Abstract
Free volume plays an important role in the analysis of physical aging,both experimentally and theoretically. In this work, the Doolittle freevolume equation and the KAHR model are used to predict isothermal responsesfollowing temperature down- and up-jumps for poly(vinyl acetate), PVAc, inthe T g-region. The constant B of the Doolittleequation is less than unity when the equation is combined with the Kovacsdifferential equation for free volume collapse for isothermal contractionpredictions. Using B values in the range 0.3 to 0.5 allows goodprediction of the isothermal contraction. It is shown that the equationyields aging rates approaching realistic values only for temperatures muchbelow T g. Isothermal expansion could not be predicted. Volumerelaxation kinetics is analysed based on the Doolittle equation and comparedwith stress relaxation kinetics near T g, where the slope ofthe inflexion region is calculated. The transient response of PVAc in thesame aging experiments is obtained using the KAHR model.
Similar content being viewed by others
References
Batchinski, A.J., ‘Untersuchungen über die innere Reibung der Flüssigkeiten. I’, Z. Phys. Chemie 84, 1913, 643–644.
Berry, G.C. and Fox, T.G., ‘Viscosity of polymers and their concentrated solutions’, Adv. Polym. Sci. 5, 1967, 261–357.
Bondi, A., ‘Free volumes and free rotations in simple liquids and liquid saturated hydrocarbone’, J. Phys. Chem. 58, 1954, 929–939.
Cohen, H.H. and Turnbull, D., ‘Molecular transport in liquids and glasses’, J. Chem. Phys. 31, 1959, 1164–1169.
Curro, J.G. and Lagasse, R.R., ‘Use of a theoretical equation of state to interprete time-dependent free volume in polymer glasses’, J. Appl. Phys. 52, 1981, 5892–5897.
De Bolt, M.A., Easteal, A.J., Macedo, P.B. and Moynihan, C.T., ‘Analysis of structural relaxation in glass using rate heating data’, J. Am. Ceram. Soc. 59, 1976, 16–29.
Delin, M., Rychwalski, R.W., Kubáat, J. and Kubáat, J., ‘Volume changes during stress relaxation in polyethylene’, Rheol. Acta 34, 1995, 182–195.
Delin, M., Rychwalski, R.W., Kubát, J., Klason, C. and Hutchinson, J.M., ‘Physical aging time scales and rates for poly(vinyl acetate) stimulated mechanically in the Tg-region’, Polym. Eng. Sci. 36(24), 1996, 2955–2967.
Doolittle, A.K. and Doolittle, D.B., ‘Studies in Newtonian flow. V. Further verification of the freespace viscosity equation’, J. Appl. Phys. 28, 1957, 901–905.
Ferry, J.D., Viscoelastic Properties of Polymers, Wiley, New York, 1980, chapter 11.
Fillers, R.W. and Tschoegl, N.W., ‘The effect of pressure on the mechanical properties of polymers’, Trans. Soc. Rheol. 21, 1977, 51–100.
Greener, J., O'Reilly, J.M. and Ng, K.C., ‘The volumetric response of polymeric glasses to complex thermomechanical histories: A critical evaluation of the KAHR model’, in Structure, Relaxation, and Physical Aging of Glassy Polymers, R.J. Roe and J.M. O'Reilly (eds), Materials Research Society Symposium, Proceedings Vol. 215, Pittsburgh, 1991, 99–107.
Higuchi, H., Yu, Z., Jamieson, A.M., Simha, R. and McGervey, J.D., ‘Thermal history temperature dependence of viscoelastic properties of polymer glasses’, J. Polym. Sci., Part B: Polym. Phys. 33, 1995, 2295–2305.
Hodge, I.M., ‘Effects of annealing and prior history on enthalpy relaxation in glassy polymers. 4. Comparison of five polymers’, Macromolecules 16, 1983, 898–902.
Hodge, I.M., ‘Effects of annealing and prior history on enthalpy relaxation in glassy polymers. 6. Adam–Gibbs formulation on nonlinearity’, Macromolecules 20, 1987, 2897–2908.
Hutchinson, J.M., ‘Physical aging of polymers’, Prog. Polym. Sci. 20, 1995, 703–760.
Hutchinson, J.M. and Kovacs, A.J., ‘A simple phenomenological approach to the thermal behavior of glass during uniform heating and cooling’, J. Polym. Sci. Polym. Phys. Ed. 14, 1975. 1575–1590.
Hutchinson, J.M. and Ruddy, M., ‘Thermal cycling of glasses. II. Experimental evaluation of the structure (or nonlinearity) parameter x’, J. Polym. Sci.: Polym. Phys. Ed. 26, 1988, 2341–2366.
Kovacs, A.J., ‘Transition vitreuse dans les polymèeres amorphes. Etude phéenoméenologique’, Fortsch. Hochpolym. Forsch. 3, 1963, 394–507.
Kovacs, A.J., Stratton, R.A. and Ferry, J.D., ‘Dynamic mechanical properties of polyvinyl acetate in shear in the glass transition temperature range’, J. Phys. Chem. 67, 1963, 152–161.
Kovacs, A.J., Hutchinson, J.M. and Aklonis, J.J., ‘Isobaric volume and enthalpy recovery of glasses. (I) A critical survey of recent phenomenological approaches’, in The Structure of NonCrystalline Materials, P.H. Gaskell (ed.), Taylor and Francis, London, 1977, 153–163.
Kovacs, A.J., Aklonis, J.J., Hutchinson, J.M. and Ramos, A.R., ‘Isobaric volume and enthalpy recovery of glasses. II. A transparent multiparameter theory’, J. Polym. Sci.: Polym. Phys. Ed. 17, 1979, 1079–1162.
Kubát, J., ‘Stress relaxation in solids’, Nature 204, 1965, 378–379.
Kubát, J. and Rigdahl, M., ‘Stess-relaxation behavior of solid polymers’, in Failure of Plastics, W. Brostow and R.D. Corneliussen (eds), Hanser, New York, 1986, 60–63.
Litt, M., ‘Free volume and its relationship to the temperature effect on zero shear melt viscosity: A new correlation’, Trans. Soc. Rheol. 20, 1976, 47–64.
Matsuoka, S., ‘Free volume, excess entropy and mechanical behavior of polymeric glasses’, Polym. Eng. Sci. 21, 1981, 907–921.
Matsuoka, S., Bair, H.E., Bearder, S.S., Kern, H.E. and Ryan, J.T., ‘Analysis of nonlinear stress relaxation in polymeric glasses’, Polym. Eng. Sci. 18, 1978, 1073–1080.
McKenna, G.B., ‘Dilatometric evidence for the apparent decoupling of glassy structure from the mechanical stress field’, J. NonCryst. Solids 172–174, 1994, 756–764.
McKenna, G.B., Leterrier, Y. and Schultheisz, C.R., ‘The evolution of material properties during physical aging’, in Use of Plastics and Plastic Composites: Materials and Mechanics Issues, V.K. Stokes (ed.), ASME, Vol. MD46, New York, 1993, 245–260.
Moynihan, C.T., Bruce, A.J., Gavin, D.L., Loehr, S.R. and Opalka, S.M., ‘Physical aging of heavy metal fluoride glasses-sub-Tg enthalpy relaxation in a ZrF4-BaF2-LaF3-AIF3 glass’, Polym. Eng. Sci. 24, 1984, 1117–1122.
Narayanaswamy, O.S., ‘A model of structural relaxation in glass’, J. Am. Ceram. Soc. 54, 1971, 491–498.
Perez, J., Cavaille, J.Y., DiazCalleja, R., Gommez-Ribelles, J.L., Pradas, M.M. and Ribes-Greus, A., ‘Physical ageing of amorphous polymers. Theoretical analysis and experiments on poly(methyl methacrylate)’, Macromol. Chem. 172, 1991, 2141–2161.
Plazek, D.J. and Andrekanic, R.A., ‘The physical aging of amorphous polymers’, in Keynote Lectures in Selected Topics of Polymer Science, E. Riande (ed.), CSIC, Madrid, 1995, 117–138.
Roe, R.-J. and Millman, G.M., ‘Physical aging in polystyrene: Comparison of the changes in creep behavior with the enthalpy relaxation’, Polym. Eng. Sci. 23, 1983, 318–322.
Sperling, L.H., Introduction to Physical Polymer Science, Wiley, New York, 1986, chapter 6.
Struik, L.C.E., Physical Aging in Amorphous Polymers and Other Materials, Elsevier, Amsterdam, 1978.
Struik, L.C.E., ‘Dependence of relaxation times of glassy polymers on their specific volume’, Polymer 29, 1988, 1347–1353.
Tool, A.M., ‘Relation between inelastic deformability and thermal expansion of glass in its annealing range’, J. Am. Ceram. Soc. 29, 1946, 240–253.
Williams, M.F., Landel, R.F. and Ferry, J.D., ‘The temperature dependence of relaxation mechanism in amorphous polymers and other glass-forming liquids’, J. Am. Chem. Soc. 77, 1955, 3701–3707.
Wortmann, F.-J. and Schultz, K.V., ’Nonlinear viscoelastic performance of Nomex, Kevlar and polypropylene fibres in a single-step stress relaxation test: 1. Experimental data and principles of analysis’, Polymer 35, 1994, 2108–2116.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rychwalski, R., Delin, M. & Kubát, J. Remarks on Single and Multiparameter Free Volume Calculations in Physical Aging of Poly(vinyl acetate) in the T g-Region. Mechanics of Time-Dependent Materials 1, 161–180 (1997). https://doi.org/10.1023/A:1009716800710
Issue Date:
DOI: https://doi.org/10.1023/A:1009716800710