Cholesterics of colloidal helices: predicting the macroscopic pitch from the particle shape and thermodynamic state

Building a general theoretical framework to describe the microscopic origin of macroscopic chirality in (colloidal) liquid crystals is a long-standing challenge. Here, we combine classical density functional theory with Monte Carlo calculations of virial-type coefficients to obtain the equilibrium cholesteric pitch as a function of thermodynamic state and microscopic details. Applying the theory to hard helices, we observe both right- and left-handed cholesteric phases that depend on a subtle combination of particle geometry and system density. In particular, we find that entropy alone can even lead to a (double) inversion in the cholesteric sense of twist upon changing the packing fraction. We show how the competition between single-particle properties (shape) and thermodynamics (local alignment) dictates the macroscopic chiral behavior. Moreover, by expanding our free-energy functional, we are able to assess, quantitatively, Straley's theory of weak chirality, which is used in several earlier studies. Furthermore, by extending our theory to different lyotropic and thermotropic liquid-crystal models, we analyze the effect of an additional soft interaction on the chiral behavior of the helices. Finally, we provide some guidelines for the description of more complex chiral phases, like twist-bend nematics. Our results provide new insights into the role of entropy in the microscopic origin of this state of matter.