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

110 N. Hadjichristidis, S. Pispas, M. Pitsikalis, H. Iatrou, C. Vlahos
been adsorbed may be very high and does not occur. This conclusion was also
supported by the similar D inter values, where D inter =1/s 1/2 is the interchain distance,
obtained for stars with two and three polar groups. The adsorbed stars
were found to be less stretched than the linear chains. The adsorption energy
was calculated to be (9±1) kT per group from the linear polymer data.
The adsorption kinetics from time resolved ellipsometry measurements
showed two regimes: (a) a diffusion controlled process at the initial stages and
(b) at longer times, an exponential behavior where the arriving chain must penetrate
the barrier formed by the already adsorbed chains. The experimental data
indicated that the stars penetrate this barrier faster than the linear chains.
3.2
Bulk Properties
3.2.1
Theory
Few theoretical studies deal with the behavior of miktoarm star copolymers in
the solid state. Issues like the phase diagram and the order-disorder transitions
however have been studied in considerable detail.
Olvera de la Cruz and Sanchez [76] were first to report theoretical calculations
concerning the phase stability of graft and miktoarm A nB n star copolymers with
equal numbers of A and B branches. The static structure factor S(q) was calculated
for the disordered phase (melt) by expanding the free energy, in terms of
the Fourier transform of the order parameter. They applied path integral methods
which are equivalent to the random phase approximation method used by
Leibler. For the copolymers considered S(q) had the functional form S(q) –1 =
(Q(q)/N)-2c where N is the total number of units of the copolymer chain, c the
Flory interaction parameter and Q a function that depends specifically on the
copolymer type. S(q) has a maximum at q * which is determined by the equation
Q/Q=0.
For the graft copolymers they found that q * (graft)‡q * (diblock) and there is
no symmetry around the composition f=1/2 due to the inherent asymmetry in a
graft copolymer. The spinodal curves where S(q * ) diverges at the spinodal temperature
or at the characteristic value of (cN) s are plotted in Figs. 5 and 6 as
functions of the composition. They predicted that a simple graft has no critical
point for any f. Irrespective of the position of the branch point, the minimum
value of the spinodal appears at volume fraction f=0.5. For the special case of the
symmetric graft (an A 2 B miktoarm star) (cN) s =13.5. This means that it is more
difficult for the chain to phase separate in this kind of architecture than it is for
linear diblock copolymers. Miktoarm copolymers of the A nB n type are predicted
to have critical point at (cN 0) c=10.5 (the same value as for the diblocks when f=
0.5) which implies that the microphase separation of nearly symmetrical miktoarms
depends solely on the molecular weight of the span diblock copolymer
N 0 and not on that of the whole star chain.