Regular particles, dimensions

The equivalent diameter can be calculated from the dimensions of regular particles, such as cubes, pyramids. 

These two nomographs provide a convenient means of estimating the equivalent diameter of almost any type of particle Figure 1 of regular particles from their dimensions, and Figure 2 of irregular particles from fractional free volume, specific surface, and shape. 

Also, in cases where the dimensions of a regular particle vary throughout a bed of such particles or are not known, but where the fractional free volume and specific surface can be measured or calculated, the shape factor can be calculated and the equivalent diameter of the regular particle determined from Figure 2. 

Because of the diversity of filler particle shapes, it is difficult to clearly express particle size values in terms of a particle dimension such as length or diameter. Therefore, the particle size of fillers is usually expressed as a theoretical dimension, the equivalent spherical diameter (esd), ie, the diameter of a sphere having the same volume as the particle. An estimate of regularity may be made by comparing the surface area of the equivalent sphere to the actual measured surface area of the particle. The greater the deviation, the more irregular the particle. 

The relationship between effectiveness factor p and Thiele modulus < >l may be calculated for several other regular shapes of particles, where again the characteristic dimension of the particle is defined as the ratio of its volume to its surface area. It is found that... 

Analytical (flow-pattern) characterization is more difflcult as the particle bed is not transparent and covers most of the flow-through chamber. Another drawback stems from the size distribution of the particles of the catalyst bed, giving interstices which vary in typical dimensions. Here, however, today s considerable efforts in nano- and micro-material research may provide regular, mono-sized particles in the near future which will allow one to create much improved micro flow-packed beds. 

There is actually no sharp distinction between the crystalline and amorphous states. Each sample of a pharmaceutical solid or other organic material exhibits an X-ray diffraction pattern of a certain sharpness or diffuseness corresponding to a certain mosaic spread, a certain content of crystal defects, and a certain degree of crystallinity. When comparing the X-ray diffuseness or mosaic spread of finely divided (powdered) solids, the particle size should exceed 1 um or should be held constant. The reason is that the X-ray diffuseness increases with decreasing particle size below about 0.1 J,m until the limit of molecular dimension is reached at 1-0.1 nm (10-1 A), when the concept of the crystal with regular repetition of the unit cell ceases to be appropriate. 

Data indicate the presence of a maximum in the performances that is nearly independent on the metal loading. Transmission electron micrographs of the Pd particles indicate that the larger particles (around 15-16 nm) show an irregular, multifaced structure. A more regular structure is observed in the smaller round particles, but apparently with different preferential orientation depending on the dimensions. Note that in the claims of Headwaters Nanokinetix Inc. patents the existence of an optimal diameter for Pd particles is also indicated, to which the preferential exposure ofthe active/selective surface is related. Data in Figure 8.11 do not prove this statement, but are in line with this indication. 

The two methanation reactions are strongly exothermic. The temperature rise for typical methanator gas compositions in hydrogen plants is about 74°C (133°F) for each 1% of carbon monoxide converted and 60°C (108°F) for each 1% of carbon dioxide converted. At higher temperatures, the intrinsic rates of both methanation reactions can become sufficiently fast for diffusion effects to become important as shown in Figure 5.42. Under these conditions, film diffusion controls the overall rate of reaction. Diffusion limitations can be overcome to some extent by using a catalyst with a smaller particle size (3.1mm diameter by 3.6 mm long compared to regular catalyst dimensions of 5.4 mm by... 

Isometric particles are those for which all three dimensions are roughly the same. Spherical, regular polyhedral, or particles approximating these shapes belong in this class. Most knowledge regarding aerosol behavior pertains mainly to isometric particles. 

The size of a cubic particle is uniquely defined by its edge length. The size of a spherical particle is uniquely defined by its diameter. Other regular shapes have equally appropriate dimensions. With some r ular particles more than one dimension is necessaiy to specify the geometiy of the particle as, for example, a cylinder, which has a diameter and a length. With irregulariy shaped particles, many dimensions... 

The boron so formed resembled other amorphous borons in appearance and was found to be similar in structure to jS-rhombohedral boron. Individual particles were random in shape, consisting mainly of platelets between 200 and 7500 A in diameter. The presence of regular dodecagonal platelets of boron was also observed, in the product, which had typical diameters of 7000 A and a unit cell lattice constant of 30 A. This unit cell dimension is considerably larger than any previously reported form of boron and was considered to be a further modification of known boron structures. 

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