Crystalline multilayers of charged colloids in soft confinement: experiment versus theory

Phase Reentrances and Solid Deformations in Confined Colloidal Crystals

A simple geometric constraint often leads to novel, complex crystalline phases distinct from the bulk. Using thin-film charge colloidal crystals, a model system with tunable interactions, we study the effects of geometric constraints. Through a combination of experiments and simulations, we systematically explore phase reentrances and solid deformation modes concerning geometrical confinement strength, identifying two distinct categories of phase reentrances below a characteristic layer number, N_{c}: one for bcc bulk-stable and another for fcc bulk-stable systems. We further verify that the dominant thermodynamic origin is the nonmonotonic dependence of solids' free energy on the degree of spatial confinement. Moreover, we discover transitions in solid deformation modes between interface-energy and bulk-energy dominance: below a specific layer number, N_{k}, geometric constraints generate unique soft deformation modes adaptive to confinement. These findings on the N-dependent thermodynamic and kinetic behaviors offer fresh insights into understanding and manipulating thin-film crystal structures.

Structures Formed by Particles with Shoulderlike Repulsive Interaction in Thin Systems

When particles are constructed in thin systems between two parallel flat walls, structures that are not observed in bulk systems are created and the created structures change, depending on the width between the walls. In this study, the structures formed by particles constructed in thin systems were investigated through performing isothermal-isobaric Monte Carlo simulations, where the interaction between the particles is given by the hard-core square shoulder potential. By controlling the width of the shoulder-like repulsive interaction and the system width, several novel structures such as the connection of rhombuses and the square lattice of the (100) face of the body-centered cubic lattice were created.

Square Lattice Formation in a Monodisperse Complex Plasma

We present the first observations of a square lattice formation in a monodisperse complex plasma system, a configurational transition phenomenon that has long been an experimental challenge in the field. The experiments are conducted in a tabletop L-shaped dusty plasma experimental device in a dc glow discharge Argon plasma environment. By a careful control of the vertical potential confining the charged particles as well as the strength of the ion wake charge interactions with the dust particles, we are able to steer the system toward a crystalline phase that exhibits a square lattice configuration. The transition occurs when the vertical confinement strength is slightly reduced below a critical value leading to a buckling of the monodisperse hexagonal 2D dust crystal to form a narrowly separated bilayer state (a quasi-2D state). Some theoretical insights into the transition process are provided through molecular dynamics simulations carried out for the parameters relevant to our experiment.

Structural properties of liquids in extreme confinement

We simulate a hard-sphere liquid in confined geometry where the separation of the two parallel, hard walls is smaller than two particle diameters. By systematically reducing the wall separation we analyze the behavior of structural and thermodynamic properties, such as inhomogeneous density profiles, structure factors, and compressibilities when approaching the two-dimensional limit. In agreement with asymptotic predictions, we find for quasi-two-dimensional fluids that the density profile becomes parabolic and the structure factor converges toward its two-dimensional counterpart. To extract the compressibility in polydisperse samples a perturbative expression is used which qualitatively influences the observed nonmonotonic dependence of the compressibility with wall separation. We also present theoretical calculations based on fundamental-measure theory and integral-equation theory, which are in very good agreement with the simulation results.

The rheology of confined colloidal hard disks

Colloids may be treated as “big atoms” so that they are good models for atomic and molecular systems. Colloidal hard disks are, therefore, good models for 2d materials, and although their phase behavior is well characterized, rheology has received relatively little attention. Here, we exploit a novel, particle-resolved, experimental setup and complementary computer simulations to measure the shear rheology of quasi-hard-disk colloids in extreme confinement. In particular, we confine quasi-2d hard disks in a circular “corral” comprised of 27 particles held in optical traps. Confinement and shear suppress hexagonal ordering that would occur in the bulk and create a layered fluid. We measure the rheology of our system by balancing drag and driving forces on each layer. Given the extreme confinement, it is remarkable that our system exhibits rheological behavior very similar to unconfined 2d and 3d hard particle systems, characterized by a dynamic yield stress and shear-thinning of comparable magnitude. By quantifying particle motion perpendicular to shear, we show that particles become more tightly confined to their layers with no concomitant increase in density upon increasing the shear rate. Shear thinning is, therefore, a consequence of a reduction in dissipation due to weakening in interactions between layers as the shear rate increases. We reproduce our experiments with Brownian dynamics simulations with Hydrodynamic Interactions (HI) included at the level of the Rotne–Prager tensor. That the inclusion of HI is necessary to reproduce our experiments is evidence of their importance in transmission of momentum through the system.

Particle movements provoke avalanche-like compaction in soft colloid filter cakes

During soft matter filtration, colloids accumulate in a compressible porous cake layer on top of the membrane surface. The void size between the colloids predominantly defines the cake-specific permeation resistance and the corresponding filtration efficiency. While higher fluxes are beneficial for the process efficiency, they compress the cake and increase permeation resistance. However, it is not fully understood how soft particles behave during cake formation and how their compression influences the overall cake properties. This study visualizes the formation and compression process of soft filter cakes in microfluidic model systems. During cake formation, we analyze single-particle movements inside the filter cake voids and how they interact with the whole filter cake morphology. During cake compression, we visualize reversible and irreversible compression and distinguish the two phenomena. Finally, we confirm the compression phenomena by modeling the soft particle filter cake using a CFD-DEM approach. The results underline the importance of considering the compression history when describing the filter cake morphology and its related properties. Thus, this study links single colloid movements and filter cake compression to the overall cake behavior and narrows the gap between single colloid events and the filtration process.

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.

Oscillatory shear-induced bcc-fcc martensitic transformation in a colloidal suspension with long-range repulsive interactions

We perform non-equilibrium Brownian dynamics simulations to investigate the out-of-equilibrium phase behavior of a suspension of charged colloids under external oscillatory shear. We independently vary the frequency f and the maximum strain amplitude γ_max of the oscillations and map out an out-of-equilibrium phase diagram in the f-γ_max plane. Similar to what has been observed in earlier studies on colloidal hard spheres, we find the formation of a twinned face-centered-cubic phase in a specific range of γ_max, which displays a martensitic transition to a body-centered-cubic crystal within half of the oscillation cycle. We provide a comprehensive analysis of these structures and show how the system transforms from one to the other. We also report evidence of a sliding layer phase and a string phase.

Strongly coupled Yukawa trilayer liquid: Structure and dynamics

The equilibrium structure and the dispersion relations of collective excitations in trilayer Yukawa systems in the strongly coupled liquid regime are examined. The equilibrium correlations reveal a variety of structures in the liquid phase, reminiscent of the corresponding structures in the solid phase. At small layer separation substitutional disorder becomes the governing feature. Theoretical dispersion relations are obtained by applying the quasilocalized charge approximation (QLCA) formalism, while numerical data are generated by microcanonical molecular dynamics simulations. The dispersions and polarizations of the collective excitations obtained through both of these methods are compared and discussed in detail. We find that the QLCA method is, in general, very satisfactory, but that there are phenomena not covered by the QLCA. In particular, by analyzing the dynamical longitudinal and transverse current fluctuation spectra we discover the existence of a structure not related to the collective mode spectra. This also provides insight into the long-standing problem of the gap frequency discrepancy, observed in strongly coupled layered systems in earlier studies.

Buckling of two-dimensional plasma crystals with nonreciprocal interactions

Laboratory realizations of two-dimensional (2D) plasma crystals typically involve monodisperse microparticles confined into horizontal monolayers in radio-frequency (rf) plasma sheaths. This gives rise to the so-called plasma wakes beneath the microparticles. The presence of wakes renders the interactions in such systems nonreciprocal, a fact that can lead to a quite different behavior from the one expected for their reciprocal counterparts. Here we examine the buckling of a hexagonal 2D plasma crystal, occurring as the confinement strength is decreased, taking explicitly into account the nonreciprocity of the system via a well-established point-wake model. We observe that for a finite wake charge, the monolayer hexagonal crystal undergoes a transition first to a bilayer hexagonal structure, unrealizable in harmonically confined reciprocal Yukawa systems, and subsequently to a bilayer square structure. Our theoretical results are confirmed by molecular dynamics simulations for experimentally relevant parameters, indicating the potential of their observation in state-of-the-art experiments with 2D complex plasmas.

Effect of Patch Area and Interaction Length on Clusters and Structures Formed by One-Patch Particles in Thin Systems

Assuming that the interaction between particles is given by the Kern-Frenkel potential, Monte Carlo simulations are performed to study the clusters and structures formed by one-patch particles in a thin space between two parallel walls. In isothermal-isochoric systems with a short interaction length, tetrahedral tetramers, octahedral hexamers, and pentagonal dipyramidal heptamers are created with increasing patch area. In isothermal-isobaric systems, the double layers of a triangular lattice, which is the (111) face of the face-centered cubic (fcc) lattice, form when the pressure is high. For a long interaction length, a different type of cluster, trigonal prismatic hexamers, is created. The structures in the double layers also changed as follows: a simple hexagonal lattice or square lattice, which is the (100) face of the fcc structure, is created in isothermal-isobaric systems.

Approaches to self-assembly of colloidal monolayers: A guide for nanotechnologists

Self-assembly of quasi-spherical colloidal particles in two-dimensional (2D) arrangements is essential for a wide range of applications from optoelectronics to surface engineering, from chemical and biological sensing to light harvesting and environmental remediation. Several self-assembly approaches have flourished throughout the years, with specific features in terms of complexity of the implementation, sensitivity to process parameters, characteristics of the final colloidal assembly. Selecting the proper method for a given application amidst the vast literature in this field can be a challenging task. In this review, we present an extensive classification and comparison of the different techniques adopted for 2D self-assembly in order to provide useful guidelines for scientists approaching this field. After an overview of the main applications of 2D colloidal assemblies, we describe the main mechanisms underlying their formation and introduce the mathematical tools commonly used to analyse their final morphology. Subsequently, we examine in detail each class of self-assembly techniques, with an explanation of the physical processes intervening in crystallization and a thorough investigation of the technical peculiarities of the different practical implementations. We point out the specific characteristics of the set-ups and apparatuses developed for self-assembly in terms of complexity, requirements, reproducibility, robustness, sensitivity to process parameters and morphology of the final colloidal pattern. Such an analysis will help the reader to individuate more easily the approach more suitable for a given application and will draw the attention towards the importance of the details of each implementation for the final results.

Shear-induced laning transition in a confined colloidal film

Using Brownian dynamics simulations, we investigate a dense system of charged colloids exposed to shear flow in a confined (slit-pore) geometry. The equilibrium system at zero flow consists of three well-pronounced layers with a squarelike crystalline in-plane structure. We demonstrate that, for sufficiently large shear rates, the middle layer separates into two sublayers where the particles organize into moving lanes with opposite velocities. The formation of this "microlaned" state results in a destruction of the applied shear profile; it also has a strong impact on the structure of the system, and on its rheology as measured by the elements of the stress tensor. At higher shear rates, we observe a disordered state and finally a recrystallization reminiscent of the behavior of bilayer films. We also discuss the system size dependence and the robustness of the microlaned state against variations of the slit-pore width. In fact, for a pore width allowing for four layers, we observe a similar shear-induced state in which the system splits into two domains with opposite velocities.

Diverging Time Scale in the Dimensional Crossover for Liquids in Strong Confinement

We study a strongly interacting dense hard-sphere system confined between two parallel plates by event-driven molecular dynamics simulations to address the fundamental question of the nature of the 3D to 2D crossover. As the fluid becomes more and more confined the dynamics of the transverse and lateral degrees of freedom decouple, which is accompanied by a diverging time scale separating 2D from 3D behavior. Relying on the time-correlation function of the transversal kinetic energy, the scaling behavior and its density dependence is explored. Surprisingly, our simulations reveal that its time dependence becomes purely exponential such that memory effects can be ignored. We rationalize our findings quantitatively in terms of an analytic theory which becomes exact in the limit of strong confinement.

Confinement Induced Plastic Crystal-to-Crystal Transitions in Rodlike Particles with Long-Ranged Repulsion

Colloidal particles in geometrical confinement display a complex variety of packing structures different from their three-dimensional (3D) bulk counterpart. Here, we confined charged rodlike colloids with long-ranged repulsions to a thin wedge-shaped cell and show, by quantitative 3D confocal microscopy, that not only their positional but also their orientational order depends sensitively upon the slit width. Synchronized with transitions in lattice symmetry and number of layers confinement induces plastic crystal-to-crystal transitions. A model analysis suggests that this complex sequence of more or less rotationally ordered states originates from the subtle competition between the electrostatic repulsion of a rod with the wall and with its neighbors.

Charged colloidal model systems under confinement in slit geometry: a new setup for optical microscopic studies

A new experimental setup for optical microscopic studies of charged colloidal model systems under confinement between two flat walls is presented. The measurement cell consists of optically flat quartz substrates attached to piezo actuators. Those facilitate fast and flexible adjustment of the confining geometry. Optionally, the local cell height can be quantitatively controlled by in situ interferometric measurements. Proper choice of materials guarantees sufficient chemical inertia against contamination with salt ions. For efficient preparation of charged colloidal suspensions under strongly deionized conditions, the cell can be connected to a conventional pump circuit including a mixed bed ion exchanger column. The usefulness of this setup, in particular for investigating the equilibrium phase behavior of colloids at low background salt concentrations, is demonstrated recalling recent experiments.