Co-assembly Towards Janus Micelles - Self Organized Nanostructures of Amphiphilic Block Copolymers - page 176

c BD below which the two corona chains mix, and above
which the Janus configuration becomes stable. For the symmetric system it was
found [ 67 ] that this threshold interaction obeys the relationship

There exists a threshold χ

c BD N m

χ ϕ ≈ 2, where

m the maximum density of chains in the
corona (somewhere close to the core). In general, this value should (slightly) depend
on chain lengths and chain length differences, solvent quality of the corona chains,
etc. Up to now, we have chosen a relatively high

N is the length of the corona chains and ϕ

χ BD that is significantly larger
than the threshold value mentioned above. We will now limit ourselves to the strong
segregation case, mainly for illustration purposes.
Let us therefore move to the 2G SCF computations and focus on micellar objects
with two sides. Again, it is obvious that we need repulsion between the two types of
segments (as in Fig. 7 ) , or poor solvent conditions for one of the chains (as in Fig. 8 )
for this to occur. The exact structures that are formed may be further influenced
by the adsorption strength, the chain length differences and/or the grafting density
disparities. We cannot deal here with all these degrees of freedom and therefore we
choose to take the system of Fig. 8 and consider how this system behaves in a 2G
analysis.
When the corona is laterally segregated and, hence, when there is an interface
running in the radial direction between the two species of the corona, one should
expect a non-trivial shape of the core. To investigate such phenomena, it is not
appropriate to take an inert core (as described above). We thus extend the molec-
ular model with a core-forming block. As in previous studies [ 67 ], we use triblock
copolymers with a central block that (strongly) segregates from the monomeric sol-
vent, i.e. ( B ) N B − ( C ) N C − ( D ) N D . The length of the central block is chosen such

that the core has a radius R = 5 when it is spherical. Again we focus on micelles

with aggregation numbers n 15. In the first example, we wish to remain close to

the system discussed in Fig. 8 and therefore we choose a strong segregation of C
with the solvent such that

=

2. This leads to a high interfacial tension between
core and corona and, for this reason, minimal deviations of the core shape from the
sphere are expected. The SCF machinery for the 2G cylindrical coordinate system is
not much more complex than the 1G spherical ones. All quantities now are function
of two coordinates, where z runs along the axis of the cylinder and the r -coordinate
goes in the radial direction.
Figures 9 - 11 give volume fraction contour plots in the ( z , r ) plane that cuts
through the centre of the micelle. As above, the B chain is represented by solid
lines and the D chain by dashed ones. For these graphs, we only varied the solvent
quality of the longer B chain, ranging from a good solvent (Fig. 9 ) to a theta solvent
(Fig. 10 ) to a poor solvent (Fig. 11 ) . The shorter D chain is in good solvent con-
ditions in all cases. As expected, we see a Janus structure in all three graphs. The
micelle is oriented such that the B chain is situated at lower z -values and the D chain
at higher z -values. The interface between the two types of chains is, at least quali-
tatively, seen from the figures. When the solvent quality decreases for the B chain,
the volume occupied by B chains diminishes and the interface goes away from the
equatorial plane, to close to an angle of 45 ◦ in the poor solvent case.

χ C =