Structure and phase behavior of colloidal rod suspensions

Abstract

The first chapter of the thesis provides the general background on the subject. Overview of experimental results and some key theoretical developments is given and the simulational methods are briefly discussed. In the Chapter 2 sedimentation and multi-phase equilibria in a suspension of hard colloidal rods are explored by analyzing the (macroscopic) osmotic equilibrium conditions. We observe that gravity enables the system to explore a whole range of phases varying from the most dilute phase to the densest phase, i.e., from the isotropic (I), nematic (N), smectic (Sm), to the crystal (K) phase. We determine the phase diagrams for hard spherocylinders with a length-to-diameter ratio of 5 for a semi-infinite system and a system with fixed container height using a bulk equation of state obtained from simulations. X-ray diffraction is frequently used to distinguish the different liquid crystalline phases in experiment. The accuracy of measuring the nematic order from X-ray diffraction is the subject of the Chapter 3. We find that the nematic order parameter determined from the scattered intensity underestimates the actual value by 2-9\%. We also find that the values of $S$ and the ODF are insensitive to the absolute value of the scattering vector for $1.2\pi < |\vec{q}|D < 2\pi$ which agrees well with the assumption proposed by Leadbetter that $I(q,\psi)$ along the equatorial arc is independent of $|\vec{q}|$. The structure of a fluid can be described by means of so-called correlation functions. The correlation functions completely determine the thermodynamics of a system, while their asymptotic behavior is important for understanding the interfacial properties. Such asymptotic behavior of the total correlation function $h(1,2)$ in molecular fluids was investigated in the chapter 4. To this end, we expand the angular dependence of $h(1,2)$ and the direct correlation function $c(1,2)$ in the Ornstein-Zernike equation in a complete set of rotational invariants. We show that all the harmonic expansion coefficients $h_{l_1l_2l}(r)$ are governed by a common exponential decay length and a common wavelength of oscillations in the isotropic phase. We find that the asymptotic decay of $h(1,2)$ is exponentially damped oscillatory for hard spherocylinders with a length-to-diameter ratio $L/D\leqslant 10$ for all statepoints in the isotropic fluid phase. Finally, the Chapter 5 is devoted to the phase behavior of a mixture of colloidal hard rods with a length-to-diameter ratio of $L/\sigma_c=5$ and non-adsorbing ideal polymer. We map our binary mixture onto an effective one-component system by integrating out the degrees of freedom of the polymer. We determine numerically on a grid the free volume available for the ideal polymer coils ``on the fly