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

100 N. Hadjichristidis, S. Pispas, M. Pitsikalis, H. Iatrou, C. Vlahos
3
Properties
3.1
Solution Properties
3.1.1
Theory
Relatively few theoretical studies have been devoted to the conformational characteristics
of asymmetric star polymers in solution. Vlahos et al. [63] studied the
conformational properties of AnBm miktoarm copolymers in different solvents.
Analytical expressions of various conformational averages were obtained from
renormalization group calculations at the critical dimensionality d=4 up to the
first order of the interaction parameters uA, uB, and uAB between segments of the
same or different kind, among them the radii of gyration of the two homopolymer
parts (k=An or Bm) and the whole miktoarm chain , the
mean square distance between the centers of mass of the two homopolymer
parts A and B and the mean square distance between the center of
mass of a homopolymer part and the star common origin (k=An or Bm). The critical exponents, n, of these conformational averages (~M2n < >
) were
found to be unaffected by the cross interactions between dissimilar units and are
determined only by the prevailing solvent conditions within the homopolymer
arms. Thus in common theta solvents, n is equal to 1/2, while for common good
and selective solvents, n=1/2+e/16, where e=4–d. From the analytical expressions
and those corresponding to the homopolymer precursors (i.e., a homopolymer
star chain with the same number of branches and units as the k homopolymer
part in the miktoarm star copolymer) they arrived at the following ratios
Sk 2
< > S 2
AB n m
< > G 2
AB n m
< > Gk 2
s G = G /
Ø
G + G
ºŒ
2 2 2
AnBm Anstar Bnstar g 2 2
S = S S k A
k k k,star = n or Bm
, / ( )
g 2 2
G = G G k A
k k k,star = n or Bm
/ ( )
ø
ߜ
These ratios are the most important means of quantitatively characterizing
the effects of heterointeractions in copolymers, since their analytical formulas
depend only on the chain composition and the cross excluded volume parameter
u AB *. For a particular miktoarm chain the ratio s G increases from a common
good to selective and then to a common theta solvent since the intensity of heterointeractions
increases. In Fig. 3 is illustrated the dependence of the chain topology
as function of the length fraction of the B branch F B =N B /(N A +N B ). Similarly,
the ratios g have higher values in a common theta than in a common good
(1)
(2)
(3)