Binary superlattices from colloidal nanocrystals and giant polyoxometalate clusters

The significance of multipole interactions for the stability of regular structures composed from charged particles

Identifying the forces responsible for stabilising binary particle lattices is key to the controlled fabrication of many new materials. Experiments have shown that the presence of charge can be integral to the formation of ordered arrays; however, a complete analysis of the forces responsible has not included many of the significant lattice types that may form during fabrication. A theory of many-body electrostatic interactions has been applied to six lattice stoichiometries, AB, AB2, AB3, AB4, AB5 and AB6, to show that induced multipole interactions can make a very significant (>80 %) contribution to the total lattice energy of arrays of charged particles. Particle radii ratios which favour global minima in electrostatic energy are found to be the same or a close match to those observed by experiment. Although certain lattice types exhibit local energy minima, the calculations show that many-body rather than two-body interactions are ultimately responsible for the structures observed by experiment. For a lattice isostructural with CFe4, a particle size ratio not previously observed is found to be particularly stable due to many-body effects.

Keplerate {Mo132}-Stearic Acid Conjugates: Supramolecular Synthons for the Design of Dye-Loaded Nanovesicles, Langmuir-Schaefer Films, and Infochemical Applications

Self-assembly gives rise to the versatile strategies of smart material design but requires precise control on the supramolecular level. Here, inorganic-organic synthons (conjugates) are produced by covalently grafting stearic acid tails to giant polyoxometalate (POM) Keplerate-type {Mo132} through an organosilicon linker (3-aminopropyltrimethoxysilane, APTMS). Using the liposome production approach, the synthons self-assemble to form hollow nanosized vesicles (100-200 nm in diameter), which can be loaded with organic dyes─eriochrome black T (ErChB) and fluorescein (FL)─where the POM layer serves as a membrane with subnanopores for cell-like communication. The dye structure plays an essential role in embedding dyes into the vesicle's shell, which opens the way to control the colloidal stability of the system. The produced vesicles are moved by an electric field and used for the creation of an infochemistry scheme with three types of logic gates (AND, OR, and IMP). To design 2D materials, synthons can form spread films, from simple addition on the water-air interface to lateral compression in the Langmuir bath, and highly ordered structures appear, demonstrating electron diffraction in Langmuir-Schaefer (LS) films. These results show the significant potential of POM-based synthons and nanosized vesicles to supramolecular design the diversity of smart materials.

A dual-model immobilization-free photoelectrochemical/visual colorimetric bioanalysis based on microemulsion self-assemblies mediated multifunctional signal amplification strategy

Herein, a novel silver ion-loaded gold microemulsion assemblies (Au/Ag+ MAs) mediated multifunctional signal amplification strategy was proposed to construct a sensitive immobilization-free photoelectrochemical (PEC)/colorimetric biosensor for carcinoembryonic antigen (CEA) detection. Through the sandwiched reaction among CEA, the CEA aptamer (DNA1) loaded on the Au nanoparticles (NPs) functionalized iron oxide (Fe3O4) nanospheres and another CEA aptamer (DNA2) immobilized on Au/Ag+ MAs, a complex is formed and acquired by magnetic separation. Then, Au/Ag+ MAs of the complex are disassembled into Au NPs and Ag+ ions driven by an acetone response, and the obtained demulsification solution is transferred to the cadmium sulfide/cadmium telluride (CdS/CdTe) photoactive composites modified electrode. Based on the multiple inhibition functions (blocking effect of oleylamine; energy transfer effect of Au NPs; and electron snatching effect of Ag+), the photocurrent of the electrode decreases obviously, resulting in the ultrasensitive detection of CEA (a detection limit of 16 fg mL-1). Interestingly, the ion-exchange reactions between CdS/CdTe composites and Ag+ ions generate silver sulfide/silver telluride (Ag2S/Ag2Te) composites, and a color change of composites can be distinguished directly, leading to a quick visual detection of CEA. Compared with the traditional single-modal assay for CEA, such dual-modal PEC/colorimetric assay is a more accurate and reliable due to different mechanisms and independent signal conversion. This work will offer a new perspective for the applications of various self-assemblies in PEC bioanalysis.

Fabricating sub-nanometer materials through cluster assembly

The self-assembly of clusters provides a feasible approach for the bottom-up fabrication of functional materials with tailored properties. Sub-nanometer cluster assembly with a well-defined construction presents a precisely controllable structure and extraordinary properties, which provides an ideal model for the investigation of structures and properties at the molecular level. Non-covalent interactions between clusters may dominate the assembly behavior, appearing as tunable structures different from their nano-counterparts. Interactions between clusters and their superatom orbitals can significantly influence the electronic structures, because of which exceptional properties may emerge. In this paper, recent progress on cluster-based assemblies is introduced, including sub-nanometer building blocks of noble metal and polyoxometalate (POM) clusters. The structures, formation mechanism and properties of these cluster assemblies are discussed from experimental and theoretical aspects. This perspective aims to provide a new insight into the design and manufacture of sub-nanometer materials based on clusters.

Unconventional-Phase Crystalline Materials Constructed from Multiscale Building Blocks

Crystal phase, an intrinsic characteristic of crystalline materials, is one of the key parameters to determine their physicochemical properties. Recently, great progress has been made in the synthesis of nanomaterials with unconventional phases that are different from their thermodynamically stable bulk counterparts via various synthetic methods. A nanocrystalline material can also be viewed as an assembly of atoms with long-range order. When larger entities, such as nanoclusters, nanoparticles, and microparticles, are used as building blocks, supercrystalline materials with rich phases are obtained, some of which even have no analogues in the atomic and molecular crystals. The unconventional phases of nanocrystalline and supercrystalline materials endow them with distinctive properties as compared to their conventional counterparts. This Review highlights the state-of-the-art progress of nanocrystalline and supercrystalline materials with unconventional phases constructed from multiscale building blocks, including atoms, nanoclusters, spherical and anisotropic nanoparticles, and microparticles. Emerging strategies for engineering their crystal phases are introduced, with highlights on the governing parameters that are essential for the formation of unconventional phases. Phase-dependent properties and applications of nanocrystalline and supercrystalline materials are summarized. Finally, major challenges and opportunities in future research directions are proposed.

An Artificial Neural Network Reveals the Nucleation Mechanism of a Binary Colloidal AB13 Crystal

Colloidal suspensions of two species have the ability to form binary crystals under certain conditions. The hunt for these functional materials and the countless investigations on their formation process are justified by the plethora of synergetic and collective properties these binary superlattices show. Among the many crystal structures observed over the past decades, the highly exotic colloidal icosahedral AB₁₃ crystal was predicted to be stable in binary hard-sphere mixtures nearly 30 years ago, yet the kinetic pathway of how homogeneous nucleation occurs in this system is still unknown. Here we investigate binary nucleation of the AB₁₃ crystal from a binary fluid phase of nearly hard spheres. We calculate the nucleation barrier and nucleation rate as a function of supersaturation and draw a comparison with nucleation of single-component and other binary crystals. To follow the nucleation process, we employ a neural network to identify the AB₁₃ phase from the binary fluid phase and the competing fcc crystal with single-particle resolution and significant accuracy in the case of bulk phases. We show that AB₁₃ crystal nucleation proceeds via a coassembly process where large spheres and icosahedral small-sphere clusters simultaneously attach to the nucleus. Our results lend strong support for a classical pathway that is well-described by classical nucleation theory, even though the binary fluid phase is highly structured and exhibits local regions of high bond orientational order.

Protective Effect of Polyoxometalates in {Mo132}/Maghemite Binary Superlattices Under Annealing

The binary assembly DDA-{Mo₁₃₂}/OA-γ-Fe₂O₃ (DDA = didodecyldimethylammonium, {Mo₁₃₂} = [Mo₁₃₂O₃₇₂(CH₃COO)₃₀(H₂O)₇₂]^42-, OA = oleic acid) constitutes one of the two examples in the literature of binary superlattices made of a mixing of nanocrystals and oxo-clusters. In a precedent work, we reported in details the preparation of such magnetic binary systems and studied the effect of the nature of the polyoxometalates (POMs) on the magnetic properties. In the present paper, we study the stability of this model binary assembly under heating at various temperatures. Indeed, especially if magnetic and/or transport properties are targeted, an annealing can be essential to change the phase of the nanocrystals in a more magnetic one and/or to desorb the organic capping of the nano-objects that can constitute an obstacle to the electronic communication between the nano-objects. We gave evidence that the maghemite organization in the binary assembly is maintained until 370°C under vacuum thanks to the presence of the POMs. This latter evolve in the phase MoO₃, but still permits to avoid the aggregation of the nanocrystals as well as preserve their periodical arrangement. On the contrary, an assembly made of pure γ-Fe₂O₃ nanocrystals displays a clear aggregation of the nano-objects from 370°C, as attested by transmission and scanning electronic microscopies and confirmed by magnetic measurements. The stability of the magnetic nanocrystals in such POMs/nanocrystals assemblies opens the way to (i) the elaboration of new binary assemblies from POMs and numerous kinds of nanocrystals with a good control on the magnetic properties and to (ii) the investigation of new physical properties as exchange coupling, or magneto-transport in such systems.

Single molecule-mediated assembly of polyoxometalate single-cluster rings and their three-dimensional superstructures

The assembly of atomically precise clusters into superstructures has tremendous potential in structural tunability and applications. Here, we report a series of single-cluster nanowires, single-cluster nanorings, and three-dimensional superstructure assemblies built by POM clusters. By stepwise tuning of interactions at molecular levels, the configurations can be varied from single-cluster nanowires to nanorings. A series of single-cluster nanostructures in different configurations can be achieved with up to 15 kinds of POM clusters. The single-cluster nanowires and three-dimensional superstructures perform enhanced activity in the catalytic and electrochemical sensing fields, illustrating the universal functionality of single-cluster assemblies.

Multiple-scale structures: from Faraday waves to soft-matter quasicrystals

For many years, quasicrystals were observed only as solid-state metallic alloys, yet current research is now actively exploring their formation in a variety of soft materials, including systems of macromolecules, nanoparticles and colloids. Much effort is being invested in understanding the thermodynamic properties of these soft-matter quasicrystals in order to predict and possibly control the structures that form, and hopefully to shed light on the broader yet unresolved general questions of quasicrystal formation and stability. Moreover, the ability to control the self-assembly of soft quasicrystals may contribute to the development of novel photonics or other applications based on self-assembled metamaterials. Here a path is followed, leading to quantitative stability predictions, that starts with a model developed two decades ago to treat the formation of multiple-scale quasiperiodic Faraday waves (standing wave patterns in vibrating fluid surfaces) and which was later mapped onto systems of soft particles, interacting via multiple-scale pair potentials. The article reviews, and substantially expands, the quantitative predictions of these models, while correcting a few discrepancies in earlier calculations, and presents new analytical methods for treating the models. In so doing, a number of new stable quasicrystalline structures are found with octagonal, octadecagonal and higher-order symmetries, some of which may, it is hoped, be observed in future experiments.

The Interfacial Assembly of Polyoxometalate Nanoparticle Surfactants

Polyoxometalates (POMs) using {Mo₇₂V₃₀} as an example, dissolved in water, can interact with amine-terminated polydimethylsiloxane (PDMS-NH₂) dissolved in toluene at the water/toluene interface to form POM-surfactants that significantly lower the interfacial tension and can be used to stabilize liquids via interfacial elasticity. The jamming of the POM-surfactants at the water/oil interface with consequent wrinkling occurs with a decrease in the interfacial area. The packing density of the POM-surfactants at the interface can be tuned by varying the strength of screening with the addition of cations with differing hydrated radii.

Polyoxometalate-Surfactant Hybrids Directed Assembly of Ni3S2 into Hollow Microsphere as Pt-Comparable Electrocatalyst for Hydrogen Evolution Reaction in Alkaline Medium

A large surface area of catalytic sites and low electric resistance are desirable properties for electrocatalysts that lower the overpotential required for electrochemical reactions, such as the hydrogen evolution reaction (HER), in this study. In the presence of polyoxometalate (POM) and triblock copolymer pluronic (P123) as a hybrid soft template, the hydrothermal sulfurization of nickel foam leads to the formation of a hollow microsphere, assembled from the Ni₃S₂ motif. Sonication for preparing POM+P123 hybrids, while adjusting the POM content, is an effective strategy for synthesizing a Pt-like electrocatalyst with excellent hydrogen evolution efficiency. The reason is that both sonication and optimal POM content can simultaneously enhance the electroactive surface area and electron transfer of the Ni₃S₂ electrocatalyst. Adopting the optimal conditions, the three-dimensional porous network, composed of Ni₃S₂ hollow microspheres on the nickel foam, shows that the HER in an alkaline medium requires only 77 mV overpotential for a current density of 10 mA cm^-2, with a robust long-term stability during a 25 h test. The performance at a large current density outperforms the current benchmark electrocatalyst (Pt) for HER.

On the formation of stripe, sigma, and honeycomb phases in a core-corona system

Using Monte Carlo simulations and free-energy calculations, we investigate the phase behaviour of a two-dimensional core-corona system. We model this system as particles consisting of an impenetrable hard core of diameter σ_HD surrounded by a purely repulsive soft corona of diameter δ = 1.95σ_HD. At low densities, we observe the spontaneous formation of a phase with a stripe texture as well as a honeycomb-like phase driven by both energy and entropy considerations. At high densities, we find that a two-dimensional analogue of the periodic sigma phase, considered as an approximant of dodecagonal quasicrystals, is energetically stabilised with respect to two distinct dodecagonal quasicrystals, namely, a square-triangle tiling and a square-triangle-shield tiling. We also find the formation of stable hexagonal phases at three distinct density ranges, which are energetically driven, i.e. by minimising the overlap of coronas. Furthermore, our calculations show that the low-density dodecagonal quasicrystal that was previously reported by Dotera et al., [Nature, 2014, 506, 208] is kinetically formed in the coexistence region between the honeycomb and the medium-density hexagonal phase.

The effect of temperature, interaction range, and pair potential on the formation of dodecagonal quasicrystals in core-corona systems

A two-dimensional dodecagonal quasicrystal was previously reported by Dotera et al (2014 Nature 506 208) in a system of particles interacting with a hard core of diameter σ and a repulsive square shoulder of diameter [Formula: see text]. In the current work, we examine the formation of this quasicrystal using bond orientational order parameters, correlation functions and tiling distributions. We find that this dodecagonal quasicrystal forms from a fluid phase. We further study the effect of the width of the repulsive shoulder by simulating the system over a range of values of δ. For the range of densities and temperatures considered, we observe the formation of the dodecagonal quasicrystal between [Formula: see text] and [Formula: see text]. We also study the effect of shape of the interaction potential by simulating the system using three other interaction potentials with two length scales, namely hard-core plus a linear ramp, modified exponential, or Buckingham (exp-6) potential. We observe the presence of the quasicrystal in all three systems. However, depending on the shape of the potential, the formation of the quasicrystal takes place at lower temperatures (or higher interaction strengths). Using free-energy calculations, we demonstrate that the quasicrystal is thermodynamically stable in the square-shoulder and linear-ramp system.

Molecular dynamics study of colloidal quasicrystals

Colloidal quasicrystals have received increased interest recently due to new insight in exploring their potential for photonic materials as well as for optical devices [Vardeny et al., Nat. Photonics, 2013, 7, 177]. Colloidal quasicrystals in aqueous solutions have been found in systems of micelles with impenetrable cores [Fischer et al., Proc. Natl. Acad. Sci. U. S. A., 2011, 108, 1810]. A simple model potential for micelle-micelle interaction is the step potential, which is infinite for core overlaps and constant for shell overlaps. Dotera et al. performed Monte Carlo simulations of the step potential model and found quasicrystals for specific values of the packing fraction η and the shell-core ratio λ [Dotera et al., Nature, 2014, 506, 208 ]. However, the overlap of real micelles causes repulsive forces, which increase with decreasing core distance. We consider this by introducing a novel model potential with repulsive forces depending on a third parameter α. In a systematic manner we study this more realistic potential with two-dimensional molecular dynamics simulations. For α = 0 the model is similar to the step potential model. For the first time, we provide a comprehensive overview of crystalline, quasicrystalline, and disordered structures as a function of η and λ. Simulations performed with α > 0 show the impact of the repulsive forces. We find that quasicrystalline structures at high densities vanish while new quasicrystalline structures appear at intermediate densities. Our results help to tailor colloidal systems for today's advanced applications in photonics and optical devices.

Self-Assembly of Colloidal Nanocrystals: From Intricate Structures to Functional Materials

Chemical methods developed over the past two decades enable preparation of colloidal nanocrystals with uniform size and shape. These Brownian objects readily order into superlattices. Recently, the range of accessible inorganic cores and tunable surface chemistries dramatically increased, expanding the set of nanocrystal arrangements experimentally attainable. In this review, we discuss efforts to create next-generation materials via bottom-up organization of nanocrystals with preprogrammed functionality and self-assembly instructions. This process is often driven by both interparticle interactions and the influence of the assembly environment. The introduction provides the reader with a practical overview of nanocrystal synthesis, self-assembly, and superlattice characterization. We then summarize the theory of nanocrystal interactions and examine fundamental principles governing nanocrystal self-assembly from hard and soft particle perspectives borrowed from the comparatively established fields of micrometer colloids and block copolymer assembly. We outline the extensive catalog of superlattices prepared to date using hydrocarbon-capped nanocrystals with spherical, polyhedral, rod, plate, and branched inorganic core shapes, as well as those obtained by mixing combinations thereof. We also provide an overview of structural defects in nanocrystal superlattices. We then explore the unique possibilities offered by leveraging nontraditional surface chemistries and assembly environments to control superlattice structure and produce nonbulk assemblies. We end with a discussion of the unique optical, magnetic, electronic, and catalytic properties of ordered nanocrystal superlattices, and the coming advances required to make use of this new class of solids.

Multi-component superstructures self-assembled from nanocrystal building blocks

More than three decades of intensive study to make high-quality nanocrystals have created a unique toolbox for building multi-component superstructures, which have been recognized as a new generation of metamaterials important to both fundamental sciences and applied technologies. This minireview summarizes recent advances in this exciting field. We will focus our discussion on the synthetic strategies and superstructures of this multi-component metamaterial, and highlight their novel properties and potential applications. Additionally, some perspectives on possible developments in this field are offered at the end of this review. We hope that this minireview will both inform and stimulate research interests for the design and fabrication of these nanocrystal-based multi-component metamaterials for diverse applications in the future.

Binary Superlattices from {Mo132} Polyoxometalates and Maghemite Nanocrystals: Long-Range Ordering and Fine-Tuning of Dipole Interactions

In the present article, the successful coassembly of spherical 6.2 nm maghemite (γ-Fe2O3) nanocrystals and giant polyoxometalates (POMs) such as 2.9 nm {Mo132} is demonstrated. To do so, colloidal solutions of oleic acid-capped γ-Fe2O3 and long-chain alkylammonium-encapsulated {Mo132 } dispersed in chloroform are mixed together and supported self-organized binary superlattices are obtained upon the solvent evaporation on immersed substrates. Both electronic microscopy and small angles X-ray scattering data reveal an AB-type structure and an enhanced structuration of the magnetic nanocrystals (MNCs) assembly with POMs in octahedral interstices. Therefore, {Mo132} acts as an efficient binder constituent for improving the nanocrystals ordering in 3D films. Interestingly, in the case of didodecyldimethylammonium (C12)-encapsulated POMs, the long-range ordered binary assemblies are obtained while preserving the nanocrystals magnetic properties due to weak POMs-MNCs interactions. On the other hand, POMs of larger effective diameter can be employed as spacer blocks for MNCs as shown by using {Mo132} capped with dioctadecyldimethylammonium (C18) displaying longer chains. In that case, it is shown that POMs can also be used for fine-tuning the dipolar interactions in γ-Fe2O3 nanocrystal assemblies.

A functional mesoporous ionic crystal based on polyoxometalate

A mesoporous ionic crystal is synthesized with a polyoxometalate and a macrocation with polar cyano groups. The compound possesses one-dimensional mesopores and shows high proton conductivity and catalytic activity, which are due to the water molecules in the mesopores.

Interparticle Forces Underlying Nanoparticle Self-Assemblies

Studies on the self-assembly of nanoparticles have been a hot topic in nanotechnology for decades and still remain relevant for the present and future due to their tunable collective properties as well as their remarkable applications to a wide range of fields. The novel properties of nanoparticle assemblies arise from their internal interactions and assemblies with the desired architecture key to constructing novel nanodevices. Therefore, a comprehensive understanding of the interparticle forces of nanoparticle self-assemblies is a pre-requisite to the design and control of the assembly processes, so as to fabricate the ideal nanomaterial and nanoproducts. Here, different categories of interparticle forces are classified and discussed according to their origins, behaviors and functions during the assembly processes, and the induced collective properties of the corresponding nanoparticle assemblies. Common interparticle forces, such as van der Waals forces, electrostatic interactions, electromagnetic dipole-dipole interactions, hydrogen bonds, solvophonic interactions, and depletion interactions are discussed in detail. In addition, new categories of assembly principles are summarized and introduced. These are termed template-mediated interactions and shape-complementary interactions. A deep understanding of the interactions inside self-assembled nanoparticles, and a broader perspective for the future synthesis and fabrication of these promising nanomaterials is provided.

Nano-beam X-ray microscopy of dried colloidal films

We report on a nano-beam small angle X-ray scattering study on densely-packed, dried binary films made out of spherical silica particles with radii of 11.2 and 19.3 nm. For these three-dimensional thin films prepared by drop casting, only a finite number of colloidal particles contributes to the scattering signal due to the small beam size of 400 × 400 nm(2). By scanning the samples, the structure and composition of the silica particle films are determined spatially resolved revealing spatial heterogeneities in the films. Three different types of domains were identified: regions containing mainly large particles, regions containing mainly small particles, and regions where both particle species are mixed. Using the new angular X-ray cross-correlations analysis (XCCA) approach, spatial maps of the local type and degree of orientational order within the silica particle films are obtained. Whereas the mixed regions have dominant two-fold order, weaker four-fold and marginal six-fold order, regions made out of large particles are characterized by an overall reduced orientational order. Regions of small particles are highly ordered showing actually crystalline order. Distinct differences in the local particle order are observed by analyzing sections through the intensity and XCCA maps. The different degree of order can be understood by the different particle size polydispersities. Moreover, we show that preferential orientations of the particle domains can be studied by cross-correlation analysis yielding information on particle film formation. We find patches of preferential order with an average size of 8-10 μm. Thus, by this combined X-ray cross-correlation microscopy (XCCM) approach the structure and orientational order of films made out of nanometer sized colloids can be determined. This method will allow to reveal the local structure and order of self-assembled structures with different degree of order in general.

Prospects of nanoscience with nanocrystals

Colloidal nanocrystals (NCs, i.e., crystalline nanoparticles) have become an important class of materials with great potential for applications ranging from medicine to electronic and optoelectronic devices. Today's strong research focus on NCs has been prompted by the tremendous progress in their synthesis. Impressively narrow size distributions of just a few percent, rational shape-engineering, compositional modulation, electronic doping, and tailored surface chemistries are now feasible for a broad range of inorganic compounds. The performance of inorganic NC-based photovoltaic and light-emitting devices has become competitive to other state-of-the-art materials. Semiconductor NCs hold unique promise for near- and mid-infrared technologies, where very few semiconductor materials are available. On a purely fundamental side, new insights into NC growth, chemical transformations, and self-organization can be gained from rapidly progressing in situ characterization and direct imaging techniques. New phenomena are constantly being discovered in the photophysics of NCs and in the electronic properties of NC solids. In this Nano Focus, we review the state of the art in research on colloidal NCs focusing on the most recent works published in the last 2 years.

A series of coordination polymers based on varied polycarboxylates and different imidazole-containing ligands: syntheses, crystal structures and physical properties

To investigate the effect of organic ligands on the coordination frameworks, seven nickel(ii) coordination polymers, based on varied polycarboxylates and different imidazole-containing ligands, are synthesized under hydrothermal method.

A series of d10metal coordination polymers based on a flexible bis(2-methylbenzimidazole) ligand and different carboxylates: synthesis, structures, photoluminescence and catalytic properties

Six d¹⁰metal coordination polymers have been prepared and characterized. Complexes possess structural diversities with interesting topologies and high catalytic activities for the degradation of methyl orange.

Controlled self-assembly of periodic and aperiodic cluster crystals

Soft particles are known to overlap and form stable clusters that self-assemble into periodic crystalline phases with density-independent lattice constants. We use molecular dynamics simulations in two dimensions to demonstrate that, through a judicious design of an isotropic pair potential, one can control the ordering of the clusters and generate a variety of phases, including decagonal and dodecagonal quasicrystals. Our results confirm analytical predictions based on a mean-field approximation, providing insight into the stabilization of quasicrystals in soft macromolecular systems, and suggesting a practical approach for their controlled self-assembly in laboratory realizations using synthesized soft-matter particles.