Pattern Formation in Binary Colloidal Assemblies: Hidden Symmetries in a Kaleidoscope of Structures

Heat: A powerful tool for colloidal particle shaping

Colloidal particles of spherical shape are important building blocks for nanotechnological applications. Materials with tailored physical properties can be directly synthesized from self-assembled particles, as is the case for colloidal photonic crystals. In addition, colloidal monolayers and multilayers can be exploited as a mask for the fabrication of complex nanostructures via a colloidal lithography process for applications ranging from optoelectronics to sensing. Several techniques have been adopted to modify the shape of both individual colloidal particles and colloidal masks. Thermal treatment of colloidal particles is an effective route to introduce colloidal particle deformation or to manipulate colloidal masks (i.e. to tune the size of the interstices between colloidal particles) by heating them at elevated temperatures above a certain critical temperature for the particle material. In particular, this type of morphological manipulation based on thermal treatments has been extensively applied to polymer particles. Nonetheless, interesting shaping effects have been observed also in inorganic materials, in particular silica particles. Due to their much less complex implementation and distinctive shaping effects in comparison to dry etching or high energy ion beam irradiation, thermal treatments turn out to be a powerful and competitive tool to induce colloidal particle deformation. In this review, we examine the physicochemical principles and mechanisms of heat-induced shaping as well as its experimental implementation. We also explore its applications, going from tailored masks for colloidal lithography to the fabrication of colloidal assemblies directly useful for their intrinsic optical, thermal and mechanical properties (e.g. thermal switches) and even to the synthesis of supraparticles and anisotropic particles, such as doublets.

Quantifying order in breath figure patterns through Voronoi entropy

In this study, we simulate breath figures that are evolving two-dimensional assemblies of droplets on a substrate. We focus on the Voronoi/Shannon entropy of these figures, which quantifies the order related to the coordination number of droplets. We show that the Voronoi entropy of the complete breath figure pattern converges to a value that is the one of a randomly distributed point system. Conversely, the subset containing exclusively large droplets of the breath figure exhibits significantly lower entropy than that obtained for all droplets. Using molecular dynamics simulations, we show that coalescence events in breath figures induce the same Voronoi entropy as that caused by repulsive interactions in a bidimensional atomic system.

Quantifying the Microstructure of Dried Deposits Using Height-Height Correlation Function

Colloidal self-assembly has garnered significant attention in recent research, owing to applications in medical and engineering domains. Understanding the arrangement of particles in self-assembled systems is crucial for comprehending the underlying physics and synthesizing complex nano- and microscale structures. In this study, we introduce a novel methodology for analyzing the spatial distribution of particles in colloidal assemblies, focusing specifically on quantifying the microstructure of deposits formed by the evaporation of colloidal particle-laden drops. Utilizing a height-height correlation-function-based approach, we quantify variations in the height profile of deposits in radial and azimuthal directions. This approach enables the classification of the patterns into typical examples encountered in an evaporation-driven assembly. The method is demonstrated to be robust for quantifying synthetic and experimentally obtained deposit patterns, exhibiting excellent agreement in the estimated parameters. The mapping developed between pattern morphology and the quantitative measures introduced in this work may be used in a variety of applications including disease diagnosis as well as in developing pattern recognition tools.

Confinement Effects in Droplet Formation on a Solid Particle

Formation of a droplet around a spherical solid particle in supersaturated vapor is considered. The number and stability of equilibrium solutions in a closed small system are studied in the canonical ensemble in comparison to an open system in the grand canonical ensemble. Depending on the system's parameters, two modes exist in the canonical ensemble: the first one with only one solution and the second one with three solutions; the presence of the third solution is due to confinement. The analysis is conducted first on a macroscopic thermodynamic level of description, and then the results are supported by studies within two versions of classical density functional theory: the square-gradient approximation with the Carnahan-Starling equation of state for hard spheres on a completely wettable particle and the random-phase approximation with the fundamental measure theory on a poorly wettable particle. In the latter case, a solution breaking the spherical symmetry is observed at a small total number of molecules.

Voronoi Tessellations and the Shannon Entropy of the Pentagonal Tilings

We used the complete set of convex pentagons to enable filing the plane without any overlaps or gaps (including the Marjorie Rice tiles) as generators of Voronoi tessellations. Shannon entropy of the tessellations was calculated. Some of the basic mosaics are flexible and give rise to a diversity of Voronoi tessellations. The Shannon entropy of these tessellations varied in a broad range. Voronoi tessellation, emerging from the basic pentagonal tiling built from hexagons only, was revealed (the Shannon entropy of this tiling is zero). Decagons and hendecagon did not appear in the studied Voronoi diagrams. The most abundant Voronoi tessellations are built from three different kinds of polygons. The most widespread is the combination of pentagons, hexagons, and heptagons. The most abundant polygons are pentagons and hexagons. No Voronoi tiling built only of pentagons was registered. Flexible basic pentagonal mosaics give rise to a diversity of Voronoi tessellations, which are characterized by the same symmetry group. However, the coordination number of the vertices is variable. These Voronoi tessellations may be useful for the interpretation of the iso-symmetrical phase transitions.

Two-Dimensional Structures Formed by Triblock Patchy Particles with Two Different Patches

Two-dimensional structures formed by spherical triblock patchy particles are examined by performing Monte Carlo simulations. In the model, the triblock patchy particles have two different types of patches at the polar positions. The patch sizes are different from each other, and the attractive interaction acts only between the same types of patches. The particles translate on a flat plane and rotate three-dimensionally. When varying the two patch sizes, the pressure, and interaction energy, various structures are observed. When the difference between two patch sizes is small, kagome lattices, hexagonal structures, and two-dimensional dodecagonal quasi-crystal structures are observed. When the difference between two patch sizes is large, chain-like structures are created. With lower temperature, sparse structures such as ring-like structures form.

Size-Dependent Spontaneous Separation of Colloidal Particles in Sub-Microliter Suspension by Cations

Great efforts have been made to separate micro/nanoparticles in small-volume specimens, but it is a challenge to achieve the simple, maneuverable and low-cost separation of sub-microliter suspension with large separation distances. By simply adding trace amounts of cations (Mg2+/Ca2+/Na+), we experimentally achieved the size-dependent spontaneous separation of colloidal particles in an evaporating droplet with a volume down to 0.2 μL. The separation distance was at a millimeter level, benefiting the subsequent processing of the specimen. Within only three separating cycles, the mass ratio between particles with diameters of 1.0 μm and 0.1 μm can be effectively increased to 13 times of its initial value. A theoretical analysis indicates that this spontaneous separation is attributed to the size-dependent adsorption between the colloidal particles and the aromatic substrate due to the strong hydrated cation-π interactions.

Manipulating the morphology of colloidal particles via ion beam irradiation: A route to anisotropic shaping

Ion beam irradiation of spherical colloidal particles is a viable route to induce particle deformation, especially to get anisotropic shapes. Even though less common in comparison with dry etching techniques, different types of morphological changes can be attained depending on the process parameters (angle of incidence, energy, fluence of the ion beam, type of ion, temperature) and on particle material and initial particle arrangement (crystalline or disordered, made up of isolated or closely-packed particles). The technique can be harnessed to get anisotropic deformation of spherical colloidal particles into an ellipsoidal shape, but also to tailor the interstices between closely-packed colloidal particles, to get particle necking and coalescence as well as particle rearrangement. As such, particle deformation based on ion irradiation can find diverse applications from synthesis of ellipsoidal particles to modified templates for colloidal lithography. In this review, we examine in detail the principles and models of colloidal particle shaping via ion beam irradiation, the influence of process parameters on particle morphology and the applications of irradiated particles.

Line Patterns and Fractured Coatings in Deposited Colloidal Hydrochar on Glass Substrates after Evaporation of Water

Patterns of assembled colloidal particles can form on substrates due to solvent evaporation, and here we studied such phenomena in the drying of monodispersed colloidal hydrochar dispersions prepared by the hydrothermal carbonization of glucose and purified by dialysis. During the evaporation of water, line patterns or, in some cases, mud-like patterns formed. The line formation was investigated as a function of the pH of the dispersion, substrate shape, particle concentration, and concentration of sodium dodecylsulfate (SDS). The lines comprised dense assemblies of hydrochar particles. The line width increased with the successive evaporation of water. Sharper lines formed with the addition of SDS, which was ascribed to the effects of solubilization or moderated interactions. At greater particle concentrations, we also observed a continuous layer of colloidal particles between the lines. A mechanism for the line pattern formation derived from the literature on other colloids was proposed. Mud-like patterns formed on the substrate in concentrated samples without SDS addition and were put in the context of the formation of cracks in the drying of colloidal coatings. Hydrochars belong to carbon-rich colloids, which are of fundamental and technological importance. This research could be useful for in situ line printing within microfluidic devices, for example.

Self-organization of agitated microspheres on various substrates

The vibration dynamics of relatively large granular grains is extensively treated in the literature, but comparable studies on the self-assembly of smaller agitated beads are lacking. In this work, we investigate how the particle properties and the properties of the underlying substrate surface affect the dynamics and self-organization of horizontally agitated monodisperse microspheres with diameters between 3 and 10 μm. Upon agitation, the agglomerated hydrophilic silica particles locally leave traces of particle monolayers as they move across the flat uncoated and fluorocarbon-coated silicon substrates. However, on the micromachined silicon tray with relatively large surface roughness, the agitated silica agglomerates form segregated bands reminiscent of earlier studies on granular suspensions or Faraday heaps. On the other hand, the less agglomerated hydrophobic polystyrene particles form densely occupied monolayer arrangements regardless of the underlying substrate. We explain the observations by considering the relevant adhesion and friction forces between particles and underlying substrates as well as those among the particles themselves. Interestingly, for both types of microspheres, large areas of the fluorocarbon-coated substrates are covered with densely occupied particle monolayers. By qualitatively examining the morphology of the self-organized particle monolayers using the Voronoi approach, it is understood that these monolayers are highly disordered, i.e., multiple symmetries coexist in the self-organized monolayers. However, more structured symmetries are identified in the monolayers of the agitated polystyrene microspheres on all the substrates, albeit not all precisely positioned on a hexagonal lattice. On the other hand, both the silica and polystyrene monolayers on the bare silicon substrates transition into less disordered structures as time progresses. Using Kelvin probe force microscopy measurements, we show that due to the tribocharging phenomenon, the formation of particle monolayers is promoted on the fluorocarbon surface, i.e., a local electrostatic attraction exists between the particle and the substrate.

Depletion Induced Demixing and Crystallization in Binary Colloids Subjected to an External Potential Barrier

Depletion interaction plays an important role in determining the structural and dynamical properties of binary colloidal mixtures. We have investigated the effect of the attractive depletion interaction between an external potential barrier and larger species in the binary mixture on the phase behavior of a binary colloidal mixture using canonical-isokinetic ensemble molecular dynamics simulations. The demixing of the binary mixture due to this depletion interaction increases as the volume fraction increases, and a pure phase of larger particles forms in the region of the potential barrier. The local density of this pure phase is high enough that a face centered cubic crystalline domain is formed at this region. This crystalline phase diffuses perpendicular to the external potential barrier, indicating that moving crystals can be obtained in an equilibrium system. The temperature dependence of diffusivity of larger particles is non-Arrhenius and changes from sub-Arrhenius to super-Arrhenius as the volume fraction increases. This crossover from sub-Arrhenius to super-Arrhenius diffusion coincides with the crystalline formation near the potential barrier.

Morphology of Mixed Langmuir and Langmuir-Schaefer Monolayers with Covered CdSe/CdS/ZnS Quantum Dots and Arachidic Acid

The process of formation of a Langmuir-Schaefer (LS) matrix based on a mixed monolayer of arachidic acid (AA) and 8 nm CdSe/CdS/ZnS quantum dots (QDs) stabilized by molecules of trioctylphosphine oxide (TOPO) was investigated. The change in the morphology, monolayer compressibility, and area per elementary cell of the created mixed monolayers, depending on the ratio of the components, was studied. It is shown that the change in the morphology of Langmuir-Blodgett (LB) monolayers begins to occur at a ratio between the number of QDs and AA molecules of 1:24. Dendrimeric structures with a thickness of the order of 30-40 nm appear in the mixed monolayer when LB film deposition was carried out above the collapse surface pressure of a Langmuir film from only TOPO-covered QDs. Information on the dependence of the morphology of such structures on the molar ratio of the components is necessary for the production of ordered 2D nanostructures containing 0D and 1D objects with quantum bonds. Such nanostructures can be used in nanoelectronic and optoelectronic devices as a sensitive sensor element. The obtained results would be relevant for any type of spherical shape nanoparticles.

Recent Advances in Binary Colloidal Crystals for Photonics and Porous Material Fabrication

In the past few years, binary colloidal crystals (BCCs) composed of both large and small particles have attracted considerable attention from the scientific community as an exciting alternative to single colloidal crystals (SCCs). In particular, more complex structures with diverse nanotopographies and desirable optical properties of BCCs can be obtained by various colloidal assembly methods, as compared to SCCs. Furthermore, high accuracy in crystal growth with controllable stoichiometries allows for a great deal of promising applications in the fields of both interfacial and material sciences. The visible-light diffraction property of BCCs is more superior than that of SCCs, which makes them have more promising applications in the fabrication of photonic crystals with full band gaps. On the other hand, their spherical shapes and ease of removal property make them ideal templates for ordered porous material fabrication. Hence, this perspective outlined recent advances in assembly approaches of BCCs, with an emphasis on their promising applications for advanced photonics and multifunctional porous material fabrication. Eventually, some challenging yet important issues and some future perspectives are further discussed.

Evaporative self-assembly of the binary mixture of soft colloids

We have reported experimental studies on the self-assembly and degree of ordering of a binary mixture of soft colloids in monolayer deposits obtained by controlled evaporation. A sessile drop containing soft colloids is evaporated on a solid surface to achieve a loosely-packed two-dimensional deposit with a hexagonal arrangement. The soft microgel particles possess a hard core with a compliant corona, which plays a crucial role in retaining the crystallinity of the binary particle monolayer. The ordered arrangement of the binary mixture is observed even when the bulk diameter of one type of particle is 25% higher than the other, irrespective of their mixing ratio (1 : 3, 1 : 1, and 3 : 1). The microgel particles of both sizes are found to be homogeneously distributed throughout the deposit, completely suppressing the size-dependent particle segregation. Furthermore, in contrast to the self-assembly of bidisperse hard colloids, wherein the lattice distorts to accommodate particles of disparate sizes, in soft colloids, the particles deform at the interface to preserve the crystalline lattice. Moreover, unlike the gradual order-to-disorder transition observed in the deposits consisting of monodisperse microgel particles, the deposits of a binary mixture of microgels exhibit no noticeable trend. The areal disorder parameter, pair correlation function and the shape factor which quantifies the local ordering of particles in the deposit indicate the absence of a distinct order-to-disorder transition for the binary mixtures.

Quantifying patterns in optical micrographs of one- and two-dimensional ellipsoidal particle assemblies

Current developments in colloidal science include the assembly of anisotropic colloids with broad geometric diversity. As the complexity of particle assemblies increases, the need for ubiquitous algorithms that quantitatively analyze images of the assemblies to deliver key information such as quantification of crystal structures becomes more urgent. This contribution describes algorithms capable of image analysis for classifying colloidal structures based on abstracted interparticle relationship information and quantitatively analyzing the abundance of each structure in mixed pattern assemblies. The algorithm parameters can be adjusted, allowing for the algorithms to be adapted for different image analyses. Three different ellipsoidal particle assembly images are presented to demonstrate the effectiveness of the algorithms: a one-dimensional (1D) particle chain assembly and two two-dimensional (2D) polymorphic crystals each consisting of assemblies of two distinct plane symmetry groups. Angle relationships between neighbouring particles are calculated and neighbour counts of each particle are determined. Combining these two parameters as rules for classification criteria allows for the labeling and quantification of each particle into a defined symmetry class within an assembly. The algorithms provide a labelled image comprising classification results and particle counts of each defined class. For multiple images or individual frames from a video, the script can be looped to achieve automatic processing. The yielded classification data allow for more in-depth image analysis of mixed pattern particle assemblies. We envision that these algorithms will have utility in quantitative analysis of images comprising ellipsoidal colloidal materials, nanoparticles, or biological matter.

Pattern detection in colloidal assembly: A mosaic of analysis techniques

Characterization of the morphology, identification of patterns and quantification of order encountered in colloidal assemblies is essential for several reasons. First of all, it is useful to compare different self-assembly methods and assess the influence of different process parameters on the final colloidal pattern. In addition, casting light on the structures formed by colloidal particles can help to get better insight into colloidal interactions and understand phase transitions. Finally, the growing interest in colloidal assemblies in materials science for practical applications going from optoelectronics to biosensing imposes a thorough characterization of the morphology of colloidal assemblies because of the intimate relationship between morphology and physical properties (e.g. optical and mechanical) of a material. Several image analysis techniques developed to investigate images (acquired via scanning electron microscopy, digital video microscopy and other imaging methods) provide variegated and complementary information on the colloidal structures under scrutiny. However, understanding how to use such image analysis tools to get information on the characteristics of the colloidal assemblies may represent a non-trivial task, because it requires the combination of approaches drawn from diverse disciplines such as image processing, computational geometry and computational topology and their application to a primarily physico-chemical process. Moreover, the lack of a systematic description of such analysis tools makes it difficult to select the ones more suitable for the features of the colloidal assembly under examination. In this review we provide a methodical and extensive description of real-space image analysis tools by explaining their principles and their application to the investigation of two-dimensional colloidal assemblies with different morphological characteristics.

Drying-induced back flow of colloidal suspensions confined in thin unidirectional drying cells

A clear back flow was observed in the thin unidirectional drying cell of a colloidal suspension. Flow around the colloidal-particle packing front was more complex than expected, even though a colloidal suspension was confined in a narrow space with a submillimeter-scale or shorter gap height. We propose that an increase in particle concentration around the packing front induces downward flow, which is the origin for back flow inside the cell. A mathematical model, which considered both a drying induced horizontal flow and a circulation flow caused by a concentration gradient of particles, showed a reasonable agreement with experimental data for the width of the back-flow region. The concentration gradient of particles was not negligible and it generated a rather complicated flow even in a thin drying liquid film.

Shape Deformation in Ion Beam Irradiated Colloidal Monolayers: An AFM Investigation

Self-assembly of colloidal monolayers represents a prominent approach to the fabrication of nanostructures. The modification of the shape of colloidal particles is essential in order to enrich the variety of attainable patterns which would be limited by the typical assembly of spherical particles in a hexagonal arrangement. Polymer particles are particularly promising in this sense. In this article, we investigate the deformation of closely-packed polystyrene particles under MeV oxygen ion irradiation at normal incidence using atomic force microscopy (AFM). By developing a procedure based on the fitting of particle topography with quadrics, we reveal a scenario of deformation more complex than the one observed in previous studies for silica particles, where several phenomena, including ion hammering, sputtering, chemical modifications, can intervene in determining the final shape due to the specific irradiation conditions. In particular, deformation into an ellipsoidal shape is accompanied by shrinkage and polymer redistribution with the presence of necks between particles for increasing ion fluence. In addition to casting light on particle irradiation in a regime not yet explored, we present an effective method for the characterization of the colloidal particle morphology which can be applied to describe and understand particle deformation in other regimes of irradiation or with different techniques.

A Journey Through the Landscapes of Small Particles in Binary Colloidal Assemblies: Unveiling Structural Transitions from Isolated Particles to Clusters upon Variation in Composition

Two-dimensional (2D) amorphous binary colloidal assemblies composed of particles of two different sizes are characterized by the loss of hexagonal close-packing for larger particles, occurring when the size ratio between small (S) and large (L) particles dSdL exceeds a certain threshold value. For moderately low particle number ratios NSNL large particles still retain a denser arrangement with transitions from hexagonal symmetry to the coexistence of different types of symmetries as NSNL progressively departs from 0 to higher values. On the other hand, small particles reveal sparser arrangements: shape identification and quantification of structural transitions in small particle arrangements appear particularly challenging. In this article, we investigate their shapes and transitions for amorphous binary colloidal particles assembled at the air/water interface. For the quantitative characterization of the evolution in particle arrangements for NSNL variable between 0.5 and 2, we develop an innovative procedure for morphological analysis, combining Minkowski functionals, Voronoi diagrams and ad hoc techniques to recognize and classify specific features. Such a powerful approach has revealed a wide variety of landscapes featuring isolated particles, dimers, chains, small clusters evolving with the colloidal suspension composition. Our method can be applied to the analysis of spatial configurations of sparse colloidal patterns obtained in different conditions.