Networks made up of nonlinear chains

The single chain partition function 2i (/, T) under the action of the tension / for the random flight model chain with a bond length a takes the asymptotic form 

Let us solve this relation for t, and express it as f = tACO. The free energy of the chain is then given by 

The elastic free energy of an affine network made up of such Langevin chains is written as 

The tension / is derived by the differential / = 9 AF(X)/9(XLo) with Lq being the length before the deformation is given. It is 

Moreover, the integration with respect to I is approximated by the value at the mean square end-to-end distance Ro = sfna of a Gaussian chain, or equivalently I = Iq = ajna = 1 /, so that the tension takes a simple form 

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