Particle Size Distributions and Averaged Diameters

Typically, the phase Doppler method is good for the measurement of particle sizes ranging from 1 /u.m to 10 mm with a variation by a factor of 40 at one instrument setting. As a rule of thumb, the maximum measurable concentration is 1,000 particles per cubic millimeter (mm3). Commercial instruments using this technique are available, e.g., the phase Doppler particle analyzer (PDPA) (Aerometrics) and the Dantec particle dynamics analyzer (DPDA) (Dantec Electronics). 

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Particle Size. The soHds in a fluidized bed are never identical in size and foUow a particle size distribution. An average particle diameter, is generally used for design. It is necessary to give relatively more emphasis to the low end of the particle size distribution (fines), which is done by using the surface mean diameter, to calculate an average particle size ... 

An ICI-Joyce Loebl Disc Centrifuge MK III, a photosedimento-meter, was used to measure the latex particle size distribution. The latex had a unimodal particle size distribution with a diameter of 1.05 micrometers (surface area average). The methods of separating latex particles by a centrifugal field and detecting the size distribution by a photocell may be found in the literature. 

The shear stabihties of mini- and macroemulsion latexes were compared and quantitatively evaluated with respect to their particle size distributions by Rodrigues and Schork [146]. Although miniemulsion latexes exhibit many of the properties of macroemulsion latexes, there may be subtle differences in particle size distribution and surface characteristics due to differences in their polymerization mechanisms. To study the effects of these differences on the shear stabihties of the miniemulsions, a quantitative approach was developed where changes in the average diameter and total number of particles have been related to the particle size distribution before and after shearing. 

FIGURE 10.1 (a) Effect of the number of particles counted on the average mean primary particle diameter, r/j (circles), and Sauter mean primary particle diameter, (squares), as well as the geometric standard deviation (that is, a measure of the width of the size distribution, triangles), (b) The corresponding primary particle size distribution and a TEM picture of the investigated titania nanoparticles collected with a thermophoretic sampler directly from a premixed TiOj flame at a height of 0.5 cm above the burner. (Courtesy of H.K. Kammler and S.E. Pratsinis.)... 

For polyolefin films, ECC s FilmLink, in powder or pellet form, comprises very fine particles, averaging 1 pm in diameter, with narrow particle size distribution and surface coated with a substance compatible with organic compounds. Loadings are 60% or higher. They give increases in film strength that are described as dramatic . 

Cationic latex particles with surface amino groups were prepared by a multi-step batch emulsion polymerisation. Monodisperse cationic latex particles to be used as the seed were synthesised first. Then the amino-functionalised monomer, aminoethylmethacrylate hydrochloride, was used to synthesise the final functionalised latex particles. Three different azo initiators were used 2,2 -azobisisobutyramidine dihydrochloride, 2,2 -azobisdimethyleneisobutyramidine dihydrochloride, and 2,2 -azobisisobutyronitrile. Hexadecyltrimethylammonium bromide was used as the emulsifier. The latices were characterised by photon correlation spectroscopy to study the mean particle diameters, transmission electron microscopy to deteimine the particle size distributions, and hence the number- and weight-average diameters and the polydispersity index. The conversion was determined gravimetrically, the surface density of the amino groups was detemiined by conductimetric titrations, and the... 

Statistically, the particle size distribution can be characterized by three properties mode, median, and mean. The mode is the value that occurs most frequently. It is a value seldom used for describing particle size distribution. The average or arithmetic mean diameter, d, is affected by all values actually observed and thus is influenced greatly by extreme values. The median particle size, is the size that divides the frequency distribution into two equal areas. In practical application, the size distribution of a typical dust is typically skewed to the right, i.e., skewed to the larger particle size. The central tendency of a skewed frequency distribution is more adequately represented by the median rather than by the mean (see Fig. 9). Mathematically, the relationships among the mean, median, and mode diameter can be expressed as... 

The gel-filtration medium is normally packed into a stainless steel column characterized by an i.d. between 4 and 25 mm and a length between 300 and 600 mm. Four important factors in characterizing SEC packings are the average particle size, the particle size distribution, the average pore diameter, and the pore size distribution. The particle size and the particle size distribution have a significant influence on the column efficiency, which is most decisive in SEC, because the biopolymers are eluted isocraticaUy in a small elution window with... 

Figure 7.21 Particle-size distribution and number average hydrodynamic diameter () estimated by DLS measurements of 23d (left side) and 23a (right side) in chloroform.

A powder is characterized by the extent of the particle size distribution and by the average size (denoted d5o), size for which 50% of the particle poprrlation has a size lower than djg (see Figure 5.2). These characteristics are determined by sedimentation methods (detection by x-ray absorption) or by lazer diffraction methods. These techniqnes generally calcrrlate an eqrrivalent diameter of spherical particles. In case of spherical or equiaxed particles, the calcrrlated valne is therefore close to the actiral valne, while in case of anisotropic particles we have an approximate theoretical valne. 

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