Structure of polymer networks

This chapter studies the local and global structures of polymer networks. For the local structure, we focus on the internal structure of cross-Unk 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 coUoid particles interacting with the adhesive square well potential. 

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Definition and Structure of Polymer Networks A polymer network can be defined as a highly crosslinked macromolecule in which essentially all units are connected to each other in some way, either via chemical bonds or physical associations. 

Figure 9.6 Representation of a trifunctional monomer according to the classical theory of gelation. The monomer can hold four reactive states, from 0 to 3, which indicate the numher of functional groups that have been reacted, linking this unit with its neighbor. Source Adapted with permission from Dusek K, MacKnight WJ. Crosslinking and structure of polymer networks. In Labana SS, Dickie RA, Bauer RS, editors. CrossLinked Polymers. American Chemical Society 1988. p. 2 [88]. Copyright 1988 American Chemical Society.

Dusek K, MacKnight WJ. Crosslinking and structure of polymer networks. In Labana SS, Dickie RA, Bauer RS, editors. CrossLinked Polymers. American Chemical Society. Washington DC, 1988. p 2. 

A detailed theoretical characterization of the network structure of the polymer carrier in terms of the correlation length, in combination with diffusion studies of model drugs and proteins provide an invaluable insight into the very complex structure of polymer networks and aid in the design of drug delivery carriers (Narasimhan and Peppas, 1997a). 

HgEl l Plausible structure of polymer network based on H-bonded rodlike dimers formed by carboxyl monomer units Incorporated In the polymer side... 

A. K. Whittaker, The Structure of Polymer Networks , in Modern Magnetic Resonance, Part 1, ed. G. A. Webb, Springer, Dordrecht, Netherlands, 2006, p. 579. 

A. Jakli, L. Bata, K. Fodor-Csorba, L.l. Rosta, and L. Noirez, Structure of polymer networks dispersed in liquid crystals small angle neutron scattering study, Liq. Cryst. 17, 227 (1994). 

Considerable progress has been made in recent years in theoretical as well as experimental studies of the relation between the elastic behaviour and the structure of polymer networks. Theoretical studies were published by Flory " Ronca and Allegra, Edwards Freed a.o., while Rempp c.s. published an excellent survey of the synthesis and properties of Model Networks . For earlier surveys of the field we refer to DuSek and Prins and Graessley ... 

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