Linear
ABC triblock copolymers with frustrated interactions of χAC
N ≪ χAB
N ∼ χBC
N can self-assemble
into double- and triple-helical superstructures, where the B blocks
form the helical domains wrapping around hexagonally packed A core
cylinders in a C matrix. It has been argued that larger length ratio
between the B helices and the A cylinder tends to form a larger number
of helices on each cylinder. On the basis of this argument, we propose
to branch the C block to enlarge the B helical domain relative to
the A core cylinder and thus to reduce the length ratio, i.e., altering
the linear ABC to branching ABC2 terpolymer, aiming to
obtain stable single-helical superstructure. For a typical group of
interaction parameters, χAC
N = 15
and χAB
N = χBC
N = 60, we construct the triangular phase diagram using
self-consistent field theory. In this phase diagram, the single-helical
phase (H1C) exhibits a notable stability region. Our calculations
indicate that the length ratio of H1C is only slightly
larger than 3, close to that of the triple cylinders-on-cylinder superstructure
(C3). As a consequence, the C3 phase occupies
a considerable region neighboring to H1C. In fact, we find
that the stabilization mechanism of the single-helical phase against
the double-helical or triple-helical phase is far more complicated
than the qualitative argument on the basis of the length ratio. Nevertheless,
our work demonstrates a facile way to modulate the number of helices
by tailoring the topological architecture of ABC-type block terpolymers.