Elastic force ideal entropy

In our statistical treatment of an ideal elastomer, we have assumed that the elastic force is entirely attributable to the conformational entropy of deformation, energy effects being neglected. That the theory reproduces the essential features of the elasticity of real elastomers attests to the basic soundness of this assumption. On the other hand, we know that in real elastomers such energy effects cannot be entirely absent, and deviations from the ideal elastomer model may be expected to occur. Let us now examine in greater detail the extent to which the neglect of energy effects is justified. We can rewrite equation (6-28) ... 

In contrast to ideal entropy-elastic bodies, real entropy-elastic bodies have an energy-elastic component. The force Fe resulting from this component is given for a uniaxial deformation by... 

In an ideal or perfect elastomer the energy repeatedly invested in extension is repeatedly and completely recovered during relaxation. Ideality increases as the elastic force results from a decrease in entropy upon extension, because this occurs without stressing bonds to the breaking point. Elastin models and elastin itself in water provide examples of such entropic elastomers with about 90% of the elastic force being entropic, that is, the /e//ratio of Equation (4) is about 0.1. This is essential to human life expectancy, because the half-life of elastin in the mammalian elastic fiber is on the order of 70 years. This means that the elastic fibers of the aortic arch and thoracic aorta, where there is twice as much elastin as collagen, will have survived some billion demanding stretch-relaxation cycles by the start of the seventh decade of life. This represents an ultimate in ideal elasticity. 

An ideal elastomer has Young s modulus about 10 -10 dyn/cm (10- -10 N/m ) and reversible elasticity of hundreds of percent elongation. The force required to hold this entropy spring at fixed length falls as the temperature is lowered. This implies that (9(7/9/)t = 0. 

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