Intramolecular reaction trifunctional networks

The deviations from Gaussian stress-strain behaviour for the tetrafunctional polyurethane networks of Figure 9 are qualitatively similar to these found for the trifunctional polyester networks (Z5), and the error bars on the data points for systems 4 and 5 in Figure 9 indicate the resulting uncertainties in Mc/Mc. It is clear that such uncetainties do not mask the increases in Mc/Mc with amount of pre-gel intramolecular reaction. 

The reactants used to form the networks studied are generally of lower molar mass than those used by other workers to form perfect networks (e.g. (35)). However, the present results do indicate that very little pre-gel intramolecular reaction can have a marked effect on modulus. For example, for pr,c = 0.05, or ac = 0.58, with a trifunctional polyurethane-forming system of Me = 635g mol l, the modulus is reduced by a factor of five below that calculated on the basis of the small-strain(affine) behaviour of the perfect network. As a result, it is recommended that the effective absence of pre-gel intramolecular reaction in endlinking reactions to form perfect networks be confirmed by experiment rather than be assumed. 

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. 

Experimental results on reactions forming tri- and tetrafunctional polyurethane and trifunctional polyester networks are discussed with particular consideration of intramolecular reaction and its effect on shear modulus of the networks formed at complete reaction. The amount of pre-gel intramolecular reaction is shown to be significant for non-linear polymerisations, even for reactions in bulk. Gel-points are delayed by an amount which depends on the dilution of a reaction system and the functionalities and chain structures of the reactants. Shear moduli are generally markedly lower than those expected for the perfect networks corresponding to the various reaction systems, and are shown empirically to be closely related to amounts of pre-gel intramolecular reaction. Deviations from Gaussian stress-strain behaviour are reported which relate to the low molar-mass of chains between junction points. 

The relative posiMons of the lines for the various systems can be related to M(.o(or v), f, and the chain structures of the reactants(1.2.9-12). The slopes of the lines show that the reduction in modulus with pre-gel intramolecular reaction is larger for trifunctional compared with tetrafunctional networks (c.f. systems 1 and 2 with 4 and 5), although higher values of p- Q obtain for tetrafunctional reaction systems (c.f. Figure 2 . 

---