Appendix to chapter 4. The random phase approximation

Now assume that our polymer blend is incompressible - the two volume fractions 0a and 0b cannot change independently and we know that 

Now it is convenient to define an exchange chemical potential Ap, the free energy change on replacing an A monomer by a B monomer. Using (4.6.2) we can write the response of the system to a change in exchange chemical potential as 

We know from thermodynamics that there is a general relation between this 

For an ideal random walk we know the explicit forms of /S a( ) and SBiq), they are given in terms of the Debye function f,(x) as 

by the same reasoning that led to equation (4.6.5), we can write for the q-dependent response function of the ideal mixture 

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