Self-Assembly Principles of Helicates - Metallofoldamers: Supramolecular Architectures from Helicates to Biomimetics - page 96

k i M

k i M · EM

+

Figure 3.3 Schematic view and the thermodynamic description of intramolecular macro-
cyclic connections in the self-assembly of double-stranded helicates (i.e., Ref. [19]).

dinuclear double-stranded helicate in Figure 3.3. The initial intermolecular connection
of a metal ion to the ligand coordination site i occurs with the microscopic binding
affinity k i . The intramolecular ring closure follows with the stability constant
K intra ¼ k i EM ,where EM is the effective molarity for the macrocyclization process.

The associated free energy contribution is given by the relation

D G M;L
intra

k i

. Similarly to the chelate effect, effective molarity is obtained
as the ratio of stability constants measured for the intramolecular and reference inter-
molecular reactions. In the absence of strains, EM is a purely entropic contribution and
indicates the advantage ( EM

¼ RT ln ð EM Þ

1M) of an intramolecular con-
nection with respect to its intermolecular counterpart. However, the values of EM in mac-
rocyclization processes are much smaller compared to the chelate effect [15,20], and the
interplay between EM and the ligand concentration plays a more important role. While
the ligand concentration is a driving force for disassembly and dissociation [11], the mag-
nitude of EM directly controls the balance between intra- and intermolecular interactions
and measures the system preorganization.
The deliberate manipulating of EM through the ligand structure represents an important
tool in controlling self-assembly processes. The thought-out design of spacers between
binding sites (length, spatial orientation, stacking interactions, etc.) contributes to the sys-
tem preorganization for the next binding event. Using intersite linkers of differing rigidity
may control the topology of the resulting assemblies. However, the formed edifice may
escape the planned supramolecular design, for instance, due to too restricted degrees of
freedom when connecting the binding units. For instance, the introduction of a rigid
spacer between binding sites hinders the second intramolecular connection for steric rea-
sons [21]. The most stable self-assembled complex thus contains an unoccupied metal
binding site, which violates the principle of maximum occupancy. Another manipulation
of EM is shown for assemblies with tripodal ligands, where a deliberate programming of
low effective molarity, resulting from ligand steric strains, prevents the formation of
mononuclear complexes, to the benefit of tetranuclear three-dimensional helicates [22].

> 1M) or hindrance ( EM <

3.2.2.2 Theoretical Models for Effective Molarity
The effective molarity term EM , which was introduced for describing intramolecular
interactions, is considered by chemists as the empirical experimental parameter. However,
the theoretical concept of effective molarity is cited in literature as effective concentration
c eff [16]. Theoretical models for estimating EM in chelate and macrocyclization processes
are available, but account only for the entropic part of EM in the absence of enthalpic
contributions (D H intra ¼ D H inter ). Let us briefly resume here two situations from the liter-
ature, detailed discussions of which can be found in Refs [13,15c].