 Pa
s for PE7) but a lower n (0.82 for PE6 and 0.88 for PE7) than PE7, which suggests PE6 has higher LCBD than PE7. The two homo-polyethylene samples, PE5 and PE9, also exhibit significantly higher Z0 (about three times higher) than their respective estimated value using Equation (2), suggesting the presence of LCB. In Table 2, lower n values can be found for these two homopolymers compared to their corresponding LLDPE counterparts prepared at the same temperature. As well as LCB, the higher PDI of these two polymers can contribute to the reduced n values. Therefore, no comparison in LCBD between the homopolymer and LLDPE samples can be made from their shear-thinning behaviors. Dynamic Moduli, G0 (o) and G00 (o) Figure 3(a) shows and compares the dynamic modulus [G0 (o) and G00 (o)] curves measured at 170 8C for the set of LLDPE samples, PE1–PE4. A noticeable deviation in the frequency of the crossover point of the storage modulus (G0 ) and loss modulus (G00 ) curves for each polymer can be clearly identified, which decreases in the following manner: PE1 > PE2  PE3 > PE4. The modulus crossover point reflects the viscoelasticity of polymers and its frequency is virtually dependent on the polymer chain structural parameters, including M w , PDI, LCBD, and chain topology. For the LCB polymers of similar M w and PDI, numerous studies[10,11,14,15,49] have shown that the frequency of the crossover point decreases sensitively with an increase in the polymer LCBD owing to the greater enhancement of polymer elasticity. Given the similar M w and PDI for the four polymers (PE1–PE4), the different locations of the crossover points in Figure 3(a) provide additional evidence of the presence of LCB structure. Furthermore, one can derive that LCBD increases qualitatively in the following order: PE1 < PE2  PE3 < PE4, which is consistent with our finding in the previous section based on the shear-thinning behavior for the four polymers. A plot of log G0 versus log G00 has been proven to be a useful tool to investigate the effects of LCB and PDI on polymer rheological properties.[9,18,19,49] For high-MW polymers with narrow MWD, the log G0 versus log G00 curve does not depend on MW but it is a weak function of temperature. Hence, all the data measured at various temperatures and MWs can be described by a single master curve. For linear polyethylenes of narrow MWD, the correlation ß 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 2101 Long-Chain Branching and Rheological Properties of Ethylene-1-Hexene Copolymers Synthesized from Ethylene Stock . . . 1000000 (a) 1000000 (a) PE3 PE4 100000 PE1 G', G" (Pa) G', G" (Pa) 100000 PE2 10000 PE1-G' PE1-G" PE2-G' PE2-G" PE3-G' PE3-G" PE4-G' PE4-G" 1 10 100 Angular Frequency (rad/s) 10 1 0.01 1000 1000000 1000 100 1000 0.1 10000 0.1 PE6-G' PE6-G" PE7-G' PE7-G" PE8-G' PE8-G" PE9-G' PE9-G" 1 10 100 Angular Frequency (rad/s) 1000 1.0E+6 (b) (b) PE6 1.0E+5 100000 PE7 PE8 G' (Pa) G' (Pa) 1.0E+4 10000 PE1 1000 PE2 PE9 linear PE 1.0E+3 1.0E+2 PE3 1.0E+1 PE4 100 Linear PE 1.0E+0 10 1.0E+1 100 1000 10000 G" (Pa) 100000 1000000 between G0 and G00 was found to be:[18,19] G0 ¼ 0:00541ðG Þ ð4Þ Short-chain branched linear polyethylenes have been found to obey the above correlation. However, for polymers with LCB and/or broad MWD, a deviation from the correlation with an up-shift of the curve is usually observed in the terminal region and it becomes more pronounced with the increase of LCBD and PDI.[9,18,19,49] Figure 3(b) compares the log G0 versus log G00 master curves for samples PE1–PE4 with the curve for linear PE obtained using Equation (4). An obvious up-shift of the master curves from the linear PE behavior, particularly in the low-modulus region, can be observed for the four polymers, thereby suggesting a more elastic nature of the polymer melts and the presence of LCB. Also, a very minor yet discernible difference in the degree of up-shift of the four master curves can be seen. The degree of up-shift becomes more pronounced in the following sequence: PE1 < PE2  PE3 < PE4. Considering their similar PDI, we obtain the same sequence for LCBD difference in the four polymers. Macromol. Chem. Phys. 2005, 206, 2096–2105 1.0E+3 1.0E+4 1.0E+5 1.0E+6 G" (Pa) Figure 3. (a) G0 and G00 curves for the set of LLDPE samples, PE1–PE4, measured at 170 8C. (b) Log G0 versus log G00 master curves for polymers PE1–PE4. The solid line is for linear polyethylene based on Equation (4). 00 1:42 1.0E+2 www.mcp-journal.de Figure 4. (a) G0 and G00 curves for the set of LLDPE samples, PE6–PE9, measured at 170 8C. (b) Log G0 versus log G00 master curves for polymers PE6–PE9. The solid line is for linear polyethylene based on Equation (4). Figure 4(a) shows the dynamic modulus curves for samples PE6–PE9 measured at 170 8C. With the exception of PE9, the polymers do not have the modulus crossover point within the experimental frequency window because of low M w. Figure 4(b) compares the log G0 versus log G00 curves for the four polymers. The obvious up-shift of the curves from the solid line for linear PE of low PDI suggests the deviation of the four polymers from linear polymers with narrow MWD. Although the difference in the deviation degree for the four polymers is very small, one can still see a discernible deviation that becomes more significant as follows: PE9  PE8 < PE7 < PE6. Taking the MWD into consideration, which has a similar effect in up-shifting the curve as LCB, we can conclude that LCBD increases in the following manner: PE9  PE8 < PE7 < PE6. Phase Angle Phase angle is an even more sensitive indicator of the presence of LCB.[22] In a plot of phase angle versus angular frequency, the presence of LCB will not only lead to reduced phase angles of the polymer but also change the ß 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 2102 90 90 80 80 Phase Angle (degree) Phase Angle (degree) Z. Ye, F. AlObaidi, S. Zhu, R. Subramanian 70 60 PE1 50 PE2 increasing LCBD PE3 40 PE4 70 60 PE6 PE7 50 PE8 PE9 40 30 0.001 0.1 10 Angular Frequency (rad/s) 1000 0.01 Figure 5. Phase angle versus angular frequency for polymers PE1–PE4 measured at 190 8C. shape of the phase angle curve due to the added long-time relaxation mode in the viscoelastic behavior. Such effects on the phase angle curve will become more pronounced with the increase of LCBD.[9,22] Figure 5 shows the phase angle curves for the four polymers, PE1–PE4, measured at 190 8C. It should be noted that polymer PE5 was not included in this comparison due to its much higher M w and broader MWD. From Figure 5, it can be seen that the phase angle at a given frequency decreases in the following manner coupled with a change of the shape of the curves: PE1 > PE2  PE3 > PE4. The phase angle difference between PE2 and PE3 is minor compared to those between other polymer pairs. In general, PE3 has slightly lower phase angle than PE2. In addition to LCB, the slightly higher PDI of PE3 can also be seen as a factor contributing to this difference. Therefore, from the phase angle behavior in Figure 5 we can conclude the LCBD increases in the order: PE1 < PE2  PE3 < PE4, which is again consistent with our findings obtained in previous sections. It has been reported in many investigations[9,13–15,22,49] that when the LCBD is high enough in LCB polymers, a plateau in the phase angle curve can be usually identified and the frequency width of the plateau increases with the LCBD. In Figure 5, the change in the shape of the curves can be clearly observed. However, no obvious plateau in the curves can be found even for PE4, which has the highest LCBD among the four polymers, suggesting a comparatively low level of LCBD in these polymers. Figure 6 shows the phase angle curves for PE6–PE9 measured at 190 8C. Compared to PE7, PE6 exhibits significantly reduced phase angle in the frequency range although the two polymers possess very similar M w and PDI. Therefore, it can be inferred again that PE6 has higher LCBD than PE7. However, a similar comparison with PE8 and PE9 in LCBD cannot be made from the phase angle curves due to their higher MW and PDI. Macromol. Chem. Phys. 2005, 206, 2096–2105 30 www.mcp-journal.de 0.1 1 10 100 Angular Frequency (rad/s) 1000 Figure 6. Phase angle versus angular frequency for polymers PE6–PE9 measured at 190 8C. Activation Energy and Thermorheological Complexity Linear polymers are considered thermorheologically simple because their rheological properties obey the timetemperature superposition principle. However, the superposition principle is not valid for LCB polymers because of constraints imposed by branching points on chain relaxation, and the polymers are termed thermorheologically complex.[23] The temperature dependence of modulus shift factor, aT, for rheologically simple polymers often follows the Arrhenius relation at temperatures well above polymer glass transitional temperature (Tg). The flow activation energy Ea, which is a measure of temperature sensitivity, is given by    Ea 1 1  ð5Þ aT ¼ exp R T T0 Thermorheologically complex LCB polymers, however, do not follow this simple relation. These polymers do not have single activation energy but exhibit modulus-dependent temperature sensitivity.[23] Figure 7 shows the activation energy spectra for the set of samples PE1–PE5 at a reference temperature of 190 8C. These spectra were plotted on the basis of the experimental loss modulus data (G00 vs. o) according to the method summarized by Wood-Adams et al.[23] For these five polymers, with the increase in angular frequency, the activation energy gradually decreases and reaches a plateau value at the high-frequency end, which indicates the thermorheological complexity of the polymers and the presence of LCB structure. The plateau activation energy values, which are dependent on SCBD of the polymers, are different for the five polymers with PE1 and PE5 having the highest and lowest values, respectively. This reflects the difference in SCBD of the polymers. In the high-frequency region, the stress relaxation behavior of a LCB polymer is ß 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 2103 Long-Chain Branching and Rheological Properties of Ethylene-1-Hexene Copolymers Synthesized from Ethylene Stock . . . PE1 PE3 PE5 Ea from G" (kJ/mol) 40 40 PE2 PE4 Ea from G" (kJ/mol) 44 36 32 28 35 30 PE6 PE7 PE8 PE9 25 24 20 20 0.01 0.1 1 10 100 o Angular Frequency at 190 C (rad/s) Figure 7. Activation energy spectra from G00 (reference temperature ¼ 190 8C) for polymers PE1–PE5. dominated by the repetition of linear chains. Hence, the activation energy in this region should converge to approximately the same activation energy for a purely linear polymer of equivalent microstructure.[23] For linear polyethylenes, the activation energy is dependent on the SCBD. Conventional HDPE has an activation energy of approximately 27 kJ
mol1.[23] For conventional linear LLDPE, activation energy increases with SCBD and activation energy values up to 45 kJ
mol1 has been reported for highly short-chain branched ethylene-hexene copolymers,[18] and various correlations have been established in the literature to correlate the effect of SCBD on activation energy.[9,18,23] From Figure 7, a clear general trend of the increase of the plateau activation energy with SCBD can be observed from 26 kJ
mol1 for PE5 (SCBD ¼ 0) to 35 kJ
mol1 for PE1 (SCBD ¼ 40/1 000 carbons). Unlike the SCBD-dependent plateau activation energy, the activation energy in the low-frequency region of the spectrum is related more to the LCBD of the polymers as the stress relaxation behavior in this region is dominated by the LCB molecules that are more sensitive to temperature. Higher LCBD generally leads to higher activation energy in the low-frequency range and larger changes in the activation energy from low frequency to high frequency.[23] However, owing to the experimental difficulty in obtaining accurate viscoelastic data in the extremely lowfrequency range, activation energy at frequency lower than 0.04 rad
s1 could not be accurately determined. Therefore, a comparison of the LCBD of the five polymers based on the activation energy difference in the low frequency end could not be performed. Figure 8 shows the activation energy spectra for polymers PE6–PE9 at a reference temperature of 190 8C. Surprisingly, these polymers exhibited an almost constant activation energy within the studied frequency range, although other rheological evidences, such as enhanced Z0 Macromol. Chem. Phys. 2005, 206, 2096–2105 www.mcp-journal.de 0.01 0.1 1 10 100 1000 o Angular Frequency at 190 C (rad/s) Figure 8. Activation energy spectra from G00 (reference temperature ¼ 190 8C) for polymers PE6–PE9. and up-shifted log G0 versus log G00 curve, have indicated the presence of LCB in these polymers. This discrepancy might be due to an even lower level of LCBD in these polymers and the relative insensitivity of Ea toward LCB compared to other rheological properties. In addition, the activation energy values for these polymers are very close (33–35 kJ
mol1), suggesting that the LCBD and SCBD are very low and close to each other. Effect of Catalyst Ratio in Tandem Catalysis on LCBD The above investigation and analysis of the rheological properties of the two sets of polymers prepared with concurrent tandem catalysis have provided strong evidences for the presence of sparse LCB in these polymers. We believe the mechanism for the LCB formation in this concurrent tandem catalysis system is no different from that in the single CGC catalyst system, which has been well studied for producing LCB polymers. During LLDPE preparation with the concurrent tandem catalysis system, the trimerization catalyst 1 trimerizes ethylene to 1-hexene and the CGC catalyst 2 copolymerizes ethylene with 1-hexene and in situ generates vinyl-ended poly(ethyleneco-hexene) macromonomers, which are further incorporated by catalyst 2 into growing chains to form LCB polymers. In several studies[7,10–12,14,15] on the preparation of LCB LLDPE by ethylene-olefin copolymerization with a single metallocene catalyst, it has been found that olefin concentration within the copolymerization system greatly affects LCBD of the polymers. The incorporation of a small amount of olefin comonomer at low olefin concentrations can improve the solubility and flexibility of the macromonomer and thus facilitate its reincorporation to generate LCB LLDPE with enhanced LCBD. However, at high olefin ß 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 2104 Z. Ye, F. AlObaidi, S. Zhu, R. Subramanian contents, excessive olefin incorporation leads to significant undesirable chain terminations generating unincorporable vinylidene-terminated chains and thus produce polymers with reduced LCBD and even linear polymers.[14,15] From the above rheological results, we can observe a similar phenomenon with the LLDPE prepared here with concurrent tandem catalysis. For the set of polymers prepared at 45 8C (PE6–PE9), we can summarize from the above rheological data that LCBD increases qualitatively according to the order: PE9  PE8 < PE7 < PE6, i.e., LCBD increases with the molar ratio of catalyst 1/catalyst 2 during preparation. The concentration level of 1-hexene remains to be very low in the polymerization system at 45 8C[28,29,44] due to a significant deactivation of trimerization catalyst 1 at this temperature. An increase in the molar ratio of catalyst 1/catalyst 2 leads to higher 1-hexene concentration and increased solubility and flexibility for the macromonomer without causing excessive undesirable chain termination. Hence, LCBD tends to increase with an enhancement in the catalyst ratio at this elevated temperature. However, for the polymer set prepared at 25 8C (PE1–PE5), the above rheological properties suggest that LCBD increases in the following sequence: PE1 < PE2  PE3 < PE4, i.e., LCBD increases with a decrease in the molar ratio of catalyst 1/catalyst 2 during preparation. At this reduced temperature, the trimerization catalyst 1 does not experience pronounced deactivation and retains high activity toward ethylene trimerization.[28,29,44] 1-Hexene concentration in the polymerization system is thus high enough to lead to significant undesirable chain terminations, thereby producing unincorporable macromonomers. Therefore, at this temperature lowering the ratio of catalyst 1/catalyst 2 will suppress such undesirable chain terminations and increase LCBD in the polymer. Conclusion In this study, we have examined for the first time the rheological properties of LLDPE prepared using concurrent tandem catalysis system with ethylene as the sole monomer stock. Two sets of ethylene-hexene derived LLDPE (PE1– PE5 and PE6–PE9) were prepared with binary tandem catalysis system comprising (Z5-C5H4CMe2C6H5)TiCl3 (1)/MMAO and [(Z5-C5Me4)SiMe2(tBuN)]TiCl2 (2)/ MMAO catalysts with various catalyst ratios and at two temperature levels (25 and 45 8C). The melt rheological properties of these polymers were extensively evaluated and compared utilizing small-amplitude dynamic oscillation measurements. These polymers have been found to possess some typical rheological properties characteristic of LCB polymers, such as enhanced zero-shear viscosity, improved shear-thinning, elevated dynamic moduli, and thermorheological complexity, which suggest the presence of LCB in the polymers. The LCBD of the two respective Macromol. Chem. Phys. 2005, 206, 2096–2105 www.mcp-journal.de sets of polymers were qualitatively compared and correlated to the polymerization conditions including catalyst ratio and temperature. 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