Small Spheroidal Particles Research Articles

Comparison of dynamic corrections to the quasistatic polarizability and optical properties of small spheroidal particles.

The optical properties of small spheroidal metallic nanoparticles can be simply studied within the quasistatic/electrostatic approximation, but this is limited to particles much smaller than the wavelength. A number of approaches have been proposed to extend the range of validity of this simple approximation to a range of sizes more relevant to applications in plasmonics, where resonances play a key role. The most common approach, called the modified long-wavelength approximation, is based on physical considerations of the dynamic depolarization field inside the spheroid, but alternative empirical expressions have also been proposed, presenting better accuracy. Recently, an exact Taylor expansion of the full electromagnetic solution has been derived [Majic et al., Phys. Rev. A 99, 013853 (2019)], which should arguably provide the best approximation for a given order. We here compare the merits of these approximations to predict orientation-averaged extinction/scattering/absorption spectra of metallic spheroidal nanoparticles. The Taylor expansion is shown to provide more accurate predictions over a wider range of parameters (aspect ratio and prolate/oblate shape). It also allows us to consider quadrupole and octupole resonances. This simple approximation can therefore be used for small and intermediate-size nanoparticles in situations where computing the full electromagnetic solution is not practical.

Effects of aging on the stress-induced martensitic transformation and cyclic superelastic properties in Co-Ni-Ga shape memory alloy single crystals under compression

Co-Ni-Ga shape memory alloys attracted scientific attention as promising candidate materials for damping applications at elevated temperatures, owing to excellent superelastic properties featuring a fully reversible stress-strain response up to temperatures as high as 500 °C. In the present work, the effect of aging treatments conducted in a wide range of aging temperatures and times, i.e. at 300–400 °C for 0.25–8.5 h, was investigated. It is shown that critical features of the martensitic transformation are strongly affected by the heat treatments. In particular, the formation of densely dispersed γ’-nanoparticles has a strong influence on the martensite variant selection and the morphology of martensite during stress-induced martensitic transformation. Relatively large, elongated particles promote irreversibility. In contrast, small spheroidal particles are associated with excellent functional stability during cyclic compression loading of 〈001〉-oriented single crystals. In addition to mechanical experiments, a detailed microstructural analysis was performed using in situ optical microscopy and neutron diffraction. Fundamental differences in microstructural evolution between various material states are documented and the relations between thermal treatment, microstructure and functional properties are explored and rationalized.

Preface to the special issue dedicated to Professor Richard P. Van Duyne (1945–2019)

Preface to the special issue dedicated to Professor Richard P. Van Duyne (1945–2019)

Acoustic radiation force and torque on spheroidal particles in an ideal cylindrical chamber.

In this article, the acoustic radiation force and torque exerted on a small spheroidal particle immersed in a nonviscous fluid inside an ideal cylindrical chamber is theoretically investigated. The ideal chamber comprises a hard top and bottom (rigid boundary condition) and a soft or hard lateral wall. By assuming that the particle is much smaller than the acoustic wavelength, analytical expressions of the radiation force and torque caused by an acoustic wave of arbitrary shape are presented. Unlike previous results, these expressions are given relative to a fixed laboratory frame. The model is showcased for analyzing the behavior of an elongated metallic microspheroid (with a 10:1 aspect ratio) in a half-wavelength acoustofluidic chamber with a diameter of a few millimeters. The results show that the radiation torque aligns the microspheroid along the nodal plane, and the radiation force causes a translational motion with a speed of up to one body length per second. Finally, the implications of this study on propelled nanorods by ultrasound are discussed.

T-matrix formulation of electromagnetic wave scattering by charged non-spherical scatterers

In this paper, a method is proposed to solve the scattering of electromagnetic waves (EMWs) by a uniformly charged non-spherical scatterer. Based on Waterman's extended boundary method, a transition matrix between coefficient of the scattering field and incident field of a charged non-spherical scatterer is derived, called Tc-matrix. By using Tc-matrix, the scattering fields of charged non-spherical scatterers can be numerically solved. In the case of a charged rotationally symmetric non-spherical scatterer, the analytic mathematical expression of Tc-matrix is obtained, thus the analytical expression of scattering field is obtained. And the extinction characteristics of charged non-spherical scatterers, making use of charged spheroids as examples, are investigated. It is found that absorption is still the dominant mechanism of attenuation when electromagnetic waves travels through small charged spheroidal particles suspended in atmosphere, though the net surface charges can enhance the extinction/scattering/absorption of particle. The enhancement factors of extinction/absorption increases with increasing surface charge density and are much higher than the enhancement factor of scattering. It is shown that the equivalent sphere assumption, which was used in theoretical models of optical or scattering properties of charged or uncharged atmospheric or interstellar particles, could result in large errors, e.g., even over 100% for charged prolate spheroids, in theoretical prediction of absorption/extinction. Moreover, this inaccuracy due to the sphere assumption worsens for spheroids with either low or high aspect ratios h (i.e., prolate spheroid with h << 1, or oblate spheroids with h >> 1).

Inorganic mesoporous silica foams for use in stabilization and controlled release of isothiazolinone-based biocides: influence of silica textural properties

The synthesis of mesocellular siliceous foam materials (MCFs) was performed at different stirring rates. In this way, foam samples composed of solid particles differing in size and morphology were obtained. Afterwards, the influence of these physical properties on the adsorptive behavior of the synthesized samples was checked for the adsorption/desorption of an isothiazolone-based commercial biocide (BIO). Results show that at low stirring rates small spheroidal particles were produced. In the absence of stirring, large blocks of silica presenting their external surface fully covered by small homogeneous silica spheres were obtained. Cauliflower-type morphologies were obtained at intermediate stirring rates, while the particle shape became irregular when the stirring rate was increased. On the contrary, the mesostructure and pore size of the particles obtained in the different samples were comparable. The biocide adsorption as well as its subsequent release in aqueous media were strongly affected by the particle size of the silica foam. Adsorption and release tests show that BIO encapsulation in silica foams preserves the biocide structure, obtaining the best performance of controlled release with the matrix synthesized at 400 rpm.

Gelation properties and thermal gelling mechanism of golden threadfin bream myosin containing CaCl2 induced by high pressure processing

The effects and mechanism of high-pressure processing (HPP) (100–500 MPa) and CaCl2 addition on golden threadfin bream myosin gel were investigated. Results for water holding capacity (WHC) and gel strength revealed the HPP at 100–300 MPa could markedly improve the gelation properties. The increase in the proportion of immobilized water with a reduction of water relaxation time indicated that Ca2+ and mild HPP pre-treatments contributed to restricting the water mobility within the gel matrix. Dynamic rheological measurements suggested that the thermal gelling ability of the pressurized myosin/Ca2+ increased at 100 MPa, but gradually decreased as the pressure further increased (100–500 MPa). Analysis of atomic force microscopy (AFM) results revealed that myosin modified by CaCl2 and 100–300 MPa HPP tended to aggregate into small subunits and spheroidal particles simultaneously with the decrease in surface roughness. Scanning electron microscopy (SEM) images showed that a compact, networked myosin/Ca2+ composite gel microstructure with regular and small cavities was formed by thin cross-linked strands under 300 MPa. Changes in molecular forces were used to explain the above results. CaCl2 and modest HPP enhanced and stabilized various molecular forces within the gel system. This study illustrated that CaCl2 and HPP processed a synergistic effect on the gelation properties of myosin gel.

Rayleigh Approximation for Multilayer Nonconfocal Spheroids

We consider the light scattering by layered spheroids that are small compared to the wavelength of the incident radiation. Simple approximate formulas are obtained for the polarizability of such particles with nonconfocal spheroidal surfaces of layers by reducing infinite matrices in the rigorous solution of the problem to matrices of dimensions 2 × 2 and 4 × 4. In the first case, the approximate expression for the polarizability formally coincides with the well-known expression for spheroids with confocal surfaces of layers and, correspondingly, represents an accurate result for such particles. The second case is, in essence, taking into account in the first approximation the effect of nonconfocality of core surfaces and particle layers. The results of numerical calculations carried out for two- and three-layer particles using both approximate expressions and formulas of the rigorous solution showed that, in a wide range of parameters, the relative error of the simpler approximation (2 × 2) is lower than 1%, while the error of the other approximation (4 × 4) is smaller than 0.1%. It is inferred that the found approximate formulas are rather accurate and universal, and they can be efficiently used in calculations of the optical properties of small multilayer spheroidal particles.

Приближение Релея для многослойных несофокусных сфероидов

AbstractWe consider the light scattering by layered spheroids that are small compared to the wavelength of the incident radiation. Simple approximate formulas are obtained for the polarizability of such particles with nonconfocal spheroidal surfaces of layers by reducing infinite matrices in the rigorous solution of the problem to matrices of dimensions 2 × 2 and 4 × 4. In the first case, the approximate expression for the polarizability formally coincides with the well-known expression for spheroids with confocal surfaces of layers and, correspondingly, represents an accurate result for such particles. The second case is, in essence, taking into account in the first approximation the effect of nonconfocality of core surfaces and particle layers. The results of numerical calculations carried out for two- and three-layer particles using both approximate expressions and formulas of the rigorous solution showed that, in a wide range of parameters, the relative error of the simpler approximation (2 × 2) is lower than 1%, while the error of the other approximation (4 × 4) is smaller than 0.1%. It is inferred that the found approximate formulas are rather accurate and universal, and they can be efficiently used in calculations of the optical properties of small multilayer spheroidal particles.

Acoustic radiation force exerted on a small spheroidal rigid particle by a beam of arbitrary wavefront: Examples of traveling and standing plane waves.

The analytical solution of the acoustic radiation force exerted by a beam of arbitrary shape on a small spheroidal rigid particle suspended in an ideal fluid is presented. The particle is assumed to be much smaller than the wavelength, i.e., the so-called long-wavelength approximation. Based on this theoretical development, closed-form expressions for the radiation force of a traveling and standing plane wave exerted on a prolate spheroidal particle are derived in the dipole approximation. As validation, the previous analytical result considering a standing wave interacting with a spheroid in axisymmetric configuration is recovered, as well as numerical results obtained with the boundary-element method.

Dynamically controllable anisotropic metamaterials with simultaneous attenuation and amplification

Anisotropic homogeneous metamaterials that are neither wholly dissipative nor wholly active at a specific frequency are permitted by classical electromagnetic theory. Well-established homogenization formalisms indicate that such a metamaterial may be realized quite simply as a random mixture of electrically small (possibly nanoscale) spheroidal particles of at least two different isotropic dielectric materials, one of which must be dissipative but the other active. The dielectric properties of this metamaterial are influenced by the volume fraction, spatial distribution, particle shape and size, and the relative permittivities of the component materials. Similar metamaterials with more complicated linear as well as nonlinear constitutive properties are possible. Dynamic control of the active component material, for example via stimulated Raman scattering, affords dynamic control of the metamaterial.

Computation of stress on the surface of a soft homogeneous arbitrarily shaped particle.

Prediction of the stress on the surface of an arbitrarily shaped particle of soft material is essential in the study of elastic properties of the particles with optical force. It is also necessary in the manipulation and sorting of small particles with optical tweezers, since a regular-shaped particle, such as a sphere, may be deformed under the nonuniform optical stress on its surface. The stress profile on a spherical or small spheroidal soft particle trapped by shaped beams has been studied, however little work on computing the surface stress of an irregular-shaped particle has been reported. We apply in this paper the surface integral equation with multilevel fast multipole algorithm to compute the surface stress on soft homogeneous arbitrarily shaped particles. The comparison of the computed stress profile with that predicted by the generalized Lorenz-Mie theory for a water droplet of diameter equal to 51 wavelengths in a focused Gaussian beam show that the precision of our method is very good. Then stress profiles on spheroids with different aspect ratios are computed. The particles are illuminated by a Gaussian beam of different waist radius at different incidences. Physical analysis on the mechanism of optical stress is given with help of our recently developed vectorial complex ray model. It is found that the maximum of the stress profile on the surface of prolate spheroids is not only determined by the reflected and refracted rays (orders p=0,1) but also the rays undergoing one or two internal reflections where they focus. Computational study of stress on surface of a biconcave cell-like particle, which is a typical application in life science, is also undertaken.

Computation of radiation pressure force on arbitrary shaped homogenous particles by multilevel fast multipole algorithm

A full-wave numerical method based on the surface integral equation for computing radiation pressure force (RPF) exerted by a shaped light beam on arbitrary shaped homogenous particles is presented. The multilevel fast multipole algorithm is employed to reduce memory requirement and to improve its capability. The resultant matrix equation is solved by using an iterative solver to obtain equivalent electric and magnetic currents. Then RPF is computed by vector flux of the Maxwell's stress tensor over a spherical surface tightly enclosing the particle. So the analytical expressions for electromagnetic fields of incident beam in near region are used. Some numerical results are performed to illustrate the validity and capability of the developed method. Good agreements between our method and the Lorenz-Mie theory for spherical and small spheroidal particle are found while our method has powerful capability for computing RPF of any shaped beam on a relatively large particle of complex shape. Tests for ellipsoidal and red blood cell-like particles illuminated by Gaussian beam have shown that the size of the particle can be as large as 50-100 wavelengths, respectively, for the relative refractive of 1.33 and 1.1.

The Dragon Project origins, achievements and legacies

The lineage of the Dragon Project can be traced back to 1955 when the United Kingdom launched a nuclear power programme which involved the construction of large graphite moderated reactors fuelled with natural uranium and cooled by carbon dioxide. Not long afterwards the European Nuclear Energy Agency (ENEA) of the then newly formed Organisation for European Economic Cooperation (OEEC), in the spirit of the time, sought to encourage the construction of nuclear power stations and the development of joint nuclear undertakings. The United Kingdom Atomic Energy Research Establishment (AERE) had, since 1949, been studying possible long term improvements in energy conversion efficiency resulting from higher coolant gas temperatures and the use of ceramic materials. A 1955 paper on gas-cooled reactors using the U-233/thorium cycle attracted interest and this progressed to the definition of an initial programme. The high temperature work led to a proposal for a 20MW(Th) Reactor Experiment and one important consequence of the ENEA/OEEC initiative was the setting up in April 1959 of the international Dragon Project Agreement.Initial experiments at Harwell in 1957 had involved the coating of small spheroidal particles of uranium carbide or oxide with pyrolytic carbon which were then bonded with carbonaceous material. But experiments demonstrated that fission products such as caesium, strontium or barium could diffuse through such coatings. This led in 1961 to the modification of the coated particle design by the addition of an intermediate layer of silicon or zirconium carbide. The small size of the particles necessitated a statistical approach to quality during manufacture and effort was concentrated on the minimisation of the broken or defective particle fraction.The subsequent operation of the Dragon Reactor for over 10 years confirmed the benign nature of a HTR. It also proved that fuel bodies made with coated particles were capable of maintaining a high degree of fission product containment at high temperatures and for high burn-ups. What is remarkable is the speed with which the particle design evolved. The success of the choices that were made resulted in the High Temperature Gas Cooled Reactor system being studied in its various forms by many countries.Irrespective of the particular core design, the basic component of HTR fuel is the coated particle. In the intervening years since the early HTRs were launched it has been realised worldwide that there are now even more factors favouring the use of high temperature reactors. They enable more efficient use of fissile isotopes as well as providing inherent reactor safety. Unlike most other reactor designs, the HTR can take economic advantage from operation at high gas outlet temperatures, whilst maintaining the good retention of fuel and fission products within the fuel elements. The fuel cycle can use uranium, thorium or plutonium. In addition the burn-up can be high, permitting safe disposal of spent fuel without the need for reprocessing. Fast reactors based on coated particle fuel may be a future possibility.The Dragon Project was a successful political collaboration and a technical triumph in demonstrating a new type of reactor. However, overstretched resources coupled with a world-wide trend in that era to favour water reactors caused work on Dragon to be terminated in March 1976. By then the main objectives for the Dragon Project had been successfully achieved and extensively reported. The progression from the 20MWE(Th) Dragon to a 1200MW(e) power station as a single jump in technology was too large a step for the time. The experiences of the other major civil HTR projects of the same period in Germany and the United States of America resulted in the high temperature reactor system being studied in its various forms by many countries as is evidenced by the large number of papers presented at the biennial HTR conferences. In the intervening years since the early HTRs were launched it has been realised that there are now even more factors favouring the use of high temperature reactors.

Amorphous calcium phosphate and its application in dentistry

Amorphous Calcium Phosphate (ACP) is an essential mineral phase formed in mineralized tissues and the first commercial product as artificial hydroxyapatite. ACP is unique among all forms of calcium phosphates in that it lacks long-range, periodic atomic scale order of crystalline calcium phosphates. The X-ray diffraction pattern is broad and diffuse with a maximum at 25 degree 2 theta, and no other different features compared with well-crystallized hydroxyapatite. Under electron microscopy, its morphological form is shown as small spheroidal particles in the scale of tenths nanometer. In aqueous media, ACP is easily transformed into crystalline phases such as octacalcium phosphate and apatite due to the growing of microcrystalline. It has been demonstrated that ACP has better osteoconductivity and biodegradability than tricalcium phosphate and hydroxyapatite in vivo. Moreover, it can increase alkaline phosphatase activities of mesoblasts, enhance cell proliferation and promote cell adhesion. The unique role of ACP during the formation of mineralized tissues makes it a promising candidate material for tissue repair and regeneration. ACP may also be a potential remineralizing agent in dental applications. Recently developed ACP-filled bioactive composites are believed to be effective anti-demineralizing/remineralizing agents for the preservation and repair of tooth structures. This review provides an overview of the development, structure, chemical composition, morphological characterization, phase transformation and biomedical application of ACP in dentistry.

The effect of citric acid on the sintering of calcium phosphate bioceramics

Biphasic calcium phosphate particles were prepared using a rapid increase of the pH value by adding an amount of concentrated ammonia solution, into a well-mixed solution containing Ca(H 2PO 4) 2·H 2O and CaCl 2 with Ca/P = 1.667 molar ratio; with or without the presence of citric acid (CiA). The precipitation of Calcium Phosphates took place at 97 °C using high-speed dispersing equipment. The samples were characterized using XRD, FT-IR, BET and SEM techniques. The thermal behaviour was studied by TG, DTG and DTA techniques. The modified precipitation method leads to the formation of biphasic needle-like particles consisted of crystalline hydroxyapatite (HA) and β-tricalcium phosphate (β-TCP). The presence of CiA in the initial solution leads to the formation of aggregated nonporous small spheroidal particles consisted of low crystallinity phases of HA and octacalcium phosphate (OCP). The later facilitates the sintering process. The calcined samples at 900 °C were consisted of calcium pyrophosphate (CPP) and TCP. α-TCP is formed in the presence of a large amount of calcium citrate complexes. The main sintering process took place at the temperature range between 750 and 1150 °C, which were strongly depended on the initial amount of the CiA in the precipitation process. These results indicated that the citrate presence in the initial solution have a strong influence on the nucleation and growth processes by complexation with calcium ions and incorporation into the solid structure during particle growth.

Midpoint numerical technique for stochastic Landau-Lifshitz-Gilbert dynamics

The implicit midpoint time-integration technique is applied to the stochastic Landau-Lifshitz-Gilbert (LLG) equation. The numerical scheme converges to the Stratonovich solution in the limit of vanishing time step. It preserves the magnetization magnitude and the main energy balance properties of the LLG equation independently of the time step. The numerical technique is then applied to the study of superparamagnetic state in a small spheroidal particle, and the numerical results are compared with the theory.

Sound attenuation by small spheroidal particles due to visco-inertial coupling

The sound attenuation at ultrasonic frequencies caused by small spheroidal particles in a fluid is examined with regard to the size parameters that determine the shape of the attenuation spectrum. Our investigations are based on a coupled phase model for spheroids with arbitrary orientation, thus facilitating the calculation of average attenuation for a given orientation distribution. Since the model just considers the visco-inertial coupling, its applicability is restricted to small solid particles with high density contrast. The calculated attenuation spectra of mono-sized, randomly aligned spheroidal particles are compared with the attenuation spectra of mono-sized spheres. When the latter approximate the former to a reasonable degree the size of the spheres is called attenuation equivalent diameter. It is shown that the concept of attenuation equivalent diameter can be applied only to slightly elongated prolates. Oblates and very stretched prolates yield considerably broader attenuation spectra than mono-sized spheres. While for oblates and for slightly elongated prolates the characteristic frequency of the attenuation spectrum is determined by the volume specific surface, no such attenuation determining size parameter could be identified for very stretched prolates.

Investigation of threshold laser intensities for melting and evaporation of spherical and spheroidal nanoparticles in media by short laser pulses

Theoretical investigations and estimations of threshold laser intensities for melting and evaporation of a small metal (solid) spherical and spheroidal particle placed in a liquid or gaseous medium by short laser pulses are carried out. The time dependencies of nanoparticle temperature are used for estimations of threshold laser intensities and their dependencies on pulse duration and radius of particles are discussed. Comparison of some predicted values of the threshold laser intensities for melting and evaporation of gold spherical nanoparticle in liquid media with experimental data is given and agreement of theoretical results with experimental data validates the model developed. These results can be used in the processes of treatment of nanoparticles in laser technologies.

Shape effects in scattering and absorption by randomly oriented particles small compared to the wavelength

We study the effects of particle shape on the absorption and scattering cross sections of randomly oriented particles in the Rayleigh domain, i.e. particles that are very small compared to the wavelength of radiation both inside and outside the particle. In particular, we investigate the validity of the so-called statistical approach. In this approach it is assumed that the scattering and absorption properties of irregularly shaped particles can be simulated by the average properties of a distribution of simple shapes. We depart from the assumption of homogeneous spherical particles in two ways: 1) by using various distributions of elongated and flattened homogeneous ellipsoids and spheroids, 2) by using a distribution of hollow spherical particles. We derive explicit formulas for the shape averaged scattering and absorption cross sections as functions of the refractive index for various distributions of particle shapes in the Rayleigh limit. We compare the absorption cross sections as functions of the refractive index of the various distributions with each other and with those of homogeneous spheres. We also study the effects of the distributions on the shapes of absorption spectra. We find that there is a strong similarity between the absorption spectra of distributions of various non-spherical homogeneous particles and a distribution of hollow spheres. We show that the positions of features in the shape averaged mass absorption coefficient as a function of wavelength of small ellipsoidal, spheroidal or hollow spherical crystalline forsterite particles coincide with those deduced from the spectral energy distributions of various astronomical sources and with measurements of the mass absorption coefficients of small particles. This is not the case when we use homogeneous spherical particles.