Gaussian Size Distribution Research Articles

Inertial impaction-dominated fibrous filtration with rectangular or cylindrical fibers

Fibrous filter, being simple in structure and low cost in material, is widely used in fine particulate removal. The collection efficiency of a fibrous filter is heavily dependent on the collection efficiency of a single fiber. Despite the availability of a reasonable formulation for single fiber collection by diffusion, most expressions of collection efficiencies by interception and impaction are empirically based and few simple analytical formulations are available, especially for impaction-dominated collection. In this paper, impaction-dominated fibrous filtration with rectangular fibers for particulate size much smaller than that of the collecting fibers are both numerically and analytically investigated. The effects of fiber aspect ratio, filter packing density, particulate size and Stokes number on the collection efficiency of a rectangular fiber in the impaction-dominated filtration are numerically determined. In addition, simple analytical expressions of single fiber collection efficiencies due to interception and inertial impaction of fine powders are derived based on Kuwabara flow analysis around a cylinder. Hence, using the equivalent hydraulic diameter concept for rectangular fibers with moderate fiber aspect ratios, the effect of particulate polydispersion on the filter collection efficiency is investigated based on presumed mass-based Gaussian size distribution and log-normal size distribution, respectively. Differences between overall size-averaged collection efficiency and mean size collection efficiency can, thus, be estimated.

An improved small-angle X-ray scattering analysis of δ′ precipitation in an Al–Li alloy for growth kinetic studies

An improved method for small-angle X-ray scattering (SAXS) data analysis is developed to reconstruct the free-form particle size distribution of δ′ precipitation in an Al–Li alloy. This improved method consists of four iterative steps; the interparticle interference is also included. The indirect transform method (ITM) plus a hard-sphere (HS) model which considers the depleted zones are used in the analysis of δ′ precipitation in an Al–Li alloy. Two parameters, namely the hard-sphere volume fraction, ηHS, and the ratio of hard-sphere radius to the particle radius,RHS/R, which determine the structure factor of the interparticle effect, are iteratively calculated using the monodisperse assumption and Gaussian size distribution. These two parameters are finally used in reconstructing the particle size distribution by the ITM + HS method. This method is tested by analysing simulated SAXS data and shows a better agreement than found in similar studies. This improved method is applied to analyse a set of experimental SAXS intensities from δ′ (Al3Li particles) precipitation in an Al–9.7 at.% Li alloy. The monodisperse results are compared with the polydisperse ITM + HS results. The current ITM + HS method fits the SAXS data better than the other methods. The variations of average radii with aging time were found to follow the kinetic power law. The SAXS results are used to investigate the theoretical kinetic model of the volume-fraction effect on late-stage coarsening (Ostwald ripening). By comparing both experimentally obtained asymptotic size distributions of δ′ particles as well as coarsening rate constants with those predicted by the various kinetic models, the modified Lifshitz–Slyozov–Wagner (MLSW) theory is found to be in better agreement with the experimental results than the other theories.

Water in Local Free Volumes of Polyimides: A Positron Lifetime Study

Positron annihilation lifetime (PAL) spectroscopy was used to study the effect of water uptake on the free volume in 6FDA-ODA polyimide (PI2566, DuPont). Orthopositronium (o-Ps) lifetime (τ3) and intensity (I3) data were analyzed assuming a Gaussian size distribution of preexisting (excess free volume) holes and further assuming that holes occupied by water molecules would not be detected in the measurement. When exposed to humidity, both the mean hole volume and the number of holes not occupied by water molecules decrease with increasing relative humidity, as indicated by decreasing τ3 and I3. Our PAL results correlated with humidity-induced mass uptake and volume expansion support a model according to which water absorption in polyimides occurs in two stages. At relative humidities smaller than about 30%, water is absorbed mostly in large, preexisting holes, with each hole typically occupied by a single water molecule. At larger humidities, an increasing fraction of the sorbed water molecules will occupy sites other than preexisting empty holes. A multiple occupation of larger holes by water molecules is discussed as a possible mechanism.

A heterogeneously structured composite based on poly(lactic-co-glycolic acid) microspheres and poly(vinyl alcohol) hydrogel nanoparticles for long-term protein drug delivery.

To prepare a heterogeneously structured composite based on poly (lactic-co-glycolic acid) (PLGA) microspheres and poly(vinyl alcohol) (PVA) hydrogel nanoparticles for long-term protein drug delivery. A heterogeneously structured composite in the form of PLGA microspheres containing PVA nanoparticles was prepared and named as PLGA-PVA composite microspheres. A model protein drug, bovine serum albumin (BSA), was encapsulated in the PVA nanoparticles first. The BSA-containing PVA nanoparticles was then loaded in the PLGA microspheres by using a phase separation method. The protein-containing PLGA-PVA composite microspheres were characterized with regard to morphology, size and size distribution, BSA loading efficiency, in vitro BSA release, and BSA stability. The protein-containing PLGA-PVA composite microspheres possessed spherical shape and nonporous surface. The PLGA-PVA composite microspheres had normal or Gaussian size distribution. The particle size ranged from 71.5 microm to 282.7 microm. The average diameter of the composite microspheres was 180 microm. The PLGA-PVA composite microspheres could release the protein (BSA) for two months. The protein stability study showed that BSA was protected during the composite microsphere preparation and stabilized inside the PLGA-PVA composite microspheres. The protein-containing PLGA-PVA composite may be suitable for long-term protein drug delivery.

Size distribution of coherently strained InAs quantum dots

The influence of the InAs coverage on the size and density of coherently strained InAs islands was investigated. At moderate InAs coverages the photoluminescence signal reflects the Gaussian size distribution of small coherently strained islands. However, before the coherently strained islands transform into dislocated ones the Gaussian line shape of their photoluminescence signal changes and a narrow peak appears on the low-energy tail. We attribute this change to an accumulation of coherently strained islands at a maximum size before dislocated island transformation occurs. Effects of luminescence from dislocated islands, size-dependent relaxation processes, capture efficiencies, and dot-dot coupling are also discussed. However, our calculations and the magnetophotoluminescence, as well as the photovoltage experiments, confirm our interpretation of a size accumulation process of coherently strained islands.

A novel approach to stabilization of protein drugs in poly(lactic-co-glycolic acid) microspheres using agarose hydrogel

A novel approach has been taken to stabilize protein drugs in poly(lactic-co-glycolic acid) (PLGA) microspheres. This approach creates a new protein drug delivery system, which is based on the combination of agarose hydrogel particles and PLGA microspheres. This combination produces a heterogeneously structured polymeric composite. The protein drug molecules are encapsulated in the agarose hydrogel particles and the drug-containing agarose hydrogel particles are further dispersed in the PLGA microspheres. One PLGA microsphere may contain many agarose hydrogel particles to form a PLGA–agarose composite microsphere. The PLGA–agarose composite microspheres have spherical shape and a smooth surface. They possess a normal or Gaussian size distribution and an average diameter of 150 μm. The PLGA–agarose composite microspheres have higher protein loading efficiency than that of the conventional PLGA microspheres. The hydration of the PLGA–agarose composite microsphere matrix is faster than that of the conventional PLGA microspheres. Protein drugs can be slowly released from the PLGA–agarose composite microspheres. The agarose hydrogel particles can stabilize protein drugs in the PLGA matrix, which is the major advantage of this novel protein drug delivery system over the conventional PLGA microspheres.

Polarized light scattering by aerosols in the marine atmospheric boundary layer

The intensity and polarization of light scattered from marine aerosols affect visibility and contrast in the marine atmospheric boundary layer (MABL). The polarization properties of scattered light in the MABL vary with size, refractive index, number distributions, and environmental conditions. Laboratory measurements were used to determine the characteristics and variability of the polarization of light scattered by aerosols similar to those in the MABL. Scattering from laboratory-generated sea-salt-containing (SSC) [NaCl, (NH(4))(2) SO(4), and seawater] components of marine aerosols was measured with a scanning polarization-modulated nephelometer. Mie theory with Gaussian and log normal size distributions of spheres was used to calculate the polarized light scattering from various aerosol composition models and from experimentally determined distributions of aerosols in the marine boundary layer. The modeling was verified by comparison with scattering from distilled water aerosols. The study suggests that polarimetric techniques can be used to enhance techniques for improving visibility and remote imaging for various aerosol types, Sun angles, and viewing conditions.

Modeling the relationships between particle and pore size distributions in multicomponent sphere packs: application to the water retention curve

A probabilistic approach that computes the distribution of the volume of the voids in packed spheres given their size distribution is applied to determine the corresponding water retention curves. The assumption of dense random packing is adopted. The volume of the void determined by four spheres mutually in contact is approximated by the volume of the osculatory sphere. Every void is accessible through four openings. The size of these openings is assumed to be represented by the respective osculatory discs. Applying the law of capillarity to the radii of the voids and their openings, the hysteretic water retention function characterizing multicomponent sphere packs is defined. The approach is applied to power law, Gaussian and log-normal sphere size distributions. The water retention function and the hysteretic domain are found to depend upon the distribution type, the power exponent and the standard deviation. The power law distribution generates the narrowest hysteretic domain and the highest water capacity. The normally distributed sphere sizes generate the wides hysteretic domain and the lowest water capacity. Increasing the standard deviation of the sphere size distribution reduces the hysteretic domain for most of the effective saturation range, mainly because of the effect on the drying curve.

Analytical approximations of the effect of a fiber size distribution on the performance of hollow fiber membrane separation devices

This work provides approximate analytical expressions for the effect of a fiber size distribution on the performance of a hollow fiber membrane separation device. The analysis considers a Gaussian size distribution in two limiting mass transfer regimes, membrane and lumen-fluid resistance dominated. The results indicate that the effective mass transfer coefficient for a fiber distribution is smaller than that calculated assuming that all fibers are of the average size and decreases as either the ratio of the Sherwood number to the Graetz number or the standard deviation of the fiber size distribution increases. Furthermore, for a given fiber size distribution, the reduction in the effective mass transfer coefficient is greatest when the lumen-fluid mass transfer resistance controls the overall transport rate.

Quantum confinement effects of CdS nanocrystals in a sodium borosilicate glass prepared by the sol-gel process

Experimental evidences of both weak and strong confinement regimes are reported on CdS nanocrystals embedded in a sodium borosilicate glass matrix. A method, based on the sol-gel technique, is used for the preparation of CdS-activated glass. This route is capable of providing nanocrystals covering a wide range of radii with small size dispersion. Low-temperature linear-absorption spectra have been analyzed in terms of excitons and electron-hole confinements by fitting the results of a numerical calculation to experimental findings. The model used, in the envelope-function formalism, involves both a Lorentzian broadening of the exciton energy states inside each nanocrystal and a Gaussian size distribution. The improvement of crystal quality and the sharpening of the size distribution by thermal annealing is also studied versus both time and temperature of treatment. It is shown that we can keep a tight control on the crystallinity, average size, and size distribution of the nanocrystals by rather simple adjustments and short treatments.

ASAXS from CdS1−x-doped silicate glasses

Anomalous small-angle X-ray scattering (ASAXS) was employed to analyze CdSxSe1 − x-doped silicate glasses, x = 0.4 and 0.6. From the intensity variations, as measured for four X-ray energies near the K-absorption edge of Se and at 9.5 keV, reliable values for the ratio of molecular densities in the crystalline CdSxSe1 − x phase and the surrounding amorphous matrix were found. Combination of this with the integrated intensity yields values for the CdSxSe1 − x volume fraction of 0.7 to 3%. Mean particle radii between 5 and 7 nm and number densities in the range 1 to 8 × 1016 cm−3 were obtained from fitted Gaussian and log-normal size distributions, respectively.

Brownian dynamics of polydisperse colloidal hard spheres: Equilibrium structures and random close packings

Recently we presented a new technique for numerical simulations of colloidal hard-sphere systems and showed its high efficiency. Here, we extend our calculations to the treatment of both 2- and 3-dimensional monodisperse and 3-dimensional polydisperse systems (with sampled finite Gaussian size distribution of particle radii), focusing on equilibrium pair distribution functions and structure factors as well as volume fractions of random close packing (RCP). The latter were determined using in principle the same technique as Woodcock or Stillinger had used. Results for the monodisperse 3-dimensional system show very good agreement compared to both pair distribution and structure factor predicted by the Percus-Yevick approximation for the fluid state (volume fractions up to 0.50). We were not able to find crystalline 3d systems at volume fractions 0.50–0.58 as shown by former simulations of Reeet al. or experiments of Pusey and van Megen, due to the fact that we used random start configurations and no constraints of particle positions as in the cell model of Hoover and Ree, and effects of the overall entropy of the system, responsible for the melting and freezing phase transitions, are neglected in our calculations. Nevertheless, we obtained reasonable results concerning concentration-dependent long-time selfdiffusion coefficients (as shown before) and equilibrium structure of samples in the fluid state, and the determination of the volume fraction of random close packing (RCP, glassy state). As expected, polydispersity increases the respective volume fraction of RCP due to the decrease in free volume by the fraction of the smaller spheres which fill gaps between the larger particles.

Absorption properties of CdS nanocrystals in glasses; evidence of both weak and strong confinement regimes

Experimental evidence of both weak and strong confinement regimes is reported on CdS nanocrystals embedded in glass matrix. Classic methods for nanocrystallite preparation meet a principal difficulty, the polydispersion in size of crystallites due to several difficulties such as coalescence and decomposition of particles with time and high temperatures. In this work, we used a new route to elaborate CdS-doped sodium borosilicate glass from gel formed in an aqueous medium. Our vitreous matrix is fully and swiftly densified at relatively low temperature, providing us with CdS nanocrystallites yielding fine band-edge structure and small size dispersion. Low temperature absorption spectra have been interpreted in terms of excitons and electron-hole confinements, taking account of both a Lorentzian broadening of the energy states inside each nanocrystal and a Gaussian size-distribution. It has been shown that, for very small crystallites, the strong blue-shift of the absorption edge due to the quantum size effects, is partially compensated by a red-shift associated to the size distribution.

Preparation of π-vi Semiconductor Nanocrystallites in a Glass Matrix Using Chalcogenizing Agent: Application to cdse

ABSTRACTA new route for preparing CdX (X = S, Se, Te, S+Se) nanocrystallites dispersed in a sodium borosilicate glass matrix from a hydrogel is proposed. Chalcogenizing complexing molecules - for instance a mixture of NH4SCN + H2SeO3 - introduced in the starting solution allowed an in situ crystallite preparation concomitant to gel densification. Prevention of crystallite oxidation is thus obtained. Moreover, coalescence is minimized because of the low gel-glass transition temperature. Low temperature absorption spectra have been interpreted in terms of exciton and electron-hole confinements, accounting for both an intrinsic broadening of energy states inside each nanocrystal and a Gaussian size distribution. Crystallite sizes and size dispersion can be adjusted by changing the initial Cd concentration. The crystallinity of the nanoparticles without change in dispersion is strongly improved by thermal treatment above the Tg of the glass matrix.

Non-Arrhenius response of glass-forming liquids.

A Gaussian size distribution of independently relaxing domains is used to model the response of various glass-forming liquids. With a single temperature-dependent parameter, the model accurately characterizes the observed dielectric susceptibility of salol and glycerol [P. K. Dixon et al., Phys. Rev. Lett. 65, 1108 (1990); N. Menon et al., J. Non-Cryst. Solids 141, 61 (1992)] over more than 13 orders of magnitude in frequency. The quality and range of these data allow quantitative confirmation of all assumptions of the model. As a function of temperature, the model gives excellent agreement with observed asymptotic relaxation rates (${\mathit{w}}_{\mathrm{\ensuremath{\infty}}}$) via [ln(l/${\mathit{w}}_{\mathrm{\ensuremath{\infty}}}$)-ln(1/${\mathit{w}}_{0}$)]\ensuremath{\propto}s\ifmmode\bar\else\textasciimacron\fi{}, where s\ifmmode\bar\else\textasciimacron\fi{} is a temperature-dependent average domain size, and ${\mathit{w}}_{0}$ a constant intrinsic relaxation rate. Thus, the model provides a physical explanation for non-Arrhenius primary response, without resorting to the three adjustable parameters of the Vogel-Tammann-Fulcher law.

Slow Magnetic Relaxation in Iron: A Ferromagnetic Liquid

The remanent magnetization of single-crystal iron whiskers has been measured from 10(-5) to 10(4) seconds after the removal of an applied field. The observed response is accurately modeled by localized magnon relaxation on a Gaussian size distribution of dynamically correlated domains, virtually identical to the distribution of excitations in glass-forming liquids. When fields of less than 1 oersted are removed, some relaxation occurs before 10(-5) second has elapsed; but when larger fields are removed, essentially all of the response can be accounted for by magnon relaxation over the available time window. The model provides a physical picture for the mechanism and observed distribution of Landau-Lifshitz damping parameters.

Crystallite size determination in μc-Ge films by x-ray diffraction and Raman line profile analysis

Experimental Raman spectra were used to evaluate the average crystallite size of μc-Ge films. The experimental curves were fitted with a theoretical expression obtained by Richter et al. assuming a Gaussian size distribution. X-ray Diffraction line profile analysis was performed to obtain crystallite size and shape information. Comparison of the results from both techniques proves that the crystallite dimensions obtained can only be expected to be similar in those cases in which the approximation of “spherical” grains is valid.

Differential Fourier transform technique for the inverse scattering problem

An inversion technique was developed for determining the size distribution of randomly distributed tenuous scatterers from the forward scattering pattern. This technique is applicable for 1-D, 2-D, and 3-D scatterers. It does not require matrix inversion or a priori knowledge of functional forms of the size distribution, and it takes advantage of the fast Fourier transform and digital filtering techniques in spectral analysis. A typical error for 10% noise was within a few percent in the estimation of Gaussian size distribution using 1024-point FFT. The usefulness of this technique in practice was shown in experiments with latex spheres and bacteria.

Computer simulation of random packings of hard spheres

Computer simulation is used to study the effect of particle size distribution on the structure of sediments of hard spheres in three dimensions. The sediments are obtained by ballistic random deposition according to the rain model, followed by a compression process by means of Monte Carlo simulation. It appears that the Monte Carlo technique is an effective method to obtain loose random packings with densities up to 0.60, but that the method is less effective in producing dense random packings with densities of about 0.64. The polydisperse packings clearly show a size segregation effect. The structure of the sediments changes from medium-range ordered to short-range ordered if the width of the Gaussian particle size distribution is increased from 0 to 0.5 mean particle radius units. The pore structure of the sediments is investigated on a 100 3 grid by means of the Hoshen—Kopelman algorithm. It is shown that the pore structure of the loose random packings is such that particles with radii up to 0.15 units can percolate through the sediments.

SANS studies of the microstructure of a three-componnent microemulsion

Small-angle neutron scattering measurements have been performed on a three-component microemulsion system consisting of water, hexane and didodecyl-dimethylammonium bromide. For a water-to-surfactant weight ratio of 0.95 and less than 5 wt% surfactant, these measurements are best fit by a model with a Gaussian size distribution of spherical water droplets in hexane. The average water core radius is determined to be about 2.9 nm. On addition of water while the same water-to-surfactant ratio is maintained, there is some evidence that the basic unit of the microstructure remains a sphere with the same radius. The interaction between the spheres is found to be attractive, and the spheres may be connected for volume fractions of water larger than 5%.