Liquid crystals of bent-shaped molecules: modelling their unconventional properties and phase behaviour

The fascinating behaviour of liquid crystals is a consequence of the shape anisotropy of their constituent molecules. Conventional mesogens have a rod-like or disc-like shape: their simplest and most common mode of liquid crystalline organization is the nematic phase (N), where the molecules preferentially align along a common axis, called the director n. Recently a new class of thermotropic liquid crystals has emerged, made of achiral molecules with a bent (banana-like) shape. From a chemical point of view, two molecular architectures can be distinguished: bent-core compounds and odd liquid crystal dimers. The first are characterized by a fairly rigid aromatic core and terminal flexible chains; the second are made of two terminal mesogenic units connected by a flexible spacer having an odd number of atoms. Liquid crystals of bent molecules are unconventional materials, in that they exhibit remarkable physical properties and new phase organizations, different from those of conventional liquid crystals. In particular, unusually low values of the bend elastic constant K33 and relatively high flexoelectric couplings were measured for both bent-core compounds and odd liquid crystal dimers in their N phase. The origin of this behaviour is not clear and different hypotheses have been proposed. Its understanding is important both for fundamental reasons and also for applications, including the design of materials optimized for new display modes or for electromechanical energy conversion. For what regards the phase organization, there is currently considerable interest for a new kind of nematic phase, which has been discovered only a few years ago in odd liquid crystals dimers, at temperatures below the common N phase. 2H-NMR experiments, which provide information on the molecular order, demonstrated that this phase is chiral, despite the molecules being achiral, and a twist-bend nematic organization was proposed (NTB). This is characterized by a modulated director n which precesses in space around an axis forming a conical helix, with conical angle theta0 and pitch p, thus featuring spontaneous local bend distorsions and local polar order. This discovery has given rise to an intense debate, in relation to both the phase structure and origin. Either flexoelectric couplings or an elastic instability have been proposed as possible driving mechanisms of the NTB-N transition. Segregation of chiral molecular conformations has also been invoked to explain the phase chirality. Another aspect which needs clarification is the strong sensitivity of the NTB phase formation to small changes in the molecular structure. In this thesis the phase and material properties of liquid crystals of bent molecules have been investigated using theoretical and computational methods, with the aim to establish a connection between the macroscopic behaviour and the molecular structure. This is a challenging task: computational methods such as quantum mechanical calculations and atomistic Molecular Dynamics simulations are in many cases insufficient and alternatives routes must be found. In this work different methods have been used and developed, suitable to cover or connect the different length scales involved. (i) To investigate the molecular origin of the NTB-N phase transition, and to obtain qualitative information on the structure of the NTB phase, a molecular field model was developed, by generalizing the Maier-Saupe theory to apolar rigid V-shaped molecules in an N or NTB environment. Our findings show that the key molecular feature at the origin of the NTB phase is the bent molecular shape, indicating that flexoelectric couplings are not essential. We showed that the phase behaviour is extremely sensitive to the molecular bend angle, with the NTB-N phase transition occurring only for a limited range of values. This result allowed us to elucidate the experimentally observed sensitivity of the NTB phase formation to small changes in the molecular structure. The model also allowed us to make some general predictions about the elastic behaviour and to clarify the relationship between the NTB-N phase transition and the elastic properties of the nematic phase, showing that transition is accompanied by softening of the bend elastic mode in the N phase. To get insight into the molecular organization in the NTB phase, Molecular Dynamics simulations of rigid, apolar, achiral, purely repulsive bent-shaped particles were performed. In this way we could explicitly take into account the possible effects of intermolecular correlations and further check the relationship between the molecular features and the phase behaviour. Our results are in line with the formation of an NTB organization, and, given the molecular model used, point to the crucial role of the bent shape, in agreement with the conclusions of our generalized Maier-Saupe model. In particular, the observation of a chiral organization in a system of achiral rigid particles clearly indicates that conformational chirality is not essential for the formation of the NTB organization. (ii) An Integrated Methodology (IM), which couples an atomistic representation of the molecular structure with a molecular field model of orientational order, was set up to obtain quantitative information about the phase and material properties, and their dependence on the chemical structure. In this context quantum mechanical DFT calculations were performed to obtain accurate values of the relevant molecular structural parameters (geometry, torsional potentials and atomic charges) and Monte Carlo conformational sampling was used to take into account the molecular flexibility. Much of the work has been dedicated to understanding the elastic and flexoelectric behaviour of bent-core compounds and liquid crystals dimers in their nematic (N) phase. Collaboration with experimental groups allowed us to validate the methodology on a large number of systems with different molecular structures. Very good agreement was obtained between our predictions and the experimental findings, showing the sensitivity of our methodology to details of the chemical structure and thus its usefulness as a tool for materials design for applications. The variety of chemical structures investigated allowed us to build a library of molecular parameters for the most common mesogenic groups, which can be reused and incremented in the future. Modelling allowed us to identify the molecular origin of the small bend elastic constant K33 exhibited by nematics of bent molecules and also to explain apparent exceptions to this behaviour. In particular we showed that the main parameter governing the elasticity of these systems is the molecular bend angle. The IM approach appears promising also for the development of a molecular-based understanding of flexoelectricity in liquid crystals. We could identify some general features in the flexoelectric properties of bent-core compounds and connect them to the molecular structure, offering a consistent interpretation of different experimental results. The molecular field model at the basis of the IM methodology has been extended to describe the orientational order in the NTB phase. In this way it was possible to analyse the detailed information provided by 2H-NMR experiments. By combining the theoretical predictions with the experimental data we could obtain quantitative estimates of the pitch and conical angle of the NTB phase on the basis of the molecular structure. We also investigated the origin of the strong enantiotopic discrimination observed in the NTB phase. Our results indicate that this is not related to presence of chiral molecular conformations, but it is a direct consequence of the high chirality of the NTB environment, resulting from its extremely small pitch. The thesis is organized as follows. The Introduction is intended as an overview on liquid crystalline order (Chapter 1) and on the unconventional phase and material properties of liquid crystals of bent-shaped molecules (Chapter 2). Part I (Chapter 3) presents the generalized Maier-Saupe model and its results. Part II (Chapter 4) is devoted to the Molecular Dynamics simulations. Part III illustrates the IM methodology (Chapter 5), its applications to the investigation of phase and materials properties of bent-shape molecules in their nematic phase (Chapters 6-8), and finally its extension to the twist-bend nematic phase (Chapter 9