  Binary mixtures of amphiphiles in solution can self-assemble into a wide
range of structures when the two species individually form aggregates of
different curvatures. A specific example of this is seen in solutions of lipid
mixtures where the two species form lamellar structures and spherical micelles
respectively. Here, vesicles connected by thread-like micelles can form in a
narrow concentration range of the sphere-forming lipid. We present a
self-consistent field theory (SCFT) study of these structures. Firstly, we show
that the addition of sphere-forming lipid to a solution of lamella-former can
lower the free energy of cylindrical, thread-like micelles and hence encourage
their formation. Next, we demonstrate the coupling between composition and
curvature; specifically, that increasing the concentration of sphere-former in
a system of two bilayers connected by a thread leads to a transfer of
amphiphile to the thread. We further show that the two species are segregated
within the structure, with the concentration of sphere-former being
significantly higher in the thread. Finally, the addition of larger amounts of
sphere-former is found to destabilize the junctions linking the bilayers to the
cylindrical micelle, leading to a breakdown of the connected structures. The
degree of segregation of the amphiphiles and the amount of sphere-former
required to destabilize the junctions is shown to be sensitive to the length of
the hydrophilic block of the sphere-forming amphiphiles.
