The elasticity of a molecular network

We wish to calculate the strain-energy function for a molecular network, assuming that this is given by the change in entropy of a network of chains as a function of strain. 

The actual network is replaced by an ideal network in which each segment of a molecule between successive points of cross-linkage is considered to be a Gaussian chain. 

In either the strained or unstrained state, each junction point may be regarded as fixed at its mean position. 

The effect of the deformation is to change the components of the vector length of each chain in the same ratio as the corresponding dimensions of the bulk material (the affine deformation assumption). 

The mean square end-to-end distance for the whole assembly of chains in the unstrained state is the same as for a corresponding set of free chains and is therefore given by Equation (3.20). 

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