become more or less completely attached to the wall. But, even in the weakly
adsorbed regime, such as ε ¼ 1.25, one finds clear evidence that the backbone
extension exhibits a scaling with the number of backbone monomers N b compatible
with 2D self-avoiding walks, L / N b
2ν(2d )
¼ N b
3/2 [68]. The snapshots in Fig. 45
show only the backbone chain, whereas Fig. 46 shows snapshots of a rather short
bottle brush (N b ¼ 131, N s ¼ 24) in the weakly adsorbed (ε ¼ 1.25) and strongly
adsorbed (ε ¼ 2.0) cases. Note that for N b ¼ 131 and ε ¼ 2.0, the rod regime still
holds and the contour length L of the (coarse-grained) cylindrical macromolecule
does not exceed the persistence length l p . Note also that the side chains are not fully
adsorbed linear “spikes”, but rather exhibit an irregular sequence of loops and
trains: so the picture of a comb lying flat on the surfaces is not yet appropriate.
3.10 Conclusions
Cylindrical brushes constitute a hybrid between a branched polymer and a molecular
object. Their shape is strongly anisotropic but both main and side chains preserve
their intrinsic flexibility, although with strongly reduced degrees of freedom. The
presented simulations demonstrate that the established wormlike chain models are
not applicable for the determination of chain stiffness, which could well be the origin
of diverging experimental results in the past. Particularly valuable is the finding that a
global relation between the main chain stiffness and the cross-sectional diameter of
the brushes is much more promising than subtle bond angle correlation functions in
order to obtain a good measure of the directional persistence.
The unique structure of cylindrical brushes makes them ideal candidates to
(1) experimentally and theoretically study the phase separation in quasi -1D
molecular objects, (2) investigate the properties of polyelectrolyte complexes of
shape-persistent polyions, (3) elucidate the adsorption on planar surfaces, and
eventually (4) develop novel cationic carriers for gene transfection, as described
in detail in Sect. 4.
4 Supramolecular Structure Formation by Directed
Interactions
4.1 Introduction
The formation of intermolecular structure of the cylindrical brushes described in the
previous section is mainly governed by their anisotropic shape, which enables them
to form even lyotropic phases. Other driving forces are of ionic and/or entropic
Structure Formation of Polymeric Building Blocks: Complex Polymer Architectures
165
adsorbed regime, such as ε ¼ 1.25, one finds clear evidence that the backbone
extension exhibits a scaling with the number of backbone monomers N b compatible
with 2D self-avoiding walks, L / N b
2ν(2d )
¼ N b
3/2 [68]. The snapshots in Fig. 45
show only the backbone chain, whereas Fig. 46 shows snapshots of a rather short
bottle brush (N b ¼ 131, N s ¼ 24) in the weakly adsorbed (ε ¼ 1.25) and strongly
adsorbed (ε ¼ 2.0) cases. Note that for N b ¼ 131 and ε ¼ 2.0, the rod regime still
holds and the contour length L of the (coarse-grained) cylindrical macromolecule
does not exceed the persistence length l p . Note also that the side chains are not fully
adsorbed linear “spikes”, but rather exhibit an irregular sequence of loops and
trains: so the picture of a comb lying flat on the surfaces is not yet appropriate.
3.10 Conclusions
Cylindrical brushes constitute a hybrid between a branched polymer and a molecular
object. Their shape is strongly anisotropic but both main and side chains preserve
their intrinsic flexibility, although with strongly reduced degrees of freedom. The
presented simulations demonstrate that the established wormlike chain models are
not applicable for the determination of chain stiffness, which could well be the origin
of diverging experimental results in the past. Particularly valuable is the finding that a
global relation between the main chain stiffness and the cross-sectional diameter of
the brushes is much more promising than subtle bond angle correlation functions in
order to obtain a good measure of the directional persistence.
The unique structure of cylindrical brushes makes them ideal candidates to
(1) experimentally and theoretically study the phase separation in quasi -1D
molecular objects, (2) investigate the properties of polyelectrolyte complexes of
shape-persistent polyions, (3) elucidate the adsorption on planar surfaces, and
eventually (4) develop novel cationic carriers for gene transfection, as described
in detail in Sect. 4.
4 Supramolecular Structure Formation by Directed
Interactions
4.1 Introduction
The formation of intermolecular structure of the cylindrical brushes described in the
previous section is mainly governed by their anisotropic shape, which enables them
to form even lyotropic phases. Other driving forces are of ionic and/or entropic
Structure Formation of Polymeric Building Blocks: Complex Polymer Architectures
165