A 4TH-ORDER, DENSITY-FUNCTIONAL, RANDOM-PHASE APPROXIMATION STUDY OF MONOMER SEGREGATION IN PHASE-SEPARATED, LAMELLAR, DIBLOCK-COPOLYMER MELTS

We show that the random-phase approximation (RPA) for correlations in block-copolymer melts derives from the free energy functional of ideal chains augmented by a random-mixing approximation for the interactions between monomers. The derivation facilitates comparisons to other approaches to monomer segregation. We apply the RPA functional to the segregation of symmetric, lamellar, block-copolymer phases while employing the full wave-vector dependence of the third- and fourth-order vertex functions. Compared to calculations which accurately treat only the second-order vertex function, the fourth-order theory shows that the wave-vector dependence of the higher-order terms plays an important role in determining the degree of segregation of the melt. The approach to the strong-segregation limit (SSL) is very slow, so the scaling of the domain size D with the polymerization number N obeys the predicted relation D is-proportional-to N2/3 only for very long chains and low temperatures. In contrast, the second-order theory approaches the SSL scaling result more rapidly, again underscoring the importance of higher-order vertex functions. In the weak-segregation limit (WSL), the interfacial width rises rapidly, reaching a maximum before decreasing and then relaxing to an almost constant value in the SSL.