Session V12: Colloidal Particles and Clusters

Optical trapping of small particles: The breakdown of the ray optics regime

Laser trapping, or the manipulation small particles by a highly focused light beam, is now a ubiquitous experimental technique. The understanding of how forces on these particles are generated by their interaction with the light beam was developed by Ashkin in the context of geometric optics. However, recent experiments [1] on the laser trapping of dielectric particles having complex shapes and characteristic dimensions in the micron range suggest that the geometric optics based theory is inadequate. Solving the ray optics problem for a variety of complex particle shapes and comparing to the experiments of Ref. [1], we explore the limits of the ray optics based theory. Using a combination of numerics and analytic calculations in the physical optics regime, we extend the theory of optical trapping to the case where at least some of the dimensions of the particles are smaller than the wavelength of the light. By using these calculations, one can design particle shapes to program their dynamics in the light field, creating spinners and gliders, as well as particles that can and cannot be trapped. [1] JN Wilking, TG Mason, Europhys Lett, 81, 58005 (2008).   

Multidimensional optical fractionation with holographic verification

Colloidal particles driven through a periodic potential energy landscape can become kinetically locked in to symmetry-selected directions. The path a given particle follows has been predicted to depend sensitively on such properties as the particle's size and refractive index. These predictions, however, have not been tested experimentally. We present experimental observations of colloidal silica spheres' trajectories through specially structured arrays of holographic optical traps, using quantitative methods of holographic video microscopy to track the particles' motions in three dimensions and simultaneously to measure their radii and refractive indexes with part-per-thousand resolution. Single-particle tracking and characterization enable us to demonstrate sorting of colloidal particles into spatially separated fractions with part-per-thousand resolution in either particle size or refractive index. Even more dramatically, these results agree quantitatively with previously untested predictions for the threshold of kinetically locked-in transport.   

Dielectrophoresis Force of PMMA Colloidal Clusters

DEP has long been applied to be a means for manipulating and separation of colloidal subjects. Here, we report quantitative analysis of DEP force under controlled parameters has been missing due to the difficulty in the direct measurements of the forces. Using IR laser to trap an individual colloidal cluster in a DEP field and to function as a pico-Newton force sensor, we were able to measure the frequency dependent DEP force for PMMA colloidal clusters with different aggregation number (n). We found that the crossover frequencies decrease with increasing size and follow a power-law dependence R$^{-2}$ where R is the effective radius of the clusters.   

Measurement of barrier potentials between colloidal particles and liquid-liquid interfaces

We measure the repulsive barrier between micron-sized colloidal particles and liquid-liquid interfaces. Particles of polystyrene and silica (suspended in water/glycerol) are confined individually to an optical trap, and translated towards an interface between the aqueous phase and an oil (decane) phase. We fit holographic micrographs of the particles to Lorentz-Mie theory to calculate the positions of the particles within the trap, including axial displacement. Since the force between a particle and the interface is directly related to the particle's displacement from the trap center, we are able to measure the particle-interface repulsion. We compare the force profiles with those predicted by DLVO theory resulting from ``image charges" in the oil phase.   

Formation of colloidal-particle ``tails'' at oil/water interfaces

The spontaneous assembly of microparticles at liquid interfaces is a well known and commonly observed process. Here we report a surprising phenomenon that occurs when the interfacial microparticles are displaced by nanoparticles. We used 2.1-um-diameter polystyrene particles, functionalized with amidine, which assemble at the surface of a fluorohexane droplet in water. The particles are strongly bound, with an adsorption energy of 0.9$\times $10$^{6}$ k$_{B}$T per particle. Then, 4.5-nm-diameter gold nanoparticles, stabilized with (1-mercaptoundec-11-yl)tetra(ethylene glycol) ligand are added to the suspension. The nanoparticles assemble at the interface, lowering the interfacial tension and displacing the microparticles. As the microparticles desorb, they flow along the droplet's surface and form a tail-like structure that flows into the solution. The tails are a few microns in diameter and flow a distance of several cm before disappearing from view. We discuss the desorption of the microparticles and the role of hydrodynamic flow and particle interactions in the formation and stability of the tails.   

Capillary interactions among colloidal spheres at a curved liquid interface

Colloidal particles tend to adsorb on liquid interfaces, where in-plane interactions can arise from a variety of mechanisms. We focus on capillary interactions induced by the curvature of the liquid interface, where particles were assumed to have a constant Young-Laplace contact angle at the three-phase contact line. Whereas spherical particles can adsorb on flat or spherical interfaces without deforming the interface, we predict that adsorption on a cylindrical interface deforms the interface because of the lack of azimuthal symmetry around the contact line. We present an analytical model of the interfacial shape and energy upon adsorption of single particle as well as the interaction between two particles. Long-range deformation of interface was found from the solution of a partial differential equation based on constant mean curvature of the interface. The binding energy will be discussed as well as interactions between particles. The results will be compared to predictions of a simpler model that assumes a nearly flat interface near the adsorbed sphere. This study provides an important step toward understanding the interactions among interfacial particles when the interface is distorted by an external field. We acknowledge support from the NSF-supported MRSEC on Polymers at UMass (DMR-0820506).   

Dynamics of colloidal particles sticking to an oil-water interface

We observe micron sized colloids as they adsorb to an oil-water interface.~ We make a flat oil-water interface and can use an optical trap to bring particles from either phase to the interface.~ Using digital holographic microscopy, colloids are tracked as they encounter and stick to the interface.~ We observe particles slowly adsorbing to the interface over the course of seconds.~ We also observe the dynamics of stuck particles and track their out-of-plane motion.   

Critical Casimir Effect provides novel Control of Colloidal Interactions

The Casimir Effect is a celebrated phenomenon in quantum physics. It manifests itself as the effective attraction between two dielectrics brought close to each other to confine fluctuations of the electromagnetic field. A similar force arises between two surfaces in a liquid mixture close to its critical point: Confinement of critical fluctuations of the liquid results in an attractive force between the walls, when the wall separation is of the order of the correlation length of the liquid. We use this effect for a fine control of colloidal interactions. The temperature dependence of the correlation length allows us to `freeze' a colloidal gas into a colloidal liquid, and a liquid into a solid. This offers novel opportunities for the assembly of micro- and nanomaterials. I will present recently developed optically transparent systems that allow use of conventional light scattering and confocal microscopy to study Critical Casimir-mediated particle assembly.   

Elastic Excitations in Colloidal Crystals Confined in an Emulsion Droplet

We confine colloidal crystals in emulsion droplets and study the lattice dynamics using video microscopy. The colloids are temperature-sensitive spherical microgels; the diameter of the microgel particles and hence the volume fraction of the crystal can be changed by tuning the temperature. We measure the vibrational modes in this system as a function of volume fraction and degree of confinement. Finally, we compare our measurements to simulations on vibrational modes in crystal drops. This work has been partially supported by the NSF through Grants DMR-0619424 and DMR-0645596, by ACS-PRF, and by the Alfred P. Sloan foundation.   

Lock and Key Colloids through Polymerization-Induced Buckling of Monodispersed Silicon Oil Droplets

Colloidal particles can spontaneously associate into larger structured aggregates when driven by selective and directional interactions. Colloidal organization can be programmed by engineering shapes and interactions of basic building blocks in a manner similar to molecular self-assembly. Examples of successful strategies that allow non-trivial assembly of particles include template-directed patterning, capillary forces and, most commonly, the functionalization of the particle surfaces with ``sticky patches'' of biological or synthetic molecules. The level of complexity of the realizable assemblies, increases when particles with well defined shape anisotropies are used. In particular depletion forces and specific surface treatments in combination with non spherical particles have proven to be powerful tools to self-assembly complex microstructures. We describe a simple, high yield, synthetic pathway to fabricate monodisperse hybrid silica spheres with well defined cavities. Because the particle morphologies are reproducible and tunable with precision, the resulting particles can be used as basic building blocks in the assembly of larger monodisperse clusters. This is demonstrated using depletion to drive the self-assembly.   

Rational Self-Assembly of Nano-Colloids using DNA Interaction

DNA is an attractive tool to direct the rational self-assembly of nano-colloids since its interaction is specific and reversible. This tunable attractive interaction should lead to a diverse and rich phase diagram of higher ordered structures which would not otherwise be entropically favored.\footnote{Tkachenko AV, Morphological Diversity of DNA-Colloidal Self-Assembly, Phys. Rev. Lett 89 (2002)} We compare our latest experimental observations to a simulation framework that precisely replicates the experimental phase behavior and the crystal growth kinetics.\footnote{Kim AJ, Scarlett R., Biancaniello PL, Sinno T, Crocker JC, Probing interfacial equilibration in microsphere crystals formed by DNA-directed assembly, Nature Materials 8, 52-55 (2009)} We will discuss the crystallography of novel structures and address how particle size and heterogeneity affect nucleation and growth rates.   

Getting a grasp of sticky ends: numerical simulations of DNA-mediated particle interactions

We will present the results of a Monte Carlo model for particles functionalized with short, rigid DNA constructs. We determine the dependence of the particle-particle interaction on the DNA grafting density, the binding strength of the sticky ends and the size of the beads, and predict the resulting phase behavior. We will also highlight the unique entropic costs and gains associated with the hybridization of tethered sticky ends and we will give some guidelines for experiments aimed at the DNA-mediated self-organization of micro- and nano-particles.   

Different modulation mechanisms of attractive colloidal interaction by lipid and protein functionalization

The nature of attractions observed between like-charged colloidal particles near a confining wall is still mysterious, due in part to the lack of experimental systems with tunable interparticle interactions. Biomembranes are appealing candidates for colloidal functionalization, enabling access to electrostatic and chemical properties that influence inter-particle relations. We have generated two classes of particles, derivatized with lipid-only and lipid-plus-protein membranes, each of which show attractive pair interactions whose magnitude can be tuned over a range of about 1k$_{B}$T. However, the two particle types exhibit profoundly different correlations between the depth of the attractive potential well and the spatial range of the interaction as well as between well depth and distance to the confining wall. This indicates that separation from the wall is not the decisive determinant of like-charge attraction and, more importantly, that there may be more than one mechanism responsible for observed attractive phenomena.   

Direct measurement of modified drag coefficient for a colloidal particle near flat walls

For colloidal particles, the Stokes drag force is well known for particles in a virtually infinite reservoir of quiescent fluid, since boundary effects can drastically alter drag on the particle. To investigate the effects of a physical boundary on the drag force, we directly measured the hydrodynamic drag exerted on a particle for two different cases; near a single flat wall and sandwiched between two flat walls. Measurements of drag coefficients were made using a calibrated oscillating optical tweezer composed of two lasers, one for trapping and one for particle tracking. A lock-in amplifier used to detect the harmonically modulated particle motion allowed us to isolate the response of the particle to the tweezers force against the effects of Brownian motion. Results of measured drag coefficients are presented for both the single and two-wall cases as a function of particle separation from the wall, and are compared to the expected results from the rigorous hydrodynamic flow calculations.   

Shear-Induced Rotation of Axisymmetric Particles in Poiseuille Flow in the Electric Field

Rotation of axisymmetric ellipsoidal particles in a slow viscous flow with uniform shear is described by Jeffery orbits; spherical models for biological particles and cells ignore this effect. We investigate fundamental aspects of Jeffery rotation and its effects on the change of impedance associated with a particle passing over a pair of coplanar electrodes in a microfluidic channel. Periodically changing orientation of a rotating non-spherical particle as it passes the electrodes results in impedance anisotropy and a varying signal amplitude. This periodic variation places limits on the uncertainty in flow impedance detection of axisymmetric model particles and biological cells. Conversely, calculations of Jeffery orbits predict that the period of these variations will yield estimates of the ellipticity of a single cell, an outcome that can be exploited in studies of composition, cycles and kinetics of a wide variety of biological cells in a short period of time. This work will lead to the ability to better discriminate between the particles exclusively on the basis of the electrical signal, vital to highly integrated lab-on-chip applications.