Interfacial phenomena in hard-rod fluids

Abstract

This thesis addresses questions of interfacial ordering in hard-rod fluids at coexistence of the isotropic and nematic phases and in their contact with simple model substrates. It is organized as follows.

Chapter II provides some background information about the relation between the statistical mechanical and thermodynamical level of descriptions of bulk hard-rod fluids, as well as introduces the asymptotically exact Onsager model, and some basic facts of interfacial thermodynamics.

Chapter III represents studies of the simplest free IN interface in a fluid of monodisperse Onsager hard rods. For the analysis of this system we develop an efficient perturbative method to determine the (biaxial) one-particle distribution function in inhomogeneous systems.

Studies of the free planar isotropic-nematic interfaces are continued in Chapter IV, where they are considered in binary mixtures of hard rods. For sufficiently different particle shapes the bulk phase diagrams of these mixtures exhibit a triple point, where an isotropic (I) phase coexists with two nematic phases (N1 and N2) of different composition. For all explored mixtures we find that upon approach of the triple point the IN2 interface shows complete wetting by an intervening N1 film. We compute the surface tension of isotropic-nematic interfaces, and find a remarkable increase with fractionation.

These studies are complemented by an analysis of bulk phase behavior and interfacial properties of nonadditive binary mixtures of thin and thick hard rods in Chapter V. The formulation of this model was motivated by recent experiments in the group of Fraden, who explored the phase behavior of a mixture of viruses with different effective diameters. In our model, species of the same types are considered as interacting with the hard-core repulsive potential, whereas the excluded volume for dissimilar rods is taken to be larger (smaller) then for the pure hard rods. Such a nonadditivity enhances (reduces) fractionation at the isotropic-nematic (IN) coexistence and may induce (suppress) a demixing of the high-density nematic phase into two nematic phases of different composition (N1 and N2). Studies of their interfaces show an increase of the surface tension with fractionation at the IN interface, and complete wetting of the IN2 interface by the N1 phase upon approach of the triple point coexistence. In all explored cases bulk and interfacial properties of the nonadditive mixtures exhibit a surprising similarity with the properties of additive mixtures of larger diameter ratio.

In Chapter VI we consider properties of a monodisperse hard-rod fluid in contact with the single wall (W). Studies of surface properties of a fluid of Onsager hard rods represent significant numerical difficulties, therefore we consider a simpler model fluid of hard rods with a restricted number of allowed orientations. Within this model, known as the Zwanzig model, we explore the thermodynamic properties of a fluid of monodisperse hard rods in contact with a model substrate represented by a hard wall with a short-ranged attractive or repulsive ``tail''. The attraction enhances the orientational ordering near the wall in both isotropic and nematic phases, and shifts the transition from uniaxial (U) to biaxial (B) symmetry in the isotropic surface layer to lower chemical potentials, whereas the wetting properties of the substrate remain similar to those of the pure hard wall. The soft repulsion reduces the density in the surface layer, which leads to the shift (or even suppression) of the UB transition, and strong modification of wetting properties. At the WI interface one always finds the wetting transition at sufficiently large repulsion, whereas a drying transition at the WN interface is observed only for sufficiently long-ranged potentials.

In Chapter VII we explore some limitations of models of hard-rod fluids with a finite number of allowed orientations. Within Onsager's second virial theory we construct their bulk phase diagrams. For a one-component fluid, we show that the discretization of the orientations leads to the existence of an artificial (almost) perfectly aligned nematic phase, which coexists with the (physical) nematic phase if the number of orientations is sufficiently large, or with the isotropic phase if the number of orientations is small. Its appearance correlates with the accuracy of the sampling of the nematic orientation distribution within its typical opening angle. For a binary mixture this artificial phase also exists, and a much larger number of orientations is required to shift it to such high densities that it does not interfere with the physical part of the phase diagram.