The correlation hole in two dimensions

Let us return to the correlation function Sn between the heads of all chains in a molten system. In the three-dimensional world this has the general appearance shown in Fig. II.7. What would happen if we could measure it in two dimensions (e.g., with chains adsorbed on a flat surface)  

Our prediction is that the correlation hole is much deeper. The sum rule [e.g. (11.14)] still holds, but the domain of integration is now an area of order Na. Thus we must have 

Thus the depletion is a finite fraction of the maximum concentration. This is another version of the discussion in Section II. 1.4, showing that segregation is important for two-dimensional systems. 

In the above discussion, we assumed that all chains were partly labeled, each with the same sequence of labels. Now we turn to a different experiment, where a fraction / of the chains is completely deuterated and the remaining fraction, 1 - is entirely hydrogenated (we always assume that the deuterated and normal species are entirely identical in their interactions). 

When / is small, we measure the scattering due to individual chains. This is the limit used by various workers to prove that chains in a melt are gaussian. The scattering intensity per site (in the lattice model) is 

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