There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The isotropic–nematic phase transition in semiflexible hard chain fluids is investigated via an Onsager type density functional theory. The angle-dependent excluded volume of two chains required in the theory is obtained via Monte Carlo simulations. The theory predicts an isotropic to nematic phase transition at lower densities than those predicted by previous theories. These results compare favorably with available simulation data.

Phase Behavior of Semiflexible Tangent Hard Sphere Chains

A density-functional theory of the isotropic–nematic phase transition in both rigid and semiflexible hard-sphere chain fluids is described. The theory is based on an exact analytical evaluation of the excluded volume and second virial coefficient B2 for rigid chain molecules, which demonstrates that B2 in these cases is equivalent to that of a binary mixture of hard spheres and hard diatomic molecules. It is assumed that the same binary-mixture representation applies to semiflexible chains, while scaled particle theory is used to obtain the properties of the fluid at arbitrary densities. The results of the theory are in very good agreement with Monte Carlo (MC) simulation data for rigid tangent hard-sphere chains, but in lesser agreement with available MC studies of rigid fused hard-sphere chains. We find that there is reasonable agreement between the theory and MC data for semiflexible tangent chains, which improves with increasing chain length. The behavior predicted by the theory for semiflexible chain...

The nematic-isotropic phase transition in semiflexible fused hard-sphere chain fluids

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Thermotropic Liquid Crystals

1 What is a liquid crystal 2 1.1 Nematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Cholesterics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Smectics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Columnar phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Lyotropic liquid crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Introduction to Liquid Crystals

In this thesis I aim to contribute to a molecular understanding and -description of the phase behaviour of liquid crystalline materials. In particular, I aim at the development of a molecular-based equation of state (EoS) for describing nematic (only orientationally ordered) liquid crystals (LCs) and their mixtures. Special emphasis is put on the role of intra-molecular flexibility on the liquid crystalline phase behaviour. Also, the solubility of small gases in nematic solvents is studied—an area that could be important for potential applications of LCs as novel solvents in gas-absorption processes. In the first part of this introductory chapter, the reader is provided with some background on the liquid crystalline state of matter, the status of LC research, and common and potential applications of LCs (Sections 1.1 and 1.2). Subsequently, available theories for the nematic state are briefly reviewed, and the foundations of the perturbation methodology which is at the basis of the EoS developed in this work are discussed (Section 1.3). Finally, an outline of the work performed in this thesis is presented (Section 1.4).

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Development of an equation of state for nematic liquid crystals

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Development of an equation of state for nematic liquid crystals