Free Energy and Orientation Distribution of the Chain Segments

3 Free Energy and Orientation Distribution of the Chain Segments 

The elastic free energy of an individual polymer chain at the chain extension h/Na reads [16] 

Time evolution of the average elastic free energy per unit volume, fe t)i and the orientation distribution of chain segments in the system, w a,i), are controlled by time-dependent distribntion of chain end-to-end vectors, W h,t), 

Using Fade approximation of the inverse Langevin function (4.13) the elastic free energy of a non-Gaussian chain with the chain extension h/Na expresses by the following closed formula. 

The last term in (4.26) which introduces the non-linearity can be approximated by 

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