The effect of entanglements in rubber elasticity

Abstract This paper presents a theory of rubber elasticity based on the concept of entanglements. It is shown that for small deformation the molecular mechanism of stretching is dominated by the slippage of chains. Hardening of the rubber at a high deformation is due to inextensibility as described by the tube concept. This free energy of deformation agrees well with experiment. The resulting free energy is F k B T = 1 2 N c ∑ i=1 3 (1−α 2 )λ i 2 1−α 2 Z λ i 2 − log 1−α 2 ∑ i=3 3 λ i 2 + 1 2 n s ∑ i=1 3 λ i 2 (1+η)(1−α 2 ) (1+ηλ i 2 )(1−α 2 σλ i 2 ) + log (1+ηλ i 2 ) − log (1−α 2 σλ i 2 ) where α is a measure of the inextensibility and η of the slippage, Nc is the number of crosslinks and Ns the number of slip links.

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