Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-25T16:14:01.768Z Has data issue: false hasContentIssue false

Elasticity of networks with permanent and thermoreversible cross-links

Published online by Cambridge University Press:  31 January 2011

Jack F. Douglas*
Affiliation:
jack.douglas@nist.gov, NIST, Polymers Division, Gaithersburg, Maryland, United States
Get access

Abstract

Simplified models of flexible chain and stiff fiber networks are introduced to address how the network elasticity becomes modified when the cross-linking is thermoreversible in nature and changes in the stability of the network with deformation. These idealized models apparently able to capture many aspects of the elastic properties of real networks.

Type
Research Article
Copyright
Copyright © Materials Research Society 2010

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

1 Douglas, J. F., in Elastomeric Polymer Networks, edited by Mark, J. E. and Erman, B. (Prentice Hall, Englewood Cliffs, N.J., 1992).Google Scholar
2 Kong, H. J., Wong, E., and Mooney, D. J., Macromolecules 36, 4582 (2003).Google Scholar
3 Wen, Q., Basu, A., Winer, J. P., Yodh, A., and Janmey, P. A., New J. Phys. 9, 428 (2007).Google Scholar
4 Wall, F. T. and Flory, P. J., J. Chem. Phys. 19, 1435 (1951).Google Scholar
5 James, H. M. and Guth, E., J. Chem. Phys. 11, 455 (1943).Google Scholar
6 Deam, R. T. and Edwards, S. F., Philos. Trans. R. Soc. Lond. A 280, 317 (1976).Google Scholar
7 Busse, W. F., J. Phys. Chem. 32, 2862 (1932).Google Scholar
8 Kramer, O., Violeta, T., and Ferry, J. D., Proc. Natl. Acad. Sci. 69, 2216 (1972).Google Scholar
9 Langley, N. R., Macromolecules 1, 348 (1968).Google Scholar
10 Gumbrell, S. M., Mullins, L., and Rivlin, R. S., Trans. Faraday Soc. 49, 1495 (1953).Google Scholar
11 Gaylord, R. J. and Douglas, J. F., Polym. Bull. 18, 347 (1987).Google Scholar
12 Gaylord, R. J. and Douglas, J. F., Polym. Bull. 23, 529 (1990).Google Scholar
13 Douglas, J. F. and McKenna, G. B., Macromolecules 26, 3282 (1993).Google Scholar
14 Edwards, S. F., Proc. Phys. Soc. 92, 9 (1967).Google Scholar
15 Douglas, J. F. and Hubbard, J. B., Macromolecules 24, 3163 (1991).Google Scholar
16 Flory, P. J., Gordon, M., and McCrum, N. G., Proc. R. Soc. Lond. A 351, 351 (1976).Google Scholar
17 Dossin, L. M. and Graessley, W. W., Macromolecules 12, 123 (1979).Google Scholar
18 Fetters, L. J., Lohse, D. J., Richter, D., Witten, T. A., and Zirkel, A., Macromolecules 27, 4639 (1994).Google Scholar
19 Rivlin, R. S., J. Appl. Phys. 18, 444 (1947).Google Scholar
20 McKenna, G. B., Douglas, J. F., Flynn, K. M., and Chen, Y., Polymer 32, 2128 (1991).Google Scholar
21 Gaylord, R. J., Twardowski, T. E., and Douglas, J. F., Polym. Bull. 20, 305 (1988).Google Scholar
22 Twardowski, T. E. and Gaylord, R. J., Polym. Bull. 21, 393 (1989).Google Scholar
23 Han, W. H., Horkay, F., and McKenna, G. B., Math. Mech. Solids 4, 139 (1999).Google Scholar
24 Vilgis, T. A., Boue, F., and Edwards, S. F., in Moelcular Basis of Polymer Network 1988: Workshop Proceedings, edited by Baumgartner, A. and Picot, C. E. (Springer-Verlag, Berlin, 1989).Google Scholar
25 Zhou, J. and Fung, Y. C., Proc. Natl. Acad. Sci. 94, 14255 (1997).Google Scholar
26 Fung, Y. C., Amer. J. Physiol. 213, 1532 (1967).Google Scholar
27 Feng, S. and Thorpe, M. F., Phys. Rev. B 31, 276 (1985).Google Scholar
28 Thorpe, M. F., J Non-Cryst. Solids 76, 109 (1985).Google Scholar
29 Douglas, J. F., Dudowicz, J., and Freed, K. F., J. Chem. Phys. 128, 224901 (2008).Google Scholar
30 Peleg, M., Rheol. Acta 32, 575 (1993).Google Scholar
31 Peleg, M., Cereal Chem. 73, 712 (1996).Google Scholar
32 Nakanishi, S., Yoshikawa, H., Shoji, S., Sekkat, Z., and Kawata, S., J. Phys. Chem. B 112, 3586 (2008).Google Scholar
33 Bell, G. I., Dembo, M., and Bongrand, P., Biophys. J. 45, 1051 (1984).Google Scholar
34 Bongrand, P., Rep. Prog. Phys. 62, 921 (1999).Google Scholar
35 Rivlin, R. S. and Saunders, D. W., Philos. Trans. R. Soc. A 243, 251 (1951).Google Scholar
36 Chaudhuri, O., Parekh, S. H., and Fletcher, D. A., Nature 445, 295 (2007).Google Scholar
37 Groot, R. D., Bot, A., and Agterof, W. G. M., J. Chem. Phys. 104, 9202 (1996).Google Scholar
38 Shah, J. V. and Janmey, P. A., Rheol. Acta 36, 262 (1997).Google Scholar
39 Storm, C., Pastore, J. J., MacKintosh, F. C., Lebensky, T. C., and Janmey, P. A., Nature 435, 191 (2005).Google Scholar
40 Seitz, M. E., Martina, D., Baumberger, T., Krishnan, V. R., Hui, C. Y., and Shull, K. R., Soft Matter 5, 447 (2009). Seitz et al. confine themselves to the relatively small deformation regime where strain stiffening is observed, but more recent work by Kendra Erk (unpublished) from Ken Shull's group has examined the strain softening regime for the same block copolymer system.Google Scholar
41 Fung, Y. C., Fronek, K., and Patitucci, P., Amer. J. Physiol. Heart Circ. Physiol. 237, H620 (1979).Google Scholar
42 Horgan, C. O. and Saccomandi, G., Biomech. Model. Mechanobiol. 1, 251 (2003).Google Scholar
43 Pandit, A., Lu, X., Wang, C., and Kassab, G. S., Amer. J. Physiol. Heart Circ. Physiol. 288, H2581 (2005).Google Scholar
44 Delfino, A., Stergiopulos, N., Moore, J. E., and Meister, J. J., Biomech, J.. Amer. J. Physiol. Heart Circ. Physiol 30, 777 (1997).Google Scholar
45 Lin, D. C., Douglas, J. F. and Horkay, F., “Development of minimal models of the elastic properties of flexible, semi-flexible and stiff polymer networks with permanent and thermoreversible cross-links”, Soft Matter (submitted).Google Scholar