Network imperfections

Another type of network imperfection, resulting from cross-linking of two units not distantly related structurally, is indicated in Fig. 94. Cross-linkages such as B are wasted (except insofar as the loop may be involved in entanglements not otherwise operative). The proportion of these short path cross-linkages should be small ordinarily but could become very large if the cross-linking process were carried out in a dilute solution of the polymer. 

The use of the same reactants at different initial dilutions to give dry networks of different moduli not only helps to define a scale of network imperfections but also enables the range of materials which can be prepared from given reactants to be usefully extended. 

Note 3 In addition to loose ends, model networks usually contain ring structures as network imperfections. 

Other imperfections are developed in the process of crosslinking network defects (unreacted functionalities, intramolecular loops, chain entanglements), inhomogeneity in crosslink distribution, or heterogeneity of the network due to phase separation. These four types of network imperfections are interdependent and a sharp borderline between them does not exist. 

Equation (6-83) assumes that the network is a perfect one in that all chains in the network are effective in giving rise to the elastic stress. Ideally each crosslink connects four network chains, while each such chain is terminated by two crosslinks. However, as illustrated in Figure 6-2, a number of network imperfections are possible. Each linear polymer chain with molecular weight M, even if all crosslinks are "normal," must give rise to two terminal chains that are incapable of supporting stress. Thus the number of effective chains must not include the imperfections due to chain ends. On incorporating this correction, the shear modulus can be written as 18... 

In addition to terminal chains and entanglements, there are other types of network imperfections. Figure 6-2 shows that if a short chain were crosslinked only once, the crosslink is a wasted one because the chain cannot support elastic stress. Also, if a crosslink forms an intrachain loop, it is again an ineffective crosslink. Unfortunately, owing to its very complexity, it is at present impossible to completely characterize the network structure of an elastomer. 

The populations of the I and Y free ends are independent of molecular ureight, as illustrated in Figure 7. On the other hand, it can be seen in Figure 6 that the occurrence of one-chain loops in the network agrees with the trend shown by the sol cyclics as described in the previous section. The observed increase in one-chain loop probabilities with shorter chain lengths is consistent with the Gaussian statistics assumed by the molecules. Network imperfections do not vanish at cong>lete conversion because of the loops. It is estimated by extrapolation that at 100% conversion, ca. 3% of the primary chains react to form loops for n>50. 

The number average molar mass of a chain section between two junction points in the network is an important factor controlling elastomeric behavior when is small, the network is rigid and exhibits limited swelling, but when is large, the network is more elastic and swells rapidly when in contact with a compatible liquid. Values of can be estimated from the extent of swelling of a network, which is considered to be ideal but rarely is, and interpretation of the data is complicated by the presence of network imperfections. A real elastomer is never composed of chains linked solely at tetrafunctional junction points but will inevitably contain defects such as (1) loose chain ends, (2) intramolecular chain loops, and (3) entangled chain loops. 

The relation T P has already been assumed to reflect the influence of network imperfections on mechanical properties Experimentally, this assumption can be confirmed by comparing the parameters of end-linked and randomly crosslinked,... 

Sharaf, M. A., The Effects of Network Imperfections on the Small-Strain Moduli of Polydimethylsiloxane Elastomers Having High Functionality Cross-Links. Int. J. Polym. Mater. 1992,18(3-4), 237-252. 

Figures 4.2,4.3, and 4.4 show the modulus predicted by equation (4.8) vs. Young s modulus, E (experiment). As with the swelling data, the network imperfections and the contributions of the physical crosslinks, if any, were minimized by determining the two crosslink levels required for E (theory) on the separate homopolymer networks. Unfortunately, Millar did not report modulus data for his polystyrene/polystyrene homo-IPNs.

Rubber failure by application of stress has been studied extensively owing to its overwhelming scientific and practical interest. In particular, two mechanisms have been pul- forward as relevant in delaying rubber failure. The first mechanism is based on viscoelastic energy dissipation, which can be increased by increasing the glass transition of the base polymer, or by other routes such as the use of additives or controlled network imperfection. The second mechanism is... 

Previous correlations of shear moduli and extents of reaction at the gel point (fig 2) have shown that the network imperfections increase with pre-gel intramolecular reaction and thus depend to some extent on the same parameters, namely, v, b and f. A more detailed analysis shows clearly that. 

An increase in the network imperfection also takes place in the case with the quartz filler, but because of a high surface energy of the filler there is a great probability of the formation of adhesive bonds of macromolecules with the filler surface which is equivalent to an increase in the network dermty. 

The Flory-Rehner equation in its original form does not take account of network imperfections due to the random distribution of lengths of effective chains or cilia consisting of chains that are bound to the network by only one end. To account for such imperfections in the network, Flory proposed the following modification [91], which was subsequently confirmed [92] ... 

---