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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].

Schematic illustration 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

      Source: Winter et al. [39]. © 2012 Elsevier B.V.

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; 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.

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