Cross-link elastomer networks

Polymers with the mechanical and chemical properties we have discussed in this section are called elastomers. In the next couple of sections we shall examine the thermodynamic basis for elasticity and then apply these ideas to cross-linked polymer networks. 

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

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 The present paper is a discussion of recently published and unpublished work. 

Thus, the simplified Two-Network experiment shows by a direct comparison of forces at constant length that the trapped entangled structure of a well cross-linked elastomer contributes to the equilibrium modulus by an amount that is approximately equal to the rubber plateau modulus. The modulus contribution from the trapped entangled structure will be less for lower molecular weights and especially at low degrees of cross-linking (14). 

Only when chemical bonds between neighboring molecules are introduced is a raw elastomer converted into a rubber vulcanizate, which is essentially a three-dimensional network structure (see Figure 5.3). The process is referred to as vulcanizahon or curing, or more accurately, as cross-linking. A cross-linked elastomer, or rubber vulcanizate, is capable of large reversible deformations within a broad temperature range and does not dissolve, but only swells in solvents and other liquids. 

Regardless of the method of cross-linking, mechanical properties of a cross-linked elastomer depend on cross-link density. Modulus and hardness increase monotonically with cross-link density, and at the same time, the network becomes more elastic. Fracture properties, i.e., tensile and tear strength, pass through a maximum as the cross-link density increases (see Figure 5.4). 

It is possible to classify polymers by their structure as linear, branched, cross-linked, and network polymers. In some polymers, called homopolymers, merely one monomer (a) is used for the formation of the chains, while in others two or more diverse monomers (a,p,y,...) can be combined to get different structures forming copolymers of linear, branched, cross-linked, and network polymeric molecular structures. Besides, on the basis of their properties, polymers are categorized as thermoplastics, elastomers, and thermosets. Thermoplastics are the majority of the polymers in use. They are linear or branched polymers characterized by the fact that they soften or melt, reversibly, when heated. Elastomers are cross-linked polymers that are highly elastic, that is, they can be lengthened or compressed to a considerable extent reversibly. Finally, thermosets are network polymers that are normally rigid and when heated do not soften or melt reversibly. 

It may be recalled that Eq. (2.77) was derived for an ideal network. The actual behavior of real cross-linked elastomers, however, shows much better accord with the Mooney-Rivlin equation (Mooney, 1948 Rivlin, 1948) ... 

A cross-linked elastomer cannot dissolve in a solvent. Dispersion is resisted because the cross-links restrict the movement and complete separation of the chains, but the elastomer does swell when the solvent molecules diffuse into the network and cause the chains to expand. This expansion is counteracted by the traidency of the chains to coil up and, eventually, an equihbiium degree of swelling is established that depends on the solvent and the cross-hnk density i.e., the higher the cross-Unk density, the lower the swelling. 

Although the dynamically vulcanized blends such as EPDM/PP (Santoprene ) and NBR/PP (Geolast ) have sometimes been referred to in the literature as semi-lPNs, we considered them as blends of cross-linked elastomer dispersions in a thermoplastic matrix and as such treated them under the elastomer blends. There is yet another class of thermoplastic/thermoset blend system in which a minor amount of the cross-linkable monomer(s) is allowed to polymerize in the thermoplastic matrix forming a loose network. Examples of such systems are silicone semi-IPNs in thermoplastics that have been recently commercialized (Rimplast , Petrarch, div. of Hiils) (Anonymous 1983). 

Cross-linked elastomers have been studied with regard to their moduli (particularly plateau values), effects of peroxide cross linking, adhesive interactions with atomic force microscopy tips, and the effects of phenyl-group modifications. Investigations on networks containing fillers include the effects of silica or polysilicate nanoparticles, zero... 

Materials with molecular networks, such as cross-linked elastomers and crystalline polymers, do not flow and so are classified as viscoelastic solids. Shear stresses do not decay to zero with time, ie, equilibrium stresses can be supported. Above Tg, such amorphous materials are still classified as solids, but most of their physical properties such as thermal expansivity, thermal conductivity, and heat capacity are liquid-like. 

Filled rubbers form a complex network of cross-linked chains connected to surface-active particles such as carbon black or amorphous silica (see Carbon Black). Here we will only indicate the structural features of importance in unfilled cross-linked elastomers. Two breakdown mechanisms are conceivable the initiation and growth of a cavity in a moderately strained matrix and the accelerating, cooperative rupture of interconnected, highly loaded network chains. The second mechanism is more important imder conditions, which permit the largest breaking elongation Xbmax to be attained (29). In that case, the quantity >-bmax is expected to be proportional to the inverse square root of the cross-link density Vg in fact, an increase of A,bmax with to is found experimentally for a... 

A quantitative analysis of the shape of the decay curve is not always straightforward due to the complex origin of the relaxation function itself (12,81,87-89) and the structural heterogeneity of the long-chain molecules. Nevertheless, several examples of the detection of structural heterogeneity by T2 experiments have been published, for example the analysis of the gel/sol content in cured (90,91) and filled elastomers (85,86), the estimation of the fraction of chain-end blocks in linear and network elastomers (91,92), and the determination of a distribution function for the molecular mass of network chains in cross-linked elastomers (93,94). 

The polymer is cross-linked. In this case the dotted line in Figure 8.2 is followed, and improved rubber elasticity is observed, with the creep portion suppressed. The dotted line follows the equation E = 3nRT, where n is the number of active chain segments in the network and RT represents the gas constant times the temperature see equation (9.36). An example of a cross-linked polymer above its glass transition temperature obeying this relationship is the ordinary rubber band. Cross-linked elastomers and rubber elasticity relationships are the primary subjects of Chapter 9. 

Bliimich and co-workers have investigated the possibility to enhance sensitivity to the changes in the values of residual dipolar coupUngs by measuring the higher-order multiple-quantum coherences for static samples with a complex dipolar coupling network like elastomers. They were the first who measured proton four-quantum coherences for cross-linked elastomers. 

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