Article pubs.acs.org/IECR
Expanded Linear Low-Density Polyethylene Beads: Fabrication, Melt Strength, and Foam Morphology Peng Guo, Yaohui Xu, Mingfu Lu,* and Shijun Zhang Beijing Research Institute of Chemical Industry, Sinopec, Beijing 100013, People’s Republic of China ABSTRACT: A linear low-density polyethylene copolymerized with 1-hexene (H-LLDPE) was synthesized by gas-phase polymerization, using the metallocene catalyst systems. The HLLDPE exhibited longer ethylene average sequence length, narrower molecular weight distribution, and higher melt strength, compared with linear low-density polyethylene copolymerized with 1-butene (B-LLDPE). The expanded polyethylene (EPE) beads were prepared by a batch foaming process using above two LLDPEs as base resins. Both ethylene average sequence length and comonomer content were measured by solid-state nuclear magnetic resonance (NMR). Influences of melt strength and molecular structure on the cellular morphology of EPE are investigated using scanning electron microscopy (SEM) and a melt strength meter, respectively. The influence of saturation temperature and pressure on cell density and morphology are examined by homogeneous and heterogeneous nucleation theory. Results indicate that, with higher melt strength and longer ethylene average sequence length, the demonstrated H-LLDPE facilitates the entire batch-foaming process and yields improved cellular structure of EPE beads over that of B-LLDPE.
1. INTRODUCTION Polyethylene (PE) is a thermoplastic polymer that has the chemical formula (C2H4)n. Since 1898, when Pechmann casually discovered polyethylene, it has been arousing considerable worldwide interest and has been used in various applications, because of its good performance, such as high toughness, ductility, impact strength, and chemical resistance.1,2 Considering increasing industrial requirement, it is predicted that the demand and capacity will reach 82 and 90 M tons, respectively, in 2016.3 Among the various PE compounds, linear low density polyethylene (LLDPE) is a type of polymer with linear structure and many short branches, usually made via the copolymerization of ethylene with α-olefin such as 1butene, 1-hexene, and 1-octene.4,5 Among them, LLDPE copolymerized with 1-hexene is considered to be cost-effective, compared with LLDPE copolymerized with 1-octene, and possesses superior properties to those of LLDPE copolymerized with 1-butene.6 During the early stage, LLDPE is mainly polymerized by a Ziegler−Natta catalyst or a zirconium catalyst.7,8 Since the 1950s, metallocene catalyst has been used for LLDPE synthesis.9−11 The mechanical and rheological properties of LLDPE are strongly influenced by chemical composition distribution (CCD) and molecular weight distribution (MWD). LLDPE prepared by metallocene catalyst generally displays excellent mechanical properties, as a result of its narrower MWD.5 Generally, the melt strength of PE declines rapidly when temperature approaches its melting point. Therefore, when polyethylene is used to produce PE foams, potential cell coalescence and rupture may occur. In order to address the above-mentioned issues, network structure into the PE resin by physical and chemical modification is © XXXX American Chemical Society
expected to improve the viscoelasticity and melt strength of PE.12 Cross-linked expanded polyethylene has long been used for packaging applications. Despite its lightweight and good mechanical properties, the applications of cross-linked expanded PE have been actually limited, because of nonrecyclability. Expanded polyethylene (EPE) beads are currently used for thermal insulation, electronic packaging, household articles, toys, and automobile parts. EPE exhibits much better performance, including better impact resistance and comfort, compared with expanded polypropylene (EPP) beads in the fields of low-temperature applications and bedding. EPE is commercially utilized in mold shaping, which is a sintering process that fabricates an EPE foam profile.13 Therefore, PE resin that is used for the preparation of EPE beads could not possess a cross-linked structure. Hence, the development of polyethylene with improved chemical composition distribution and good ductility in situ is highly desired by industry. Behravesh et al. prepared autoclave-based EPE foams using the polyethylene blends.12 They utilized differential scanning calorimetry (DSC) to investigate the effects of PE blends on the thermal behaviors and found that the ternary blend (LDPE, LLDPE, and HDPE) contributed to the production of multiple peaks in the DSC results. Furthermore, some companies including KANEKA, JSP, and BASF have reported the preparation and application of EPE beads and corresponding moldings.14−16 Received: April 21, 2016 Revised: June 24, 2016 Accepted: July 4, 2016
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DOI: 10.1021/acs.iecr.6b01545 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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served as a cell nucleation agent. Other functional agents including glycerol, polyethylene glycol, antistatic agent, and antioxidants were mixed in the system at the same time. We sieved the as-prepared micropellets with a vibrating screen to eliminate the undersized and oversized pellets. EPE beads were fabricated using an autoclave foaming process. Pellets with a mass of 100 g were blended with stabilizers and 3 L of water in a pressure vessel. Sodium dodecylbezene sulfonate (0.2 g) and 0.05 g of aluminum sulfate were introduced as a suspension stabilizer and enhancer, respectively, to stop the PE micropellets from melting together during the foaming process.18,19 CO2 was introduced into the vessel and infiltrated into the PP pellets floating in the water for ∼30 min near the melting point of PE.12,18,19 In order to determine this saturation temperature, the melting points of the PE micropellets were measured using DSC (PerkinElmer) and at a heating−cooling−heating rate of 10 °C/min. Until the saturation of gas in the pellets, the pellets were released from the pressure vessel rapidly so that they could expand quickly, as a result of the thermodynamic instability. The suspension stabilizers were washed away using deionized water from EPE beads. The foam beads were dried in a 65 °C over for 6 h. Finally, the dried beads were placed into an autoclave and kept there until the internal pressure of bead reached atmospheric pressure. The preparation of EPE using an autoclave foaming process is similar to that of EPP.19 2.3. Characterization. The mechanical properties were evaluated using universal testing machines (Instron, Model 5967, USA) and pendulum impact testing machines (Zwick Roell HIT, Germany), according to ISO 527, ISO 178, and ISO 179 procedures. The melt flow rate (MFR) was measured using a melt flow indexer (Tinius Olsen, Model MP600, USA), according to ISO1133 at 190 °C with a load of 2.16 kg. The density was tested by analytical balance with a density tester (Satorius CPA225D, Germany), according to ASTM D792. The heat deflection temperature and Vicat softening temperature were measured using a heat distortion tester (Model 148HDPC/HDPC, Yasuda Seiki Seisakusho, Japan) according to ISO75 and ISO306, respectively. The melt strength was measured using a RHEOTENs melt strength meter (Göttfert Werkstoff Pruefmaschinen, Germany).19 The extrude temperatures were 170, 180, and 190 °C, respectively. The initial velocity of rollers was in direct proportion to the line speed of the extrudate. The measurement of the molecular weight and molecular weight distribution of PE was performing, utilizing gel permeation chromatography (GPC) (Model PL-GPC220, Polymer Laboratories, Inc., U.K.) and an IRS detector (Polymer Char, Inc., Spain) GPC.19 Analytical temperature rising elution fractionation (ATREF) was utilized to analyze the components of LLDPE resins by temperature rising elution fractionation system (TREF) (TERF300, Polymer Char, Spain), which contains crystallization and elution steps.20−22 The characterization of cell morphology of the EPP beads was conducted using scanning electron microscopy (SEM) (Model SL-30, FEI, USA).19 Both average cell diameter and density were determined by SEM figures. The cell diameter was an average value of at least 100 cells. The cell density (N0), which is defined as the number of cells per cubic centimeter, was calculated by eq 1:18,19
So far, little research has been reported on investigating the effects of comonomer and molecular structure of PE on resulting morphology and properties of EPE preparing using an autoclave process. In this work, we demonstrated an improved method for LLDPE (ethylene copolymerized with 1-hexene, HLLDPE) using metallocene catalyst systems. Another commercial LLDPE (ethylene copolymerized with 1-butene, BLLDPE), using the Ziegler−Natta catalyst, was also studied in this work. We used H-LLDPE and B-LLDPE as the base resins to prepare EPE beads (called H-EPE and B-EPE, respectively), using a batch foaming process. We compared the cell morphology and foaming ratio of H-EPE and B-EPE that were prepared under different saturation pressure and temperature. The relationship between molecular components/ structure of basic PE resin and properties of EPE beads is preliminarily discussed.
2. EXPERIMENTAL SECTION 2.1. Preparation of H-LLDPE. We prepared the ethylene1-hexene copolymer (H-LLDPE) in a polyethylene pilot plant that consisted mainly of a gas-phase reactor. The polymerization process steps are as follows. Ethylene and 1-hexene are copolymerized using a single supported bridged metallocene catalyst to obtain H-LLDPE.17 The purity of ethylene and 1-hexene is 99.96 wt % and 99.75 wt %, respectively. The special silicone-supported bridged metallocene catalyst comprises a bridged metallocene compound, a co-catalyst and a supporter. The bridged metallocene compound has a chemical formula of Cw′YCw′MP2. Herein, Cw′ in the formula is a metallocene ligand selected from cyclopentadiene derivative groups. Y in the formula is a bridged group. M in the formula is one selected from elements in Group IVB in elemental periodic table, and P in the formula is selected from halogens. The co-catalyst is aluminoxane, and the supporter consists of an inorganic Si supporter or an organic Si supporter. The polymerization was conducted under N2 atmosphere at 30 psi in the gas-phase reactor. The reactor is a 3 m in diameter, has a fluidization zone 10 m long and a 2 m in diameter, and a velocity reduction zone 5 m long, which are linked with a transition section having tapered walls. In this work, polymerization was performed at a temperature of 70 °C and pressure of 20 bar, and the reaction time was 4.5 h. Ethylene, 1-hexene, and hydrogen were introduced into the bottom of the reactor and then through a gas distributor plate. The flow of the gas through the gas distributor plate was 6 times the minimum particle fluidization velocity. During the reaction, most of the suspended solids were separated from the reduction zone. Unreacted gases exited the top of the fluidization zone and passed through a dust filter to remove any particles. The gases then passed through a gas booster pump. The total system pressure was kept constant during the reaction by regulating the ethylene gas flow into the reactor. Solid polymer was collected from the reactor when the reaction was finished. Herein, a commercial B-LLDPE with the tradename 7042 was provided by SINOPEC Yangzi Petrochemical Corporation, Ltd., China. 2.2. Preparation of Expanded Polyethylene Beads. A twin-screw extruder and an underwater pelletizer (BKG Labline 100, Germany) were utilized to prepare the PE micropellets with diameters of 5 MPa. Moreover, the cell morphology and distribution of H-EPE are displayed distinctly in Figure 7. The observation of cell density from SEM photographs is consistent with Figure 6. The average cell diameter first decreases and then increases with enhancing pressure. According to Colton and Suh’s theory,38 the formula of homogeneous nucleation rate is expressed as described in eq 5:
(5)
where f 0 is the frequency factor of homogeneous nucleation, C0 is the concentration of gas molecules, ΔG*homo is the activation energy of homogeneous nucleation, k is the Boltzmann constant, and T is the absolute temperature. ΔGhomo * is expressed as described in eq 6: * = ΔG homo
16πσ 3 3ΔP 2
(6)
where ΔP = Psat − Ps (where Psat is the saturation pressure and Ps is the ambient pressure) and σ is the surface energy of the polymer/bubble interface. According to Uhlmann and Chalmers,39 the heterogeneous nucleation rate can be expressed as described in eq 7: ⎛ ΔG * ⎞ hetero ⎟ Nhetero = C1f1 exp⎜ − kT ⎝ ⎠
(8)
where f(θ) = [(2 + cos θ)(1 − cos θ)2]/4 (where f(θ) is dependent on the wetting angle θ, which has values of ≤1), ΔP = Psat − Ps, Psat is the saturation pressure, and Ps is the ambient pressure, and σ is the surface energy of the polymer/bubble interface. Herein, both ΔG*homo and ΔG*hetero are inversely proportional to the pressure drop.38−40 Therefore, both average cell diameter and density are dependent on the pressure drop in both homogeneous and heterogeneous nucleation systems when the addition of a nucleation agent, such as talc power, is constant in each sample. From Figure 7a to Figure 7c, with the increment of saturation pressure (3−5 MPa), the higher cell density and smaller average cell diameter are obtained. When the saturation pressure attains 5 MPa, the CO2 is basically saturated in the PE micropellets. The cell density did not increase further and generally decreases when the saturation pressure increases to 6 MPa, while the foaming ratio continues to be enhanced, as shown in Figure 6a. It might be ascribed that the cell wall becomes thinner because of a decline of melt strength derived from potential plasticization of CO2. Herein, both tie chains and longer ethylene average sequence length protect cells from rupture during the quick releasing process when the saturation pressure reaches 6 MPa. Similarly, the average cell diameter of B-EPE also exhibits, first, a decrease and then an increase in tendency in Figure 8. However, the average cell diameter is much larger than that of H-EPE at the same saturation pressure. Moreover, the distribution of cell diameter is not uniform as that of H-EPE. Especially, when saturation pressure is over 5 MPa, as shown in Figures 8c and 8d, the potential cell coalescence and burst could be found. This will lead to the lower cell density, compared with H-EPE, which is due to lower melt strength under the same foaming conditions. The influence of saturation temperature on the properties of H-EPE and B-EPE at the same saturation pressure (5 MPa) also is investigated. The saturation temperature of two types of EPE is selected from Tm − 2 °C to Tm + 4 °C in intervals of 2 °C. Figure 9a shows the relationship between foaming ratio and saturation temperature. It is found that the foaming ratio displays a linear growth when the saturation temperature increases from Tm − 2 °C to Tm + 2 °C. However, when the saturation temperature reaches Tm + 4 °C, two types of EPE beads indicate different variations. The foaming ratio of H-EPE continues to be enhanced but the slope decreases, because of the potential decline in melt strength.37 Controversially, B-EPE displayed a remarkable decrease in foaming ratio. It is ascribed that more serious cell coalescence and burst is caused by lower melt strength, compared with H-EPE. Figure 9b shows the increase−decrease tendency of cell density with increasing saturation temperature for H-EPE. It is found that the cell density of H-EPE jumps to 7.7 × 108 cm−3 when the saturation temperature increases from Tm − 2 °C to Tm. It might be explained that the activation energy declines drastically with the assistance of homogeneous and heterogeneous nucleation together, considering eq 7. Then, with further increases in saturation temperature, more gas dissolved in PE micropellets resulted in the decline of cell density. However, the cell density of B-EPE exhibits a continuous decline, because of poor cell
Figure 9. (a) Foaming ratio and (b) cell density, each as a function of saturation temperature at the same pressure (5 MPa).
⎛ −ΔG * ⎞ homo ⎟ Nhomo = f0 C0 exp⎜ ⎝ kT ⎠
16πσ 3 f (θ ) 3ΔP 2
(7)
where C1 is the concentration at the heterogeneous nucleation point, f1 is the frequency factor of heterogeneous nucleation, ΔG*hetero is the activation energy of heterogeneous nucleation, k G
DOI: 10.1021/acs.iecr.6b01545 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Figure 10. Cellular morphology of H-EPE at 5 MPa: (a) at 119 °C, (b) at 121 °C, (c) at 123 °C, and (d) at 125 °C.
strength decreases with increasing temperature. When the saturation temperature is low (Tm − 2 °C), the activation energy is not high enough to generate more bubbles in the PE melts while the saturation pressure is 5 MPa. This generates cell growth, leading to the observation of lower cell density and larger cell diameter in Figure 10a. With increasing temperature, both activation energy and melt strength further decreased, as shown in eq 8. Thus, smaller and intensively distributed cells are obtained (Figure 10b). With continuously increasing saturation temperature, the reduced melt strength forces an increasing amount of CO2 into the micropellets, resulting in a decrease in cell density when the saturation temperature is more than Tm (see Figures 10c and 10d). The higher melt strength of H-LLDPE efficiently prevents cell coalescence. At the same time, we also study the influence of saturation temperature on the cell structure of B-EPE, as shown in Figure 11. It is observed that the cell morphology of B-EPE is not as well-dispersed as that of H-EPE. Furthermore, with increasing saturation temperature, the cell density continued to decrease. Obvious cell coalescence and deformation appeared when the saturation temperature was over Tm for B-EPE, as seen in Figures 11c and 11d. It is guessed that the lower melt strength is unfavorable for the preservation of gas in the bubble. As some small holes appear on the cell wall, strong gas turbulence leads to cell rupture during the quick release of pressure. The less intercrystalline tie molecules and chain entanglements, as well as short ethylene average sequence length introduced by 1butene addition exerts negative effects on the melt strength of B-LLDPE, which results in the poor morphology and
nucleation and low melt strength. Moreover, the cell density of B-HPE is 1 order of magnitude lower than that of H-EPE. In the heterogeneous nucleation system, the nucleation rate will increase to some extent with increasing temperature, according to the above-mentioned relationship in eq 7. In addition, the activation energy of heterogeneous nucleation could decrease with increasing saturation temperature, considering eq 8.41 On the one hand, the enhancement of nucleation rate and decline of activation energy contributed to an increase in cell density. On the other hand, the decrease in melt strength is conducive to coal coalescence with increasing temperature. It is estimated that the competition of decreasing melt strength and declining activation energy leads to the increase−decrease tendency of cell density. For H-EPE, a slight decrease in melt strength did not prevent more cell growth, as a result of declining activation energy. However, remarkable decreases in the melt strength of B-LLDPE totally hinders increases in cell density. Herein, the effects of saturation temperature on the foaming ratio of EPE are different from those of EPP.19 It is similar to the effect of saturation pressure on the foaming ratio. It is surmised that the lower melt strength of H-LLDPE, relative to that of high-meltstrength polypropylene, is beneficial to further increases in the foaming ratio when the saturation temperature is over Tm + 2 °C. Figure 10 shows the morphology of H-EPE beads prepared at the same saturation pressure (5 MPa) and small temperature intervals around the melting point. The cell diameter first decreased, then increased and finally remained almost constant. It is explained that the cell continuously grows and melt H
DOI: 10.1021/acs.iecr.6b01545 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Figure 11. Cellular morphology of B-EPE at 5 MPa: (a) at 122 °C, (b) at 124 °C, (c) at 126 °C, and (d) at 128 °C.
performance of B-HPE beads. Thus, melt strength is an important factor for the cell growth and formation. It is proposed that, with the increase of temperature, the indistinctively changed melt strength of H-LLDPE potentially leads to a larger processing temperature range. This result is in accordance with previous research on the effects of melt strength on the cell morphology of EPP.19
controlling the cell structure and properties of EPE beads. It is inferred that ethylene copolymerized with α-olefin having a longer carbon chain length is suggested for the production of EPE. Moreover, considering the high cost performance, moderate saturation pressure (∼5 MPa) and temperature (near the melting point) is recommended for the preparation of EPE in order to obtain good cellular morphology. The preliminary results can contribute to research and development in the field of LLDPE and EPE production.
4. CONCLUSION We prepared LLDPE copolymerized with 1-hexene by gaseous phase polymerization using the metallocene catalyst. This HLLDPE (using 1-hexene as a comonomer) exhibits a homogeneous short-chain branch distribution structure, narrower molecular weight distribution, and longer ethylene average sequence length, compared with B-LLDPE. Therefore, H-LLDPE indicates higher melt strength than that of conventional B-LLDPE (7042). The melt strength of HLLDPE is not sensitive to temperature fluctuation, compared with conventional B-LLDPE. As similar to EPP, a higher melt strength of base resin contributes to integrated and uniform cell structure of EPE. Through preparation of EPE beads by two types of LLDPE, the influence of foaming conditions on the morphology and performances of EPE are investigated preliminarily. Through a series of experiments, it is suggested that H-LLDPE will be given high priority for the production of EPE beads. The homogeneous short-chain branch distribution, more intercrystalline tie molecules, and longer ethylene average sequence length of basic PE resin is potentially beneficial for
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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 want to thank Sinopec for permission to publish this original research article. This work was supported by SINOPEC (Nos. 214093 and G6001-14-ZS-0464).
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REFERENCES
(1) Moore, S. J.; Wanke, S. E. Solubility of ethylene, 1-butene and 1hexene in polyethylenes. Chem. Eng. Sci. 2001, 56, 4121. (2) Natta, G. Properties of isotactic, atactic, and stereoblock homopolymers, random and block copolymers of α-olefins. J. Polym. Sci. 1959, 34, 531.
I
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Industrial & Engineering Chemistry Research (3) Chum, P. S.; Swogger, K. W. Olefin polymer technologies-history and recent progress at the Dow chemical company. Prog. Polym. Sci. 2008, 33, 797. (4) Carlini, C.; D’Alessio, A.; Giaiacopi, S.; Po, R.; Pracella, M.; Galletti, A. M. R.; Sbrana, G. Linear low-density polyethylenes by copolymerization of ethylene with 1-hexene in the presence of titanium precursors and organoaluminium co-catalysts. Polymer 2007, 48, 1185. (5) Park, H. W.; Chung, J. S.; Baeck, S. H.; Song, I. K. Physical property and chemical composition distribution of ethylene−hexene copolymer produced by metallocene/Ziegler−Natta hybrid catalyst. J. Mol. Catal. A: Chem. 2006, 255, 69. (6) Miyata, H.; Yamaguchi, M.; Akashi, M. Structure and viscoelastic properties of amorphous ethylene/1-hexene copolymers obtained with metallocene catalyst. Polymer 2001, 42, 5763. (7) Matsko, M. A.; Echevskaya, L. G.; Zakharov, V. A.; Nikolaeva, M. I.; Mikenas, T. B.; Vanina, M. P. Study of Multi-Site Nature of Supported Ziegler−Natta Catalysts in Ethylene-Hexene-1 Copolymerization. Macromol. Symp. 2009, 282, 157. (8) Tshuva, E. Y.; Goldberg, I.; Kol, M. Isospecific Living Polymerization of 1-Hexene by a Readily Available Nonmetallocene C2-Symmetrical Zirconium Catalyst. J. Am. Chem. Soc. 2000, 122, 10706. (9) Sinn, H.; Kaminsky, W. Ziegler−Natta Catalysis. Adv. Organomet. Chem. 1980, 18, 99. (10) Miyata, H.; Yamaguchi, M.; Akashi, M. Structure and viscoelastic properties of amorphous ethylene/1-hexene copolymers obtained with metallocene catalyst. Polymer 2001, 42, 5763. (11) Jongsomjit, B.; Praserthdam, P.; Kaewkrajang, P. A comparative study on supporting effect during copolymerization of ethylene/1olefins with silica-supported zirconocene/MAO catalyst. Mater. Chem. Phys. 2004, 86, 243−246. (12) Behravesh, A. H.; Park, C. B.; Lee, E. K. Formation and characterization of polyethylene blends for autoclave-based expandedbead foams. Polym. Eng. Sci. 2010, 50, 1161. (13) Nofar, M.; Guo, Y.; Park, C. B. Double Crystal Melting Peak Generation for Expanded Polypropylene Bead Foam Manufacturing. Ind. Eng. Chem. Res. 2013, 52, 2297. (14) Nakayama, K. Expanded particle of noncrosslinked polyethylenebased resin and expansion molded article of noncrosslinked polyethylenebased resin. U.S. Patent 8,779,019, July 15, 2014. (15) Okamura, K.; Nakaguki, H. Expandable polyethylene resin particle and method for production thereof. U.S. Patent 7,964,652, June 21, 2011. (16) Maletzko, C.; Keppeler, U.; Hahn, K.; De Grave, I. Expandable polyolefin particles. U.S. Patent 6,864,298, March 8, 2005. (17) Zheng, G.; Wang, W.; Deng, X.; Fan, G.; Wang, H.; Liu, C.; Hu, Q.; Wang, H. Method for preparing a kind of polyethylene with metallocene catalyst. Chin. Patent CN103087241A, Oct. 31, 2011. (18) Guo, P.; Liu, Y.; Xu, Y.; Lu, M.; Zhang, S.; Liu, T. Effects of saturation temperature/pressure on melting behavior and cell structure of expanded polypropylene bead. J. Cell. Plast. 2014, 50, 321. (19) Guo, P.; Xu, Y.; Lu, M.; Zhang, S. High melt strength polypropylene with wide molecular weight distribution used as basic resin for expanded polypropylene beads. Ind. Eng. Chem. Res. 2015, 54, 217. (20) Usami, T.; Gotoh, Y.; Takayama, S. Generation mechanism of short-chain branching distribution in linear low-density polyethylenes. Macromolecules 1986, 19, 2722. (21) Gabriel, C.; Lilge, D. Comparison of different methods for the investigation of the short-chain branching distribution of LLDPE. Polymer 2001, 42, 297. (22) Zhang, M.; Lynch, D. T.; Wanke, S. E. Characterization of commercial linear low-density polyethylene by TREF-DSC and TREFSEC cross-fractionation. J. Appl. Polym. Sci. 2000, 75, 960. (23) Gupta, P.; Wilkes, G. L.; Sukhadia, A. M.; Krishnaswamy, R. K.; Lamborn, M. J.; Wharry, S. M.; Tso, C. C.; DesLauriers, P. J.; Mansfield, T.; Beyer, F. L. Does the length of the short chain branch affect the mechanical properties of linear low density polyethylenes? An investigation based on films of copolymers of ethylene/1-butene,
ethylene/1-hexene and ethylene/1-octene synthesized by a single site metallocene catalyst. Polymer 2005, 46, 8819. (24) Randall, J. C. Carbon-13 NMR of ethylene−1-olefin copolymers: Extension to the short-chain branch distribution in a low-density polyethylene. J. Polym. Sci., Polym. Phys. Ed. 1973, 11, 275. (25) Hsieh, E. T.; Randall, J. C. Ethylene-1-butene copolymers. 1. Comonomer sequence distribution. Macromolecules 1982, 15, 353. (26) Hsieh, E. T.; Randall, J. C. Monomer sequence distributions in ethylene-1-hexene copolymers. Macromolecules 1982, 15, 1402. (27) Hosoda, S.; Nozue, Y.; Kawashima, Y.; Suita, K.; Seno, S.; Nagamatsu, T.; Wagener, K. B.; Inci, B.; Zuluaga, F.; Rojas, G.; Leonard, J. K. Effect of the sequence length distribution on the lamellar crystal thickness and thickness distribution of poly-ethylene: perfectly equisequential admet polyethylene vs ethylene/α-olefin copolymer. Macromolecules 2011, 44, 313. (28) Flory, P. J. Theory of crystallization in copolymers. Trans. Faraday Soc. 1955, 51, 848. (29) Allegra, G.; Marchessault, R. H.; Bloembergen, S. Crystallization of markoffian copolymers. J. Polym. Sci., Part B: Polym. Phys. 1992, 30, 809. (30) Karssenberg, F. G.; Mathot, V. B. F.; Zwartkruis, T. J. G. Chain microstructure of homogeneous ethylene-1-alkene copolymers and characteristics of single site catalysts using a direct 13C NMR peak method I. Theory and models. J. Polym. Sci., Part B: Polym. Phys. 2006, 44, 722. (31) Crist, B.; Howard, P. R. Crystallization and melting of model ethylene−butene copolymers. Macromolecules 1999, 32, 3057. (32) Alamo, R. G.; Viers, B. D.; Mandelkern, L. Phase structure of random ethylene copolymers: A study of counit content and molecular weight as independent variables. Macromolecules 1993, 26, 5740. (33) Mauler, R. S.; Galland, G. B.; Scipioni, R. B.; Quijada, R. The effect of the ethylene pressure on its reaction with 1-hexene, 1-octene and 4-methyl-1-pentene. Polym. Bull. 1996, 37, 469. (34) Lau, H. C.; Bhattacharya, S. N.; Field, G. J. Melt strength of polypropylene: Its relevance to thermoforming. Polym. Eng. Sci. 1998, 38, 1915. (35) Hoffman, J. D. Role of reptation in the rate of crystallization of polyethylene fractions from the melt. Polymer 1982, 23, 656. (36) Seguela, R. Critical review of the molecular topology of semicrystalline polymers: The origin and assessment of intercrystalline tie molecules and chain entanglements. J. Polym. Sci., Part B: Polym. Phys. 2005, 43, 1729. (37) Pandey, P.; Chauhan, R. S.; Shrivastava, A. K. Carbon-dioxideinduced plasticization effects in solvent-cast polyethylene membranes. J. Appl. Polym. Sci. 2002, 83, 2727. (38) Colton, J. S.; Suh, N. P. The nucleation of microcellular thermoplastic foam with additives: Part I: Theoretical considerations. Polym. Eng. Sci. 1987, 27, 485. (39) Uhlmann, D. R.; Chalmers, B.; Jackson, K. A. Interaction between particles and a solid−liquid interface. J. Appl. Phys. 1964, 35, 2986. (40) Colton, J. S.; Suh, N. P. Nucleation of microcellular foam: Theory and practice. Polym. Eng. Sci. 1987, 27, 500. (41) Sullivan, D. E. Surface tension and contact angle of a liquid− solid interface. J. Chem. Phys. 1981, 74, 2604.
J
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