The recently discovered scaling law for the relaxation times, , where is temperature and the specific volume, is derived by a revision of the entropy model of the glass transition dynamics originally proposed by Avramov [J. Non-Cryst. Solids 262, 258 (2000)]. In this modification the entropy is calculated by an alternative route. The resulting expression for the variation of the relaxation time with and is shown to accurately fit experimental data for several glass-forming liquids and polymers over an extended range encompassing the dynamic crossover. From this analysis, which is valid for any model in which the relaxation time is a function of the entropy, we find that the scaling exponent can be identified with the Grüneisen constant.
REFERENCES
1.
M. H.
Cohen
and D.
Turnbull
, J. Chem. Phys.
31
, 1164
(1959
).2.
3.
M.
Goldstein
, J. Chem. Phys.
51
, 4767
(1969
).4.
5.
S.
Sastry
, Nature (London)
409
, 164
(2001
).6.
C. A.
Angell
, K. L.
Ngai
, G. B.
McKenna
, P. F.
McMillan
, and S. F.
Martin
, J. Appl. Phys.
88
, 3113
(2000
).7.
Proceedings of the Third and Fourth International Discussion Meeting on Relaxation in Complex Systems
, edited by K. L.
Ngai
et al. [J. Non-Cryst. Solids
235–237
(1997
);307–310
(2001
)].8.
9.
K.
Frick
, C.
Alba-Simionesco
, K. H.
Andersen
, and L. P.
Willner
, Phys. Rev. E
67
, 051801
(2003
).10.
A.
Tölle
, H.
Schober
, J.
Wuttke
, O. G.
Randl
, and F.
Fujara
, Phys. Rev. Lett.
80
, 2374
(1998
).11.
A.
Tölle
, Rep. Prog. Phys.
64
, 1473
(2001
).12.
G.
Fytas
, Th.
Dorfmuller
, and C. H.
Wang
, J. Phys. Chem.
87
, 5041
(1983
).13.
14.
G.
Fytas
, A.
Patkowski
, G.
Meier
, and Th.
Dorfmuller
, Macromolecules
15
, 870
(1982
).15.
G.
Fytas
, G.
Meier
, A.
Patkowski
, and Th.
Dorfmuller
, Colloid Polym. Sci.
260
, 949
(1982
).16.
G.
Fytas
, A.
Patkowski
, G.
Meier
, and Th.
Dorfmuller
, J. Chem. Phys.
80
, 2214
(1984
).17.
C.
Dreyfus
, A.
Aouadi
, J.
Gapinski
, M.
Matos-Lopes
, W.
Steffen
, A.
Patkowski
, and R. M.
Pick
, Phys. Rev. E
68
, 011204
(2003
).18.
M.
Paluch
, R.
Casalini
, A.
Best
, and A.
Patkowski
, J. Chem. Phys.
117
, 7624
(2002
).19.
L.
Comez
, D.
Fioretto
, H.
Kriegs
, and W.
Steffen
, Phys. Rev. E
66
, 032501
(2002
).20.
H. E.
King
, E.
Herbolzheimer
, and R. L.
Cook
, J. Appl. Phys.
71
, 2071
(1992
).21.
H. E.
King
and C. T.
Prewitt
, Rev. Sci. Instrum.
51
, 1037
(1980
).22.
R. E.
Cook
, H. E.
King
, and D. G.
Peiffer
, Phys. Rev. Lett.
69
, 3072
(1992
).23.
R. L.
Cook
, C. A.
Herbst
, and H. E.
King
, J. Phys. Chem.
97
, 2355
(1993
).24.
R. L.
Cook
, H. E.
King
, C. A.
Herbst
, and D. R.
Herschbach
, J. Chem. Phys.
100
, 5178
(1994
).25.
26.
C.
Liebske
, H.
Behrens
, F.
Holtz
, and R.
Lange
, Geochim. Cosmochim. Acta
67
, 473
(2003
).27.
28.
C. M.
Roland
, S.
Hensel-Bielowka
, M.
Paluch
, and R.
Casalini
, Rep. Prog. Phys.
68
, 1405
(2005
).29.
G.
Floudas
, in Broadband Dielectric Spectroscopy
, edited by F.
Kremer
and A.
Schonhals
(Springer-Verlag
, Berlin
, 2003
), Chap. 8.30.
G.
Williams
, Trans. Faraday Soc.
62
, 2091
(1966
).31.
G.
Williams
and D. A.
Edwards
, Trans. Faraday Soc.
62
, 1329
(1966
).32.
G.
Williams
, Trans. Faraday Soc.
61
, 1564
(1965
).33.
G.
Williams
, Trans. Faraday Soc.
60
, 1548
(1964
).34.
35.
H.
Sasabe
, S.
Saito
, M.
Asahina
, and H.
Kakutani
, J. Polym. Sci., Polym. Phys. Ed.
7
, 1405
(1969
).36.
37.
J. P.
Johari
and E.
Whalley
, Faraday Symp. Chem. Soc.
6
, 23
(1972
).38.
H.
Sasabe
and S.
Saito
, Polym. J. (Tokyo, Jpn.)
3
, 624
(1972
).39.
40.
R.
Casalini
and C. M.
Roland
, Phys. Rev. E
69
, 062501
(2004
).41.
R.
Casalini
and C. M.
Roland
, Colloid Polym. Sci.
283
, 107
(2004
).42.
C. M.
Roland
, R.
Casalini
, and M.
Paluch
, J. Polym. Sci., Polym. Phys. Ed.
42
, 4313
(2004
).43.
44.
C.
Dreyfus
, A.
Le Grand
, J.
Gapinski
, W.
Steffen
, and A.
Patkowski
, Eur. Phys. J. B
42
, 309
(2004
).45.
G.
Tarjus
, D.
Kivelson
, S.
Mossa
, and C.
Alba-Simionesco
, J. Chem. Phys.
120
, 6135
(2004
).46.
J. D.
Weeks
, D.
Chandler
, and H. C.
Andersen
, J. Chem. Phys.
54
, 5237
(1971
).47.
M. S.
Shell
, P. G.
Debenedetti
, E.
La Nave
, and F.
Sciortino
, J. Chem. Phys.
118
, 8821
(2003
).48.
N. H.
March
and M. P.
Tosi
, Introduction to Liquid State Physics
(World Scientific
, Singapore
, 2002
).49.
50.
P. G.
Debenedetti
, F. H.
Stillinger
, T. M.
Truskett
, and C. J.
Roberts
, J. Phys. Chem. B
103
, 7390
(1999
).51.
M. S.
Shell
, P. G.
Debenedetti
, E.
La Nave
, and F.
Sciortino
, J. Chem. Phys.
118
, 8821
(2003
).52.
I.
Avramov
, J. Chem. Phys.
95
, 4439
(1991
).53.
I.
Avramov
, J. Non-Cryst. Solids
262
, 258
(2000
).54.
55.
I.
Avramov
and A.
Milchev
, J. Non-Cryst. Solids
104
, 253
(1988
).56.
M.
Paluch
, S.
Hensel-Bielowka
, and T.
Psurek
, J. Chem. Phys.
113
, 4374
(2000
).57.
S. P.
Andersson
and O.
Andersson
, Macromolecules
31
, 2999
(1998
).58.
C. M.
Roland
and R.
Casalini
, Macromolecules
36
, 1361
(2003
).59.
A.
Drozd-Rzoska
, Phys. Rev. E
72
, 041505
(2002
).60.
C. A.
Angell
, in Relaxation in Complex Systems
, edited by K. L.
Ngai
and G. B.
Wright
(National Technical Information Service
, Washington DC
, 1985
).61.
62.
M.
Paluch
, C. M.
Roland
, and S.
Pawlus
, J. Chem. Phys.
116
, 10932
(2002
).63.
M.
Paluch
and C. M.
Roland
, J. Non-Cryst. Solids
316
, 413
(2003
).64.
65.
R.
Casalini
, M.
Paluch
, and C. M.
Roland
, Phys. Rev. E
67
, 031505
(2003
).66.
M.
Paluch
, C. M.
Roland
, R.
Casalini
, G.
Meier
, and A.
Patkowski
, J. Chem. Phys.
118
, 4578
(2003
).67.
C. M.
Roland
, R.
Casalini
, P. G.
Santangelo
, M.
Sekula
, J.
Ziolo
, and M.
Paluch
, Macromolecules
36
, 4954
(2003
).68.
M.
Paluch
, R.
Casalini
, and C. M.
Roland
, Phys. Rev. B
66
, 092202
(2002
).69.
R.
Casalini
, M.
Paluch
, and C. M.
Roland
, J. Chem. Phys.
118
, 5701
(2003
).70.
S.
Hensel-Bielowka
, M.
Paluch
, J.
Ziolo
, and C. M.
Roland
, J. Phys. Chem. B
106
, 12459
(2002
).71.
S.
Pawlus
, R.
Casalini
, C. M.
Roland
, M.
Paluch
, S. J.
Rzoska
, and J.
Ziolo
, Phys. Rev. E
70
, 061501
(2004
).72.
M.
Paluch
, C. M.
Roland
, and S.
Pawlus
, J. Chem. Phys.
116
, 10932
(2002
).73.
R.
Casalini
and C. M.
Roland
, Phys. Rev. E
72
, 031503
(2005
).74.
I.
Avramov
, J. Non-Cryst. Solids
238
, 6
(1998
).75.
G.
Hartwig
, Polymer Properties at Room and Cryogenic Temperatures
(Plenum
, New York
, 1994
), Chap. 4.76.
77.
G.
Adam
and J. H.
Gibbs
, J. Chem. Phys.
43
, 139
(1965
).78.
S. S.
Chang
and A. B.
Bestul
, J. Chem. Phys.
56
, 503
(1972
).79.
B.
Wünderlich
, ATHAS database, http://web.utk.edu/~athas/80.
W.
Wunderlich
, Polymer Handbook
, edited by J.
Brandrup
, E. H.
Immergut
, and E. A.
Grulke
(Wiley
, New York
, 1999
).81.
M.
Hanaya
, T.
Hikima
, M.
Hatase
, and M.
Oguni
, J. Chem. Thermodyn.
34
, 1173
(2002
).82.
83.
I.
Avramov
, J. Chem. Phys.
95
, 4439
(1991
).84.
I.
Avramov
, J. Non-Cryst. Solids
262
, 258
(2000
).85.
86.
87.
G. S.
Fulcher
, J. Am. Ceram. Soc.
8
, 339
(1923
).88.
V. G.
Tammann
and W.
Hesse
, Z. Anorg. Allg. Chem.
156
, 245
(1926
).89.
F.
Stickel
, E. W.
Fischer
, and R.
Richert
, J. Chem. Phys.
104
, 2043
(1996
).90.
K. L.
Ngai
and C. M.
Roland
, Polymer
43
, 567
(2002
).91.
R.
Casalini
, K. L.
Ngai
, and C. M.
Roland
, Phys. Rev. B
68
, 14201
(2003
).92.
R.
Casalini
and C. M.
Roland
, Phys. Rev. Lett.
92
, 245702
(2004
).93.
R.
Casalini
, S.
Capaccioli
, M.
Lucchesi
, P. A.
Rolla
, and S.
Corezzi
, Phys. Rev. E
63
, 031207
(2001
).94.
R.
Casalini
, S.
Capaccioli
, M.
Lucchesi
, P. A.
Rolla
, M.
Paluch
, S.
Corezzi
, and D.
Fioretto
, Phys. Rev. E
64
, 041504
(2001
).95.
R.
Casalini
, M.
Paluch
, J. J.
Fontanella
, and C. M.
Roland
, J. Chem. Phys.
117
, 4901
(2002
).96.
J. P.
Johari
, J. Chem. Phys.
119
, 635
(2003
).97.
D.
Prevosto
, M.
Lucchesi
, S.
Capaccioli
, R.
Casalini
, and P. A.
Rolla
, Phys. Rev. B
67
, 174202
(2003
).98.
M.
Goldstein
, Phys. Rev. B
71
, 136201
(2005
).99.
D.
Prevosto
, M.
Lucchesi
, S.
Capaccioli
, P. A.
Rolla
, and R.
Casalini
, Phys. Rev. B
71
, 136202
(2005
).100.
R.
Richert
and C. A.
Angell
, J. Chem. Phys.
108
, 9016
(1998
).101.
U.
Schneider
, P.
Lunkenheimer
, R.
Brand
, and A.
Loidl
, Phys. Rev. E
59
, 6924
(1999
).102.
H. Z.
Cummins
, Phys. Rev. E
54
, 5870
(1996
).103.
M.
Paluch
, R.
Casalini
, and C. M.
Roland
, Phys. Rev. E
67
, 021508
(2003
).104.
M. H.
Cohen
and G. S.
Grest
, Phys. Rev. B
20
, 1077
(1979
);G. S.
Grest
and M. H.
Cohen
, Phys. Rev. B
21
, 4113
(1980
);105.
S.
Corezzi
, S.
Capaccioli
, R.
Casalini
, D.
Fioretto
, M.
Paluch
, and P. A.
Rolla
, Chem. Phys. Lett.
320
, 113
(2000
).106.
107.
L. D.
Landau
and E. M.
Lifshitz
, Statistical Physics
(Pergamon
, New York
, 1977
), Vol. 5
.© 2006 American Institute of Physics.
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