Definition of Ideal or Perfect Elasticity
Ideal elasticity is the property whereby the energy expended in deformation of the elastomer is completely recovered on removal of the deforming force. Because the energy expended in deformation is given by the area under the force, f, versus increase in length, ΔL, curve, a perfectly reversible force-extension curve means complete recovery on relaxation of the energy expended on deformation. Therefore, ideal elastomers exhibit perfectly reversible force-extension curves.
Perhaps our earliest perspective of the mechanism underlying ideal elasticity comes from a fundamental observation concerning rubber elasticity. In the mid-nineteenth century, Joule and Thomson noted a quantitative correlation between the increase in temperature of the elastomer due to stretching and the increase in force due to increasing the temperature (Flory, 1968). Thermodynamics provides for the analysis underlying this correlation, and the Boltzmann relation provides the bridge between experimental thermodynamic quantities and statistical mechanical description of molecular structures.
Continuing qualitatively with the Joule and Thomson correlation, heat produces motion, and the energy represented by heat distributes into the various available degrees of freedom in the chain molecules comprising the elastomer. Accordingly, the release of heat on stretching correlates with a loss of motion. By means of statistical mechanics, the loss of motion is seen as a decrease in entropy on extension. In addition, should solvent be essential for elasticity, this requires explicit consideration.
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