Direct Probing of the Free-Energy Penalty for Helix Reversals and Chiral Mismatches in Chiral Supramolecular Polymers

Abstract

The amplification of chirality, where a small imbalance in a chiral constituent is propagated into a strong optical purity, can occur in the spontaneous formation of helical 1-D stacks of molecules stabilized by hydrogen bonding, also known as supramolecular polymers. We have extended a statistical model by van Gestel et al. describing the highly nonlinear relationship between supramolecular helicity and enantiomeric excess for mixtures of enantiomers (the majority-rules effect) and quantitatively account for how this affects the thermodynamic stability of the assemblies. Our method allows for a direct comparison with experimental data, providing an unambiguous determination of the key parameters of the model (i.e., the mismatch and the helix reversal penalties). We demonstrate the successful application of this model to calorimetry data for bis-urea-based helical nanotubes, showing that reversals in the handedness of these nanotubes are not all that rare even though the helix reversal penalty is fairly large. By contrast, the mismatch penalty we obtain is small, implying that a large proportion of enantiomers are present in tube fractions not of their preferred handedness.