Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-08T17:33:03.984Z Has data issue: false hasContentIssue false

8 - Structure of polymer networks

Published online by Cambridge University Press:  16 May 2011

Fumihiko Tanaka
Affiliation:
Kyoto University, Japan
Get access

Summary

This chapter studies the local and global structures of polymer networks. For the local structure, we focus on the internal structure of cross-link junctions, and study how they affect the sol–gel transition. For the global structure, we focus on the topological connectivity of the network, such as cycle ranks, elastically effective chains, etc., and study how they affect the elastic properties of the networks. We then move to the self-similarity of the structures near the gel point, and derive some important scaling laws on the basis of percolation theory. Finally, we refer to the percolation in continuum media, focusing on the coexistence of gelation and phase separation in spherical colloid particles interacting with the adhesive square well potential.

Local structure of the networks–cross-linking regions

Most physical gels have complex multiple junctions. In Section 7.4, we studied thermoreversible gelation with junctions of variable multiplicity. In this section, we consider a new method to find the local structure of the networks, i.e., the structure of the network junctions.

Junction multiplicity k was defined by the number of chains connected to a single junction. Simple pairwise cross-links, for example, have multiplicity k = 2, whose sol–gel transition is detailed in Section 7.4 and in the classical literature [1]. For networks with junctions of multiplicity larger than two, the conventional Eldridge–Ferry procedure [2] to find the enthalpy of melting, which plots the logarithm of the gelation concentration ln c* against the inverse temperature, does not work because it assumes pairwise crosslinking.

Type
Chapter
Information
Polymer Physics
Applications to Molecular Association and Thermoreversible Gelation
, pp. 247 - 280
Publisher: Cambridge University Press
Print publication year: 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

[1] Flory, P. J., Principles of Polymer Chemistry. Cornell University Press: Ithaca, NY, 1953.Google Scholar
[2] Eldridge, J. E.; Ferry, J. D., J. Phys. Chem. 58, 992 (1954).CrossRef
[3] Tanaka, F.; Stockmayer, W. H., Macromolecules 27, 3943 (1994).CrossRef
[4] Tanaka, F.; Nishinari, K., Macromolecules 29, 3625 (1996).CrossRef
[5] Nishinari, K.; Tanaka, F., Journal de Chimie et Physique 93, 880 (1996).CrossRef
[6] Tanaka, F., Polym. J. 34, 479 (2002).CrossRef
[7] Ohkura, M.; Kanaya, T.; KKaji, K., Polymer 33, 3686 (1992).CrossRef
[8] Brandrup, J.; Immergut, E. H., Polymer Handbook. Wiley: New York, 1975; p. III-13.Google Scholar
[9] Scanlan, J., J. Polym. Sci. 43, 501 (1960).CrossRef
[10] Case, L. C., J. Polym. Sci. 45, 397 (1960).CrossRef
[11] Pearson, D. S.; Graessley, W. W., Macromolecules 11, 528 (1978).CrossRef
[12] Graessley, W. W., Polymeric Liquids & Networks: Structure and Properties, Chapter 9. Garland Science: London, 2004.Google Scholar
[13] Langley, N. R., Macromolecules 1, 348 (1968).CrossRef
[14] Tanaka, F.; Ishida, M., Macromolecules 29, 7571 (1996).CrossRef
[15] Clark, A. H.; Ross-Murphy, S. B., Adv. Polym. Sci. 83, 57 (1987).CrossRef
[16] Annable, T.; Buscall, R.; Ettelaie, R.; Whittlestone, D., J. Rheol. 37, 695 (1993).CrossRef
[17] Yekta, A.; Xu, B.; Duhamel, J.; Adiwidjaja, H.; Winnik, M. A., Macromolecules 28, 956 (1995).CrossRef
[18] Stauffer, D.; Coniglio, A.; Adam, M., Adv. Polym. Sci. 44, 103 (1982).CrossRef
[19] Stauffer, D.; Aharony, A., Introduction to Percolation Theory, 2nd edn. Taylor & Francis: London, 1991.Google Scholar
[20] de Gennes, P. G., Scaling Concepts in Polymer Physics. Cornell University Press: Ithaca, NY, 1979.Google Scholar
[21] de Gennes, P. G., J. Physique 1976, 37, L1.
[22] Sykes, M. F.; Essam, J. W., J. Math. Phys. 5, 1117 (1964).CrossRef
[23] Coniglio, A.; Angelis, U. D.; Forlani, A., J. Phys. A: Math. Gen. 10, 1123 (1977).CrossRef
[24] Chiew, Y. C.; Glandt, E. D., J. Phys. A: Math. Gen. 16, 2599 (1983).CrossRef
[25] Stell, G., J. Phys. A: Math. Gen. 1984, 17, L855.CrossRef
[26] Mandelbot, B. B.; Gouyet, J.-F., Physics and Fractal Structures. Springer: New York, 1996.Google Scholar
[27] Feng, S.; Sen, P. N., Phys. Rev. Lett. 52, 216 (1984).CrossRef
[28] Winter, H. H.; Chambon, F., J. Rheol. 30, 367 (1986).CrossRef
[29] Durand, D.; Delsanti, M.; Adam, M.; Luck, J. M., Europhys. Lett. 3, 297 (1987).CrossRef
[30] Winter, H. H.; Mours, M., Adv. Polym. Sci. 134, 165 (1997).CrossRef
[31] Ziman, J. M., Models of Disorder. Cambridge University Press: Cambridge, 1979.Google Scholar
[32] Scher, H.; Zallen, R., J. Chem. Phys. 53, 3759 (1970).CrossRef
[33] Ziman, J. M., J. Phys. C 1, 1532 (1968).CrossRef
[34] Hill, T. L., J. Chem. Phys. 23, 617 (1955).CrossRef
[35] Mayer, J. E.; Mayer, M. G., Statistical Mechanics. Wiley: New York, 1940.Google Scholar
[36] Stillinger, F. H., J. Chem. Phys. 38, 1486 (1963).CrossRef
[37] Cohen, C.; Gibbs, J. H.; Fleming, P. D. III, J. Chem. Phys. 59, 5511 (1973).CrossRef
[38] Baxter, R. J., J. Chem. Phys. 49, 2770 (1968).CrossRef
[39] Xu, J.; Stell, G., J. Chem. Phys. 89, 1101 (1988).CrossRef
[40] Miller, M. A.; Frenkel, D., Phys. Rev. Lett. 2003, 90113.
[41] Kranendonk, W. G.; Frenkel, D., Mol. Phys. 64, 403 (1988).CrossRef

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×