Log-normal Size Distribution Research Articles

Comparing nadir and limb observations of polar mesospheric clouds: The effect of the assumed particle size distribution

Nadir viewing observations of Polar Mesospheric Clouds (PMCs) from the Cloud Imaging and Particle Size (CIPS) instrument on the Aeronomy of Ice in the Mesosphere (AIM) spacecraft are compared to Common Volume (CV), limb-viewing observations by the Solar Occultation For Ice Experiment (SOFIE) also on AIM. CIPS makes multiple observations of PMC-scattered UV sunlight from a given location at a variety of geometries and uses the variation of the radiance with scattering angle to determine a cloud albedo, particle size distribution, and Ice Water Content (IWC). SOFIE uses IR solar occultation in 16 channels (0.3–5μm) to obtain altitude profiles of ice properties including the particle size distribution and IWC in addition to temperature, water vapor abundance, and other environmental parameters. CIPS and SOFIE made CV observations from 2007 to 2009. In order to compare the CV observations from the two instruments, SOFIE observations are used to predict the mean PMC properties observed by CIPS. Initial agreement is poor with SOFIE predicting particle size distributions with systematically smaller mean radii and a factor of two more albedo and IWC than observed by CIPS. We show that significantly improved agreement is obtained if the PMC ice is assumed to contain 0.5% meteoric smoke by mass, in agreement with previous studies. We show that the comparison is further improved if an adjustment is made in the CIPS data processing regarding the removal of Rayleigh scattered sunlight below the clouds. This change has an effect on the CV PMC, but is negligible for most of the observed clouds outside the CV. Finally, we examine the role of the assumed shape of the ice particle size distribution. Both experiments nominally assume the shape is Gaussian with a width parameter roughly half of the mean radius. We analyze modeled ice particle distributions and show that, for the column integrated ice distribution, Log-normal and Exponential distributions better represent the range of masses that contribute to the IWC. We further show that agreement between SOFIE and CIPS is further improved with the assumption of either Log-normal or Exponential ice particle size distributions. This improvement suggests that the range of mass bearing particle radii is larger, but not significantly shifted from what is obtained by assuming a Gaussian distribution. The assumption of an Exponential particle size distribution, as shown to be justifiable here, has the attractive benefits of being characterized with a single parameter, the mean radius, which greatly facilitates studies of the spatial and temporal variation of PMC particle size distributions as well as comparisons between observations and models. Overall, our results represent a validation of both the CIPS and SOFIE datasets.

Synthesis, structural characterization and magnetic properties of Fe/Pt core-shell nanoparticles

Structural and magnetic properties of Fe/Pt core-shell nanostructure prepared by a sequential reduction process are reported. Transmission electron microscopy shows nearly spherical particles fitting a lognormal size distribution with Do = 3.0 nm and distribution width λD = 0.31. In x-ray diffraction, Bragg lines only from the Pt shell are clearly identified with line-widths yielding crystallite size = 3.1 nm. Measurements of magnetization M vs. T (2 K–350 K) in magnetic fields up to 90 kOe show a blocking temperature TB = 13 K below which hysteresis loops are observed with coercivity HC increasing with decreasing T reaching HC = 750 Oe at 2 K. Temperature dependence of the ac susceptibilities at frequencies fm = 10 Hz–5 kHz is measured to determine the change in TB with fm using the Vogel-Fulcher law. This analysis shows the presence of significant interparticle interaction, the Neel-Brown relaxation frequency fo = 5.3 × 1010 Hz and anisotropy constant Ka = 3.6 × 106 ergs/cm3. A fit of the M vs. H data up to H = 90 kOe for T > TB to the modified Langevin function taking particle size distribution into account yields magnetic moment per particle consistent with the proposed core-shell structure; Fe core of 2.2 nm diameter and Pt shell of 0.4 nm thickness.

Magnetic relaxation and correlating effective magnetic moment with particle size distribution in maghemite nanoparticles

The role of particle size distribution inherently present in magnetic nanoparticles (NPs) is examined in considerable detail in relation to the measured magnetic properties of oleic acid-coated maghemite (γ-Fe2O3) NPs. Transmission electron microscopy (TEM) of the sol–gel synthesized γ-Fe2O3 NPs showed a log-normal distribution of sizes with average diameter 〈D〉=7.04nm and standard deviation σ=0.78nm. Magnetization, M, vs. temperature (2–350K) of the NPs was measured in an applied magnetic field H up to 90kOe along with the temperature dependence of the ac susceptibilities, χ′ and χ″, at various frequencies, fm, from 10Hz to 10kHz. From the shift of the blocking temperature from TB=35K at 10Hz to TB=48K at 10kHz, the absence of any significant interparticle interaction is inferred and the relaxation frequency fo=2.6×1010Hz and anisotropy constant Ka=5.48×105erg/cm3 are determined. For T<TB, the coercivity HC is practically negligible. For T>TB, the data of M vs. H up to 90kOe at several temperatures are analyzed two different ways: (i) in terms of the modified Langevin function yielding an average magnetic moment per particle μp=7300(500) μB; and (ii) in terms of log-normal distribution of moments yielding 〈μ〉=6670µB at 150K decreasing to 〈μ〉=6100µB at 300K with standard deviations σ≃〈μ〉/2. It is argued that the above two approaches yield consistent and physically meaningful results as long as the width parameter, s, of the log-normal distribution is less than 0.83.

Chronoamperometric study of elemental sulphur (S) nanoparticles (NPs) in NaCl water solution: new methodology for S NPs sizing and detection.

BackgroundElemental sulfur (S) persists in natural aquatic environment in a variety of forms with different size distributions from dissolved to particulate. Determination of S speciation mainly consists of the application of chromatographic and electrochemical techniques while its size determination is limited only to the application of microscopic and light scattering techniques. S biological and geochemical importance together with recent increases of S industrial applications requires the development of different analytical tools for S sizing and quantification. In recent years the use of electrochemical measurements as a direct, fast, and inexpensive technique for the different nanoparticles (NPs) characterization (Ag, Au, Pt) is increasing. In this work, electrochemical i.e. chronoamperometric measurements at the Hg electrode are performed for determination of the size distribution of the S NPs.ResultsS NPs were synthesized in aqueous medium by sodium polysulphide acidic hydrolysis. Chronoamperometric measurements reveal the polydisperse nature of the formed suspension of S NPs. The electrochemical results were compared with dynamic light scattering measurements parallel run in the same S NPs suspensions. The two methods show fairly good agreement, both suggesting a log-normal size distribution of the S NPs sizes characterized by similar parameters.ConclusionsThe preliminary results highlight the amperometric measurements as a promising tool for the size determination of the S NPs in the water environment.

Optical and radiative-transfer properties of mixed atmospheric aerosols

The optical and radiative-transfer properties of mixed atmospheric aerosols have been investigated. The aerosol medium is considered as a plane-parallel anisotropic scattering medium with diffusive reflecting boundaries and containing an internal radiation source. The basic components are defined by their complex refractive index, a lognormal size distribution and humidity dependence in hygroscopic particles. The aerosol particles are assumed to be spherical, so the scattering parameters in the form of single scattering albedo, asymmetry factor, scattering, absorption, extinction efficiencies and linear anisotropic coefficient are calculated using the Mie theory. The calculations have been performed for individual aerosol particles, internal and external mixing media. Radiation transfer problem through the considered aerosol medium has been solved in terms of the solution of the corresponding source-free problem with simple boundary conditions. For the solution of the source-free problem, the Variational Pomraning–Eddington technique has been employed. The variation of the radiative-transfer properties (partial radiative fluxes at the medium boundaries) have been calculated and represented graphically for the different aerosols with their different mixing states. A comparison of the obtained results versus available published data has been performed and a very good agreement was observed.

On the relationship between hydrodynamic characteristics and the kinetics of flotation. Part II: Model validation

The estimation of the flotation rate constant is generally considered difficult because of the number of variables – not always measurable – determining its value. Among them, the particle size distribution and hydrodynamic characteristics are considered key elements.Part 1 of this paper introduced the interfacial area of bubbles (Ib) as a hydrodynamic variable providing more information about the size distribution than the bubble surface area flux (Sb). Fundamental expressions were proposed to characterize Ib using the population mean and standard deviation. Experimental results indicated that for lognormal bubble size distributions, Ib correlates very well with the gas hold-up and d32.Part 2 investigates the correlation between the flotation rate constant and particle size as well as given hydrodynamic variables using a Projection to Latent Structures (PLS) analysis. The tests were conducted under ‘ideal’ conditions (i.e. shallow froth, low mineral concentration and pure mineral particles). Results suggest that for the fine particle sizes, the bubble surface area flux (Sb) should be considered for the kinetic constant modeling. For coarser particle, the gas hold-up (εg) is the determining parameter. In practice though, the particle size distribution often lies between these two extreme cases, and can either span a very large range or contains intermediate size particles. In such cases, the interfacial area of bubbles (Ib) better correlates with the flotation kinetics.

Closed‐Form Model for Hydraulic Properties Based on Angular Pores with Lognormal Size Distribution

We previously presented a mathematical model for hysteretic soil hydraulic properties based on bundles of angular pores. Upscaling to sample‐scale hydraulic properties was done analytically, assuming a Gamma density distribution of pore sizes. The required parameter constraint for getting the closed‐form solution limited the model's applicability for soils with wide pore‐size distributions. The objective of this study was to improve the model by developing a new analytical solution based on a lognormal density function of the pore‐size distribution. Closed‐form expressions were derived for liquid retention, saturated–unsaturated hydraulic conductivity, liquid–vapor interfacial area, and specific surface area at the sample scale. The new model was applied to retention and conductivity data for three soils with different pore‐size distributions. The results show that the previous model is suitable only for sandy materials, whereas the new one describes the soil hydraulic functions of a wider range of soil types quite well.

ELISPOTs Produced by CD8 and CD4 Cells Follow Log Normal Size Distribution Permitting Objective Counting.

Each positive well in ELISPOT assays contains spots of variable sizes that can range from tens of micrometers up to a millimeter in diameter. Therefore, when it comes to counting these spots the decision on setting the lower and the upper spot size thresholds to discriminate between non-specific background noise, spots produced by individual T cells, and spots formed by T cell clusters is critical. If the spot sizes follow a known statistical distribution, precise predictions on minimal and maximal spot sizes, belonging to a given T cell population, can be made. We studied the size distributional properties of IFN-γ, IL-2, IL-4, IL-5 and IL-17 spots elicited in ELISPOT assays with PBMC from 172 healthy donors, upon stimulation with 32 individual viral peptides representing defined HLA Class I-restricted epitopes for CD8 cells, and with protein antigens of CMV and EBV activating CD4 cells. A total of 334 CD8 and 80 CD4 positive T cell responses were analyzed. In 99.7% of the test cases, spot size distributions followed Log Normal function. These data formally demonstrate that it is possible to establish objective, statistically validated parameters for counting T cell ELISPOTs.

Effects of process method and quiescent coarsening on dispersed-phase size distribution in polymer blends: comparison of solid-state shear pulverization with intensive batch melt mixing

We compare how solid-state shear pulverization (SSSP), batch melt mixing (BMM), and static melt-state annealing affect the morphology of an immiscible blend of polypropylene (PP) and ethylene-α-olefin copolymer (EOC). For 85/15 wt% PP/EOC blends, SSSP and BMM led to log-normal distributions of dispersed-phase particle size. The SSSP blend had smaller average particle diameters (e.g., D n = 0.24 μm) and a narrower particle size distribution (e.g., D w/D n = 1.17; D v/D n = 1.56) than the BMM blend (D n = 0.28 μm; D w/D n = 1.25; D v/D n = 1.79). The fact that BMM is subject to thermodynamically and flow-induced coalescence while SSSP is not, can lead to smaller particle sizes and a narrower distribution by SSSP. Although annealing at 200 °C for 30 and 90 min led to continuous growth of average particle size in the BMM blend, the particle-size dispersity remained virtually unchanged. In contrast, after 30-min annealing at 200 °C, the SSSP blend showed less growth in $$D_{{_{n} }}^{{^{3} }}$$ than the BMM blend but a dramatic increase in particle-size dispersity and a loss of the log-normal size distribution. Between 30 and 90 min, there was at most slight growth in $$D_{{_{n} }}^{{^{3} }}$$ , consistent with partial compatibilization caused by in situ block copolymer formation during SSSP, and major reductions in D w/D n and D v/D n close to those of the BMM blend and recovery of the log-normal size distribution. These results suggest that caution should be used in correlating immiscible blend properties to a particular average particle size as that value may not reflect possible complexity of the underlying size distribution.

Inverse Problem of Air Filtration of Nanoparticles: Optimal Quality Factors of Fibrous Filters

Application of nanofibers has become an emerging approach to enhance filtration efficiency, but questions arise about the decrease in Quality factor (QF) for certain particles due to the rapidly increasing pressure drop. In this paper, we theoretically investigate the QF of dual‐layer filters for filtration of monodisperse and polydisperse nanoparticles. The inverse problem of air filtration, as defined in this work, consists in determining the optimal construction of the two‐layer fibrous filter with the maximum QF. In comparison to a single‐layer substrate, improved QF values for dual‐layer filters are found when a second layer with proper structural parameters is added. The influences of solidity, fiber diameter, filter thickness, face velocity, and particle size on the optimization of QF are studied. The maximum QF values for realistic polydisperse particles with a lognormal size distribution are also found. Furthermore, we propose a modified QF (MQF) accounting for the effects of energy cost and flow velocity, which are significant in certain operations. The optimal MQF of the dual‐layer filter is found to be over twice that of the first layer. This work provides a quick tool for designing and optimizing fibrous structures with better performance for the air filtration of specific nanoparticles.

On the Use of Nonlinear Boundary-Value Problems to Estimate the Cloud-Formation Potential of Aerosol Particles

This paper investigates the transient growth of aerosol particles in a humid environment. It seeks to explore the dependence of the fraction of droplet-forming particles on statistical properties of the distribution of dry particle diameters, as well as on the rate of temperature decay associated with vertical motion through the atmosphere. Low-dimensional, autonomous models are investigated using basic tools of dynamical systems analysis that establish the parameter-dependent existence and stability of families of equilibrium distributions of wet particle diameters. In the fully nonautonomous case, an original heuristic parameterization of the fraction of droplet-forming particles is derived in terms of a scalar, nonlinear boundary-value problem. To address the failure of the heuristic parameterization to account for the potential of a dynamic reversal of growth following an initial increase in particle diameter, a finely resolved, high-dimensional boundary-value formulation for the aerosol dynamics is investigated using methods of numerical continuation. In order to reduce the computational complexity of the numerical scheme, an adaptive asynchronous discretization algorithm is developed in which the state variables are partitioned across distinct temporal meshes. Results obtained from the proposed numerical scheme are compared with the estimated fractions of droplet-forming particles based on available approximate criteria in the literature and demonstrate relative errors as large as 20The analysis further uncovers a hitherto-unknown linear relationship between the arithmetic expectation and variance of a log-normal size distribution of dry diameters for fixed fractions of droplet-forming particles.

RE-EXAMINING SUNSPOT TILT ANGLE TO INCLUDE ANTI-HALE STATISTICS

Sunspot groups and bipolar magnetic regions (BMRs) serve as an observational diagnostic of the solar cycle. We use Debrecen Photohelographic Data (DPD) from 1974-2014 that determined sunspot tilt angles from daily white light observations, and data provided by Li & Ulrich that determined sunspot magnetic tilt angle using Mount Wilson magnetograms from 1974-2012. The magnetograms allowed for BMR tilt angles that were anti-Hale in configuration, so tilt values ranged from 0 to 360{\deg} rather than the more common $\pm$ 90{\deg}. We explore the visual representation of magnetic tilt angles on a traditional butterfly diagram by plotting the mean area-weighted latitude of umbral activity in each bipolar sunspot group, including tilt information. The large scatter of tilt angles over the course of a single cycle and hemisphere prevents Joy's law from being visually identified in the tilt-butterfly diagram without further binning. The average latitude of anti-Hale regions does not differ from the average latitude of all regions in both hemispheres. The distribution of anti-Hale sunspot tilt angles are broadly distributed between 0 and 360{\deg} with a weak preference for east-west alignment 180{\deg} from their expected Joy's law angle. The anti-Hale sunspots display a log-normal size distribution similar to that of all sunspots, indicating no preferred size for anti-Hale sunspots. We report that 8.4% $\pm$ 0.8% of all bipolar sunspot regions are misclassified as Hale in traditional catalogs. This percentage is slightly higher for groups within 5{\deg} of the equator due to the misalignment of the magnetic and heliographic equators.

Determination of small soot particles in the presence of large ones from time-resolved laser-induced incandescence

A novel strategy for the analysis of time-resolved laser-induced incandescence (TiRe-LII), called two-exponential reverse fitting (TERF), is introduced. The method is based on combined monoexponential fits to the LII signal decay at various delay times and approximates the particle-size distribution as a weighted combination of one large and one small monodisperse equivalent mean particle size without requiring assumption on the particle-size distribution. The effects of particle size, heat-up temperature, aggregate size, and pressure on the uncertainty of this method are evaluated using numerical experiments for lognormal and bimodal size distributions. TERF is applied to TiRe-LII measured in an atmospheric pressure laminar non-premixed ethylene/air flame at various heights above burner. The results are compared to transmission electron microscopy (TEM) measurements of thermophoretically sampled soot. The particle size of the large particle-size class agreed well for both methods. The size of the small particle-size class and the relative contribution did not agree which is attributed to missing information in the TEM results for very small particles. These limitations of TEM measurements are discussed and the effect of the exposure time of the sampling grid is evaluated.

On the relationship between hydrodynamic characteristics and the kinetics of column flotation. Part I: Modeling the gas dispersion

Modeling of flotation has been the subject of many investigations aiming at better understanding the process behavior per se, and as well for process design, control and optimization purposes. With this regard, the importance of hydrodynamic characteristics, either as manipulated or measured variables, are paramount. The interfacial area of bubbles (Ib) is introduced in Part 1 of this paper as a hydrodynamic variable providing more information about the size distribution than the commonly used bubble surface area flux (Sb). Experimental evidence shows that the bubble size distribution can exhibit normal, lognormal, and even multi-modal shape. Unlike the Sauter mean diameter (d32) and Sb, the interfacial area of bubbles is derived from the complete bubble size distribution, and takes into account these specific characteristics. Fundamental expressions are proposed to allow characterising Ib using the population mean and standard deviation. Experimental results indicate that for lognormal bubble size distributions, Ib correlates well with the gas hold-up and d32. Part 2 of the paper analyzes the correlation of gas dispersion characteristics with flotation rate constant.

Magnetic nanoparticles for biophysical applications synthesized by high-power physical dispersion

The low cost and high output methods of high-power physical dispersion: the electrical explosion of wire and the laser target evaporation were elaborated for the production of iron oxide magnetic nanoparticles (MNPs) with controlled dispersion parameters and highly reproducible functional properties. The synthesized MNPs were spherical in shape with mean diameter 10nm and lognormal particle size distribution. The phase composition, shape, particle size and functional properties of MNPs were cross-examined by a variety of contemporary experimental techniques. The phase structure of MNPs corresponds to the inverse spinel of magnetite. Meanwhile, due to the non-equilibrium conditions of the dispersion chemical composition of MNPs is close to maghemite—γ-Fe2O3. Their magnetic properties are reproducible and very close to the single domain superparamagnetic behavior. The stability of the suspensions of these MNPs and their applicability in the biophysical purposes such as magneto-induced heating have been demonstrated.

Grain growth, anomalous scaling, and grain boundary grooving in polycrystalline CdTe thin films

We examine the evolution of the surface morphology as well as the dynamics of grain growth and grain boundary (GB) grooving in polycrystalline CdTe films sputter deposited on CdS/glass substrates. Anomalous scaling behavior is found with local roughness exponent αloc = 1 and global (local) growth exponent β = 0.36 (βloc = 0.14). In good agreement with the scaling relation, βloc = β − nαloc, we obtain the correlation length exponent n=1/z≃0.23. We also find that the grain size coarsening exponent p and GB groove growth exponent βg are both equal to β, while the grain size distribution is well described by a log-normal distribution. These results suggest that GB grooving is responsible for the enhanced anomalous scaling and a deviation from the theoretical prediction of p = 1/2, along with the observed log-normal grain size distribution.

Photocatalytical and antibacterial activity of TiO2 nanoparticles obtained by laser ablation in water

This work focuses on the study of photocatalytic and antibacterial activity of TiO2 nanoparticles synthesized by laser ablation in water. The nanoparticles have a log normal size distribution with a mean diameter of 34nm and are composed by a mixture of small crystallites and disordered TiO2; they show good stability and are extremely pure. High photocatalytic (Methylene-Blue dye discoloration under UV illumination) and antibacterial (tested on Escherichia coli) activities comparable to that of commercial nanoparticles under the same experimental conditions were observed. Optical and structural properties were correlated to the photocatalytic and antibacterial activity, and compared to that of commercial TiO2 nanoparticles. An explanation of the high photo-activity yield is proposed taking into account the nanoparticles structure resulting from the peculiar synthesis procedure.

Bimodal distribution of the magnetic dipole moment in nanoparticles with a monomodal distribution of the physical size

High-frequency applications of magnetic nanoparticles, such as therapeutic hyperthermia and magnetic particle imaging, are sensitive to nanoparticle size and dipole moment. Usually, it is assumed that magnetic nanoparticles with a log-normal distribution of the physical size also have a log-normal distribution of the magnetic dipole moment. Here, we test this assumption for different types of superparamagnetic iron oxide nanoparticles in the 5–20 nm range, by multimodal fitting of magnetization curves using the MINORIM inversion method. The particles are studied while in dilute colloidal dispersion in a liquid, thereby preventing hysteresis and diminishing the effects of magnetic anisotropy on the interpretation of the magnetization curves. For two different types of well crystallized particles, the magnetic distribution is indeed log-normal, as expected from the physical size distribution. However, two other types of particles, with twinning defects or inhomogeneous oxide phases, are found to have a bimodal magnetic distribution. Our qualitative explanation is that relatively low fields are sufficient to begin aligning the particles in the liquid on the basis of their net dipole moment, whereas higher fields are required to align the smaller domains or less magnetic phases inside the particles.

Determination of the optical properties and size dispersion of Si nanoparticles within a dielectric matrix by spectroscopic ellipsometry

We report on a comparative study between dielectric functions of Si nanoparticles (Si-NPs) obtained from Bruggeman effective medium approximation (BEMA), Maxwell-Garnett (MG), and a modified Maxwell-Garnett (MMG) models. Unlike BEMA and MG, a size-distribution dependent dielectric function of Si-NPs is considered in the introduced MMG model. We show that the standard deviation σ of a size distribution can be evaluated by analyzing the imaginary part of the dielectric functions of Si-NPs extracted from BEMA and MMG. In order to demonstrate this, several samples composed of Si-NPs embedded in silicon-rich silicon nitride are investigated by spectroscopic ellipsometry over the photon energy range varying between 2 and 4 eV. Assuming a lognormal size distribution of the Si nanoparticles, it is evidenced that the parameter σ ranges between 1.15 and 1.35. The values of size dispersion deduced by this methodology are in good agreement with TEM observations.

Microstructure and micromechanics of polydisperse granular materials: Effect of the shape of particle size distribution

The uniaxial compression of polydisperse spheres with continuous: normal, log-normal, arbitrary and discrete uniform particle size distribution was modelled with the discrete element method (DEM). The evolution of solid fraction, coordination number and fabric tensor with increasing compressive stress was investigated in granular packings of equal mean particle diameter and standard deviation of particle mean diameter. The study of the relationship between the shape of particle size distribution and the micromechanical properties of granular packings included the determination of the contact forces and the degree of mobilisation of friction in contacts between particles. Slight influence of the shape of continuous particle size distribution on the solid fraction and coordination number in polydisperse packings was observed. The discrete uniform distribution provided the number of contacts lower by 7% as compared to continuous distribution. Concerning the mobilisation of friction in contacts between spheres, the average ratio of the tangential: normal contact forces in packing with discrete distribution was 25% higher than the one calculated for normal particle size distribution.