Sphericity of particle

Hellen L, Yliruusi J. Process variables of instant granulator and spheroniser III. Shape and shape distributions of pellets. Int J Pharm 1993 96 217-223. Chapman SR, Rowe RC, Newton JM. Characterization of the sphericity of particles by the one plane critical stability. J Pharm Pharmacol 1988 40 503-505. Rowe RC, Sadeghnejad GR. The rheology of mcc powder/water mixes-measurement using a mixer torque rheometer. Int J Pharm 1987 38 227-229. O Connor RE, Schwartz JB. Spheronization II Drug release from drug-diluent mixtures. Drug Dev Ind Pharm 1985 11 (9-10) 1837-1857. 

Chapman SR, Rowe RC, Newton JM. Characterization of the sphericity of particles by the one plane critical stability. J Pharm niarmacol 1988 40(7) 503-5. 

Marmur [12] has presented a guide to the appropriate choice of approximate solution to the Poisson-Boltzmann equation (Eq. V-5) for planar surfaces in an asymmetrical electrolyte. The solution to the Poisson-Boltzmann equation around a spherical charged particle is very important to colloid science. Explicit solutions cannot be obtained but there are extensive tabulations, known as the LOW tables [13]. For small values of o, an approximate equation is [9, 14]... 

STM and AFM profiles distort the shape of a particle because the side of the tip rides up on the particle. This effect can be corrected for. Consider, say, a spherical gold particle on a smooth surface. The sphere may be truncated, that is, the center may be a distance q above the surface, where q < r, the radius of the sphere. Assume the tip to be a cone of cone angle a. The observed profile in the vertical plane containing the center of the sphere will be a rounded hump of base width 2d and height h. Calculate q and r for the case where a - 32° and d and h are 275 nm and 300 nm, respectively. Note Chapter XVI, Ref. 133a. Can you show how to obtain the relevent equation ... 

The long-range interactions between a pair of molecules are detemiined by electric multipole moments and polarizabilities of the individual molecules. MuJtipoJe moments are measures that describe the non-sphericity of the charge distribution of a molecule. The zeroth-order moment is the total charge of the molecule Q = Yfi- where q- is the charge of particle and the sum is over all electrons and nuclei in tlie molecule. The first-order moment is the dipole moment vector with Cartesian components given by... 

Kofman R ef al 1991 Melting of non-spherical ultrafine particles Z. Phys. D 20 267... 

The truncated octahedron and the rhombic dodecahedron provide periodic cells that are approximately spherical and so may be more appropriate for simulations of spherical molecules. The distance between adjacent cells in the truncated octahedron or the rhombic df)decahedron is larger than the conventional cube for a system with a given number of particles and so a simulation using one of the spherical cells will require fewer particles than a comparable simulation using a cubic cell. Of the two approximately spherical cells, the truncated octahedron is often preferred as it is somewhat easier to program. The hexagonal prism can be used to simulate molecules with a cylindrical shape such as DNA. 

An interesting historical application of the Boltzmann equation involves examination of the number density of very small spherical globules of latex suspended in water. The particles are dishibuted in the potential gradient of the gravitational field. If an arbitrary point in the suspension is selected, the number of particles N at height h pm (1 pm= 10 m) above the reference point can be counted with a magnifying lens. In one series of measurements, the number of particles per unit volume of the suspension as a function of h was as shown in Table 3-3. 

It will be convenient to deal first with the distribution aspect of the problem. One of the clearest ways in which to represent the distribution of sizes is by means of a histogram. Suppose that the diameters of SOO small spherical particles, forming a random sample of a powder, have been measured and that they range from 2-7 to 5-3 pm. Let the range be divided into thirteen class intervals 2-7 to 2-9 pm, 2-9 to 3-1 pm, etc., and the number of particles within each class noted (Table 1.5). A histogram may then be drawn in which the number of particles with diameters within any given range is plotted as if they all had the diameter of the middle of the... 

An exactly similar expression is obtained for spherical particles, where L and A now refer to the diameters of particles rather than their edge length. 

Fig. 4. Terminal velocities in air of spherical particles of different densities settling at 21°C under the action of gravity. Numbers on curves represent tme (not bulk or apparent) specific gravity of particles relative to water at 4°C. Stokes-Cunningham correction factor is included for settling of fine particles.

Tear Resistance. The resistance of an elastomer to tearing is affected by the particle size and shape of the filler it contains. Tear resistance generally increases with decreasing particle size and increasing sphericity of fillers. 

Fluidized-bed design procedures requite an understanding of particle properties. The most important properties for fluidization are particle size distribution, particle density, and sphericity. 

Emulsion—Suspension Polymerized Pigment Ink. Polymerization of a polar prepolymer as the internal phase in an oil-based external phase (24) gives a fluorescent ink base in which spherical fluorescent particles are dispersed. This base is suitable for Htho and letterpress inks (qv). An... 

Size. The precise determination of particle size, usually referred to as the particle diameter, can actually be made only for spherical particles. For any other particle shape, a precise determination is practically impossible and particle size represents an approximation only, based on an agreement between producer and consumer with respect to the testing methods (see Size measurement of particles). 

Specific Surface. The total surface area of 1 g of powder measured ia cm /g is called its specific surface. The specific surface area is an excellent iadicator for the conditions under which a reaction is initiated and also for the rate of the reaction. It correlates in general with the average particle size. The great difference in surface area between 6-p.m reduced iron powder and 7-p.m carbonyl iron powder (Table 3) cannot be explained in terms of particle size, but mainly by the difference between the very inregular-shaped reduced and the spherical carbonyl iron powders. 

The characteristics of a powder that determine its apparent density are rather complex, but some general statements with respect to powder variables and their effect on the density of the loose powder can be made. (/) The smaller the particles, the greater the specific surface area of the powder. This increases the friction between the particles and lowers the apparent density but enhances the rate of sintering. (2) Powders having very irregular-shaped particles are usually characterized by a lower apparent density than more regular or spherical ones. This is shown in Table 4 for three different types of copper powders having identical particle size distribution but different particle shape. These data illustrate the decisive influence of particle shape on apparent density. (J) In any mixture of coarse and fine powder particles, an optimum mixture results in maximum apparent density. This optimum mixture is reached when the fine particles fill the voids between the coarse particles. 

Sedimentation. Gravity makes all particles that ate mote dense than the suspending Hquid move downward, and also causes beds of particles to compress toward the state of minimum-included Hquid. The sedimentation force,for a single spherical particle (not part of a bed) submerged in a Hquid is as foUows ... 

Spherical, Fine-Particle Titanium Dioxide. Spherical, fine-particle titanium dioxide that has no agglomeration and of mono-dispersion can be manufactured by carrying out a gas-phase reaction between a tetraalkyl titanate vapor and methanol vapor in a carrier gas to form an initial fine particle, which can then be hydrolyzed with water or steam (572). 

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