Physics of colloidal dispersions in nematic liquid crystals
Section snippets
Motivation and contents
Dispersions of particles in a host medium are part of our everyday life and an important state of matter for fundamental research. One distinguishes between emulsions, where surfactant-coated liquid droplets are dispersed in a fluid environment, colloidal suspensions, where the particles are solid, and aerosols, with fluid or solid particles floating in a gaseous phase. Colloidal dispersions, whose particle size ranges from 10 nm to , appear in food, with milk being the best-known
Phenomenological description of nematic liquid crystals
Typical liquid crystalline compounds consist of organic molecules. According to their elongated or disc-like shape one distinguishes between calamatic and discotic liquid crystals. Fig. 1a presents the molecular structure of the well-studied compound N-(p-methoxybenzylidene)-p-butylaniline (MBBA). Its approximate length and width are 20 and . At sufficiently high temperatures, the liquid crystalline compound behaves like a conventional isotropic liquid; the molecules do not show any
Nematic colloidal dispersions
In this section we first give a historic account of the topic relating it to recent developments in the liquid crystal field and reviewing the work performed on colloidal dispersions in nematic liquid crystals. Then, with nematic emulsions, we introduce one particular model system for such colloidal dispersions.
The paradigm—one particle
The multiple nematic emulsions that we introduced in Section 3.2 are already a complicated system. In this section we investigate thoroughly by both analytical and numerical means what I regard as the paradigm for the understanding of inverted nematic emulsions. We ask which director field configurations do occur when one spherical particle that prefers a radial anchoring of the director at its surface is placed into a nematic solvent uniformly aligned at infinity. This constitutes the simplest
Two-particle interactions
To understand the properties of, e.g., multi-droplet emulsions, we need to determine the nature of particle–particle interactions. These interactions are mediated by the nematic liquid crystal in which they are embedded and are in general quite complicated. Since interactions are determined by distortions of the director field, there are multi-body as well as two-body interactions. We will content ourselves with calculations of some properties of the effective two-particle interaction. To
The Stokes drag of spherical particles
In Section 2.3 we introduced the Ericksen–Leslie equations that govern the hydrodynamics of a nematic liquid crystal. Due to the director as a second hydrodynamic variable besides the fluid velocity, interesting new dynamical phenomena arise. With the Miȩsowicz viscosities and Helfrich's permeation, we presented two of them in Section 2.3. Here we deal with the flow of a nematic around a spherical particle in order to calculate the Stokes drag, which is a well-known quantity for an isotropic
Colloidal dispersions in complex geometries
In this section we present a numerical investigation of water droplets in a spherically confined nematic solvent. It is motivated by experiments on multiple nematic emulsions which we reported in Section 3.2. However, it also applies to solid spherical particles. Our main purpose is to demonstrate that the topological dipole provides a key unit for the understanding of multiple emulsions. In 7.1 Questions and main results, 7.2 Geometry and numerical details, 7.3 Results and discussion of the
Temperature-induced flocculation above the nematic-isotropic phase transition
Ping Sheng [210], [211] was the first to study the consequences of surface-induced liquid crystalline order above the nematic-isotropic phase transition. He introduced the notion paranematic order in analogy to the paramagnetic phase, in which a magnetic field causes a non-zero magnetization. He realized that the bounding surfaces of a restricted geometry influence the bulk transition temperature Tc. In nematic films, e.g., the phase transition even vanishes below a critical thickness [210].
Final remarks
In this article we have demonstrated that the combination of two soft materials, nematic liquid crystals and colloidal dispersions, creates a novel challenging system for discovering and studying new physical effects and ideas.
Colloidal dispersions in a nematic liquid crystal introduce a new class of long-range two-particle interactions mediated by the distorted director field. They are of either dipolar or quadrupolar type depending on whether the single particles exhibit the dipole,
Acknowledgements
I am grateful to Tom Lubensky, Philippe Poulin and Dave Weitz for their close and inspiring collaboration on nematic emulsions at the University of Pennsylvania which initiated the present work. I thank Anamarija Borštnik, Andreas Rüdinger, Joachim Stelzer, Dieter Ventzki, and Slobodan Žumer for collaborating on different aspects of nematic colloidal dispersions. The results are presented in this review article. A lot of thanks to Eugene Gartland, Thomas Gisler, Randy Kamien, Axel Kilian, R.
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