Shape particle

Particle shape is a fundamental powder property affecting powder packing and thus bulk density, porosity, permeability, cohesion, flowability, caking behavior [6] attrition, interaction with fluids and the covering power of pigments, although little quantitative work has been carried out on these relationships. Davies [7] gives other examples where information on shape is needed to describe powder behavior. 

Many papers have been written on shape determination but there are few articles that relate the measurements to powder behavior and end-use properties. Hawkins [8] critically reviews nearly 300 articles on particle shape measurement and Singh and Ramakrishnan [9]review seventy-six articles on powder characterization by particle shape assessment. 

Angular sharp-edged or having a rough polyhedral shape Crystalline freely developed in a fluid medium of geometric shape 

Granular having approximately an equi-dimensional irregular shape Irregular lacking any symmetry 

Qualitative terms [10] may be used to give some indication of particle shape but these are of limited use as a measure of particle properties ( Fable 2.4). Such general terms are inadequate for the determination of shape factors that can be incorporated as parameters into equations concerning particle properties where shape is involved as a factor. In order to do this, it is necessary to be able to measure and define shape quantitatively. 

Cellulose particles used in WPC are typically fibers, with aspect ratio between 3 and 4, or longer, particularly in case of long cellulose fiber. Hardwoods wood flour 

Particle shape is observed by optical or electron microscopes, depending on the size of the particles. The shape is expressed quantitatively by the shape factor. Shape factor is calculated from the knowledge of the length and breadth of the particles, or surface area. The ratio of length to breadth or surface area to particle size gives the shape factor. 

The particle shape determines the particles specific surface area and the observed order in increasing codeposition of the AI2O3 particle shapes corresponds to a decrease in the specific surface area.108 The amount of 

Estimation of the particle shape was mentioned in the previous section on particle-size analysis. Historically, the particle shape was assumed to be spherical to simplify calculations. With the advent of inexpensive high-speed computers and high-resolution imaging systems, image analysis has become a viable option to study the shape and size of particles in greater detail [92] the systems and software programs currently available are numerous. In conjunction with 

It is well known that particle shape affects many secondary properties relevant to powder handling such as the bulk density, failure properties or particle-gas interaction. For non-spherical particles, the results obtained with different methods of particle size measurement are, in general, not comparable. From the point of view of powder handling, flaky or stringy particles like wood shavings, mica or asbestos fibres are known to be difficult because they interlock and form obstructions to flow. 

A number of methods have been proposed for particle shape analysis these include verbal description, various shape coefficients and shape factors, curvature signatures, moment invariants, solid shape descriptors, the octal chain code and mathematical functions like Fourier series expansion or fractal dimensions. As in particle size analysis, here one can also detect intense preoccupation with very detailed and accurate description of particle shape, and yet efforts to relate the shape-describing parameters to powder bulk behaviour are relatively scarce.10 

It is also worth noting that, in many cases, particle size and shape do not exist independently, and shape can be size-dependent. This presents difficulties for example, when conversions from one type of size distribution to another are necessary large errors are introduced because such conversions assume a constant shape factor throughout the whole size range. Some instruments even perform such conversions automatically and the user often does not realise the existence and the consequence of this assumption. 

As with the different definitions of particle size, the choice is made of a shape factor most relevant in the application in question. The following is a list of the definitions of the most frequently used, simple shape factors. 

SPHERICITY is the ratio of the surface area of a sphere having the same volume as the particle, to the actual particle surface area the reciprocal is known as the coefficient of rugosity or angularity. It can be shown that sphericity is also equal to the ratio of the surface-volume diameter to the equivalent volume diameter this makes sphericity a useful conversion factor between 

Pigments vary not only in size but also in particle shape. Although the inherent shape of pigment particles is determined from its crystal 

The particle shape of a pigment can be observed through a light microscope. Nowadays, expensive but precise and more reliable techniques like electron microscopy are widely used to determine the particle shape of a pigment. 

The temperature should be lower than that of fusion of the ceramic powder produced in the reactor to stop sticking aggregation of the particles. The energy of fusion must be accounted for in this energy balance for detailed calculations for temperatures below the fusion point of the ceramic powder when particle loading is high. 

When the contribution of the particles to the heat capacity of the gas stream is important (i.e., the high particle loading case), the mass, momentum and energy balance equations in (7.77) must be solved simultaneously. Typically, the details of streams 1 and 2 are known, and we need to calculate the outlet velocity and temperature (i.e., stream 3). Using the mass balance, we can calculate. With Wg, we 

The ceramic particles produced by gas phase reactions exhibit several different shapes depending on the conditions under which they were made. If the flame temperature is much higher than the melting 

Chapter 7 Powder Synthesis with Gas Phase Reactants 

Of the experimental investigations that have looked into the possibilities of tailoring particle shape in microemulsion-mediated syntheses, those of Pileni and colleagues are the most well-documented. The shape control exhibited in case of copper metal particles [240] is highly instructive, but is apparently case-specific. One can however summarize the results obtained by Pileni and colleagues in the system Cu(AOT)2 /isooctane/water for the sake of understanding (see Sections 2.6 and 2.7)  

Pileni and colleagues [100] have also used cylindrical droplet formation for synthesis of rod-like particles by increasing the surfactant content. In a later work [250], Pileni showed that the presence of salt anions, instead of the available template, may control the particle shape. Thus, chloride ions help formation of nanorods, while nitrate ions can hinder formation of cylinders and rods. 

The rod- or wire-like morphology is common in some other systems, though the reasons of their formation may not be the same as in the case of copper described above. Synthesis of specifically nanorods of CdS and CdSe has been reported by Chen et al. [251] from a CTAB / cyclohexane / water system. The amount of cyclohexane seemed to control the morphology. Another possible factor was the degree of sonication that might have led to the formation of bilayer vesicles. 

Accounts of aqueous synthesis [33] of ZnO are replete with examples of changes in morphology (including acicular and rodlike shapes) as a complex function of chemical parameters. For rod-like shapes, the presence of amines has been found to be important. In a similar way, in micellar synthesis of ZnO from alkoxides [252], it has been found that the presence of ammonia was vital for the formation of rod-like particles. 

Rod-like morphology has also been reported for gold nanoparticles [232]. It has been shown that in partial agreement with Pileni s work discussed above, increase in water/surfactant ratio could increase the percentage of rod-like particles, though in a limited way. In addition, other factors like reactant ratio have been considered to influence the morphology. 

Note that we have only presented a few examples. Bulk density is a measure of how well particles pack together in a defined volinne. It depends on the shape of the particles comprising the powder. Most of the organic compounds (pharmaceuticals) will exhibit elongated shaped particles. Note that at least 50% of the voliunes presented in 4.1.12 are. in most cases, unoccupied space, i.e.-porosity. We conclude that if someone measures the particle size and the size distribution, we need to know exactly what was measured, often in terms of the particle shape. Particle size is customarily measured in terms of two-dimensioned (physical eispect) or three-dimensioned (volume) values. However, the particle size is often deseribed in terms of spheroidal diameters even though the peirticles may be aclcular in nature. 

Fortunately, there are methods which we can use to describe how particle shape and particle size are measured. An obvious method is to use the microscope, as shown in the following  

One then proceeds to count particles. It has been found that if one wishes to determine an accurate value of the mean diameter, one must count at least 450 particles. As the number of counts Increases, the mean comes closer and closer to the true value, as shown in the following  

If we wish to obtain an average of the diameters, we siun the number of 

Measuring particle size and growing single crystals 

Relatively little appears to be known about the influence of shape on the behaviour of particulate solids and it is notoriously difficult to measure. Whilst a sphere may be characterised uniquely by its diameter and a cube by the length of a side, few natural or manufactured food particles are truly spherical or cubic. For irregular particles, or for regular but non-spherical particles, an equivalent spherical diameter de can be defined as the diameter of a sphere with the same volume V as the original particle. Thus 

More commonly, a generalised volume shape factor K is used to relate particle volume V to the cube of particle size 

The following has been suggested (Richardson and Zaki, 1954 Richardson, 1971) for fluidized cubes and cylinders 

The sphericity of a particle, where the respective surface areas of the particle and an equivalent sphere are compared, has also been found to be useful in characterising shape. Thus 

For non-spherical particles, values of sphericity lie in the range 0 1. Thus, the effective particle diameter for fluidization purposes is the product of the surface-volume mean diameter and the sphericity (Kunii and Levenspiel, 1991). The sphericity of regular-shaped particles can be deduced by geometry whilst the sphericity of irregular-shaped 

The shape of an object is a descriptor of the outline of its external surface only. Thus the shape of an object is a property that reflects the recognized pattern of relationships among all the points that constitute its external surface. The difference between the shapes of two objects arises from the differences between the patterns of relationships among these point coordinates corresponding to the two shapes. While the size of an object, for example a material particle, is an indicator of the quantity of matter contained in it, its shape is concerned with the pattern according to which this quantity of matter is assembled together. Shape is an intrinsic rather than an extrinsic characteristic in that it is not additive. 

This is a fundamental property affecting powder packing, bulk density, porosity, permeability, flowability, attrition and the interaction with 

The sphericity / can be calculated exactly for such geometrical shapes as cuboids, rings and manufactured shapes, see Table 3. However, most particles are irregular and there is no simple generally accepted method for measuring their sphericity. Values for some common solids have been published (see Ref 4). However, these should be regarded as estimates only. Table 4 shows that / is between 1 and 0.64 for most materials. 

Other methods are available for quantifying shape factors and these are described in detail in Refs. 2 and 5. Using a Scanning Electron Microscope (SEM), for example, the shape and surface characteristics of 

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Figure C2.17.2. Transmission electron micrograph of a gold nanoneedle. Inverse micelle environments allow for a great deal of control not only over particle size, but also particle shape. In this example, gold nanocrystals were prepared using a photolytic method in surfactant-rich solutions the surfactant interacts strongly with areas of low curvature, thus continued growth can occur only at the sharjD tips of nanocrystals, leading to the fonnation of high-aspect-ratio nanostmctures [52].

This ideal case is rarely if ever encountered in practice in general there will be a distribution of particle sizes rather than a single size, and in addition there will usually be a range of particle shapes, many of them highly irregular. 

In all other cases the quantity / calculated from the specific surface is a mean diameter. Unless there is some definite and detailed evidence as to particle shape, the simplest such diameter to aim at is the mean diameter obtained by substituting the measured value of A in Equation (1.79)... 

Various attempts have been made to allow for particle shapes, through the use of volumes and shape factors. From general considerations it is clear that the volume v of the particles from p grams of solid will be proportional to and the area Ap proportional to... 

The intrinsic viscosity of a solution of particles shaped like ellipsoids of revolution is given by the expression... 

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. 

The term essentially a drag coefficient for the dust cake particles, should be a function of the median particle size and particle size distribution, the particle shape, and the packing density. Experimental data are the only reflable source for predicting cake resistance to flow. Bag filters are often selected for some desired maximum pressure drop (500—1750 Pa = 3.75-13 mm Hg) and the cleaning interval is then set to limit pressure drop to a chosen maximum value. 

Particle shapes are classified as acicular. A, monoclinic and blocky, M, or monoclinic and needle, N. 

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. 

Hardness. The resistance of a fabricated mbber article to indentation, ie, hardness, is influenced by the amount and shape of its fillers. High loadings increase hardness. Fillers in the form of platelets or flakes, such as clays or mica, impart greater hardness to elastomers than other particle shapes at equivalent loadings. 

Particle Shape and Size. With few exceptions, resins are supplied as small, round beads having a diameter between 0.3 and 1.2 mm. Some resins are reduced to a smaller size by grinding to satisfy specific requirements in applications for electric power generation (qv) and pharmaceuticals (qv). 

Particle Size. Wet sieve analyses are commonly used in the 20 )J.m (using microsieves) to 150 )J.m size range. Sizes in the 1—10 )J.m range are analyzed by light-transmission Hquid-phase sedimentation, laser beam diffraction, or potentiometric variation methods. Electron microscopy is the only rehable procedure for characterizing submicrometer particles. Scanning electron microscopy is useful for characterizing particle shape, and the relation of particle shape to slurry stabiUty. 

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). 

Surfa.ce, Any reaction between two powder particles starts on the surface. The amount of surface area compared to the volume of the particle is, therefore, an important factor in powder technology. The particle—surface configuration, whether it is smooth or contains sharp angles, is another. The particle surface area depends strongly on the method of production, as shown in Table 1. The method of production usually determines the particle shape. 

Table 1. Particle Shapes and Surface Areas of Fabricated Powder Particles ...

Deterrnination of the specific surface area can be made by a variety of adsorption measurements or by air-permeability deterrninations. It is customary to calculate average particle size from the values of specific surface by making assumptions regarding particle size distribution and particle shape, ie, assume it is spherical. 

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. 

Table 4. Effect of Particle Shape on Apparent and Tap Density ...

The manufacture of metal in powder form is a complex and highly engineered operation. It is dominated by the variables of the powder, namely those that are closely connected with an individual powder particle, those that refer to the mass of particles which form the powder, and those that refer to the voids in the particles themselves. In a mass of loosely piled powder, >60% of the volume consists of voids. The primary methods for the manufacture of metal powders are atomization, the reduction of metal oxides, and electrolytic deposition (15,16). Typical metal powder particle shapes are shown in Figure 5. 

Fig. 5. Metal powder particle shapes (a) atomized copper (b) sponge iron and (c) atomized iron.

The value of pigments results from their physical—optical properties. These ate primarily deterrniaed by the pigments physical characteristics (crystal stmcture, particle size and distribution, particle shape, agglomeration, etc) and chemical properties (chemical composition, purity, stabiUty, etc). The two most important physical—optical assets of pigments are the abiUty to color the environment in which they ate dispersed and to make it opaque. 

Some particle size measuring techniques ate more particle shape sensitive than others. Data obtained by different methods can be significantly different, and whenever a particle size is reported, the measuring technique and conditions should always be mentioned. Even using the same equipment, the extremes of the distributions (low and high 10%) are usually not readily reproducible. 

Rehydration Bonded Alumina. Rehydration bonded aluminas are agglomerates of activated alumina, which derive their strength from the rehydration bonding mechanism. Because more processing steps are involved in the manufacture, they are generally more expensive than activated aluminum hydroxides. On the other hand, rehydration bonded aluminas can be produced in a wider range of particle shape, surface area, and pore size distribution. 

Particle Shape. Whereas the Stokes particle is assumed to be a sphere, very few real soHds are actually spherical. Flat and elongated particles sediment slower than spheres. For maximum sedimentation rate, the particle should be as spherical as possible. 

Fig. 4. Static force index (Tesla(ATesla/Adistance)) for varying particle shapes, where K is the bulk density of material in kg/m. The plate has dimensions of 6 X 76 X 76 mm the bolt has dimensions of 6 x 25 mm. The horizontal line represents the distance from the magnet face.

Particle shape is also important. Disk-shaped as well as cylindrical-shaped conductors have a high response because large induced current loops are formed. Small randomly shaped conductors, such as those present in cmshed slag, also respond favorably. Sphere-shaped particles generate small-current loops, however, and do not have a high response. Multiple-current loops occur in conductors that have irregular bends, producing counteractive forces that tend to nullify each other. 

Selection of the most suitable machine for a given requirement is an extremely complex process. Added to variations in the properties of the different materials, many of the machines involved have been specifically developed or adapted to perform only particular tasks. The principal factors which must be addressed are toughness/britdeness, hardness, abrasiveness, feed size, cohesity, particle shape and stmcture, heat sensitivity, toxicity, explodability, and specific surface. 

Abrasiveness. This property is closely related to hardness in homogenous materials, but can be affected by particle shape, eg, the presence of sharp corners. In many cases a small proportion, as low as 0.5%, of a hard impurity is enough to cause severe wear to many high speed machines. 

Particle Shape and Structure. Some materials exhibit particular properties owing to their particle shape or form, eg, the plate-like minerals talcum and mica or acicular woUastonite. It is often desired to maintain particle shape in such cases, an impact-type mill is usually chosen rather than a ball mill, as the latter tends to alter the original particle shape. 

The characteristics of WC, especially grain size, are determined by purity, particle shape and grain size of the starting material, and the conditions employed for reduction and carburization. The course of the reaction WO3 — W — WC is dependent on temperature, gas flow rates, water-vapor concentration in the gas, and the depth of the powder bed. All these factors affect the coarsening of the grain. 

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