External chain force, rubber elasticity

The early molecular theories of rubber elasticity were based on models of networks of long chains in molecules, each acting as an entropic spring. That is, because the configurational entropy of a chain increased as the distance between the atoms decreased, an external force was necessary to prevent its collapse. It was understood that collapse of the network to zero volume in the absence of an externally applied stress was prevented by repulsive excluded volume (EV) interactions. The term nonbonded interactions was applied to those between atom pairs that were not neighboring atoms along a chain and interacting via a covalent bond. 

To establish a useful equation of state for the mechanical behavior of a rubber network, it is necessary to predict the most probable overall dimensions of the molecules under the influence of various externally applied forces. An interesting approach to rubber elasticity consists of simulating network chain configurations (and thus the distribution of end-to-end distances) by the rotational isomeric state technique cited above. Based on the actual chemical structure of the chains, it enables one to circumvent the limitations of the Gaussian distribution function in the high deformation range. Nonetheless, the Gaussian distribution function of the end-to-end distance is very useful. It is obtained from a simple hypothetical model, the so-called freely jointed chain, which can be treated either exactly or at various levels of approximation. 

Still, we could think of an elastic constant of a polymer chain it would be the coefficient of the linear relation betw een the force f and the deformation R. According to (7.20), it happens to be ZhsT/NC. First, notice that it is proportional to 1/AT, which makes it a very small quantity if the chains are fairly long. This means that polymer chains are very susceptible to external forces this is exactly what accounts for the high elasticity of rubber and other similar polymers. The second thing we can notice is that the elastic constant is proportional to the temperature T. This is because the elastic forces are due to entropy, as you can see from (7.3). 

The sulfide linkages greatly improved the temperature range of rubber s elasticity. Vulcanized rubber maintains its elasticity even at high temperatures, because the disulfide linkages help snap the chains back into their original shape after the external force is removed. The vulcanized elastomer produced in greatest quantity is styrene-butadiene rubber (SBR). SBR is commercially prepared from styrene and butadiene via a free-radical polymerization process. It is called a copolymer, because it is made from two different monomers ... 

The viscoelastic state is also known as the rubber state. A piece of rubber under external force can be stretched. When the external force stops, the rubber recovers to its original position. Usually long-chain polymers can be induced to exhibit typical rubberlike behavior, for example, chains such as polyesters, polyamides, elastic sulfur (sulfur cooled from the liquid), and cellulose derivatives. 

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