Elasticity and Swelling of a Gaussian Network

The network is considered as a collection of chains, of which the a priori probability of observing an end-to-end distance f is given by 

The constant-temperature network partition function Q under a given deformation, specified by the deformation ratios %x, Xy and A, is obtained by assuming that there are no interactions between the chains other than those imposed by the presence of volume-less crosslinks. 

Here vt is the number of chains with end-to-end distance rt- the summation is over all vt sets subject to the restriction that Svt = v. The permutation term vljllvil appears in this formulation of Hermans (82) as 

(HI-2) is subsequently simplified by using only the maximum term. It is assumed that a reference state exists in which the vt set belonging to this state, Q( 1,1,1) is given by 

The vrset, belonging to ( max(A, Xy, 7Z) is then determined by imposing the condition 

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