Counterintuitive consequences of competitive pathways in supramolecular polymerizations (2019)

Competition between supramolecular polymers for the same monomers can lead to strong responses in these systems. Using numerical simulations, we show that the sharpness and asymmetry of the transition from one thermodynamically stable polymer to another upon changing temperature is determined by the most unstable rather than the most stable supramolecular polymer. The width and asymmetry of the transitions are shown to depend on the relative and absolute nucleation penalties of the competing supramolecular polymerizations. The performance of molecular and polymeric materials in various applications, such as optoelectronics, is highly dependent on the defined morphology and order in these materials.1, 2 In supramolecular polymeric systems, high degrees of helical order are typically achieved in strongly cooperative polymerizations.3 Upon installation of stereocenters in the monomer, one helicity of the polymer is preferred over the other, which is easily detected with circular dichroism spectroscopy. The cooperative nature of the polymerization process strongly amplifies the small energetic differences caused by the helical preference of the monomers and as a result, only one helicity of the supramolecular polymer is typically observed at thermodynamic equilibrium. However, in the last decade it has been shown that also the thermodynamically nonpreferred helicity can be formed under kinetic control due to the pathway complexity of the polymerization.4 Control over the kinetic stability has paved the way of living supramolecular polymers5-8 and the synthesis of kinetically controlled supramolecular block copolymers.9, 10 Many of these studies are inspired by the seminal science of Kris Matyjaszewski on covalent macromolecules, where kinetic information is combined with the synthesis of novel architectures. Similarly, several systems that show multiple thermodynamically rather than kinetically controlled polymer morphologies at various temperatures or solvent compositions have been experimentally observed and these reports have recently gained more attention.11-20 Interestingly, these thermodynamically controlled competitive polymerizations show concentration-independent polymer–polymer transitions that are solely determined by the relative stabilities of the aggregates, making them very responsive to changes in solvent19 or temperature.20 However, in addition to concentration independency, these transitions between supramolecular polymers have been shown to exhibit more intricate features, such as gradual or sharp onsets and asymmetry in the transition [Fig. 1(a)], for which no explanation has been given yet. Moreover, these additional features in the thermal or solvent-induced transitions between two supramolecular polymers impair straightforward analysis and interpretation of the thermodynamic properties of the polymerizations. Using numerical simulations, we here show that the subtle details of these transitions between supramolecular polymers give information on the relative and absolute measures of cooperativity of each polymer state. Counterintuitively, the sharpness and asymmetry of a transition between two supramolecular polymers upon changing temperature or solvent quality is shown to be determined by the cooperativity of the most unstable rather than the most stable supramolecular polymer. The thermodynamic values of the elongation phases, which determine the elongation temperatures of the polymers,21 have been chosen such that the elongation temperature of state A is at 80 °C, and the system is predominantly polymerized below this temperature and monomerically dissolved above the elongation temperature. The stabilities of the elongation phases of states A and B are equal at 20 °C, with state B being more stable below 20 °C, which results in the A-B transition between the two polymer states at that temperature.19, 22 Although the elongation and transition temperatures are equal for all simulations, Figure 2 clearly shows that varying the cooperativities of the supramolecular polymerizations has a strong influence on the shape of the A-B transition at 20 °C. Upon reducing the nucleation penalty of State B at constant NPA [Fig. 2(a)], the A-B transition at temperatures above 20 °C, where state A is most stable, becomes more gradual, while the A-B transition below 20 °C, where state B is most stable, is largely unaffected. Conversely, varying the nucleation penalty of state A at constant NPB leads to a more isodesmic elongation at 80 °C, but also to a more gradual transition at temperatures below 20 °C, where state B is most stable. Thus, counterintuitively, a change in cooperativity of one polymer state manifests itself in a more gradual transition at temperatures where the other polymer state is the thermodynamically most stable structure. In the case of two competing cooperative supramolecular polymerizations, we consider the case where polymer state A is the most stable supramolecular polymer. When state A is thermodynamically more stable than state B, and so Ke,A > Ke,B, the maximum concentration of free monomers in the system is determined by the stability of polymer A and not polymer B (see eq 2). However, at temperatures close to the transition between the polymer states, the stabilities of the supramolecular polymers are very similar22, 24 and the monomers have a large tendency to be aggregated. Consequently, when polymer state B is only weakly cooperative and nucleation of state B occurs relatively easily, the small amount of free monomers can already assemble into supramolecular polymers of state B, even when state B is not the most stable thermodynamic structure. As a result, the two polymer states coexist at that temperature. When the transition is monitored with spectroscopy, the coexistence of the weakly cooperative polymer B with the most stable polymer A leads to a relatively gradual onset of the transition between states A and B upon decreasing the temperature, as is shown in Figure 2(a) (dark curves). Conversely, when state B is strongly cooperative yet not the thermodynamically most stable polymer, nucleation does not occur easily when the free monomer concentration does not approach Ke,B−1 and no polymers of state B will be formed. However, when state B becomes the most stable supramolecular polymer, the free monomer concentration set by state A suddenly becomes larger than Ke,B−1 and very abruptly, monomers are transferred from polymer A to polymer B. This then gives rise to the very sharp transition just above the temperature where polymer B becomes the most stable structure [Fig. 2(a), light curves]. Thus, the cooperativity of the thermodynamically least stable polymer state B leads to a sharper or more gradual A-B transition by being less or more competitive at sequestering monomers that do not polymerize into state A. Below 20 °C, the A-B transition in Figure 2(a) is not affected by a change in nucleation penalty of polymer B. This is because at those temperatures, polymer B is the most stable supramolecular polymer and hence determines the maximum free monomer concentration. Therefore, in this regime, the sharpness of the transition is determined by the cooperativity and nucleation penalty of polymer A [Fig. 2(b)]. The origin of this feature can be rationalized using the same arguments as were used in the discussion of the regime where the polymers have opposite stability (vide supra). Thus, the relative sharpness of the transition from one supramolecular polymer to another supramolecular polymer is indicative of the nucleation penalty and cooperativity of not the polymer that is predominantly present at that temperature and solvent quality, but rather of the polymer that is the least present at these conditions. In addition to insights into the relative nucleation penalties and cooperativity parameters of competing supramolecular polymerizations, the shape of the polymer–polymer transition also sheds light on the absolute value of these thermodynamic properties, as can be seen in Figure 2(c). When both polymers are only weakly cooperative, the two pathways can compete in an effective manner over the limited concentration of monomers over an extended temperature range. As a result, the transition between the polymers will span a broad temperature range and a small slope is observed. Conversely, when the polymers are both strongly cooperative, nucleation of the thermodynamically least stable polymer can only occur at temperatures very close to the temperature where both states have equal Gibbs free energies of elongation. Since the competition in the case of two strongly competitive polymerizations only occurs in a very small temperature range, a high slope is observed for the transition between supramolecular polymers that have high absolute values of the nucleation penalties. The principles outlined above can serve as simple guidelines to assess the cooperativities of the competing supramolecular polymerizations. As such, the general trends that can be observed in the literature [Fig. 1(a)] can be classified in systems that have a more cooperative state A and less cooperative state B [Fig. 1(a), Panel I], systems in which states A and B have comparable cooperativity [Fig. 1(a), Panel II] and systems in which state A is less cooperative than state B [Fig. 1(a), Panel III]. These results also show that the unusually sharp and asymmetric experimentally observed transitions, which can easily be regarded as artifacts, are rather a consequence of highly competitive supramolecular polymerizations. Counterintuitively, a sharp transition occurs when the competing, least stable polymer is very cooperative, irrespective of the cooperativity of the most stable supramolecular polymer. In conclusion, the shape of transitions between strongly cooperative supramolecular polymers can give valuable insights into thermodynamic properties of these competitive systems. Although strong cooperativity in supramolecular polymers is associated with high degrees of aggregation and order, these systems can still be sensitive to competition from weakly cooperative polymers. Here, we show that the depolymerization of a supramolecular polymer in a competitive polymerization process is governed predominantly by not the cooperativity of the depolymerizing polymer, but rather by the cooperativity of the newly formed polymer state. Counterintuitively, newly formed weakly cooperative polymer states are more effective than strongly cooperative polymers at depolymerizing the already present supramolecular polymers, because the increased isodesmic character of the weakly cooperative polymers is more effective at sequestering free monomers. Therefore, the shape and width of such polymer–polymer transitions can be used to obtain valuable insights into relative and absolute cooperativities of both polymer states. We anticipate that straightforward guidelines for the interpretation of complex supramolecular polymerizations will facilitate the analysis of increasingly responsive systems for optoelectronics and soft materials. The entropies of the nucleation and elongation phases are taken to be equal. The cooperativity parameter, which relates the nucleation and elongation equilibrium constant, is determined by the nucleation penalty through eq 1. For the simulations, varying nucleation penalties are used with constant thermodynamic properties of the elongation phase. The enthalpies and entropies of the elongation phases of states A and B are ΔHe,A = −60 kJ mol−1, ΔSA = −87.6 J mol−1 K−1 for positive signal state A and ΔHe,B = −80 kJ mol−1, ΔSB = −155.8 J mol−1 K−1 for negative signal state B. The entropies of the nucleation and elongation phase are taken equal. The signal intensities per state are chosen arbitrarily to show a clear distinction between the population of States A and B. Elisabeth Weyandt and Marcin Ślęczkowski are acknowledged for fruitful discussions. The authors acknowledge the financial support from NWO (TOP-PUNT Grant 10018944) and the Dutch Ministry of Education, Culture and Science (Gravitation program 024.001.035).