Salvador Herrera-Velarde

Structure and dynamics of interacting Brownian particles in one-dimensional periodic substrates

We study both the structural and dynamic properties of charged colloids in one-dimensional periodic substrates. The dependence of the static structure and diffusion properties on the density and substrate parameters is investigated by means of Brownian dynamics simulations. We find that the competition between both particle–particle and particle–substrate interactions leads to a rich variety of adsorbate phases or particle distributions. We also demonstrate that the mean-square displacement, W(t), at long times shows the typical non-Fickian behaviour, , even for periodic substrates. Moreover, we show that the depinning of the particles can be directly quantified through a loss of correlations in the structure or an enhancement of the particle mobility factor.

Disorder-induced vs temperature-induced melting of two-dimensional colloidal crystals

We present molecular-dynamics simulations of a two-dimensional colloidal system interacting with a disordered substrate. Evidence is provided that at zero temperature the system can show an order → disorder phase transition. It is signalled by a switch from an algebraic to an exponential decay of translational order. Being the same switch that also indicates temperature-induced melting, one may consider this a disorder–induced melting transition—even though the word “melting” seems to be in conflict with the fact that the temperature is zero. We have performed simulations with pinning disorder at zero temperature and without such disorder, but at finite temperature. This permits us to make a detailed comparison between temperature-induced and disorder-induced melting. We show that there are differences in the microscopic mechanism leading to the phase transition: while temperature leads to melting by inducing an unbinding of dislocation pairs that are formed already in the ordered phase, pinning disorder can cause melting by inducing so much strain that a distribution of single dislocations are suddenly required to efficiently relieve this strain.

Hydrodynamic correlations in three-particle colloidal systems in harmonic traps

We report on the hydrodynamic correlations between colloids immersed in a low Reynolds number fluid. We consider colloidal arrays composed of three particles; each colloid is trapped in a single harmonic potential and interacts with the other colloids only via hydrodynamic forces. We focus on the role of a third body in the two-body correlation functions. We give special attention to a collinear configuration of particles, although the salient features of an equilateral triangle configuration are outlined. The correlation functions are computed both by means of Brownian dynamics simulations, and by solving analytically and numerically the Langevin equation under the assumption of constant diffusion tensor; this approximation is validated through computer simulations. We explicitly show that the presence of a third body affects the auto- and cross-correlation functions and that their behaviour, in some specific conditions, can be different from that commonly seen in a two-particle system. In particular, we have found that the auto-correlation functions show a slower decay, while the cross-correlation ones exhibit a temporal shift and a weaker amplitude. Moreover, an unexpected behaviour related to a positive correlation and associated with the appearance of new dynamical modes is observed in the case of the collinear array of three particles. This interesting effect might be used to tune the degree of hydrodynamic correlation in few-body colloidal systems.

One-dimensional Gaussian-core fluid: ordering and crossover from normal diffusion to single-file dynamics

The peculiarity of a bounded pair potential in combination with strong confinement brings some quite interesting new phenomenology in the structure and dynamics of one-dimensional colloidal systems. Such behaviour is atypical in comparison with colloidal systems interacting with potentials that diverge at the origin. In this contribution, by means of molecular dynamics simulations, a confined one-dimensional model of particles interacting via a Gaussian-core pair potential is studied. We explore the effects of confinement, density and temperature on the structural and dynamical correlation functions. Our findings indicate that the static and dynamic liquid-state anomalies already reported in open systems are also present in this 1D model system. Using the radial distribution function and the static structure factor to characterise the spatial ordering, it is observed that the system remains fluid at all densities. However, when the reduced temperature is above 0.03, it displays typical features of a liquid regime, i.e., there exist short-range spatial correlations among particles. In contrast, at lower temperatures and densities, where the particle-particle interaction dominates, the system behaves structurally and dynamically similar to a hard-core repulsive system. In such a region, interestingly, there is a crossover from a liquid to a solid-like regime. At any given temperature, the system undergoes a sort of reentrant structural behaviour as the density increases. At either high densities or temperatures, particle correlations vanish, thus, the system exhibits structural and dynamical properties similar to those of an ideal gas. To examine a possible correlation between the structural anomalies and the diffusive behaviour, the mean-square displacement and the self-intermediate scattering function are also computed. From these observables, we establish the thermodynamic phase-space points where the dynamical behaviour is non-monotonic. In conjunction with the observed anomalous diffusion, we have found a dynamical crossover from single-file diffusion, which is characteristic of one-dimensional systems with a well-defined hard-core, to the ordinary Fickian diffusion present in open systems.

Structural transitions and long-time self-diffusion of interacting colloids confined by a parabolic potential

We report on the ordering and dynamics of interacting colloidal particles confined by a parabolic potential. By means of Brownian dynamics simulations, we find that by varying the magnitude of the trap stiffness, it is possible to control the dimension of the system and, thus, explore both the structural transitions and the long-time self-diffusion coefficient as a function of the degree of confinement. We particularly study the structural ordering in the directions perpendicular and parallel to the confinement. Further analysis of the local distribution of the first-neighbors layer allows us to identify the different structural phases induced by the parabolic potential. These results are summarized in a structural state diagram that describes the way in which the colloidal suspension undergoes a structural re-ordering while increasing the confinement. To fully understand the particle dynamics, we take into account hydrodynamic interactions between colloids; the parabolic potential constricts the available space for the colloids, but it does not act on the solvent. Our findings show a non-linear behavior of the long-time self-diffusion coefficient that is associated to the structural transitions induced by the external field.

Short-time dynamics of monomers and dimers in quasi-two-dimensional colloidal mixtures.

We report on the short-time dynamics in colloidal mixtures made up of monomers and dimers highly confined between two glass plates. At low concentrations, the experimental measurements of colloidal motion agree well with the solution of the Navier-Stokes equation at low Reynolds numbers; the latter takes into account the increase in the drag force on a colloidal particle due to wall-particle hydrodynamic forces. More importantly, we find that the ratio of the short-time diffusion coefficient of the monomer and that of the center of mass of the dimmer is almost independent of both the dimer molar fraction, x_{d}, and the total packing fraction, ϕ, up to ϕ≈0.5. At higher concentrations, this ratio displays a small but systematic increase. A similar physical scenario is observed for the ratio between the parallel and the perpendicular components of the short-time diffusion coefficients of the dimer. This dynamical behavior is corroborated by means of molecular dynamics computer simulations that include explicitly the particle-particle hydrodynamic forces induced by the solvent. Our results suggest that the effects of colloid-colloid hydrodynamic interactions on the short-time diffusion coefficients are almost identical and factorable in both species.

Modeling soft matter with colloids

Colloids are present in a large variety of biological, chemical and physical systems. In the last few years, they have been used as model systems which allow understanding fundamental processes in atomic systems or elucidating problems in soft condensed matter. The success of colloids to be used as well‐controlled model systems resides in the fact that the relevant interactions between colloids are easily and independently tuneable and the colloid position is accessible by means of optical techniques, thus allowing a direct comparison with simulations and theoretical calculations. In this contribution, we briefly show the versatility of colloids as model systems to, on one hand, understand the effective interactions that emerge in soft matter physics when unobservable components of the system are integrated out or contracted of the description and, on the other hand, to quantify the effects of soft and periodic external fields on the structural and dynamics properties of many‐body systems.