Theory of physical aging in polymer glasses

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 78, Issue 3, 2008, Pages

  Chen, Kang ^a   Schweizer, Kenneth S ^a  

^a United States of America   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; FORECASTING; GLASS; INTEGRAL EQUATIONS; NONLINEAR EQUATIONS; PARAMETER ESTIMATION; POLYMERS; RELAXATION PROCESSES; STRESSES; YIELD STRESS;

AGING RESPONSE; AGING TIME; ARRHENIUS; COHESIVE ENERGIES; COOPERATIVITY; DENSITY FLUCTUATIONS; DYNAMIC CROSSOVER; DYNAMIC ORDER; EXPERIMENTAL MEASUREMENTS; FICTIVE TEMPERATURES; FIRST-ORDER KINETIC; GLASS TEMPERATURES; HIGH TEMPERATURES; HOPPING PROCESSES; LANGEVIN EQUATION; MECHANICAL RELAXATIONS; MOLTEN STATES; NONLINEARLY COUPLED; PHENOMENOLOGICAL MODELING; PHYSICAL AGEING; POLY-METHYL METHACRYLATE; POLYMER GLASSES; POWER LAWS; SCALE THEORY; SEGMENTAL RELAXATION; SHEAR RELAXATION; TEMPERATURE JUMPS; TEMPERATURE-DEPENDENT; TEMPORAL EVOLUTIONS; TIME VARYING;

ACTIVATION ENERGY;

EID: 52649163919     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.78.031802     Document Type: Article

References (73)

1. C. A. Angell, K. L. Ngai, G. B. McKenna, P. F. McMillan, and S. W. Martin, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.1286035 88, 3113 (2000);
2. K. L. Ngai, J. Non-Cryst. Solids JNCSBJ 0022-3093 10.1016/S0022-3093(00) 00238-6 275, 7 (2000).
3. L. C. E. Struick, Physical Aging in Amorphous Polymers and Other Materials (Elsevier, Amsterdam, 1978).
4. G. B. McKenna, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/15/11/301 15, S737 (2003).
5. A. J. Kovacs, Fortschr. Hochpolym.-Forsch. FHOFAL 0341-020X 3, 394 (1964).
6. S. Kolla and S. L. Simon, Polymer POLMAG 0032-3861 10.1016/j.polymer. 2004.11.086 46, 733 (2005);
7. G. B. McKenna, M. G. Vangel, A. L. Rukhin, S. D. Leigh, B. Lotz, and C. Straupe, Polymer POLMAG 0032-3861 10.1016/S0032-3861(98)00668-5 40, 5183 (1999).
8. P. Badrinarayanan and S. L. Simon, Polymer POLMAG 0032-3861 10.1016/j.polymer.2007.01.064 48, 1464 (2007);
9. I. Echeverria, P. L. Kolek, D. J. Plazek, and S. L. Simon, J. Non-Cryst. Solids JNCSBJ 0022-3093 10.1016/S0022-3093(03)00245-X 324, 242 (2003).
10. G. W. Scherer, Relaxation in Glass and Composites (Wiley, New York, 1986).
11. S. Brawer, Relaxation in Viscous Liquids (American Ceramic Society, Columbus, Ohio, 1985).
12. A. Q. Tool, J. Am. Chem. Soc. JACSAT 0002-7863 37, 73 (1946);
13. O. S. Narayanswamy, J. Am. Chem. Soc. JACSAT 0002-7863 54, 491 (1971);
14. C. T. Moynihan, P. B. Macedo, C. J. Montrose, P. K. Gupta, M. A. DeBolt, and J. F. Dill, Ann. N.Y. Acad. Sci. ANYAA9 0077-8923 10.1111/j.1749-6632.1976. tb39688.x 279, 15 (1976).
15. V. Lubchenko and P. G. Wolynes, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1771633 121, 2852 (2004).
16. V. Luchenko and P. G. Wolynes, Annu. Rev. Phys. Chem. ARPLAP 0066-426X 10.1146/annurev.physchem.58.032806.104653 58, 235 (2007).
17. J. Rottler and M. O. Robbins, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.225504 95, 225504 (2005).
18. M. Warren and J. Rottler, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.76.031802 76, 031802 (2007).
19. K. S. Schweizer and E. J. Saltzman, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1756854 121, 1984 (2004);
20. E. J. Saltzman and K. S. Schweizer, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1756856 121, 2001 (2004).
21. E. J. Saltzman and K. S. Schweizer, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/19/20/205123 19, 205123 (2007).
22. K. Chen and K. S. Schweizer, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2428306 126, 014904 (2007).
23. K. Chen and K. S. Schweizer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.167802 98, 167802 (2007).
24. M. Rubinstein and R. H. Colby, Polymer Physics (Oxford Press, Oxford, 2003).
25. G. B. McKenna, in Comprehensive Polymer Science, edited by, C. Booth, and, C. Price, (Pergamon, Oxford, 1989), Vol. 2, p. 311.
26. K. S. Schweizer, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2137701 123, 244501 (2005).
27. N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group (Addison-Wesley, New York, 1994).
28. K. S. Schweizer and J. G. Curro, Adv. Chem. Phys. ADCPAA 0065-2385 10.1002/9780470141571.ch1 98, 1 (1997).
29. K. S. Schweizer and G. Yatsenko, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2780861 127, 164505 (2007).
30. G. Yatsenko and K. S. Schweizer, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.76.041506 76, 041506 (2007).
31. T. R. Kirkpatrick and P. G. Wolynes, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.35.3072 35, 3072 (1987).
32. K. S. Schweizer and E. J. Saltzman, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1578632 119, 1181 (2003).
33. T. Inoue and K. Osaki, Macromolecules MAMOBX 0024-9297 10.1021/ma950981d 29, 1595 (1996).
34. T. P. Lodge and T. C. B. MacLeish, Macromolecules MAMOBX 0024-9297 10.1021/ma9921706 33, 5278 (2000).
35. V. N. Novikov and A. P. Sokolov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.031507 67, 031507 (2003).
36. M. D. Ediger, Annu. Rev. Phys. Chem. ARPLAP 0066-426X 10.1146/annurev.physchem.51.1.99 51, 99 (2000);
37. R. Richert, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/14/23/201 14, R703 (2002);
38. S. F. Swallen, P. A. Bonvallet, R. J. McMahon, and M. D. Ediger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.015901 90, 015901 (2003).
39. O. Urakawa, S. F. Swallen, M. D. Ediger, and E. D. von Meerwall, Macromolecules MAMOBX 0024-9297 10.1021/ma0352025 37, 1558 (2004).
40. F. H. Stillinger and P. G. Debennedetti, Nature (London) NATUAS 0028-0836 10.1038/35065704 410, 259 (2001);
41. F. H. Stillinger, P. G. Debennedetti, and S. Sastry, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.476997 109, 3983 (1998);
42. W. Kob, F. Sciortino, and P. Tartaglia, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2000-00191-8 49, 590 (2000).
43. See Ref. for a detailed discussion of the x-ray scattering measurements of S (q=0) for polymer glasses and a list of original references. For polymer compressibility data near the glass transition see G. Floudas, T. Pakula, M. Stamm, and E. W. Fischer, Macromolecules MAMOBX 0024-9297 10.1021/ma00059a028 26, 1671 (1993).
44. For a review of dynamic light scattering studies of polymer glasses see G. D. Patterson and A. Munoz-Rojas, Annu. Rev. Phys. Chem. ARPLAP 0066-426X 10.1146/annurev.pc.38.100187.001203 38, 191 (1987).
45. N. Ashcroft and D. Mermin, Solid State Physics (Holt, Rinehart, and Winston, New York, 1976).
46. L. David, G. Vigier, S. Etienne, A. Faivre, C. L. Soles, and A. F. Yee, J. Non-Cryst. Solids JNCSBJ 0022-3093 235-237, 383 (1998).
47. K. Chen and K. S. Schweizer, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/79/26006 79, 26006 (2007).
48. M. L. Cerrada and G. B. McKenna, Macromolecules MAMOBX 0024-9297 10.1021/ma990400a 33, 3065 (2000), and references therein.
49. P. A. O'Connell and G. B. McKenna, Polym. Eng. Sci. PYESAZ 0032-3888 10.1002/pen.11797 37, 1485 (1997).
50. W. Gotze and L. Sjogren, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/55/3/001 55, 241 (1992).
51. K. S. Schweizer and E. J. Saltzman, J. Phys. Chem. B JPCBFK 1089-5647 10.1021/jp047763j 108, 19729 (2004).
52. V. Kobelev and K. S. Schweizer, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.021401 71, 021401 (2005).
53. The determination of the fictive temperature is not unique. One typical approach is based on the measurement of specific volume V- V∞ = (Tf -T) (αl - αg), where V and V∞ stand for the actual and equilibrium specific volume, respectively, and αl (αg) is the volume expansion coefficients of the liquid (glass). An alternative choice assumes τ (Tf) = τeq (T) where τ (Tf) refers to the characteristic time achieved by thermally stimulated modulus relaxation measurement [see, for example, H. Wagner and R. Richert, Polymer POLMAG 0032-3861 10.1016/S0032-3861(97)00122-5 38, 5801 (1997)].
54. P. Lunkenheimer, R. Wehn, U. Schneider, and A. Loidl, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.055702 95, 055702 (2005).
55. P. A. O'Connell and G. B. McKenna, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.479046 110, 11054 (1999).
56. J. M. Hutchinson, S. Smith, B. Horne, and G. M. Gourlay, Macromolecules MAMOBX 0024-9297 10.1021/ma981391t 32, 5046 (1999).
57. M. Delin, R. Rychwalski, J. Kubat, C. Klason, and J. M. Hutchinson, Polym. Eng. Sci. PYESAZ 0032-3888 10.1002/pen.10697 36, 2955 (1996).
58. A. Alegria, L. Goitiandia, I. Telleria, and J. Colmenero, Macromolecules MAMOBX 0024-9297 10.1021/ma961266m 30, 3881 (1997).
59. C. T. Thurau and M. D. Ediger, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1472508 116, 9089 (2002).
60. K. C. Rusch, J. Macromol. Sci., Phys. JMAPBR 0022-2348 10.1080/00222346808212448 B2, 179 (1968).
61. J. Vernel, R. w. Rychwalski, V. Pelisek, P. Saha, M. Schmidt, and F. H. J. Mauer, Thermochim. Acta THACAS 0040-6031 10.1016/S0040-6031(99)00291-9 342, 115 (1999).
62. K. Chen and K. S. Schweizer, Macromolecules MAMOBX 0024-9297 10.1021/ma800778v 41, 5908 (2008).
63. L. Guerdoux, R. A. Duckett, and D. Froelich, Polymer POLMAG 0032-3861 10.1016/0032-3861(84)90098-3 25, 1392 (1984).
64. Y. Nanzai, A. Miwa, and S. Z. Cui, Polym. J. (Tokyo, Jpn.) POLJB8 0032-3896 10.1295/polymj.32.51 32, 51 (2000).
65. H. E. H. Meijer and L. E. Govaert, Prog. Polym. Sci. PRPSB8 0079-6700 10.1016/j.progpolymsci.2005.06.009 30, 915 (2005).
66. K. Ding and A. P. Sokolov, Macromolecules MAMOBX 0024-9297 10.1021/ma052607b 39, 3322 (2006).
67. K. S. Schweizer and J. G. Curro, Macromolecules MAMOBX 0024-9297 10.1021/ma00188a028 21, 3082 (1988).
68. H. Li, J. G. Curro, D. T. Wu, and A. Habenschuss, Macromolecules MAMOBX 0024-9297 10.1021/ma702748v 41, 2694 (2008).
69. A. Habenschuss, M. Tsige, J. G. Curro, G. S. Grest, and S. K. Nath, Macromolecules MAMOBX 0024-9297 10.1021/ma0702290 40, 7036 (2007).
70. L. Onsager, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.37.405 37, 405 (1931);
71. L. Onsager, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.38.2265 38, 2265 (1931).
72. K. S. Schweizer, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2780863 127, 164506 (2007).
73. J. C. Dyre, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.76.041508 76, 041508 (2007).