142 Advances in Polymer Science Editorial Board: A. Abe. A.-C ...

112 N. Hadjichristidis, S. Pispas, M. Pitsikalis, H. Iatrou, C. Vlahos
Fig. 7. Phase diagram in the strong- segregation limit for starblock copolymers with n A A
arms and n B B arms as a function of the volume fraction of the B monomer (reproduced
with permission from [77])
Milner [77] studied the phase diagram of A n B m miktoarm copolymers in the
strong segregation limit in which the interface between A and B chains is sharp.
The morphology of microphases and their length scale are determined by a
competition of the interfacial tension and the increase in the stretching free energy
as the copolymer arms stretch away from the interface. Calculations are
made in terms of the cross sectional area relative to the outer surface from different
“wedges” corresponding to spherical, cylindrical, and OBDD phases. The
surface tension contribution is the area of the dividing surface times the surface
tension g, while the stretching energy was calculated by considering the miktoarm
stars as brushes. The copolymer chains are added one by one and the
work to add each one is summed. The total free energy of each structure (the
sum of the stretching and interfacial energy) is then minimized. The phase diagram
is determined by the cross lines of the free energy of different structures
and is presented in Fig. 7 as a function of the volume fraction of the B units F B
12 /
n
and the parameter A( lA)
e = which expresses the polymer asymmetry. n
12
/
A,
nB( lB)
nB are the numbers of A or B arms and lA , lB are material parameters expressing
the elasticity of the A and B homopolymers. The consideration of miktoarm
stars as brushes (branches without common origin) with A and B arms crossing
the interface will make no sense for small number of arms but in the other case,