Viscoelasticity

George D. J. Phillies

doi:10.1017/CBO9780511843181.014

13 - Viscoelasticity

Published online by Cambridge University Press: 05 August 2012

George D. J. Phillies

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George D. J. Phillies: Affiliation:
Worcester Polytechnic Institute, Massachusetts

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This chapter presents a phenomenological description of viscoelastic properties of polymer solutions. While aspects of the description will appear familiar, this chapter is fundamentally unlike other chapters in this book. In Chapter 2 we discussed sedimentation. Much of the literature appeared before younger readers were born, but the sedimentation coefficient s is the coefficient familiar to everyone who has ever been interested in the method. In Chapter 3 we discussed capillary electrophoresis in polymer solutions. The notion that this method gives information about the polymer solutions being used as support media is nearly novel, but the electrophoretic mobility μ is the coefficient familiar to everyone who uses the technique. Similar statements apply to each of the other chapters. The perspective in prior chapters on a solution property may not be the same as seen elsewhere, but the parameters used to characterize the property have been familiar.

To treat viscoelasticity we need to do something different.

The classical viscoelastic properties are the dynamic shearmoduli, written in the frequency domain as the storage modulus G′(ω) and the loss modulus G″(ω), the shear stress relaxation function G(t), and the shear-dependent viscosity η(κ). Optical flow birefringence and analogousmethods determine related solution properties. Nonlinear viscoelastic phenomena are treated briefly in Chapter 14.

Solution properties depend on polymer concentration and molecular weight, originally leading to the hope that one could apply reduction schemes and transform measurements of the shear moduli at different c and M to a few master curves.

Type: Chapter
Information: Phenomenology of Polymer Solution Dynamics , pp. 397 - 444

DOI: https://doi.org/10.1017/CBO9780511843181.014 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2011

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References

[1] J. D., Ferry. Viscoelastic Properties of Polymers, (New York: Wiley, 1980) pp. 506–507.Google Scholar

[2] D. S., Pearson. Recent advances in the molecular aspects of polymer viscoelasticity. Rubber Chem. Tech., 60 (1987), 439–496.Google Scholar

[3] G. D. J., Phillies. Polymer solution viscoelasticity from two-parameter temporal scaling. J. Chem. Phys., 110 (1999), 5989–5992.Google Scholar

[4] R. B., Bird, H. H., Saab, and C. F., Curtis. A kinetic theory for polymer melts. 3. Elongational flows. J. Phys. Chem., 86 (1982), 1102–1106.Google Scholar

[5] R. B., Bird, H. H., Saab, and C. F., Curtis. A kinetic-theory for polymer melts. 4. Rheological properties for shear flows. J. Chem. Phys., 77 (1982), 4747–4757.Google Scholar

[6] W. W., Graessley. Molecular entanglement theory of flow behavior in amorphous polymers. J. Chem. Phys., 43 (1965), 2696–2703.Google Scholar

[7] W. W., Graessley. Viscosity of entangling polydisperse polymers. J. Chem. Phys., 47 (1967), 1942–1953.Google Scholar

[8] E., Raspaud, D., Lairez, and M., Adam. On the number of blobs per entanglement in semidilute and good solvent solution–melt influence. Macromolecules, 8 (1995), 927–933.Google Scholar

[9] A. R., Altenberger and J. S., Dahler. Application of a new renormalization group to the equation of state of a hard-sphere fluid. Phys. Rev. E, 54 (1996), 6242–6252.Google Scholar

[10] G. D. J., Phillies. Derivation of the universal scaling equation of the hydrodynamic scaling model via renormalization group analysis. Macromolecules, 31 (1998), 2317–2327.Google Scholar

[11] S. C., Merriam and G. D. J., Phillies. Fourth-order hydrodynamic contribution to the polymer self-diffusion coefficient. J. Polym. Sci. B, 42 (2004), 1663–1670.Google Scholar

[12] G. D. J., Phillies. Low-shear viscosity of non-dilute polymer solutions from a generalized Kirkwood–Riseman model. J. Chem. Phys., 116 (2002), 5857–5866.Google Scholar

[13] G. D. J., Phillies. Self-consistency of hydrodynamic models for low-shear viscosity and self-diffusion. Macromolecules, 35 (2002), 7414–7418.Google Scholar

[14] G. D. J., Phillies and C. A., Quinlan. Analytic structure of the solutionlike–meltlike transition in polymer solution dynamics. Macromolecules, 28 (1995), 160–164.Google Scholar

[15] R. H., Colby, L. J., Fetters, W. G., Funk, and W. W., Graessley. Effects of concentration and thermodynamic interaction on the viscoelastic properties of polymer solutions. Macromolecules, 24 (1991), 3873–3882.Google Scholar

[16] L. A., Holmes, S., Kusamizu, K., Osaki, and J. D., Ferry. Dynamic mechanical properties of moderately concentrated polystyrene solutions. J. Polym. Sci. A-2, 9 (1971), 2009–2021.Google Scholar

[17] T., Inoue, Y., Yamashita, and K., Osaki. Viscoelasticity of an entangling polymer solution with special attention on a characteristic time for nonlinear behavior. Macromolecules, 35 (2002), 1770–1775.Google Scholar

[18] Y., Isono, T., Fujimoto, N., Takeno, H., Kijura, and M., Nagasawa. Viscoelastic properties of linear polymers with high molecular weights and sharp molecular weight distributions. Macromolecules, 11 (1978), 888–893.Google Scholar

[19] T., Masuda,Y., Ohto, M., Kitamura, et al.Rheological properties of anionic polystyrenes. 7. Viscoelastic properties of six-branched star polystyrenes and their concentrated solutions. Macromolecules, 14 (1981), 354–360.Google Scholar

[20] E. V., Menezes and W. W., Graessley. Nonlinear rheological behavior of polymer systems for several shear-flow histories. J. Polym. Sci. Polym. Phys. Ed., 20 (1982), 1817–1833.Google Scholar

[21] M., Milas, M., Rinaulde, M., Knipper, and J. L., Schuppiser. Flow and viscoelastic properties of xanthan gum solutions. Macromolecules, 23 (1990), 2506–2511.Google Scholar

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

[23] L. M., Quinzani, G. H., McKinley, R. A., Brown, and R. C., Armstrong. Modelling the rheology of polyisobutylene solutions. J. Rheology, 34 (1990), 705–748.Google Scholar

[24] D. V., Boger. A highly elastic constant-viscosity fluid. J. Non-Newtonian Fluid Mech., 3 (1977/1978), 87–91.Google Scholar

[25] V. R., Raju, E. V., Menezes, G., Marin, W. W., Graessley, and L. J., Fetters. Concentration and molecular weight dependence of viscoelastic properties in linear and star polymers. Macromolecules, 14 (1981), 1668–1676.Google Scholar

[26] P., Tapadia and S.-Q., Wang. Nonlinear flow behavior of entangled polymer solutions. Yieldlike entanglement–disentanglement transition. Macromolecules, 37 (2004), 9083–9095.Google Scholar

[27] R. I., Wolkowicz and W. C., Forsman. Entanglement in concentrated solutions of polystyrene with narrow distributions of molecular weight. Macromolecules, 4 (1971), 184–192.Google Scholar

[28] X., Ye and T., Sridhar. Effects of polydispersity on rheological properties of entangled polymer solutions. Macromolecules, 38 (2005), 3442–3449.Google Scholar

[29] X., Ye and T., Sridhar. Shear and extensional properties of three-arm polystyrene solutions. Macromolecules, 34 (2001), 8270–8277.Google Scholar

[30] S. T., Milner and T. C., McLeish. Parameter-free theory for stress relaxation in star polymer melts. Macromolecules, 30 (1997), 2159–2166.Google Scholar

[31] W. P., Cox and E. H., Merz. Correlation of dynamic and steady viscosities. J. Polym. Sci. A-2 28 (1958), 619–622.Google Scholar

[32] G. C., Berry, B. L., Hager, and C.-P., Wong. Rheological studies on concentrated solutions of poly (α-methylstyrene). Macromolecules, 9 (1976), 361–365.Google Scholar

[33] W. W., Graessley, R. L., Hazleton, and L. R., Lindeman. The shear-rate dependence of viscosity in concentrated solutions of narrow-distribution polystyrene. Trans. Soc. Rheology, 11 (1967), 267–285.Google Scholar

[34] W. W., Graessley and L., Segal. Flow behavior of polystyrene systems in steady shearing flow. Macromolecules, 2 (1969), 49–57.Google Scholar

[35] W. W., Graessley, T., Masuda, J. E. L., Roovers, and N., Hadjichristidis. Rheological properties of linear and branched polyisoprene. Macromolecules, 9 (1976), 127–141.Google Scholar

[36] Y., Isono and M., Nagasawa. Solvent effects on rheological properties of polymer solutions. Macromolecules, 13 (1980), 862–867.Google Scholar

[37] Y., Ito and S., Shishido. Modified Graessley theory for non-Newtonian viscosities of polydimethylsiloxanes and their solutions. J. Polym. Sci. Polym. Phys. Ed., 12 (1971), 617–628.Google Scholar

[38] Y., Ito and S., Shishido. Non-Newtonian behavior in steady flow over the range from the lower to the upper Newtonian region for polystyrene solution. J. Polym. Sci. Polym. Phys. Ed., 13 (1975), 35–41.Google Scholar

[39] H., Kajiura, Y., Ushiyama, T., Fujimoto, and M., Nagasawa. Viscoelastic properties of star-shaped polymers in concentrated solutions. Macromolecules, 11 (1978), 894–899.Google Scholar

[40] K., Osaki, M., Fukuda, S.-I., Ohta, B. S., Kim, and M., Kurata. Nonlinear viscoelasticity of polystyrene solutions. II. Non-Newtonian viscosity. J. Polym. Sci. Polym. Phys. Ed., 13 (1975), 1577–1589.Google Scholar

[41] K., Osaki, M., Fukuda, and M., Kurata. Relaxation spectra of concentrated polystyrene solutions. J. Polym. Sci., 13 (1975), 775–786.Google Scholar

[42] G. H., Koenderinck, S., Sacanna, D. G. A., L. Aarts, and A. P. Philipse. Rotational and translational diffusion of fluorocarbon tracer spheres in semidilute xanthan solutions. Phys. Rev. E, 69 (2004), 021804 1–12.Google Scholar

[43] J. O., Park and G. C., Berry. Moderately concentrated solutions of polystyrene. 3. Viscoelastic measurements at the Flory Θ temperature. Macromolecules, 22 (1989), 3022–3029.Google Scholar

[44] S., Ueda and T., Kataoka. Steady-flow viscous and elastic properties of polyisobutylene solutions in low molecular weight polybutene. J. Polym. Sci., 11 (1973), 1975–1984.Google Scholar

[45] W. C., Uy and W. W., Graessley. Viscosity and normal stresses in poly(vinyl acetate) systems. Macromolecules, 4 (1971), 458–463.Google Scholar

[46] D., Gupta and W. C., Forsman. Newtonian viscosity–molecular weight relationship for concentrated solutions of monodisperse polystyrene. Macromolecules, 2 (1969), 304–306.Google Scholar

[47] R. de L., Kronig. On the theory of the dispersion of X-rays. J. Opt. Soc. America, 12 (1926), 547–557.Google Scholar

[48] R. de L., Kronig and H. A., Kramers. La diffusion de la lumiere par les atomes. Atti Cong. Inter n. Fisica, Como (Transactions of Volta Centenary Congress), 2 (1927), 545–557.Google Scholar

[49] G. F., Fuller. Optical Rheometry of Complex Fluids, (Oxford, UK: Oxford University Press, 1995) Chapter 10.Google Scholar

[50] T. P., Lodge and J. L., Schrag. Initial concentration dependence of the oscillatory flow birefringence properties of polystryene and poly (α-methylstyrene solutions. Macromolecules, 15 (1982), 1376–1384.Google Scholar

[51] C. J. T., Martel, T. P., Lodge, M. G., Dibbs, et al.Studies of the concentration dependence of the conformational dynamics of solutions containing linear, star or comb homopolymers. Faraday Symp. Chem. Soc., 18 (1983), 173–188.Google Scholar

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13 - Viscoelasticity

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