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Volumn 68, Issue 3 1, 2003, Pages 315021-3150219

Entropy crisis, ideal glass transition, and polymer melting: Exact solution on a Husimi cactus

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; CRYSTAL LATTICES; CRYSTALLINE MATERIALS; CRYSTALLIZATION; ENTROPY; FREE ENERGY; GLASS TRANSITION; MELTING; PHASE DIAGRAMS;

EID: 0242664693     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (18)

References (63)
  • 8
    • 0742294357 scopus 로고
    • J.H. Gibbs and E.A. DiMarzio, J. Chem. Phys. 28, 373 (1958); 28, 807 (1958); J. Polym. Sci. 40, 121 (1963); G. Adams and J.H. Gibbs, J. Chem. Phys. 43, 139 (1965).
    • (1958) J. Chem. Phys. , vol.28 , pp. 373
    • Gibbs, J.H.1    Dimarzio, E.A.2
  • 9
    • 0042115063 scopus 로고
    • J.H. Gibbs and E.A. DiMarzio, J. Chem. Phys. 28, 373 (1958); 28, 807 (1958); J. Polym. Sci. 40, 121 (1963); G. Adams and J.H. Gibbs, J. Chem. Phys. 43, 139 (1965).
    • (1958) J. Chem. Phys. , vol.28 , pp. 807
  • 10
    • 0742294357 scopus 로고
    • J.H. Gibbs and E.A. DiMarzio, J. Chem. Phys. 28, 373 (1958); 28, 807 (1958); J. Polym. Sci. 40, 121 (1963); G. Adams and J.H. Gibbs, J. Chem. Phys. 43, 139 (1965).
    • (1963) J. Polym. Sci. , vol.40 , pp. 121
  • 11
    • 0347936294 scopus 로고
    • J.H. Gibbs and E.A. DiMarzio, J. Chem. Phys. 28, 373 (1958); 28, 807 (1958); J. Polym. Sci. 40, 121 (1963); G. Adams and J.H. Gibbs, J. Chem. Phys. 43, 139 (1965).
    • (1965) J. Chem. Phys. , vol.43 , pp. 139
    • Adams, G.1    Gibbs, J.H.2
  • 16
    • 23544453410 scopus 로고
    • R.G. Petschek, Phys. Rev. B 32, 474 (1985); A. Baumgartner and D.Y. Yoon, J. Chem. Phys. 79, 521 (1983).
    • (1985) Phys. Rev. B , vol.32 , pp. 474
    • Petschek, R.G.1
  • 22
    • 33645090764 scopus 로고    scopus 로고
    • See the Proceedings of the Conference on 40 Years of Entropy and the Glass Transition
    • See the Proceedings of the Conference on 40 Years of Entropy and the Glass Transition [J. Res. Natl. Inst. Stand. Technol. 102, (1997)].
    • (1997) J. Res. Natl. Inst. Stand. Technol. , vol.102
  • 32
    • 0001077830 scopus 로고    scopus 로고
    • L. Angelani, G. Parisi, G. Ruocco, and G. Viliani, Phys. Rev. Lett. 81, 4648 (1998); Phys. Rev. E 61, 1681 (2000).
    • (2000) Phys. Rev. E , vol.61 , pp. 1681
  • 39
  • 41
    • 33645058741 scopus 로고    scopus 로고
    • note
    • conf(T) in lattice models. For this reason, we will not use the subscript "conf" to denote the configurational entropy in this work.
  • 48
    • 5244331276 scopus 로고
    • See, for example, H.W. Blote and B. Nienhuis, Phys. Rev. Lett. 72, 1372 (1994); M.T. Batchelor, J. Suzuki, and C.M. Yung, ibid. 73, 2646 (1994); J. Kondev and J.L. Jacobsen, ibid. 81, 2922 (1998).
    • (1994) Phys. Rev. Lett. , vol.72 , pp. 1372
    • Blote, H.W.1    Nienhuis, B.2
  • 49
    • 0000663210 scopus 로고
    • See, for example, H.W. Blote and B. Nienhuis, Phys. Rev. Lett. 72, 1372 (1994); M.T. Batchelor, J. Suzuki, and C.M. Yung, ibid. 73, 2646 (1994); J. Kondev and J.L. Jacobsen, ibid. 81, 2922 (1998).
    • (1994) Phys. Rev. Lett. , vol.73 , pp. 2646
    • Batchelor, M.T.1    Suzuki, J.2    Yung, C.M.3
  • 50
    • 0001449831 scopus 로고    scopus 로고
    • See, for example, H.W. Blote and B. Nienhuis, Phys. Rev. Lett. 72, 1372 (1994); M.T. Batchelor, J. Suzuki, and C.M. Yung, ibid. 73, 2646 (1994); J. Kondev and J.L. Jacobsen, ibid. 81, 2922 (1998).
    • (1998) Phys. Rev. Lett. , vol.81 , pp. 2922
    • Kondev, J.1    Jacobsen, J.L.2
  • 54
    • 0018001919 scopus 로고
    • R.F. Boyer, Polymer 19, 732 (1979); R.F. Boyer and R.L. Miller, Macromolecules 17, 365 (1984).
    • (1979) Polymer , vol.19 , pp. 732
    • Boyer, R.F.1
  • 59
    • 33645056786 scopus 로고    scopus 로고
    • note
    • It should be stressed at this point that the existence of a negative entropy in our exact calculation is caused by the use of the continuation and/ or of solutions that are not the equilibrium one, i.e., solutions that do not have the lowest possible free energy F̃. Recall that the exact calculation of the free energy through the use of the partition function only requires that the free energy has the correct convexity property, which in this case corresponds to having a non-negative specific heat. This remains true for all states in our calculation, equilibrium or not. The requirement that the entropy be non-negative is an additional postulate, justified by the obvious fact that the number of realizable configurations be at least one. The continuation need not satisfy the entropy requirement, the latter being completely independent of the convexity property of the free energy. There will never be a negative-entropy equilibrium solution in any exact calculation, as the equilibrium state must correspond to a number of realizable configurations. This also means that if there is no phase transition in a model, there will be no possibility of any continuation that can then violate the entropy requirement. In this case, there cannot exist any Kauzmann temperature.
  • 63
    • 33645071413 scopus 로고    scopus 로고
    • private communication
    • F. Semerianov (private communication).
    • Semerianov, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.