The Gaussian statistical model of rubber elasticity

In the theory of Meyer et al. (1932) of rubber elasticity the development follows a statistieal-meehanies approaeh. The segments of the rubber molecules are in thermal equilibrium, interaeting only with the thermal motions of surrounding molecules, without experieneing any important intermoleeular or intra-molecular interactions. In this sense the rubber molecules act as if they were part of a liquid that is, however, maintaining shape through a density of cross links between molecules. 

The configurational entropy of a molecule in the statistical theory is given by the Boltzmann expression 

The separability of the component probabilities in the x, y, and z directions permits statement of eq. (6.20) also as 

The probability density p(x,y,z) at the end point B can then be given more 

Consider now that in the initial unstretched state of a chain 

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