Elasticity elastomeric networks

As is obvious from the above discussion, a very detailed understanding of entangling in elastomeric networks is required for interpretation of the elastic modulus, in particular its dependence on deformation and swelling. 

The principle rheological properties which reflect the polymer process dynamics are the loss modulus (C), storage modulus (G"), dynamic complex viscosity (n ), and tan delta parameters. In simplified form the loss modulus describes the viscous or fluid component of viscosity. That is, how easily the molecules can move past each other. The storage modulus describes the elastic or network entanglement structure of the polymers. It is, therefore, sensitive to cross linking, reaction formation and the elastomeric modifiers. The complex dynamic viscosity is the combined effect of both moduli discussed. It, therefore. 

Although such studies are inherently very interesting, they are not directly relevant to the many unresolved questions in the area of rubberlike elasticity that involve the interactions among the chains making up an elastomeric network. 

Molecular theories of rubber elasticity (see Network Models in Section 29.2.2) allow the interpretation of the experimental data obtained for elastomeric materials in terms of structural characteristics of the network. The most frequently used experimental techniques are stress-strain measurements and swelling measurements. 

Linear Elastic and Rubber Elastic Behavior. Although stiffening is quite noticeable in the glassy regime of the amorphous phase, the most spectacular effect is seen in the rubber elastic regime phase, as already evoked in the case of reinforcement by cellulose whiskers (2). The PA6-clay hybrids example presented in Table 3 is quite representative of the situation encoimtered with semi crystalline thermoplastics, but elastomeric networks benefit as well of clay layer dispersion with a two- to threefold increase in modulus for polyurethane or epoxy networks... 

The Theory of Kuhn and Grun. The theory of birefringence of deformed elastomeric networks was developed by Kuhn and Griin and by Treloar on the basis of the same procedure as that used for the development of the classical theories of rubber-like elasticity (48,49). The pioneering theory of Kuhn and Griin is based on the affine network model that is, upon the application of a macroscopic deformation the components of the end-to-end vector for each network chain are assumed to change in the same ratio as that of the corresponding dimensions of the macroscopic sample. 

The theory of rubber elasticity (Section 9.7) assumes a monodisperse distribution of chain lengths. Earher, the weakest link theory of elastomer rupture postulated that a typical elastomeric network with a broad distribution of chain lengths would have the shortest chains break first, the cause of failure. This was attributed to the limited extensibility presumably associated with such chains, causing breakage at relatively small deformations. The flaw in the weakest link theory involves the implicit assumption that all parts of the network deform affinely (24), whereas chain deformation is markedly nonaffine see Section 9.10.6. Also, it is commonly observed that stress-strain experiments are nearly reversible right up to the point of rupture. 

Polymer networks can usually sustain large recoverable deformations due to the presence of chemical crosslinks which serve to bind long chains into a permanent network structure. The elasticity of the network chains is considered to originate primarily in terms of the entropy of the chains (1). The elastic free energy of an elastomeric network is usually treated as the sum of the contributions of its individual chains. Therefore, the most important parameter in describing the properties of a network is the molecular weight of the chain between crosslinks (M ),... 

Rubberlike elasticity is a unique property of long, flexible chains with weak interchain interactions joined together by cross-linking points to form tridimensionally stable networks. Early in the 1940 s statistical mechanics formalism has been developed to understand the molecular mechanism governing the behavior of the large ensemble of chains constituting elastomeric networks Two models of Gaussian networks, i.e. networks... 

One of the simplest ways to introduce the crosslinks required for rubber-like elasticity is to carry out a copolymerization in which one of the comonomers has a functionality of three or higher [9,21]. This method, however, has been used primarily to prepare materials so heavily crosslinked that they are in the category of hard thermosets rather than elastomeric networks, as it has already been mentioned [11]. The more common techniques include vulcanization (addition of sulfur atoms to unsaturated sites), peroxide thermolysis (covalent bonding through free-radical generation), end linking of functionally terminated chains (isocyanates to hydroxyl-terminated polyethers, organosilicates to hydroxyl-terminated polysiloxanes, and silanes to vinyl-terminated polysiloxanes) [18],... 

Mark JE. Bimodal elastomeric networks. In Mark JE, Lai J, editors. Elastomers and rubber elasticity. Washington, DC American Chemical Society 1982. p. 349-66. 

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