Theoretical Analysis of Racemization Kinetics of the Helical Foldamer: Extended Chain Inhibits Propagation of Helical Reversal from One End to Another

The helical foldamer has been paid increasing attention due to its unique chiral structure and functions. However, little is known about their kinetical stability. To clarify the dynamics of the racemization, we derived the general and approximated equations analytically, assuming that the helical reversal is generated at one end of the helical sequence and travels to another. The general solution was in the form of double exponential while the approximated solution was in a single exponential form. The approximated solution clarified that the kinetic constant is in inverse proportion to the number of helical units (n). Analysis of the previously reported helical foldamers (o-phenylene oligomers and aromatic oligoamide) revealed that the two ends of the helical units are capped by the loose-end domains. The theory suggests the larger n stabilizes the helical structure because the fraction of the helical domain relative to the loose domain increases, and the multiple inversion barrier in the helical domain prevents the helical reversal from traveling from one end to the other.