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Since NC hydrogels show extraordinarily large reversible deformation, and the polymer chains in the swollen state at ambient temperature could be regarded as flexible polymer chains just like those in the rubbery state of solid polymer above glass transition temperature [22], the effective cross-link chain density of NC hydrogels can be evaluated by the kinetic theory for rubber elasticity, which was developed on the basis of the entropy elasticity of flexible polymer chains. From the rubber elasticity theory, the equation of state of the swollen network for tensile strains is
¦Ò = ¦ÍeRT(¦Ë ¨C1/¦Ë2)
                         = RT¦Ñ/Mc(1 ¨C 2 Mc/ Mn)( ¦Ë ¨C1/¦Ë2)       (2)
where ¦Ò is the tensile stress, ¦Íe is the effective crosslink chain density, R is gas constant, T is the absolute temperature, and ¦Ë = L/L0 is the draw ratio, ¦Ñ is the density of the hydrogel, Mc is the molecular weight of chain between cross-links, Mn is the average molecular weight of the primary molecular chains. The term (2Mc/Mn) is a traditional correction for chain ends not effectively tied into conventional cross-linked networks and becomes negligible when the number of chain ends is small relative to cross-linked chains.
   Values of ¦Íe and Mc can be calculated at a given draw ratio by Eq. (2).

¡¾À´Ô´¡¿Yuanqing Xiang, Zhiqin Peng, Dajun Chen. A new polymer/clay nano-composite hydrogel with improved response rate and tensile mechanical properties. European Polymer Journal 42 (2006) 2125¨C2132.
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