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

114 N. Hadjichristidis, S. Pispas, M. Pitsikalis, H. Iatrou, C. Vlahos
because of the presence of the core, the arms will be stretched more than the
present theory predicts.
Floudas et al. have developed [78] a mean field theory to treat the phase stability
criteria for the most general case of miktoarm star copolymers, namely,
A n B m , with asymmetric number of branches m„n. The case of AB n was treated
in detail. The static structure factor in the disordered phase was calculated and
the resulting spinodal curves for the series of AB n miktoarms are plotted in
Fig. 8a. They found that these copolymers are more difficult to phase separate
than linear diblocks since the critical values of cN t (N t =N A +nN B ) are higher
than the diblock case at any composition. The spinodal curves are asymmetric
due to the inherent asymmetry of miktoarm stars. The critical values corresponding
to the minima of the spinodal and the respective compositions are
plotted in Fig. 8b for miktoarms with different n. For n up to 3 there is a considerable
increase in the value of (cN t) c which indicates an increasing compatibility
between A and B blocks. However for n>3 there is a reversal in (cN t) c which, for
n>10, differs only slightly from that of the A-b-B diblock copolymers. The maximum
value of (cN t) c at n=3 results from a delicate balance between the stretching
free energies of the A and B blocks while for higher number of arms the free
energy of the system is mainly determined by the B blocks forming the star.
These theoretical predictions have been tested experimentally by SAXS measurments.
Kosmas [79] studied the behavior of miktoarm stars at the interface of two
different phases using a simple mesoscopic model that incorporates the thermodynamic
parameters into the size of the Kuhn length. The latter depends on the
distance z perpendicular to the interface by the simple discontinuous function
l(z)=l + for z‡0, l(z)=l – for z£0. From the discontinuity of the Kuhn length only
the P Z component of the probability distribution function P(z 0,z)=P xP yP z of
finding the end of an homopolymer chain at z distance from the origin (z 0 ) is affected.
The weight of a macrostate W(z 0 ) of finding the one end at z 0 and the other
anywhere then is obtained from the entropy S=-kT P(z 0,z)lnP(z 0, z) which
connects P(z 0,z) with W(z 0),S=kTlnW(z 0). The density profiles of the chain end
as a function of the distance z 0 from the interface in the limit of large available
volume is given then by
( )
W( z )
. In the case of miktoarm
Wz
= 0
0
dz W( z )
stars consisting of i arms (i=1, 2, ..., f) the weight of macrostate W mikto is the
product of the weights of the macrostates of the f different arms Wmikto= Wi .
The density profile of the star common junctions is given by the relation
W
2r
erfc( 3z0 / Ri ( z 0)
2)
mikto = ri
1+
Pii
r [ ] i
L
-L
0 0
where R i (z 0 )=R i+ for z‡0 and R i (z 0 )=R i+
i