Soft random solids and their heterogeneous elasticity

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

Volumn 80, Issue 3, 2009, Pages

  Mao, Xiaoming ^a,b   Goldbart, Paul M ^a   Xing, Xiangjun ^c   Zippelius, Annette ^d,e  

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

^b UNIVERSITY OF PENNSYLVANIA   (United States)

^c SYRACUSE UNIVERSITY   (United States)

^d UNIVERSITY OF GÖTTINGEN   (Germany)

^e MAX PLANCK INSTITUTE FOR DYNAMICS AND SELF ORGANIZATION   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ELASTIC MEDIUM; ELASTIC PROPERTIES; FIELD THEORY; FORMING SYSTEMS; MEAN SHEAR; PHENOMENOLOGICAL DESCRIPTION; QUENCHED DISORDER; REFERENCE STATE; SEMIMICROSCOPIC MODELS; SOLID TRANSITION; SPATIAL HETEROGENEITY; SPONTANEOUS SYMMETRY BREAKING; THERMAL FLUCTUATIONS; UNIVERSAL PARAMETERS;

CORRELATORS; RESIDUAL STRESSES; RUBBER; VULCANIZATION;

ELASTICITY;

EID: 70349930995     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.031140     Document Type: Article

References (39)

1. Physical Properties of Polymeric Gels, edited by, J. P. C. Addad, (Wiley, Chichester, 1996).
2. L. R. G. Treloar, The Physics of Rubber Elasticity (Clarendon Press, Oxford, 1975).
3. P. M. Goldbart, H. E. Castillo, and A. Zippelius, Adv. Phys. 45, 393 (1996). 10.1080/00018739600101527
4. D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor & Francis, New York, 1994).
5. M. Rubinstein and S. Panyukov, Macromolecules 30, 8036 (1997). 10.1021/ma970364k
6. G. Glatting, R. Winkler, and P. Reineker, Macromolecules 28, 5906 (1995). 10.1021/ma00121a029
7. T. Hölzl, H. L. Trautenberg, and D. Göritz, Phys. Rev. Lett. 79, 2293 (1997). 10.1103/PhysRevLett.79.2293
8. C. Svaneborg, G. S. Grest, and R. Everaers, Polymer 46, 4283 (2005). 10.1016/j.polymer.2005.03.008
9. D. A. Head, A. J. Levine, and F. C. MacKintosh, Phys. Rev. Lett. 91, 108102 (2003). 10.1103/PhysRevLett.91.108102
10. C. Heussinger, B. Schaefer, and E. Frey, Phys. Rev. E 76, 031906 (2007). 10.1103/PhysRevE.76.031906
11. J. P. Wittmer, A. Tanguy, J.-L. Barrat, and L. Lewis, Europhys. Lett. 57, 423 (2002). 10.1209/epl/i2002-00471-9
12. B. Utter and R. P. Behringer, Phys. Rev. Lett. 100, 208302 (2008). 10.1103/PhysRevLett.100.208302
13. B. A. DiDonna and T. C. Lubensky, Phys. Rev. E 72, 066619 (2005). 10.1103/PhysRevE.72.066619
14. X. Mao, P. M. Goldbart, X. Xing, and A. Zippelius, Europhys. Lett. 80, 26004 (2007). 10.1209/0295-5075/80/26004
15. S. Ulrich, X. Mao, P. M. Goldbart, and A. Zippelius, Europhys. Lett. 76, 677 (2006). 10.1209/epl/i2006-10310-7
16. K. Broderix, M. Weigt, and A. Zippelius, Eur. Phys. J. B 29, 441 (2002). 10.1140/epjb/e2002-00325-4
17. X. Mao, P. M. Goldbart, M. Mezard, and M. Weigt, Phys. Rev. Lett. 95, 148302 (2005). 10.1103/PhysRevLett.95.148302
18. P. M. Goldbart, S. Mukhopadhyay, and A. Zippelius, Phys. Rev. B 70, 184201 (2004). 10.1103/PhysRevB.70.184201
19. X. Xing, P. M. Goldbart, and L. Radzihovsky, Phys. Rev. Lett. 98, 075502 (2007). 10.1103/PhysRevLett.98.075502
20. M. Mézard, G. Parisi, and M. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).
21. S. Alexander, Phys. Rep. 296, 65 (1998). 10.1016/S0370-1573(97)00069-0
22. P. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, New York, 1979).
23. R. T. Deam and S. F. Edwards, Philos. Trans. R. Soc. London, Ser. A 280, 317 (1976). 10.1098/rsta.1976.0001
24. M. Doi and S. Edwards, The Theory of Polymer Dynamics (Clarendon Oxford, 1986).
25. H. E. Castillo, P. M. Goldbart, and A. Zippelius, Europhys. Lett. 28, 519 (1994). 10.1209/0295-5075/28/7/011
26. W. Peng, H. E. Castillo, P. M. Goldbart, and A. Zippelius, Phys. Rev. B 57, 839 (1998). 10.1103/PhysRevB.57.839
27. M. Warner and E. Terentjev, Liquid Crystal Elastomers (Oxford University Press, Oxford, 2003).
28. T. C. Lubensky, R. Mukhopadhyay, L. Radzihovsky, and X. Xing, Phys. Rev. E 66, 011702 (2002). 10.1103/PhysRevE.66.011702
29. X. Xing, S. Pfahl, S. Mukhopadhyay, P. M. Goldbart, and A. Zippelius, Phys. Rev. E 77, 051802 (2008). 10.1103/PhysRevE.77.051802
30. J. Hubbard, Phys. Rev. Lett. 3, 77 (1959). 10.1103/PhysRevLett.3.77
31. R. Stratonovich, Sov. Phys. Dokl. 2, 416 (1957).
32. Rigidity Theory and Applications, edited by, M. F. Thorpe, and, P. M. Duxbury, (Kluwer Academic, New York/ Plenum, New York, 1999).
33. S. Mukhopadhyay, P. M. Goldbart, and A. Zippelius, Europhys. Lett. 67, 49 (2004). 10.1209/epl/i2003-10278-8
34. X. Xing, S. Mukhopadhyay, and P. M. Goldbart, Phys. Rev. Lett. 93, 225701 (2004). 10.1103/PhysRevLett.93.225701
35. P. Erdos and A. Rényi, Magyar Tud. Akad. Mat. Kut. Int. Közl. 5, 17 (1960), especially Theorem 9b;
36. reprinted in P. Erdos, The Art of Counting, edited by, J. Spencer, (MIT Press, Cambridge, MA, 1973), Chap. 14, article [324].
37. For additional discussion, see P. Erdos and A. Rényi, Bull. Internat. Statist. Inst. 38, 343 (1961);
38. reprinted in P. Erdos, The Art of Counting, edited by, J. Spencer, (MIT Press, Cambridge, MA, 1973), Chap. 14, article [v].
39. S. M. Clarke, E. M. Terentjev, I. Kundler, and H. Finkelmann, Macromolecules 31, 4862 (1998). 10.1021/ma980195j