Rubbers Gaussian statistical model

Rusakov 107 108) recently proposed a simple model of a nematic network in which the chains between crosslinks are approximated by persistent threads. Orientional intermolecular interactions are taken into account using the mean field approximation and the deformation behaviour of the network is described in terms of the Gaussian statistical theory of rubber elasticity. Making use of the methods of statistical physics, the stress-strain equations of the network with its macroscopic orientation are obtained. The theory predicts a number of effects which should accompany deformation of nematic networks such as the temperature-induced orientational phase transitions. The transition is affected by the intermolecular interaction, the rigidity of macromolecules and the degree of crosslinking of the network. The transition into the liquid crystalline state is accompanied by appearence of internal stresses at constant strain or spontaneous elongation at constant force. 

In this equation the final term on the right-hand side remains non-zero even when the rubber is incompressible. As with eqn (3.45) this expression is still only valid under those conditions where Gaussian statistics are valid, viz when rchain model to take into account the fact that A, 17, and A1A2A3 may all have values that are not equal to unity. 

The most important fact that you should grasp from this discussion is the entro-pic nature of rubber elasticity. Although the agreement between the simple model described here and experiment is not that great you have to keep in mind that there are both theoretical assumptions (e.g., affine deformation) and mathematical approximations (Gaussian chain statistics) that have... 

STATISTICAL THEORY OF RUBBER ELASTICITY 9.6.1 Affine and Phantom Gaussian Models... 

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