Experimental study of structure and dynamics in a monolayer of paramagnetic colloids confined by parallel hard walls

Ordering and Dynamics of Interacting Colloidal Particles under Soft Confinement

Confinement can induce substantial changes in the physical properties of macromolecules in suspension. Soft confinement is a particular class of restriction where the boundaries that constraint the particles in a region of the space are not well-defined. This scenario leads to a broader structural and dynamical behavior than observed in systems enclosed between rigid walls. In this contribution, we study the ordering and diffusive properties of a two-dimensional colloidal model system subjected to a one-dimensional parabolic trap. Increasing the trap strength makes it possible to go through weak to strong confinement, allowing a dimensional transition from two- to one-dimension. The non-monotonic response of the static and dynamical properties to the gradual dimensionality change affects the system phase behavior. We find that the particle dynamics are connected to the structural transitions induced by the parabolic trap. In particular, at low and intermediate confinement regimes, complex structural and dynamical scenarios arise, where the softness of the external potential induces melting and freezing, resulting in faster and slower particle diffusion, respectively. Besides, at strong confinements, colloids move basically along one direction, and the whole system behaves structurally and dynamically similar to a one-dimensional colloidal system.

Self-Assembly of Silica-Gold Core-Shell Microparticles by Electric Fields Toward Dynamically Tunable Metamaterials

Metamaterials, rationally engineered composite materials with exotic properties, have provided unprecedented opportunities to manipulate the propagation of electromagnetic waves and control light-matter interactions in a prescribed manner. At present, most metamaterials are in solid states, and their functions are fixed once fabricated. Applying external electric fields to assemble metallic and metallodielectric particles into distinct configurations is an approach to realize dynamically tunable or reconfigurable metamaterials. In this paper, we show that core-shell microparticles can be self-assembled into chain structures under an alternating current (AC) electric field at different oscillation frequencies. We have conducted optical characterizations of silica-gold core-shell particles by Fourier transform infrared (FTIR) spectroscopy, which show distinct optical responses at mid-infrared wavelengths before and after the chain formation. Full-wave simulations unveil that the spectral features arise from the coupling between the sophisticated plasmonic resonant modes of individual core-shell particles. The reconfigurable metamaterials based on the manipulation and assembly of metallic and metallodielectric particles have potential applications in optofluidic devices, liquid-borne microcircuits, and optical sensing.

Adsorption anomalies in a two-dimensional model of cluster-forming systems

Adsorption on a boundary line confining a monolayer of particles self-assembling into clusters is studied by Monte Carlo simulations. We focus on a system of particles interacting via competing interaction potential in which effectively short-range attraction is followed by long-range repulsion. For the chemical potential values below the order-disorder phase transition the adsorption isotherms were shown to undergo nonstandard behavior, i.e., the adsorption exhibits a maximum on structural transition between structureless and disordered cluster fluid. In particular, we have found that the adsorption decreases for increasing chemical potential when (i) clusters dominate over monomers in the bulk, (ii) the density profile in the direction perpendicular to the confining line exhibits an oscillatory decay, and (iii) the correlation function in the layer near the adsorption wall exhibits an oscillatory decay in the direction parallel to this wall. Our report indicates striking differences between simple and complex fluid adsorption processes.

Dynamic ordering of driven spherocylinders in a nonequilibrium suspension of small colloidal spheres

The ordering effects of driven spherocylinder-shaped rods in a colloidal suspension of small spheres confined to a two-dimensional channel geometry are observed via Brownian dynamics simulations without hydrodynamics. To describe the ordering, an order parameter and an expression for a potential of mean force of an equivalent equilibrium system are defined and analyzed. By varying the application point of the external force along the rods and thus the resulting lever, a transition from a preferred orientation parallel to the direction of the force to a preferred orientation perpendicular to the direction of the force was observed. It is shown that this effect can only be found if the spheres and multiple rods are present. Furthermore, a dependency of the order parameter on the absolute value of the force was discovered. The analysis of the potential of mean force further indicates a transition between two different phases of mean orientation. An observation of the flow equilibrium mean velocity in channel direction led to a s-shaped progression regarding the lever dependency, also marking a transition between two states linked to the mean orientation of the rods. A finite size analysis was conducted. Its results indicate that the transition between the two orientation states is a general phenomenon of the observed rod-sphere mixture.

Discrete and Continuum Models for the Salt in Crowded Environments of Suspended Charged Particles

Electrostatic forces greatly affect the overall dynamics and diffusional activities of suspended charged particles in crowded environments. Accordingly, the concentration of counter- or co-ions in a fluid-''the salt"-determines the range, strength, and order of electrostatic interactions between particles. This environment fosters engineering routes for controlling directed assembly of particles at both the micro- and nanoscale. Here, we analyzed two computational modeling schemes that considered salt within suspensions of charged particles, or polyelectrolytes: discrete and continuum. Electrostatic interactions were included through a Green's function formalism, where the confined fundamental solution for Poisson's equation is resolved by the general geometry Ewald-like method. For the discrete model, the salt was considered as regularized point-charges with a specific valence and size, while concentration fields were defined for each ionic species for the continuum model. These considerations were evolved using Brownian dynamics of the suspended charged particles and the discrete salt ions, while a convection-diffusion transport equation, including the Nernst-Planck diffusion mechanism, accounted for the dynamics of the concentration fields. The salt/particle models were considered as suspensions under slit-confinement conditions for creating crowded "macro-ions", where density distributions and radial distribution functions were used to compare and differentiate computational models. Importantly, our analysis shows that disparate length scales or increased system size presented by the salt and suspended particles are best dealt with using concentration fields to model the ions. These findings were then validated by novel simulations of a semipermeable polyelectrolyte membrane, at the mesoscale, from which ionic channels emerged and enable ion conduction.

The effect of boundary adaptivity on hexagonal ordering and bistability in circularly confined quasi hard discs

The behaviour of materials under spatial confinement is sensitively dependent on the nature of the confining boundaries. In two dimensions, confinement within a hard circular boundary inhibits the hexagonal ordering observed in bulk systems at high density. Using colloidal experiments and Monte Carlo simulations, we investigate two model systems of quasi hard discs under circularly symmetric confinement. The first system employs an adaptive circular boundary, defined experimentally using holographic optical tweezers. We show that deformation of this boundary allows, and indeed is required for, hexagonal ordering in the confined system. The second system employs a circularly symmetric optical potential to confine particles without a physical boundary. We show that, in the absence of a curved wall, near perfect hexagonal ordering is possible. We propose that the degree to which hexagonal ordering is suppressed by a curved boundary is determined by the "strictness" of that wall.

Tunable diffusion of magnetic particles in a quasi-one-dimensional channel

The diffusion of a system of ferromagnetic dipoles confined in a quasi-one-dimensional parabolic trap is studied using Brownian dynamics simulations. We show that the dynamics of the system is tunable by an in-plane external homogeneous magnetic field. For a strong applied magnetic field, we find that the mobility of the system, the exponent of diffusion, and the crossover time among different diffusion regimes can be tuned by the orientation of the magnetic field. For weak magnetic fields, the exponent of diffusion in the subdiffusive regime is independent of the orientation of the external field.

Stochastic transport of particles across single barriers

Transport phenomena of interacting particles are of high interest for many applications in biology and mesoscopic systems. Here we present measurements on colloidal particles, which are confined in narrow channels on a substrate and interact with a barrier, which impedes the motion along the channel. The substrate of the particle is tilted in order for the particles to be driven towards the barrier and, if the energy gained by the tilt is large enough, surpass the barrier by thermal activation. We therefore study the influence of this barrier as well as the influence of particle interaction on the particle transport through such systems. All experiments are supported with Brownian dynamics simulations in order to complement the experiments with tests of a large range of parameter space which cannot be accessed in experiments.

Packing and melting of mesoscopically confined two-dimensional Coulomb crystals in straight narrow channels

The microstructure and melting dynamics of the two-dimensional mesoscopic Coulomb crystal with 1/r-type mutual interaction force and parabolic transverse confining potential, under different degrees of incommensurability, are investigated through molecular-dynamics simulation. To tune the degree of incommensurability, N(a) extra particles are added into the commensurate uniform triangular lattice which has seven-layer structure and 40 particles in each layer with the periodic longitudinal boundary condition, until the system reaches another commensurate packing with eight-layer structure at N(a)=40. It is found that the increasing incommensurability with the increasing N(a) or 40-N(a) gradually deteriorates the structural order with the presence of intrinsic defects and the anisotropic bond-length distribution, except for the defect-free configurations at a few magic N(a)'s. The system prefers the seven- and the eight-layer single structures through the entire crystal for the low- and the high-N(a) regimes, respectively, and the configurations with seven- and eight-layer domain mixtures for 18≤N(a)≤24. The increasing strain or the worse local particle interlocking around the intrinsic defects with the increasing incommensurability also causes the easier structural rearrangement associated with the easier particle hopping and the earlier onset of melting transition. The transverse confinement suppresses the transverse motion, induces nonuniform melting, and sustains the layered structure after melting.

Colloidal systems in three-dimensional microchannels: lattice control via channel width and external force

The structural behavior of hard spheres interacting with repulsive (screened Coulomb) interaction in narrow constrictions is investigated using Brownian dynamics simulations. The system of particles adapts to the confining potential and the interaction energies by a self-consistent arrangement of the particles. It results in the formation of planes throughout the three-dimensional channel. The presence of hard walls leads to structural deviations from the unbounded (infinite) crystal. The arrangement of the particles is perturbed by diffusion and an external driving force leading to a density gradient along the channel. The particles accommodate to the density gradient by reducing the number of planes if it is energetically favorable. This reduction in the number of planes is analogous to the reduction in the number of layers in two-dimensional systems. The influence of a self-organized order within the system is reflected in the velocity of the particles and their diffusive behavior.

A two-component mixture of charged particles confined in a channel: melting

The melting of a binary system of charged particles confined in a quasi-one-dimensional parabolic channel is studied through Monte Carlo simulations. At zero temperature the particles are ordered in parallel chains. The melting is anisotropic and different melting temperatures are obtained according to the spatial direction, and the different kinds of particles present in the system. Melting is very different for the single-, two- and four-chain configurations. A temperature induced structural phase transition is found between two different four-chain ordered states which is absent in the mono-disperse system. In the mixed regime, where the two kinds of particles are only slightly different, melting is almost isotropic and a thermally induced homogeneous distribution of the distinct kinds of charges is observed.

Density reduction and diffusion in driven two-dimensional colloidal systems through microchannels

The behavior of particles driven through a narrow constriction is investigated in experiment and simulation. The system of particles adapts to the confining potentials and the interaction energies by a self-consistent arrangement of the particles. It results in the formation of layers throughout the channel and of a density gradient along the channel. The particles accommodate to the density gradient by reducing the number of layers one by one when it is energetically favorable. The position of the layer reduction zone fluctuates with time while the particles continuously pass this zone. The flow behavior of the particles is studied in detail. The velocities of the particles and their diffusion behavior reflect the influence of the self-organized order of the system.

Structure of binary colloidal systems confined in a quasi-one-dimensional channel

The structural properties of a binary colloidal quasi-one-dimensional system confined in a narrow channel are investigated through modified Monte Carlo simulations. Two species of particles with different magnetic moment interact through a repulsive dipole-dipole force are confined in a quasi-one-dimensional channel. The impact of three decisive parameters (the density of particles, the magnetic-moment ratio, and the fraction between the two species) on the transition from disordered phase to crystal-like phases and the transitions among the different mixed phases are summarized in a phase diagram.

Structure of quasi-one-dimensional ribbon colloid suspensions

We report the results of an experimental study of a colloid fluid confined to a quasi-one-dimensional (q1D) ribbon channel as a function of channel width and colloid density. Our findings confirm the principal predictions of previous theoretical studies of such systems. These are (1) that the density distribution of the liquid transverse to the ribbon channel exhibits stratification; (2) that even at the highest density the order along the strata, as measured by the longitudinal pair correlation function, is characteristic of a liquid; and (3) the q1D pair correlation functions in different strata exhibit anisotropic behavior resembling that found in a Monte Carlo simulation for the in-plane pair correlation function of a hard sphere fluid in a planar slit.

Layer reduction in driven 2D-colloidal systems through microchannels

The transport behavior of a system of gravitationally driven superparamagnetic colloidal particles is investigated. The motion of the particles through a narrow channel is governed by magnetic dipole interactions, and a layered structure forms parallel to the walls. The arrangement of the particles is perturbed by diffusion and the motion induced by gravity leading to a density gradient along the channel. Our main result is the reduction of the number of layers. Experiments and Brownian dynamics simulations show that this occurs due to the density gradient along the channel.