Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T15:40:47.053Z Has data issue: false hasContentIssue false

Length scales of interactions in magnetic, dielectric, and mechanical nanocomposites

Published online by Cambridge University Press:  18 May 2011

R. Skomski
Affiliation:
Department of Physics and Astronomy and Center for Materials Research and Analysis, University of Nebraska, Lincoln, NE 68588
B. Balamurugan
Affiliation:
Department of Physics and Astronomy and Center for Materials Research and Analysis, University of Nebraska, Lincoln, NE 68588
E. Schubert*
Affiliation:
Department of Physics and Astronomy and Center for Materials Research and Analysis, University of Nebraska, Lincoln, NE 68588
A. Enders
Affiliation:
Department of Physics and Astronomy and Center for Materials Research and Analysis, University of Nebraska, Lincoln, NE 68588
D. J. Sellmyer
Affiliation:
Department of Physics and Astronomy and Center for Materials Research and Analysis, University of Nebraska, Lincoln, NE 68588
*
*Department of Electrical Engineering, University of Nebraska, Lincoln, Nebraska
Get access

Abstract

It is investigated how figures of merits of nanocomposites are affected by structural and interaction length scales. Aside from macroscopic effects without characteristic lengths scales and atomic-scale quantum-mechanical interactions there are nanoscale interactions that reflect a competition between different energy contributions. We consider three systems, namely dielectric media, carbon-black reinforced rubbers and magnetic composites. In all cases, it is relatively easy to determine effective materials constants, which do not involve specific length scales. Nucleation and breakdown phenomena tend to occur on a nanoscale and yield a logarithmic dependence of figures of merit on the macroscopic system size. Essential system-specific differences arise because figures of merits are generally nonlinear energy integrals. Furthermore, different physical interactions yield different length scales. For example, the interaction in magnetic hard-soft composites reflects the competition between relativistic anisotropy and nonrelativistic exchange interactions, but such hierarchies of interactions are more difficult to establish in mechanical polymer composites and dielectrics.

Type
Research Article
Copyright
Copyright © Materials Research Society 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] Bruggeman, D. A. G., Ann. Phys. (5) 24 (1935) 637.Google Scholar
[2] Christensen, R. M., Mechanics of Composite Materials, Wiley, New York 1979.Google Scholar
[3] Verdier, C., J. Theor. Med. 5 (2003) 67.Google Scholar
[4] Skomski, R., J. Phys.: Condens. Matter 15 (2003) R841.Google Scholar
[5] Chipara, A., Hul, D., Sankar, J., Leslie-Pelecky, D., Bender, A., Yue, L., Skomski, R., and Sellmyer, D. J., Composites B: Engineering 35 (2004) 235.Google Scholar
[6] Chipara, M., Skomski, R., Sellmyer, D. J., Mater. Lett. 61 (2007) 2412.Google Scholar
[7] Ali, N., Chipara, M., Balascuta, S., Skomski, R., and Sellmyer, D. J., J. Nanosci. Nanotechnol. 9 (2009) 4437.Google Scholar
[8] Garnett, J. C. M., Philos. Trans. R. Soc. (London) A 203 (1904) 385.Google Scholar
[9] Skomski, R. and Coey, J. M. D., Phys. Rev. B 48 (1993) 15812.Google Scholar
[10] Hashin, Z. and Shtrikman, S., J. Appl. Phys. 33 (1962) 3125.Google Scholar
[11] Erman, B. and Mark, J. E., Structures and Properties of Rubberlike Networks, Oxford University Press, Oxford 1997.Google Scholar
[12] Dewey, J. M., J. Appl. Phys. 18 (1947) 578.Google Scholar
[13] Schmidt, D., Kjerstad, A. C., Hofmann, T., Skomski, R., Schubert, E., and Schubert, M., J. Appl. Phys. 105 (2009) 113508.Google Scholar
[14] Chakrabarti, B. K. and Benguigui, L. G., Statistical Physics of Fracture and Breakdown in Disordered Systems, University Press, Oxford 1997.Google Scholar
[15] Skomski, R., Li, J.-Y., Zhou, J., and Sellmyer, D. J., in: Materials for Space Applications, Eds. Chipara, M., Edwards, D. L., Benson, R. S., Phillips, S., Mater. Res. Soc. Symp. Proc. 851 (2005) NN1.7.Google Scholar
[16] Polder, D. and van Santen, J. H., Physica 12 (1946) 257.Google Scholar
[17] Kärkkäinen, K. K., Sihvola, A. H., and Nikoskinen, K. I., IEEE Trans. Geosci. and Remote Sensing 38 (2000) 1303.Google Scholar
[18] Velický, B., Kirkpatrick, S., and Ehrenreich, H., Phys. Rev. 175 (1968) 747 .Google Scholar
[19] Kirkpatrick, S., Phys. Rev. Lett. 27 (1971) 1722.Google Scholar
[20] Choy, T. C., Effective Medium Theory, University Press, Oxford 1999.Google Scholar
[21] Doyle, W. T., J. Appl. Phys. 85 (1999) 2323.Google Scholar
[22] Skomski, R. and Coey, J. M. D., Permanent Magnetism, Institute of Physics, Bristol 1999.Google Scholar
[23] Skomski, R., Simple Models of Magnetism, University Press, Oxford (2008).Google Scholar
[24] Hashin, Z., J. Appl. Mech. 29 (1962) 143.Google Scholar
[25] Li, J. Y., Zhang, L., and Ducharme, S., Appl. Phys. Lett. 90 (2007) 132901.Google Scholar
[26] Levy, O. and Stroud, D., Phys. Rev. B 56 (1997) 8035.Google Scholar
[27] Ward, I. M. and Hadley, D. W., Mechanical Properties of Solid Polymers, Wiley, New York 1993.Google Scholar
[28] Banerjee, P., Perez, I., Henn-Lecordier, L., Lee, S. B., and Rubloff, G. W., Nature Nanotechnology 4 (2009) 292.Google Scholar
[29] Lakhtakia, A., Michel, B., and Weiglhofer, W. S., J. Phys. D: Appl. Phys. 30 (1997) 230.Google Scholar
[30] Osborn, J. A., Phys. Rev. 67 (1945) 351.Google Scholar
[31] Yeomans, J. M., Statistical Mechanics of Phase Transitions, University Press, Oxford 1992.Google Scholar
[32] Chow, T. S., Mesoscopic Physics of Complex Materials, Springer, Berlin 2000.Google Scholar
[33] Einstein, A., Ann. Phys. 19, 289 (1906); Erratum: 34 (1911) 591.Google Scholar
[34] Skomski, R., Theory of Elasticity of Filled Polymer Networks, THLM Leuna-Merseburg (Diplomarbeit, unpublished, 1986).Google Scholar
[35] Duxbury, P. M., Beale, P. D., Bak, H. and Schroedert, P. A., J. Phys. D: 23 (1990) 1546.Google Scholar
[36] Dang, Zh.-M., Lin, Y.-H., and Nan, C.-W., Adv. Mater. 15 (2003) 1625.Google Scholar
[37] Kim, J.-H., Lee, Y.-W., Kim, M. G., Souchkov, A., Lee, J. S., Drew, H. D., Oh, S.-J., Nan, C. W., and Choi, E. J., Phys. Rev. B 70 (2004) 172106.Google Scholar
[38] Murphy, G., Advanced Mechanics of Materials, McGraw-Hill, New York 1946.Google Scholar
[39] Alper, H. E. and Levy, R. M., J. Phys. Chem. 94 (1990) 8401.Google Scholar
[40] Skomski, R., J. Magn. Magn. Mater. 272276 (2004) 1476.Google Scholar
[41] Coehoorn, R., de Mooij, D.B., and de Waard, C., J. Magn. Magn. Mater. 80 (1989) 101.Google Scholar
[42] Skomski, R., Oepen, H.-P., and Kirschner, J., Phys. Rev. B 58 (1998) 3223.Google Scholar
[43] Skomski, R. and Sellmyer, D. J., J. Appl. Phys. 87 (2000) 4756.Google Scholar
[44] Botti, A., Pyckhout-Hintzena, W., Richter, D., Urban, V., and Straube, E. J. Chem. Phys. 124, 174908 (2006).Google Scholar
[45] Straube, E., Urban, V., Pyckhout-Hintzen, W., Richter, D., and Glinka, C. J., Phys. Rev. Lett. 74, 4464 (1995).Google Scholar
[46] Dionne, G. F., Fitzgerald, J. F., and Aucoin, R. C., J. Appl. Phys. (1976) 1708.Google Scholar
[47] Balamurugan, B., Kraemer, K. L., Reding, N. A., Skomski, R., Ducharme, S., and Sellmyer, D. J., ACS Nano 4 (2010) 1893.Google Scholar
[48] Li, J. Y., Phys. Rev. Lett. 90 (2003) 217601.Google Scholar
[49] Mindlin, R. D., International Journal of Solids and Structures 4 (1968) 637.Google Scholar
[50] Askar, A., Lee, P. C., and Cakmak, A. S., Phys. Rev. B 1-3537 (1970) 3525.Google Scholar
[51] Skomski, R., Kashyap, A., and Enders, A., J. Appl. Phys., in press (2011).Google Scholar