Shape Anisotropy Of Particles Research Articles

How to calculate structure factors of self-assembling anisotropic particles

We put forward a theoretical approach to analyse the structure factors obtained experimentally for solutions of self-assembling anisotropic particles. This method is applicable for any system of particles forming chains in thermodynamic equilibrium and is based on studying the behaviour of the centre– centre structure factor first peak. In order to calculate the structure factor analytically, we first derive the radial distribution function. For that we use the combination of the density functional theory and density expansion of the pair correlation functions. The first theory allows for the equilibrium chain formation, and the second takes into account particles’ shape anisotropy at the level of the Gay–Berne potential. We apply our method to describe centre–centre structure factors of self-assembling short DNA duplexes with various semiaxes ratios. Extensive comparison of the theoretical predictions with the Monte Carlo simulation data shows a very good agreement. We show that the particle shape anisotropy exerts a crucial influence on the behaviour of the structure factors.

Granular materials composed of shape-anisotropic grains

Granular physics has made considerable progress during the past decades in the understanding of static and dynamic properties of large ensembles of interacting macroscopic particles, including the modeling of phenomena like jamming, segregation and pattern formation, the development of related industrial applications or traffic flow control. The specific properties of systems composed of shape-anisotropic (elongated or flattened) particles have attracted increasing interest in recent years. Orientational order and self-organization are among the characteristic phenomena that add to the special features of granular matter of spherical or irregularly shaped particles. An overview of this research field is given.

Engineering shape: the novel geometries of colloidal self-assembly

This article investigates the role of shape in colloidal self-assembly and argues for the importance of a tight synergy between particle design and assembly strategies. To this end, we review synthetic methodologies developed to impart colloidal building blocks with anisotropic shapes and self-assembly mechanisms that exploit geometry to direct and control the particles' organization. This paper, which deliberately focuses on micron-scale colloids, is divided into two main sections. Firstly, we discuss the impact of shape on particles' interactions and how this has been exploited to develop heuristic rules for the creation of self-assembling architectures. Secondly, we examine state-of-the-art advances in colloidal synthesis with a clear emphasis on design rules and bulk methods, which are aimed at producing shape-anisotropic particles.

Crystal-structure prediction via the Floppy-Box Monte Carlo algorithm: Method and application to hard (non)convex particles

In this paper, we describe the way to set up the floppy-box Monte Carlo (FBMC) method [L. Filion, M. Marechal, B. van Oorschot, D. Pelt, F. Smallenburg, and M. Dijkstra, Phys. Rev. Lett. 103, 188302 (2009)] to predict crystal-structure candidates for colloidal particles. The algorithm is explained in detail to ensure that it can be straightforwardly implemented on the basis of this text. The handling of hard-particle interactions in the FBMC algorithm is given special attention, as (soft) short-range and semi-long-range interactions can be treated in an analogous way. We also discuss two types of algorithms for checking for overlaps between polyhedra, the method of separating axes and a triangular-tessellation based technique. These can be combined with the FBMC method to enable crystal-structure prediction for systems composed of highly shape-anisotropic particles. Moreover, we present the results for the dense crystal structures predicted using the FBMC method for 159 (non)convex faceted particles, on which the findings in [J. de Graaf, R. van Roij, and M. Dijkstra, Phys. Rev. Lett. 107, 155501 (2011)] were based. Finally, we comment on the process of crystal-structure prediction itself and the choices that can be made in these simulations.

Electrochemical Studies of Capping Agent Adsorption Provide Insight into the Formation of Anisotropic Gold Nanocrystals

The ability of the 4-dimethylaminopyridine (DMAP) to stabilize and control the formation of anisotropic gold nanocrystals produced via the borohydride reduction of gold(III) salts is reported here. Electrochemical measurements of DMAP electrosorption on different low-index single crystal and polycrystalline electrodes is provided and shows a propensity for DMAP to preferentially adsorb on {100} facets. Measuring the electrochemical potential during nanocrystal formation shows that experimental conditions can easily be manipulated so that the growth of nanoseeds occurs at potentials that support preferential DMAP adsorption on {100} surfaces giving rise to highly anisotropic nanocrystals (nanorods, bipyramids, and nanopods). Nanopods with nearly 50 nm arm lengths are shown to form and produce a surface plasmon mode that extends well into the near IR (λ(max) ≈ 1350 nm). Evidence is provided of the slow, partial reduction of tetrachloroaurate to a DMAP stabilized Au(I) species. Shape control is achieved simply by varying the length of time, τ, that DMAP is allowed to partially reduce the Au(III) ions prior to the addition of the strong reducing agent, NaBH(4). Thus the role of DMAP in producing anisotropic particle shapes is shown to be multifunctional. A mechanism accounting for the dependence of particle shape on τ is provided.

Rheology of dense suspensions of shape anisotropic particles designed to show pH-sensitive anisotropic pair potentials

Here we investigate the flow properties of suspensions of dicolloidal particles composed of interpenetrating spheres where one sphere is rich in polystyrene and the second is rich in poly 2-vinyl pyridine. The synthesis method is designed to create both anisotropic shape and anisotropic interaction potentials that should lead to head to tail clustering. These particles are referred to as copolymer dicolloids (CDCs). The viscoelastic properties of stable and gelled suspensions of CDC particles are compared with analogs composed of homopolymer dicolloids (HDCs), having the same shape but not displaying the anisotropic attractions. After coating the particles with a nonionic surfactant to minimize van der Waals attractions, the flow properties of glassy and gelled suspensions of CDCs and HDCs are studied as a function of volume fraction, ionic strength and pH. Suspensions of HDC particles display a high kinetic arrest volume fraction (ϕg > 0.5) over a wide range of pH and ionic strength up to [I]=0.5 M, demonstrating that the particles experience repulsive or weakly attractive pair potentials. Suspensions of CDC particles behave in a similar manner at high or low pH when [I]=0.001 M, but gel at a volume fraction of ϕg < 0.3 and display anomalously large elastic moduli at and above the gel transition point for intermediate pH or for pH=9 when [I]=0.5 M. The gelation processes for the CDC particles are reversible by adjusting the solution pH. Interaction potential anisotropy is evident in the processes, during which the CDC particles yield on increasing oscillatory strain.

Evolution of phase, texture, microstructure and magnetic properties of Fe–Cr–Co–Mo–Ti permanent magnets

Magnetic phase evolution, crystallographic texture, microstructure and magnetic properties of Fe–28Cr–15Co–3.5Mo–1.8Ti alloy have been investigated by X-ray diffractometry, scanning transmission electron microscopy and magnetometry techniques as a function of processing conditions. Heat treatment conditions for obtaining optimum textural, microstructural and magnetic properties have been established by the experimentations. The Goss {110}〈001〉 and cube type {001}〈010〉 textures have been developed in an optimal treated Fe–28Cr–15Co–3.5Mo–1.8Ti magnets. The coercive force in Fe–28Cr–15Co–3.5Mo–1.8Ti magnets depends critically on the shape anisotropy of rod-like Fe Co Ti-rich α1 particles and remanence on the alignment and elongation of α1 particles parallel to applied magnetic field 〈100〉 directions. The optimum magnetic properties obtained in Fe–28Cr–15Co–3.5Mo–1.8Ti alloy are intrinsic coercive force, iHc, of 78.8kA/m (990Oe), remanence, Br of 1.12T (11.2kG) and energy product, (BH)max of 52.5kJ/m3 (6.5MGOe). The development of Fe–28Cr–15Co–3.5Mo–1.8Ti magnets as well as characterization of texture, microstructural and magnetic properties in the current study would be helpful in designing the new Fe–Cr–Co–Mo based magnets suitable for scientific and technological applications.

Branched Networks by Directed Assembly of Shape Anisotropic Magnetic Particles

The directed assembly of shape anisotropic magnetic particles into targeted macrostructures requires judicious particle design. We present a framework to understand the self-assembly of magnetic non-Brownian H-shaped particles and the formation of branched networks under an applied magnetic field. A finite element integration (FEI) method is developed to identify the preferred particle orientation (relative to the applied field) at different values of the geometric parameters defining H shapes, and used to construct a phase diagram to generalize the results. Theoretical predictions are validated by comparing with experiments performed using magnetic hydrogels synthesized using stop-flow lithography (SFL). We demonstrate the ability of H-shaped particles to form chains parallel to the field that can thicken in a direction orthogonal to the field, and in some cases with branching. The assembly of a suspension containing H-shaped particles, or rods, or a combination of both, is reported.

Cell clarification and size separation using continuous countercurrent magnetophoresis

Magnetophoresis of iron oxide magnetic nanoparticle (IOMNP) under low magnetic field gradient (<100 T/m) is significantly enhanced by particle shape anisotropy. This unique feature of magnetophoresis is influenced by the particle concentration and applied magnetic field gradient. By comparing the nanosphere and nanorod magnetophoresis at different concentration, we revealed the ability for these two species of particles to achieve the same separation rate by adjusting the field gradient. Under cooperative magnetophoresis, the nanorods would first go through self- and magnetic field induced aggregation followed by the alignment of the particle clusters formed with magnetic field. Time scale associated to these two processes is investigated to understand the kinetic behavior of nanorod separation under low field gradient. Surface functionalization of nanoparticles can be employed as an effective strategy to vary the temporal evolution of these two aggregation processes which subsequently influence the magnetophoretic separation time and rate.

Microfluidic Synthesis of Highly Shape-Anisotropic Particles from Liquid Crystalline Elastomers with Defined Director Field Configurations

In this article, we present the synthesis of highly shape-anisotropic, micrometer-sized particles from liquid crystalline elastomers, which have the ability to reversibly change their shape in response to a certain external stimulus. For their preparation, we utilized a microfluidic setup. We succeeded in preparing sets of particles with differing degrees of shape anisotropy in their ground state including highly anisotropic fiber-like objects. All samples produced movement during the phase transition from the nematic to the isotropic phase of the liquid crystal. Depending on the direction of this shape change, we classified the samples in two groups. One type showed a contraction, while the other showed an expansion during the actuation, generating displacements of 60% and 80%, respectively. Using X-ray diffraction experiments, we could show that the different actuation properties arise from different director patterns of the liquid crystalline moieties in the microparticles. While the weakly shape-anisotropic microparticles possess a concentric director field (director perpendicular to the symmetry axis), the highly anisotropic fiber-like particles show an alignment of the director along the fiber axis. We present an explanation, claiming that this is the result of two different orientation mechanisms involving elongational flow on the one side and "log-rolling" on the other.

Polymer-assisted formation of hydrophobized, shape-anisotropic zinc oxide nanoparticles via an inverse emulsion technique

A one-step inverse emulsion process using amphiphilic surface-active copolymers for the synthesis of hydrophobized, shape-anisotropic inorganic nanoparticles is presented. While such structures are normally prepared sequentially by particle formation and hydrophobization, we have combined both reactions. This approach is demonstrated exemplarily with zinc oxide (ZnO) nanoparticles. A key issue is the design of amphiphilic copolymers that act as emulsifiers to enable an aggregate-free redispersion of the particles and to stabilize the inverse emulsion for the precipitation in the droplets. In a first approach, the stabilizing as well as the hydrophobizing property of the copolymers are combined with the ability to control the crystallization in one polymer (structure-directing emulsifier—SDE). In a second approach, a mixture of two polymers is applied: an amphiphilic copolymer for hydrophobizing/stabilizing the inorganic nanoparticles and a polar or double hydrophilic polymer that induces the anisotropic growth of the ZnO nanocrystals (structure-directing agents—SDA). Homopolymers and block copolymers, consisting of phosphonic acid groups or propylene oxide groups, were used as SDAs. Typically, hydrophobized shape-anisotropic particles of up to 600 nm in length and with an aspect ratio of 1:4 were obtained.

Re-entrant kinetic arrest and elasticity of concentrated suspensions of spherical and nonspherical repulsive and attractive colloids

We have designed and studied a new experimental colloidal system to probe how the weak shape anisotropy of uniaxial particles and variable repulsive (Coulombic) and attractive (van der Waals) forces influence slow dynamics, shear elasticity, and kinetic vitrification in dense suspensions. The introduction of shape anisotropy dramatically delays kinetic vitrification and reduces the shear elastic modulus of colloidal diatomics relative to their chemically identical spherical analogs. Tuning the interparticle interaction from repulsive, to nearly hard, to attractive by increasing suspension ionic strength reveals a nonmonotonic re-entrant dynamical phase behavior (glass-fluid-gel) and a rich variation of the shear modulus. The experimental results are quantitatively confronted with recent predictions of ideal mode coupling and activated barrier hopping theories of kinetic arrest and elasticity, and good agreement is generally found with a couple of exceptions. The systems created may have interesting materials science applications such as flowable ultrahigh volume fraction suspensions, or responsive fluids that can be reversibly switched between a flowing liquid and a solid nonequilibrium state based on in situ modification of suspension ionic strength.

Self-diffusion in two-dimensional hard ellipsoid suspensions

We studied the self-diffusion of colloidal ellipsoids in a monolayer near a flat wall by video microscopy. The image processing algorithm can track the positions and orientations of ellipsoids with subpixel resolution. The translational and rotational diffusions were measured in both the laboratory frame and the body frame along the long and short axes. The long-time and short-time diffusion coefficients of translational and rotational motions were measured as functions of the particle concentration. We observed the nondiffusive crossover region in the intermediate time regime due to the caging of neighboring particles. Both the beginning and the ending times of the intermediate regime exhibit power-law dependence on concentration. The long-time and short-time diffusion anisotropies change nonmonotonically with concentration and reach minima in the semidilute regime because the motions along long axes are caged at lower concentrations than the motions along short axes. The time derivatives of mean-square displacements change linearly with the inverse of time in the intermediate time regimes at various particle densities. This indicates that their relaxation functions decay as 1/t which provides new challenges in theory. The effects of coupling between rotational and translational Brownian motions were demonstrated and the two time scales corresponding to anisotropic particle shape and anisotropic neighboring environment were measured.

Superparamagnetic Magnetite Nanoparticle Superstructures for Optical Modulation/Chopping

We experimentally demonstrate proof of concept operation of superparamagnetic magnetite nanoparticles and magnetite−TiO2 peapod superstructures for laser intensity modulation and chopping. The frequency of the modulation is shown to be twice that of the driving signal and a function of the size of the particles. Specifically, optical modulation with round nanoparticles of sizes 86, 140, and 190 nm is compared with optical modulation with magnetite−TiO2 peapod superstructures of lengths of around 1 μm. The former gave rise to modulations of up to 2 kHz in frequency, a number comparable to that of commercial optical choppers, the latter up to 100 Hz. We also show that particle shape asymmetry and anisotropy enhance optical modulation and that modulation frequency is inversely proportional to the inertia of the particles used.

In-situ characterization of metal clusters supported on a birefringent substrate using reflectance difference spectroscopy

Reflectance difference spectroscopy has been applied for the in-situ characterization of the growth of Ag cluster films on insulating birefringent Al2O3 $(10\overline{1}0)$ substrates in the spectral range of 1.5–5 eV. Information on the individual cluster, cluster film morphology and growth are derived from the anisotropy of the in-plane plasmon resonances in comparison with scanning electron microscopy images. In particular, the evolution of the dipolar resonance has been attributed to two distinct stages of coarsening involving particle aggregation and ripening, and to the development of anisotropic particle shapes for higher Ag coverages. The effect of the formation of anisotropic electrostatic images in the birefringent substrate is used to explain the spectra even in the absence of structural anisotropies.

Avalanches in anisotropic sheared granular media

We study the influence of particle shape anisotropy on the occurrence of avalanches in sheared granular media. We use molecular dynamic simulations to calculate the relative movement of two tectonic plates. Our model considers irregular polygonal particles constituting the material within the shear zone. We find that the magnitude of the avalanches is approximately independent of particle shape and in good agreement with the Gutenberg–Richter law, but the aftershock sequences are strongly influenced by the particle anisotropy yielding variations on the exponent characterizing the empirical Omori’s law. Our findings enable one to identify the presence of anisotropic particles at the macro-mechanical level only by observing the avalanche sequences of real faults. In addition, we calculate the probability of occurrence of an avalanche for given values of stiffness or frictional strength and observe also a significant influence of the particle anisotropy.

Scanning tunneling microscopy studies of TiO 2-supported hydrotreating catalysts: Anisotropic particle shapes by edge-specific MoS 2–support bonding

By means of scanning tunneling microscopy (STM) studies of MoS 2 nanoparticles on a rutile TiO 2(110) support, we have studied fundamental atomic-scale aspects of the particle–support interactions for metal-sulfide hydrotreating catalysts on a metal oxide support. The STM results reveal that strong particle–support interactions at the particle edges have an overriding effect on the equilibrium shape of single-layer MoS 2 nanoparticles on the TiO 2 support. The single-layer MoS 2 nanoparticles are observed to be in flat contact with the metal oxide surface and preferentially adopt the shape of uniform elongated platelets oriented along one of the high-symmetry directions of the two-fold symmetric TiO 2 substrate. Depending on the specific orientation relative to the substrate, the MoS 2 particles exhibit two distinct widths of 33 or 38 Å which originate from the optimized lattice matching distances of the MoS 2 lattice along either of the high symmetry directions of the TiO 2(110) support. Atom-resolved STM images furthermore reveal that the (0001) basal plane of MoS 2 appears unperturbed showing that predominantly strong edge bonding effects control the particle morphology in this catalyst. The experimental STM results thus give strong support to recent edge-bonding models from the literature investigating the adhesion of MoS 2 nanoparticles to metal oxides by chemical linkages at the particle edges.

Magnetic Nanorods: Genesis, Self-Organization and Applications

Magnetic-field-assisted self-assembly of magnetic dipole moment carrying iron nanoparticles is shown to result in the formation of magnetic and mechanically stiff nanoscale rods. The cooperative behavior of an ensemble of such rods and bundles thereof exhibits self-organized pattern formation on different length scales. Pattern formation on large length scales reveals great similarity with physical systems undergoing spinodal decomposition. Possible applications for dipolar magnetic nanorods in the field of perpendicular storage media are highlighted. We discuss an aerosol-synthesis-route allowing to prepare ferrofluids (FF) with shape-anisotropic particles constituting the magnetic phase immersed in the nonmagnetic carrier fluid. These so-called nanorod FF unveil a two orders of magnitude increase of viscosity enforced by an applied field of 10mT even at shear rates larger than 10-2s. This raises prospects for applications in microfluidics and MEMS.

Synthesis and assembly of structured colloidal particles

Synthesis and self-assembly of structured colloids is a nascent field. Recent advances in this area include the development of a variety of practical routes to produce robust photonic band-gap materials, colloidal lithography for nanopatterns, and hierarchically structured porous materials with high surface-to-volume ratios for catalyst supports. To improve their properties, non-conventional suprastructures have been proposed, which could be built up using binary or bimodal mixtures of spherical particles and particles with internal or surface nanostructures. This Feature Article will describe the state-of-the-art in colloidal particles and their assemblies. The paper consists of three main sections categorized by the type of colloid, namely shape-anisotropic particles, chemically patterned particles and internally structured particles. In each section, we will discuss not only synthetic routes to uniform colloids with a range of structures, features and shapes, but also self-organization of these colloids into macrocrystalline structures with varying nanoscopic features and functionalities. Finally, we will outline future perspectives for these colloidal suprastructures.

Numerical models of stiffness and yield stress growth in crystal-melt suspensions

Magmas and other suspensions that develop sample-spanning crystal networks undergo a change in rheology from Newtonian to Bingham flow due to the onset of a finite yield stress in the crystal network. Although percolation theory provides a prediction of the crystal volume fraction at which this transition occurs, the manner in which yield stress grows with increasing crystal number densities is less-well understood. This paper discusses a simple numerical approach that models yield stress in magmatic crystalline assemblies. In this approach, the crystal network is represented by an assembly of soft-core interpenetrating cuboid (rectangular prism) particles, whose mechanical properties are simulated in a network model. The model is used to investigate the influence of particle shape and alignment anisotropy on the yield stress of crystal networks with particle volume fractions above the percolation threshold. In keeping with previous studies, the simulation predicts a local minimum in the onset of yield stress for assemblies of cubic particles, compared to those with more anisotropic shapes. The new model also predicts the growth of yield stress above (and close to) the percolation threshold. The predictions of the model are compared with results obtained from a critical path analysis. Good agreement is found between a characteristic stiffness obtained from critical path analysis, the growth in assembly stiffness predicted by the model (both of which have approximately cubic power-law exponents) and, to a lesser extent, the growth in yield stress (with a power-law exponent of 3.5). The effect of preferred particle alignment on yield stress is also investigated and found to obey similar power-law behavior.