Scattering function of associating polymer mixtures

To study microphase separation transition (MST), we next consider the correlation function of concentration fluctuations, whose Fourier components give the intensity of scattered waves. We have polydisperse clusters whose polydispersity is controlled by the temperature T and the composition 4 . 

To study the scattering intensity from such polydisperse binary blends, we tentatively give a sequential number a = 1,2. iV = v to the clusters. Let the set of the numbers a, i) show the i-th monomer in the a-th cluster. The monomer density for (a, i) at lattice site r is then defined by 

The intensity of the scattered waves (of X-ray or neutrons) with the scattering vector q is most generally given by the formula 

Let us assume that the scattering amplitude bf takes the value bf = A for A monomers and bf = B for B monomers. We then decompose it into the form 

Substituting (5.53) into (5.51) and using the incompressibility eondition (5.50), we find 

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