Average Particle Radius Research Articles

Experimental investigation of particle size distribution influence on diffusion controlled coarsening

The influence of initial particle size distribution on coarsening during liquid phase sintering has been experimentally investigated using W-14Ni-6Fe alloy as a model system. It was found that initially wider size distribution particles coarsened more rapidly than those of an initially narrow distribution. The well known linear relationship between the cube of the average particle radius, r3, and time was observed for most of the coarsening process, although the early stage coarsening rate constant changed with time, as expected with concomitant early changes in the tungsten particle size distribution. The instantaneous transient rate constant was shown to be related to the geometric standard deviation, lnσ, of the instantaneous size distributions, with higher rate constants corresponding to larger lnσ values. The form of the particle size distributions changed rapidly during early coarsening and reached a quasi-stable state, different from the theoretical asymptotic distribution, after some time. A linear relationship was found between the experimentally observed instantaneous rate constant and that computed from an earlier model incorporating the effect of particle size distribution. The above results compare favorably with those from prior theoretical modeling and computer simulation studies of the effect of particle size distribution on coarsening, based on the DeHoff communicating neighbor model.

Sound Attenuation In A Coarse Granular Medium

In order to investigate the deviation of the spherical particle model from practical granular media in nature, the sound attenuation in a kind of water-saturated riverbed coarse sand was measured in the high frequency range 40-600 kHz. The results reveal that the rough surface and non-spherical shape factors of the sand particles have strong effects on the acoustic attenuation under experimental conditions in which βR̄ is greater than 60 in the whole frequency range and in which kR̄ is not far less than 1 when the frequency is higher than 300 or 400 kHz, where β is the viscous wavenumber, k is the compressional wavenumber and R̄ is the average radius of the sand particles.

The Structure of Shear Bands in Idealized Granular Materials

The structure of shear bands in granular materials was investigated by numerically simulating an idealized assembly of two-dimensional particles. Flexible stress-controlled boundaries were used instead of periodic boundaries to avoid constraining the motion of particles within the tested specimen. The particle displacement, particle rotations and rotations of the particle neighborhoods (macro-rotation) were examined within the shear band. The shear band width was found to decrease with axial strain from 18 and 15 times the average particle radius. The particle rotations and macro-rotations were concentrated inside the shear bands. The numerical simulations suggest that the particle rotations are induced by macro-rotations, and support the use of the micropolar theory for examining instable phenomena within granular materials.

Critical current and penetration depth in (Tl0.5Pb0.5)(YxCa1-x)Sr2Cu2O7- delta

The authors report a series of Jc measurements made on (Tl0.5Pb0.5)(YxCa1-x)Sr2Cu2O7- delta , over a range of x. The results show a clear peak in intragrain Jc with x corresponding to the peak in Tc, but a continuous decrease in intergrain Jc. This lack of correspondence is unique amongst the doped materials they have studied. The behaviour of the London penetration depth with x has also been estimated. The data indicate an increase in lambda L across the range, but a coincident fall in the average particle radius makes this conclusion uncertain.

The effects of convection on Ostwald ripening in solid-liquid mixtures

The effects of convection on Ostwald ripening in solid-liquid mixtures have been studied using a SnPb alloy over a wide range of volume fraction solid. The convection was induced by a slow rotation of a disk shaped sample with the axis of rotation perpendicular to the gravity vector. At low volume fractions of solid the experiments show that convection can alter the exponent of the temporal power law for the average intercept length from its classical value of 1 3 to 0.37. For intermediate volume fractions of solid the temporal exponent is 1 3 , but the amplitude of the temporal power law for the average particle radius depends on the rate of rotation. At very high volume fractions of solid, where a stable skeletal structure was present, rotation had no effect on the kinetics of the ripening process. A theoretical analysis of Ostwald ripening in the low Peclet number limit was undertaken in an effort to understand the experimental results. The analysis showed that temporal power law solutions to the equations describing ripening do not exist when the particles move in the fluid with either a constant velocity or according to Stokes law. However, if the magnitude of the fluid flow scales with time in the proper way, temporal power law solutions can be found which are qualitatively consistent with the experiments.

UV spectroscopy of Titan's atmosphere, planetary organic chemistry and prebiological synthesis: II. Interpretation of new IUE observations in the 220–335 nm Range

We report on new observations of Titan with the International Ultraviolet Explorer in the mid-UV range ( λ ≈ 220−335 nm). We use these data to determine upper limits for the abundances of simple organic compounds in the gas phase and to further constrain the properties of the high altitude haze on Titan. As a baseline, we adopted the parametrized microphysical model of McKay et al. (1989) which is successful at reproducing Titan's thermal structure while satisfying several other observational constraints in the visible and IR regions. However, we find that such a model—in which all particles at a given altitude are assumed to have the same size—cannot match simultaneously the IUE observations and the visible/IR data, even when allowance is made for a wide range of values in the adjustable parameters. On the other hand, a good overall agreement is obtained when considering a bimodal size distribution, with small haze particles or “polymers” ( r <0.02 μm) acting as strong Rayleigh absorbers below 300 nm and larger haze particles ( r ≈ 0.1−0.5 μm) being responsible for the characteristics of the albedo spectrum in the near-UV, visible, and IR regions. This approach is consistent with the results of several previous investigations of the properties of Titan's haze, although our preferred vertical structure for the haze + polymer material somewhat differs from earlier solutions. On the basis of simple dynamical considerations, we adopted a uniformly mixed layer between 150 and 600 km. The IUE data allow us to place fairly stringent constraints on the abundance of the Rayleigh absorbers, if we assume that their optical properties are similar to those of laboratory-synthesized “tholins”: The column-mass density of this material—the essential observable that can be determined from our study—is of the order of 5 μg cm −2. This would correspond to number-densities between 10 3 and 10 7 cm −3 in the 150–600 km altitude range, if the average particle radius is between 0.001 and 0.02 μm. Such high number densities are a priori at odds with the estimated coagulation lifetime for particles of that size. Thus, our proposed bimodal size distribution is plausible only if inhibiting processes act to slow down considerably the coagulation of polymers in Titan's stratosphere.

Synchrotron radiation study of silver and chromium particles supported on graphite

Silver and chromium particles in the size range 10 nm to 25 nm formed by deposition in ultra-high vacuum on graphite have been studied using synchrotron radiation. We have determined the island size by measuring the spectral dependence of the reflectivity of each sample using light in the photon energy range 35 eV to 190 eV. Comparing this measurement to a calculation of the reflectivity modified by the size-dependent extinction, determined using Mie theory, gives the average particle radius. Using this sizing technique we find that, for the growth of silver at room temperature, the average radius increases linearly with the cube root of evaporation time. Deposition with the substrate at elevated temperatures produces, for similar coverages, an increase in the average size for temperatures between 200°C and 225°C followed by a rapid decrease above 225°C.

Aerodynamic properties of fractal aerosol particles

Theoretical relations between the mass equivalent and the mobility equivalent radii of fractalparticles are derived for step as well as for exponential cutoff conditions. These are used to determine the fractal dimension and the average radius of the primary particles from form factor measurements. A computer simulation study demonstrates the enormous effect of low fractal dimensions on the sedimentation and coagulation behaviour of aerosol systems.

Formation of Au Colloid Particles in Silica Glass by Ion Implantation.

ABSTRACTFormation of Au colloid particles and their optical property have been investigated in silica glasses implanted with Au+ ions at an acceleration energy of 1.5MeV and fluence levels of 1016-1017 ions/cm2. The Au colloid particles are formed in the as-implanted glasses. It is inferred that the average radius of Au colloid particles depends on the fluence level, although the fluence level does not affect the distribution of Au atomic concentration. The heat-treatment little affects the Au atomic distribution. The Au colloid particles grow to 4.3nm in average radius during heat treatment. It is revealed that the large nonlinear optical property of the Au+ -ion-implanted silica glass is attributed to the high concentration of the Au colloid particles in the narrow region.

Comparative study of production of dextransucrase and dextran by cells of Leuconostoc mesenteroides immobilized on Celite and in calcium alginate beads

In fed-batch fermentation, cells of L. mesenteroides immobilized on three types of Celite were used to produce dextransucrase (DS) followed by production of dextran. A layer of calcium alginate on the porous Celite R630 particles improved their mechanical stability, increased the amount of soluble DS produced and decreased the cell leakage from the highly porous support. Enzyme production with the immobilized cell cultures was significantly affected by both pore and particle size. Immobilized cultures using Celite R648 (average particle radius of 200 microm and pore size of 0.14 microm) produced the highest total enzymatic activity, followed by Celite R633, alginate-coated Celite R630, Celite R630, and then calcium alginate beads. Culture of free cells produced about 18% more total enzymatic activity than immobilized cells in calcium alginate beads, but about 64% less than immobilized cells on Celite R630. It is expected that larger amounts of enzymatic activity than measured are immobilized inside the alginate-coated Celite R630 and calcium alginate beads due to the mass transfer limitation conferred by the dextran product formed therein. The dextran yield from conversion of sucrose to dextran and fructose with all such enzyme-enriched, immobilized-cell cultures was higher than that obtained from free-cell culture under similar conditions.

Coarsening in binary solid-liquid mixtures

A theory of Ostwald ripening has been developed for a solid-liquid mixture consisting of a low volume fraction array of spherical solid particles in a liquid wherein the coarsening process proceedsvia the transport of both heat and mass. We find that the simultaneous transport of heat and mass during ripening does not alter the exponents of the temporal power laws governing the ripening process from their classical values but does alter the amplitudes of these power laws. The growth rate of the cube of the average particle radius, the rate constant, is found to depend both on the alloy solute concentration and the ratio of the thermal to solutal diffusivities. In most metallic systems, a large decrease in the rate constant can be expected with small additions of solute to a pure metal. The mean-field temperature and concentration in the liquid will vary with time during ripening and will approach their equilibrium values along a unique path which is dependent only on the materials parameters of an alloy. Possible extensions of this theory to the analogous problem of ripening in isothermal ternary alloys are also discussed.

Hardening mechanisms in Al-Sc alloys

The hardening mechanism in Al-Sc alloys with scandium content of 0.11 and 0.19 at% is studied. Applying theoretical results due to the yield stress and work hardening of two phase alloys as a function of volume fraction and precipitate particle size, it is shown that after ageing at above 300° C the Orowan mechanism operates in these alloys. Using the experimental results, the volume fraction and average radius of the precipitate particles are determined.

Mössbauer and magnetic characterization of subdomain Feo clusters on surface modified carbons

Highly dispersed Fe-species supported on high surface area carbons treated with NaOH and HNO3 were investigated by Mossbauer spectroscopy and magnetization measurements. The superparamagnetic Feo clusters formed on the NaOH-treated carbons showed an average particle radius of 2.0 nm, a blocking temperature lower than 88 K and significant metal-support interaction. On exposure to syngas (H2+CO) the Mossbauer spectrum revealed the presence of Hagg Carbide (Fe5C2), believed to be the active component of Fischer-Tropsch reaction.

SANS study of particle nucleation in emulsion polymerization

We describe the use of small-angle neutron scattering (SANS) to measure the average radius of polystyrene particles in the early stages of emulsion polymerization. Polymerization was started by placing monomer in contact with an aqueous polyacrylamide gel containing intiator, in the absence of sufractant. Reaction was allowed to occur for 12, 24 and 48 h, and slices were removed from the gels in each system at various distances (of order 10 mm) from the interface. SANS meausrements on these slices showed the presence of particles of radius 6 ± 1 nm. These experiments show that, in these systems, one can halt the growth (by propagation and coagulation) of very small colloidal particles for a sufficiently long time to measure physical properties such as the amount of monomer imbibed at equilibrium swelling, surface charge, etc.

Mercury photosensitization of toluene vapor and aerosol formation

Abstract The triplet-mercury photosensitized decomposition of toluene vapor was performed at 298 K to determine the nature of the aerosols formed. The major product was bibenzyl, which was identified by gas chromatography—mass spectrometry, Fourier transform IR spectroscopy (FTIR) and 13 C and 1 H nuclear magnetic resonance spectroscopy, and its quantum yield was 1.05 × 10 −2 . Other products identified included methane, benzene and dimeric species. Aerosols were analyzed in situ by FTIR spectrometry and their FTIR spectra shown to correspond to bibenzyl. The rates of aerosol formation at different substrate pressures were studied using a laser light extinction photometer and shown to correlate linearly with the rate of bibenzyl formation. The average aerosol particle radii determined from differential settling measurements were 0.23, 0.30, and 0.43 μm at toluene pressures of 10 Torr, 15 Torr and 20 Torr respectively. Scanning electron microscopy measurements corroborated the particle sizes deduced from the light extinction measurements. Finally, ab initio molecular orbital calculations using the 3-21G basis set found Hartree—Fock energies of the 1 A′ and 3 A′ states of toluene and the benzyl radical plus hydrogen atom, anticipated dissociation products, to be −268.24022 a.u., −268.13720 a.u., and −268.13738 a.u. respectively. The benzene ring is significantly distorted in the triplet state, suggesting that considerable vibrational excitation occurs upon intersystem crossing. The benzyl radical is planar, as expected. Optimized geometries are reported.

Bidirectional reflectance spectroscopy: 4. The extinction coefficient and the opposition effect

The extinction coefficient and the opposition effect in a particulate medium are discussed. Simple analytic expressions that describe these quantities are rigorously derived using a few physically realistic mathematical approximations. The particles of the medium may have a distribution of sizes, and the particle density is allowed to vary with depth. The expression for the extinction coefficient is valid for both large and small porosities and is more accurate than the one commonly used. The opposition effect arises from the hiding of extinction shadows and occurs even if the particles are transparent. The angular half-width of the opposition peak is shown to be equal to the ratio of the average particle radius to extinction length at unit slant path optical depth in the medium, and depends on both the filling factor (ratio of bulk to solid density) F and the particle size distribution. To illustrate the theory, it is fitted to observations of the Moon, an asteroid, and a satellite of Uranus; Europa is also discussed. For the Moon, a value of F = 0.41 is derived, in good agreement with data on Apollo soils. For Oberon, the width of the opposition effect peak gives F = 0.10, which is similar to values for terrestrial frosts and snow. Thus, the narrow opposition effects of the Uranian satellites do not require any unusual particles or microstructures on their surfaces. More photometric observations of Europa are needed.

Aqueous latex polymerization of acrylonitrile. Kinetics, particle numbers and particle sizes

Unseeded latex polymerization of acrylonitrile has been studied in water at 50 °C using potassium persulphate as initiator. Volume changes were monitored dilatometrically and particle size distributions were determined by transmission electron microscopy. The particle number density in each run became constant before the earliest sample could be taken for analysis. The same value [1.56 (s= 0.21)× 1012 cm–3] was found for four different initial concentrations of monomer and initiator. The rate of polymerization was proportional to the average particle radius. This deduction was confirmed by the observation that plots of (amount of polymer)2/3 against time are linear. The process was first order in the concentration of monomer and of order 0.5 in concentration of initiator. The ‘exposure’, an adjusted time variable, is introduced and used. It is intended to facilitate analysis of cases in which the extent of reaction is not small enough to use the ‘initial rate’ approach and in which the integrated rate law is inconvenient.

The influence of particle motion on ostwald ripening in liquids

A general method for the calculation of the coarsening of a dilute dispersed system (Ostwald Ripening) is applied to the case of concurrent diffusive and convective matter transport between fluid or solid particles which are suspended in a liquid matrix. Depending on the nature of convective motion (constant velocity, Stokes or Marangoni flow), remarkable differences arise when compared to purely diffusional Ostwald ripening as predicted by the classical LSW theory. The steeper the concentration gradient at the particle matrix interface and thus the higher the flux from or to a particle, the faster the growth of the average particle radius and the broader the distribution function.

Quantitative analysis of soil structure with the microcomputer system

The present structure estimation methods are rather long-termed and expensive; moreover, they are sometimes impossible to use in reason of difficulty of sampling large sized specimens. The soil structure estimation in SEM enabling to obtain quick and reliable quantitative structure characteristics of small size samples (≈0,5 cm3) are becoming very important at present. SEM investigation of identical areas on both conjugated surfaces of sample fracture, total binary SEM image with real structure of undisturbed sample, discrimination and digitization of the image and its processing by computer with specially designed algorithms is the core of this method. The quantitative structure analysis is made practically instantly and the following data may be obtained: the number of pores and particles, average perimeter, square and radius of pores and particles, porosity, specific surface, pore shape index, the number of contacts between particles, pore and particle distribution according to the sizes. The quickness and reliability of the results obtained as well as the application which enables to cover all kinds of soils is an evident advantage of the method. The most important factor is the tracing of soil genesis and the nature of the strengths.

Solution to the multi-particle diffusion problem with applications to ostwald ripening—II. Computer simulations

The multi-particle diffusion solution developed in Paper I is used to determine the collective behavior of a system of dispersed second phase particles undergoing Ostwald ripening. Since the multi-particle diffusion solution was employed to determine the diffusion field within the matrix, interparticle diffusional interactions are specifically included in the treatment. Both the transient and long-time behavior of given initial distributions of particle sizes were examined over a wide range of volume fractions of the coarsening phase. It was found in the transient region that the collective behavior of the coarsening ensemble was highly dependent on the initial distribution. When these distributions were scaled by the average particle radius, they all eventually evolved to identical time-independent distributions which were functions of the volume fraction of the coarsening phase. These time-independent distributions are, in general, significantly different from the classic Lifshitz-Slyozov-Wagner distribution, and become progressively broader and more symmetric with increasing volume fraction. The ripening kinetics were also found to be a function of the volume fraction, the kinetics increasing by a factor of five upon changing the volume fraction from zero to 0.5. The statistical nature of Ostwald ripening was investigated by examining the influence of the volume fraction on the distribution of individual particle source/sink strengths. This statistical information is used to show the self-consistency of the numerical approach.