8.3 Possibility of Ideal Glass Transitions
175
view, experimental dependences of relaxation time on temperature represented by
the Angell plot (Fig. 8.5) reflect the variation of the activation energy sensed by a
rearranging molecule in varied surroundings. Note that the k B [d(ln τ )/d(1/T )] does
not reflect the activation energy at T , although the Arrhenius law is assumed in this
view.
It is a critical issue to identify the difference between the equilibrium liquid
and the glass of the same material in order to discuss the possibility of ideal glass
transitions as not a crossover but a phase transition. Since there exists some disorder
in the system, inhomogeneity itself, irrespective of static or dynamic, cannot be an
intrinsic indicator of the “glassiness.” In this respect, it is interesting to mention a
recent report [44], which identified a structural difference between modeled liquid
and glass by applying an emerging methodology based on applied mathematics.
There are some theoretical attempts to rationalize the presence of ideal glass
transition(s) [3, 45]. Even so, every glass transition ever reported is practically due
to the prolonged relaxation time of systems, leading to the fact that no one has ever
observed the ideal glass transition. It is also emphasized that theoretical attempts have
treated idealized systems consisting of spherical particles without rotational degrees
of freedom. Little has been clarified about molecular nature, such as rotational degrees
of freedom with anisotropy and the possibility of molecular deformation, all of which
potentially contribute to the occurrence and properties of glass transitions. Indeed, it
is inevitable that internal motional degrees of freedom (configurational change) are
involved deeply in real glass transitions in polymers.
References
1. C.A. Angell, Science 267, 1924–1935 (1995)
2. P.G. Debenedetti, F.H. Stillinger, Nature 410, 259–267 (2001)
3. L. Bertier, G. Biroli, Rev. Mod. Phys. 83, 587–645 (2011)
4. E.R. Andrew, R.G. Eades, Proc. Roy. Soc. London 218A, 537–552 (1953)
5. H. Kawaji, Thesis for the Master’s Degree of Science (in Japanese), Osaka University, Graduate
School of Science (1986)
6. Y. Yamamura, Y. Suzuki, M. Sumita, K. Saito, J. Phys. Chem. B 116, 3938–3943 (2012)
7. N.O. Birge, Phys. Rev. B 34, 1631–1642 (1986)
8. M. Sorai, S. Seki, Bull. Chem. Soc. Jpn. 44, 2887–2887 (1971)
9. K. Adachi, H. Suga, S. Seki, Bull. Chem. Soc. Jpn. 41, 1073–1087 (1968)
10. W.F. Giauque, M.F. Ashley, Phys. Rev. 43, 81–82 (1933)
11. W.F. Giauque, J.W. Stout, J. Am. Chem. Soc. 58, 1144–1150 (1936)
12. L. Pauling, J. Am. Chem. Soc. 57, 2680–2684 (1935)
13. J.F. Nagle, J. Math. Phys. 7, 1484–1491 (1966)
14. T. Atake, H. Chihara, Bull. Chem. Soc. Jpn. 47, 2126–2136 (1974)
15. Y. Tozuka, H. Akutsu, Y. Yamamura, K. Saito, M. Sorai, Bull. Chem. Soc. Jpn. 73, 2279–2282
(2000)
16. O. Haida, T. Matsuo, H. Suga, S. Seki, J. Chem. Thermodyn. 6, 815–825 (1977)
17. H. Akutsu, K. Saito, Y. Yamamura, K. Kikuchi, H. Nishikawa, I. Ikemoto, M. Sorai, J. Phys.
Soc. Jpn. 68, 1968–1974 (1999)
18. K. Saito, H. Akutsu, M. Sorai, Solid State Commun. 111, 471–475 (1999)
19. H. Akutsu, K. Saito, M. Sorai, Phys. Rev. B 61, 4346–4352 (2000)
175
view, experimental dependences of relaxation time on temperature represented by
the Angell plot (Fig. 8.5) reflect the variation of the activation energy sensed by a
rearranging molecule in varied surroundings. Note that the k B [d(ln τ )/d(1/T )] does
not reflect the activation energy at T , although the Arrhenius law is assumed in this
view.
It is a critical issue to identify the difference between the equilibrium liquid
and the glass of the same material in order to discuss the possibility of ideal glass
transitions as not a crossover but a phase transition. Since there exists some disorder
in the system, inhomogeneity itself, irrespective of static or dynamic, cannot be an
intrinsic indicator of the “glassiness.” In this respect, it is interesting to mention a
recent report [44], which identified a structural difference between modeled liquid
and glass by applying an emerging methodology based on applied mathematics.
There are some theoretical attempts to rationalize the presence of ideal glass
transition(s) [3, 45]. Even so, every glass transition ever reported is practically due
to the prolonged relaxation time of systems, leading to the fact that no one has ever
observed the ideal glass transition. It is also emphasized that theoretical attempts have
treated idealized systems consisting of spherical particles without rotational degrees
of freedom. Little has been clarified about molecular nature, such as rotational degrees
of freedom with anisotropy and the possibility of molecular deformation, all of which
potentially contribute to the occurrence and properties of glass transitions. Indeed, it
is inevitable that internal motional degrees of freedom (configurational change) are
involved deeply in real glass transitions in polymers.
References
1. C.A. Angell, Science 267, 1924–1935 (1995)
2. P.G. Debenedetti, F.H. Stillinger, Nature 410, 259–267 (2001)
3. L. Bertier, G. Biroli, Rev. Mod. Phys. 83, 587–645 (2011)
4. E.R. Andrew, R.G. Eades, Proc. Roy. Soc. London 218A, 537–552 (1953)
5. H. Kawaji, Thesis for the Master’s Degree of Science (in Japanese), Osaka University, Graduate
School of Science (1986)
6. Y. Yamamura, Y. Suzuki, M. Sumita, K. Saito, J. Phys. Chem. B 116, 3938–3943 (2012)
7. N.O. Birge, Phys. Rev. B 34, 1631–1642 (1986)
8. M. Sorai, S. Seki, Bull. Chem. Soc. Jpn. 44, 2887–2887 (1971)
9. K. Adachi, H. Suga, S. Seki, Bull. Chem. Soc. Jpn. 41, 1073–1087 (1968)
10. W.F. Giauque, M.F. Ashley, Phys. Rev. 43, 81–82 (1933)
11. W.F. Giauque, J.W. Stout, J. Am. Chem. Soc. 58, 1144–1150 (1936)
12. L. Pauling, J. Am. Chem. Soc. 57, 2680–2684 (1935)
13. J.F. Nagle, J. Math. Phys. 7, 1484–1491 (1966)
14. T. Atake, H. Chihara, Bull. Chem. Soc. Jpn. 47, 2126–2136 (1974)
15. Y. Tozuka, H. Akutsu, Y. Yamamura, K. Saito, M. Sorai, Bull. Chem. Soc. Jpn. 73, 2279–2282
(2000)
16. O. Haida, T. Matsuo, H. Suga, S. Seki, J. Chem. Thermodyn. 6, 815–825 (1977)
17. H. Akutsu, K. Saito, Y. Yamamura, K. Kikuchi, H. Nishikawa, I. Ikemoto, M. Sorai, J. Phys.
Soc. Jpn. 68, 1968–1974 (1999)
18. K. Saito, H. Akutsu, M. Sorai, Solid State Commun. 111, 471–475 (1999)
19. H. Akutsu, K. Saito, M. Sorai, Phys. Rev. B 61, 4346–4352 (2000)