Theory and Simulation Studies of Self-Assembly of Helical Particles

Helically nanostructured materials have been attracting increasing attention, also because of their unique electrical and mechanical properties. This chapter briefly recalls the main features of liquid crystal phases, with special attention to their chiral versions. It presents an outline of the Onsager theory, and then extends it to helically modulated nematic phases. The chapter reviews the definitions of the order parameters and correlation functions necessary to identify the various phases. This is followed by a discussion on the physical origin of the chiral nematic phases formed by helical particles. A rigid helical particle is a chiral object, in that left-handed helices cannot be superimposed on their right-handed counterparts. The chapter gives an overview of the phase behavior of hard helices. It compares theoretical predictions to experimental data and considers a combination of Monte Carlo simulations and density functional theory.