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.
Similar content being viewed by others
References
Bernstein B, Kearsley EA, Zapas LJ (1963) A study of stress relaxation with finite strain. Trans Soc Rheol 7:391–410
Bird RB, Hassager O, Armstrong RC, Curtiss CF (1977) Dynamics of polymer liquids. Volume 2, Wiley, New York
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
Doi M, Edwards SF (1978) Dynamics of concentrated polymeric systems. Part 1 and 2. J Chem Soc Faraday Trans II 74:1789–1817
Doi M, Edwards SF (1986) The theory of polymer dynamics. Clarendon Press, Oxford
Doi M, Kuzuu N (1980) Rheology of star polymers in concentrated solutions and melts. J Polym Sci Polym Letter Ed 18:775–780
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
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
Fukuda M, Osaki K, Kurata M (1975) Nonlinear viscoelasticity of polystyrene solutions I. J Polym Sci, Polym Phys Ed 13:1563–1576
Ferry JD (1980) Viscoelastic properties of polymers. 3rd ed. Wiley, New York
Graessley WW (1982) Entangled linear, branched and network polymer systems — molecular theories. Adv Polym Sci 47:67–117
Isono Y, Itoh K, Komiyatani T, Fujimoto T (1991) Differential dynamic modulus of polyisobutylene with high molecular weight 1. Macromolecules 24:4429–4432
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
Kimura S, Osaki K, Kurata M (1981) Stress relaxation of polybutadiene at large deformation. J Polym Sci, Polym Phys Ed 19:151–163
Larson RG (1985) Nonlinear shear relaxation modulus for a linear low-density polyethylene. J Rheology 29:823–831
Larson RG (1988) Constitutive equations for polymer melts and solutions. Butterworth, Boston
Larson RG, Khan SA, Raju VR (1988) Relaxation of stress and birefringence in polymers of high molecular weight. J Rheology 32:145–161
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
Laun HM (1986) Prediction of elastic strains of polymer melts in shear and elongation. J Rheology 30:459–501
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
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
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
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
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
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
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
Osaki K, Nishizawa K, Kurata M (1982) Material time constant characterizing the nonlinear viscoelasticity of entangled polymeric systems. Macromolecules 82:1068–1071
Osaki K, Takatori E, Tsunashima Y, Kurata M (1987) On the universality of viscoelastic properties of entangled polymeric systems. Macromolecules 20:525–529
Osaki K, Takatori E, Kurata M (1987) Nonlinear viscoelasticity of semidilute polystyrene solutions. Effect of molecular weight distribution. Macromolecules 20:1681–1687
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
Osaki K, Takatori E, Watanabe H, Kotaka T (1993) Viscoelastic properties of semidilute poly(methyl methacrylate) solutions. Rheol Acta 32:132–139
Papanastasiou AC, Scriven LE, Macosko CW (1983) An integral constitutive equation for mixed flows. J Rheology 27:387–410
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
Samurkas T, Larson RG, Dealy JM (1989) Strong extensional and shearing flows of a branched polyethylene. J Rheology 33:559–578
Soskey PR, Winter H (1984) Large step shear strain experiments with parallel-disk rotational rheometer. J Rheology 28:625–645
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
Takatori E, Osaki K, Kurata M, Hirayama T (1988) Viscoelasticity of solutions of polystyrene with low molecular weights. Nihin Reoroji Gakkaishi 16:99–103
Venerus DC, Vrentas CM, Vrentas JS (1990) Step strain deformations for viscoelastic fluids. J Rheology 34:657–683
Vrentas CM, Graessley WW (1982) Study of shear stress relaxation in well-characterized polymer liquids. J Rheology 26:359–371
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
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Osaki, K. On the damping function of shear relaxation modulus for entangled polymers. Rheol Acta 32, 429–437 (1993). https://doi.org/10.1007/BF00396173
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00396173