Session Q8: Colloidal Phase Behavior

Studies of colloids on spherical interfaces using digital holographic microscopy

Colloidal particles pinned to the surface of an oil droplet in water form robust equilibrium structures at low area fractions. To better understand the interactions in this system, we are studying these structures and their dynamics during quasistatic changes in the area fraction. We do so by imaging the 3D structures with fast temporal resolution using digital holographic microscopy (DHM). To keep the particles in non-density matched colloidal samples in the field of view, we have constructed a new apparatus to perform DHM under time-averaged zero gravity using a rotating stage. In DHM, we illuminate a sample with a laser beam and then magnify and digitally record the interference patterns between the scattered and unscattered light. Subsequent numerical reconstruction of the recorded 2D holograms allows 3D particle tracking with millisecond time resolution and submicron spatial resolution.   

Confinement Finds a Length Scale for the Colloidal Glass Transition

We study a colloidal suspension confined between two parallel walls as a model system for glass transitions in confined geometries. We use confocal microscopy to directly observe the motion of the colloidal particles, which are slower when confined. This slower motion produces glassy behavior in a sample that is liquid-like when not confined. Our results, from a range of volume fractions, demonstrate that the maximum thickness where confinement is effective defines a length scale for a given particle volume fraction. The length scale increases as the glass transition is approached. We observe that near the glass transition particle motion is strongly spatially correlated. We investigate the relationship between the length scales of these correlations and the established confinement length scale.   

Dislocation nucleation and motion observed in a 2D Yukawa triangular lattice

Dislocation nucleation and motion were studied experimentally in a 2D Yukawa triangular lattice. Edge dislocations were created in pairs in lattice locations where the internal shear stress exceeded a threshold and then moved apart in the glide plane at a speed higher than the sound speed of shear waves. The early stage of this process is identified as a stacking fault. At a later stage, supersonically moving dislocations generated shear-wave Mach cones. The experimental system, a plasma crystal, allowed observation of this process at an atomistic (kinetic) level. We used a monolayer suspension of microspheres in a plasma, i.e., a complex plasma, which is like a colloidal suspension, but with an extremely low volume fraction and a partially-ionized rarefied gas instead of solvent. At our experimental conditions, the suspension forms a highly ordered 2D triangular lattice. Dislocations were generated in this lattice due to the shear introduced by its differential rotation, with two ``rigid'' domain walls imbedded in it. We used digital video microscopy for direct imaging and particle tracking.   

Low-electric-field phase behaviour of Brownian colloidal suspensions in sedimentation equilibrium

We study the phase diagram of the suspension of micron-scale fluorescent labeled silica colloids in aqueous suspension as a function of concentration in the presence of a moderate (less than 1 volt per $\mu m$) AC electric field. Confocal microscopy was used to track three-dimensional structure and dynamics of colloidal suspensions in sedimentation equilibrium. We characterize thresholds for field-induced organization in monodisperse colloidal suspensions of two particle diameters using orientational order parameters. We then study structure formation at moderate fields above the field threshold. At concentrations greater than $10\%$, and electric fields much larger than the field threshold measured, the colloidal suspension crystallizes to form a body centered tetragonal structure as has been previously reported. At lower concentrations and moderate fields, we uncover complex structure formation phenomena that include equilibrium cellular structures.   

Benchmarks for simulations of colloidal suspensions

There are now a number of methods available to investigate the dynamics of colloidal suspensions; among the most popular are Stokesian dynamics, the lattice-Boltzmann equation, dissipative particle dynamics, and stochastic rotation dynamics. One of the most commonly asked questions is how do the various methods compare in terms of accuracy and computational cost. At present there is no meaningful answer, in part because it is not straightforward to construct clean test calculations and obtain reference solutions to these problems. I will outline some principles that may be helpful in developing a basis for comparison and describe preliminary results obtained with the lattice-Boltzmann method.   

Non-equilibrium Crystallization Kinetics of an Induced Transition Observed in a Nano-Colloidal Liquid Crystal-Aerosil Dispersions

A new transition feature, termed ``Induced Crystallization'' (IC), has been observed in a nano-colloidal liquid crystal (octylcyanobiphenyl, 8CB) and aerosil gel system dependent on silica content. This IC feature exhibits apparent activated kinetics following Arrhenius-like behavior. Temperature scans were performed on heating using a DSC technique at ramp rates from 1 to 20~K/min and the aerosil density varied from 0 to 0.2~g/cc. For the 8CB+sil, a well resolved exothermic peak was found as an additional feature on heating scan before the melting transition, absent in bulk 8CB. As the sil density increases, the observed the enthalpy increases while the effective activation energy decreases for this IC feature, eventually saturating at the highest density studied. This behavior appears consistent with molecular disorder imposed by the surface molecular interaction, inducing slow glassy crystallization of the 8CB liquid crystal.   

Phase separation in asymmetric 2D binary hard-sphere mixtures

We investigate the phase behavior and structural properties of highly asymmetric binary mixtures of additive hard spheres in two dimensions, using Monte Carlo simulations in both the canonical and restricted Gibbs ensembles. To tackle large diameter ratios between the large and small species we use an efficient geometric cluster algorithm. Results for the pair correlation functions, compressibility, and depletion potentials are presented and compared to theoretical predictions, for diameter ratios from $q=2$ to $q=400$ and over a wide range of packing fractions. We explore and comment on the possibility of a demixing transition at high $q$ and total packing fraction.   

Experiments on a two dimensional lattice of charged colloids above a water-oil interface

Charged hydrophobic (PMMA) colloids in an oil phase (cyclohexyl bromide) are attracted, without wetting, by image charge effects to an oil-water interface. The micron size spheres form a monolayer on the interface and interact via screened coulomb interactions to form a crystalline or hexatic lattice, depending on the tunable ratio of lattice spacing to screening length. We study the statics and dynamics of this system in periodic, commensurate, incommensurate, random and quasi-periodic potentials applied by holographic optical tweezers. The use of holographic tweezers allows considerable control over the character and strength of the applied potential. A similar system has been used to study the effects of a curved fluid interface on the particle density and on topological defects.   

Nematic Order on Foams

We investigate the competition between nematic order and area minimization in nematic foams, in particular, how the structure is affected by the bending of the nematic director, and whether these systems will continue to obey Plateau's laws. We study the minimum energy configurations of the director field on a one parameter family of perturbed Reuleaux tetrahedra with special attention to the location of topological defects. We determine the energy distribution at the Plateau borders versus the film surface and relate the change in structure to changes in elastic constants and surface tension.   

Restricted Defect Dynamics in Colloidal Peanut Crystals

We report that monolayers of hard peanut-shaped colloidal particles consisting of two connected spherical lobes order into a crystalline phase at high area fractions. In this ``lobe-close-packed'' (LCP) crystal, the peanut particle lobes occupy triangular lattice sites, much like close-packed spheres, while the connections between lobe pairs are randomly oriented, uniformly populating the three crystalline directions of the underlying lattice. Using optical microscopy, we directly observe defect nucleation and dynamics in sheared LCP crystals. We find that many particle configurations form obstacles blocking dislocation glide. Consequently, in stark contrast to colloidal monolayers of close-packed spheres, single dislocation pair nucleation is not the only significant energetic barrier to relieving an imposed shear strain. Dislocation propagation beyond such obstructions can proceed only through additional mechanisms such as dislocation reactions. We discuss the implications of such restricted defect mobility for the plasticity of LCP crystals.   

Two-dimensional Dimer System

We report on an experimental study of the two-dimensional phase behavior of colloidal dumbbells (dimers) trapped at a water-air interface. The dimers are made out of $1.6\,\mu {\rm m}$ silica microspheres that are fused together at a point. The water-air interface is very slightly concave so that the dimers are gently compressed by gravity towards the center of interface. The spheres form a stable dense state after a few days. For this dense phase, the location of peaks of both positional and angular pair correlation functions of the dimers reveals that many different orientations and configurations of the dimers are present and this is in agreement with the disorder crystal phase predicted by Monte Carlo Simulation. \footnote{ K. W. Wojciechowski, A. C. Bra\'{n}ka and D. Frenkel, Physica A {\bf 196}, 519 (1993).} We found that there is a relatively long range angular correlation, but the positional correlation is short-ranged. This long range angular correlation is limited by the domain sizes which are determined by the density of the defects in the system.   

Observing liquid-gas nucleation in a colloid-polymer solution using digital holographic microscopy

We study liquid-gas nucleation in a colloid-polymer solution. Though the colloidal particles are too small to resolve, we are able to observe nucleating droplets due to the refractive index mismatch between the two fluid phases. By using digital holographic microscopy we are able to observe the three-dimensional structure of the nucleating phase. The experimental setup and algorithms for reconstructing the holography data will be discussed. We hope that our data will allow us to better understand nucleation kinetics and that analysis of the fluctuating droplets will provide us with the surface tension between the two phases.   

Soft Spheres Make More Mesophases

We use both mean-field methods and numerical simulation to study the phase diagram of classical particles interacting with a hard-core and repulsive, soft shoulder. Despite the purely repulsive interaction, this system displays a remarkable array of aggregate phases arising from the competition between the hard-core and shoulder length scales. In the limit of large shoulder width to core size, we argue that this phase diagram has a number of universal features, and classify the set of repulsive shoulders that lead to aggregation at high density. Surprisingly, the phase sequence and aggregate size adjusts so as to keep almost constant inter-aggregate separation.   

Correlations between Dynamical Heterogeneities and Visco-elastic properties of Confined Colloidal Thin Films

Our recent study on confined hard-sphere colloidal suspensions demonstrates that glass transition can be observed `sooner' as film thickness approaches a critical value while volume fraction remains constant. In this talk, we present a new study of the rheological properties of strongly confined colloidal thin films by using a home-designed micro-rheometer interfaced with a confocal microscope. We visualize the shear-induced structural relaxation at a single particle level and measure the rheological properties of confined colloidal thin films between two surfaces at narrow gap spacing ranging from 50 $\mu $m to 1-2 $\mu $m. The application of shear excitation greatly accelerates structural relaxation compared to quiescent colloidal fluids and we visualize particle displacements during the ``bond breakage'' process in strongly confined thin films. Additionally, we characterize their patterns, size and lifetimes under varied shear rates, and correlate their behaviors to the measured visco-elastic and visco-plastic properties of confined colloidal thin films.   

Direct Imaging of the Collapsed Langmuir Monolayers and Multilayer Formation

\textit{In-situ} ellipsometry imaging was used to monitor Langmuir monolayer of arachidic-acid spread on water and on CaCl$_{2}$ solution before and after collapse. The Langmuir monolayer was collapsed by compressing it beyond the minimal closely-packed surface molecular area. The ellipsometry image showed clear domains of collapsed regions, and analysis of the image allowed determination of thicknesses of these domains. It was found that the structure of multilayer domain in the collapsed region was bilayer of arachidic acid on the surface of CaCl$_{2}$ solution, while the trilayer was formed on the pure water surface.