Session B8: Colloidal Self-Assembly II

Orthogonal Tracking Microscopy for Nanofabrication Research

Constructing 2D lateral particle trajectories from digital video sequences of nanoparticle motion in a liquid is straightforward and fairly common, requiring only the use of centroid-finding algorithms. On the other hand, extracting particle trajectories in the third (out-of-plane) dimension has been more difficult, requiring detailed calibration of the radius of the defocused diffracted rings which result from vertical fluctuations of particle position. We introduce a new technique, termed orthogonal tracking microscopy or orthogonal projection microscopy, in which integrated micromirrors produce one or more reflected images of a particle within the same field of view as the direct image. The reflected images project vertical motion into lateral motion. Thus, we are able to construct a fully 3D particle trajectory from 2D digital video using only centroid-finding algorithms. We use this technique to study particle-surface interactions relevant to directed assembly of nanoparticles.   

Self-Assembly of Colloidal Membranes

Symmetric monolayer membranes are observed to self-assemble in a colloidal suspension of hard rods with soft attractions. This attractive component to the interaction is enough to drive the self-assembly of stable two dimensional fluid-like surfaces of rods. Simultaneous measurements are made at both the molecular, via direct imaging of individual fluorescently labeled particles, and the continuum length scales. At the continuum scale, the elastic Hamiltonian for a two dimensional fluid-like surface is verified for a symmetric monolayer, and measured material constants such as the bending modulus and the area compression modulus are demonstrated to obey a simple elastic relationship.   

Self-Assembled 3D Ordered Macroporous Structures for Tissue Engineering Scaffolds

A simple, inexpensive and fast microfluidic method to fabricate three-dimensional ordered macroporous gel is demonstrated using alginate as the scaffold material. The microfluidic device consists of two concentric micropipettes where one is nested inside the other. Nitrogen gas and aqueous alginate solution with Pluronic F127 are pumped through the inner and the outer channel respectively. Under appropriate conditions, bubbles of a uniform size are generated within the device at few thousand Hz. We show the control over bubble size by the gas pressure and quantitatively predict the size dependence from the geometry of fluidic device. Monodisperse bubbles are collected and self-assemble into crystal structures as wet foam. The alginate solution between bubbles is crosslinked by divalent calcium ions and turns into 3D ordered macroporous gel where the pores are highly interconnected. The pore size can be directly controlled by the bubble size which ranges from few tens microns to few millimeters. This technique promises a versatile and robust way to make 3D ordered tissue engineering scaffolds.   

Five-fold attractor in two-dimensional diffusion processes.

We introduce an algorithm to generate two-dimensional diffusion-limited star-branched polymers (DLSP) attaching monomers successively to a central colloidal particle with any desired number of reactive sites. The proposed algorithm produces star-shaped aggregates whose final structure at relatively large distances from the central colloid has five-fold symmetry independently of the initial number of reactive sites. Therefore, the final morphology can be considered as a universal attracting distribution for this irreversible diffusion-limited aggregation process.   

Template-Guided Langmuir-Blodgett Deposition of Colloidal Particles

We present a new method of fabricating highly-ordered two-dimensional (2D) colloid crystals with non-closed-packed symmetries. In this method, using the Langmuir-Blodgett (LB) monolayer deposition technique, we transfer a Langmuir monolayer of colloidal particles constructed at the air-water interface onto a substrate which contains micro-fabricated topological patterns. We demonstrate that by using this template-guided LB deposition method, a perfect single 2D colloid crystal structure that is homogeneous throughout the entire area of the patterned substrate can be economically fabricated under appropriate LB processing conditions. We investigate the effects of various control parameters (such as the initial particle density at the air-water interface, the substrate lifting speed, and the humidity condition during the LB monolayer deposition) on the structural properties of the resultant LB colloid monolayer. As the compression area or the lifting speed is increased, the average density of the deposited particles in the resultant LB colloid monolayer becomes reduced. The evaporation of water causes an undulation in the deposited particle density profile along the substrate lifting direction. We present a theoretical model which can quantitatively explain all these experimental observations.   

Clustering in Hard Core/Soft Shoulder Lattice Gas Models

Isotropic hard core/soft shoulder interacting particle models have been shown to display a wide variety of thermodynamic phases: structured liquids, micellar solids, layered and columnar liquid crystals, and a variety of modulated solid phases. We have explored the phase diagram of a class of lattice gas models that are designed to approximate continuum models. We use generalizations of Baxter's hard hexagon model on a two-dimensional hexagonal lattice to model the hard core repulsions. The longer-ranged repulsive soft shoulder is included to induce a Klein/Likos clustering instability. The clustering instability creates softly interacting fluidic micelles, as well as several type of modulated solid phases. The lattice gas model allows for efficient Monte Carlo simulation in order to quickly explore the phase diagram. Two dimensional lattice gas models typically only display liquid phases with short-range order and solids with long-range order that is commensurate with the underlying lattice. Preliminary results indicate the model exhibits soft solid phases composed of fluidic micelles that form a quasi-long ranged solid phase characteristic of continuum solid phases in two dimensions. We will also present a mean field theory analysis of the initial clustering instability.   

Elastic Theory of Defects in Toroidal Crystals

Crystalline assemblages of identical sub-units packed together and elastically bent in the form of a torus have been found in the past ten years in a variety of systems of surprisingly different nature, such as viral capsids, self-assembled monolayers and carbon nanomaterials. We investigate the structural properties of toroidal crystals and we provide a unified description based on the elastic theory of defects in curved geometries.   

Two-dimensional hopping of aqueous colloidal clusters on commensurate surface wells.

Hopping of colloidal clusters in various shapes and sizes that are mainly confined within commensurate surface wells except for diffusing between them by Brownian motion is studied. The mobility of clusters decreases nonmonotonically with increasing cluster size. The mobility proceeds, depending on cluster shape, by different jumping mechanisms such as zigzagging or translation without rotation; this produces nonmonotonic changes of mobility when, at fixed cluster size, cluster shape varies. Unlike atomic clusters that change configuration and dissociate easily, these colloidal clusters are very stable and each type of jump can be identified separately. Hopping rate, diffusion and different jumping mechanisms that are associated with them will be discussed for various sizes and shapes of clusters.   

Complexity from Specificity: Light Scattering and Colloidal Studies of Dscam Self-Association

The self-assembly of complex structures from nanometer-sized building blocks is of great technological importance(i.e. for the development of tissue scaffolds and photonic crystals) and is of significant basic scientific interest. Here I present light scattering and colloidal aggregation studies of Dscam, a protein with over 18,000 splice variants which all (or almost all) exhibit exclusively homophilic binding, and which is necessary for the generation of structural complexity in the brain of insects. Static and dynamic light scattering data reveal the statistical mechanical properties of Dscam self-association, including the free energy, second virial coefficient, and oligomer molecular weight. Finally, I demonstrate how to exploit Dscam's unprecedented level of molecular diversity and specificity for the self-assembly of custom nano- and micro-structures out of Dscam-conjugated colloids.   

Non-spherical Depletants in Colloidal Suspensions

We investigate the effective interactions between spherical colloids induced by rigid rod-like depletants. The size disparity between the colloids and the rods makes conventional simulation methods inefficient. We overcome this by extending the generalized geometric cluster algorithm for colloidal suspensions [J. Liu and E. Luijten, Phys.\ Rev.\ Lett. \textbf{92}, 035504 (2004)] to systems of non-spherical particles. We investigate both uncharged and charged colloids and rods, where the electrostatic potential is modeled through a screened interaction. The dependence of the induced depletion potential on both the strength and the range of the electrostatic interactions is quantified. In case of a rod-sphere repulsion, the depletion attraction between the colloids is enhanced as the screening length becomes larger, owing to the increased effective size of the rods. Systems with a rod-sphere attractions are also explored.   

Magnetically assembled ``ring-shaped'' colloidal particle structures

We demonstrate a convenient method for assembling ring-shaped colloidal structures by applying uniform magnetic field to a mixture of 2.7-$\mu$m paramagnetic beads, 1-$\mu$m non-magnetic polystyrene beads, and a fluid dispersion of 10-nm iron oxide nanoparticles (i.e., ferrofluid). The ferrofluid serves as a magnetic contrast medium and induces dipole moments in both the paramagnetic and non-magnetic beads when an external magnetic field is applied. We discovered that for certain volume fractions of ferrofluid, the attractive forces generated between the smaller non-magnetic beads and the larger magnetic beads induce the non-magnetic particles to form a ring structure around the circumference of the paramagnetic beads. This method differs from similar self-assembly techniques in that the ring structures form solely through magnetic force, rather than depending on random motion and patterned bonding.   

Effects of surface biotin density on lipid monolayer-assisted 2D crystallization of streptavidin at the aqueous solution-vapor interface

Adsorption and two-dimensional (2D) crystallization of soluble protein streptavidin on a biotinylated lipid monolayer at an aqueous solution-vapor interface have been studied extensively since the 1990s. These previous studies, largely based on fluorescence microscopy and \textit{ex-situ} electron microscopy measurements, revealed the effects of protein modifications and aqueous buffer conditions, such as pH and ionic strength. We have examined the dependence of 2D streptavidin crystallization on the areal biotin density in the lipid monolayer template, using Brewster-angle microscopy (BAM) and \textit{in-situ} x-ray reflectivity and grazing-incidence x-ray diffraction (GID). The lipid monolayer consisted of a binary mixture of DMPC and DPPE-x-biotin, and the biotin density was controlled by varying the lipid composition while keeping the area per lipid fixed. Both BAM and GID results demonstrate that in order for 2D crystallization of streptavidin to occur, the surface biotin density must exceed a threshold, corresponding to approximately two biotins per protein. The results highlight the importance of well-defined molecular orientations to the 2D crystallization of proteins.   

Self-Assembly of 2D TMV Arrays on Substrate-Supported and Langmuir Lipid Monolayers

Bionanoparticles (large proteins, viruses) are ideal building blocks for creating ordered two-dimensional (2D) arrays. These 2D protein crystals or ordered arrays are of great scientific and technological interest. Here, we demonstrate the use of in-situ x-ray scattering and Brewster angle microscopy (BAM) to monitor the formation of self-assembled, 2D ordered arrays by tobacco mosaic viruses (TMVs) on a lipid layer that was either supported by a solid substrate or formed at the liquid-vapor interface. The lipid monolayer not only confined the viral particles within a plane, but also provided the lateral mobility that is crucial for developing structural order. In-situ X-ray scattering was used to provide real time information on the structure of the virus array and guide optimizations of the surrounding chemical environment to improve in-plane structural order. The presence of Ca$^{2+}$ ions is also essential to the formation of well ordered, closely packed 2D arrays of TMV. Atomic Force Microscopy was also used to directly image the final structure to provide real space confirmation of developed structural order.   

Non-equilibrium dynamics of virus capsid assembly

The process of self-assembly of nano-structures under non-equilibrium conditions has recently received a lot of attention in various fields. A viral shell (capsid) is, for sure, one of the most interesting biological structures that can spontaneously form (from statistical mechanics point of view) at the right pH and ionic strength. While the viral capsids are by far less complex than most other biological objects, the process of virus assembly remains poorly understood. Viruses are found to adopt many different shapes. The mechanisms involved in the self-assembly of capsids into a particular shape as well as the transitions from spherical to non-spherical shells are the subject of this presentation. We show that the kinetic formation of the protein building blocks into the intermediate states (dimmers, trimmers, pentamers and hexamers) can lead to the construction of shells with different morphologies.   

Thermal transport in colloidal silica system: effect of particle size and aggregation

Knowledge of the size and distribution of nanoparticles in solution is critical to understanding the observed enhancements of thermal conductivity in colloidal systems. We have applied small-angle x-ray scattering (SAXS) to study particle size and distribution of monodispersed and aggregated silica colloids. A hot-wire method has been used to measure thermal conductivity of the colloidal system. The results indicate that the thermal conductivity depends not only on the particle concentration, but also on the particle size and distribution. The experimental data contradict thermal transport models based on fluid interfacial layers or Brownian motion but shed light on the detrimental role of liquid-particle interface on the thermal transport properties.