The twist-bend nematic phase: molecular insights from a generalised Maier–Saupe theory

Bent-shaped liquid crystal dimers exhibit a non-conventional nematic phase, which in the last few years has been actively investigated. A structural model of this phase has been proposed, which is characterised by a helical modulation with a periodicity of the order of few molecular lengths. Such a model, which is generally denoted as twist-bend nematic (NTB), is consistent with various experimental evidences and is supported by theories and simulations. Here, we will examine in more detail the features and the implications of a generalised Maier–Saupe theory, which was recently proposed to explain the origin and structure of the NTB phase. In particular we will analyse the relevant molecular order parameters, with special attention to the polar and biaxial ones, and we will discuss the concept of ‘tilted director’, which may give rise to some ambiguity. The phase behaviour will be described as a function of the bend angle between the mesogenic moieties of a dimer, which in the generalised Maier–Saupe theory is the key molecular feature. Extension of the theory to include fluctuations of the bend angle will allow us to examine the effect of the molecular flexibility on the phase diagram.