Abstract
The detection of long-chain branches (LCBs) is an issue of significant importance in both basic research and industrial applications, as LCBs provide excellent means to improve the processing behavior, especially in elongation-dominated processing operations. In this article, different methods for the detection of very low amounts of LCBs in metallocene-catalyzed polyethylene are presented and compared with respect to their sensitivity. Depending on the molar mass, the zero shear rate viscosity increase factor η 0/\(\eta_{0}^{\rm lin}\), the steady-state elastic recovery compliance \(J_{e}^{0}\), the complex modulus functions G′(ω) and G″(ω), and the thermorheological complexity were found to be sensitive. In general, the higher the molar mass, the more important the transient quantities become and the easier finding the long-chain branches gets. Although rheology is very sensitive, rheological methods in combination with size exclusion chromatography proved to be the most sensitive combination to detect even very low amounts of LCBs. Especially methods involving the elastic properties (G′(ω), \(J_{\rm e}^{0}\), and J r(t)) react very sensitively, but these are also very distinctly influenced by the molar mass distribution.
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Notes
The two main relaxation times in lightly branched LCB-mPE are determined by the molar mass M w. The shorter one (λ 2), scaling with \(M_{\rm w}^{3.6}\), corresponds to the characteristic relaxation time λ of linear PE, while the longer one (λ 1), scaling with \(M_{\rm w}^{5.15}\), is also influenced by the degree of branching and longer than the shorter one by a factor of about 1,000 at M w ≈ 50 kg/mol (Stadler and Münstedt 2009).
To reach the terminal regime fully, a frequency of at least two more likely four decades would have to be measured, which would mean unreasonably long measurement times in the order of months. Besides the limitation of the lowest frequency the rheometer can obtain, also it is very doubtful that the thermal stability would be sufficiently long to allow such a measurement.
Many more reports of the activation energy E a exist, but the determination of E a is also dependent on the laboratory procedure (e.g., Keßner et al. 2009). E a of mHDPE was reported to be in the interval between 22 and 31 kJ/mol by different authors (see references in Stadler et al. (2007b) for an overview). For this reason, only activation energies reported by the same group, using the same methods should be compared.
Alternative models, e.g., by Vega et al. (1998) require individual parameters for each comonomer length.
References
Archer LA (1999) Separability criteria for entangled polymer liquids. J Rheol 43(6):1555–1571
Archer LA, Varshney SK (1998) Synthesis and relaxation dynamics of multiarm polybutadiene melts. Macromolecules 31(18):6348–6355
Arikan B, Stadler FJ, Kaschta J, Münstedt H, Kaminsky W (2007) Synthesis and characterization of ethene-graft-ethene-/propene-copolymers. Macromol Rapid Commun 28(14):1472–1478. doi:10.1002/marc.200700161
Auhl D, Stadler FJ, Münstedt H (2012) Comparison of molecular structure and rheological properties of electron-beam- and gamma-irradiated polypropylene. Macromolecules 45:2057–2065
Bach A, Almdal K, Rasmussen HK, Hassager O (2003) Elongational viscosity of narrow molar mass distribution polystyrene. Macromolecules 36(14):5174–5179
Ball RC, Mcleish TCB (1989) Dynamic dilution and the viscosity of star polymer melts. Macromolecules 22(4):1911–1913
Berry GC, Fox TG (1968) The viscosity of polymers and their concentrated solutions. Adv Polym Sci 5:261–357
Bubeck RA (2002) Structure–property relationships in metallocene polyethylenes. Mater Sci Eng R 39:1–28
Chen X, Stadler FJ, Münstedt H, Larson RG (2010) Method for obtaining tube model parameters for commercial ethene/α-olefin copolymers. J Rheol 54(2):393
Costeux S, Wood-Adams P, Beigzadeh D (2002) Molecular structure of metallocene-catalyzed polyethylene: rheologically relevant representation of branching architecture in single catalyst and blended systems. Macromolecules 35(7):2514–2528
Doi M, Edwards SF (1986) The theory of polymer dynamics. Oxford Press, Oxford
Ferry JD (1980) Viscoelastic properties of polymers. Wiley, New York
Fetters LJ, Kiss AD, Peareon DS, Quack GF, Vitus FJ (1993) Rheological behavior of star-shaped polymers. Macromolecules 26(4):647–654
Fetters LJ, Lohse DJ, Colby RH (2007) Chain dimensions and entanglement spacings physical properties of polymers, 2nd edn. JE Mark. Springer, Heidelberg
Fleury G, Schlatter G, Muller R (2004) Non linear rheology for long chain branching characterization, comparison of two methodologies: fourier transform rheology and relaxation. Rheol Acta 44(2):174–187
Flory PJ (1953) Principles of polymer chemistry. Cornell University Press, Ithaca
Fulchiron R, Verney V, Marin G (1993) Determination of the elongational behavior of polypropylene melts form transient shear experiments using Wagner model. J Non-Newton Fluid Mech 48:49–68
Gabriel C (2001) Einfluss der molekularen Struktur auf das viskoelastische Verhalten von Polyethylenschmelzen. Aachen, Shaker-Verlag
Gabriel C, Munstedt H (1999) Creep recovery behavior of metallocene linear low-density polyethylenes. Rheol Acta 38(5):393–403
Gabriel C, Münstedt H (2002) Influence of long-chain branches in polyethylenes on linear viscoelastic flow properties in shear. Rheol Acta 41(3):232–244
Gabriel C, Münstedt H (2003) Strain hardening of various polyolefins in uniaxial elongational flow. J Rheol 47(3):619–630
Gabriel C, Kokko E, Löfgren B, Seppälä J, Münstedt H (2002) Analytical and rheological characterization of long-chain branched metallocene-catalyzed ethylene homopolymers. Polymer 43(24):6383–6390
Guzman JD, Schieber JD, Pollard R (2005) A regularization-free method for the calculation of molecular weight distributions from dynamic moduli data. Rheol Acta 44(4):342–351
Hatzikiriakos SG, Ansari M, Sukhadia AM, Rohlfing DC (2011) Rheology of Ziegler-Natta and metallocene high-density polyethylenes: broad molecular weight distribution effects. Rheol Acta 50(1):17–27
Hepperle J, Münstedt H (2006) Rheological properties of branched polystyrenes: nonlinear shear and extensional behavior. Rheol Acta 45(5):717–727
Kaminsky W (2004) The discovery of metallocene catalysts and their present state of the art. J Polym Sci A Polym Chem 42(16):3911–3921
Kaminsky W, Piel C, Scharlach K (2005) Polymerization of ethene and longer chained olefins by metallocene catalysis. Macromol Symp 226(1):25–34
Kapnistos M, Vlassopoulos D, Roovers J, Leal LG (2005) Linear rheology of architecturally complex macromolecules: comb polymers with linear backbones. Macromolecules 38(18):7852–7862
Kapnistos M, Koutalas G, Hadjichristidis N, Roovers J, Lohse DJ, Vlassopoulos D (2006) Linear rheology of comb polymers with star-like backbones: melts and solutions. Rheol Acta 46(2):273–286
Kapnistos M, Kirkwood KM, Ramirez J, Vlassopoulos D, Leal LG (2009) Nonlinear rheology of model comb polymers. J Rheol 53(5):1133–1153
Karjala TP, Sammler RL, Mangnus MA, Hazlitt LG, Johnson MS, Wang JA, Hagen CM, Huang JWL, Reichek KN (2011) Detection of low levels of long-chain branching in polydisperse polyethylene materials. J Appl Polym Sci 119(2):636–646
Kaschta J, Schwarzl FR (1994a) Calculation of discrete retardation spectra from creep data: 2. Analysis of measured creep curves. Rheol Acta 33(6):530–541. doi:10.1007/BF00366337
Kaschta J, Schwarzl FR (1994b) Calculation of discrete retardation spectra from creep data: 1. Method. Rheol Acta 33(6):517–529. doi:10.1007/BF00366336
Kasehagen LJ, Macosko CW (1998) Nonlinear shear and extensional rheology of long-chain randomly branched polybutadiene. J Rheol 42(6):1303–1327
Keßner U, Münstedt H (2009) Thermorheology as a method to analyze long-chain branched polyethylenes. Polymer 51:507–513. doi:10.1016/j.polymer.2009.11.005
Keßner U, Kaschta J, Münstedt H (2009) Determination of method-invariant activation energies of long-chain branched low-density polyethylenes. J Rheol 53(4):1001–1016. doi:10.1122/1.3124682
Keßner U, Münstedt H, Kaschta J, Stadler FJ, Le Duff CS, Drooghaag X (2010) Thermorheological behaviour of various short- and long-chain branched polyethylenes and its correlations with their molecular structure. Macromolecules 43(17):7341–7350. doi:10.1021/ma100705f
Kessner U, Kaschta J, Stadler FJ, Le Duff CcS, Drooghaag X, Münstedt H (2010) Thermorheological behavior of various short- and long-chain branched polyethylenes and their correlations with the molecular structure. Macromolecules 43(17):7341–7350
Klimke K, Parkinson M, Piel C, Kaminsky W, Spiess H-W, Wilhelm M (2006) Optimised polyolefin branch quantification by melt-state 13C NMR spectroscopy. Macromol Chem Phys 207(4):382–395. doi:10.1002/macp.200500422
Kokko E, Malmberg A, Lehmus P, Löfgren B, Seppälä JV (2000) Influence of the catalyst and polymerization conditions on the long-chain branching of metallocene-catalyzed polyethenes. J Polym Sci A Polym Chem 38(2):376–388
Larson RG (1984) A constitutive equation for polymer melts based on partially extending strand convection. J Rheol 28(5):545
Larson RG (1985) Nonlinear shear relaxation modulus for a linear low-density polyethylene. J Rheol 29(6):823–831
Laun HM (1987) Orientation of macromolecules and elastic deformations in polymer melts. Influence of molecular structure on the reptation of molecules. Progr Colloid Polym Sci 75:111–139. doi:10.1007/BFb0109414
Leal LG, Kirkwood KM, Vlassopoulos D, Driva P, Hadjichristidis N (2009) Stress relaxation of comb polymers with short branches. Macromolecules 42(24):9592–9608
Leblans PJR, Sampers J, Booij HC (1985) The mirror relations and nonlinear viscoelasticity of polymer melts. Rheol Acta 24(2):152–158
Lehmus P, Kokko E, Harkki O, Leino R, Luttikhedde HJG, Nasman JH, Seppala JV (1999) Homo- and copolymerization of ethylene and alpha-olefins over 1- and 2-siloxy- substituted ethylenebis(indenyl)zirconium and ethylenebis (tetrahydroindenyl)zirconium dichlorides. Macromolecules 32(11):3547–3552
Liu CY, He JS, van Ruymbeke E, Keunings R, Bailly C (2006) Evaluation of different methods for the determination of the plateau modulus and the entanglement molecular weight. Polymer 47(13):4461–4479
Liu CY, Keunings R, Bailly C (2007) Direct rheological evidence of monomer density reequilibration for entangled polymer melts. Macromolecules 40(8):2946–2954
Liu JY, Yu W, Zhou CX (2011) Polymer chain topological map as determined by linear viscoelasticity. J Rheol 55(3):545–570
Lohse DJ, Milner ST, Fetters LJ, Xenidou M, Hadjichristidis N, Mendelson RA, Garcia-Franco CA, Lyon MK (2002) Well-defined, model long chain branched polyethylene. 2. Melt rheological behavior. Macromolecules 35(8):3066–3075
Malmberg A, Kokko E, Lehmus P, Löfgren B, Seppälä J (1998) Long-chain branched polyethene polymerized by metallocene catalysts Et[Ind]2ZrCl2/MAO and Et[IndH4]2ZrCl2/ MAO. Macromolecules 31(24):8448–8454
Malmberg A, Liimatta J, Lehtinen A, Lofgren B (1999) Characteristics of long chain branching in ethene polymerization with single site catalysts. Macromolecules 32(20):6687–6696
Malmberg A, Gabriel C, Steffl T, Münstedt H, Lofgren B (2002) Long-chain branching in metallocene-catalyzed polyethylenes investigated by low oscillatory shear and uniaxial extensional rheometry. Macromolecules 35(3):1038–1048
Meissner J (1969) Rheometer for the study of mechanical properties of deformation of plastic melts under definite tensile stress. Rheol Acta 8(1):78–88
Münstedt H (1980) Dependence of the elongational behavior of polystyrene melts on molecular weight and molecular weight distribution. J Rheol 24(6):847–867
Münstedt H (1986) Polymerschmelzen Fließverhalten von Stoffen und Stoffgemischen, pp 238–279. W Kulicke. Hüthig&Wepf-Verlag, Basel, Heidelberg, New York
Münstedt H, Gabriel C, Auhl D (2003) Long-chain branching and elongational properties of polyethylene and polypropylene melts. Abstr Pap Am Chem Soc 226:U382–U382
Neidhöfer T, Sioula S, Hadjichristidis N, Wilhelm M (2004) Distinguishing linear from star-branched polystyrene solutions with Fourier-transform rheology. Macromol Rapid Commun 25(22):1921–1926
Osaki K, Kurata M (1980) Experimental appraisal of the Doi–Edwards theory for polymer rheology based on the data for polystyrene solutions. Macromolecules 13(3):671
Osaki K, Takatori E, Kurata M, Watanabe H, Yoshida H, Kotaka T (1990) Viscoeleastic properties of solutions of star-branched polystyrene. Macromolecules 23(20):4392–4396
Otte T, Pasch H, Macko T, Brull R, Stadler FJ, Kaschta J, Becker F, Buback M (2011) Characterization of branched ultrahigh molar mass polymers by asymmetrical flow field–flow fractionation and size exclusion chromatography. J Chromatogr A 1218(27):4257–4267
Park SJ, Shanbhag S, Larson RG (2005) A hierarchical algorithm for predicting the linear viscoelastic properties of polymer melts with long-chain branching. Rheol Acta 44(3):319–330
Piel C, Stadler FJ, Kaschta J, Rulhoff S, Münstedt H, Kaminsky W (2006a) Structure–property relationships of linear and long-chain branched metallocene high-density polyethylenes and SEC-MALLS. Macromol Chem Phys 207(1):26–38
Piel C, Starck P, Seppälä JV, Kaminsky W (2006b) Thermal and mechanical analysis of metallocene-catalyzed ethylene-a-olefin copolymers: the influence of length and number of the crystallizing side-chains. J Polym Sci A Polym Chem 44(5):1600–1612. doi:10.1002/pola.21265
Plazek DJ, Agarwal PK (1976) The creep behavior of some commercial polystyrenes. In: Proc - Int Conrg Rheol, 7th, pp 488–489
Plazek DJ, Echeverria I (2000) Don’t cry for me Charlie Brown, or with compliance comes comprehension. J Rheol 44(4):831–841
Read DJ, Auhl D, Das C, den Doelder J, Kapnistos M, Vittorias I, McLeish TCB (2011) Linking models of polymerization and dynamics to predict branched polymer structure and flow. Science 333(6051):1871–1874
Resch JA, Keßner U, Stadler FJ (2011) Thermorheological behavior of polyethylene—a sensitive probe to molecular structure. Rheol Acta 50(5–6):559–575
Roovers J (1979) Melt rheology of model branched polystyrenes. Polym Prepr 20(2):144–148
Rouse PE Jr (1953) A theory of the linear viscoelastic properties of dilute solutions of coiling polymers. J Chem Phys 21:1272–1280
Shanbhag S (2011) Analytical rheology of branched polymer melts: identifying and resolving degenerate structures. J Rheol 55(1):177–194
Shroff R, Mavridis H (1999) Long-chain-branching index for essentially linear polyethylenes. Macromolecules 32(25):8454–8464
Soares JBP, Hamielec AE (1996) Bivariate chain length and long chain branching distribution for copolymerization of olefins and polyolefin chains containing terminal double-bonds. Macromol Theory Simul 5(3):547–572
Stadler FJ, Münstedt H (2008a) Erratum to “Numerical description of shear viscosity functions of long-chain branched metallocene-catalyzed polyethylenes”. J Non-Newt Fluid Mech 151:227. doi:10.1016/j.jnnfm.2008.05.001
Stadler FJ, Münstedt H (2008b) Terminal viscous and elastic rheological characterization of ethene-/α-olefin copolymers. J Rheol 52(3):697–712. doi:10.1122/1.2892039
Stadler FJ, Münstedt H (2008c) Numerical description of shear viscosity functions of long-chain branched metallocene-catalyzed polyethylenes. J Non-Newton Fluid Mech 151(1–3):129–135
Stadler FJ, Münstedt H (2009) Correlations between the shape of viscosity functions and the molecular structure of long-chain branched polyethylenes. Macromol Mater Eng 294(1):25–34
Stadler FJ, Mahmoudi T (2011) Understanding the effect of short-chain branches by analyzing viscosity functions of linear and short-chain branched polyethylenes. Kor-Austr Rheol J 23(4):185–193
Stadler FJ, Karimkhani V (2011) Correlations between terminal rheological quantities and molecular structure in long-chain branched metallocene catalyzed polyethylene. Macromolecules 44(13):5401–5413
Stadler FJ, Piel C, Klimke K, Kaschta J, Parkinson M, Wilhelm M, Kaminsky W, Münstedt H (2006a) Influence of type and content of very long comonomers on long-chain branching of ethene-/α-olefin copolymers. Macromolecules 39(4):1474–1482. doi:10.1021/ma0514018
Stadler FJ, Piel C, Kaminsky W, Münstedt H (2006b) Rheological characterization of long-chain branched polyethylenes and comparison with classical analytical methods. Macromol Symp 236(1):209–218
Stadler FJ, Piel C, Kaschta J, Rulhoff S, Kaminsky W, Münstedt H (2006c) Dependence of the zero shear-rate viscosity and the viscosity function of linear high-density polyethylenes on the mass-average molar mass and polydispersity. Rheol Acta 45(5):755–764
Stadler FJ, Nishioka A, Stange J, Koyama K, Münstedt H (2007a) Comparison of the elongational behavior of various polyolefins in uniaxial and equibiaxial flows. Rheol Acta 46(7):1003–1012
Stadler FJ, Gabriel C, Munstedt H (2007b) Influence of short-chain branching of polyethylenes on the temperature dependence of rheological properties in shear. Macromol Chem Phys 208(22):2449–2454
Stadler FJ, Auhl D, Münstedt H (2008a) Influence of the molecular structure of polyolefins on the damping function in shear. Macromolecules 41(10):3720–3726
Stadler FJ, Kaschta J, Münstedt H (2008b) Thermorheological behavior of various long-chain branched polyethylenes. Macromolecules 41(4):1328–1333
Stadler FJ, Kaschta J, Münstedt H, Becker F, Buback M (2009) Influence of molar mass distribution and long-chain branching on strain hardening of low density polyethylene. Rheol Acta 48(5):479–490
Stadler FJ, Arikan B, Kaschta J, Kaminsky W (2010) Long-chain branches in syndiotactic polypropene induced by vinyl chloride. Macromol Chem Phys 211(13):1472–1481
Stange J, Uhl C, Münstedt H (2005) Rheological behavior of blends from a linear and a long-chain branched polypropylene. J Rheol 49(5):1059–1079
Struglinski MJ, Graessley WW (1985) Effects of polydispersity on the linear viscoelastic properties of entangled polymers. 1. Experimental-observations for binary-mixtures of linear polybutadiene. Macromolecules 18(12):2630–2643
Sun T, Brant P, Chance RR, Graessley WW (2001) Effect of short chain branching on the coil dimensions of polyolefins in dilute solution. Macromolecules 34(19):6812–6820
Tackx P, Tacx JCJF (1998) Chain architecture of LDPE as a function of molar mass using size exclusion chromatography and multi-angle laser light scattering (SEC-MALLS). Polymer 39(14):3109–3113
Takeh A, Worch J, Shanbhag S (2011) Analytical rheology of metallocene-catalyzed polyethylenes. Macromolecules 44(9):3656–3665
Trinkle S, Walter P, Friedrich C (2002) Van Gurp-Palmen Plot II—Classification of long chain branched polymers by their topology. Rheol Acta 41(1–2):103–113
Tuminello WH (1986) Molecular weight and molecular weight distribution from dynamic measurements of polymer melts. Polym Eng Sci 26
van Gurp M, Palmen J (1998) Time–temperature superposition for polymeric blends. Rheol Bull 67(1):5–8
van Ruymbeke E, Stéphenne V, Daoust D, Godard P, Keunings R, Bailly C (2005) A sensitive method to detect very low levels of long chain branching from the molar mass distribution and linear viscoelastic regime. J Rheol 49(6):1503–1520
Vega JF, Munoz-Escalona A, Santamaria A, Munoz ME, Lafuente P (1996) Comparison of the rheological properties of metallocene-catalyzed and conventional high-density polyethylenes. Macromolecules 29(3):960–965
Vega JF, Santamaria A, Munoz-Escalona A, Lafuente P (1998) Small-amplitude oscillatory shear flow measurements as a tool to detect very low amounts of long chain branching in polyethylenes. Macromolecules 31(11):3639–3647
Vega JF, Fernandez M, Santamaria A, Munoz-Escalona A, Lafuente P (1999) Rheological criteria to characterize metallocene catalyzed polyethylenes. Macromol Chem Phys 200(10):2257–2268
Vinogradov GV, Malkin AY (1966) Rheological properties of polymer melts. J Polym Sci A-2: Polym Phys 4(1):135–154
Vrentas CM, Graessley WW (1982) Study of shear-stress relaxation in well-characterized polymer liquids. J Rheol 26(4):359–371
Wagner MH (1997) Damping functions and nonlinear viscoelasticity—a review. J Non-Newton Fluid Mech 68(2–3):169–171
Wagner MH, Laun HM (1978) Nonlinear shear creep and constrained elastic recovery of a LDPE melt. Rheol Acta 17:138–148
Wagner MH, Rubio P, Bastian H (2001) The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release. J Rheol 45(6):1387–1412
Walter P, Trinkle S, Lilge D, Friedrich C, Mulhaupt R (2001) Long chain branched polypropene prepared by means of propene copolymerization with 1,7-octadiene using MAO-activated rac-Me2Si(2-Me-4-phenyl-Ind)(2)ZrCl2. Macromol Mater Eng 286(5):309–315
Wang WJ, Kharchenko S, Migler K, Zhu SP (2004) Triple-detector GPC characterization and processing behavior of long-chain-branched polyethylene prepared by solution polymerization with constrained geometry catalyst. Polymer 45(19):6495–6505
Wilhelm M, Reinheimer P, Ortseifer M (1999) High sensitivity Fourier-transform rheology. Rheol Acta 38(4):349–356
Wood-Adams PM (2001) The effect of long chain branches on the shear flow behavior of polyethylene. J Rheol 45(1):203–210
Wood-Adams PM, Dealy JM (2000) Using rheological data to determine the branching level in metallocene polyethylenes. Macromolecules 33(20):7481–7488
Wood-Adams PM, Costeux S (2001) Thermorheological behavior of polyethylene: effects of microstructure and long chain branching. Macromolecules 34(18):6281–6290. doi:10.1021/ma0017034
Wood-Adams PM, Dealy JM, deGroot AW, Redwine OD (2000) Effect of molecular structure on the linear viscoelastic behavior of polyethylene. Macromolecules 33(20):7489–7499
Zimm BHM, Stockmayer WH (1949) The dimensions of molecules containing branching and rings. J Chem Phys 17(12):1301–1314
Acknowledgements
The author would like to thank the German Research Foundation for the financial support and Prof. Dr. H. Münstedt, Dr. J. Kaschta, and Mrs. I. Herzer (University Erlangen) for the GPC-MALLS measurements. The authors would also like to acknowledge Dr. Christian Piel, Dr. Burçak Arikan, and Prof. Dr. Walter Kaminsky (University Hamburg) for the synthesis of most of the samples used in this article and Dr. Katja Klimke and Dr. Matthew Parkinson of the Max-Planck Institute of Polymer Research in Mainz (group of M. Wilhelm) for the solid-state NMR measurements. The financial support from “Human Resource Development (201040100660)” of the Korea Institute of Energy Technology Evaluation and Planning and from the National Research Foundation (Rheological Characterization of Intelligent Hydrogels) is gratefully acknowledged.
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Stadler, F.J. Detecting very low levels of long-chain branching in metallocene-catalyzed polyethylenes. Rheol Acta 51, 821–840 (2012). https://doi.org/10.1007/s00397-012-0642-x
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DOI: https://doi.org/10.1007/s00397-012-0642-x