One long chain among shorter chains

The Flory approach to this problem is simply to consider that all monomers of the long chain interact between themselves through the screened interaction for the excluded volume parameter v of Chapter I we must substitute the virial coefficient A2s- More precisely we have 

We can now write the dimensionfess parameter C [introduced in eq. (1.42)] which tells us whether the chain (Ni) is ideal or not. 

Consider first the usual three-dimensional case, d = 3. Then we have 

At first one might be inclined to use eq. (II. 10) also for one short chain among larger chains Ni N). However, in this limit, the simple recipe [eq. (n.7)] breaks down. Because the screening radius (/ = o) is now larger than the size of the chain of interest ( Ni a), it is not possible to replace 1/ of eq. (II. 1) by a poiiit interaction with one coefficient A2s- (A more detailed study suggests that C stays of order unity at all Ni AO- 

Some years ago there existed among polymer scientists some dispute between two opposite views on polymer melts as represented in Fig. II.6 a, b). In the standard model (a) the chains interpenetrate very strongly. 

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One long chain among shorter chains", J. Appl. Polym. Sci. Polym. Syme , 61, 313-315 (1977). 

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