Energy landscape of colloidal dumbbells in a periodic distribution of light.

Using a ray tracing calculation, the energy landscape of dumbbells, made of spherical colloidal particles, interacting with a periodic distribution of light is calculated. As shown previously [E. Sarmiento-Gomez, J. A. Rivera-Moran and J. L. Aruaz-Lara, Soft Matter, 2018, 14, 3684], planar aggregates of spherical particles adopt discrete configurations in such light distribution. Here we focus on the case of colloidal dumbbells both symmetric and asymmetric from an experimental and theoretical point of view. It has been shown that the direct calculation using the ray tracing approximation is in excellent agreement with the experiment in spite of the fact that the particles size and the wavelength of the trapping light are comparable. We also corroborate, at least for the more simple case of a single particle in a parabolic light distribution, that the simple method used here provides the same results as the more complex and general Lorenz-Mie approach giving a more simple yet reliable method for the calculation of the energy landscape of colloidal aggregates in periodic light distributions.

Single particle states of colloidal particles in 2D periodic potentials.

Colloidal particles when subjected to a periodic array of potential wells are observed to adopt discrete stable configurations depending on the particle size/array wavelength ratio. Experimentally, the configuration states are determined for singlets, doublets and triplets of identical spheres in a periodic array of traps. The energy landscape of a single spherical particle is obtained by considering the refraction of the incident light as it passes throughout the particle. Then, the energy of a dumbbell is determined as the superposition of two singlets. The energy of a triplet is calculated as the superposition of a dumbbell and a single particle. As it is shown here, this direct method predicts accurately the stable particle configurations as observed in the experiments. The method can be generalized to obtain the potential energy of an n-particle aggregate, using as building blocks the energies of singlets and doublets.

Transition from diffusive to subdiffusive motion in colloidal liquids.

In this work we report experimental and theoretical results for the motion of single colloidal particles embedded in complex fluids with different interparticle interactions. The motion of particles is found to follow a similar behavior for the different systems. In particular, the transition from the short-time diffusive motion to the subdiffusive intermediate-time motion is found to occur when the square root of its mean squared displacement is in the order of 1 tenth of the neighbors' interparticle distance, thus following a quantitative criterion similar to Lindemann's criterion for melting.

Brownian motion of optically anisotropic spherical particles in polymeric suspensions.

We studied the rotational and translational diffusion of optically anisotropic liquid crystal particles embedded in semidiluted polymer solutions of Poly-Ethylene-Oxide (PEO) at different concentrations and different molecular weights. The polymer radius of gyration was chosen to be similar to the size of the probe particles and the polymer concentrations used are just above the crossover concentration. Thus, the system consists of solid probe particles moving in a sea of overlapping particles of similar size. We found that the behavior of both particle dynamics, rotational and translational, is similar in the range of concentrations considered here. In both cases, two linear diffusive regimes are observed, separated by a subdiffusive time interval. The spatial scale at which this intermediate regime appears shows a dependence on both the polymer concentration and molecular weight, and has a value similar to the thickness of the polymer-depleted layer usually found in this kind of systems. Additionally, we observe that the colloidal dynamic scales with the overlapping degree of the polymer particles.

Glass- and crystal-forming model based on a granular two-dimensional system.

We study a two-dimensional system of magnetic particles under an alternating magnetic field. The particles are settled on the surface of a negative lens where they tend to sediment toward the center due to gravity. The effective temperature is controlled by the intensity of the applied magnetic field. The system is cooled down from a gaslike state to a solidlike state at different rates. We observe that for some slow cooling rates the final configuration of system is a hexagonal compact arrange, while for the faster cooling rates the final configurations are glasslike states. We followed the time evolution of the system, which allows us to determine in detail changes in quantities such as the interparticle distance. We determine the glass transition temperature for different cooling rates, finding that such temperature increases as the cooling rate decreases, in contrast with some other glass-forming liquids.

Brownian motion in non-equilibrium systems and the Ornstein-Uhlenbeck stochastic process.

The Ornstein-Uhlenbeck stochastic process is an exact mathematical model providing accurate representations of many real dynamic processes in systems in a stationary state. When applied to the description of random motion of particles such as that of Brownian particles, it provides exact predictions coinciding with those of the Langevin equation but not restricted to systems in thermal equilibrium but only conditioned to be stationary. Here, we investigate experimentally single particle motion in a two-dimensional granular system in a stationary state, consisting of 1 mm stainless balls on a plane circular surface. The motion of the particles is produced by an alternating magnetic field applied perpendicular to the surface of the container. The mean square displacement of the particles is measured for a range of low concentrations and it is found that following an appropriate scaling of length and time, the short-time experimental curves conform a master curve covering the range of particle motion from ballistic to diffusive in accordance with the description of the Ornstein-Uhlenbeck model.

Multifractality in dilute magnetorheological fluids under an oscillating magnetic field.

A study of the multifractal characteristics of the structure formed by magnetic particles in a dilute magnetorheological fluid is presented. A quasi-two-dimensional magnetorheological fluid sample is simultaneously subjected to a static magnetic field and a sinusoidal magnetic field transverse to each other. We analyzed the singularity spectrum f(α) and the generalized dimension D(q) of the whole structure to characterize the distribution of the aggregates under several conditions of particle concentration, magnetic field intensities, and liquid viscosity. We also obtained the fractal dimension D(g), calculated from the radius of gyration of the chains, to describe the internal distribution of the particles. We present a thermodynamic interpretation of the multifractal analysis, and based on this, we discussed the characteristics of the structure formed by the particles and its relation with previous studies of the average chain length. We have found that this method is useful to quantitatively describe the structure of magnetorheological fluids, especially in systems with high particle concentration where the aggregates are more complex than simple chains or columns.

Lateral aggregation induced by magnetic perturbations in a magnetorheological fluid based on non-Brownian particles.

A study of lateral aggregation, induced by an oscillatory field, in a magnetorheological fluid based on non-Brownian magnetic particles is presented. We investigate the behavior of chains formed by the particles, due to the simultaneous application of a static magnetic field and a sinusoidal magnetic field transverse to each other. We show that the effective oscillating field enhances the aggregation process. We discuss this result in terms of an effective particle concentration induced by the oscillating field when chains oscillate angularly and sweep the area around them. The oscillating field produces a lateral aggregation similar to that observed in systems composed of Brownian particles which is induced by thermal fluctuations. We study the effect of the oscillating field on the angular amplitude described by single chains. It is observed that the angular amplitude decreases as the frequency of the oscillating field increases; we discuss this behavior numerically in terms of a simple model for this system. Lateral aggregation is studied in detail in isolated pairs of chains of equal length at several conditions of separation and displacement. From the results, a phase diagram is obtained showing the conditions under which aggregation is possible.

Hydrodynamic interactions between colloidal particles in a planar pore.

The correlation between the motion of pairs of colloidal particles confined in a planar pore is measured using optical microscopy. The systems studied here are aqueous suspensions of polystyrene spheres of diameter 1.9 µm, interacting as effective hard spheres, confined between two parallel planar plates separated by 2.9 µm. The lateral motion, along the plane parallel to the plates, of the particles is recorded with a time resolution of 30 frames s(-1). From the short-time motion, the hydrodynamic diffusion coefficients are determined as functions of the interparticle distance for various particle concentrations. At low concentrations, when the static correlation between particles is also low, the diffusion coefficients exhibit some symmetry, and at higher concentrations they are modulated by the structure of static correlation.

Colloidal diffusion inside a spherical cell.

The hydrodynamic hindering of a single-particle dynamics under total confinement is measured by optical microscopy. The three-dimensional trajectories of single-colloidal particles confined in spherical water globules of sizes only a few times the particle's diameter are tracked as they sample the entire volume of the globule. The hydrodynamic interactions between the particle and the spherical wall produce a dependence of the short-time diffusion on the particle's distance to the surface and an asymmetry in the radial and tangential components of the local diffusion coefficient, with the diffusion along the tangential direction being faster than along the radial direction. The latter decreasing close to the wall while the former being practically constant.

Hydrodynamic interactions in quasi-two-dimensional colloidal suspensions.

The effects of the hydrodynamic interactions on the short-time dynamics of colloidal, hard-sphere-like particles confined between two parallel walls are measured by digital videomicroscopy. We find that such effects can be described in terms of an effective two-dimensional hydrodynamic function H(k), defined as a straightforward adaptation to two dimensions of the corresponding object describing collective dynamics for the three-dimensional (3D) suspensions. Interestingly, the behavior of H(k) is qualitatively similar to the hydrodynamic function of 3D suspensions of hard spheres. We also found that for values of k where the static structure factor is 1, the dynamics is determined only by self-diffusion.