Spinodal condition in RPA

Substituting this equation back into (5.69), and solving it with respect to (5p , we Anally And 

The true correlation function T is thus expressed in terms of the intracluster correlation function S this is the fundamental idea of the RPA. Now the simple algebra gives 

Two extreme cases of the polymer blends of A-chains/B-chains and chemically connected block copolymers A-block-B have been historically important, and will be detailed in Section 6.1. 

To express the k-functions in terms of the average quantities, we take the derivative of the two relations (5.27a) and (5.27b) with respect to 4 , and And 

The /c-functions have thus been expressed in terms of the average cluster sizes and their fluctuations. Substituting the result into (5.46), we confirm that it is equivalent to (5.63) with =0. The RPA scattering function has thus been most generally proved to give the lattice-theoretical spinodals in the limit of vanishing wavenumber. 

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