Supramolecular Polymers and Assemblies. Andreas Winter
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with carboxylic acids (see Chapter 2) [98], and the equilibrium between linear, tape‐like, and cyclic structures that can be observed in stoichiometric mixtures of cyanuric acid and melamine derivatives (see Chapter 3) [99].
Figure 1.12 Schematic representation of the formation of a poly(pseudorotaxane) via a ring‐chain equilibrium.
Source: Cantrill et al. [95]. © 2001 American Chemical Society.
1.3.3 (Anti)‐cooperative Supramolecular Polymerization
The third and last mechanism for supramolecular polymerization to be discussed herein involves (at least) two distinct stages, resulting in a cooperative or an anti‐cooperative growth of the polymer chains. At first glance, the mechanism of the cooperative supramolecular polymerization is reminiscent to the one for the IDP; however, the polymerization initially occurs via the reversible binding of monomers to the growing chain (as for the IDP, all these steps basically possess the same equilibrium constant Kn). At a certain DP, a nucleus is formed and, from this point on, the binding of monomers to the polymer chain features an association constant Ke, which is higher than Kn (Figure 1.13). In such a nucleation‐elongation polymerization (NEP) model, the supramolecular polymerization proceeds via a linear IDP. In this elongation phase, the actual association constant is now Ke rather than Kn [26, 43, 100, 101].
Figure 1.13 Schematic representation of a typical cooperative supramolecular polymerization reaction (nucleation‐elongation mechanism). Kn and Ke represent the association constants for the nucleation and the elongation phase, respectively (Kn < Ke).
Source: Winter et al. [39]. © 2012 Elsevier B.V.
The complex thermodynamics of the (anti‐)cooperative supramolecular polymerization have already been summarized by de Greef et al.; the reader is referred to this review for a more in‐depth discussion [26]. In the following, a few general aspects concerning the different types of cooperative supramolecular polymerization shall be named. First, one can distinguish between the nucleated and the downhill cooperative supramolecular polymerizations. Ferrone defined a nucleated supramolecular polymerization as a process wherein the initial steps of the chain growth are characterized by an increase of ΔG0 of the oligomers relative to the monomer (Figure 1.14a) [102]. Beyond the point of nucleation, characterized by a maximum in ΔG0, polymerization becomes energetically favorable. Now, the nucleus represents the least stable and, thus, the least abundant species in the supramolecular polymerization; as a result, the formation of new polymer chains is retarded (the so‐called bottleneck effect). It is widely accepted that formation of the nucleus occurs via homogeneous nucleation (the analysis of various examples of nucleated supramolecular polymerization has suggested this feature). Noteworthy, however, heterogeneous nucleation is also known, but commonly refers to the nucleation processes on foreign substrates [103]: foreign molecules (e.g. impurities) [104–106], external surfaces (e.g. substrates) [107], dust particles, or secondary nucleation of monomers. The latter eventually give a supramolecular polymer on an already existing one. In particular, the latter has been reported to be dominant in various bio‐supramolecular polymerizations [26].
Figure 1.14 Schematic illustration of the energy diagrams of a cooperative nucleated (a) and a cooperative downhill supramolecular polymerization (b). In both plots, the axis of abscissae represents the oligomer's size (i), whereas the ordinate measures the ΔG0 in arbitrary units. In diagram (a), the size of the nucleus is 2 (i.e. dimeric nucleus); in diagram (b), a tetrameric nucleus is depicted.
Source: de Greef et al. [26]. © 2009 American Chemical Society.
In summary, three key criteria can be listed according to Frieden to distinguish between an NEP and an IDP [280]:
1 The supramolecular polymerization process is retarded time dependently;
2 This delay of the polymerization can be compensated by adding a preformed nucleus (i.e. seeding); and
3 An equilibrium between the monomer and the supramolecular polymer is established at a certain critical concentration (or temperature).
In contrast to the cooperative nucleated supramolecular polymerization, the cooperative downhill counterpart does not exhibit any increase of ΔG0 in the initial steps. Instead, the initial growth of the polymer is characterized by a lower association constant than the following elongation (i.e. Kn > Ke; Figure 1.14b). Thus, the monomer is always the species of highest energy in such a cooperative polymerization for which Powers and Powers defined the “nucleus” as the critical chain length at which the absolute (dΔG0/di)‐increment steeply increases [108]. The distinction between the two aforementioned possibilities for cooperative polymerization is associated to the concentration, and, at high total monomer concentrations, a nucleated polymerization process can even be converted into a downhill one [108, 109]. Concentration‐dependent kinetic measurements might, for example, be utilized to distinguish between the two different types of cooperative supramolecular polymerization [108]: in the downhill supramolecular polymerization, the nucleus will be different from the one to be found in a nucleated process (i.e. the nucleus represents a stable or an unstable species, respectively).
For the second type of mechanism, the anti‐cooperative supramolecular polymerization, the initial oligomer formation features an association constant that is much higher than the one for the elongation process. So far, the anti‐cooperative growth in supramolecular polymerizations has attracted less attention, though discrete objects of low dispersity might be obtained (on the contrary, cooperative growth typically gives supramolecular polymers with high Đ values). For example, Mukerjee [110–114] as well as Tanford [115] reported the formation of large aggregates due to the self‐assembly of the surfactants. Due to a high degree of cooperativity in the early stages of the micellar growth, the formation of molecular clusters (i.e. dimers and trimers) was almost fully suppressed. Moreover, (electro)static interactions between the polar head groups of the molecules were identified as the origin of the anti‐cooperative effects, affording micelles of finite size.
What is the covalent counterpart to cooperative supramolecular polymerization? In typical chain‐growth polymerizations (either ionic or radical), the initiation step is analogous to the formation of the nucleus in the NEP; both systems also feature a sequence of propagation steps;