Fluctuation kinetics of the formation of nanoparticles

The method of stochastic simulations was applied to studying the kinetics of nucleation and growth of nanoparticles from solution in the presence of a ligand-yielding stabilizer. It was established that, at large stabilizer concentrations the process is not described within the framework of the law of mass action, being appreciably dependent on stochastic fluctuations in the number of free vacancies at the surface of the growing particle. This factor is responsible for the limitation of particle growth and for the formation of stable particles with a loose packing and dendrite-like structure. With decreasing stabilizer concentration, the kinetic characteristics of the process approach those typical of classical kinetics, whereas the packing density increases.     

Microflow reactor synthesis of palladium nanoparticles stabilized with poly(benzyl ether) dendron ligands

A simple glass capillary microflow reactor system has been applied for the synthesis of palladium nanoparticles by thermal decomposition of palladium acetate (Pd(OAc)₂) in diphenyl ether in the presence of poly(benzyl ether) dendron ligands (PBED Gn-NH₂, n = 1–3) as a stabilizer. Effect of hydrodynamic parameters (capillary diameter, linear flow rate, volume flow rate, and reaction temperature) and concentrations (precursor and stabilizer) on the particle size was investigated. The particle size can be controlled by varying linear flow rate and temperature as well as ligand/precursor concentration ratio. Volume flow rate does not affect the particle size when the linear flow rate is held constant for different capillary diameters (150–320 μm). Unlike batch systems, in this microreactor system, smaller particles are produced at low ligand concentrations when the molar ratio of the ligand to metal precursor ranged from 1 to 5. As another characteristic of the microreactor synthesis, the concentration of the Pd precursor can be increased (up to 27 mM) with maintaining a constant particle size (3.1 ± 0.2 nm) and a good monodispersity, while in the batch system a significant increase and broadening in the particle size are observed with increasing precursor concentration.     

Error Estimates in the Sampling From Particle Size Distributions

It is often necessary to estimate the properties of particle size distributions from limited samples taken from large populations. When the distributions are broad, and higher order moments required, as in the case of volume based particle size distributions, the inferred parameters d_3,50 (volume median diameter) and GSD (geometric standard deviation) can have high intrinsic errors not immediately obvious to the measuring scientist. We show that there is a critical number of particles, N_crit, which must be counted or else the error may blow up catastrophically. N_crit is very sensitive to the width of the distribution, and is approximately proportional to GSD¹¹ We develop formulae to estimate the random sampling error inherent in measured values of the d_3,50 and GSD for the log-normal distribution; compare the predictions to a typical experimental particle size measurement; and then generalize to the median of any arbitrary moment, d_{r, 50}.     

Mixing Properties for Mechanical Motion¶of a Charged Particle in a Random Medium

We study a one-dimensional semi-infinite system of particles driven by a constant positive force F which acts only on the leftmost particle of mass M, called the heavy particle (the h.p.), and all other particles are mechanically identical and have the same mass m < M. Particles interact through elastic collisions. At initial time all neutral particles are at rest, and the initial measure is such that the interparticle distances ξ _i are i.i.d. r.v. Under conditions on the distribution of ξ which imply that the minimal velocity obtained by each neutral particle after the first interaction with the h.p. is bigger than the drift of an associated Markovian dynamics (in which each neutral particle is annihilated after the first collision) we prove that the dynamics has a strong cluster property, and as a consequence, we prove existence of the discrete time limit distribution for the system as seen from the first particle, a ψ-mixing property, a drift velocity, as well as the central limit theorem for the tracer particle. Received: 22 March 2000 / Accepted: 8 December 2000     

Influence of synthesis parameters on iron nanoparticle size and zeta potential

Zero valent iron nanoparticles are of increasing interest in clean water treatment applications due to their reactivity toward organic contaminants and their potential to degrade a variety of compounds. This study focuses on the effect of organophosphate stabilizers on nanoparticle characteristics, including particle size distribution and zeta potential, when the stabilizer is present during nanoparticle synthesis. Particle size distributions from DLS were obtained as a function of stabilizer type and iron precursor (FeSO₄·7H₂O or FeCl₃), and nanoparticles from 2 to 200 nm were produced. Three different organophosphate stabilizer compounds were compared in their ability to control nanoparticle size, and the size distributions obtained for particle volume demonstrated differences caused by the three stabilizers. A range of stabilizer-to-iron (0.05–0.9) and borohydride-to-iron (0.5–8) molar ratios were tested to determine the effect of concentration on nanoparticle size distribution and zeta potential. The combination of ferrous sulfate and ATMP or DTPMP phosphonate stabilizer produced stabilized nanoparticle suspensions, and the stabilizers tested resulted in varying particle size distributions. In general, higher stabilizer concentrations resulted in smaller nanoparticles, and excess borohydride did not decrease nanoparticle size. Zeta potential measurements were largely consistent with particle size distribution data and indicated the stability of the suspensions. Probe sonication, as a nanoparticle resuspension method, was minimally successful in several different organic solvents.     

Size analysis and magnetic structure of nickel nanoparticles

The size distribution of an assembly of fcc nickel nanoparticles is studied by measuring the temperature dependent magnetization curves fitted by a uniform model and a core-shell model, both based on the Langevin function for superparamagnetism with a log-normal particle volume distribution. The uniform model fits lead to a spontaneous magnetization M_s much smaller than the M_s for bulk nickel and to particle sizes larger than the ones evaluated by transmission electron microscopy; the core-shell model fits can result in a correct size distribution but the M_s in the core becomes significantly greater than the M_s for bulk nickel. It is concluded that there is a core-shell magnetic structure in nickel particles. Although the enhanced M_s in the core may be related to the narrowing of the energy bands of 3d electrons in small fcc nickel particles, the modeling values of M_s are over large compared with previous calculations on nickel clusters of different structures, which implies possible existence of an exchange interaction between the core and the shell, which is not considered in the simple core-shell model.     

On Measuring and Modeling Local Average Particle Velocities for particle ensembles in classifying systems

In most multi-phase flow problems, the particulate phase is exposed to an external field which causes dispersion. Therefore, local velocity measurements of the disperse phase are no longer equivalent with respect to averaging in time and averaging in volume. While the local time-averaged velocity still characterizes the transport of the ensemble in the Eulerian sense, one has to be be careful in modeling this velocity average by considering the ensemble's composition. It is shown for different particle ensembles that the conventional particle velocity average M_1,0 calculated with respect to the dispersion relationship and a particle size number density distribution is far below the measured ensemble average; the deviation depends on the width of the particle size distribution. It is deduced that Eulerian particle velocity values referring to a certain time interval can be modeled by a ratio of velocity moments M_2,0/M_1,0 calculated with particle size number distributions referring to a certain probe volume. This relationship was confirmed by measurements.     

Magnetic properties of Co nanoparticles in zirconia matrix

Granular films composed of nanometric Co particles embedded in an insulating ZrO₂ matrix were prepared by pulsed laser deposition in a wide range of Co volume concentrations (0.06<x_v<0.42). High-resolution electron microscopy (HREM) shows very sharp interfaces between the crystalline particles and the amorphous matrix, with no evidence of intermixing. The mean particles size and width of the distribution determined by fitting the low-field magnetic susceptibility and magnetization curves in the paramagnetic regime to a distribution of Langevin functions are in agreement with the parameters extracted from direct TEM observations. Ferromagnetic correlations between Co particles are evident in the field-cooled state when increasing Co concentration. The effective anisotropy constant estimated from magnetic measurements is about two orders of magnitude larger than the bulk value, and decreases as particle size increases.     

Use of an electrical aerosol detector (EAD) for nanoparticle size distribution measurement

Recently, Nanoparticle Surface Area Monitor (NSAM, TSI model 3550) and EAD (EAD, TSI Model 3070A) have been commercially available to measure the integral parameters (i.e., total particle surface area and total particle length) of nanoparticles. By comparison, the configuration of the EAD or NSAM is similar to that of electrical mobility analyzer of the early generation for particle size distribution measurement. It is therefore possible to use the EAD or NSAM as a particle sizer. To realize the objective of using the EAD as a sizer, we characterized the average electrical charges of monodisperse particles passing through the EAD particle charger and ion trap set at voltages ranging from 20 to 2500 V. The average charge data collected at different ion-trap voltages were then summarized by the empirical correlation using the parameter of Z _p *V, where Z _p is the particle electrical mobility and V is the ion-trap voltage. A data-reduction scheme was further proposed to retrieve the size distribution of sampled particles from the EAD readout at different ion-trap voltages. In the scheme, the functional format of each mode in a number size distribution of particles was assumed as log-normal, but the number of modes in an entire size distribution is not limited. A criterion was used to best fit the simulated EAD readouts with experimental ones by varying the count median diameter (CMD), geometric standard deviation (σ _g), and total particle number (N _t ) of each mode in a particle size distribution. Experiments were performed to verify the proposed scheme.     

Sizing Polydisperse Dispersions by Focused Beam Reflectance and Small Angle Static Light Scattering

In this work, two different methods for particle characterization, namely focused beam reflectance and small angle static light scattering, are quantitatively compared. The results are presented in the form of moment ratios of the particle size distribution, i.e., the number weighted diameter, D_1/0, and the volume weighted diameter, D_4/3, for a broad range of particle size distributions ranging from 20 to 400 μm. Various aqueous dispersions including narrow, broad, and bimodal particle size distributions of spherical shaped ceramic beads were used in the comparison. It was found that the moment ratios obtained by focused beam reflectance measurements and small angle static light scattering correlate well, in the case of spherical particles. Furthermore, it was found that the D_1/0 values obtained by focused beam reflectance measurements are more sensitive to the presence of a small fraction of fine particles in a bimodal distribution than those obtained by small angle static light scattering.     

Growth of gas phase nanoparticles with an accretion mechanism

Nano-droplet growth in a supersaturated vapor has been investigated in a gas aggregation source using laser-ionization time-of-flight mass spectrometry. During its propagation into an atomic vapor, a small particle grows by sticking atoms on its surface. This accretion process has been highlighted through the clustering of homogeneous particles M_n and heterogeneous M_n(M₂O) and M_n(MOH)₂ particles in a metallic vapor and a helium buffer gas (M = Na or K). A modelization is introduced so as to connect the measured cluster mass distributions to the pertinent physical parameters. The mass distribution width is particularly sensitive to the efficiency of the first steps in the growth sequence. We used this property to compare the ability of this vapor-condensed matter phase transition to occur around various homogeneous and heterogeneous nucleation seeds.     

Surface effects in maghemite nanoparticles

A consistent model is presented for the variation of saturation magnetization with particle size in maghemite nanoparticles, based on the existence of a magnetically disordered layer with a constant thickness of 1 nm. For particles smaller than 3 nm, layer thickness increases rapidly, and M_S is already zero for 2.5 nm particle size. Magnetization measurements have been performed on maghemite–polymer nanocomposites with low size dispersion and a regular distribution of particles in the matrix. A representative number of samples have been studied with a diameter size in the range from 1.5 to 15 nm and ±10% of size dispersion.     

Effect of instrumental particle sizing resolution on the modelling of aerosol radiative parameters

A more realistic estimation of the scattering and hemispheric backscattering coefficients, σ_sp and σ_bsp, and their respective optical cross section, C_sca and C_bk, of aerosol particles is presented on the basis of the exact resolution of the width of the size bins of the particle counter instruments when size distribution measurements are used, and, with the exact optical detector instruments ability. The scattering and hemispheric backscattering cross sections, C_sca and C_bk, of the particles are averaged over the full size bins of the particle counter instrument, while these quantities are usually estimated only on the value of the mean geometric diameter of each size bin. Six instruments, the APS, ASASP-X, DMPS, FSSP-100, ELPI, and SMPS frequently used in particle size distribution measurements are reviewed, for spherical sea-salt particles at a wavelength λ=0.55 μm. The comparison using the conventional geometric mean diameter versus the use of the full size bin leads to large amount of errors for the optical cross section with non-negligible effects on their respective optical coefficients. The maximal accuracy expected for these optical quantities depend on the particle diameter as well as on the channel width of the instruments, and are also function of the angular detector probe used to measure them.     

Vacancy ordering in γ-Fe2O3 small particles

The effect of particle size on the formation of vacancy-ordered superstructure in γ-Fe₂O₃ powders has been investigated by using X-ray, Mössbauer and chemical analyses. Powders of γ-Fe₂O₃ with different average particle size were prepared by chemical precipitation and subsequent heat-treatment. The X-ray diffraction intensity of the superlattice lines decreases with the particle size of γ-Fe₂O₃ and finally disappears at a particle-size between 300-175 Å, possibly around 200 Å. Therefore ordering of the cation vacancies in ultrafine γ-Fe₂O₃ particles is ruled out. Although the vacancies do not form an ordered structure, they do exclusively occupy B-sites.     

Simulation of diffusion instability of a mercury atomic distribution in the cadmium-mercury-tellurium alloy

The formation of inhomogeneities in Cd_xHg_1-x Te alloys upon post-growth cooling or upon low-temperature annealing is simulated numerically. The mechanism of the formation of inhomogeneities is based on the diffusion instability in a system involving mercury atoms located at lattice sites, interstitial mercury atoms, and cation vacancies. It is revealed that, upon prolonged annealing of the Cd_xHg_1-x Te alloys with a cadmium content x = 0.2 at a temperature of ∼200°C, the concentrations of mercury atoms at lattice sites, interstitial mercury atoms, and vacancies are characterized by an inhomogeneous nearly periodical distribution arising from a small fluctuation when the initial equilibrium concentration of interstitial mercury atoms exceeds a threshold value (∼3 × 10¹⁷ cm⁻³). The spatial and time scales of the concentration distribution are determined primarily by the equilibrium concentration of vacancies and do not depend on the type of fluctuation involved. The spatial period of the concentration distribution increases linearly from 0.01 to 3.00 μm as the equilibrium concentration of vacancies changes from 10¹⁹ to 10¹⁴ cm⁻³. At lower concentrations of vacancies, the periodic structure is formed for a considerably longer time.     

Preparation of AgBr Nanoparticles in Microemulsions Via Reaction of AgNO<Subscript>3</Subscript> with CTAB Counterion

Nanoparticles of AgBr were prepared by precipitating AgBr in the water pools of microemulsions consisting of CTAB, n-butanol, isooctane and water. An aqueous solution of AgNO₃ added to the microemulsion was the source of Ag⁺ ions. The formation of AgBr nanoparticles in microemulsions through direct reaction with the surfactant counterion is a novel approach aimed at decreasing the role of intermicellar nucleation on nanoparticle formation for rapid reactions. The availability of the surfactant counterion in every reverse micelle and the rapidity of the reaction with the counterion trigger nucleation within individual reverse micelles. The effect of the following variables on the particle size and size distribution was investigated: the surfactant and cosurfactant concentrations, moles of AgNO₃ added, and water to surfactant mole ratio, R. High concentration of the surfactant or cosurfactant, or high water content of the microemulsion favored intermicellar nucleation and resulted in the formation of large particles with broad size distribution, while high amounts of AgNO₃ favored nucleation within individual micelles and resulted in small nanoparticles with narrow size distribution. A blue shift in the UV absorption threshold corresponding to a decrease in the particle size was generally observed. Notably, the variation of the absorption peak size with the nanoparticle size was opposite to those reported by us in previous studies using different surfactants.     

The effect of polystyrene-block-poly(4-vinylpyridine) prepared by a RAFT method in the dispersion polymerization of styrene

The dispersion polymerization of styrene has been carried out using polystyrene-block-poly(4-vinylpyridine) copolymer [P(S-b-4VP)], prepared by a reversible addition-fragmentation chain transfer (RAFT) method, as a steric stabilizer in alcohol media. These block copolymer contains a long poly(4-vinylpyridine) block and a short polystyrene block. The stable spherical particles were obtained when the block copolymer concentrations increased from 2 to 20 wt.% relative to the monomer and the average particle sizes decreased from 340 to 200 nm with increasing concentration of the block copolymer. Alcoholic solvents, from methanol to n-hexanol, are responsible for the particle size. These results indicate that the poly(S-b-4VP) block copolymer is effective for providing polystyrene nano-sized particles with a low content of it working as a good stabilizer in any kind of alcoholic medium.     

分子动力学模拟尺寸对纳米Cu颗粒等温晶化过程的影响

采用分子动力学方法和镶嵌原子势, 模拟了4000个Cu原子和13500个Cu原子(简称Cu₄₀₀₀和Cu₁₃₅₀₀)组成的纳米颗粒以及块体Cu的等温晶化过程. 通过对这些颗粒在晶化过程中结构和动力学行为的分析研究, 发现低温时, 不同尺寸的纳米Cu颗粒均出现多步晶化, 且晶化时间的分布曲线远比高温时范围大; 除了温度, 颗粒尺寸对晶化行为也有重要的影响, 尺寸越大, 晶化时间越长, 最终的晶化程度越高; 但是晶化时间随尺寸增大而增加的趋势不会一直持续, 发现存在一个临界尺寸r_c, 小于r_c时, 晶化时间随颗粒尺寸增大而增加, 大于r_c时,晶化时间随尺寸增大而减小.     

Effect of particles on the flow structure and dispersion of solid impurities in a two-phase axisymmetric jet

The Euler approach is used for studying the structure of a flow and the propagation of a disperse impurity in a submerged two-phase jet for small values of the mass concentration of particles (M _L1 = 0 to 0.5) upon a variation of the size and material of particles in a wide range. The effect of particles on the propagation of a two-phase jet, gas turbulence, and solid phase dispersion is analyzed. The addition of particles decreases the jet opening angle, increases the jet range, suppresses turbulence, and deteriorates turbulent mixing with the surrounding submerged space. It is shown that at the first stage, particle accumulation effects (pinching) in the axial region of the jet appear upon an increase in the particle size and the density of the particle material. Then, upon an increase in the inertia of particles, pinching changes to intense scattering of the disperse phase in the initial cross sections of the jet. The results are compared with the results of measurements for mono- and polydisperse two-phase jet flows.     

Effect of HPC and Water Concentration on the Evolution of Size,Aggregation and Crystallization of Sol-gel Nano Zirconia

Nano-sized zirconia (ZrO₂) powder is synthesized using sol-gel technique involving hydrolysis and condensation of zirconium(IV) n-propoxide in an alcohol solution, utilizing hydroxypropyl cellulose (HPC) polymer as a steric stabilizer. It is demonstrated that ZrO₂ nanoparticle size can be reduced using high R-value (defined as the ratio of molar concentrations of water and alkoxide). It is also shown that ZrO₂ nanoparticle size can be reduced further by synthesizing these particles in the presence of HPC polymer. The agglomeration tendency of ZrO₂ nanoparticles is demonstrated to decrease due to the steric hindrance created by the adsorbed polymer. The nanocrystallite size and their 'hard-aggregates' formation tendency are observed to affect the high temperature metastable tetragonal phase stabilization at room temperature within ZrO₂ particles.