Self-assembly of repulsive interfacial particles via collective sinking

Versatile Deposition of Complex Colloidal Assemblies from the Evaporation of Hanging Drops

Existing strategies designed to produce ordered arrangements of colloidal particles on solid supports are of great interest for their wide range of applications, from colloidal lithography, plasmonic and biomimetic surfaces to tags for anti-counterfeiting, but they all share various degrees of complexity hampering their facile implementation. Here, a drastically simplified methodology is presented to achieve ordered particle deposition, consisting in adding micromolar amounts of cationic surfactant to a colloidal suspension drop and let it evaporate in an upside-down configuration. Confinement at the air/water interface enables particle assembly into monolayers, which are then transferred on the substrate producing highly ordered structures displaying vivid, orientation-dependent structural colors. The method is compatible with many particle types and substrates, while controlling system parameters allows tuning the deposit size and morphology, from monocrystals to polycrystalline disks and "irises", from single-component to crystal alloys with Moiré patterns, demonstrating its practicality for a variety of processes.

Tuning Electrostatic Interactions of Colloidal Particles at Oil-Water Interfaces with Organic Salts

Monolayers of colloidal particles at oil-water interfaces readily crystallize owing to electrostatic repulsion, which is often mediated through the oil. However, little attempts exist to control it using oil-soluble electrolytes. We probe the interactions among charged hydrophobic microspheres confined at a water-hexadecane interface and show that repulsion can be continuously tuned over orders of magnitude upon introducing nanomolar amounts of an organic salt into the oil. Our results are compatible with an associative discharging mechanism of surface groups at the particle-oil interface, similar to the charge regulation observed for charged colloids in nonpolar solvents.

Field-mediated locomotor dynamics on highly deformable surfaces

Studies of active matter-systems consisting of individuals or ensembles of internally driven and damped locomotors-are of interest to physicists studying nonequilibrium dynamics, biologists interested in individuals and swarm locomotion, and engineers designing robot controllers. While principles governing active systems on hard ground or within fluids are well studied, another class of systems exists at deformable interfaces. Such environments can display mixes of fluid-like and elastic features, leading to locomotor dynamics that are strongly influenced by the geometry of the surface, which, in itself, can be a dynamical entity. To gain insight into principles by which locomotors are influenced via a deformation field alone (and can influence other locomotors), we study robot locomotion on an elastic membrane, which we propose as a model of active systems on highly deformable interfaces. As our active agent, we use a differential driven wheeled robotic vehicle which drives straight on flat homogeneous surfaces, but reorients in response to environmental curvature. We monitor the curvature field-mediated dynamics of a single vehicle interacting with a fixed deformation as well as multiple vehicles interacting with each other via local deformations. Single vehicles display precessing orbits in centrally deformed environments, while multiple vehicles influence each other by local deformation fields. The active nature of the system facilitates a differential geometry-inspired mathematical mapping from the vehicle dynamics to those of test particles in a fictitious "spacetime," allowing further understanding of the dynamics and how to control agent interactions to facilitate or avoid multivehicle membrane-induced cohesion.

A broad perspective to particle-laden fluid interfaces systems: from chemically homogeneous particles to active colloids

Particles adsorbed to fluid interfaces are ubiquitous in industry, nature or life. The wide range of properties arising from the assembly of particles at fluid interface has stimulated an intense research activity on shed light to the most fundamental physico-chemical aspects of these systems. These include the mechanisms driving the equilibration of the interfacial layers, trapping energy, specific inter-particle interactions and the response of the particle-laden interface to mechanical perturbations and flows. The understanding of the physico-chemistry of particle-laden interfaces becomes essential for taking advantage of the particle capacity to stabilize interfaces for the preparation of different dispersed systems (emulsions, foams or colloidosomes) and the fabrication of new reconfigurable interface-dominated devices. This review presents a detailed overview of the physico-chemical aspects that determine the behavior of particles trapped at fluid interfaces. This has been combined with some examples of real and potential applications of these systems in technological and industrial fields. It is expected that this information can provide a general perspective of the topic that can be exploited for researchers and technologist non-specialized in the study of particle-laden interfaces, or for experienced researcher seeking new questions to solve.

Exploiting Additives for Directing the Adsorption and Organization of Colloid Particles at Fluid Interfaces

The self-assembly of colloids at fluid interfaces is a well-studied research field both for gaining fundamental insights and for material fabrication. The fluid interface allows the confinement of particles in two dimensions and may act as a template for guiding their organization into soft and reconfigurable structures. Additives (e.g., surfactants, salts, and polymers) in the colloidal suspension are routinely used as a practical and effective tool to drive particle adsorption and tune their interfacial organization. However, some phenomena lying at the heart of the accumulation and self-assembly of particles at fluid interfaces remain poorly understood. This Feature Article aims to critically analyze the mechanisms involved in the adsorption and self-organization of micro- and nanoparticles at various fluid interfaces. In particular, we address the role of additives in both promoting the adsorption of particles from the bulk suspension to the fluid interface and in mediating the interactions between interfacial particles. We emphasize how different types of additives play a crucial role in controlling the interactions between suspended particles and the fluid interface as well as the interactions between adsorbed particles, thus dictating the final self-assembled structure. We also critically summarize the main experimental protocols developed for the complete adsorption of particles initially suspended in the bulk. Furthermore, we highlight some special properties (e.g., reconfigurability upon external stimulation and dissipative self-assembly) and the application potential of structures formed by colloid self-organization at fluid interfaces mediated/promoted by additives. We believe our contribution serves both as a practical roadmap to scientists coming from other fields and as a valuable information resource for all researchers interested in this exciting research field.

Photothermally Reconfigurable Colloidal Crystals at a Fluid Interface, a Generic Approach for Optically Tunable Lattice Properties

Optically addressable colloidal assembly at fluid interfaces is a highly desired component to generate reconfigurable 2D materials but has rarely been achieved and only with specific interface engineering. Here we describe a generic method to get optically reconfigurable colloidal crystals at the air/water interface and emphasize a new mechanism to convert light into tunable lattice properties. We use light-absorbing anionic particles adsorbed at the air/water interface in the presence of minute amounts of cationic surfactant, which self-assembled into closely packed polycrystalline structures by collectively deforming the surrounding interface. Low-intensity irradiation of these colloidal crystals results in unprecedented control of the interparticle spacing in a preserved crystalline state while, at a higher intensity, cycles of melting/recrystallization with a controllable transition kinetics can be achieved upon successive on/off stimulations. We show that this photoreversible melting originates from an initial thermocapillary stress, expanding the colloidal assembly against the local confinement, and an increase in particles diffusivity imposing the transition kinetics. With this mechanism, local irradiation leads to highly dynamic patterns, including self-healing or self-fed "living" crystals, while multiresponsive assembly is also achieved by controlling particle organization with both light and magnetic stimuli.

From bulk crystallization of inorganic nanoparticles at the air/water interface: tunable organization and intense structural colors

The "flipping method" is a new straightforward way to both adsorb and organize microparticles at a liquid interface, with ultralow amounts of a surfactant and no other external forces than gravity. Here we demonstrate that it allows the adsorption of a variety of inorganic nanoparticles at an air/water interface, in an organized way, which is directly controlled by the surfactant concentration, ranging from amorphous to highly crystalline two-dimensional assemblies. With micromolar amounts of a conventional cationic surfactant (dodecyltrimethylammonium bromide, DTAB), nanoparticles of different compositions (silica, silver, and gold), sizes (down to 100 nm) and shapes (spheres and cubes) adsorb from the bulk and directly organize at the air/water interface, resulting in marked optical properties such as reflectivity or intense structural coloration.

Particle clusters at fluid-fluid interfaces: equilibrium profiles, structural mechanics and stability against detachment

We investigate clustering of particles at an initially flat fluid-fluid interface of surface tension γ under an external force f directed perpendicular to the interface. We employ analytical theory, numerical energy minimization (Surface Evolver) and computational fluid dynamics (the Lattice-Boltzmann method) to study the equilibrium deformation of the interface and structural mechanics of the clusters, in particular at the onset of instability. In the case of incompressible clusters, we find that the equilibrium 3D interface profiles are uniquely determined by the length scale γ/(fn0), where n0 is the particle surface number density, and a non-dimensional shape parameter f2Nn0/γ2. The scaling remains valid in the whole regime of forces f, i.e., even close to the stability limit fcrit. In the cases with an initial hexagonal arrangement of the particles, upon f approaching fcrit, our simulations additionally reveal the emergence of curvature-induced defects and 2D stress anisotropy. We develop stability diagrams in terms of f, N (we study 7 ≤ N ≤ 61), and the contact angle θp at the particles and identify three unstable regimes corresponding to (i) collective detachment of the whole cluster from the interface, (ii) ejection of individual particles, and (iii) both detachment and ejection. We also discuss possible metastable states. Altogether, our results may help in better understanding and controlling the particle interfacial instabilities with potential uses in synthesis of new materials, environmental sciences and microfluidics.

Photoswitchable Dissipative Two-Dimensional Colloidal Crystals

Control over particle interactions and organization at fluid interfaces is of great importance both for fundamental studies and practical applications. Rendering these systems stimulus-responsive is thus a desired challenge both for investigating dynamic phenomena and realizing reconfigurable materials. Here, we describe the first reversible photocontrol of two-dimensional colloidal crystallization at the air/water interface, where millimeter-sized assemblies of microparticles can be actuated through the dynamic adsorption/desorption behavior of a photosensitive surfactant added to the suspension. This allows us to dynamically switch the particle organization between a highly crystalline (under light) and a disordered (in the dark) phase with a fast response time (crystallization in ≈10 s, disassembly in ≈1 min). These results evidence a new kind of dissipative system where the crystalline state can be maintained only upon energy supply.

Adsorption and Crystallization of Particles at the Air-Water Interface Induced by Minute Amounts of Surfactant

Controlling the organization of particles at liquid-gas interfaces usually relies on multiphasic preparations and external applied forces. Here, we show that micromolar amounts of a conventional cationic surfactant induce, in a single step, both adsorption and crystallization of various types of nanometer- to micrometer-sized anionic particles at the air-water interface, without any additional phase involved or external forces other than gravity. Contrary to conventional surfactant-induced particle adsorption through neutralization and hydrophobization at a surfactant concentration close to the critical micellar concentration (CMC), we show that in our explored concentration regime (CMC/1000-CMC/100), particles adsorb with a low contact angle and maintain most of their charge, leading to the formation of two-dimensional assemblies with different structures, depending on surfactant ( C_s) and particle ( C_p) concentrations. At low C_s and C_p, particles are repulsive and form disordered assemblies. Increasing C_p in this regime increases the number of adsorbed particles, leading to the formation of mm-sized, highly ordered polycrystalline assemblies because of the long-range attraction mediated by the collective deformation of the interface. Increasing C_s decreases the particle repulsion and therefore the interparticle distance within the monocrystalline domains. A further increase in C_s (≈CMC/10) leads to a progressive neutralization of particles accompanied by the formation of disordered structures, ranging from densely packed amorphous ones to loosely packed gels. These results emphasize a new role of the surfactant to mediate both adsorption and crystallization of particles at liquid-gas interfaces and provide a practical manner to prepare two-dimensional ordered colloidal assemblies in a remarkably robust and convenient manner.

Capillary interactions between dynamically forced particles adsorbed at a planar interface and on a bubble

We investigate the dynamic interfacial deformation induced by micrometric particles exerting a periodic force on a planar interface or on a bubble, and the resulting lateral capillary interactions. Assuming that the deformation of the interface is small, neglecting the effect of viscosity, and assuming point particles, we derive analytical formulas for the dynamic deformation of the interface. For the case of a planar interface the dynamic point force simply generates capillary waves, while for the case of a bubble it excites shape oscillations, with a dominat deformation mode that depends on the bubble radius for a given forcing frequency. We evaluate the lateral capillary force acting between two particles, by superimposing the deformations induced by two point forces. We find that the lateral capillary forces experienced by dynamically forced particles are non monotonic and can be repulsive. The results are applicable to micrometric particles driven by different dynamic forcing mechanisms such as magnetic, electric or acoustic fields.

Self-assembly of cubic colloidal particles at fluid-fluid interfaces by hexapolar capillary interactions

Colloidal particles adsorbed at fluid-fluid interfaces can self-assemble, thanks to capillary interactions, into 2D ordered structures. Recently, it has been predicted by theoretical and numerical calculations [G. Soligno et al., Phys. Rev. Lett., 2016, 116, 258001] that cubes with smooth edges adsorbed at a flat fluid-fluid interface generate hexapolar capillary deformations that cause the particles to self-assemble into honeycomb and hexagonal lattices, at equilibrium and for Young's contact angle π/2. Here we extend these results. Firstly, we show that capillary interactions induced by hexapolar deformations can drive the particles at the interface to form also thermodynamically-stable square lattices, in addition to honeycomb and hexagonal lattices. Then, we study the effects of tuning the particle shape on the particle self-assembly at the interface, considering, respectively, smooth-edge cubes, sharp-edge cubes, slightly truncated-edge cubes, and highly truncated-edge cubes. In our calculations, both capillary and hard-particle interactions are taken into account. We show that such variations in the particle shape significantly affect both qualitatively and quantitatively the self-assembly of the particles at the interface, and we sum up our results in the form of temperature-density phase diagrams. For example, using typical experimental parameters, our results show that only 4-to-5 nm sized sharp-edge and smooth-edge cubes can self-assemble into a honeycomb lattice, while slightly and highly truncated-edge cubes can form a honeycomb lattice only if they have a 8-to-12 and 10-to-16 nm size, respectively, for the same experimental parameters. Also, our results show that the capillarity-induced square lattice phase is stable only for the smooth-edge and truncated-edge cubes, but not for the sharp-edge cubes.

Floating and Sinking of a Pair of Spheres at a Liquid-Fluid Interface

Spheres floating at liquid-fluid interfaces cause interfacial deformations such that their weight is balanced by the resultant forces of surface tension and hydrostatic pressure while also satisfying a contact angle condition. Determining the meniscus shape around several floating spheres is a complicated problem because the vertical locations of the spheres and the horizontal projections of the three-phase contact lines are not known a priori. Here, a new computational algorithm is developed to simultaneously satisfy the nonlinear Laplace-Young equation for the meniscus shape, the vertical force balance, and the geometric properties of the spheres. We implement this algorithm to find the shape of the interface around a pair of floating spheres and the horizontal force required to keep them at a fixed center-center separation. Our numerical simulations show that the ability of a pair of spheres to float (rather than sink) depends on their separation. Similar to previous work on horizontal cylinders, sinking may be induced at close range for small spheres that float when isolated. However, we also discover a new and unexpected behavior: at intermediate inter-particle distances, spheres that would sink in isolation can float as a pair. This effect is more pronounced for spheres of radius comparable to the capillary length, suggesting that this effect is a result of hydrostatic pressure, rather than surface tension. An approximate solution confirms these phenomena and shows that the mechanism is indeed the increased supporting force provided by the hydrostatic pressure. Finally, the horizontal force of capillary attraction between the spheres is calculated using the results of the numerical simulations. These results show that the classic linear superposition approximation (due to Nicolson) can lose its validity for relatively heavy particles at close range.