Two-dimensional Particle Arrays Research Articles

Magnetization Dynamics in Two-Dimensional Arrays of Square Microelements

The collective magnetization motion in an array of magnetostatically interacting ferromagnetic square elements is studied theoretically and experimentally. Dispersion laws are obtained for collective modes for some particular cases of the distribution of the topological charges π T of magnetic vortices in particles. Resonance curves are plotted with allowance for dissipation for various values of π T . An experimental investigation of the ferromagnetic resonance in a two-dimensional array of particles qualitatively supports the calculation results.

An Interacting Particle Process Related to Young Tableaux

We discuss a stochastic particle system consisting of a two-dimensional array of particles living in one space dimension. The stochastic evolution bears a certain similarity to Hammersley’s process, and the particle interaction is governed by the combinatorics of Young tableaux. Bibliography: 7 titles.

Two-dimensional array of particles originating from dipole-dipole interaction as evidenced by potential curve measurements at vertical oil/water interfaces.

We propose a new method to evaluate the interaction potential energy between the particles adsorbed at an oil/water interface as a function of interparticle distance. The method is based on the measurement of the interparticle distance at a vertical oil/water interface, at which the gravitational force is naturally applied to compress the particle monolayer in the in-plane direction. We verified the method by examining whether we obtained the same potential curve upon varying the gravitational acceleration by tilting the interface. The present method is applicable in the force range from ∼0.1 to ∼100 pN, determined by the effective weight of the particles at the interface. The method gives a rather simple procedure to estimate a long range interaction among the particles adsorbed at oil/water interfaces. We applied this method to polystyrene particles at the decane/aqueous surfactant solution interface, and obtained the interparticle potential curves. All the potential curves obtained by the present method indicated that the interparticle repulsion is due to the electrical dipole-dipole interaction based on the negative charge of the particles. The mechanism of the dipole-dipole interaction is further discussed on the basis of the effects of surfactants.

Uniform growth of clusters of magnetic nanoparticles in a rotating magnetic field

It was recently shown that the exposure of magnetic microbeads to a homogeneous magnetic field, which rotates around the axis perpendicular to the field direction, generates highly ordered two-dimensional particle arrays. In this work, the impact of downscaling such systems is analyzed. Dilutions of cobalt nanoparticles with an average diameter of 6 nm were brought into a rotating homogeneous magnetic field. A strong localization of the number of particles within a certain cluster size can be observed if the rotation frequency is adjusted to a specific particle concentration. In particular, we obtain an increase of 85 % of the maximum of the cluster size distribution, when changing the rotation frequency of the magnetic field from 300 to 750 rpm for a cobalt concentration of 35.95 mmol/l. We propose a heuristic model to explain the observed frequency dependence.

Optical trapping via guided resonance modes in a Slot-Suzuki-phase photonic crystal lattice

A novel photonic crystal lattice is proposed for trapping a two-dimensional array of particles. The lattice is created by introducing a rectangular slot in each unit cell of the Suzuki-Phase lattice to enhance the light confinement of guided resonance modes. Large quality factors on the order of 10⁵ are predicted in the lattice. A significant decrease of the optical power required for optical trapping can be achieved compared to our previous design.

Magnetic Field Induced Assembly of Highly Ordered Two-Dimensional Particle Arrays

Suspended magnetic beads are exposed to an external homogeneous magnetic field which rotates around the axis perpendicular to the field direction. Because of dipolar interactions, magnetic beads assemble in highly ordered two-dimensional hexagonal arrays perpendicular to the rotation axis. By continuous provision of the particle concentration, the growth modes of two-dimensional particle clusters and monolayers are observed. The structure of the resulting assembled objects is analyzed for different field frequencies and particle concentrations. We identify dynamic processes which enhance stability and reduce lattice distortions and, thus, allow for the application of these particle agglomerations as dynamic components in lab-on-a-chip technologies.

Silver Nanoparticles with Controlled Dispersity and Their Assembly into Superstructures

In this paper we report on the influence of particle size distribution, particle substrate interaction, and drying behavior on the self-assembly process using ligand stabilized silver particles. Two-dimensional particle arrays were characterized using transmission electron microscopy and extensive image analysis. The formation of such structures was observed in situ using an environmental scanning electron microscope in WET-STEM mode. The results confirm that a small particle size distribution is crucial for the formation of regular particle patterns with long range order, but also the particle substrate interaction and the particle density have an influence on the degree of ordering. Additionally, we find that separated binary particle assemblies keep the orientation of their two-dimensional hexagonal lattices over alternating domains of small and big particles. This is probably enabled due to the formation of dislocations and a small change of the course of the lattice lines within the respective boundary.

Controlled photochemical particle growth in two-dimensional ordered metal nanoparticlearrays

We report on a universal technique which allows us to precisely manipulate thediameter of metal nanoparticles in two-dimensional particle arrays. The approach isdemonstrated here for hexagonally ordered gold nanoparticle arrays fabricated bymeans of diblock copolymer micelle lithography (BCML). The particles are used asnucleation centers in seed-mediated photochemical metal deposition, whereby theparticle diameter increases. Repeatedly combining photochemical growth withthermal annealing steps additionally facilitates controlling the shape of the particles.

Optical and electron microscopy studies of Schiller layer formation and structure

Iridescent Schiller layers were prepared by centrifugation of β-FeOOH sols with an initial particle concentration of 10 14 particles/mL, reducing the Schiller layer formation time from over 2 months to 3 weeks. The formation and structure of the Schiller layers were investigated using optical and transmission electron microscopy. Microscopy studies revealed the self-assembly to proceed by the formation of two-dimensional particle arrays followed by the stacking of these arrays to form the final iridescent state. Varying the pH showed that Schiller layer formation occurs only in the pH range 1.4–2.0, indicating that electrostatic interactions play a pivotal role in the self-assembly. Decreasing the particle concentration of the sols was found to inhibit the assembly. DLVO theory and order–disorder phase transition models were found to be insufficient to accurately model the experimental behavior. Several approaches were investigated in an attempt to make ferrimagnetic arrays from the Schiller layers. The most promising was via electron beam irradiation, which transforms the β-FeOOH into γ-Fe 2O 3 without altering the shape of the nanorods.

Single- and multi-layered patterns of polystyrene and silica particles assembled with a simple dip-coating

A simple dip-coating method was examined to fabricate two-dimensional particle arrays on glass substrate with the use of submicron-sized, highly monodisperse particles of silica and polystyrene (PSt). This method was demonstrated to be applicable to the fabrication of particle monolayer with high regularity. The monolayer of PSt particles arranged with the dip-coating could be separated from the substrate by immersing it into water, leading to formation of a mono-layered film of the PSt particles. Repetition of the dip-coating was also applicable to multi-layering with silica and PSt particles. A dip-coating with 520 nm PSt particles accompanied by a dip-coating with 233 nm silica particles formed Kagome lattice composed of the silica particles under the monolayer of hexagonally arranged PSt particles. The lattice formation indicated that the silica particles crept under the monolayer of PSt particle in the second coating with the silica particle suspension. Double dip-coatings with different silica particle sizes in the second coating were performed to examine the effect of particle size on creeping under the monolayer. Silica particles much smaller than the PSt particles were gathered in a void between the substrate and the monolayer of PSt particles hexagonally arranged. A high concentration of the small silica particles in the second dip-coating could form hemi-sphere-typed inverse opal with little defects of silica particles after heat treatment at 600 °C.

Preparation of ordered mono-particulate film from colloidal solutions on the surface of water and continuous transcription of film to substrate

By spreading an alcohol suspension of hydrophobic mono-disperse silica particles on the surface of water, an ordered mono-particulate film might be self-assembled on it. In this investigation, the formation mechanism of an ordered mono-particulate film on the water's surface was elucidated. During the initial stage of the suspension spreading, the floating hydrophobic particles that appeared on the surface of water formed many small particle film fragments. These fragmented films fastly move through the water's surface by two-dimensional Marangoni convection. As the particle film coverage of the water's surface increased, the two-dimensional motion of the fragmented films on the surface of water gradually became weak. These aggregated and then formed a large two-dimensional particle film. The particle film was compressed by the two-dimensional pressure induced by the Marangoni convection. This compression would drive the two-dimensional ordering. The formation of ordered two-dimensional particle arrays on the surface of water would be a kind of Kirkwood-Alder phase transition phenomenon. The prepared particle films are easily transferred to a substrate by withdrawing the immersed substrate. The SEM observations of the transferred particulate films reveal that the particle film formed on the surface of water was transferred to the substrate without any significant deterioration of the ordering regularity. Furthermore, it can be concluded that both the optimum hydrohobicity of the particles and Marangoni surface convection are required to form a highly ordered arrangement of the particles. Especially, the Marangoni convection plays an important role in the particle ordering process. The continuous fabrication of the particulate film on a substrate will become possible by transcribing it on the substrate at the same time while forming the particle film on the surface of water.

Influence of substrate on self-assembled photonic crystal.

Freestanding monolayers of two-dimensional particle arrays, in which fine particles are two-dimensionally self-assembled in a highly oriented manner, was prepared to examine the influence of substrate on the transmission spectra of 2D particle array; as a result, the spectrum of the freestanding 2D particle array has less noise than that of the 2D particle array on the substrate, and besides, agree with the theoretical result particularly in the near-field discussion.

FLEXIBLE TWO-DIMENSIONAL FINE-PARTICLE ARRAYS AND THEIR PHOTONIC CHARACTERS

Flexible two-dimensional particle arrays, which are periodic structures in the optical region, were prepared utilized a thermosetting resin. This type of arrays can be bent easily and repeatedly. Beautiful light propagation patterns such as micro-circle or micro-star-like shapes were observed inside of flexible two-dimensional particle arrays from the emission of fluorescent particles in the arrays. This flexible two-dimensional particle array might be changed the general idea of self-assembled structures; which normally exist on solid substrates.

Combinatorial Templates Generated by Dip-Pen Nanolithography for the Formation of Two-Dimensional Particle Arrays

Einzelne Partikel in zweidimensionalen Anordnungen präzise zu positionieren, das ist mit der DPN-Methode möglich, bei der mithilfe einer Kraftmikroskop-Spitze Moleküle von einem Wassermeniskus auf eine Oberfläche übertragen werden (DPN=dip-pen nanolithography). DPN wurde eingesetzt zur Erzeugung von 16-Thiohexadecansäure-Templaten auf einer Goldoberfläche, um die zweidimensionale Anordnung von amin- und amidinmodifizierten Partikeln zu untersuchen (siehe Bild).

Combinatorial templates generated by dip-pen nanolithography for the formation of two-dimensional particle arrays.

Lattices of single polystyrene particles were constructed by using a combinatorial approach to analyze particle pattern recognition properties. Dip-pen nanolithography was used to generate chemical templates of 16-thiohexadecanoic acid on a gold surface to study the two-dimensional assembly of amine- and amidine-modified particles.

Exact Solutions for Transient Wave Propagation in a Two-Dimensional Array of Particles

We derive exact analytical solutions for transient waves propagating in an array of particles occupying the half-plane. x ≥0, forced by general external excitations applied at the top horizontal row x = 0. We consider only nearest neighbour interactions between the particles, resulting in four-particle interactions throughout the array. First, we assume spatially periodic forces and internal displacements, and apply Fourier and Z-transforms to obtain closed form transformed solutions. Next, we relax the spatial periodicity assumption by resorting to the following limiting analysis: We let the wavelength of the force distribution tend to infinity, and employ continuity arguments to obtain the exact transformed wave responses. These transformed solutions are Fourier-inverted in closed form by employing previous results of WANG and LEE [10]. We perform numerical simulations using the exact analytical formulas, and compute transient waves in the array due to a single transient force of trapezoidal form applied at the top row. Assuming spatially harmonic force we compute propagation and attenuation zones of the array. Finally, we consider a second limiting process by allowing the horizontal distances between particles to tend to zero. Performing rescalings and limiting calculations we derive an additional closed form solution for transient waves propagating in a half-plane continuum of borizontal strings transversely coupled by distributed elasticities, due to forces applied to the top string.

Gravity effect on the electric field deposition of two-dimensional particle arrays

We developed a method for the deposition of colloidal particle layers in a horizontal electrophoretic cell. The particles accumulate on the surface of the (upper) working electrode. The particle nuclei increase in size to form islands, which are then bridged and converted into a dense array: monolayer or bilayer. Uniform coating of electroconductive glass by micrometer and submicrometer size latex particles of negative charge has been obtained. The transportation stage of the process is described theoretically. The use of colloidal particles made visible with an optical microscope also provides a new look inside electrode processes.

Dynamical Transitions in Correlated Driven Diffusion in a Periodic Potential

The diffusion of a two-dimensional array of particles driven by a constant force in the presence of a periodic external potential exhibits a hierarchy of dynamical phase transitions when the driving force is varied. This behavior can be explained by a simple phenomenological approach which reduces the system of strongly interacting particles to weakly interacting quasiparticles (kinks). The richness of the strongly coupled system is, however, not lost because, contrary to a single Brownian particle, the array shows an hysteretic behavior even at nonzero temperature. The present investigation can be viewed as a first step toward understanding nanotribology.

Steady-state unidirectional convective assembling of fine particles into two-dimensional arrays

We formed millimeter-sized two-dimensional particle arrays on inclined microslides using water suspensions of the particles. We found that the array porosity depended on the particle diameter, the particle volume fraction, and the rate of array growth. Deriving an equation for the steady-state array growth process, we found that these parameters, together with the rate of water evaporation, govern the overall array growth process. Our results illustrate a promising technology for producing fine particle coatings on solid surfaces.

A computer simulation method for particle sintering

A new computer simulation method is developed for treating topological effects during early stage sintering in large-scale particle arrays. The approach is based on a stress-free transformation concept using two-body sintering models where elastic distortions are introduced in order to retain the particle network connectedness. The internal stresses associated with these distortions can drive creep mechanisms. An initial implementation of the simulation method has been made for two-dimensional particle arrays, but it can also be applied in three dimensions. Empirical parameters were used to demonstrate the viability of the method. The results showed that the elastic stiffness parameters of the particle network can affect topological rearrangement as well as the distribution of internal stress. A sintering-creep interaction was found such that, when creep effects are present, the densification rate can be significantly reduced.