Abstract
The mechanical properties of polymeric materials quite generally dependon time, i.e., on whether they are deformed rapidly or slowly. The timedependence is often remarkably large. The complete description of themechanical properties of a polymeric material commonly requires thatthey be traced through 10, 15, or even 20 decades of time. The class ofpolymeric materials referred to as thermorheologically and/orpiezorheologically simple materials allows use of the superposition ofthe effects of time and temperature and/or time and pressure in suchmaterials as a convenient means for extending the experimental timescale.
This paper presents a critical review of models proposed todescribe the effect of temperature and/or pressure on time-dependentthermorheologically and/or piezorheologically simple polymericmaterials. The emphasis here is on the theoretical aspects, althoughexperimental results are used as illustrations wherever appropriate.
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References
Adam, G. and Gibbs, J.H., 'On the temperature dependence of cooperative relaxation properties in glass-forming liquids', J. Chem. Phys. 43, 1965, 139-146.
Baumgaertel, M. and Winter, H.H., 'Determination of discrete relaxation and retardation time spectra from dynamic mechanical data', Rheol. Acta 28, 1989, 511-519.
Bestul, A.B. and Chang, S.S., 'Excess entropy at glass transformation', J. Chem. Phys. 40, 1964, 3731-3733.
Bianchi, U., 'Pressure effects on glass transition in polymers', J. Phys. Chem. 69, 1965, 1497-1504.
Boldizar, A., Kubát, J. and Rigdahl, M., 'Influence of mold filling rate and gate geometry on the modulus of high pressure injection-moulded polyethylene', J. Appl. Polym. Sci. 39, 1990, 63-71.
Bridgman, P.W., The Physics of High Pressure, G. Bell and Sons, London, 1949.
Brinson, L.C. and Knauss,W.G., 'Thermorheologically complex behavior of multi-phase viscoelastic materials', J. Mech. Phys. Solids 39(7), 1991, 859-880.
Brinson, L.C. and Knauss,W.G., 'Finite element analysis of multi-phase viscoelastic solids', J. Appl. Mech. 59, 1992, 730-737.
Bueche, F., 'Rate and pressure effects in polymers and other glass-forming substances', J. Chem. Phys. 36, 1962, 2940-2946.
Caruthers, J.M. and Cohen, R.E., 'Consequences of thermorheological complexity in viscoelastic materials', Rheol. Acta 19, 1980, 606-613.
Chang, S.S., Bestul, A.B. and Horman, J.A., 'Critical configurational entropy at glass transformation', in Proceedings of the VII International Congress on Glass, Brussels, 1965.
Cohen, R.E. and Tschoegl, N.W., 'Comparison of the dynamic mechanical properties of two SBS triblock copolymers with 1,2-and 1,4-polybutadiene central blocks', Trans. Soc. Rheol. 20, 1976, 153-169.
Curro, J.G., Lagasse, R.R. and Simha, R., 'Use of a theoretical equation of state to interpret timedependent free volume in polymer glasses', J. Appl. Phys. 52, 1981, 5892.
Deng, T.H. and Knauss, W.G., 'The temperature and frequency dependence of the bulk compliance of Poly(Vinyl Acetate). A re-examination', Mech. Time-Dependent. Mater. 1, 1997, 33-49.
DiMarzio, E.A. and Gibbs, J.H., 'Chain stiffness and the lattice theory of polymer phases', J. Chem. Phys. 28, 1958, 807-813.
DiMarzio, E.A. and Gibbs, J.H., 'Glass temperature of copolymers', J. Polym. Sci. 40, 1959, 121-131.
DiMarzio, E.A. and Gibbs, J.H., 'Molecular interpretation of glass temperature depression by plasticizers', J. Polym. Sci. A1, 1963, 1417-1428.
DiMarzio, E.A. and Gibbs, J.H., 'On the second order transition of a rubber', J. Res. Nat. Bur. Stand. A68, 1964, 611-617.
DiMarzio, E.A., Gibbs, J.H., Fleming III, P.D. and Sanchez, I.C., 'Effects of pressure on the equilibrium properties of glass-forming polymers', Macromolecules 9, 1976, 763-771.
Doolittle, A.K. and Doolittle, D.B., 'Studies in Newtonian flow. Further verification of the free-space viscosity equation', J. Appl. Phys. 28, 1957, 901-905.
Duperray, B. and Leblanc, J.L., 'The time-temperature superposition principle as applied to filled elastomers', Kautschuck + Gummi · Kunststoffe 35(4), 1982, 298-307.
Eisenberg, A. and Saito, S., 'Possible experimental equivalence of the Gibbs-DiMarzio and free volume theories of the glass transition', J. Chem. Phys. 45, 1966, 1673-1678.
Emri, I. and Tschoegl, N.W., 'Generating line spectra from experimental responses. Part I: Relaxation modulus and creep compliance', Rheol. Acta 32, 1993, 311-321.
Emri, I. and Tschoegl, N.W., 'Generating line spectra from experimental responses. Part IV: Application to experimental data', Rheol. Acta 33, 1994, 60-70.
Emri, I. and Tschoegl, N.W., 'An iterative computer algorithm for generating line spectra from linear viscoelastic response functions', Internat. J. Polym. Mater. 40, 1998, 55-79.
Emri, I., Knauss,W.G. and Tschoegl, N.W., 'Non-equilibrium time-dependent behavior of polymeric materials', 2002, in preparation.
Ferry, J.D., Viscoelastic Properties of Polymers, 3rd edn., Wiley and Sons, New York, 1980.
Ferry, J.D. and Stratton, R.A., 'The free volume interpretation of the dependence of viscosities and viscoelastic relaxation times on concentration, pressure, and tensile strain', Kolloid-Z. 171, 1960, 107-111.
Fesko, D.G. and Tschoegl, N.W., 'Time-temperature superposition in thermorheologically complex materials', J. Polym. Sci., Part C, Symposia 35, 1971, 51-69.
Fesko, D.G. and Tschoegl, N.W., 'Time-temperature superposition in styrene/butadiene/styrene block copolymers', Internat. J. Polym. Mater. 3, 1974, 51-79.
Fillers, R.W. and Tschoegl, N.W., 'The effect of pressure on the mechanical properties of polymers', Trans. Soc. Rheol. 21, 1977, 51-100.
Freeman, B.D., Bokobza, L. and Monnerie, L., 'The effect of hydrostatic pressure on local polymer dynamics in polyisoprene', Polymer 31, 1990, 1045-1050.
Gee, G., 'The thermodynamic analysis of the effect of pressure on the glass temperature of polystyrene', Polymer 7, 1966, 177-191.
Gibbs, J.A., Modern Aspects of the Vitreous State, Butterworths, London, 1960.
Gibbs, J.A. and DiMarzio, E.A., 'Nature of the glass transition and the glassy state', J. Chem. Phys. 28, 1958, 373-383.
Goldstein, M., 'Some thermodynamic aspects of the glass transition: Free volume, entropy, and enthalpy theories', J. Chem. Phys. 39, 1963, 3369-3374.
Gross, B., Mathematical Structure of the Theories of Viscoelasticity, Hermann et Cie., Paris, 1968.
Gross, B., 'Time-temperature superposition principle in relaxation theory', J. Appl. Phys. 40, 1969, 3397.
Havlí?ek, I., Ilavský, M. and Hrouz, J., 'Effect of pressure on the cooperative relaxation properties and glass transition temperature of amorphous polymers', J. Macromol. Sci. Phys. B21, 1982, 425-441.
Hutchinson, J.M. and Kovacs, A.J., 'A simple phenomenological approach to the thermal behavior of glasses during uniform heating or cooling', J. Polym. Sci.: Polym. Phys. Ed. 14, 1976, 1575-1590.
Kaplan, D. and Tschoegl, N.W., 'Time-temperature superposition in two-phase polyblends', Polym. Engrg. Sci. 14, 1974, 43-49.
Kauzmann, W., 'Dielectric relaxation as a chemical rate process', Rev. Mod. Phys. 14, 1942, 12-44.
Knauss, W.G. and Zhu,W.D., 'Nonlinearly viscoelastic behavior of polycarbonate. I. Response under pure shear', Mech. Time-Dependent Mater., 2002, to appear.
Kovacs, A.J., 'Transition vitreuse dans les polymères amorphes. Etude phénomenologique', Adv. Polym. Sci. 3, 1964, 394-507.
Kralj, A., Prodan, T. and Emri, I., 'Effect of pressure and temperature on the mechanical properties of polymers', J. Rheol., 2001, to appear.
Matheson, A.J., 'Role of free-volume in the pressure dependence of the viscosity of liquids', J. Chem. Phys. 44, 1966, 695-699.
McCrum, N.G., 'The kinetics of the relaxation in an amorphous polymer at temperatures close to the glass transition', Polymer 25, 1984, 309-317.
McCrum, N.G. and Morris, E.L., 'On measurement of activation energies for creep and stress relaxation', Proc. Roy. Soc. A281, 1964, 258-273.
McCrum, N.G., Read, B.E. and Williams, G., Anelastic and Dielectric Effects in Polymeric Solids, Wiley and Sons, New York, 1967.
McKinney, J.E. and Belcher, H.V., 'Dynamic compressibility of poly(vinyl acetate) and its relation to free volume', J. Res. Nat. Bur. Stand. 67A, 1963, 43-53.
McLaughlin, J.R. and Tobolsky, A., 'The viscoelastic behavior of polymethyl methacrylate', J. Colloid Sci. 7, 1952, 555-568.
Moonan, W.K. and Tschoegl, N.W., 'The effect of pressure on the mechanical properties of polymers. 2. Expansivity and compressibility measurements', Macromolecules 16, 1983, 55-59.
Moonan, W.K. and Tschoegl, N.W., 'The effect of pressure on the mechanical properties of polymers. 3. Substitution of the glassy parameters for those of the occupied volume', Internat. Polym. Mater. 10, 1984, 199-211.
Moonan, W.K. and Tschoegl, N.W., 'The effect of pressure on the mechanical properties of polymers. IV. Measurements in torsion', J. Polym. Sci., Polym. Phys. Ed. 23, 1985, 623-651.
Murnaghan, F.D., Finite Deformation of Elastic Solids, Wiley, New York, 1951, 68.
O'Reilly, J.M., 'The effect of pressure on glass temperature and dielectric relaxation time of polyvinyl acetate', J. Polym. Sci. 57, 1962, 429-444.
O'Reilly, J.M., Tribone, J.J. and Greener, J., 'Effect of combined pressure and temperature changes on structural recovery of glass-forming materials I. Extension of the KAHR model', Polym. Sci., Polym. Phys. Ed. 26, 1988, 501-513.
Paterson, M.S., 'Effect of pressure on Young's modulus and the glass transition in rubbers', J. Appl. Phys. 35, 1964, 176-179.
Plazek, D.J., 'Temperature dependence of viscoelastic behavior of polystyrene', J. Phys. Chem. 69, 1965, 3480-3487.
Plazek, D.J., 'Magnetic bearing torsional creep apparatus', J. Polym. Sci. A2(6), 1968, 621-638.
Prodan, T., 'The effect of pressure and temperature on the shear relaxation behavior of timedependent materials', Ph.D. Thesis, Department of Mechanical Engineering, University of Ljubljana, Slovenia, 2001, in preparation.
Ramos, A.R, Kovacs, A.J., O'Reilly, J.M., Tribone, J.J. and Greener, J., 'Effect of combined pressure and temperature changes on structural recovery of glass forming materials. I. Extension of the KAHR model', J. Polym. Sci., Polym. Phys. Ed. 26, 1988, 501-513.
Rusch, K.C., 'Time-temperature superposition and relaxational behavior in polymeric glasses', J. Macromol. Sci.-Phys. B2, 1968a, 179-204.
Rusch, K.C., 'The relaxational behavior of heterogeneous polymers', J. Macromol. Sci.-Phys. B2, 1968b, 421-447.
Sane, S. and Knauss,W.G., 'The time-dependent bulk response of poly(methyl methacrylate)', Mech. Time-Dependent Mater. 5, 2001, 293-324.
Schwarzl, F.R. and Zahradnik, F., 'The time temperature superposition of the glass-rubber transition of amorphous polymers and the free volume', Rheol. Acta 19, 1980, 137-152.
Shen, M.C. and Eisenberg, A., 'Glass transitions in polymers', Prog. Solid State Chem. 3, 1966, 407-481.
Simha, R. and Somcynsky, T., 'Statistical thermodynamics of spherical and chain molecule fluids', Macromolecules 2, 1969, 342-350.
Simha, R. and Wilson, P.S., 'Thermal expansion of amorphous polymers at atmospheric pressure. II. Theoretical considerations', Macromolecules 6, 1973, 902-913.
Somcynsky, T. and Simha, R., 'Hole theory of liquids and glass transition', J. Appl. Phys. 42, 1971, 4545-4548.
Stacer, R.G. and Husband, D.M., 'Small deformation viscoelastic response of gum and highly filled elastomers', Rheol. Acta 29, 1990, 152-162.
Tait, P., Physics and Chemistry of the Voyage of H.M. Ship Challenger, Vol. II, Cambridge University Press, Cambridge, 1900, 1.
Tobolsky, A.V., Properties and Structure of Polymers, Wiley and Sons, New York, 1960.
Tool, A.Q., 'Relation between inelastic deformability and thermal expansion of glass in its annealing range', J. Amer. Ceram. Soc. 29, 1946, 240-253.
Tribone, J.J., O'Reilly, J.M. and Greener, J., 'Pressure-jump volume-relaxation studies of polystyrene in the glass transition region', J. Polym. Sci.: Part B: Polym. Phys. 27, 1989, 837-857.
Tschoegl, N.W., The Phenomenological Theory of Linear Viscoelastic Behavior, Springer-Verlag, Berlin, 1989.
Tschoegl, N.W., Fundamentals of Equilibrium and Steady-State Thermodynamics, Elsevier, Amsterdam, 2000.
Tschoegl, N.W. and Emri, I., 'Generating line spectra from experimental responses. Part III: Interconversion between relaxation and retardation behavior', Internat. J. Polym. Mater. 18, 1992, 117-127.
Tschoegl, N.W. and Emri, I., 'Generating line spectra from experimental responses. Part II: Storage and loss functions', Rheol. Acta 32, 1993, 322-327.
Tschoegl, N.W., Knauss, W.G. and Emri, I., 'Poisson's ratio in linear viscoelasticity-A critical review', Mech. Time-Dependent. Mater. 6, 2002, 3-51.
Utracki, L.A., 'Pressure dependence of Newtonian viscosity', Polym. Engrg. Sci. 23, 1983a, 446-451.
Utracki, L.A., 'Pressure and temperature dependent liquid viscosities', Polym. Prep., Amer. Chem. Soc. 24, 1983b, 113.
Ward, I.M., Mechanical Properties of Solid Polymers, Wiley-Interscience, London, 1971.
Williams, M.L., Landel, R.F. and Ferry, J.D., 'The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids', J. Amer. Chem. Soc. 77, 1955, 3701-3707.
Wunderlich, B., Macromolecular Physics, Volume I, Crystal Structure, Morphology, Defects, Academic Press, New York, 1973.
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Tschoegl, N., Knauss, W.G. & Emri, I. The Effect of Temperature and Pressure on the Mechanical Properties of Thermo- and/or Piezorheologically Simple Polymeric Materials in Thermodynamic Equilibrium – A Critical Review. Mechanics of Time-Dependent Materials 6, 53–99 (2002). https://doi.org/10.1023/A:1014421519100
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DOI: https://doi.org/10.1023/A:1014421519100