Particle Size Distribution and Surface Area

Particle size distribution (PSD) is another unique feature of crystals. Crystals have different shapes and different sizes. PSD function is a very effective way to describe the distribution of the particle size of crystals over a wide range of sizes. Although crystals have a three-dimensional length, the one-dimensional PSD function is frequently used in practice. Extending the one-dimensional PSD function to two-dimensional or three-dimensional PSD functions may be closer to reality. But these functions are definitely more complex, and their advantages over the one-dimensional PSD function are not always apparent. 

Mathematically, the one-dimensional PSD function can be expressed as m(L), where n is the population density function and L is the characteristic crystal length. For cube-Uke (or spherical) crystals, the characteristic length is approximately the diameter of the crystal. For crystals of other shape there are various definitions for the characteristic length. Most commonly, the characteristic length of the particle with an irregular shape is defined as the equivalent diameter of a sphere which has the same behaviors under the measurement conditions, for example sieving, laser scattering, and sedimentation (Mullin 2(X)1, Chapter 2). 

By definition of n L) above, N L, Lq), which represents the total number of particles within the size range between L and L, can be expressed as 

All other formulae can be derived based upon the above definition. For example. A, which is the surface area per unit mass of crystal, can be expressed as 

It should be pointed out that gO ) and g(In(x,)), or g(x ) and (ln(x,)), are mathematically equivalent. The former expression is defined over the Unear scale of length, whereas the latter expression is defined over the natural log scale of length. 

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We have studied the key physical properties of samples of TEG, NGF and NGZ using an SK laser micron sizer and BET surface area analyzer. Unless otherwise stated, the particle size distribution and surface area measurements for this work have been carried out at the Institute for Problems of Materials Science of the National Academy of Sciences of... 

Table 6.3 Particle size distributions and surface areas of some common fillers.

Particle size distribution and surface area The particle size distribution of the drug may determine what grade of an excipient (e.g., microcrystalline cellulose) to use. 

Sorption coefficients quantitatively describe the extent to which an organic chemical is distributed at equilibrium between an environmental solid (i.e., soil, sediment, suspended sediment, wastewater solids) and the aqueous phase it is in contact with. Sorption coefficients depend on (1) the variety of interactions occurring between the solute and the solid and aqueous phases and (2) the effects of environmental and/or experimental variables such as organic matter quantity and type, clay mineral content and type, clay to organic matter ratio, particle size distribution and surface area of the sorbent, pH, ionic strength, suspended particulates or colloidal material, temperature, dissolved organic matter (DOM) concentration, solute and solid concentrations, and phase separation technique. 

Fagherazzi, G., Cocco, G., SchifBni, L., Enzo, S., Benedetti, A., Passerini, R. and Tauszik, G.R. (1978) Particle size distribution and surface area of supported metal catalysts. Chim. e J Industria, 60, 892. 

A survey of the physical and chemical techniques to characterize the surface structure of amorphous and crystalline silica is presented by Unger in this book (Chapter 8). Methods to measure particle size and particle size distribution and surface area are discussed by Kirkland (Chapter 18) and by Allen and Davies (69). The use of some of these techniques by Morrow et al. (Chapter 9), Burneau et al. (Chapter 10), Vidal and Papier (Chapter 12), Kohler et al. (42), and Legrand et al. (17) to provide new insights into the silica surface structure was already mentioned in the section Silica Surface in this chapter. 

Zirconium is still designated, as far as the finest commercial grade is concerned, as JAN-Z-00399B with several exceptions. Grade 120A of the Foote Mineral Company and a comparative grade made by Ventron Corporation, Metal Hydrides Division are the ones to choose from. Both conform also to particle-size distributions and surface-area recommendations that came out of DOFL (now HDL) investigations. "... 

The properties of the composite samples produced by each method are shown in Table 5.3. The particle size distribution and surface area of filler have been determined by the methods described earlier in Sect. 5.2.2.1. 

The Berea sand was obtained from Cleveland Quarries in Amherst, Ohio the montmorillonite was a clay mineral standard from Ward s Natural Science Establishment, Inc. Both solids were characterized well in terms of particle size distribution and surface area. The crushed clay and sand were sieved separately using US sieve series the fractions of sand and clay which passed through sieve No. 170 but not No. 200 were retained for use as adsorbents. The particle size distribution of these fractions is fairly narrow with the majority of particles in the 74-88 ym range (10). The surface areas of these adsorbents as determined by nitrogen adsorption were 2.86 m /g for the sand and 84.7 m 2/g for the clay. 

Particle Size Distribution and Surface Area Effects on the Burn Rate... 

A fundamental requirement in powder processing is characterization of the as-received powders (10—12). Many powder suppHers provide information on tap and pour densities, particle size distributions, specific surface areas, and chemical analyses. Characterization data provided by suppHers should be checked and further augmented where possible with in-house characterization. Uniaxial characterization compaction behavior, in particular, is easily measured and provides data on the nature of the agglomerates in a powder (13,14). 

Binder selection depends on the ceramic powder, the size of the part, how it is formed, and the green density and strength requited. Binder concentration is deterrnined by these variables and the particle size, size distribution, and surface area of the ceramic powder. Three percent binder, based on dry weight, generally works for dry pressing and extmsion. 

Attrition of particulate materials occurs wherever solids are handled and processed. In contrast to the term comminution, which describes the intentional particle degradation, the term attrition condenses all phenomena of unwanted particle degradation which may lead to a lot of different problems. The present chapter focuses on two particular process types where attrition is of special relevance, namely fluidized beds and pneumatic conveying lines. The problems caused by attrition can be divided into two broad categories. On the one hand, there is the generation of fines. In the case of fluidized bed catalytic reactors, this will lead to a loss of valuable catalyst material. Moreover, attrition may cause dust problems like explosion hazards or additional burden on the filtration systems. On the other hand, attrition causes changes in physical properties of the material such as particle size distribution or surface area. This can result in a reduction of product quality or in difficulties with operation of the plant. 

P.O.34 is supplied in a variety of types, which differ considerably in their particle size distributions. Specific surface areas range from 15 m2/g in highly opaque versions to about 75 m2/g in transparent types. It is these physical characteristics that determine the coloristic and fastness properties of each type. Even varieties of P.O.34 with fine particle sizes are generally not resinated. 

It may be deduced from KP = Koc x foc that partition coefficients of hydro-phobic organic compounds in general are dependent upon the chemical of interest (compound-specific properties affect the value of Koc) and the matrix properties of the medium in which it resides. In addition to the fraction of organic carbon present in the sorption phase, additional environmental factors affect partitioning. These factors include temperature, particle size distribution, the surface area of the sorbent, pH, ionic strength, the presence of suspended material or colloidal material, and the presence of surfactants. In addition, clay minerals may act as additional sorption phases for organic compounds. Nevertheless, organic carbon-normalized partition... 

The various bentonite samples have different physical, chemical, and colloid chemical properties. The particle size distribution, specific surface area, CEC, and swelling in water are shown in Table 3.2. For an easier comparison, some... 

Particle Size Distribution, Specific Surface Area (S), Cation-Exchange Capacity (CEC), Swelling in Water, and the Relative Amount of the Adsorbed 137Cs+ ion (x)... 

Curves F-G and H-G represent two different modes of carrying out crystallization by cooling and would be expected to result in two very different results in terms of physical properties—mean particle size (mean dp) particle size distribution (PSD), surface area, and bulk density, as well as possible differences in rejection of impurities and occlusion of solvent. Other differences can include a change of morphology and a potential for changes in polymorph formation. These differences result from the supersaturation and surface... 

Chemical Composition Particle Size Distribution Specific Surface Area. . Wet-to-Dry Shrinkage Dry Strength Base Exchange and Deflocculation Soluble Salts Fired Colour Vitrification., ... 

It is a universal rule that as particle size decreases and surface area increases, the more the particles tend to agglomerate. This is a well known and widely researched problem with nanoparticles unless these systems are stabilized, there are no individual particles or capsules. It is therefore crucial to offer the appropriate size distribution for the specific application. A size increases at a... 

The most important filler characteristics determining the properties of PP composites are particle size, particle size distribution, specific surface area and shape. None of these influence stiffness very much the reinforcing effect is a result of the orientation of the anisotropic particles. All other properties are considerably affected by these filler characteristics. Yield stress and strength usually increase with decreasing particle size and increasing surface area, while deformability and impact resistance change in the opposite direction. 

Primary phase physicochemical characterization refers to those nanoscale properties of the material in its dry or powder state. The primary phase properties related to toxicity testing of the nanomaterial include a wide range of particle features, including size, size distribution, and surface area chemical composition and surface chemistry and morphology. 

This chapter will highlight the factors of packing (bulk density, voidage), rate of flow, compressibility of packing, flowability, failure properties and angle of internal friction, cohesion, strength and adhesion. The factors of particle size distribution, specific surface area and particle shape distribution have already been dealt with elsewhere (Stanley-Wood 2000, 2005). 

In the Monte Carlo technique, a random selection is made (as in the Principality ) of those particles that will either take part in collision events or be withdrawn from the crystallizer in the time interval At. Thus, the evolution of size, size distribution and surface area (knowing the surface shape factor) of both primary and secondary particles together with their mean characteristics can be evaluated numerically. The results of some sample calculations are illustrated in Figures 8.25 and 8.26 respectively. 

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