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Some examples of possible descriptions of dynamic properties of polymers by means of the coupling model

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Abstract

Thanks to the research efforts of Prof. John D. Ferry and others over the last several decades, the viscoelastic properties of polymers have been extensively determined. From this accumulated wisdom, polymer viscoelasticity has become a mature field of research. This basic knowledge of polymer viscoelasticity has made it possible to discern the deviations from the apparently established general rules that one of us (DJP) have found, continuing the tradition of exhaustive experimental measurement started by Prof. Ferry. From many experimental studies on polymers carried out in different laboratories, it has also become clear that these viscoelastic anomalies are general and not exceptional features. Therefore, they pose significant problems in the quest of a truly satisfactory understanding of polymer viscoelasticity. The Coupling Model (CM) has been used to rationalize a number of deviations from thermorheological simplicity. In the realm of polymer viscoelastic behavior, we consider first the local segmental motion that is responsible for the glass temperature and show that the CM provides a consistent description in either the modulus or the compliance representation. Next, we elucidate several viscoelastic anomalies which originate from the different viscoelastic mechanisms being thermorheologically complex. Finally, we revisit the original formulation of the terminal relaxation of entangled polymer chains using the CM. The neglect of the lateral nature of the constraints imposed on one chain by other chains in the original formulation leads to failure in explaining the shape of the terminal relaxation, although it is successful in other aspects. A new formulation, which includes the lateral nature of the constraints and its subsequent mitigation when the terminal relaxation is reached, has restored consistency of the prediction with the terminal relaxation of a monodisperse polyisoprene melt probed dielectrically. The results can describe also the experimental data of dilute polyisoprene probes in polybutadiene matrices and in networks.

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References

  • Adachi K, Nakamoto T, Kotaka T (1989) A dielectric study of the dynamics of polyisoprene trapped in polybutadiene networks. Macromolecules 22:3111–3116

    Google Scholar 

  • Adachi K, Yoshida H, Fukui F, Kotaka T (1990) Study of subchain dynamics by dielectric normal-mode spectroscopy: butadiene-isoprene block copolymers. Macromolecules 23:3138

    Google Scholar 

  • Adachi K, Kotaka T (1990) Mechanical and dielectric relaxations of guest polymer molecules in networks. Polymer Yearbook 6:43–61

    Google Scholar 

  • Adachi K, Nishi I, Doi H, Kotaka T (1991) Study of subchain dynamics by dielectric normal-mode spectroscopy; butadiene-isoprene block copolymers. Macromolecules 24:5843–5850

    Google Scholar 

  • Adachi K, Kotaka T (1993) Dielectric normal mode relaxation. Prog Polym Sci 18:585–622

    Google Scholar 

  • Adachi K, Wada T, Kawamoto T, Kotaka T (1995) Dielectric spectroscopy on dilute blends of polyisoprene/polybutadiene: effects of matrix polybutadiene on the dynamics of probe polyisoprene. Macromolecules 28:3588–3596

    Google Scholar 

  • Arbe A, Colmenero J, Richter D (1996) Materials research society symposium series: Glass and glass-formers: current issues. Ngai KL, Angell CA, Kieffer J, Egami T, Nilhaus U (eds)

  • Bero CA, Roland CM (1996a) Normal mode relaxation in linear and branched polyisoprenes. Macromolecules 29:7521–7526

    Google Scholar 

  • Bero CA, Roland CM (1996b) Terminal relaxations in linear and 3-arm star polyisoprenes. Macromolecules 29:1561–1568

    Google Scholar 

  • Berry G, Fox T (1968) The viscosity of polymers and their concentrated solutions. Adv Polym Sci 5:261–357

    Google Scholar 

  • Boese D, Kremer F (1990) Molecular dynamics in bulk cis-polyisoprene as studied by dielectric spectroscopy. Macromolecules 23:829–835 (1990)

    Google Scholar 

  • ibid (1990) Molecular dynamics in bulk cis-polyisoprene as studied by dielectric spectroscopy. Macromolecules 23:1826–1832

    Google Scholar 

  • Bueche FJ (1954) The viscoelastic properties of plastics. Chem Phys 22:603–609

    Google Scholar 

  • Butera R, Fetters LJ, Huang JS, Richter D, Pyckhout-Hintzen W, Zirkel A, Farago B, Ewen B (1991) Microscopic and macroscopic evaluation of fundamental facets of the entanglement concept. Phys Rev Lett 66:2088–2092

    Google Scholar 

  • Cavaille J-Y, Jordan C, Perez J, Monnerie L, Johari G (1987) Time temperature superposition and dynamic mechanical behavior of atactic polystyrene. J Polym Sci, Part B Polym Phys 25:1235–1251

    Google Scholar 

  • Colmenero J, Arbe A, Alegria A (1993) Crossover from Debye to non-Debye dynamical behavior of the a relaxation observed by quasielastic neutron scattering in a glass-forming polymer. Phys Rev Lett 71:2603–2606

    Google Scholar 

  • Colmenero J, Arbe A, Alegria A (1994) The dynamics of the α- and β-relaxations in glass-forming polymers studied by quasielastic neutron scattering and dielectric spectroscopy. J Non-Cryst Solids 172–174:126–133

    Google Scholar 

  • Colmenero J, Arbe A, Coddens G, Frick B, Mijangos C, Reinecke G (1997) Phys Rev Lett (in press)

  • Connelly R (1994) unpublished, see figure in (Ngai and Plazek, 1995)

  • Cramer C, Funke K, Saatkamp T (1995a) Ion dynamics in glass-forming systems: I: conductivity spectra below the glass transformation temperature. Phil Mag B71:1103–1113

    Google Scholar 

  • Cramer C, Funke K, Buscher M, Happe A (1995b) Phil Mag B71:713

    Google Scholar 

  • Cochrane J, Harrison G, Lamb J, Phillips DW (1980) Creep, creep recovery and dynamic mechanical measurements of a poly(propylene glycol) oligomer. Polymer 21:837–844

    Google Scholar 

  • DeGennes PG (1971) Reptation of a polymer chain in the presence of fixed obstacles. J Chem Phys 55:572–579

    Google Scholar 

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

    Google Scholar 

  • Ferry JD (1980) Viscoelastic properties of polymers. 3rd edition John Wiley & Sons, New York

    Google Scholar 

  • Ferry JD (1991) Some reflections on the early development of polymer dynamics: viscoelasticity, dielectric dispersion, and self-diffusion. Macromolecules 24:5237–5242

    Google Scholar 

  • Fytas G, Ngai KL (1988) Study of viscoelastic relaxation in amorphous polypropylene near T g by dynamic light scattering and shear creep. Macromolecules 21:804–811

    Google Scholar 

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

    Google Scholar 

  • Gray RW, Harrison B, Lamb J (1977) Dynamic viscoelastic behaviour of low-molecular-mass polystyrene melts. Proc R Society Lond A356:77–102

    Google Scholar 

  • Kohlrausch R (1847) Nachtrag über die elastische Nachwirkung beim Cocon und Glasfaden, etc. Pogg Ann Physics 12(3):393–399

    Google Scholar 

  • Kotaka T, Adachi K (1994) Dielectric studies on the dynamics of polymer chains in various environments. Macromoleculer Chem Macromol Symp 79:125–138

    Google Scholar 

  • Kremer K, Grest G (1990) Dynamics of entangled linear polymer melts: a molecular-dynamics simulation. J Chem Phys 92:5057–5086

    Google Scholar 

  • Long VC, Berry GC, Hobbs LM (1964) Solution and bulk properties of branched polyvinylacetate IV-melt viscosity. Polymer 5:517–527

    Google Scholar 

  • MacKay RS, Meiss JD (1987) Hamiltonian dynamcal systems. Adam Hilger, Bristol

    Google Scholar 

  • McKenna GB, Ngai KL, Plazek DJ (1985) Differences in the molecular weight and the temperature dependences of self-diffusion and zero shear viscosity in linear polyethylene and hydrogenated polybutadiene. Polymer 26:1651–1653

    Google Scholar 

  • Ngai KL (1979) Universality of low-frequency fluctuation, dissipation and relaxation properties of condensed matter. I. Comments Solid State Phys 9:127–140

    Google Scholar 

  • Ngai KL, White CT (1979) Frequency dependence of dielectric loss in condensed matter. Physical Review B 20:2475–2486

    Google Scholar 

  • Ngai KL, Rendell RW (1982) Stress relaxation and loss moduli measurements in linear and branched polymer systems correlated with steady state viscosity: molecular weight dependences. Polymer Preprints Am Chem Soc, Division of Polymer Chemistry 23:46–47

    Google Scholar 

  • Ngai KL, Plazek DJ (1985) Relation of internal rotational isomerism barriers to the flow activation energy of entangled polymer melts in the high-temperature arrhenius region. J Polym Sci, Polym Phys Ed 23:2159–2180

    Google Scholar 

  • Ngai KL, Plazek DJ (1986) A quantitative explanation of the difference in the temperature dependences of the viscoelastic softening and terminal dispersions of linear amorphous polymers. J Polym Sci, Polym Phys Ed 24:619–632

    Google Scholar 

  • Ngai KL, Strom U (1988) High-frequency dielectric of Naß-alumina: evidence for relaxation crossover. Phys Rev B 38:10350–10356

    Google Scholar 

  • Ngai KL, Rendell RW (1991) Toward a theory of relaxation in correlated systems: diffusion in the phase space of a chaotic hamiltonian. J Non-Cryst Solids 131–133:233

    Google Scholar 

  • Ngai KL, Skolnick J (1991) Correspondence between the coupling model predictions and computer simulations: diffusion of a probe polymer in a matrix having different degrees of polymerization. Macromolecules 24:1561–1566

    Google Scholar 

  • Ngai KL (1992) Structural relaxation and conductivity relaxation in glassy ionics. J Physics (Paris) Colloq C2, 2:61–73

    Google Scholar 

  • Ngai KL, Colmenero J, Arbe A, Alegria A (1992a) Interpretation of anomalous momentum transfer dependences of local chain motion of polymers observed by quasielastic incoherent neutron scattering experiments. Macromolecules 25:6727–6729

    Google Scholar 

  • Ngai K, Schönhals A, Schlosser E (1992c) An explanation of anomalous dielectric relaxation properties of poly(propylene glycol). Macromolecules 25:4915–4919

    Google Scholar 

  • Ngai KL, Peng SL, Tsang KY (1992d) Fractal phase space transport dynamics and relaxations in complex correlated systems. Physica A 191:523–531

    Google Scholar 

  • Ngai KL (1993a) Relaxational processes in disordered systems. Richert R, Blumen A (eds) Springer Verlag, Berlin, pp 89–150

    Google Scholar 

  • Ngai KL (1993b) Comparisons between coupling model and molecular dynamics simulation for local chain motions in bulk amorphous polymers. J Chem Phys 98:7588–7592

    Google Scholar 

  • Ngai KL, Plazek DJ, Bero C (1993) Viscoelastic properties of amorphous polymers. 2. Anomalous temperature dependence of the steady-state recoverable compliance in low molecular weight polymers. Macromolecules 26:1065–1071

    Google Scholar 

  • Ngai KL, Peng SL, Skolnick J (1992) Generalized Fokker-Planck approach to the coupling model and comparison with computer simulations. Macromolecules 25:2184–2191

    Google Scholar 

  • Ngai KL, Tsang KY (1995a) From chemical structure to viscoelastic properties of polymers. Macromoleculer Chem Macromolec Symposium 90:95–129

    Google Scholar 

  • Ngai KL, Plazek DJ (1995b) Identification of different modes of molecular motion in polymers that cause thermorheological complexity. Rubber Chem Tech Rubber Review 68:376–434

    Google Scholar 

  • Ngai KL, Roland CM, Greaves GN (1995c) An interpretation of quasielastic neutron scattering and molecular dynamics simulation results on the glass transition. J Non-Cryst Solids 182:172–179

    Google Scholar 

  • Ngai KL, Cramer C, Saatkamp T, Funke K (1996a) Non-equilibrium phenomena in supercooled fluids, glasses and amorphous materials. Giordona M, Leporini D, Tosi P (eds) World Scientific Singapore 3:21

  • Ngai KL, Plazek DJ, Echeverria I (1996b) Viscoelastic properties of amorphous polymers 6. Local segmental contribution to the recoverable compliance of polymers. Macromolecules 29:1931

    Google Scholar 

  • Ngai KL, Plazek DJ, Rizos AK (1997) Viscoelastic propertis of amorphous polymers 5. A coupling model analysis of the thermorheological complexity of polyisobutylene in the glass-rubber softening dispersion. J Polym Sci Polym Phys Ed 35:599

    Google Scholar 

  • Pakula T, Geyler S (1988) Computer-simulated melts of cyclic polymers. Macromolecules 21:1665–1670

    Google Scholar 

  • Palade LI, Verney V, Attené P (1995) Time-temperature superposition and linear viscoelasticity of polybutadienes. Macromolecules 28:7051–7057

    Google Scholar 

  • Pethrick RA (1983) Ultrasonic studies of macromolecules. Prog Polym Sci 9:197–295

    Google Scholar 

  • Plazek DJ (1965a) Temperature dependence of the viscoelastic behavior of polystyrene. J Phy Chem 69:3480–3487

    Google Scholar 

  • Plazek DJ (1965b) Journal of Physical Chemistry 69:3480–3487;in this work the statement “The viscous flow in polymers involve more motion parallel to the chain backbone than do retarded elastic conformations.” Was made

    Google Scholar 

  • Plazek DJ (1968) Magnetic bearing torsional creep apparatus. J Polym Sci, Part A-29 6:621–638

    Google Scholar 

  • Plazek DJ, O'Rourke VM (1971) Viscoelastic behavior of low molecular weight polystyrene. Journal of Polymer Science, Part A-2 9:209–243

    Google Scholar 

  • Plazek DJ, Riande E, Markovitz H, Raghupathi (1979) Concentration dependence of the viscoelastic properties of polystyrene-tricresyl phoshate solutions. J Polym Sci, Polymer Phys Ed 17:2189–2213

    Google Scholar 

  • Plazek DJ (1980) The temperature dependence of the viscoelastic behavior of poly(vinyl acetate). Polymer J 12:43–53

    Google Scholar 

  • Plazek DJ (1982) The temperame dependence of the viscoelastic softening and terminal dispersions of linear amorphous polymers. J Polym Sci Polym Phys Ed 20:729

    Google Scholar 

  • Plazek DJ, Plazek DL (1983) Viscoelastic behavior of atatic polypropylene. Macromolecules 16:1469–1475

    Google Scholar 

  • Plazek DJ, Ngai KL, Rendell RW (1984) An application of a unified relaxation model to the aging of polystyrene below its glass temperature. Polymer Engin Sci 24(10):1111–1116

    Google Scholar 

  • Plazek DJ, Ngai KL (1991) Correlation of polymer segmental chain dynamics with temperature dependent time-scale shifts. Macromolecules 24:1222–1224

    Google Scholar 

  • Plazek DJ, Zheng XD, Ngai KL (1992) Viscoelastic properties of amorphous polymers. 1. Different temperature dependences of segmental relaxation and terminal dispersion. Macromolecules 25:4920–4924

    Google Scholar 

  • Plazek DJ, Schlosser E, Schönhals A, Ngai KL (1993) Breakdown of the Rouse model for polymers near the glass transition temperature. J Chem Phys 98:6488–6491

    Google Scholar 

  • Plazek DJ (1993) What's wrong with the moduli Charley Brown? or Get the H out and go to L. J Rheo 36(8):1671–1690

    Google Scholar 

  • Plazek DJ, Bero CA, Neumeister S, Floudas G, Fytas G, Ngai KL (1994) Viscoelastic properties of amorphous polymers 3: low molecular weight poly(methylhenylsiloxane). Colloid Polym Sci 272:1430–1438

    Google Scholar 

  • Plazek DJ, Chay IC, Ngai KL, Roland CM (1995) Viscoelastic properties of polymers 4. Thermorheological complexity of the softening dispersion in polyisobutylene. Macromolecules 28:6432–6436

    Google Scholar 

  • Plazek DJ (1996) 1995 Bingham medal address: Oh, thermorheological simplicity, wherefore art thou? J Rheology 40(6):987–1014

    Google Scholar 

  • Poh BT, Adachi K, Kotaka T (1987) Solution-cross-linked networks. 1. Swelling and absorption behavior of natural rubber networks. Macromolecules 20:2563–2569

    Google Scholar 

  • Raju VR, Rachapudy H, Graessley WW (1979) Properties of amorphous and crystallizable hydrocarbon polymers. IV Melt theology of linear and star-branched hydrogenated polybutadiene. J Polym Sci, Polym Phys Ed 17:1223–1235

    Google Scholar 

  • Read B (1991) Analysis of creep and physical aging in glassy polymers. J Non-Cryst Solids 131–133:408–419

    Google Scholar 

  • Reissig S, Beiner M, Korus J, Schröter K, Donth E (1995) Confirmation of Plazek's slight shoulder in the shear retardation spectrum of poly(vinyl acetate) at the dynamic glass transition. Macromolecules 28:5394–5395

    Google Scholar 

  • Rendell RW, Ngai KL, McKenna GB (1987) Molecular weight and concentration dependences of terminal relaxation time and viscosity of entangled polymer solutions. Macromolecules 20:2250

    Google Scholar 

  • Rendell RW, Ngai KL (1991) Convolution integral formulation of dispersive diffusion transport: numerical solutions for the coupling model waiting time distribution. Journal of Non-Crystalline Solids 131:133–667

    Google Scholar 

  • Rendell RW (1993) Interaction of a relaxing system with a dynamical environment. Physical Review E 48:R17-R20

    Google Scholar 

  • Rendell RW (1994) Role of dynamical cooperativity for an enhanced isotope effect during transport. J Appl Phys 75:7626–7632

    Google Scholar 

  • Rizos A, Jian T, Ngai KL (1995) Determination of the coupling parameter of local segmental motion in poly(isobutylene) by photon correlation spectroscopy. Macromolecules 28:571–521

    Google Scholar 

  • Roland CM, Ngai KL, Lewis LJ (1995) High frequency relaxation of o-terphenyl. J Chem Phys 103:4632–4636

    Google Scholar 

  • Roland CM, Bero C (1996) Normal mode relaxation in linear and branched polyisoprene. Macromolecules 29:7521–7526

    Google Scholar 

  • Russell TP, Deline VR, Dozier WD, Felcher GP, Agrawal G, Wool RP, Mays JW (1993) Direct observation of reptation at polymer interfaces. Nature 365:235–236

    Google Scholar 

  • Santangelo P, Ngai KL, Roland CM (1993) Distinctive manifestations of segmental motion in amorphous poly(tetrahydrofuran) and polyisobutylene. Macromolecules 26:2682–2687

    Google Scholar 

  • Schönhals A (1993) Relation between main and normal mode relaxation for polyisoprene studied by dielectric spectroscopy. Macromolecules 26:1309–1314

    Google Scholar 

  • Skolnick J, Kolinski A (1990) Dynamics of dense polymer systems: computer simulations and analytic theories. Advances in Chemical Physics 78:223–278

    Google Scholar 

  • Tsang KY, Ngai KL (1996) Relaxation in interacting arrays of oscillators. Physical Review E 54:R3067–3071

    Google Scholar 

  • Tsironis GP, Aubry S (1996) Slow relaxation phenomena induced by breathers in nonlinear lattices. Phys Rev Lett 77:5225–5229

    Google Scholar 

  • Watanabe H, Urakawa O, Yamada H, Yao M-L (1996) Dielectric relaxation of cispolyisoprene chains in oligo- and polybutadiene matrices: matrix effects on mode distribution and relaxation time. Macromolecules 29:755–763

    Google Scholar 

  • Watanabe H, Kotaka T (1991) Viscoelastic and related properties of binary polymer blends. Chemtracts-Macromoleculer Chemistry 2:139–174

    Google Scholar 

  • Watanabe H, Tirrell M (1989) Reptation with configuration-dependent constraint release in the dynamics of flexible polymers. Macromolecules 22:927–939

    Google Scholar 

  • Watanabe H, Yamazaki M, Yoshida H, Kotaka T (1991) Slow dielectric relaxation of cis-polyisoprene in a polybutadiene matrix. 2. Comparison of experiments and constraint release models. Macromolecules 24:5372–5379

    Google Scholar 

  • Yoshida H, Watanabe H, Adachi K, Kotaka T (1991) Dielectric normal mode process of bifurcated linear cus-polyisoprene. Macromolecules 24:2981–2985

    Google Scholar 

  • Zorn R, Arbe A, Colmenero J, Frick B, Richter D, Buchenau U (1995) Neutron scattering study of the picosecond dynamics of polybutadiene and polyisoprene. Physical Review E 52:781–795

    Google Scholar 

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Authors and Affiliations

  1. Naval Research Laboratory Code 6807, 20375-5320, Washington, D. C., USA

    Kai L. Ngai

  2. Department of Materials Science and Engineering, University of Pittsburgh, 15361, Pittsburgh, Pennsylvania, USA

    Donald J. Plazek

  3. Code 6813 Naval Research Laboratory, 20375-5320, Washington, D. C., USA

    Ronald W. Rendell

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  1. Kai L. Ngai
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  2. Donald J. Plazek
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  3. Ronald W. Rendell
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Correspondence to Kai L. Ngai.

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Dedicated to Prof. John D. Ferry on the occasion of his 85th birthday.

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Ngai, K.L., Plazek, D.J. & Rendell, R.W. Some examples of possible descriptions of dynamic properties of polymers by means of the coupling model. Rheola Acta 36, 307–319 (1997). https://doi.org/10.1007/BF00366672

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