Microwave dielectric properties of carbon black filled polymers under uniaxial tension

Journal of Applied Physics

Volumn 101, Issue 8, 2007, Pages

  Mdarhri, A ^a,c   Brosseau, C ^b   Carmona, F ^a  

^a CENTRE DE RECHERCHE PAUL PASCAL   (France)

^b UNIVERSITÉ DE BRETAGNE OCCIDENTALE   (France)

^c IBN TOFAIL UNIVERSITY   (Morocco)

Author keywords

[No Author keywords available]

Indexed keywords

CARBON BLACK PARTICLES; ETHYLENE BUTYLACRYLATE COPOLYMER; MESOSTRUCTURED POLYMERS; PERCOLATIVE MATERIALS;

AUTOMOTIVE INDUSTRY; CARBON BLACK; DIELECTRIC PROPERTIES; MICROWAVE SPECTROSCOPY; TENSILE STRESS; TRANSPORT PROPERTIES;

POLYMERS;

EID: 34247587734     PISSN: 00218979     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2718867     Document Type: Conference Paper

References (116)

1. P. G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, NY, 1979).
2. S. Redner, Physics of Finely Divided Matter (Springer, Berlin, 1985).
3. A. R. Payne, in Reinforcement of Elastomers, edited by, G. Kraus, (Wiley, New York, 1965).
4. G. Kraus, in Reinforcement of Elastomers, edited by, G. Kraus, (Wiley, New York, 1965).
5. J. B. Donnet and A. Voet, Carbon Black Physics, Chemistry and Elastomer Reinforcement (Dekker, New York, 1976).
6. Z. Rigbi, Adv. Polym. Sci. 36, 21 (1980).
7. I. M. Ward, Mechanical Properties of Polymers (Wiley, New York, 1971).
8. S. Havriliak, Jr. and S. J. Havriliak, Dielectric and Mechanical Relaxation in Materials (Hanser/Gardener, Cincinnati, 1997).
9. F. Carmona, Ann. Chim. (Paris) 13, 343 (1987).
10. See, e. g., Carbon Black, Science and Technology, 2nd ed., edited by, J. B. Donnet, R. C. Bansal, and, M. J. Wang, (Dekker, New York, 1993); G. Wypych, Handbook of Fillers (ChemTec, Toronto, 1999); T. M. Aminabhavi, P. E. Cassidy, and C. M. Thompson, Rubber Chem. Technol. 0035-9475 63, 451, (1990); M. J. Wang, Rubber Chem. Technol. 71, 520 (1998) (It is also worth keeping in mind that the vast literature related to this subject cannot be mentioned in a single review article and many details of the physics are left for the diligent reader to find in the references).
11. See, e. g., Carbon Black, Science and Technology, 2nd ed., edited by, J. B. Donnet, R. C. Bansal, and, M. J. Wang, (Dekker, New York, 1993); G. Wypych, Handbook of Fillers (ChemTec, Toronto, 1999); T. M. Aminabhavi, P. E. Cassidy, and C. M. Thompson, Rubber Chem. Technol. 0035-9475 63, 451, (1990); M. J. Wang, Rubber Chem. Technol. 71, 520 (1998) (It is also worth keeping in mind that the vast literature related to this subject cannot be mentioned in a single review article and many details of the physics are left for the diligent reader to find in the references).
12. See, e. g., Carbon Black, Science and Technology, 2nd ed., edited by, J. B. Donnet, R. C. Bansal, and, M. J. Wang, (Dekker, New York, 1993); G. Wypych, Handbook of Fillers (ChemTec, Toronto, 1999); T. M. Aminabhavi, P. E. Cassidy, and C. M. Thompson, Rubber Chem. Technol. 0035-9475 63, 451, (1990); M. J. Wang, Rubber Chem. Technol. 71, 520 (1998) (It is also worth keeping in mind that the vast literature related to this subject cannot be mentioned in a single review article and many details of the physics are left for the diligent reader to find in the references).
13. See, e. g., Carbon Black, Science and Technology, 2nd ed., edited by, J. B. Donnet, R. C. Bansal, and, M. J. Wang, (Dekker, New York, 1993); G. Wypych, Handbook of Fillers (ChemTec, Toronto, 1999); T. M. Aminabhavi, P. E. Cassidy, and C. M. Thompson, Rubber Chem. Technol. 0035-9475 63, 451, (1990); M. J. Wang, Rubber Chem. Technol. 71, 520 (1998) (It is also worth keeping in mind that the vast literature related to this subject cannot be mentioned in a single review article and many details of the physics are left for the diligent reader to find in the references).
14. T. W. Ebbesen, in Carbon Nanotubes: Preparation and Properties, edited by, T. W. Ebbesen, (CRC, Boca Raton, FL, 1997), pp. 227-248.
15. M. Sahimi, Applications of Percolation Theory (Taylor and Francis, London, 1994). See also D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor and Francis, London, 1994). Observe that for economic and environmental reasons, the achievement of extremely low conduction thresholds is important. At this time the lowest filler volume fraction required for the conduction threshold which has been observed is as low as a few 0.01 vol % for some polymer blends, i.e., P. Dutta, S. Biswas, M. Ghosh, S. K. De, and S. Chatterjee, Synth. Met. 0379-6779 10.1016/S0379-6779(00)00588-9 122, 455 (2001). Note that it has been shown both experimentally and theoretically that conduction thresholds decrease significantly as the aspect ratio of the filler particles increases.
16. M. Sahimi, Applications of Percolation Theory (Taylor and Francis, London, 1994). See also D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor and Francis, London, 1994). Observe that for economic and environmental reasons, the achievement of extremely low conduction thresholds is important. At this time the lowest filler volume fraction required for the conduction threshold which has been observed is as low as a few 0.01 vol % for some polymer blends, i.e., P. Dutta, S. Biswas, M. Ghosh, S. K. De, and S. Chatterjee, Synth. Met. 0379-6779 10.1016/S0379-6779(00)00588-9 122, 455 (2001). Note that it has been shown both experimentally and theoretically that conduction thresholds decrease significantly as the aspect ratio of the filler particles increases.
17. M. Sahimi, Applications of Percolation Theory (Taylor and Francis, London, 1994). See also D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor and Francis, London, 1994). Observe that for economic and environmental reasons, the achievement of extremely low conduction thresholds is important. At this time the lowest filler volume fraction required for the conduction threshold which has been observed is as low as a few 0.01 vol % for some polymer blends, i.e., P. Dutta, S. Biswas, M. Ghosh, S. K. De, and S. Chatterjee, Synth. Met. 0379-6779 10.1016/S0379-6779(00)00588-9 122, 455 (2001). Note that it has been shown both experimentally and theoretically that conduction thresholds decrease significantly as the aspect ratio of the filler particles increases.
18. A. K. Jonscher, Dielectric Relaxation in Solids (Chelsea Dielectric, London, 1987), A. K. Jonscher, Universal Relaxation Law (Chelsea Dielectric, London, 1996), and more recently A. K. Jonscher, IEEE Trans. Electr. Insul. 0018-9367 10.1109/14.142701 27, 407 (1992), A. K. Jonscher, J. Phys. D 0022-3727 10.1088/0022-3727/32/14/201 32, R57 (1999).
19. A. K. Jonscher, Dielectric Relaxation in Solids (Chelsea Dielectric, London, 1987), A. K. Jonscher, Universal Relaxation Law (Chelsea Dielectric, London, 1996), and more recently A. K. Jonscher, IEEE Trans. Electr. Insul. 0018-9367 10.1109/14.142701 27, 407 (1992), A. K. Jonscher, J. Phys. D 0022-3727 10.1088/0022-3727/32/14/201 32, R57 (1999).
20. A. K. Jonscher, Dielectric Relaxation in Solids (Chelsea Dielectric, London, 1987), A. K. Jonscher, Universal Relaxation Law (Chelsea Dielectric, London, 1996), and more recently A. K. Jonscher, IEEE Trans. Electr. Insul. 0018-9367 10.1109/14.142701 27, 407 (1992), A. K. Jonscher, J. Phys. D 0022-3727 10.1088/0022-3727/32/14/201 32, R57 (1999).
21. A. K. Jonscher, Dielectric Relaxation in Solids (Chelsea Dielectric, London, 1987), A. K. Jonscher, Universal Relaxation Law (Chelsea Dielectric, London, 1996), and more recently A. K. Jonscher, IEEE Trans. Electr. Insul. 0018-9367 10.1109/14.142701 27, 407 (1992), A. K. Jonscher, J. Phys. D 0022-3727 10.1088/0022-3727/32/14/201 32, R57 (1999).
22. C. Brosseau and P. Talbot, Meas. Sci. Technol. 0957-0233 10.1088/0957-0233/16/9/015 16, 1823 (2005).
23. C. Brosseau, P. Quáffelec, and P. Talbot, J. Appl. Phys. 0021-8979 10.1063/1.1343521 89, 4532 (2001).
24. C. Brosseau, J. Appl. Phys. 0021-8979 10.1063/1.1447307 91, 3197 (2002).
25. C. Brosseau, Ann. Chim. (Paris) 28, 1 (2003).
26. C. Brosseau, F. Boulic, C. Bourbigot, P. Queffelec, Y. Le Mest, J. Loac̈c, and A. Beroual, J. Appl. Phys. 0021-8979 10.1063/1.364173 81, 882 (1997).
27. F. Boulic, C. Brosseau, Y. Le Mest, J. Loac̈c, and F. Carmona, J. Phys. D 0022-3727 10.1088/0022-3727/31/15/020 31, 1904 (1998).
28. C. Brosseau, P. Moliniá, F. Boulic, and F. Carmona, J. Appl. Phys. 0021-8979 10.1063/1.1371938 89, 8297 (2001).
29. J. Baker-Jarvis and P. Kabos, Phys. Rev. E 1063-651X 10.1103/PhysRevE.64. 056127 64, 056127 (2001).
30. R. Kotsilkova, D. Nesheva, I. Nedkov, E. Krusteva, and S. Stavrev, J. Appl. Polym. Sci. 0021-8995 10.1002/app.20240 92, 2220 (2004).
31. Y. Baziard, S. Breton, S. Toutain, and A. Gourdenne, Eur. Polym. J. 0014-3057 10.1016/0014-3057(88)90043-2 24, 521 (1988).
32. T. S. Chow, Mesoscopic Physics of Complex Materials (Springer, New York, 2000).
33. G. A. Niklasson, J. Appl. Phys. 0021-8979 10.1063/1.339355 62, R1 (1987).
34. T. A. Ezquerra, F. Kremer, and G. Wegner, in Dielectric Properties of Heterogeneous Materials, Progress in Electromagnetics Research, edited by, A. Priou, (Elsevier, New York, 1992); T. A. Ezquerra, M. Mohammadi, F. Kremer, T. A. Vilgis, and G. Wegner, J. Phys. C 0022-3719 10.1088/0022-3719/21/5/011 21, 927 (1988); F. Kremer, T. A. Ezquerra, M. Mohammadi, W. Bauhofer, T. A. Vilgis, and G. Wegner, Solid State Commun. 0038-1098 10.1016/0038-1098(88)90801-0 66, 153 (1988); K. L. Ngai and R. W. Rendell, Phys. Rev. B 0163-1829 10.1103/PhysRevB.61.9393 61, 9393 (2000).
35. T. A. Ezquerra, F. Kremer, and G. Wegner, in Dielectric Properties of Heterogeneous Materials, Progress in Electromagnetics Research, edited by, A. Priou, (Elsevier, New York, 1992); T. A. Ezquerra, M. Mohammadi, F. Kremer, T. A. Vilgis, and G. Wegner, J. Phys. C 0022-3719 10.1088/0022-3719/21/5/011 21, 927 (1988); F. Kremer, T. A. Ezquerra, M. Mohammadi, W. Bauhofer, T. A. Vilgis, and G. Wegner, Solid State Commun. 0038-1098 10.1016/0038-1098(88)90801-0 66, 153 (1988); K. L. Ngai and R. W. Rendell, Phys. Rev. B 0163-1829 10.1103/PhysRevB.61.9393 61, 9393 (2000).
36. T. A. Ezquerra, F. Kremer, and G. Wegner, in Dielectric Properties of Heterogeneous Materials, Progress in Electromagnetics Research, edited by, A. Priou, (Elsevier, New York, 1992); T. A. Ezquerra, M. Mohammadi, F. Kremer, T. A. Vilgis, and G. Wegner, J. Phys. C 0022-3719 10.1088/0022-3719/21/5/011 21, 927 (1988); F. Kremer, T. A. Ezquerra, M. Mohammadi, W. Bauhofer, T. A. Vilgis, and G. Wegner, Solid State Commun. 0038-1098 10.1016/0038-1098(88)90801-0 66, 153 (1988); K. L. Ngai and R. W. Rendell, Phys. Rev. B 0163-1829 10.1103/PhysRevB.61.9393 61, 9393 (2000).
37. T. A. Ezquerra, F. Kremer, and G. Wegner, in Dielectric Properties of Heterogeneous Materials, Progress in Electromagnetics Research, edited by, A. Priou, (Elsevier, New York, 1992); T. A. Ezquerra, M. Mohammadi, F. Kremer, T. A. Vilgis, and G. Wegner, J. Phys. C 0022-3719 10.1088/0022-3719/21/5/011 21, 927 (1988); F. Kremer, T. A. Ezquerra, M. Mohammadi, W. Bauhofer, T. A. Vilgis, and G. Wegner, Solid State Commun. 0038-1098 10.1016/0038-1098(88)90801-0 66, 153 (1988); K. L. Ngai and R. W. Rendell, Phys. Rev. B 0163-1829 10.1103/PhysRevB.61.9393 61, 9393 (2000).
38. N. Axelrod, E. Axelrod, A. Gutina, A. Puzenko, P. Ben Ishai, and Yu. Feldman, Meas. Sci. Technol. 0957-0233 10.1088/0957-0233/15/4/020 15, 755 (2004). See also Yu. Feldman, T. Skodvin, and J. Sjoblom, Dielectric Spectroscopy on Colloidal Systems, Encyclopedic Handbook of Emulsion Technology (Dekker, New York, 2001), pp. 109-168.
39. N. Axelrod, E. Axelrod, A. Gutina, A. Puzenko, P. Ben Ishai, and Yu. Feldman, Meas. Sci. Technol. 0957-0233 10.1088/0957-0233/15/4/020 15, 755 (2004). See also Yu. Feldman, T. Skodvin, and J. Sjoblom, Dielectric Spectroscopy on Colloidal Systems, Encyclopedic Handbook of Emulsion Technology (Dekker, New York, 2001), pp. 109-168.
40. I. A. Youngs, J. Phys. D 0022-3727 10.1088/0022-3727/35/23/314 35, 3127 (2002).
41. J. P. Calame, J. Appl. Phys. 0021-8979 10.1063/1.1615302 94, 5945 (2003).
42. Such evidence is well known to experts in specific materials, but this evidence is often overlooked in physical models that claim to explain the microscopic origin of b.
43. C. Brosseau, J. Phys. D 0022-3727 10.1088/0022-3727/39/7/S02 39, 1277 (2006). This paper provides a complete overview of the state-of-art understanding of the dielectric properties of heterostructures up to now.
44. A. H. Sihvola, in Electromagnetic Mixing Formulas and Applications (IEE, London, 1999). See also A. H. Sihvola in Selected Papers on Linear Optical Composite Materials, edited by, A. Lakhtakia, (SPIE Optical Engineering, Bellingham, WA, 1996).
45. A. H. Sihvola, in Electromagnetic Mixing Formulas and Applications (IEE, London, 1999). See also A. H. Sihvola in Selected Papers on Linear Optical Composite Materials, edited by, A. Lakhtakia, (SPIE Optical Engineering, Bellingham, WA, 1996).
46. S. Torquato, Random Heterogeneous Materials: Microstructure and Macroscopic Properties (Springer, New York, 2002).
47. M. Sahimi, Heterogeneous Materials I: Linear Transport and Optical Properties (Springer, New York, 2003).
48. D. S. McLachlan, M. Blaszkiewics, and R. E. Newnham J. Am. Ceram. Soc. 0002-7820 10.1111/j.1151-2916.1990.tb07576.x 73, 2187 (1990). See also J. Wu and D. S. McLachlan, Phys. Rev. B 0163-1829 10.1103/PhysRevB.56.1236 56, 1236 (1997); J. Wu and D. S. McLachlan, Phys. Rev. B 0163-1829 10.1103/PhysRevB.58. 14880 58, 14880 (1998); D. S. McLachlan, W. Heiss, C. Chiteme, and J. Wu, Phys. Rev. B 0163-1829 10.1103/PhysRevB.58.13558 58, 13558 (1998); C. Chiteme and D. S. McLachlan, Phys. Rev. B 0163-1829 10.1103/PhysRevB.67.024206 67, 024206 (2003).
49. D. S. McLachlan, M. Blaszkiewics, and R. E. Newnham J. Am. Ceram. Soc. 0002-7820 10.1111/j.1151-2916.1990.tb07576.x 73, 2187 (1990). See also J. Wu and D. S. McLachlan, Phys. Rev. B 0163-1829 10.1103/PhysRevB.56.1236 56, 1236 (1997); J. Wu and D. S. McLachlan, Phys. Rev. B 0163-1829 10.1103/PhysRevB.58. 14880 58, 14880 (1998); D. S. McLachlan, W. Heiss, C. Chiteme, and J. Wu, Phys. Rev. B 0163-1829 10.1103/PhysRevB.58.13558 58, 13558 (1998); C. Chiteme and D. S. McLachlan, Phys. Rev. B 0163-1829 10.1103/PhysRevB.67.024206 67, 024206 (2003).
50. D. S. McLachlan, M. Blaszkiewics, and R. E. Newnham J. Am. Ceram. Soc. 0002-7820 10.1111/j.1151-2916.1990.tb07576.x 73, 2187 (1990). See also J. Wu and D. S. McLachlan, Phys. Rev. B 0163-1829 10.1103/PhysRevB.56.1236 56, 1236 (1997); J. Wu and D. S. McLachlan, Phys. Rev. B 0163-1829 10.1103/PhysRevB.58. 14880 58, 14880 (1998); D. S. McLachlan, W. Heiss, C. Chiteme, and J. Wu, Phys. Rev. B 0163-1829 10.1103/PhysRevB.58.13558 58, 13558 (1998); C. Chiteme and D. S. McLachlan, Phys. Rev. B 0163-1829 10.1103/PhysRevB.67.024206 67, 024206 (2003).
51. D. S. McLachlan, M. Blaszkiewics, and R. E. Newnham J. Am. Ceram. Soc. 0002-7820 10.1111/j.1151-2916.1990.tb07576.x 73, 2187 (1990). See also J. Wu and D. S. McLachlan, Phys. Rev. B 0163-1829 10.1103/PhysRevB.56.1236 56, 1236 (1997); J. Wu and D. S. McLachlan, Phys. Rev. B 0163-1829 10.1103/PhysRevB.58. 14880 58, 14880 (1998); D. S. McLachlan, W. Heiss, C. Chiteme, and J. Wu, Phys. Rev. B 0163-1829 10.1103/PhysRevB.58.13558 58, 13558 (1998); C. Chiteme and D. S. McLachlan, Phys. Rev. B 0163-1829 10.1103/PhysRevB.67.024206 67, 024206 (2003).
52. D. S. McLachlan, M. Blaszkiewics, and R. E. Newnham J. Am. Ceram. Soc. 0002-7820 10.1111/j.1151-2916.1990.tb07576.x 73, 2187 (1990). See also J. Wu and D. S. McLachlan, Phys. Rev. B 0163-1829 10.1103/PhysRevB.56.1236 56, 1236 (1997); J. Wu and D. S. McLachlan, Phys. Rev. B 0163-1829 10.1103/PhysRevB.58. 14880 58, 14880 (1998); D. S. McLachlan, W. Heiss, C. Chiteme, and J. Wu, Phys. Rev. B 0163-1829 10.1103/PhysRevB.58.13558 58, 13558 (1998); C. Chiteme and D. S. McLachlan, Phys. Rev. B 0163-1829 10.1103/PhysRevB.67.024206 67, 024206 (2003).
53. A. V. Osipov, K. N. Rozanov, N. A. Simonov, and S. N. Starostenko, J. Phys. Condens. Matter 0953-8984 10.1088/0953-8984/14/41/308 14, 9507 (2002).
54. A. J. Stoyanov, B. F. Howell, E. C. Fischer, H. Überall, and K. Chouffani J. Appl. Phys. 0021-8979 10.1063/1.371175 86, 3110 (1999). See also the recent sequel of the earlier mentioned article, A. J. Stoyanov, E. C. Fisher, and H. Überall, J. Appl. Phys. 0021-8979 10.1063/1.1352683 89, 4486 (2001).
55. A. J. Stoyanov, B. F. Howell, E. C. Fischer, H. Überall, and K. Chouffani J. Appl. Phys. 0021-8979 10.1063/1.371175 86, 3110 (1999). See also the recent sequel of the earlier mentioned article, A. J. Stoyanov, E. C. Fisher, and H. Überall, J. Appl. Phys. 0021-8979 10.1063/1.1352683 89, 4486 (2001).
56. D. K. Hale, J. Mater. Sci. 0022-2461 10.1007/BF02403361 11, 2105 (1976). See also G. Heinrich, E. Straube, and G. Helmis, Adv. Polym. Sci. 85, 33 (1988).
57. D. K. Hale, J. Mater. Sci. 0022-2461 10.1007/BF02403361 11, 2105 (1976). See also G. Heinrich, E. Straube, and G. Helmis, Adv. Polym. Sci. 85, 33 (1988).
58. See, e.g., J. D. Ferry, Viscoelastic Properties of Polymers, 3rd ed. (Wiley, New York, 1980).
59. B. Erman and J. E. Mark, Structures and Properties of Rubberlike Networks (Oxford University Press, New York, 1997). B. Erman and J. E. Mark, The interested reader may also consult Polymer Networks: Principle of Their Formation, Structure and Properties, edited by, R. F. T. Stepto, (Blackie Academic & Professional, London, 1998); J. S. Bergström and M. C. Boyce, Rubber Chem. Technol. 72, 633 (1999) 0167-6636; J. S. Bergström and M. C. Boyce, Mech. Mater. 0167-6636 10.1016/S0167-6636(00)00028-4 32, 627 (2000); L. R. G. Treloar, The Physics of Rubber Elasticity (Oxford University Press, London, 1967); E. M. Arruda and M. C. Boyce, J. Mech. Phys. Solids 0022-5096 10.1016/0022-5096(93)90013-6 41, 389 (1993).
60. B. Erman and J. E. Mark, Structures and Properties of Rubberlike Networks (Oxford University Press, New York, 1997). B. Erman and J. E. Mark, The interested reader may also consult Polymer Networks: Principle of Their Formation, Structure and Properties, edited by, R. F. T. Stepto, (Blackie Academic & Professional, London, 1998); J. S. Bergström and M. C. Boyce, Rubber Chem. Technol. 72, 633 (1999) 0167-6636; J. S. Bergström and M. C. Boyce, Mech. Mater. 0167-6636 10.1016/S0167-6636(00)00028-4 32, 627 (2000); L. R. G. Treloar, The Physics of Rubber Elasticity (Oxford University Press, London, 1967); E. M. Arruda and M. C. Boyce, J. Mech. Phys. Solids 0022-5096 10.1016/0022-5096(93)90013-6 41, 389 (1993).
61. B. Erman and J. E. Mark, Structures and Properties of Rubberlike Networks (Oxford University Press, New York, 1997). B. Erman and J. E. Mark, The interested reader may also consult Polymer Networks: Principle of Their Formation, Structure and Properties, edited by, R. F. T. Stepto, (Blackie Academic & Professional, London, 1998); J. S. Bergström and M. C. Boyce, Rubber Chem. Technol. 72, 633 (1999) 0167-6636; J. S. Bergström and M. C. Boyce, Mech. Mater. 0167-6636 10.1016/S0167-6636(00)00028-4 32, 627 (2000); L. R. G. Treloar, The Physics of Rubber Elasticity (Oxford University Press, London, 1967); E. M. Arruda and M. C. Boyce, J. Mech. Phys. Solids 0022-5096 10.1016/0022-5096(93)90013-6 41, 389 (1993).
62. B. Erman and J. E. Mark, Structures and Properties of Rubberlike Networks (Oxford University Press, New York, 1997). B. Erman and J. E. Mark, The interested reader may also consult Polymer Networks: Principle of Their Formation, Structure and Properties, edited by, R. F. T. Stepto, (Blackie Academic & Professional, London, 1998); J. S. Bergström and M. C. Boyce, Rubber Chem. Technol. 72, 633 (1999) 0167-6636; J. S. Bergström and M. C. Boyce, Mech. Mater. 0167-6636 10.1016/S0167-6636(00)00028-4 32, 627 (2000); L. R. G. Treloar, The Physics of Rubber Elasticity (Oxford University Press, London, 1967); E. M. Arruda and M. C. Boyce, J. Mech. Phys. Solids 0022-5096 10.1016/0022-5096(93)90013-6 41, 389 (1993).
63. B. Erman and J. E. Mark, Structures and Properties of Rubberlike Networks (Oxford University Press, New York, 1997). B. Erman and J. E. Mark, The interested reader may also consult Polymer Networks: Principle of Their Formation, Structure and Properties, edited by, R. F. T. Stepto, (Blackie Academic & Professional, London, 1998); J. S. Bergström and M. C. Boyce, Rubber Chem. Technol. 72, 633 (1999) 0167-6636; J. S. Bergström and M. C. Boyce, Mech. Mater. 0167-6636 10.1016/S0167-6636(00)00028-4 32, 627 (2000); L. R. G. Treloar, The Physics of Rubber Elasticity (Oxford University Press, London, 1967); E. M. Arruda and M. C. Boyce, J. Mech. Phys. Solids 0022-5096 10.1016/0022-5096(93)90013-6 41, 389 (1993).
64. B. Erman and J. E. Mark, Structures and Properties of Rubberlike Networks (Oxford University Press, New York, 1997). B. Erman and J. E. Mark, The interested reader may also consult Polymer Networks: Principle of Their Formation, Structure and Properties, edited by, R. F. T. Stepto, (Blackie Academic & Professional, London, 1998); J. S. Bergström and M. C. Boyce, Rubber Chem. Technol. 72, 633 (1999) 0167-6636; J. S. Bergström and M. C. Boyce, Mech. Mater. 0167-6636 10.1016/S0167-6636(00)00028-4 32, 627 (2000); L. R. G. Treloar, The Physics of Rubber Elasticity (Oxford University Press, London, 1967); E. M. Arruda and M. C. Boyce, J. Mech. Phys. Solids 0022-5096 10.1016/0022-5096(93)90013-6 41, 389 (1993).
65. S. R. Elliott, Adv. Phys. 0001-8732 10.1080/00018738700101971 36, 135 (1987).
66. A. Voet, A. Sircar, and T. J. Mullens, Rubber Chem. Technol. 42, 874 (1969).
67. J. Kost, M. Narkis, and A. Foux, Polym. Eng. Sci. 0032-3888 10.1002/pen.760231007 23, 567 (1983).
68. V. G. Shevchenko, A. T. Ponomarenko, and C. Klason, Smart Mater. Struct. 4, 31 (1995).
69. L. Flandin, A. Hiltner, and E. Baer, Polymer 42, 827 (2001). 0021-8995 See also L. Flandin, A. Chang, S. Nazarenko, A. Hiltner, and E. Baer, J. Appl. Polym. Sci. 76, 894 (2000).
70. L. Flandin, A. Hiltner, and E. Baer, Polymer 42, 827 (2001). 0021-8995 See also L. Flandin, A. Chang, S. Nazarenko, A. Hiltner, and E. Baer, J. Appl. Polym. Sci. 76, 894 (2000).
71. S. Wen, S. Wang, and D. D. L. Chung, J. Mater. Sci. 35, 3669 (2000). 0022-2461
72. M. Pelisková, J. Vilcáková, M. Omastová, P. Sáha, C. Li, and O. Quadrat, Smart Mater. Struct. 14, 949 (2005).
73. M. S. Ozmusul and R. C. Picu, Polym. Compos. 0272-8397 10.1002/pc.10417 23, 110 (2002); J. Qu and C. P. Wong IEEE Trans. Compon. Packag. Technol. 1521-3331 10.1109/6144.991175 25, 53 (2002); H. Vo and F. G. Shi, Microelectron. J. 0026-2692 10.1016/S0026-2692(02)00010-1 33, 409 (2002); M. Todd and F. G. Shi, Microelectron. J. 0026-2692 10.1016/S0026-2692(02)00038-1 33, 627 (2002); H. Vo, M. Todd, F. Shi, A. Shapiro, and M. Edwards, Microelectron. J. 0026-2692 10.1016/S0026-2692(00)00152-X 32, 331 (2001); M. G. Todd and F. G. Shi, J. Appl. Phys. 94, 4551 (2003).
74. M. S. Ozmusul and R. C. Picu, Polym. Compos. 0272-8397 10.1002/pc.10417 23, 110 (2002); J. Qu and C. P. Wong IEEE Trans. Compon. Packag. Technol. 1521-3331 10.1109/6144.991175 25, 53 (2002); H. Vo and F. G. Shi, Microelectron. J. 0026-2692 10.1016/S0026-2692(02)00010-1 33, 409 (2002); M. Todd and F. G. Shi, Microelectron. J. 0026-2692 10.1016/S0026-2692(02)00038-1 33, 627 (2002); H. Vo, M. Todd, F. Shi, A. Shapiro, and M. Edwards, Microelectron. J. 0026-2692 10.1016/S0026-2692(00)00152-X 32, 331 (2001); M. G. Todd and F. G. Shi, J. Appl. Phys. 94, 4551 (2003).
75. M. S. Ozmusul and R. C. Picu, Polym. Compos. 0272-8397 10.1002/pc.10417 23, 110 (2002); J. Qu and C. P. Wong IEEE Trans. Compon. Packag. Technol. 1521-3331 10.1109/6144.991175 25, 53 (2002); H. Vo and F. G. Shi, Microelectron. J. 0026-2692 10.1016/S0026-2692(02)00010-1 33, 409 (2002); M. Todd and F. G. Shi, Microelectron. J. 0026-2692 10.1016/S0026-2692(02)00038-1 33, 627 (2002); H. Vo, M. Todd, F. Shi, A. Shapiro, and M. Edwards, Microelectron. J. 0026-2692 10.1016/S0026-2692(00)00152-X 32, 331 (2001); M. G. Todd and F. G. Shi, J. Appl. Phys. 94, 4551 (2003).
76. M. S. Ozmusul and R. C. Picu, Polym. Compos. 0272-8397 10.1002/pc.10417 23, 110 (2002); J. Qu and C. P. Wong IEEE Trans. Compon. Packag. Technol. 1521-3331 10.1109/6144.991175 25, 53 (2002); H. Vo and F. G. Shi, Microelectron. J. 0026-2692 10.1016/S0026-2692(02)00010-1 33, 409 (2002); M. Todd and F. G. Shi, Microelectron. J. 0026-2692 10.1016/S0026-2692(02)00038-1 33, 627 (2002); H. Vo, M. Todd, F. Shi, A. Shapiro, and M. Edwards, Microelectron. J. 0026-2692 10.1016/S0026-2692(00)00152-X 32, 331 (2001); M. G. Todd and F. G. Shi, J. Appl. Phys. 94, 4551 (2003).
77. M. S. Ozmusul and R. C. Picu, Polym. Compos. 0272-8397 10.1002/pc.10417 23, 110 (2002); J. Qu and C. P. Wong IEEE Trans. Compon. Packag. Technol. 1521-3331 10.1109/6144.991175 25, 53 (2002); H. Vo and F. G. Shi, Microelectron. J. 0026-2692 10.1016/S0026-2692(02)00010-1 33, 409 (2002); M. Todd and F. G. Shi, Microelectron. J. 0026-2692 10.1016/S0026-2692(02)00038-1 33, 627 (2002); H. Vo, M. Todd, F. Shi, A. Shapiro, and M. Edwards, Microelectron. J. 0026-2692 10.1016/S0026-2692(00)00152-X 32, 331 (2001); M. G. Todd and F. G. Shi, J. Appl. Phys. 94, 4551 (2003).
78. M. S. Ozmusul and R. C. Picu, Polym. Compos. 0272-8397 10.1002/pc.10417 23, 110 (2002); J. Qu and C. P. Wong IEEE Trans. Compon. Packag. Technol. 1521-3331 10.1109/6144.991175 25, 53 (2002); H. Vo and F. G. Shi, Microelectron. J. 0026-2692 10.1016/S0026-2692(02)00010-1 33, 409 (2002); M. Todd and F. G. Shi, Microelectron. J. 0026-2692 10.1016/S0026-2692(02)00038-1 33, 627 (2002); H. Vo, M. Todd, F. Shi, A. Shapiro, and M. Edwards, Microelectron. J. 0026-2692 10.1016/S0026-2692(00)00152-X 32, 331 (2001); M. G. Todd and F. G. Shi, J. Appl. Phys. 94, 4551 (2003).
79. R. C. Ball, M. Doi, S. F. Edwards, and M. Warner, Polymer 0032-3861 10.1016/0032-3861(81)90284-6 22, 1010 (1981); S. F. Edwards and T. Vilgis, Polymer 0032-3861 10.1016/0032-3861(86)90231-4 27, 483 (1986); P. Thirion and T. Weil, Polymer 25, 609 (1984); S. F. Edwards, in Polymer Networks, edited by, A. J. Chrompff, and, S. Newman, (Plenum, New York, 1971).
80. R. C. Ball, M. Doi, S. F. Edwards, and M. Warner, Polymer 0032-3861 10.1016/0032-3861(81)90284-6 22, 1010 (1981); S. F. Edwards and T. Vilgis, Polymer 0032-3861 10.1016/0032-3861(86)90231-4 27, 483 (1986); P. Thirion and T. Weil, Polymer 25, 609 (1984); S. F. Edwards, in Polymer Networks, edited by, A. J. Chrompff, and, S. Newman, (Plenum, New York, 1971).
81. R. C. Ball, M. Doi, S. F. Edwards, and M. Warner, Polymer 0032-3861 10.1016/0032-3861(81)90284-6 22, 1010 (1981); S. F. Edwards and T. Vilgis, Polymer 0032-3861 10.1016/0032-3861(86)90231-4 27, 483 (1986); P. Thirion and T. Weil, Polymer 25, 609 (1984); S. F. Edwards, in Polymer Networks, edited by, A. J. Chrompff, and, S. Newman, (Plenum, New York, 1971).
82. R. C. Ball, M. Doi, S. F. Edwards, and M. Warner, Polymer 0032-3861 10.1016/0032-3861(81)90284-6 22, 1010 (1981); S. F. Edwards and T. Vilgis, Polymer 0032-3861 10.1016/0032-3861(86)90231-4 27, 483 (1986); P. Thirion and T. Weil, Polymer 25, 609 (1984); S. F. Edwards, in Polymer Networks, edited by, A. J. Chrompff, and, S. Newman, (Plenum, New York, 1971).
83. T. J. Lewis, IEEE Trans. Dielectr. Electr. Insul. 1070-9878 10.1109/94.326653 1, 812 (1994).
84. D. Bloor, K. Donnelly, P. J. Hands, P. Laughlin, and D. Lussey, J. Phys. D 0022-3727 10.1088/0022-3727/38/16/018 38, 2851 (2005).
85. J. E. Martin, R. A. Anderson, J. Odinek, D. Adolf, and J. Williamson, Phys. Rev. B 0163-1829 10.1103/PhysRevB.67.094207 67, 094207 (2003).
86. M. Taya, W. J. Kim, and K. Ono, Mech. Mater. 28, 53 (1998). 0167-6636
87. E. Tuncer, M. Wegener, and R. Gerhard-Multhaupt, J. Electrost. 0304-3886 10.1016/j.elstat.2004.06.002 63, 21 (2005); R. Gerhard-Multhaupt, Phys. Rev. B 0163-1829 10.1103/PhysRevB.27.2494 27, 2494 (1983).
88. E. Tuncer, M. Wegener, and R. Gerhard-Multhaupt, J. Electrost. 0304-3886 10.1016/j.elstat.2004.06.002 63, 21 (2005); R. Gerhard-Multhaupt, Phys. Rev. B 0163-1829 10.1103/PhysRevB.27.2494 27, 2494 (1983).
89. G. R. Strobl, The Physics of Polymers, 2nd ed. (Springer, Berlin, 1996).
90. The understanding of viscoelastic properties of traditional polymer filled systems in terms of simple contributions has traditionally demanded the development of empirical relationships and theoretical models. One of the earliest models developed to describe the strength of filled polymers is that due to Guth and Gold, and later by Guth, i.e., E. Guth and O. Gold, Phys. Rev. 0031-899X 53, 322 (1938); E. Guth, J. Appl. Phys. 0021-8979 10.1063/1.1707495 16, 20 (1945); E. Guth, J. Appl. Phys. 0021-8979 16, 21 (1951). This model is based on an expression due to Einstein relating the viscosity of a fluid containing a dilute mixture of solid spheres to their volume fraction. The derivation assumed that the polymer was perfectly bonded to the surfaces of the spherical particles and that the average distance between the particles was large enough so that the stress fields around each particle did not influence one another. Moreover, it was assumed that the enhancement to the modulus was independent of the type of filler particle considered. For a review examining variations of this theory, the interested reader is referred to S. Ahmed and F. R. Jones, J. Mater. Sci. 25, 4933 (1990) and to the book by Erman and Mark (see Ref.).
91. The understanding of viscoelastic properties of traditional polymer filled systems in terms of simple contributions has traditionally demanded the development of empirical relationships and theoretical models. One of the earliest models developed to describe the strength of filled polymers is that due to Guth and Gold, and later by Guth, i.e., E. Guth and O. Gold, Phys. Rev. 0031-899X 53, 322 (1938); E. Guth, J. Appl. Phys. 0021-8979 10.1063/1.1707495 16, 20 (1945); E. Guth, J. Appl. Phys. 0021-8979 16, 21 (1951). This model is based on an expression due to Einstein relating the viscosity of a fluid containing a dilute mixture of solid spheres to their volume fraction. The derivation assumed that the polymer was perfectly bonded to the surfaces of the spherical particles and that the average distance between the particles was large enough so that the stress fields around each particle did not influence one another. Moreover, it was assumed that the enhancement to the modulus was independent of the type of filler particle considered. For a review examining variations of this theory, the interested reader is referred to S. Ahmed and F. R. Jones, J. Mater. Sci. 25, 4933 (1990) and to the book by Erman and Mark (see Ref.).
92. The understanding of viscoelastic properties of traditional polymer filled systems in terms of simple contributions has traditionally demanded the development of empirical relationships and theoretical models. One of the earliest models developed to describe the strength of filled polymers is that due to Guth and Gold, and later by Guth, i.e., E. Guth and O. Gold, Phys. Rev. 0031-899X 53, 322 (1938); E. Guth, J. Appl. Phys. 0021-8979 10.1063/1.1707495 16, 20 (1945); E. Guth, J. Appl. Phys. 0021-8979 16, 21 (1951). This model is based on an expression due to Einstein relating the viscosity of a fluid containing a dilute mixture of solid spheres to their volume fraction. The derivation assumed that the polymer was perfectly bonded to the surfaces of the spherical particles and that the average distance between the particles was large enough so that the stress fields around each particle did not influence one another. Moreover, it was assumed that the enhancement to the modulus was independent of the type of filler particle considered. For a review examining variations of this theory, the interested reader is referred to S. Ahmed and F. R. Jones, J. Mater. Sci. 25, 4933 (1990) and to the book by Erman and Mark (see Ref.).
93. The understanding of viscoelastic properties of traditional polymer filled systems in terms of simple contributions has traditionally demanded the development of empirical relationships and theoretical models. One of the earliest models developed to describe the strength of filled polymers is that due to Guth and Gold, and later by Guth, i.e., E. Guth and O. Gold, Phys. Rev. 0031-899X 53, 322 (1938); E. Guth, J. Appl. Phys. 0021-8979 10.1063/1.1707495 16, 20 (1945); E. Guth, J. Appl. Phys. 0021-8979 16, 21 (1951). This model is based on an expression due to Einstein relating the viscosity of a fluid containing a dilute mixture of solid spheres to their volume fraction. The derivation assumed that the polymer was perfectly bonded to the surfaces of the spherical particles and that the average distance between the particles was large enough so that the stress fields around each particle did not influence one another. Moreover, it was assumed that the enhancement to the modulus was independent of the type of filler particle considered. For a review examining variations of this theory, the interested reader is referred to S. Ahmed and F. R. Jones, J. Mater. Sci. 25, 4933 (1990) and to the book by Erman and Mark (see Ref.).
94. D. K. Das-Gupta, IEEE Electr. Insul. Mag. (USA) 0883-7554 10.1109/57.285418 10, 5 (1994).
95. A. T. Ponomarenko, V. G. Shevchenko, and N. S. Enikolopyan, Adv. Polym. Sci. 96, 125 (1990).
96. J. Ravier, F. Houze, F. Carmona, O. Schneegans, and H. Saadaoui, Carbon 0008-6223 10.1016/S0008-6223(00)00242-6 39, 314 (2001); F. Houzá, R. Meyer, O. Schneegans, and L. Boyer, Appl. Phys. Lett. 0003-6951 10.1063/1.117179 69, 1975 (1996); F. Carmona and J. Ravier, Physica B (Amsterdam) 338, 247 (2003). 0921-4526
97. J. Ravier, F. Houze, F. Carmona, O. Schneegans, and H. Saadaoui, Carbon 0008-6223 10.1016/S0008-6223(00)00242-6 39, 314 (2001); F. Houzá, R. Meyer, O. Schneegans, and L. Boyer, Appl. Phys. Lett. 0003-6951 10.1063/1.117179 69, 1975 (1996); F. Carmona and J. Ravier, Physica B (Amsterdam) 338, 247 (2003). 0921-4526
98. J. Ravier, F. Houze, F. Carmona, O. Schneegans, and H. Saadaoui, Carbon 0008-6223 10.1016/S0008-6223(00)00242-6 39, 314 (2001); F. Houzá, R. Meyer, O. Schneegans, and L. Boyer, Appl. Phys. Lett. 0003-6951 10.1063/1.117179 69, 1975 (1996); F. Carmona and J. Ravier, Physica B (Amsterdam) 338, 247 (2003). 0921-4526
99. C. Grimaldi, T. Maeder, P. Ryser, and S. Strässler, Phys. Rev. B 0163-1829 10.1103/PhysRevB.67.014205 67, 014205 (2003).
100. T. Tanaka, M. Sato, and M. Kozako, in 2004 Annual Report Conference on Electrical Insulation and Dielectric Phenomena., CEIDP, 2004, p. 310.
101. Q. Zhang and L. A. Archer, Langmuir 0743-7463 10.1021/la026338j 18, 10435 (2002).
102. J. Zebrowski, V. Prasad, W. Zhang, L. M. Walker, and D. A. Weitz, Colloids Surf., A 213, 189 (2003).
103. H. A. Baghdadi, H. Sardinha, and S. R. Bhatia, J. Polym. Sci., Part B: Polym. Phys. 0887-6266 10.1002/polb.20317 43, 233 (2005).
104. M. Surve, V. Pryamitsyn, and V. Ganesan, J. Chem. Phys. 0021-9606 10.1063/1.2241150 125, 064903 (2006).
105. B. J. Ash, D. F. Rogers, C. J. Wiegand, L. S. Schadler, R. W. Siegel, B. C. Benicewicz, and T. Apple, Polym. Compos. 0272-8397 10.1002/pc.10497 23, 1014 (2002). See also B. J. Ash, L. S. Schadler, and R. W. Siegel, Mater. Lett. 0167-577X 10.1016/S0167-577X(01)00626-7 55, 83 (2002).
106. B. J. Ash, D. F. Rogers, C. J. Wiegand, L. S. Schadler, R. W. Siegel, B. C. Benicewicz, and T. Apple, Polym. Compos. 0272-8397 10.1002/pc.10497 23, 1014 (2002). See also B. J. Ash, L. S. Schadler, and R. W. Siegel, Mater. Lett. 0167-577X 10.1016/S0167-577X(01)00626-7 55, 83 (2002).
107. M. S. Dresselhaus, Nature (London) 0028-0836 10.1038/358195a0 358, 195 (1992). See also M. Dresselhaus, G. Dresselhaus, P. Eklund, and R. Saito, Phys. World 11 (1), 33 (1998).
108. M. S. Dresselhaus, Nature (London) 0028-0836 10.1038/358195a0 358, 195 (1992). See also M. Dresselhaus, G. Dresselhaus, P. Eklund, and R. Saito, Phys. World 11 (1), 33 (1998).
109. S. Iijima, Nature (London) 0028-0836 10.1038/354056a0 354, 56 (1991).
110. P. M. Ajayan, O. Stephan, C. Colliex, and D. Trauth, Science 0036-8075 10.1126/science.265.5176.1212 265, 1212 (1994).
111. M. A. Burns, B. N. Johnson, S. N. Brahmasandra, K. Handique, J. R. Webster, D. Heldsinger, C. H. Mastrangelo, and D. T. Burke, Science 0036-8075 10.1126/science.282.5388.484 282, 484 (1998).
112. Y. Saito and M. Masuda, Jpn. J. Appl. Phys., Part 1 0021-4922 10.1143/JJAP.34.5594 34, 5594 (1995). See also N. Grobert, Appl. Phys. Lett. 0003-6951 10.1063/1.125352 75, 3363 (1999); J. Bao, Q. Zhou, J. Hong, and Z. Xu, Appl. Phys. Lett. 0003-6951 10.1063/1.1526461 81, 4592 (2002); S. Karmakar, S. M. Sharma, M. D. Mukadam, S. M. Yusuf, and A. K. Sood, J. Appl. Phys. 0021-8979 10.1063/1.1858878 97, 054306 (2005).
113. Y. Saito and M. Masuda, Jpn. J. Appl. Phys., Part 1 0021-4922 10.1143/JJAP.34.5594 34, 5594 (1995). See also N. Grobert, Appl. Phys. Lett. 0003-6951 10.1063/1.125352 75, 3363 (1999); J. Bao, Q. Zhou, J. Hong, and Z. Xu, Appl. Phys. Lett. 0003-6951 10.1063/1.1526461 81, 4592 (2002); S. Karmakar, S. M. Sharma, M. D. Mukadam, S. M. Yusuf, and A. K. Sood, J. Appl. Phys. 0021-8979 10.1063/1.1858878 97, 054306 (2005).
114. Y. Saito and M. Masuda, Jpn. J. Appl. Phys., Part 1 0021-4922 10.1143/JJAP.34.5594 34, 5594 (1995). See also N. Grobert, Appl. Phys. Lett. 0003-6951 10.1063/1.125352 75, 3363 (1999); J. Bao, Q. Zhou, J. Hong, and Z. Xu, Appl. Phys. Lett. 0003-6951 10.1063/1.1526461 81, 4592 (2002); S. Karmakar, S. M. Sharma, M. D. Mukadam, S. M. Yusuf, and A. K. Sood, J. Appl. Phys. 0021-8979 10.1063/1.1858878 97, 054306 (2005).
115. Y. Saito and M. Masuda, Jpn. J. Appl. Phys., Part 1 0021-4922 10.1143/JJAP.34.5594 34, 5594 (1995). See also N. Grobert, Appl. Phys. Lett. 0003-6951 10.1063/1.125352 75, 3363 (1999); J. Bao, Q. Zhou, J. Hong, and Z. Xu, Appl. Phys. Lett. 0003-6951 10.1063/1.1526461 81, 4592 (2002); S. Karmakar, S. M. Sharma, M. D. Mukadam, S. M. Yusuf, and A. K. Sood, J. Appl. Phys. 0021-8979 10.1063/1.1858878 97, 054306 (2005).
116. See, e.g., P. Poetschke, Fullerenes, Nanotubes, Carbon Nanostruct. 13, 211 (2005).