Rubber elasticity

[CARROL ALLEN]

Elasticity

In most elastic materials, such as metals used in springs, the elastic behavior is caused by bond distortions. When force is applied, bond lengths deviate from the (minimum energy) equilibrium and strain energy is stored electrostatically. Rubber is often assumed to behave in the same way, but it turns out this is a poor description. Rubber is a curious material because, unlike metals, strain energy is stored thermally. Also, natural rubber is so elastic that when force is applied, on natural rubber when it is on a surface similar to carpet, it may be difficult to ‘pull’ across the surface. It will stick.

In its relaxed state, rubber consists of long, coiled-up polymer chains that are interlinked at a few points. Between a pair of links, each monomer can rotate freely about its neighbour, thus giving each section of chain leeway to assume a large number of geometries, like a very loose rope attached to a pair of fixed points. At room temperature, rubber stores enough kinetic energy so that each section of chain oscillates chaotically, like the above piece of rope being shaken violently. The entropy model of rubber was developed in 1934 by Werner Kuhn.

When rubber is stretched, the “loose pieces of rope” are taut and thus no longer able to oscillate. Their kinetic energy is given off as excess heat. Therefore, the entropy decreases when going from the relaxed to the stretched state, and it increases during relaxation. This change in entropy can also be explained by the fact that a tight section of chain can fold in fewer ways (W) than a loose section of chain, at a given temperature (nb. entropy is defined as S=k*ln(W)). Relaxation of a stretched rubber band is thus driven by an increase in entropy, and the force experienced is not electrostatic, rather it is a result of the thermal energy of the material being converted to kinetic energy. Rubber relaxation is endothermic, and for this reason the force exerted by a stretched piece of rubber increases with temperature (Metals, for example, become softer as temperature increases). The material undergoes adiabatic cooling during contraction. This property of rubber can easily be verified by holding a stretched rubber band to your lips and relaxing it. Stretching of a rubber band is in some ways equivalent to the compression of an ideal gas, and relaxation is equivalent to its expansion. Note that a compressed gas also exhibits “elastic” properties, for instance inside an inflated car tire. The fact that stretching is equivalent to compression may seem somewhat counter-intuitive, but it makes sense if rubber is viewed as a one-dimensional gas. Stretching reduces the “space” available to each section of chain.

Vulcanization of rubber creates more disulfide bonds between chains, so it shortens each free section of chain. The result is that the chains tighten more quickly for a given length of strain, thereby increasing the elastic force constant and making rubber harder and less extendable.

When cooled below the glass transition temperature, the quasi-fluid chain segments “freeze” into fixed geometries and the rubber abruptly loses its elastic properties, although the process is reversible. This is a property it shares with most elastomers. At very cold temperatures, rubber is actually rather brittle; it will break into shards when struck or stretched. This critical temperature is the reason that winter tires use a softer version of rubber than normal tires. The failing rubber o-ring seals that contributed to the cause of the Challenger disaster were thought to have cooled below their critical temperature. The disaster happened on an unusually cold day.

Stolen from wickapedia!

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