Supramolecular Polymerizations

514 A. Ciferri
Figure 3. (a) Bifunctional units with binding sites along the N
and S (or E and W) directions, yielding linear polymers. (b) Tetrafunctional
units with two sites along N and S, and two sites
along N-E and S-E (same side of the assembly), yielding linear
or helical double chains. (c) Tetrafunctional units with sites at
right angles within the cross-sectional or equatorial area of the
unimer, yielding planar polymers. (d) Hexafunctional units with
sites as in (c), and two additional sites on the flat surfaces or
poles, yielding three-dimensional polymers.
2. Classical supramolecular interactions (Coulombic,
hydrogen and van der Waals bonds) are localized at specific
sites or atoms of the unimers. These sites may be
distributed at discrete locations over the surface of the
unimers: the direction of interaction determines the functionality
of the unimer and, in turn, the dimensionality of
the assembly (cf. next section and Figure 3). These localized
interactions are described by the respective set of
potential functions involving combinations of point
charges, dipolar interaction and separation distances. Several
combinations of the above interactions may occur
over the surface of the unimer, additively contributing to
the overall binding free energy. [56, 72] Cooperative effects
(when the formation of the first pairwise interaction
increases the binding constant at successive sites along
the chain) are also possible. In the case of H-bonds that –
due to their strong directionality – are a primary source
of stabilization of several SPs in class A, the parallel or
antiparallel arrangement of multiple bonds may increase
or decrease the product of the single binding constants on
account of secondary electrostatic interaction.
[5, 6]
In addition to the above site-localized classical interactions,
other stabilizing interactions play an important role
in polymeric assemblies. [1] The solvophobic bond is
responsible for the micellization of amphiphiles in the
presence of a solvent. Even in the absence of a solvent,
the incompatibility of amphiphilic components produces
their ordered microsegregation. These interactions can be
described by thermodynamic parameters that control
micro- and macrophase separations. For instance, the
Flory-Huggins thermodynamic parameter v plays a primary
role in the theoretical description of microsegregation
in block copolymers (cf. ref. [1, 81] and Section 4.2).
The occurrence of liquid crystallinity in solutions of
several polymeric assemblies is an example of hierarchical
structurization (“macroscopic expression of molecular
recognition” [2] ). Again, a thermodynamic effect (e.g.,
volume exclusion resulting from the shape anisotropy of
rigid SPs) is the primary driving force for structurization.
Note that it is convenient to distinguish the role of shape
in the stabilization of individual unimers (shape I effect,
cf. (iii) above) from the role of shape anisotropy in the
development of liquid crystallinity by rigid SPs (shape II
effect, cf. ref. [1] and Section 4.1).
3 Functionality of the Unimer and
Dimensionality of the Assembly
The assessment of unimer functionality is a primary
requirement for determining the dimensionality of the
assembly. Bifunctional rod-like, disk-like or spherical
unimers (see scheme in Figure 3a) having binding sites
pointing toward the North and South directions (or
toward East and West) yield linear polymers. Note that it
is the directionality of the interaction that specifies the
functionality, e.g., the same functionality is assumed if
four H-bonds rather than a single one point in the same
direction.
Increasing the functionality of the unimers produces
more complex structures. The presence of two additional
sites produces extended or helical double chains, [1, 7] provided
the additional sites are located at the same side of
the assembly (e.g., NE and SE, Figure 3b). However, planar
assemblies are expected when four sites point toward
perpendicular directions within a cross-section of cylindrical
and disk-like unimers, or the equatorial plane of a
spherical unimer (Figure 3c). The occurrence of two
additional sites on the flat surfaces of cylinders and disks,
or the poles of a sphere, generates a three-dimensionally
ordered network (Figure 3d).
The symbols +, –, 0, and 9, in Figure 3 indicate the
functionality and refer to any possible localized supramolecular
bond (Coulombic, hydrogen, van der Waals). In
the case of non-localized effects, such as incompatibility
and shape II-induced mesophases, a more uniform distribution
of repulsive interaction ought to be assumed. In a
few cases a polymer is undoubtedly formed, but the specification
of unimer size and shape may not be straightforward.