  Mixtures of micelle-forming and lamella-forming amphiphiles in solution can
form disk-shaped bilayers, sometimes referred to as bicelles. Using
self-consistent field theory (SCFT), we investigate the structure and stability
of these aggregates in a blend of two species of PS-PDMS diblock with PDMS
homopolymer at 225C. We find that the center of each disk is mainly composed of
lamella-forming diblocks, while its thicker rim is mostly formed of
micelle-forming diblocks. However, this segregation is not perfect, and the
concentration of micelle formers is of the order of 10% on the flat central
surface of the bicelle. We also find that the addition of micelle former to the
mixture of lamella former and homopolymer is necessary for disk-like bicelles
to be stable. Specifically, the free energy density of the disk has a minimum
as a function of the disk radius when both micelle- and lamella-forming
diblocks are present, indicating that the bicelles have a preferred, finite
radius. However, it decays monotonically when only lamella former is present,
indicating that the bicelle structure is always unstable with respect to
further aggregation in these systems. Finally, we identify a concentration
range where the bicelle is predicted to have a lower free energy density than
the simple cylindrical and lamellar aggregates, and so might be
thermodynamically stable.
