L. H. Sperling

Departments of Chemical Engineering and Materials Science and Engineering, Materials Research Center, Center for Polymer Science and Engineering, and Polymer Interfaces Center,

Lehigh University, 5 E. Packer Ave., Bethlehem, PA 18015-3194

A polymer network may be defined as a structure in which essentially all mers are connected to all other mers and to the macroscopic phase boundary by many paths through the polymer’s phase; the number of such paths increases with the average number of intervening bonds and the paths much on the average be co-extensive with the polymer phase. The above definition is paraphrased from IUPAC recommendations.¹ If the permanent paths through the structure are all formed by covalent bonds, then the term covalent network is appropriate. The nomenclature also allows for physical networks, where some of the bonds arise through physical interactions. Thus, the nomenclature for polymer networks may be seen to be far from simple. As described below, it is also slightly controversial.

From a polymer physics point of view,² a network can be defined by several features: The cycle rank, x, the number of chains required to be cut to reduce the network to a tree; the average junction functionality, j; the molecular weight between two junctions, M_c, the number of junctions, m; and the number of chains, n, all on a per unit volume basis.

A macrocycle, a cyclic polymer chain, is clearly not a network (Def. 1.57, Ref. 1). However, a micronetwork (Def. 1.60, Ref. 1) may contain some cyclic structures and is of colloidal dimensions, and may debatably be a network in itself. Sometimes in industry, micronetworks are called fisheyes because of their appearance in films. Macrocycles can be linked to other macrocycles. The resulting polycatanane, while not important industrially, makes an interesting network which, while entirely physical in nature, does not relax.

A polymer network and a crosslinked polymer need not be the same thing. A polymer may be crosslinked below its gel point, and hence should be considered a branched polymer. The gel point is defined as the state where enough polymer chains are bonded together (either physically or chemically) such that at least one very large molecule is coextensive with the polymer phase. Beyond the gel point, one begins to speak of a polymer network, since increasing fractions of the system are interconnected by more than one bond.

If the polymer network is an amorphous polymer above its glass transition temperature, it usually exhibits rubber elasticity, i.e., it may stretch several hundred percent and essentially recover its original dimensions on release of the stresses. Crystalline or glassy networks do not have this behavior. Linear amorphous polymers above T_g of very high molecular weight may also exhibit rubber elasticity, but the

behavior is very much time dependent, as the physical entanglements can relax. It must be noted that all covalently crosslinked polymers also have various physical entanglements. For lightly crosslinked materials, there may be more physical entanglements than covalent (chemical) crosslinks.

A crosslink is defined (Def. 1.59, Ref. 1) as a small region in a macromolecule (polymer chain structure) from which at least four chains emanate (author’s italics). What about three chains emanating? According to Ref 1. Def. 1.54, it is a branch point. In a network a branch point may also be termed a junction point, but not a crosslink. At least two authors (besides this author) consider a trifunctional reaction site as a crosslink. These are Flory³ and Elias.⁴ A common crosslinking trifunctional monomer for such purposes is glycerol. While this author agrees that a trifunctional group can be a branch point, in an ordinary network it is better defined as a crosslink.

Incidentally, a network can also be a two-dimensional structure, sometimes called layer polymers. A common example is graphite, with its famous chicken-wire topology.

While rubber elasticity theory presumes a randomly crosslinked polymer, the several ways that polymer networks can be formed each lead to somewhat different statistics, each perhaps with distinctive nonuniformities. For example, chain polymerization leads first to microgel formation, while step polymerization leads to quite different structures. The reader is referred to Dusek⁵ and Erman and Mark⁶ for details, beyond the scope of the present brief paper.

There are two basic topologies that employ more than one kind of polymer chain. An AB-Crosslinked Polymer⁷ is composed of two kinds of polymer chains. Another name introduced very recently for substantially the same topology is bicomponent networks.⁸ An interpenetrating polymer network^9,10 is composed of two kinds of chains forming two separate networks, but in juxtaposition or interpenetrating.

1. IUPAC, Glossary of Basic Terms in Polymer Science, A. D. Jenkins, P. Kratochvíl, R. F. T. Stepto, and U. W. Suter, Pure Appl. Chem., 68, 2287 (1996), Def. 1.58.
2. B. Erman and J. E. Mark, in Science and Technology of Rubber, 2nd Ed., J. E. Mark, B. Erman, and F. R. Eirich, Eds., Academic Press, San Diego, 1994.
3. P. J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, 1953, p. 32.
4. H.-G. Elias, An Introduction to Polymer Science, VCH, Weinheim, 1997, p. 165.
5. K. Du_ek, in Advances in Polymeriation, 3, R. N. Haward, Ed., Applied Science Pub., London, 1982.
6. B. Erman and J. E. Mark, Structures and Properties of Rubberlike Networks, Oxford University Press, New York, 1997.
7. C. H. Bamford, R. W. Dyson, and G. C. Eastmond, J. Polym. Sci., 16C, 2425 (1967).
8. M. A. Sherman and J. P. Kennedy, Polym. Mater. Sci. Eng. (Prepr.), 77, 521 (1997).
9. S. C. Kim and L. H. Sperling, Eds., IPNs Around the World: Science and Engineering, Wiley, Chichester, 1997.
10. IUPAC, Source-Based Nomenclature for Non-Linear Macromolecules and Macromolecular Assemblies, A. D. Jenkins, J. Kahovec, P. Kratochvíl, I. Mita, I. M. Papisov, L. H. Sperling, and R. F. T. Stepto, Pure Appl. Chem., 69, 2511 (1997).

First published: ACS Division of Polymeric Materials: Science and Engineering (PMSE), 79 (1999).