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

104 N. Hadjichristidis, S. Pispas, M. Pitsikalis, H. Iatrou, C. Vlahos
Finally Kosmas and Hadjichristidis [66] by using a single molecule argument
predicted the analytical relations
M = f m , M = M +
n i
i
which links the average molecular weights of the homopolymer precursors and
those of the final miktoarm macromolecule; here, f i is the number of the precursors
of the i-th kind (i=1, 2 ,...n), m ni , m wi , their number and weight average molecular
weight and M w , M n the molecular weights corresponding to the miktoarm
chain. Expressing m ni , m wi and M w , M n in terms of the Laplace tranform
of the distributions of molecular weights of the precursors P i (m) and the whole
molecule P c (M) they found that both equations at Eq. 6 are valid for any P i (m).
Experimental values of M w based on LALLS and a combination of MO and SEC
are found to be close to those calculated from the theory.
3.1.2
Experimental Results
Star polymers, with a structure where chains of different molecular weight
and/or chemical nature radiate from a common junction point, are expected to
have different solution behavior compared to regular or symmetric star polymers.
By forcing chemically different arms to be joined, expansion of the molecular
dimensions is predicted (see Sect. 3.1.1) as a consequence of the increase in
the number of heterocontacts in good and theta solvents or new kinds of structures
can be formed in selective solvents.
The dilute solution properties of asymmetric three-arm polystyrene stars
were studied by Fetters and coworkers [67] under different solvent conditions.
These materials comprised two series of samples, the first having a short third
arm with half the molecular weight of the two identical arms (SAS) and the second
a long arm having twice the molecular weight of the other two arms (LAS).
In toluene, a good solvent for PS, the two types of asymmetric stars exhibited
identical values of g', defined as
g'=[h] star /[h] linear
ni w n
i
fm ( m -m)
i ni wi ni
M
where [h] linear is the intrinsic viscosity of the linear polymer with the same molecular
weight. Values of g' are a little higher than values of g' for a regular threearm
star. In the theta solvent cyclohexane at 35 °C the value of g' for SAS is lower
than that of LAS which was equal to g' value of regular three-arm stars. It has to
be mentioned that in both solvents the value of a in the Mark-Houwink-
Sakurada equation, [h]=KM a , was higher for the SAS than LAS. The latter has a
similar a value as the symmetric stars.
The dilute solution characteristics of asymmetric stars, with equal number of
short and long arms, prepared by the DVB method, were studied by Mays et al.
n
(6)
(7)