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

194 J. Roovers, B. Comanita
3
Conformation of Dendrimers
3.1
Theoretical Models
The first model for the conformation of a dendrimer was proposed by de Gennes
and Hervet [49]. It is based on a modified Edwards self-consistent field for dendrimers
with large linear segments between consecutive branch points in a good
solvent. It places the spacers of consecutive generations in concentric shells. The
segment density is rather low in the center and increases parabolically (according
to r 2 , r being the distance from the center) to a generation for which the segment
density approaches unity. As a consequence, the radius of dendrimers, R,
increases according to M 0.2 up to the steric saturation generation. The radius of
incomplete dendrimers grown beyond this generation increases according to
R~M 1/3 , i.e., like constant density objects. This model is related to the Maciejewski
box [50] and may have merit when phase separation forces the end-standing
groups to lie on the surface of the dendrimer or in case the spacers are stiff and
cannot fold back.
Simulations and models developed more recently for dendrimers with flexible
spacers provides a quite different picture. Generally, the segment density decreases
from the center of the dendrimer to zero at the surface [51–54]. In particular,
some studies suggest a small minimum in the segment density near the
core [52], others show evidence for an extended plateau region of near constant
segment density [52, 54]. The end-standing groups are found throughout the entire
dendrimer volume [52, 54] as a result of backfolding of the spacers, although
most of them are found in the large volume near the dendrimer surface. Segments
of lower generation spacers are more localized in the interior of the dendrimer
[54] and have a stretched conformation [53].
The dependence of the radius of gyration, R g , on the mass of the dendrimer
is complex. For small generation dendrimers the exponent n in
R g ~M n (4)
is 0.5 [51], 0.4 [52], and 0.5 [53]. For high generation dendrimers the limiting
value for n is 0.22 [51], 0.24 [52], 0.20 [53], and 0.3 [54]. The latter exponents are
comparable with n=0.25 for randomly branched polymers [55, 56]. There is general
agreement on the increasing sphericity of dendrimers as the number of generations
increases [57] and on a limited overlap of different dendrons inside the
dendrimer volume [54, 58]. Based on a calculation of the intrinsic viscosity of
model dendrimers, Mansfield and Klushin concluded that the hydrodynamic radius,
R h , of low generation dendrimers is smaller than R g but that the reverse is
true for high generation dendrimers [59].
The variation of the size of the dendrimer with the number of segments, n, between
two branch points, at constant architecture (generation), has been consid-