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

150 K. Ito, S. Kawaguchi
better treated as star polymers when the number of arms is small. The “bottlebrush”
conformation, characteristic of poly(macromonomers), develops as the
number of branches increases. Crossover between stars and bottlebrushes,
therefore, would be expected to appear at a certain degree of polymerization of
macromonomer, as will be described later.
The effect of branching on the solution properties is usually discussed in
terms of the comparison with those of corresponding linear polymers. The
mean-square radius of gyration of branched polymers, b , is characterized
using a dimensionless parameter, the shrinking factor, g, which is defined as
where l is the mean-square radius of gyration of the linear polymer of the
same MW. For Gaussian chains, the value of g for star- (g s ) and comb-shaped (g c )
polymers is theoretically given as [57, 58]
where f ' is the number of branches and g is the ratio of the MWs of a branch and
the backbone. When excluded-volume effects exist, the value of g s for the starshaped
branched polymer near the q-temperature may be modified to [59, 60]
where z is the excluded-volume parameter which is defined as z=(3/(2pb 2 )) 3/2 b
n 1/2 with the bond length b, the number of the bond n, and the binary cluster integral
b, and K b is given by
The g factors of some star-shaped polymacromonomers with relatively limited
number of arms have been investigated and compared with the theory mentioned
above. Tsukahara et al. [61] estimated the g factors of PSt polymacromonomers
from 24 by SEC-LALLS measurement and compared with Eqs. (6) and
(8). The results suggest that these poly(macromonomers) behave like star polymer.
The experimental value of g is larger than the theoretical one based on
Eq. (6) in agreement with results of studies on model star polymers [62].
(5)
(6)
(7)
(8)
(9)