Cross-linked elastomers chain entanglement

In the rubbery plateau, a new impediment to movement must be overcome entanglements along the polymer chain. In discussing the effects of entanglements in Chap. 2, we compared them to crosslinks. Is it any surprise, then, that rubbery behavior similar to that shown by cross-linked elastomers characterizes this region ... 

Recent Two-Network Results on the Effect of Chain Entangling in Cross-linked Elastomers... 

The role of chain entangling in cross-linked elastomers is an old issue which has not yet been settled. The success of Flory s new rubber elasticity theory 0-5) in describing some of the departures from the simple Gaussian theory has acted as a strong catalyst for new work in this area. 

Since the excellent work of Moore and Watson (6, who cross-linked natural rubber with t-butylperoxide, most workers have assumed that physical cross-links contribute to the equilibrium elastic properties of cross-linked elastomers. This idea seems to be fully confirmed in work by Graessley and co-workers who used the Langley method on radiation cross-linked polybutadiene (.7) and ethylene-propylene copolymer (8) to study trapped entanglements. Two-network results on 1,2-polybutadiene (9.10) also indicate that the equilibrium elastic contribution from chain entangling at high degrees of cross-linking is quantitatively equal to the pseudoequilibrium rubber plateau modulus (1 1.) of the uncross-linked polymer. 

In spite of these important results, the two-network method has had little impact on the discussion of the role of chain entangling in cross-linked elastomers. It was therefore decided to make a more detailed examination of the method and to try to develop a simpler method which would require fewer assumptions. The present paper is a discussion of recently published and unpublished work. 

Removal of the solvent has the additional effect of putting the chains into a "supercontracted state (figure 7.3). Experiments on strain-induced crystallization carried out on such solution cross-linked elastomers indicate that the decreased entangling is less important than the supercontraction of the chains. Crystallization required larger values of elongation compared to elastomers cross linked in the dry state. - The most recent work in this area has focused on the unusually high extensibilities of such elastomers. -102-107... 

Batsberg W, Kramer O (1981) A direct experimental determination of the elastic contribution of chain entangling in a tightly cross-linked elastomer. J Chem Phys 74(ll) 6507-6508... 

The statistical theory is remarkable in that it enables the macroscopic deformation behaviour of a rubber to be predicted from considerations of how the molecular structure responds to an applied strain. However, it is important to realize that it is only an approximation to the actual behaviour and has significant limitations. Perhaps the most obvious problem is with the assumption that end-to-end distances of the chains can be described by the Gaussian distribution. This problem has been highlighted earlier in connection with solution properties (Section 3.1) where it was shown that the distribution cannot be applied when the chains become extended. It can be overcome to a certain extent with the use of more sophisticated distribution functions, but the use of such functions is beyond the scope of this present discussion. Another problem concerns the value of N. This will be governed by the number of junction points in the polymer network which can be either chemical (cross-links) or physical (entanglements) in nature. The structure of the chain network in an elastomer has been discussed earlier (Section 4.4.5). There will be chain ends and loops which do not contribute to the strength of the network, but if their presence is ignored it follows that if all network chains are anchored at two cross-links then the density, p, of the polymer can be expressed as... 

Direct measurement of the cross-link density of thermoset polymers including those from epoxy resins remains one of the most difficult analytical challenges in the field. A far too common approach simply relates the rubbery modulus (Gr), the thermoset modulus above Tg, to the molecular weight between cross-links (Me) using the theory of rubbery elasticity (133,134). Unfortunately thermoset networks have much more complex features than do true elastomers, including non-Gaussian chain behavior, interchain interactions, and entanglements (172). 

Characterization of Poiymer Networks by Transverse Relaxation. The NMR transverse magnetisation relaxation experiments were extensively used for quantitative analysis of the density of chemical cross-links, temporary and trapped chain entanglements and physical network junctions which are formed in fllled rubbers, semicrystalline and ionic containing elastomers, and for determination of the molecular-scale heterogeneity of polymer networks ((83), and reference therein). 

---