Elasticity of Elastomers  Materials which undergo recoverable deformation of a few 100 % are called elastomers and exhibit rubber like elasticity  Elastomers → Long chain molecules with some cross-links  Cross-links keeps molecules from slipping past one another permanently  Relative mobility restricted to points between cross-links  Stress  strain  Strained equilibrium configuration reached swiftly and hence time dependence ignored (as a first approximation) i.e. Strain  f(t)  Stress  strain

Cross-link points Mobile segments

Unstretched state S t r e t c h e d state Tensile stress  Randomly coiled molecules   large number of configurations of equal potential energy   high S config & low Free Energy  Reduction in number of configurations    in S config  C-C bond angle is same  No change in enthapy Tensile stress Heating

 Enthalpy change on stretching = 0  I law of Thermodynamics  II law of Thermodynamics  F → Force applied to stretch  T → Constant temperature  L → Length of molecule  S → Entropy  Entropy change for stretch L 0 → L  Change in number of configurations  0 → 

 N 0 → number of chain segments between cross linking points Constant at constant temperature Equation Of State For a Rubbery material

Experimental Theory Bond stretching in straightened out molecules

Equation of state   → Stress   → Strain  or  If  is continuous and single valued:  ve term for elastomers

 In the elastic range E↑ as T ↑ (for a metal E↓ as T ↑)  During adiabatic stretching a elastomer gets warmer (metal gets cooler)  An unstretched elastomer → positive coefficient of thermal expansion elastomer stretched more than a few percent → negative coefficient of thermal expansion Summary of salient features