Intercomparison of Approximation Algorithms for the Determination of the Size Distribution of the "Unattached" Fraction of Radon Progeny

Starting in 1996, nonlinear approximation algorithms used for the determination of size distributions of ''unattached'' radon progeny from measurements made with diffusional size classification instruments were compared. Seven participants (one American and six European) took part using various techniques (Simplex, Expectation Maximization, Extreme Value Estimation, Twomey, and Random Walk) which are widely used for this type of work. Simulated input data was supplied to the participants. Their output data indicated that the quality of the results varied according to the algorithm used. This was particularly the case when retrieving parameters from bimodal distributions where large inaccuracies were shown. Variations were found between participants using basically identical algorithms. The influence of measurement uncertainties was investigated and indicated a serious reduction of retrieval accuracy, especially for algorithms with better than average performance for precise data. This work suggests that when high precision results are required, a random walk algorithm should be used and attention should be paid to reducing errors in the input penetration data.     

Novel methods for synthesis of high‐impact polystyrene with bimodal distribution of rubber particle size

By using in situ prepolymerization and radiation curing, high‐impact polystyrene (HIPS) with a bimodal distribution of the size of the rubber particles (bimodal HIPS) was synthesized in the presence of ultrafine full‐vulcanized powdered styrene–butadiene rubber (UFPSBR) and polybutadiene rubber (BR). TEM photographs indicated that UFPSBR was dispersed uniformly as a single particle with a diameter of about 100 nm. On the other hand, bimodal HIPS with different rubber particle size distributions could also be obtained by blending HIPS and UFPSBR grafting styrene (UFPSBR‐g‐St) with different grafting yields. The bimodal HIPS with the smallest rubber particle size, at about 100 nm, could be prepared by blending the monomodal HIPS containing big rubber particles with polystyrene/UFPSBR. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Influence of Particle Size Distribution of Bimodal Reactive Alumina on Properties of LCC Refractory Castables

The effect of particle size distribution of alumina has been investigated for silica-free tabular alumina low cement castables( LCC). Three different combinations of alumina have been included in the matrix formulation of the castables. All the three combinations are composed of a bimodal reactive alumina and a fine ground monomodal reactive alumina. The first A1 and second A2 combinations are respectively composed of bimodal and monomodal aluminas from Alteo,with a different fine /coarse particles ratio for the bimodal alumina. The two Alteo combinations have been compared with a third combination C composed of a bimodal commercially available grade and a monomodal commercially available grade. Optimization of particle size packing has been performed for the three different formulations using the Dinger and Funk model. With this optimization,the two formulations based on Alteo material( PFR,PBR and PFR40) achieve the same level of performance in applicative tests( flowability,cold physical properties,mechanical resistance,crystalline phases,thermal shocks and corrosion) as reference solutions on the market.     

Size distribution of polymers during the photoinitiated free-radical copolymerization of methyl methacrylate and ethylene glycol dimethacrylate

Summary Photoinitiated methyl methacrylate-ethylene glycol dimethacrylate (MMA/EGDM) copolymerization has been investigated in toluene at a monomer concentration of 35 w/v %. Diphenyl-2,4,6-trimethylbenzoylphosphine oxide (DPTPO) was used as a photoinitiator at 0.3 wt% concentration. Monomer conversions and the size distribution of the polymer molecules were measured as a function of the reaction time up to the onset of macrogelation. Compared to the photoinitiators benzoin or benzoin derivatives, gelation process proceeds at much higher rates in the presence of DPTPO. The size distribution curves obtained by size-exclusion chromatography (SEC) change from monomodal to bimodal distributions as the polymerization proceeds. Strongly bimodal SEC curves were obtained in the close vicinity of the gel point. This finding confirms the coagulation type gelation mechanism of compact primary particles. It also indicates that the present gelation theories cannot describe the structure dependent kinetics of free-radical crosslinking copolymerization.     

The Formation of Aerosol Particles from Solution-Based Pressurized Metered Dose Inhalers and Implications of Incomplete Droplet Drying: Theoretical and Experimental Comparison

The aerosol particle size distributions of solution-based pressurized metered dose inhalers containing 15%w/w ethanol and different quantities of nonvolatile component (NVC) (drug and glycerol) were evaluated at 25°C and 55°C, using a custom-built heating rig that preheated air prior to aerosolization. Particle size distributions were assessed using an Andersen cascade impactor and mass‐weighted cumulative aerodynamic diameter distributions were compared to a theoretical model that predicts the final size distribution, based on initial droplet size, vapor pressure of the formulation containing HFA 134a and percent NVC. In general, the mass median aerodynamic diameter was proportional to NVC^1/3, with experimental particle size distributions following theoretical values. However, when comparing theoretical vs. experimental data over the range of mass-weighted cumulative aerodynamic diameter distributions between 10 and 90%, the 55°C experimental measurements more closely fitted the theoretical equation when compared to 25°C. This was attributed to incomplete drying of some of the larger initial droplets prior to impaction. Additionally, postinduction port measurements of volumetric size distribution using laser diffraction, showed a reduction in median particle diameter at 55°C, compared to 25°C and a change from bimodal to monomodal distribution, indicating complex drying kinetics under ambient conditions.

Copyright 2015 American Association for Aerosol Research     

Emulsion copolymerization in a tubular reactor

A study was conducted on the emulsion copolymerization of vinyl acetate and butyl acrylate in a tubular reactor. It was performed at a constant temperature of 60°C and at different fluid velocities and feed compositions. Conversion, particle size distribution, and copolymer composition were measured, respectively, with gravimetric method, laser light scattering, and nuclear magnetic resonance. Maximum conversions were found for each of the monomer compositions; this maximum conversion varied, however, with the recipe used. The amount of butyl acrylate has a direct effect on the number of particles and on the final conversion. In lower levels of butyl acrylate particle size distribution is wide and bimodal. High levels of butyl acrylate leads to narrow and monomodal particle size distribution. Therefore the level of butyl acrylate and the velocity of fluid flowing inside the tube have strong effects on the shape (monomodal‐bimodal) and the width of particle size distributions. This effect may vary at different levels of butyl acrylate and flow rate. The results obtained from copolymer composition show that an alternating block copolymer is made during the reaction. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 75: 833–842, 2000     

Correlation between molecular structure and copolymer composition and the Mark-Houwink constants of methyl methacrylate/N-phenylmaleimide copolymers

The determination of Mark-Houwink constants using gel permeation chromatography data, based on a universal calibration and Ubbelohde capillary viscosimetry, for methyl methacrylate (MMA)/N-phenylmaleimide (NPI) copolymers of different molar mass or molar mass distribution has been examined. Mark-Houwink constants of bimodal molar mass distributions could not be obtained. They give, under the prerequisite of similar chemical composition, considerable deviations from the usual relation between intrinsic viscosity and molar mass. The Mark-Houwink constants determined for MMA/NPI copolymers with monomodal molar mass distributions containing 20–30 mol-% NPI at 35°C in tetrahydrofuran were K = 1.34 · 10^–4 and α = 0.73. Comparison with poly(methyl methacrylate) (PMMA) under the same measurement conditions shows constants of the Mark-Houwink relation with K = 1.43 · 10^–4 and α = 0.71, similar to those for monomodal MMA/NPI copolymers with 20–30 mol-% NPI. Higher contents of NPI in monomodal MMA/NPI copolymers or poly(N-phenylmaleimide) (PNPI) give no clear linear proportionality of the intrinsic viscosity to molar mass.     

Microstructure and high temperature 4-point bending creep of sol–gel derived mullite ceramics

Four-point bending creep behavior of mullite ceramics with monomodal and bimodal distribution of grain sizes was studied in the temperature range of 1320–1400 °C under the stresses between 40 and 160 MPa. Mullite ceramic with bimodal grain size distribution was prepared using aluminum nitrate nonahydrate as alumina precursor. When γ-Al₂O₃ or boehmite were used as alumina precursors, mullite grains are equiaxial with mean particle size of 0.6 μm for the former and 1.3 μm for the latter alumina precursor. The highest creep rate exhibited the sample with monomodal morphology and grains in size of 0.6 μm, which is about one order of magnitude greater than that for the monomodal morphology but with grains in size of 1.3 μm. The highest activation energy for creep (Q = 742 ± 33 kJ/mol) exhibits mullite with equiaxial grains of 1.3 μm, whereas for sample with smaller equiaxial grains the activation energy is much smaller and similar to mullite ceramics with bimodal grain morphology. Intergranular fracture is predominant near the tension surface, while transgranular more planar fracture is predominant near the compression surface zone.     

Effect of SiCp multimodal distribution on pitting behavior of Al/SiCp composites prepared by reactive infiltration

The effect of coated-SiC_p multimodal-size-distribution on the pitting behavior of Al/SiC_p composites was investigated. α-SiC powders (10, 54, 86, and 146 μm) were properly mixed and coated with silica to produce porous preforms with 0.6 volume fraction of the reinforcement with monomodal, bimodal, trimodal, and cuatrimodal size distribution. The preforms were infiltrated with the alloy Al–13 Mg–1.8Si (wt.%) in argon followed by nitrogen at 1100 ºC for 60 min. The composites were characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM) before and after cyclic polarization measurements in 0.1 M NaCl de-aerated solutions. Results show that whereas corrosion and passivation potentials are not influenced with increase in SiC_p particle size distribution, favorably, the susceptibility to pitting corrosion decreases. This beneficial effect is ascribed to the smaller area of the alloy matrix exposed to the chloride solution with augment in particle size distribution, substantially when going from monomodal to bimodal SiC_p particle size distribution.     

Low-Field High-Resolution PFG-NMR to Predict the Size Distribution of Inner Droplets in Double Emulsions

In double emulsions, the inner and outer droplet size distribution (DSD) determines the quality of the double emulsion and is therefore essential to be measured. Low-field high-resolution pulsed-field gradient nuclear magnetic resonance is used to measure the inner DSD in water-in-oil-in-water double emulsions. The Gaussian phase distribution approach is employed with a mixture of two normal distributions to predict bimodal inner droplets. This approach allows the prediction of the swelling of inner droplet during storage of double emulsions, and thus to validate a phenomenological population balance model estimating inner droplet swelling. Only a fraction of the inner droplets are found to swell during storage, due to differences in the Laplace pressure, thus leading to the formation of a bimodal size distribution of the inner droplets. Practical Applications: This methodology is useful to predict the evolution of double emulsions during storage, in a wide range of applications, such as food and pharmaceutical products.     

Random particle packing with large particle size variations using reduced-dimension algorithms

We present a reduced-dimension, ballistic deposition, Monte Carlo particle packing algorithm and discuss its application to the analysis of the microstructure of hard-sphere systems with broad particle size distributions.We extend our earlier approach (the “central string”algorithm) to a reduced-dimension, quasi-3D approach. Our results for monomodal hard-sphere packs exhibit a calculated packing fraction that is slightly less than the generally accepted value for a maximally random jammed state. The pair distribution functions obtained from simulations of composite structures with large particle size differences demonstrate that the algorithm provides information heretofore not attainable with existing simulation methods, and yields detailed understanding of the microstructure of these composite systems.     

Studies of the Effects of Particle Size Distribution on the Packing Efficiency of Particles

In the studies of pigment volume effects in paint films, particle packing has been shown to be very important. The effects of particle size distribution on this packing has been known but has received little quantitative consideration. In this paper we consider the packing of real and model continuous distributions of particle sizes. An extension of an algorithm for the calculation of random densest packing is given which applies to continuous distributions. Using a log-normal distribution as a model, the effect of the width of a single distribution on packing is considered. Mixtures of distributions are also considered with the calculation of packing efficiency as a function of mean size ratio and distribution widths. Maxima are shown to occur in the packing efficiency of mixtures of distributions as a function of the volume fractions of the individual distributions. The implications of these packing variations in real systems are then discussed.     

分批加分散剂时苯乙烯悬浮聚合瞬间液滴直径和分布

在苯乙烯悬浮聚合中研究了分批加分散剂体系磷酸三钙(TCP)或 TCP 和聚乙烯醇(PVA)时的加入方式对瞬间液滴大小和分布的影响。考察了体系液滴分散和合一的特点。实验观察到分批加入分散剂体系时液滴大小分布的变化规律,呈由单峰分布过渡到双峰分布,最后又发展为单峰分布。这与分散剂体系一次加入相比,后者仅出现单峰分布逐渐过渡到双峰分布。     

40 Jahre Darstellung von Partikelgrößenverteilungen — und immer noch falsch?

While the quality and variety of particle size measuring instruments have improved dramatically in recent years, both in their accuracy and in their speed of measurement, the representation of the measured data — particularly the density distribution — has generally received little attention from the manufacturers. The depiction of a continuous density distribution by a percentage value on the ordinate makes no sense. Although logarithmic density distributions serve a purpose with distinctly separated bi‐ or multimodal distributions (by analogy with analytical chemical spectra), they can lead to serious interpretation errors in the case of the monomodal distribution. Thus for monomodal distributions either the density distribution q_r(x) should be used or no representation of the density distribution attempted.     

Distinguishing between Two Aerosol Size Distributions

A technique is presented to quantitatively determine the similarity or dissimilarity between aerosol size distributions measured with cascade impactors. The method is useful regardless of the mass loading as long as an accurate size distribution can be obtained from the data. The technique uses lognormal best fits of the data and an augmented Student's t-test to quantitatively determine the difference between the two particle size distributions.     

Studies in Solvent Extraction Using Polyaphrons. I. Size Distribution,Stability, and Flotation of Polyaphrons

Abstract

Predispersed solvent extraction (PDSE) is a promising technique for the treatment of wastewater containing low solubility, hydrophobic contaminants. A stable predispersed organic solvent in the form of polyaphrons of very small diameter results in high surface areas with a minimum energy requirement for mass transfer of solutes from the aqueous phase to the organic solvent. PDSE should greatly improve the performance of a conventional extraction process. This paper focuses on the characterization and size distributions of polyaphrons. Polyaphrons were generated using different cationic, anionic, and nonionic surfactants in water and an oil-soluble nonionic surfactant. Kerosene was used as the organic solvent to form the polyaphrons. Size distributions were obtained using a particle size analyzer. The optimal instrument parameters (sample quantity, optical parameters, run time, etc.) were identified for these measurements. The size distribution based on volume fraction was found to show a bimodal behavior, with peak size maxima between 1–3 and 10–30 μm for all the polyaphrons. The effects of different surfactant types, surfactant concentrations, and storage times on the size distribution spectrum of polyaphrons were studied. The size distribution of different polyaphrons before and after flotation in an aqueous column using colloidal gas aphrons (CGAs) was also studied. Flotation was deduced to occur as a result of electrostatic forces between the CGAs and polyaphrons.     

Effect of loading-rate on fracture micromechanism of methylmethacrylate-butadiene-styrene polymer blend

Methylmethacrylate-butadiene-styrene (MBS) polymer blends having two different types of rubber particle distribution, monomodal and bimodal, were prepared, and their fracture properties and fracture mechanisms were investigated under quasi-static and impact loading. A fracture property, maximum J-integral J_max, was evaluated at both loading-rates, and it was shown that J_max values of the bimodal MBSs are much greater than that of the monomodal with small particles, and slightly better than that of the monomodal with large particles. Thick damage zones were observed in the crack-tip regions in the bimodal and monomodal with large particles, indicating larger energy dissipation during fracture initiation than in the monomodal with small particles in which damage zone is much thinner. TEM micrographs exhibit that extensive plastic deformation under quasi-static rate and multiple craze formation under impact loading rate are the primary toughening mechanisms in the bimodal MBS blends. By assessing both fracture properties and transparency, the bimodal blend with blend ratio: 2.5/7.5 (=140 nm/2.35 μm; total rubber particle content is 10 wt%) was proved to show the best performance as MBS polymer blend with satisfiable transparency and high fracture resistance.     

Reformulation of an Aqueous Alumina Slip Based on Modification of Particle-Size Distribution and Particle Packing

Six alumina casting slips with particle-size distributions varying from 44 to 0.1 μm were examined. Particle packing was calculated using the approach of Andreasen. Viscosity, green density, and pore-size distribution were measured. It was found that contouring the intermediate size distribution for particles finer than 15 μm provided the most desirable viscosity for slips composed of wide size distributions. For slips containing 50 vol% solids, the lowest viscosity obtained was 196 × 10⁻³ N · s/m² (with a two-component size distribution), and a green density of 2.52 g/cm³ (65% of theoretical) was achieved with a ternary system. These casts had bimodal pore-size distributions centered around approximately 1 and 0.1μm.     

Dilithium initiators based on 1,3-bis(1- phenylethenyl)benzene. Tetrahydrofuran and lithium sec-butoxide effects

The adduct (3) from 2 moles of sec-butyllithium with 1,3-bis(1-phenyl-ethenyl)benzene has been prepared and evaluated as a hydrocarbon-soluble, dilithium initiator for butadiene and styrene polymerization in cyclohexane or benzene solution. Under high vacuum conditions with purified reagents, bimodal molecular weight distributions are observed for polybutadienes with M _n < 150 × 10³ g/mol and for polystyrenes with M _n < 50 × 10³ g/mol; monomodal distributions are observed only for higher molecular weights. Addition of tetrahydrofuran ([THF]/[Li] = 14 to 32) or preformed lithium sec-butoxide ([LiOBu]/[3] = 1·1) produces narrow, monomodal molecular weight distributions even at M _n = 26·2 × 10³ g/mol polybutadiene and at M _n = 10 × 10³ g/mol for polystyrene. Added lithium sec-butoxide is the preferred additive since high 1,4-polybutadienes are obtained. These results provide an explanation for the contradictory results reported previously; under less rigorous experimental conditions, oxygen and hydroxylic impurities can form lithium alkoxides in situ.