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Concept: Number density


Drawing from a series of field measurement activities including the Alternative Aviation Fuels Experiments (AAFEX1 and AAFEX2), we present experimental measurements of particle number, size, and composition-resolved mass that describe the physical and chemical evolution of aircraft exhaust plumes on the time scale of 5 sec to 2-3 min. As the plume ages, the particle number emission index initially increases by a factor of 10-50, due to gas-to-particle formation of a nucleation/growth mode, and then begins to fall with increased aging. Increasing the fuel sulfur content causes the initial increase to occur more rapidly. The contribution of the nucleation/growth mode to the overall particle number density is most pronounced at idle power and decreases with increasing engine power. Increasing fuel sulfur content - but not fuel aromatic content - causes the nucleation/growth mode to dominate the particle number emissions to higher powers than for a fuel with “normal” sulfur and aromatic content. Particle size measurements indicate that the observed particle number emissions trends are due to continuing gas-to-particle conversion and coagulation growth of the nucleation/growth mode particles, processes which simultaneously increase particle mass and reduce particle number density. Measurements of nucleation/growth mode mass are consistent with the interpretation of particle number and size data and suggest that engine exit plane measurements may underestimate the total particle mass by much as a factor of between 5 and 10.

Concepts: Particle physics, Experiment, Physical quantities, Particle, Fuel, Plume, Ultra-low sulfur diesel, Number density


Magnesium and its alloys have unique advantages to act as resorbable bone fixation materials, due to their moderate mechanical properties and biocompatibility, which are similar to those of human tissue. However, early resorption and insufficient mechanical strength are the main problems that hinder their application. Herein, the effects of microstructure transformation on the mechanical properties and corrosion performance of Mg-Zn-Mn-Ca were investigated with electrochemical and immersion measurements at 37 °C in a simulated body fluid (SBF). The results showed that the number density of Ca2Mg6Zn3/Mg2Ca precipitates was remarkably reduced and grain sizes were gradually increased as the temperature increased. The alloy that received the 420 °C/24 h treatment demonstrated the best mechanical properties and lowest corrosion rate (5.94 mm/a) as well as presented a compact and denser film than the others. The improvement in mechanical properties could be explained by the eutectic compounds and phases (Mg2Ca/Ca2Mg6Zn3) gradually dissolving into a matrix, which caused severely lattice distortion and facilitated structural re-arrangement of the increased Ca solute. Moreover, the difference in potential between the precipitates and the matrix is the main essence for micro-galvanic corrosion formation as well as accelerated the dissolution activity and current exchange density at the Mg/electrolyte interface. As a result, the best Mg alloys corrosion resistance must be matched with a moderate grain size and phase volume fractions.

Concepts: Blood, Density, Liquid, Physical chemistry, Tensile strength, Alloy, Corrosion, Number density


Precise determination of particle or cell numbers is of importance for a wide array of applications in environmental studies, medical and biological applications, or manufacturing and monitoring applications in industrial production processes. A number of techniques ranging from manual counting to sophisticated equipment (e.g., flow cytometry) are available for this task. However, these methods are either labour intensive, prone to error, or require expensive equipment. Here, we present a fast, simple method for determining the number density of cells or microparticles using a microwell array. We analyze the light transmission of the microwells and categorize the microwells into two groups. As particles/cells contained in a microwell locally reduce the light transmission, these wells displayed a lower average transmission compared to unoccupied microwells. The number density of particles/cells can be calculated by Poisson statistics from the ratio of occupied to unoccupied microwells. Following this approach, the number densities of two different types of microparticles, as well as HeLa and E. Coli cells, ranging over four orders of magnitude were determined. Through the microwell array defined by microfabrication, a simple image recognition algorithm can be used with the formation of aggregates or irregular shaped samples providing no additional difficulty to the microwell recognition. Additionally, this method can be carried out using only simple equipment and data analysis automated by a computer program.

Concepts: Density, Ratio, Flow cytometry, Computer, Computer program, Number, Computer programming, Number density


The continuum decomposition of the Fe-Cr alloys from initial phase separation to steady-state coarsening with concentrations varying from 25 at % Cr and 30 at % Cr to 33 at % Cr aged at 750 K was studied by utilizing three-dimensional phase-field simulations. The dynamic stages of separation of nanoscale Cr-enriched α' phase were distinguished by the evolution of the volume fraction, particle number density and the average particle radius of the α' phase. The stage of steady-state coarsening was characterized with an equilibrium volume fraction and decreasing particle number density. The coarsening rate constant by linear fitting of the cube of average radius and aging time shows an increase with the increasing Cr concentration. The time exponents decrease from the growth and coarsening stage to the steady-state coarsening stage and show a dependence on the particles number density at different concentrations. The quantitative evolutions of α' phase via nucleation growth and spinodal decomposition are theoretically helpful for understanding the microstructure evolution with aging time in Fe-Cr alloys.

Concepts: Fundamental physics concepts, Density, Thermodynamics, Physical quantities, Nucleation, Phase diagram, Spinodal decomposition, Number density


This study proposes a new approach to produce easily redispersible spray-dried lipid-core nanocapsules (LNC) intended for oral administration, evaluating the influence of the particle number density of the fed sample. The proposed approach to develop redispersible spray-dried LNC formulations intended for oral route is innovative, evidencing the needing of an optimization of the initial particle number density in the liquid suspension of nanocapsules. A mixture of maltodextrin and L-leucine (90:10 w/w) was used as drying adjuvant. Dynamic light scattering, turbidimetry, determination of surface area and pore size distribution, electron microscopy and confocal raman microscopy (CRM) were used to characterize the proposed system and to better understand the differences in the redispersion behavior. An easily aqueous redispersion of the spray-dried powder composed of maltodextrin and L-leucine (90:10 w/w) was obtained, depending on the particle number density. Their surface area decreased in the presence of LNC. CRM enabled the visualization of the spatial distribution of the different compounds in the powders affording to better understand the influence of the particle number density of the fed sample on their redispersion behavior. This study shows the need for optimizing initial particle number density in the liquid formulation to develop redispersible spray-dried LNC powders.

Concepts: Electron, Density, Volume, Scattering, Light scattering, Dynamic light scattering, Rayleigh scattering, Number density


This work addresses the pH-triggered distribution and relocation of charge-stabilized gold nanoparticles (AuNPs) incorporated into strong polyelectrolyte brushes. Brush/particle composite materials were investigated under aqueous conditions and at different humidities using neutron and X-ray reflectivity, respectively. X-ray reflectivity measurements complement neutron reflectivity measurements and reveal results that could not be observed by neutron reflectivity measurements. Both methods allow scanning the particle density profile, but due to different contrasts, they are sensitive to different regions within the brush. More specifically, 3-mercaptopropionic acid (MPA)-coated AuNPs were incorporated into poly-[2-(methacryloyloxy)ethyl]trimethylammonium chloride (PMETAC) polyelectrolyte brushes at different pH values. The pH value triggers a change in the AuNP surface charge caused by the pH-sensitivity of the MPA ligands, while the charge of the PMETAC brush is not affected by pH variations. The particle number density as well as the particle distribution depend strongly on the pH value of the incubation medium: a rather non-homogeneous assembly (2D assembly) is found when the PMETAC brush is incubated in AuNP suspension at pH 4, while a more homogeneous assembly (3D assembly) is found when the PMETAC brush is incubated in AuNP suspension at pH 8. The main factor dominating the formation of 2D or 3D assembly is assigned to the particle-particle interaction and not to the particle-polymer interaction. No significant relocation of AuNPs within the brush can be found by changing the environmental conditions. The control of particle amount and distribution within the polymer brush has a strong impact on the optical properties of those composite materials, which is crucial for the fabrication of colorimetric sensors.

Concepts: Acid, Nanoparticle, Density, PH, Composite material, PH indicator, Hydrochloric acid, Number density


Gaussian distribution has been utilized to describe the global number density distribution of ion cloud in the Paul trap, which is known as the thermal equilibrium theory and widely used in theoretical modeling of ion clouds in the ion traps. Using ion trajectory simulations, however, the ion clouds can now also be treated as a dynamic ion flow field and the location-dependent features could now be characterized. This study was carried out to better understand the in-trap ion cloud properties, such as the local particle velocity and temperature. The local ion number densities were found to be heterogeneously distributed in terms of mean and distribution width; the velocity and temperature of the ion flow varied with pressure depending on the flow type of the neutral molecules; and the “quasi-static” equilibrium status can only be achieved after a certain number of collisions, for which the time period is pressure-dependent. This work provides new insights of the ion clouds that are globally stable but subjected to local rf heating and collisional cooling. Graphical Abstract ᅟ.

Concepts: Electron, Density, Molecule, Temperature, Thermodynamics, Normal distribution, Ideal gas, Number density


Onsager’s paper on phase transition and phase coexistence in anisotropic colloidal systems is a landmark in the theory of lyotropic liquid crystals. However, an uncompromising scrutiny of Onsager’s original derivation reveals that it would be rigorously valid only for ludicrous values of the system’s number density (of the order of the reciprocal of the number of particles). Based on Penrose’s tree identity and an appropriate variant of the mean-field approach for purely repulsive, hard-core interactions, our theory shows that Onsager’s theory is indeed valid for a reasonable range of densities.

Concepts: Fundamental physics concepts, Density, Water, Colloid, Liquid, Phase transition, Liquid crystal, Number density


To investigate the relationship in dental Cone-Beam CT (CBCT) between the manufacturer-reported image pixel data and a modified conversion to CT number densities in Hounsfield Units (HU).

Concepts: Pixel, Conversion of units, Number density, Hounsfield scale, Radiodensity


Within the framework of classical density functional theory, the thermodynamic driving forces for CO2 microbubble nucleation have been quantitatively evaluated in the foaming of polypropylene containing amorphous and crystalline structures. After the addition of fluorinated polyhedral oligomeric silsesquioxane particles into the polypropylene matrix, we construct different composite surfaces with nanoscale roughness for bubble nucleation. Meanwhile, as the dissolved CO2 molecules increase, the corresponding CO2/PP binary melts can be formulated in the systems. Due to the roughness effect coupled with the weak interactions of particle-PP, PP chains in the binary melts are depleted from the surfaces, leading to a significant enhancement of osmotic pressure in depletion regions. During the foaming process, a large number of dissolved CO2 molecules are squeezed into the regions, thus local supersaturations are dramatically improved, and the energy barriers for bubble nucleation are dramatically reduced. Moreover, when the nanocomposite surfaces display ordered nanoscale patterns, the energy barriers can be further reduced to their respective minimum values, and the bubble number densities reach their maximum. Accordingly, the bubble number densities can be enhanced by 4 or 5 orders of magnitude for bubbles nucleated on the crystalline or amorphous PP nanocomposite surface. In contrast, when the foaming pressure is increased from 15 to 20 MPa, the elevated bubble number density in the foaming PP matrix is less than one order of magnitude. As a result, the enhancement of local supersaturation induced by the controlled nanoscale roughness is much more effective than that of bulk supersaturation given by high pressure.

Concepts: Fundamental physics concepts, Density, Volume, Thermodynamics, Density functional theory, Nucleation, Bulk density, Number density