Flat platelets

In a thin flat platelet, the mass transfer process is symmetrical about the centre-plane, and it is necessary to consider only one half of the particle. Furthermore, again from considerations of symmetry, the concentration gradient, and mass transfer rate, at the centre-plane will be zero. The governing equation for the steady-state process involving a first-order reaction is obtained by substituting De for D in equation 10.172  

The concentration gradient at a distance y from the surface is therefore given by  

The mass transfer rate per unit area at the surface of the particle is then  

If there were no resistance to mass transfer, the concentration of A would be equal to CAi everywhere in the pellet and the reaction rate per unit area in the half-pellet (of volume 

The effectiveness factor rj is equal to the ratio of the rates given by equations 10.200 and 10.201, or  

The quantity W — = AL is known as the Thiele modulus, 3i) negative sign indi- 

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Titanium disulfide can also be made by pyrolysis of titanium trisulfide at 550°C. A continuous process based on the reaction between titanium tetrachloride vapor and dry, oxygen-free hydrogen sulfide has been developed at pilot scale (173). The preheated reactants ate fed iato a tubular reactor at approximately 500°C. The product particles comprise orthogonally intersecting hexagonal plates or plate segments and have a relatively high surface area (>4 /g), quite different from the flat platelets produced from the reaction between titanium metal and sulfur vapor. The powder, reported to be stable to... 

Colloidal suspensions are systems of small mesoscopic solid particles suspended in an atomic liquid [1,2]. We will use the term colloid a little loosely, in the sense of colloidal particle. The particles may be irregularly or regularly shaped (Fig. 1). Among the regular shapes are tiny spherical balls, but also cylindrical rods or flat platelets. As the particles are solid, fluctuations of their form do not occur as they do in micellar systems. Not all particles in a suspension will, in general, have the same form. This is an intrinsic effect of the mesoscopic physics. Of course in an atomic system, say silicon, all atoms are precisely similar. One is often interested in the con-... 

Flat platelets in which the mass transfer process can be regarded as onedimensional, with mass transfer taking place perpendicular to the faces of the platelets. Furthermore, the platelets will be assumed to be sufficiently thin for deviations from unidirectional transfer due to end-effects to be negligible. 

For a bed of catalyst particles in the form of flat platelets it is found that the mass transfer rate is increased by a factor of 1.2 if the velocity of the external fluid is doubled. The mass transfer coefficient ho is proportional to the velocity raised to the power of 0.6. What is the value of ho at the original velocity ... 

The plasticity of clay-water mixtures is due principally to two factors the flat platelet shape of the clay particles and their small size. When clay is wet, the water, which under such conditions is known as water of plasticity, envelops each particle, acts as a lubricant between the particles, and allows them, when an external force is applied to the mixture, to readily slide along each other, as shown in Figure 51. 

As an extension of their previous work, the Tachibana group (82, 83) studied the collapse fragments that occur when monolayers of 12-hydroxystearic acid are compressed slowly (18 A /molecule hr) at surface areas of less than 21 A /molecule, the normal cross-sectional area of a hydrocarbon chain. The collapsed monolayers were transferred from the subphase to hydrophilic supports by a horizontal lifting method for electron microscopic observation, which revealed (Fig. 30) flat platelets when the sample was racemic and twisted... 

Calcium crystallizes from sodium solution in flat platelets that have a beautiful, although irregular, dendritic structure. The particle size depends on the rate of cooling, but under ordinary circumstances varies between about 0.01 and 2.0 mm. The apparent density of the isolated powder is about 0.5. Its finely divided nature enhances its reactivity in most of the reactions wherein it is used. 

The molecular diffusivity D must be replaced by an effective diffusivity De because of the complex internal structure of the catalyst particle which consists of a multiplicity of interconnected pores, and the molecules must take a tortuous path. The effective distance the molecules must travel is consequently increases. Furthermore, because the pores are very small, their dimensions may be less than the mean free path of the molecules and Knudsen diffusion effects may arise Equation 10.170 is solved in Volume 1 to give equation 10.199 for a catalyst particle in the form of a flat platelet... 

Bismuth oxychloride (bismuth oxide chloride) with the formula BiOCI was the first synthetic nontoxic nacreous pigment. Its production in form of monocrystals takes place by hydrolysis of acidic bismuth salt solutions in the presence of chloride ions. The desired pigment crystal quality can be controlled by varying the precipitation conditions (concentration, temperature, pH, pressure, addition of surfactants). The virtually tetragonal bipyramidal crystal structure is thereby modified into a flat platelet. 

FIGURE 9.15 Potential near the surface of a flat platelet particle using linear and nonlinear Poisson-Boltzmann equation with a surface potential of % = 2.0, (51.4 mV), which is the potential at the outer Helmholtz plane in Figure 9.14. Also showing the shear plane where the zeta potential is measured. 

The VPD catalyst appears more crystalline than the VPO catalyst. XRD and P NMR both show crystalline (VO)2P207, with a small amount of VOPO4 and disorganized (VO)2P207 also visible in the spin echo mapping spectrum. The TEM study shows the characteristic rosettes make up 95% of the catalyst, with a few flat platelets. Diffraction patterns showed the rosettes to be made up of (VO)2P207 (100) planes, while the flat plates can be indexed to an-VOP04. 

Lamellae are thin, flat platelets on the order of 100 to 200 A (0.01-0.02 micron) thick and several microns in lateral dimensions, while polymer molecules... 

Fig. 11. Comparison between experimental and simulated (dashed lines) dm t)/dt growth rate of a CdSe film deposited at 45 °C from an amraonia-TEA-selenosulfite bath, without STA (curve a), in the presence of 10" M STA (curve b). The inset presents a TEM image of a CdSe deposit on a carbon membrane before coalescence showing the formation of flat platelets (from [80]). With permission of Elsevier...

All polymer single crystals have the same general appearance. Under an electron microscope, they appear as thin, flat platelets that are 100 to 120 A thick and several microns in lateral dimensions. This lamellar nature of polymer single crystals has been found to be fundamental. Growth of the crystal normal to lamellar surface occurs by the formation of additional lamellae of the same thickness as the basal lamellae thick crystals are usually multilamellar. 

Lamellae are thin, flat platelets on the order of 100-200 A (0.01-0.02 pm) thick and several microns in lateral dimensions, while polymer molecules are generally on the order of 1,000-10,000 A long. Since the polymer chain axis is perpendicular to the plane of the lamellae, as revealed by electron diffraction, the polymer molecules must therefore be folded back and forth within the crystal. This arrangement has been shown to be sterically possible. In polyethylene, for example, the molecules can fold in such a way that only about five chain carbon atoms are required for the fold, that is, for the chain to reverse its direction. Each molecule folds up and down in a regular fashion to establish a fold plane. As illustrated in Figure 1.14a, a single fold plane may contain many polymer chains. The height of the fold plane is known as the fold period. It corresponds to the thickness of the lamellae. 

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