Liquid crystal phase behaviour of colloidal mixtures

Abstract

The central aim of this thesis is to theoretically investigate the effects of mixing anisometric colloidal particles with different shapes on their (lyotropic) liquid crystal phase behaviour. Many of the studies to be described in this thesis have been triggered off by recent experimental observations in mixtures of colloids with well-controlled shapes and interactions. In particular, we mention the experimental work of Van der Kooij [F. M. van der Kooij, thesis, Utrecht University, 2000] who investigated a vast number of mixtures which display many interesting phenomena left open for theoretical interpretation. One of our primary goals in this work is to account for these experimental observations by constructing simple, yet realistic, models for the colloidal systems under consideration and by scrutinizing relevant aspects of their phase behaviour. The first part of this thesis will be devoted to binary mixtures of anisometric particles. In Chapter 2 a simple model is proposed that allows to qualitatively explain the recently observed isotropic-nematic density inversion in polydisperse systems of colloidal platelets. In the next two chapters we shall be concerned with mixtures of rods and platelets and provide a theoretical underpinning for the low-concentration part of the experimental phase diagram. We also establish the possible stability of the disputed biaxial nematic phase in experimentally realizable mixtures. In Chapter 5 we conclude the first part with an overview on demixing transitions within the isotropic and nematic phases of binary mixtures of particles whose size differs only in one particle dimension. Previously published results for rodlike particles will be combined with new results for platelets to compare phase diagram topologies and demixing mechanisms pertaining to the various mixtures. In the second part of this thesis we address the more challenging issue of calculating phase equilibria in polydisperse mixtures of anisometric particles. In Chapter 6 we present a study of isotropic-nematic phase coexistence in systems of length-polydisperse hard rods, focussing in particular on fractionation effects and the possibility of a demixing of the nematic phase. Chapter 7 deals with polydisperse systems of thickness-polydisperse platelets. The binary model, introduced in Chapter 2, is extended to a polydisperse one which allows us to provide a more realistic, albeit still qualitative, description of the experimental observations. In Chapter 8 we provide a preliminary calculation on the competition between smectic and columnar ordering in systems of polydisperse hard rods. As a first-order approximation we consider an artificial model system of perfectly aligned cylinders. The possibilities of extending the approach towards a more realistic one will be discussed. The contents of Chapter 9 of this thesis differ somewhat from the rest because of the introduction of an external field. Inspired by recent experimental observations of a significant sedimentation in dispersions of platelets we illustrate the drastic effect of gravity on the phase behaviour of colloidal mixtures. As an example we consider a system of sedimenting platelets mixed with non-sedimenting ideal polymers, as studied in experiment. Also here, the results of the calculations reveal an improved description of the experimentally observed behaviour. Finally, in Chapter 10 we present a free-volume theory for a columnar state of hard platelets by combining the traditional cell model with an appropriate fluid description, accounting for the rotational freedom of the particles in the (one-dimensional) direction of the phase. Excellent quantitative agreement is found with recent computer simulation results for various thermodynamic and structural properties of a dense columnar state.