Properties of real networks

Staverman, A.J. Properties of Phantom Networks and Real Networks. Vol. 44, pp. 73-102. 

It is shown that model, end-linked networks cannot be perfect networks. Simply from the mechanism of formation, post-gel intramolecular reaction must occur and some of this leads to the formation of inelastic loops. Data on the small-strain, shear moduli of trifunctional and tetrafunctional polyurethane networks from polyols of various molar masses, and the extents of reaction at gelation occurring during their formation are considered in more detail than hitherto. The networks, prepared in bulk and at various dilutions in solvent, show extents of reaction at gelation which indicate pre-gel intramolecular reaction and small-strain moduli which are lower than those expected for perfect network structures. From the systematic variations of moduli and gel points with dilution of preparation, it is deduced that the networks follow affine behaviour at small strains and that even in the limit of no pre-gel intramolecular reaction, the occurrence of post-gel intramolecular reaction means that network defects still occur. In addition, from the variation of defects with polyol molar mass it is demonstrated that defects will still persist in the limit of infinite molar mass. In this limit, theoretical arguments are used to define the minimal significant structures which must be considered for the definition of the properties and structures of real networks. 

Even if completely homogeneous and disordered in the relaxed state, a real network differs from the ideal network, defined in Chapter I. Three types of network defects are commonly considered to be present in polymer networks unreacted functionalities, closed loops, and permanent chain entanglements. Within each group there are several possibilities dependent on the arrangement of chains the effect of defects on the elastic properties of the network is thus by no means simple, as has been stressed e.g. by Case (28). Several possible arrangements are shown in Fig. 1, where only nearest neighbour defect structures have been drawn. 

Staverman, A, J. Properties of phantom networks and real networks. Advances in Polymer Science 44, 73 (1982). 

Since there are many important qualitative differences between real biological systems and our model networks, it is possible that the methods described above will be applicable to only a small range of model systems. Yet, there are reasons to believe that the methods will be applicable to a broad class of systems. In the remainder of this section, we discuss several different ways in which our model equation does not capture the properties of real biological systems, and then we give arguments why the methods may stiU apply. 

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