On the damping function of shear relaxation modulus for entangled polymers Original Contributions Received: 18 March 1993 Revised: 08 June 1993 DOI :
10.1007/BF00396173

Cite this article as: Osaki, K. Rheol Acta (1993) 32: 429. doi:10.1007/BF00396173 Abstract Published data of the damping function of the shear relaxation modulus, h (γ), are reviewed. This is the ratio of the relaxation modulus measured at a finite magnitude of shear, γ, to that at the limit of γ = 0. Majority of the data are in accord with the universal function of the Doi-Edwards tube model theory, in which the damping or the decrease of h (γ) is attributed to the contraction along the tube of extended polymer chains. The weaker damping seems to be attributed to 1) comb-branching such as in LDPE; 2) lack of entanglement in too short chains; 3) bimodal molecular weight distribution. However, a star-branching does not cause a deviation from the tube model theory and a broadness of molecular weight distribution is not a major origin of a weaker damping. A star-branched polystyrene with 15 arms exhibits no strain dependence: h (γ) = 1. For highly entangled systems with more than 50 entanglement points per molecule, the strain dependence is stronger than that of the Doi-Edwards theory. This could be due to a slip or an instability of deformation in the material.

Key words Polymer entanglement nonlinear viscoelasticity damping function relaxation modulus tube model

References Bernstein B, Kearsley EA, Zapas LJ (1963) A study of stress relaxation with finite strain. Trans Soc Rheol 7:391–410

Google Scholar Bird RB, Hassager O, Armstrong RC, Curtiss CF (1977) Dynamics of polymer liquids. Volume 2, Wiley, New York

Google Scholar Doi M (1981) Explanation for the 3.4 power law of viscosity of polymeric liquids on the basis of the tube model. J Polym Sci Polym Letter Ed 19:265–273

Google Scholar Doi M, Edwards SF (1978) Dynamics of concentrated polymeric systems. Part 1 and 2. J Chem Soc Faraday Trans II 74:1789–1817

Google Scholar Doi M, Edwards SF (1986) The theory of polymer dynamics. Clarendon Press, Oxford

Google Scholar Doi M, Kuzuu N (1980) Rheology of star polymers in concentrated solutions and melts. J Polym Sci Polym Letter Ed 18:775–780

Google Scholar Einaga Y, Osaki K, Kurata M, Kimura S, Tamura M (1971) Stress relaxation of polymer solutions under large strain. Polymer J (Tokyo) 2:550–552

Google Scholar Einaga Y, Osaki K, Kurata M, Kimura S, Yamada N, Tamura M (1973) Stress relaxation of polymer solutions under large strain. Polymer J (Tokyo) 5:91–96

Google Scholar Fukuda M, Osaki K, Kurata M (1975) Nonlinear viscoelasticity of polystyrene solutions I. J Polym Sci, Polym Phys Ed 13:1563–1576

Google Scholar Ferry JD (1980) Viscoelastic properties of polymers. 3rd ed. Wiley, New York

Google Scholar Graessley WW (1982) Entangled linear, branched and network polymer systems — molecular theories. Adv Polym Sci 47:67–117

Google Scholar Isono Y, Itoh K, Komiyatani T, Fujimoto T (1991) Differential dynamic modulus of polyisobutylene with high molecular weight 1. Macromolecules 24:4429–4432

Google Scholar Isono Y, Kambara T, Ohashi N, Nishitake T (1992) Differential dynamic modulus of solutions and lightly crosslinked polybutadiene. Proc 40th Rheology Conf Japan, p 207

Khan SA, Prud'homme RK, Larson RG (1987) Comparison of the rheology of polymer melts in shear, and biaxial and uniaxial extensions. Rheol Acta 26:144–151

Google Scholar Kimura S, Osaki K, Kurata M (1981) Stress relaxation of polybutadiene at large deformation. J Polym Sci, Polym Phys Ed 19:151–163

Google Scholar Larson RG (1985) Nonlinear shear relaxation modulus for a linear low-density polyethylene. J Rheology 29:823–831

Google Scholar Larson RG (1988) Constitutive equations for polymer melts and solutions. Butterworth, Boston

Google Scholar Larson RG, Khan SA, Raju VR (1988) Relaxation of stress and birefringence in polymers of high molecular weight. J Rheology 32:145–161

Google Scholar Laun HM (1978) Description of the nonlinear shear behavior of a low density polyethylene melt by means of an experimentally determined strain dependent memory function. Rheol Acta 17:1–15

Google Scholar Laun HM (1986) Prediction of elastic strains of polymer melts in shear and elongation. J Rheology 30:459–501

Google Scholar Lodge AS, Meissner J (1972) On the use of instantaneous strains, superposed on shear and elongational flows of polymeric liquids, to test the Gaussian network hypothesis and to estimate the segment concentration and its variation during flow. Rheol Acta 11:351–352

Google Scholar Marrucci G (1983) The free energy function of the Doi-Ed wards theory: analysis of the instabilities in stress relaxation. J Rheol 27:433–450

Google Scholar Morrison FA, Larson RG (1992) A study of shear-stress relaxation anomalies in binary mixtures of monodisperse polystyrenes. J Polym Sci, Polym Phys Ed 30:943–950

Google Scholar Osaki K, Kurata M (1980) Experimental appraisal of the Doi-Edwards theory for polymer rheology based on the data for polystyrene solutions. Macromolecules 13:671–676

Google Scholar Osaki K, Bessho N, Kojimoto T, Kurata M (1980) Experimental tests of a few constitutive models for polymer solutions based on birefringence data in time-dependent field. J Rheology 24:125–141

Google Scholar Osaki K, Kimura S, Kurata M (1981) Relaxation of shear and normal stresses in step-shear deformation of polystyrene solution. J Polym Sci, Polym Phys Ed 19:517–527

Google Scholar Osaki K, Kimura S, Nishizawa K, Kurata M (1981) On the material time constant characterizing the nonlinear viscoelasticity of entangled polymeric materials. Macromolecules 14:455–456

Google Scholar Osaki K, Nishizawa K, Kurata M (1982) Material time constant characterizing the nonlinear viscoelasticity of entangled polymeric systems. Macromolecules 82:1068–1071

Google Scholar Osaki K, Takatori E, Tsunashima Y, Kurata M (1987) On the universality of viscoelastic properties of entangled polymeric systems. Macromolecules 20:525–529

Google Scholar Osaki K, Takatori E, Kurata M (1987) Nonlinear viscoelasticity of semidilute polystyrene solutions. Effect of molecular weight distribution. Macromolecules 20:1681–1687

Google Scholar Osaki K, Takatori E, Kurata M, Watanabe H, Yoshida H, Kotaka T (1990) Viscoelastic properties of solutions of star-branched polystyrene. Macromolecules 23:4392–4396

Google Scholar Osaki K, Takatori E, Watanabe H, Kotaka T (1993) Viscoelastic properties of semidilute poly(methyl methacrylate) solutions. Rheol Acta 32:132–139

Google Scholar Papanastasiou AC, Scriven LE, Macosko CW (1983) An integral constitutive equation for mixed flows. J Rheology 27:387–410

Google Scholar Pearson DS (1987) private communication

Rouse PE (1953) A theory of the linear viscoelastic properties of dilute solutions of coiling polymers. J Chem Phys 21:1272–1280

Google Scholar Samurkas T, Larson RG, Dealy JM (1989) Strong extensional and shearing flows of a branched polyethylene. J Rheology 33:559–578

Google Scholar Soskey PR, Winter H (1984) Large step shear strain experiments with parallel-disk rotational rheometer. J Rheology 28:625–645

Google Scholar Takahashi M, Isaki T, Takigawa T, Masuda T (1993) Measurement of biaxial and uniaxial extensional flow behavior of polymer melts at constant rates. J Rheology, in press

Takahashi M, Nakatsuji Y, Ohta Y, Masuda T (1985) Nonlinear stress relaxation of melts of star-branched polystyrenes. 12th Annual Meeting of Society of Rheology, Japan, pp 17–20

Takahashi M, Taku K, Masuda T (1990) Evaluation of differential constitutive equations based on stress relaxation data for polymer melts. Nihon Reoroji Gakkaishi 18:18–26

Google Scholar Takatori E, Osaki K, Kurata M, Hirayama T (1988) Viscoelasticity of solutions of polystyrene with low molecular weights. Nihin Reoroji Gakkaishi 16:99–103

Google Scholar Venerus DC, Vrentas CM, Vrentas JS (1990) Step strain deformations for viscoelastic fluids. J Rheology 34:657–683

Google Scholar Vrentas CM, Graessley WW (1982) Study of shear stress relaxation in well-characterized polymer liquids. J Rheology 26:359–371

Google Scholar Yoshikawa K, Toneaki N, Moteki Y, Takahashi M, Masuda T (1990) Dynamic viscoelasticity, stress relaxation and elongational flow behavior of high density polyethylene melts. Nihon Reoroji Gakkaishi 18:80–92

Google Scholar Authors and Affiliations 1. Institute for Chemical Research Kyoto University Uji, Kyoto Japan