Randomly crosslinked macromolecular systems: Vulcanization transition to and properties of the amorphous solid state

Advances in Physics

Volumn 45, Issue 5, 1996, Pages 393-468

  Goldbart, Paul M ^a,b   Castillo, Horacio E ^a   Zippelius, Annette ^c  

^a University of Illinois at Urbana Champaign   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^c UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

AMORPHOUS MATERIALS; APPROXIMATION THEORY; COMPUTER SIMULATION; CROSSLINKING; FOURIER TRANSFORMS; GRAPH THEORY; PERCOLATION (SOLID STATE); PHASE EQUILIBRIA; PHASE TRANSITIONS; PHYSICAL PROPERTIES; STATISTICAL MECHANICS; VULCANIZATION;

AMORPHOUS SOLID STATE; CROSSLINKED MACROMOLECULAR SYSTEMS; DENSITY SECTOR CORRELATION; EDWARDS CROSSLINK DISTRIBUTION; FIELD THEORETIC REPRESENTATION; HUBBARD-STRATONOVICH DECOUPLING SCHEME; RANDOM GRAPH THEORY; REPLICA-HELMHOLTZ FREE ENERGY; SADDLE POINT APPROXIMATION; VULCANIZATION TRANSITION;

MACROMOLECULES;

EID: 0030246717     PISSN: 00018732     EISSN: 14606976     Source Type: Journal    
DOI: 10.1080/00018739600101527     Document Type: Article

References (68)

1. Deam, R.T., and Edwards, S. F., 1976, Phil. Trans. R. Soc. A, 280, 317.
2. Edwards, S. F., and Anderson, P. W., 1975, J. Phys. F, 5, 965.
3. D. Stauffer, 1985, Introduction to Percolation Theory (Philadelphia: Taylor & Francis).
4. D. Stauffer, A. Coniglio and M. Adam, 1982, Adv. Polym. Sci., 44, 103.
5. D. Stauffer, 1976, J. chem. Soc. Faraday Trans. II, 72, 1354
6. T. C. Lubensky and J. Isaacson, 1978, Phys. Rev. Lett., 41, 829
7. T. C. Lubensky and J. Isaacson, 1981, J. Phys. (France), 42, 175.
8. P. J. Flory, 1953, Principles of Polymer Chemistry (Ithaca: Cornell University Press).
9. Degennes, P.-G., 1979, Scaling Concepts in Polymer Physics (Ithaca: Cornell University Press).
10. Ball, R. C., and Edwards, S. F., 1980, Macromolecules, 13, 748.
11. Ball, R. C., 1980, Ph.D. Thesis, Cambridge University.
12. Goldbart, P. M., and Goldenfeld, N., 1987, Phys. Rev. Lett., 58, 2676.
13. Goldbart, P. M., and Goldenfeld, N., 1989, Phys. Rev. A, 39, 1402
14. Goldbart, P. M., and Goldenfeld, N., 1989, Phys. Rev. 39, 1412.
15. Goldbart, P. M., and Goldenfeld, N., 1989, Synergetics, 43: Cooperative Dynamics in Complex Physical Systems, edited by H. Takayama (Berlin: Springer), p. 208.
16. Goldbart, P. M., and Goldenfeld, N., 1989, Macromolecules, 22, 948.
17. Goldbart, P. M., and Zippelius, A., 1993, Phys. Rev. Lett., 71, 2256.
18. Castillo, H., Goldbart, P. M., and Zippelius, A., 1994, Europhys. Lett., 28, 519.
19. Panyukov, S. V., 1992, Pis'ma Zh. Eksp. Teor. Fiz., 55, 584 [1992, JETP Lett., 55, 608];
20. Panyukov, S., and Rabin, Y, 1995, Bar Ilan University Manuscript. [16] C. Itzykson and J.-M. Drouffe, 1989, Statistical Field Theory (Cam bridge: Cambridge University Press).
21. Castillo, H., Goldbart, P. M., and Zippelius, A., 1996, (work in progress).
22. Edwards, S. F., 1965, Proc. phys. Soc. (London), 85, 613.
23. M. Doi and S. F. Edwards, 1986, The Theory of Polymer Dynamics (New York: Oxford University Press).
24. Y. Oono, 1985, Adv. chem. Phys., 61, 301.
25. GIBBS, J. W., 1902, Elementary Principles in Statistical Mechanics (New York: Scribners), pp. 206-207.
26. Roos, C., ZIPPELIUS, A., and GOLDBART, R M., 1995, Random Networks of Crosslinked Manifolds, University of Illinois manuscript.
27. Sherrington, D., and Kirkpatrick, S., 1975, Phys. Rev. Lett., 35, 1792
28. Sherrington, D., and Kirkpatrick, S., 1978, Phys. Rev. B, 17, 4384.
29. Goldbart, R M., and Zippelius, A., 1994, J. Phys. A, 27, 6375.
30. Seung, H. Sompolinski and N. Tishby, 1992, Phys. Rev. A, 45, 6065.
31. M. Mezard, G. Parisi and M. A. Virasoro, 1987, Spin Glass Theory and Beyond (Singapore: World Scientific)
32. K. Binder and A. P. Young, 1986, Rev. mod. Phys., 58, 801.
33. Zippelius, A., Goldbart, P. M., and Goldenfeld, N., 1993, Europhys. Lett., 23, 451.
34. I. M. Lifshitz, A. Yu. Grosberg and A. R. Khoklov, 1978, Rev. mod. Phys., 50, 683.
35. Schrodinger, E., 1944, What is Life? (Cambridge: Cambridge University Press).
36. Einstein, A., 1907, Ann. Physik, 22, 180.
37. E. I. Shakhnovich and A. M. Gutin, 1989, J. Phys. A, 22, 1647
38. M. Mezard and G. Parisi, 1991, J. Phys. (Paris) 1, 1, 809
39. Y. Y. Goldschmidt and T. Blum, 1993, Phys. Rev. E, 48, 161
40. M. Mezard and G. Parisi, 1992, J. Phys. (Paris) 1, 2, 2231
41. A. Engel, 1994, Nucl. Phys. B, 410, [FS] 617
42. Doetsch, G., 1974, Introduction to the Theory and Application of the Laplace Transforma tion (New York: Springer-Verlag).
43. F. Mezei, 1991, Neutron scattering and collective dynamics, in Liquides, crystallisation et transition vitreuse, Les Houches Session LI, 3-28 Juillet 1989, edited by J. P. Hansen, D. Levesque and J. Zinn-Justin (Amsterdam: North Holland).
44. Oeser, R., Ewen, B., Richter, D., and Farago, B., 1988, Phys. Rev. Lett., 60, 1041.
45. Karger, J., and Fleischer, G., 1994, Trends analyt. Chem., 13, 145.
46. Skirda, V. D., Dorokinizkij, M. M., Sundukov, V. I., Maklakov, A. I., Fleischer, G., Hausler, K. G., and Straube, E., 1988, Makromol. Chem., rapid Commun., 9, 603.
47. Viana, L., and Bray, A. J., 1985, J. Phys. C, 18, 3037.
48. D. J. Amit, 1989, Field Theory, the Renormalization Group, and Critical Phenomena (Singapore: World Scientific), especially chap. 5.
49. J. Zinn-Justin, 1989, Quantum Field Theory and Critical Phenomena (Oxford: Clarendon Press), especially chap. 5.
50. Erdos, P., and Renyi, A., 1960, Magyar Tud. Akad. Mat. Kut. Int. Kozl., 5, 17
51. P. Erdos and A. Renyi, 1961, Bull. Inst. Int. Statist., 38, 343
52. Spencer, J. (Editor), 1973, Paul Erdos: The Art of Counting (Cambridge, MA: MIT Press).
53. T. W. Komer, 1988, Fourier Analysis (Cambridge: Cambridge
54. Press, W. H., Teukolsky, S. A., Vetterling, W.T., and Flannery, B. P., 1992, Numerical Recipes in FORTRAN, second edition (Cambridge: Cambridge University Press).
55. KREMER, K., and GREST, G. S., 1994, Monte Carlo and Molecular Dynamics Simulations in Polymer Science, edited by K. Binder (Oxford: Clarendon Press).
56. Barsky, S. J., and Plischke, M., 1995, Order and localization in randomly crosslinked polymer networks (Simon Fraser University manuscript).
57. C. Goodyear, 1855, Gum-Elastic and its Varieties, with a Detailed Account of its Applications and Uses, and of the Discovery of Vulcanization (New Haven).
58. H. Morawetz, 1985, Polymers: the Origins and Growth of a Science (New York: John Wiley and Sons).
59. Goldbart, P. M., and Zippelius, A., 1994, Europhys. Lett., 27, 599.
60. Kantor, Y, Kardar, M., and Nelson, D. R., 1986, Phys. Rev. Lett., SI, 791; 1987, 35, 3056.
61. D. Nelson, T. Piran, and S. Weinberg (Eds), 1989, Jerusalem Winter School for Theoretical Physics: Statistical Mechanics of Membranes and Surfaces (Singapore: World Scientific).
62. Huthmann, M., Rehkopf, M., Zippelius, A., and Goldbart, P. M., 1996, Universality of gelation: endlinking versus crosslinking, stift rods versus flexible chains (University of Illinois manuscript).
63. Gutin, A. M., and Shakhnovich, E. I., 1994, J. chem. Phys., 100, 5290.
64. J. Hertz, A. Krogh, R. G. Palmer, 1991 Introduction to the Theory of Neural Computation (Redwood City: Addison-Wesley).
65. ZIPPELIUS, A., and GOLDBART, P. M. (unpublished).
66. Sompolinsky, H., and Zippelius, A., 1981, Phys. Rev. Lett., 47, 359
67. Sompolinsky, H., and Zippelius, A., 1982, Phys. Rev. B, 25, 6860.
68. Daniel Zwillinger, 1992, Handbook of Integration (London: Jones and Bartlett), section 35.