Spontaneous sense inversion in helical mesophases

We investigate the pitch sensitivity of cholesteric phases of helicoidal patchy cylinders as a generic model for chiral (bio-)polymers and helix-shaped colloidal rods. The behaviour of the macroscopic cholesteric pitch is studied from microscopic principles by invoking a simple density functional theory generalised to accommodate weakly twisted director fields. Upon changing the degree of alignment along the local helicoidal director we find that cholesteric phases exhibit a sudden sense inversion whereby the cholesteric phase changes from left- to right-handed and vice versa. Since the local alignment is governed by thermodynamic variables such as density, temperature or the amplitude of an external directional field such pitch sense inversions can be expected in systems of helical mesogens of both thermotropic and lyotropic origin. We show that the spontaneous change of helical symmetry is a direct consequence of an antagonistic effective torque between helical particles with a certain prescribed internal helicity. The results may help opening up new routes towards precise control of the helical handedness of chiral assemblies by a judicious choice of external control parameters.