Rheologica Acta

, Volume 51, Issue 9, pp 821–840 | Cite as

Detecting very low levels of long-chain branching in metallocene-catalyzed polyethylenes

  • Florian J. Stadler
Original Contribution


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.


Long-chain-branched metallocene-catalyzed polyethylene Rheology SEC-MALLS Branch detection Zero shear rate viscosity η0 Steady-state elastic recovery compliance \(J_{e}^{0}\) 



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.


  1. Archer LA (1999) Separability criteria for entangled polymer liquids. J Rheol 43(6):1555–1571CrossRefGoogle Scholar
  2. Archer LA, Varshney SK (1998) Synthesis and relaxation dynamics of multiarm polybutadiene melts. Macromolecules 31(18):6348–6355CrossRefGoogle Scholar
  3. 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 CrossRefGoogle Scholar
  4. Auhl D, Stadler FJ, Münstedt H (2012) Comparison of molecular structure and rheological properties of electron-beam- and gamma-irradiated polypropylene. Macromolecules 45:2057–2065CrossRefGoogle Scholar
  5. Bach A, Almdal K, Rasmussen HK, Hassager O (2003) Elongational viscosity of narrow molar mass distribution polystyrene. Macromolecules 36(14):5174–5179CrossRefGoogle Scholar
  6. Ball RC, Mcleish TCB (1989) Dynamic dilution and the viscosity of star polymer melts. Macromolecules 22(4):1911–1913CrossRefGoogle Scholar
  7. Berry GC, Fox TG (1968) The viscosity of polymers and their concentrated solutions. Adv Polym Sci 5:261–357CrossRefGoogle Scholar
  8. Bubeck RA (2002) Structure–property relationships in metallocene polyethylenes. Mater Sci Eng R 39:1–28CrossRefGoogle Scholar
  9. 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):393CrossRefGoogle Scholar
  10. 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):2514–2528CrossRefGoogle Scholar
  11. Doi M, Edwards SF (1986) The theory of polymer dynamics. Oxford Press, OxfordGoogle Scholar
  12. Ferry JD (1980) Viscoelastic properties of polymers. Wiley, New YorkGoogle Scholar
  13. Fetters LJ, Kiss AD, Peareon DS, Quack GF, Vitus FJ (1993) Rheological behavior of star-shaped polymers. Macromolecules 26(4):647–654CrossRefGoogle Scholar
  14. Fetters LJ, Lohse DJ, Colby RH (2007) Chain dimensions and entanglement spacings physical properties of polymers, 2nd edn. JE Mark. Springer, HeidelbergGoogle Scholar
  15. 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):174–187CrossRefGoogle Scholar
  16. Flory PJ (1953) Principles of polymer chemistry. Cornell University Press, IthacaGoogle Scholar
  17. 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 48:49–68CrossRefGoogle Scholar
  18. Gabriel C (2001) Einfluss der molekularen Struktur auf das viskoelastische Verhalten von Polyethylenschmelzen. Aachen, Shaker-VerlagGoogle Scholar
  19. Gabriel C, Munstedt H (1999) Creep recovery behavior of metallocene linear low-density polyethylenes. Rheol Acta 38(5):393–403CrossRefGoogle Scholar
  20. Gabriel C, Münstedt H (2002) Influence of long-chain branches in polyethylenes on linear viscoelastic flow properties in shear. Rheol Acta 41(3):232–244CrossRefGoogle Scholar
  21. Gabriel C, Münstedt H (2003) Strain hardening of various polyolefins in uniaxial elongational flow. J Rheol 47(3):619–630CrossRefGoogle Scholar
  22. 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):6383–6390CrossRefGoogle Scholar
  23. 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):342–351CrossRefGoogle Scholar
  24. 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):17–27CrossRefGoogle Scholar
  25. Hepperle J, Münstedt H (2006) Rheological properties of branched polystyrenes: nonlinear shear and extensional behavior. Rheol Acta 45(5):717–727CrossRefGoogle Scholar
  26. Kaminsky W (2004) The discovery of metallocene catalysts and their present state of the art. J Polym Sci A Polym Chem 42(16):3911–3921CrossRefGoogle Scholar
  27. Kaminsky W, Piel C, Scharlach K (2005) Polymerization of ethene and longer chained olefins by metallocene catalysis. Macromol Symp 226(1):25–34CrossRefGoogle Scholar
  28. Kapnistos M, Vlassopoulos D, Roovers J, Leal LG (2005) Linear rheology of architecturally complex macromolecules: comb polymers with linear backbones. Macromolecules 38(18):7852–7862CrossRefGoogle Scholar
  29. 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):273–286CrossRefGoogle Scholar
  30. Kapnistos M, Kirkwood KM, Ramirez J, Vlassopoulos D, Leal LG (2009) Nonlinear rheology of model comb polymers. J Rheol 53(5):1133–1153CrossRefGoogle Scholar
  31. 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):636–646CrossRefGoogle Scholar
  32. 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 CrossRefGoogle Scholar
  33. 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 CrossRefGoogle Scholar
  34. Kasehagen LJ, Macosko CW (1998) Nonlinear shear and extensional rheology of long-chain randomly branched polybutadiene. J Rheol 42(6):1303–1327CrossRefGoogle Scholar
  35. 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 CrossRefGoogle Scholar
  36. 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 CrossRefGoogle Scholar
  37. 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 CrossRefGoogle Scholar
  38. 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):7341–7350CrossRefGoogle Scholar
  39. 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 CrossRefGoogle Scholar
  40. 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):376–388CrossRefGoogle Scholar
  41. Larson RG (1984) A constitutive equation for polymer melts based on partially extending strand convection. J Rheol 28(5):545CrossRefGoogle Scholar
  42. Larson RG (1985) Nonlinear shear relaxation modulus for a linear low-density polyethylene. J Rheol 29(6):823–831CrossRefGoogle Scholar
  43. 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 CrossRefGoogle Scholar
  44. Leal LG, Kirkwood KM, Vlassopoulos D, Driva P, Hadjichristidis N (2009) Stress relaxation of comb polymers with short branches. Macromolecules 42(24):9592–9608CrossRefGoogle Scholar
  45. Leblans PJR, Sampers J, Booij HC (1985) The mirror relations and nonlinear viscoelasticity of polymer melts. Rheol Acta 24(2):152–158CrossRefGoogle Scholar
  46. 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):3547–3552CrossRefGoogle Scholar
  47. 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):4461–4479CrossRefGoogle Scholar
  48. Liu CY, Keunings R, Bailly C (2007) Direct rheological evidence of monomer density reequilibration for entangled polymer melts. Macromolecules 40(8):2946–2954CrossRefGoogle Scholar
  49. Liu JY, Yu W, Zhou CX (2011) Polymer chain topological map as determined by linear viscoelasticity. J Rheol 55(3):545–570CrossRefGoogle Scholar
  50. 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):3066–3075CrossRefGoogle Scholar
  51. 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):8448–8454CrossRefGoogle Scholar
  52. Malmberg A, Liimatta J, Lehtinen A, Lofgren B (1999) Characteristics of long chain branching in ethene polymerization with single site catalysts. Macromolecules 32(20):6687–6696CrossRefGoogle Scholar
  53. 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):1038–1048CrossRefGoogle Scholar
  54. Meissner J (1969) Rheometer for the study of mechanical properties of deformation of plastic melts under definite tensile stress. Rheol Acta 8(1):78–88CrossRefGoogle Scholar
  55. Münstedt H (1980) Dependence of the elongational behavior of polystyrene melts on molecular weight and molecular weight distribution. J Rheol 24(6):847–867CrossRefGoogle Scholar
  56. Münstedt H (1986) Polymerschmelzen Fließverhalten von Stoffen und Stoffgemischen, pp 238–279. W Kulicke. Hüthig&Wepf-Verlag, Basel, Heidelberg, New YorkGoogle Scholar
  57. 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–U382Google Scholar
  58. 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):1921–1926CrossRefGoogle Scholar
  59. 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):671CrossRefGoogle Scholar
  60. Osaki K, Takatori E, Kurata M, Watanabe H, Yoshida H, Kotaka T (1990) Viscoeleastic properties of solutions of star-branched polystyrene. Macromolecules 23(20):4392–4396CrossRefGoogle Scholar
  61. 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):4257–4267CrossRefGoogle Scholar
  62. 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):319–330CrossRefGoogle Scholar
  63. 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):26–38CrossRefGoogle Scholar
  64. 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 CrossRefGoogle Scholar
  65. Plazek DJ, Agarwal PK (1976) The creep behavior of some commercial polystyrenes. In: Proc - Int Conrg Rheol, 7th, pp 488–489Google Scholar
  66. Plazek DJ, Echeverria I (2000) Don’t cry for me Charlie Brown, or with compliance comes comprehension. J Rheol 44(4):831–841CrossRefGoogle Scholar
  67. 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):1871–1874CrossRefGoogle Scholar
  68. Resch JA, Keßner U, Stadler FJ (2011) Thermorheological behavior of polyethylene—a sensitive probe to molecular structure. Rheol Acta 50(5–6):559–575CrossRefGoogle Scholar
  69. Roovers J (1979) Melt rheology of model branched polystyrenes. Polym Prepr 20(2):144–148Google Scholar
  70. Rouse PE Jr (1953) A theory of the linear viscoelastic properties of dilute solutions of coiling polymers. J Chem Phys 21:1272–1280CrossRefGoogle Scholar
  71. Shanbhag S (2011) Analytical rheology of branched polymer melts: identifying and resolving degenerate structures. J Rheol 55(1):177–194CrossRefGoogle Scholar
  72. Shroff R, Mavridis H (1999) Long-chain-branching index for essentially linear polyethylenes. Macromolecules 32(25):8454–8464CrossRefGoogle Scholar
  73. 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):547–572CrossRefGoogle Scholar
  74. 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 CrossRefGoogle Scholar
  75. 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 CrossRefGoogle Scholar
  76. 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):129–135CrossRefGoogle Scholar
  77. 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):25–34CrossRefGoogle Scholar
  78. 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):185–193CrossRefGoogle Scholar
  79. Stadler FJ, Karimkhani V (2011) Correlations between terminal rheological quantities and molecular structure in long-chain branched metallocene catalyzed polyethylene. Macromolecules 44(13):5401–5413CrossRefGoogle Scholar
  80. 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 CrossRefGoogle Scholar
  81. 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):209–218CrossRefGoogle Scholar
  82. 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):755–764CrossRefGoogle Scholar
  83. 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):1003–1012CrossRefGoogle Scholar
  84. 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):2449–2454CrossRefGoogle Scholar
  85. Stadler FJ, Auhl D, Münstedt H (2008a) Influence of the molecular structure of polyolefins on the damping function in shear. Macromolecules 41(10):3720–3726CrossRefGoogle Scholar
  86. Stadler FJ, Kaschta J, Münstedt H (2008b) Thermorheological behavior of various long-chain branched polyethylenes. Macromolecules 41(4):1328–1333CrossRefGoogle Scholar
  87. 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):479–490CrossRefGoogle Scholar
  88. Stadler FJ, Arikan B, Kaschta J, Kaminsky W (2010) Long-chain branches in syndiotactic polypropene induced by vinyl chloride. Macromol Chem Phys 211(13):1472–1481CrossRefGoogle Scholar
  89. Stange J, Uhl C, Münstedt H (2005) Rheological behavior of blends from a linear and a long-chain branched polypropylene. J Rheol 49(5):1059–1079CrossRefGoogle Scholar
  90. 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):2630–2643CrossRefGoogle Scholar
  91. 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):6812–6820CrossRefGoogle Scholar
  92. 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):3109–3113CrossRefGoogle Scholar
  93. Takeh A, Worch J, Shanbhag S (2011) Analytical rheology of metallocene-catalyzed polyethylenes. Macromolecules 44(9):3656–3665CrossRefGoogle Scholar
  94. 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):103–113CrossRefGoogle Scholar
  95. Tuminello WH (1986) Molecular weight and molecular weight distribution from dynamic measurements of polymer melts. Polym Eng Sci 26Google Scholar
  96. van Gurp M, Palmen J (1998) Time–temperature superposition for polymeric blends. Rheol Bull 67(1):5–8Google Scholar
  97. 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):1503–1520CrossRefGoogle Scholar
  98. 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):960–965CrossRefGoogle Scholar
  99. 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):3639–3647CrossRefGoogle Scholar
  100. Vega JF, Fernandez M, Santamaria A, Munoz-Escalona A, Lafuente P (1999) Rheological criteria to characterize metallocene catalyzed polyethylenes. Macromol Chem Phys 200(10):2257–2268CrossRefGoogle Scholar
  101. Vinogradov GV, Malkin AY (1966) Rheological properties of polymer melts. J Polym Sci A-2: Polym Phys 4(1):135–154CrossRefGoogle Scholar
  102. Vrentas CM, Graessley WW (1982) Study of shear-stress relaxation in well-characterized polymer liquids. J Rheol 26(4):359–371CrossRefGoogle Scholar
  103. Wagner MH (1997) Damping functions and nonlinear viscoelasticity—a review. J Non-Newton Fluid Mech 68(2–3):169–171CrossRefGoogle Scholar
  104. Wagner MH, Laun HM (1978) Nonlinear shear creep and constrained elastic recovery of a LDPE melt. Rheol Acta 17:138–148CrossRefGoogle Scholar
  105. 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):1387–1412CrossRefGoogle Scholar
  106. 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):309–315CrossRefGoogle Scholar
  107. 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):6495–6505CrossRefGoogle Scholar
  108. Wilhelm M, Reinheimer P, Ortseifer M (1999) High sensitivity Fourier-transform rheology. Rheol Acta 38(4):349–356CrossRefGoogle Scholar
  109. Wood-Adams PM (2001) The effect of long chain branches on the shear flow behavior of polyethylene. J Rheol 45(1):203–210CrossRefGoogle Scholar
  110. Wood-Adams PM, Dealy JM (2000) Using rheological data to determine the branching level in metallocene polyethylenes. Macromolecules 33(20):7481–7488CrossRefGoogle Scholar
  111. 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 CrossRefGoogle Scholar
  112. Wood-Adams PM, Dealy JM, deGroot AW, Redwine OD (2000) Effect of molecular structure on the linear viscoelastic behavior of polyethylene. Macromolecules 33(20):7489–7499CrossRefGoogle Scholar
  113. Zimm BHM, Stockmayer WH (1949) The dimensions of molecules containing branching and rings. J Chem Phys 17(12):1301–1314CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.School of Semiconductor and Chemical EngineeringChonbuk National UniversityJeonbukRepublic of Korea

Personalised recommendations