Stability of perpendicular and parallel lamellae within lamellae of multiblock terpolymers

The phase behaviors of multiblock terpolymer A(BC)(n)B (or A(BC)(n)) with equal volume fractions of A and compositional symmetric (BC)(n)B (or (BC)(n)) are investigated by using the pseudospectral method of the self-consistent mean field theory. These terpolymers can self-assemble into hierarchical lamellar phases of perpendicular or parallel lamellae within lamellae, and the number of B/C thin layers in the parallel phase can be varied. The relative stability among these hierarchical lamellar phases can be tuned by the three interaction parameters of χ(AB)N, χ(AC)N, and χ(BC)N. Two-dimensional phase diagrams, the cross sections of the three-dimensional phase diagram, are determined in our calculations. Our conclusion that the perpendicular phase is stable only in the case of χ(AC)N ≪ χ(AB)N < χ(BC)N is consistent with experimental observations by Bates's group. In addition, our results suggest that the existence of the perpendicular phase is generic in both types of terpolymers: A(BC)(n)B and A(BC)(n), with different values of n, even for the special case of A(BC)(n), that is, an ABC linear terpolymer.