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

Dendrimers and Dendrimer-Polymer Hybrids 197
3.2.2
Hydrodynamic Radii
More extensive data are available for the hydrodynamic radii of dendrimers than
for the radii of gyration, because they can be derived from intrinsic viscosity
measurements according to
R h =(3[h]M) 1/3 (10pN A ) –1/3 (5)
or from the translational diffusion coefficient, D o, according to
R h=kT(6ph sD o) –1 (6)
where N A is Avogadro's number, k is the Boltzmann constant, and h s the solvent
viscosity. R h and R h are the radii of the equivalent sphere of constant density.
Equations (5) and (6) may not apply to the smallest dendrimers whose dimensions
are comparable to the dimensions of the solvent molecules. Furthermore,
R h and R h cannot be compared directly to the predictions of the models because
the ratio R h/R g and R h/R g are not independent of the mass and branching architecture
of the dendrimers [52]. The earliest hydrodynamic radii have been obtained
on poly (a,e-L-lysine) dendrimers [72] (see Fig. 3b). For these dendrimers
it was found that [h]=2.5 ml/g independent of generation. It follows from
Eq. (5) that R h~M 1/3 , this exponent is expected for equal-density spheres and is
unusual for dendrimers and ascribed to the asymmetric nature of the branching
pattern in poly (a,e,-L-lysine) [73]. The experimental ratio R h/R g for these dendrimers
varies between 1.14 and 1.0.
Hydrodynamic radii of poly(benzyl ether) dendrimers are shown in Fig. 5.
Data for monodendrons with a hydroxyl focal group and tridendrons fall on the
same curve. The value of the exponent n in Eq. (4) is 0.46 of low MW. At high MW
it is 0.26 [48]. Data on low MW linear polystyrene in benzene [74] have been included
in Fig. 5 for comparison. They highlight the little difference in the actual
values of the hydrodynamic radii of linear polystyrene and low MW poly(benzyl
ether) dendrimers. Deviations are observed only when MW>5·10 3 . Furthermore,
the MW dependence of the radii of polystyrene and poly(benzyl ether)
dendrimers are the same at low MW. This indicates that it remains impossible to
draw major conclusions about the conformation of the low MW dendrimers
from their global properties. The low values of the hydrodynamic radii of the
high MW dendrimers, on the other hand, attest to their compact conformation.
A similar transition to more compact dendrimers has recently been shown in a
direct comparison of linear and dendritic poly(benzyl ethers) [75].
Recently, Stechemesser and Eimer published hydrodynamic radii obtained
from translational diffusion coefficients measured by means of recovery after
photobleaching experiments on selected generations of PAMAM dendrimers
[76]. The values of R h obtained in methanol are compared with R g data on the
same dendrimers in Fig. 4. It can be calculated that the ratio R h/R g~1.4 for all
but the tenth generation dendrimer. This ratio is somewhat higher than expect-