Large-size rings free-energy correction terms

5 Large-size rings free energy correction terms 

The free energy of a finite ring with N links (N P 1) can be written as the sum 

According to general arguments which have previously been expounded (see Section 1.2), SEN and 0SN should behave as follows 

Let us examine these terms in the framework of the Gaussian approximation. As this theory gives vd = 2, the term SEN must be proportional to a constant or to In iV. 

On the contrary, the second term 5Sw seems dominant. However a detailed calculation3 of the coefficient of JV2v 1 in shows that, owing to a sum rule, this coefficient vanishes. Thus Flory s terms (8.1.116) disappear, and one finds that SFf, is proportional to In N. 

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