Measurement of Particle Density

The apparent particle density (or if the particles have no closed pores, also the true particle density) can be measured by fluid displacement methods, i.e. pyknometry, which are in common use in industry today. The displacement can be measured with either liquids or gases and there are, therefore, two groups of techniques and instruments available, as follows. 

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Particle density is the density of a particle including the pores or voids within the individual solids. It is defined as the weight of the particle divided by the volume occupied by the entire particle. Particle density is sometimes referred to as the material s apparent density. Direct measurement of particle density can be made by immersing a known quantity of the material in a nonwetting fluid, such as mercury, which does not penetrate into the pores. The volume of the particle is the volume change of the fluid. 

Kelly, W P. and McMurry, P. H. Measurements of particle density by inertial classification of differential mobility analyzer-generated monodisperse aerosols, Aerosol Sci. Tech., 17, 199—212, 1992. 

To avoid having to saturate with water or air, one can calculate porosity from measurements of particle density and bulk density. From the definitions of bulk density as the solid mass per total volirme of soil and particle... 

Testing. Chemical analyses are done on all manufactured abrasives, as well as physical tests such as sieve analyses, specific gravity, impact strength, and loose poured density (a rough measure of particle shape). Special abrasives such as sintered sol—gel aluminas require more sophisticated tests such as electron microscope measurement of a-alumina crystal si2e, and indentation microhardness. 

In sohd—sohd separation, the soHds are separated iato fractions according to size, density, shape, or other particle property (see Size reduction). Sedimentation is also used for size separation, ie, classification of soHds (see Separation, size separation). One of the simplest ways to remove the coarse or dense soHds from a feed suspension is by sedimentation. Successive decantation ia a batch system produces closely controUed size fractions of the product. Generally, however, particle classification by sedimentation does not give sharp separation (see Size MEASUREMENT OF PARTICLES). 

Boyle et al (Ref 5, p 855) stated that direct measurements of particle velocity, density and pressure are not feasible at present and the indirect methods must be used. They describe a method using determination of the shock velocities in an explosive (such as Comp B) and in a Plexiglas plate placed in contact with the explosive [See under Detonation (and Explosion), Pressure of ]... 

Although the existence of charged particles in the deton waves of solid expls has been known for some time, it was Lewis and then Bone et al who indirectly demonstrated the existance of electrons as well as positive ions in condensed and gaseous deton flames. However, it was not until 1956 that measurements of electron densities in the detonation waves of solids were carried out by Cook et al (Ref 6). They found free-electron densities in excess of 10 7/cc in the de ton reaction zone dropping slharply outside the reaction zone (Ref pl44)... 

X-ray absorption furnishes an absolute measure of the density of matter. However, in many applications the important observations to be made with X-rays concern the geometrical relationships of shock fronts and contact surfaces it is in this area where X-rays, because they make it possible to sefe inside the detonating expl, provide a uniquely appropriate tool. Until recently the difficulty has been the inability of available sources to penetrate charges more than a few inches in diameter. With the advent of the PHERMEX machine this difficulty has been overcome. Phermex provides a pulsed beam of 27 Me V electrons in 0.1 microsec bursts, which impinge on a tungsten target to generate X-rays that can easily penetrate several cm of HE. Recall that density of the shocked material can be related to particle velocity thru the conservation equations (see Vol 7, HI 79)... 

It is useful to find a quantity that could serve us as a measure of these density fluctuations. Its simplest characteristic is the dispersion of a number of particles N in some volume V i.e., (N2) — (N)2. The distinctive feature of the classical ideal gas is a simple relation between the dispersion and macroscopic density (TV2) - (TV)2 = (IV) = nV. Moreover, all other fluctuation characteristics of the ideal gas, related to the quantity (Nm, could also be expressed through (TV) or density n. Therefore, in the model of ideal gas the density n is the only parameter characterizing the fluctuation spectrum. Such the particle distribution is called the Poisson distribution. It could be easily generalized for the many-component system, e.g., a mixture of two ideal gases. Each component is characterized here by its density, nA and nB density fluctuations of different components are statistically independent, (IVAIVB) = (Na)(Nb). 

MAS (Multiwavelength Aerosol Scatterometer) is able to measure the particle density and optical properties at 532, 690 and 820 nm of aerosol and PSCs. It can give information on the phase of the particles on the basis of depolarisation measurements. In conjunction with FSSP-300 is able to furnish information on the refractive index of the particle, hence make hypotheses on the particle composition. 

Methods of measurement of coal density include use of a gas pycnometer and particle density by mercury porosimetry. However, the difference in density values using different gases must be recognized since, for example, density values measured by nitrogen may be greater than those obtained when helium is used. Density measurement depends on adsorption of gas molecules, and differences (between nitrogen and helium) may be due to nitrogen adsorption on the coal surface. 

The expansion behavior of carboxylic latex particles can be studied by several methods (10). The present comparison was made using a sedimentation method which involved the measurement of particle sedimentation rates in an ultracentrifuge at various degrees of neutralization. Assuming the change in particle volume is equal to the volume of water absorbed, an expanded particle settles slower, as its density decreases, according to the equation ... 

Characterization of the Surfaces of Catalysts Measurements of the Density of Surface Faces for High Surface Area Supports. - It has always been a tenet of theories of catalysis that certain reactions will proceed at different rates on different surface planes of the same crystal. Experiments with metal single crystals have vindicated this view by showing that the rate of hydrogenolysis of ethane on a nickel surface will vary from one plane to another. In contrast the rate of methanation remains constant for the same planes.4 Because of this structure sensitivity of catalytic processes there is a requirement for methods of determining the number of each of the different planes which a catalyst and its support may expose at their surfaces. Electron microscopy studies of 5nm Pt particles supported upon graphite show them to be cubo-octahedra with surfaces bound by (111) and (100) planes.5 Similar studies of Pd and Pt prepared by evaporation reveal square pyramids of size 60-200 A bounded by incomplete (111) faces.6... 

System conditions often allow for the measurement of magma density, and in such cases is should be used as a constraint in evaluating nucleation and growth kinetics from measured population densities. This approach is especially useful in instances of uncertainty in the determination of population densities from sieving or other particle sizing techniques. 

For porous materials pp < Pabs and cannot be measured with such methods. A mercury porosimeter can be used to measure the density of coarse porous solids but is not reliable for fine materials, since the mercury cannot penetrate the voids between small particles. In this case, helium is used to obtain a more accurate value of the particle density. Methods to measure the particle density of porous solids can be found in Refs. 2 and 5. 

Sedimentation-FFF. Retention measurements give the effective particle mass m (buoyant mass). If the particle density is known, the particle mass m, particle volume Vp, and hydrodynamic diameter dH can be calculated [80,81]. Apart from the particle dimensions, the density can be determined as well [82] as the difference in the densities of the solute and the solvent, Ap, is linearly correlated to X. Fractionation can be used in regions where the solvent density is lower than the solute density (pps. The determination of particle density in a single experiment is possible by sedimentation-flotation focusing-FFF [72,73,83] analogous to density gradient ultracentrifugation. 

The equation of Heckel has been discussed again and again. One main issue of critique is that pharmaceutical powders are not purely plastically deforming materials and thus particle size and deformation mechanisms influence the derived parameters [129, 130]. Already very small errors in displacement determination or the measurement of true density can induce huge errors in the derived parameters [75-77, 129, 131, 132], Spnnergaard [126] referred the equation of Walker and Bal shin for his characterization of materials. He criticized further that the yield strength derived from the Heckel equation is directly dependent on the true density of the powders [127]. 

Particle density may be defined as the total mass of the particle divided by its total volume however, depending upon the different definitions of the total volume (or the different ways to measure the particle volume), there are various definitions of particle density in existence (see Table 4). 

The porosity of a catalyst or support can be determined simply by measuring the particle density and solid (skeletal) density or the particle and pore volumes. Particle density pp is defined as the mass of catalyst per unit volume of particle, whereas the solid density p, as the mass per unit volume of solid catalyst. The particle volume Vp is determined by the use of a liquid that does not penetrate in the interior pores of the particle. The measurement involves the determination by picnometry of the volume of liquid displaced by the porous sample. Mercury is usually used as the liquid it does not penetrate in pores smaller than 1.2/m at atmospheric pressure. The particle weight and volume give its density pp. The solid density can usually be found from tables in handbooks only in rare cases is an experimental determination required. The same devices as for the determination of the particle density can be used to measure the pore volume V, but instead of mercury a different liquid that more readily penetrates the pores is used, such as benzene. More accurate results are obtained if helium is used as a filling medium [10]. The porosity of the particle can be calculated as ... 

When evaluating the results of these measurements one has to remember that a property of the particles (light scattering or the velocity of sedimentation) is determined. With models relying on a number of assumptions (for example that all particles are spherical) and further input (for example the complex index of refraction or the density) the particle size distribution is calculated in the final step. Applying the results of the measurement this and other deviations from the model have to be taken into account. Different measurement techniques usually result in different results for the measurements of particle size distributions. 

CSIRO Minerals has developed a particle size analyzer (UltraPS) based on ultrasonic attenuation and velocity spectrometry for particle size determination [269]. A gamma-ray transmission gauge corrects for variations in the density of the slurry. UltraPS is applicable to the measurement of particles in the size range 0.1 to 1000 pm in highly concentrated slurries without dilution. The method involves making measurements of the transit time (and hence velocity) and amplitude (attenuation) of pulsed multiple frequency ultrasonic waves that have passed through a concentrated slurry. From the measured ultrasonic velocity and attenuation particle size can be inferred either by using mathematical inversion techniques to provide a full size distribution or by correlation of the data with particle size cut points determined by laboratory analyses to provide a calibration equation. 

The measurement of particle size is a key issue in the formulation of many pharmaceutical products. Particle size distribution is known to directly influence physical properties of powders, such as dissolution rate, powder flow, bulk density, and compressibility. Conventional methods of particle size measurement include sieve analysis and laser diffractometry. ... 

Porosity can be measured indirectly via the particle and bulk densities as described by equation 5.2. This is the same method as currently used in many commercial instruments for surface area measurement by permeability in that a known mass of powder is packed into a known volume (i.e. the bulk density is known) and the porosity is evaluated from the knowledge of particle density. 

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