Rheological implications of completely monotone fading memory

Journal of Rheology

Volumn 46, Issue 6, 2002, Pages 1459-1472

  Andersser, R S ^a   Loy, R J ^b  

^a CSIRO   (Australia)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

POLYMERS; RELAXATION PROCESSES; STRAIN; STRESS ANALYSIS; VISCOELASTICITY;

FADING MEMORY;

RHEOLOGY;

EID: 0036870531     PISSN: 01486055     EISSN: None     Source Type: Journal    
DOI: 10.1122/1.1514203     Document Type: Article

References (35)

1. Akyildiz, E. R. S. Jones, and K. Walters, "On the spring-dashpot representation of linear viscoelastic behaviour," Rheol. Acta 29, 482-484 (1990).
2. Anderssen, R. S., and R. J. Loy, "On the scaling of molecular weight distribution functionals," J. Rheol. 45, 891-901 (2001).
3. Anderssen, R. S., and R. J. Loy, "Completely monotone fading memory relaxation modulii," Bull. Austral. Math. Soc. 65, 449-460 (2002).
4. Anderssen, R. S., and D. W. Mead, "Theoretical derivation of molecular weight scaling for theological parameters," J. Non-Newtonian Fluid Mech. 76, 299-306 (1998).
5. Anderssen, R. S., and M. Westcott, "The molecular weight distribution problem and reptation mixing roles," ANZIAM J. 42, 26-40 (2000).
6. Benallal, A., G. Marin, J. P. Montfort, and C. Derail, "Linear viscoelasticity revisited: The relaxation function of monodisperse polymer melts," Macromolecules 26, 7229-7235 (1993).
7. Bendler, J. T., "Lévy ;stable) probability densities and mechanical relaxation in solid polymers," J. Stat. Phys. 36, 625-637 (1984).
8. Beds, A. N., and B. J. Edwards, "On the admissibility criteria for linear viscoelasticity kernels," Rheol. Acta 32, 505-510 (1993).
9. Bird, R. B., R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, Vol. 1, Fluid Mechanics (Wiley, New York, 1987).
10. Boltzmann, L., "Zur Theorie der elastischen Nachwirkung," Ann. Phys. Chem. 7, 624-657 (1876).
11. Carrot, C., and J. Guillet, "From dynamic moduli to molecular weight distribution: A study of various polydisperse linear polymers," J. Rheol. 41, 1203-1220 (1997).
12. Carrot, C., P. Revenu, and J. Guillet, "Rheological behavior of degraded polypropylene melts: from MWD to dynamic moduli," J. Appl. Polym. Sci. 61, 1887-1897 (1996).
13. Day, W. A., "On monotonicity of the relaxation functions of viscoelastic materials," Proc. Cambridge Philos. Soc. 67, 503-508 (1970).
14. de Gennes, P.-G., "Relaxation anomalies in linear polymer melts," Macromolecules 35, 3785-3786 (2002).
15. Del Piero, G., and L. Deseri, "Monotonic, completely monotonic, and exponential relaxation functions in linear elasticity," Q. Appl. Math. LIII, 273-300 (1995).
16. des Cloizeaux, J., "Double reptation vs simple reputation in polymer melts," Europhys. Lett. 5, 437-442 1988); 6, 475 (1988).
17. des Cloizeaux, J., "Double reptation vs simple reputation in polymer melts," Europhys. Lett. 5, 437-442 1988); 6, 475 (1988).
18. Doi, M., and S. F. Edwards, "Dynamics of concentrated polymer systems. Part 1. Brownian motion in be equilibrium state," J. Chem. Soc., Faraday Trans. 2 74, 1789-1801 (1978).
19. Fabrizio, M., and A. Morro, Mathematical Problems in Linear Viscoelasticity (Society for Industrial and Applied Mathematics, Philadelphia, 1992).
20. Grinshpan, A. Z., M. E. H. Ismail, and D. L. Milligan, "Complete monotonicity and diesel fuel spray," Math. Intell. 22, 43-53 (2000).
21. Léonardi, F., J.-C. Majesté, A. Allal, and G. Marin, "Rheological models based on the double reputation mixing role: The effects of a polydisperse environment," J. Rheol. 44, 675-691 (2000).
22. Lin, Y.-H., "A general linear-viscoelastic theory for nearly monodisperse flexible linear polymer melts and concentrated solutions and comparison of theory and experiment," Macromolecules 17, 2846-2856 (1984).
23. Maier, D., A. Eckstein, C. Friedrich, and J. Honerkamp, "Evaluation of models combining rheologicai data with the molecular weight distribution," J. Rheol. 42, 1153-1173 (1998).
24. McLeish, T. C. B., "Relaxation behaviour of highly polydisperse polymer melts," Polymer 33, 2852-2854 (1992).
25. McLeish, T. C. B., and R. G. Larson, "Molecular constitutive equations for a class of branched polymers: The pom-pom polymer," J. Rheol. 42, 81-110 (1998).
26. Mead, D. W., "Determination of molecular weight distributions of linear flexible polymers from linear viscoelastic material functions," J. Rheol. 38, 1797-1827 (1994).
27. Montfort, J.-P., G. Martin, and P. Monge, "Effect of constraint release on the dynamics of entangled linear polymer melts," Macromolecules 17, 1551-1560 (1984).
28. Montroll, E. W., and J. T. Bendler, "On Lévy (or stable) distributions and the Williams-Watts model of dielectric relaxation," J. Stat. Phys. 34, 129-162 (1984).
29. Ngai, K. L., and C. M. Roland, "Development of cooperativity in the local segmental dynamics of poly(vinylacetate): Synergy of thermodynamics and intermolecular coupling," Polymer 43, 567-573 (2002).
30. Rambousky, R., M. Weiss, H. Mysz, M. Moske, and K. Samwer, "Structural relaxation and viscous flow in amorphous ZrAlCu above and below the glass transition temperature," Mater. Sci. Forum 225-227, 83-88 (1996).
31. Sasaki, N., Y. Nakayama, M. Yoshikawa, and A. Enyo, "Stress relaxation function of bone and bone collagen," J. Biomech. 26, 1369-1376 (1993).
32. Thimm, W. (private communication, 2002).
33. Thimm, W., C. Friedrich, M. Marth, and J. Honerkamp, "An analytical relation between relaxation time spectrum and molecular weight distribution," J. Rheol. 43, 1663-1672 (1999).
34. Thimm, W., C. Friedrich, M. Marth, and J. Honerkamp, "On the Rouse spectrum and the determination of the molecular weight distribution," J. Rheol. 44, 429-438 (2000).
35. Widder, D. V., The Laplace Transform (Princeton University Press, Princeton, NJ, 1946).