Supramolecular Polymers and Assemblies. Andreas Winter
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ring‐chain‐mediated supramolecular polymerization features an equilibrium between supramolecular cyclic species and linear polymer chains.
3 The cooperative supramolecular polymerization shows a nonlinear growth of the polymer chains and is typically nucleated.
Figure 1.4 Schematic representation of the three main mechanisms known for the supramolecular polymerization processes: (a) isodesmic, (b) ring‐chain mediated, and (c) cooperative supramolecular polymerization.
Source: Winter et al. [39]. © 2012 Elsevier B.V.
Going beyond the “traditional” equilibrium state, supramolecular polymerizations leading to assemblies in either dissipative nonequilibrium or even non‐dissipative nonequilibrium states (i.e. kinetically trapped or metastable ones) have recently attracted substantial interest. In these cases, the progress of the polymerization is heavily dependent on the applied preparative method (the so‐called pathway selection), and an in‐depth knowledge of the kinetics is required. In particular, the association rates for each single step become more important. These issues have recently been discussed by Sorrenti et al. in a tutorial review [40].
1.3.1 Isodesmic Supramolecular Polymerization
The isodesmic supramolecular polymerization (IDP, isos: equal, desmos: bond), also often referred to as the “multi‐stage open association” mechanism [28, 41, 42], involves the formation of one type of reversible, non‐covalent interaction between monomers, oligomers, and eventually even polymer chains (Figure 1.5). All supramolecular bonds, which are formed throughout the entire process, are considered to be identical, and thus, the reactivity of all species present is considered to have the same reactivity (i.e. monomers, oligomers, and polymers). Thereby, the neighboring group effects or additional interactions with non‐adjacent sites are neglected. Each single step of the process is characterized by the intermolecular equilibrium constant K (Figure 1.5) – regardless of the chain length. As a result, from the equivalence of each individual polymerization step, IDPs do not exhibit any critical values for the concentration or temperature of the supramolecular polymerization (cpc: critical polymerization concentration, cpt: critical polymerization temperature) [41, 43]. Unlike for the ring‐chain‐mediated polymerization (vide supra), no cyclic species can be found during the self‐assembly process. The counterpart to IDP in “traditional” polymer science is the step‐by‐step reversible polycondensation where intramolecular cyclizations are absent and Flory's “principle of equal reactivity” is obeyed [44, 45]. Detailed investigations have shown that, for example, the polycondensation of decanedioyl chloride with 1,10‐decamethylene glycol in dioxane meets these requirements [46].
Figure 1.5 Schematic representation of the IDP in which the intermolecular equilibrium constant (K) is independent of the length of the assembly (the mechanism is shown for a bifunctional monomer of the Ia‐type, see also Figure 1.2).
Source: Winter et al. [39]. © 2012 Elsevier B.V.
According to the rules of thermodynamics, the free energy of the system constantly decreases when the monomeric units are successively added to the growing polymer chain; this, in turn, further supports the assumption that binding of a monomer to the terminus of a polymer chain is independent of its length (an idealized energy diagram, in which kinetic barriers within the self‐assembly process are neglected, is depicted in Figure 1.6a) [26].
Figure 1.6 (a) Schematic drawing of an energy diagram for an IDP (i: size of the oligomer, ΔG0: free energy in arbitrary units). (b) Evolution of the number‐ and weight‐averaged DP (<DP>N and <DP>W) and the dispersity (Đ) as a function of equilibrium constant and total concentration of monomer (K·ct).
Source: de Greef et al. [26]. © 2009 American Chemical Society.
The number‐ and weight‐averaged DPs (i.e. <DP>N and <DP>W, respectively) can be derived from the monomer concentration and equilibrium constant K according to Eq. (1.2) (though only valid for K·[monomer] < 1) [43]. In the ideal case, Đ converges to the limiting value of 2.0, and thus, the monomer concentration approaches 1/K (Eq. (1.2)); this scenario is comparable to a standard step‐growth polymerization as known from traditional polymer chemistry [27, 33]. The correlation of these parameters with the dimensionless concentration K·ct, where K represents the equilibrium constant and ct the total monomer concentration, is shown in Figure 1.6b. Apparently, high DPs can only be reached for high K·ct values; thus, high monomer concentrations and high K values are both required. Disadvantageously, the intrinsically poor solubility of monomers often excludes high concentrations, and thus, the equilibrium constants must be very high (K > 106) to compensate for this when aiming for supramolecular polymers with high molar masses. As a typical feature of IDP‐type processes, increasing ct automatically leads to a gradual and simultaneous increase of the concentration of monomers and polymer chains; thus, the monomer and polymer chains of various length coexist in solution. Finally, the equilibrium concentration of monomers converges to its maximum value, corresponding to K−1, when increasing the concentration further. Thereby, the monomer remains the most abundant species in solution, independent of the values of K and ct. As for their covalent counterparts, the precise stoichiometry of the functional groups in an IDP represents a prerequisite to obtain polymers with high molar masses: self‐complementary AB‐type monomers inherently bear the ideal stoichiometry, whereas complementary monomers (i.e. using a combination of AA and BB) require an exact 1 : 1 ratio. Moreover, the molar masses of the resultant polymers can be adjusted by the addition of appropriate chain‐stopping agents [47–49].
where <DP>N: number‐averaged DP, <DP>W: weight‐averaged DP, Đ: dispersity, K: equilibrium constant, [monomer]: monomer concentration.
Besides the concentration dependency, the influence of the temperature on the IDP also needs to