The fundamental mechanism of rubber elasticity

The elasticity of rubbers is very different from that of materials such as metals or even glassy or semicrystalline polymers. Young s moduli for metals are typically of the order of 10 MPa (see table 6.1) and the maximum elastic extension is usually of order 1% for higher extensions fracture or permanent deformation occurs. The elastic restoring force in the metal is due to interatomic forces, which fall off extremely rapidly with distance, so that even moderate extension results in fracture or in the slipping of layers of atoms past each other, leading to non-elastic, i.e. non-recoverable, deformation. 

As discussed in section 6.2.2, the values of Young s modulus for isotropic glassy and semicrystalline polymers are typically two orders of magnitude lower than those of metals. These materials can be either brittle, leading to fracture at strains of a few per cent, or ductile, leading to large but non-recoverable deformation (see chapter 8). In contrast, for rubbers. Young s moduli are typically of order 1 MPa for small strains (fig. 6.6 shows that the load-extension curve is non-linear) and elastic, i.e. recoverable, extensions up to about 1000% are often possible. This shows that the fundamental mechanism for the elastic behaviour of rubbers must be quite different from that for metals and other types of solids. 

In order to move the ends of the chain further apart a force is required, which increases with the separation of the ends, because the chain becomes progressively less randomly coiled as the ends move apart and this is opposed by the randomising effect of the impacts of the surrounding molecules. There is thus an entropic restoring force. This force increases with increasing temperature, because this causes harder, more frequent impacts by the surrounding molecules. 

Now imagine the chain to be dissolved in a random assembly of other chains of the same kind, i.e. to be one of the chains in a piece of rubber. If T Tg, the atoms of the surrounding chains behave hke the molecules of 

Before developing the entropic, or statistical, theory of rubber elasticity in a quantitative way, it is important to be sure that this really is the most important contribution, i.e. to be sure that any contribution to the elasticity due to changes in the internal energy on stretching is very small compared with the contribution due to changes of entropy. This is shown to be so in the following section. 

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