Rubber entropy spring

Rubber is considered as a network of molecular entropy springs (cf. p. 568) with junction points consisting of chemical cross links or molecular entanglements. The principal theoretical viewpoints dealing with the extension of such a network structure have been treated of in Chapter IV, p. 123. 

Elastomers are crosslinked rubbery polymers (i.e. rubbery networks) that can be stretched easily to high extensions (e.g. 3x to lOx their original dimensions) and which rapidly recover their original dimensions when the applied stress is released. This extremely important and useful property is a reflection of their molecular structure in which the network is of low crosslink density. The rubbery polymer chains become extended upon deformation but are prevented from permanent flow by the crosslinks, and driven by entropy, spring back to their original positions on removal of the stress. The word rubber, often used in place of elastomer, preferably should be used for describing rubbery polymers which are not crosslinked. 

The properties of elastomeric materials are controlled by their molecular structure which has been discussed earlier (Section 4.5). They are basically all amorphous polymers above their glass transition and normally crosslinked. Their unique deformation behaviour has fascinated scientists for many years and there are even reports of investigations into the deformation of natural rubber from the beginning of the nineteeth century. Elastomer deformation is particularly amenable to analysis using thermodynamics, as an elastomer behaves essentially as an entropy spring . It is even possible to derive the form of the basic stress-strain relationship from first principles by considering the statistical thermodynamic behaviour of the molecular network. 

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. 

Viscoelastic deformation results from the parallel overlapping of spring and damper deformation Elongation is delayed, but completely reversible upon relaxation. This is called entropy or rubber elasticity. 

This clearly expresses that for rubber the increase of tension on isothermal stretching is an entropy effect, whereas for the spring it is of a potential energy nature If the extension is carried out adidbatically (which is practically the case when stretching rubber very quickly), T is not constant and thus the internal energy increases. The work done is then transformed into kinetic energy (heat), in contrast... 

An interesting nonequilibrium eiqieriment involves cutting the steel spring and rubber band in an extended, strained state. Both will naturally snap quickly back to their equilibrium, unstrained state. What are the thermal effects The steel spring loses the stored potential energy and since it does no work, it must heat up as required 1 the loss of work of expansion. The rubber band, in contrast, has the same internal ener in the extended and contracted states — i.e., if there is no work done on contraction there is no change in temperature. This distinct difference between energy and entropy elasticity has important consequences for thermal analysis, and one could predict valuable applications for the stretch calorimeter mentioned in the discussion of Fig. 4.30. 

Equation (28.9-11) shows the difference between a rubber band and a spring. When a spring is stretched at constant temperature, the energy increases as work is done on the spring. When a rubber band is stretched at constant temperature, doing work on the rubber band, the energy remains constant, so that heat must flow out. Stretching a rubber band at constant temperature must decrease its entropy. This fact seems reasonable from a molecular point of view, because the polymer molecules will be more nearly parallel and more nearly ordered in the stretched state than in the relaxed state. From Eqs. (28.9-8) and (28.9-11) we can derive a relation for this decrease in entropy ... 

The classical models of rubber elasticity reduce the elastic properties to a study of entropic springs. In the phantom model the EV interaction only gives the volume conservation, while in the affine deformation model it also is responsible for the affine position transformation of the crosslinks. Otherwise the entropic forces and the excluded volume interactions and consequently the entanglements, as they are a result of the EV interaction, completely decouple from the chain elasticity. The elasticity is entirely determined by the strand entropy. It is obvious that this is a... 

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