Ising models of helical ordering in self-assembled polymers
Prof. Paul van der Schoot (TU Eindhoven)

A class of equilibrium polymers has been discovered that under appropriate conditions exhibit a helix-coil type conformational transition, as evidenced, e.g., by the emergence of a Cotton effect. Associated with the supramolecular helical transition is also a pronounced peak in the heat capacity, and a spurt-like growth of the mean molecular weight of the assemblies upon crossing the transition temperature.

Exclusively left- or right-handed helical conformations only form when the molecular building blocks of the self-assembled polymers are homochiral. In case of racemic mixtures, or when the molecules are achiral, equal numbers of left- and right-handed helical configurations form and no Cotton effect is observed. Then the helical nature of the transition presents itself through the effect of chirality amplification, whereby the addition of a very small amount of chiral material, or a small enantiomeric mismatch, is sufficient to drive almost all the assemblies into either a left- or right-handed configuration.

In my presentation I shall outline a simple yet effective theory of helical equilibrium polymerisation in dilute solution, based on what essentially is the law of mass action for a self-assembled Ising chain. The theory predicts the equilibrium polymerisation and the helical transition to be strongly coupled, producing an enhanced growth of the assemblies as found in experiments. We also find that the state of the aggregate ends dictates the strength of this coupling, and that the concept of an end-cap energy fails near the helical transition if it is sufficiently co-operative.

By fitting to data obtained by a host of experimental techniques, we are able to fix all the theoretical parameters and conclude that the helical transition in supramolecular polymers is at least as co-operative as it is in conventional polymeric systems. The theory is also able to quantitatively explain how the concentration of dissolved material impacts upon the level of chirality amplification in (so-called) sergeants-and-soldiers experiments and in majority-rules experiments. Such a concentration dependence is specific to equilibrium polymers and absent in conventional polymeric systems.