Approximately Spherical Particles

Sol-gel hydrolysis and condensation can be carried out within a polymeric matrix to generate particles of the ceramic material, typically with an average diameter of a few hundred angstroms. Silica has been 

Many of these nanocomposites have been characterized by nuclear magnetic resonance (NMR) spectroscopy, single-molecule spectroscopy, and small-angle scattering. - Some applications require other measurements, such as permeability or ionic conductivity. In the case of permeability, the presence of the filler can substantially reduce flux by blocking low-resistance pathways and by modification of the elastomer in the vicinity of the filler (figure 9.1). 

Other properties of PDMS-silica nanocomposites that have been reported include the glass transition temperatures, segmental dynamics,  

Permeability of a small molecule through PDMS as illustrated for the unfilled polymer (a), a nonpermeable filler decreasing the permeability of the PDMS by requiring a more tortuous route around the filler particles (b), and a filler that interacts so strongly with the PDMS that the PDMS segments close to the filler surface are so restricted that they are frequently called bound rubber (c).  

A variety of other nanoparticles have been formed by such in situ sol-gel reactions. Examples are the oxides of titanium, aluminum, - tanta-lum, zirconium, niobium, and vanadium. Some nanocomposites of this type have also included barium titanate, calcium oxide, calcium salts, borates, HTiNbOg, and Eu dopants.  

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By definition, the terminal velocity of a particle (ut) is the superficial gas velocity which suspends an isolated particle without translational motion—i.e., the terminal free fall velocity for that particle. From force balance on the particle, the terminal velocity for an approximately spherical particle can be shown to be... 

Oil, of density 900 kg/m3 and viscosity 3 mN s/m2, is passed vertically upwards through a bed of catalyst consisting of approximately spherical particles of diameter 0.1 mm and density 2600 kg/m3. At approximately what mass rate of flow per unit area of bed will (a) fluidisation, and (b) transport of particles occur ... 

A material of density 2500 kg/m3 is fed to a size separation plant where the separating fluid is water rising with a velocity of 1.2 m/s. The upward vertical component of the velocity of the particles is 6 m/s. How far will an approximately spherical particle, 6 mm diameter, rise relative to the walls of the plant before it comes to rest relative to the fluid ... 

Transmission electron microscopy (TEM) has been an underutilized yet valuable too in particle size characterization of MC particles in LB films. Monolayer films of trioctylphosphine oxide-capped CdSe (18), spread as a monolayer on an aqueous subphase, were transferred to a TEM grid. A close-packed hexagonal arrangement of 5.3-nm (cr —4%) crystallites was found. TEM images were also obtained for HMP-stabilized CdS incorporated in BeH/octadecylamine films (79) and for CdS formed under an amine-based surfactant monolayer and transferred to a TEM grid (14). In one study, direct viewing of CdS and CdSe particles made from Cd2+-FA films on TEM grids was not possible due to poor phase contrast between the particles and the film (30). Diffraction patterns were observed, however, that were consistent with crystalline (3-CdS or CdSe. Approximately spherical particles of CdSe could... 

The viscoelastic properties of polypropylene melts containing magnesium hydroxide fire retardant fillers have been studied using parallel plate dynamic rheology [36]. In this work the filler variants differed in particle size, surface area and morphology, ranging from approximately spherical particles formed... 

EXAMPLE 11.4 Interaction Between Spherical Particles The Use of the Derjaguin Approximation. Spherical particles can be approximated by a stack of circular rings with planar faces as shown in Figure 11.8. Use Equation (86) to describe the repulsion between rings separated by a distance z and derive an expression for the repulsion between the two spheres of equal radius Rs. Assume that the strongest interaction occurs along the line of centers and make any approximations consistent with this to obtain the final result. 

The observed pattern of segregation might well be a consequence of the accommodation of metallic particles in the free volume available in an assembly of large approximately spherical particles of PVC. For example, close packing of spheres in a face centered cubic system would provide a continuous network of open channels which in the (100) planes would provide spaces of the kind shown in Figure 7. Some features corresponding to the filling of such spaces by small metallic particles... 

Sooty carbon isotropic carbon form comprised of approximately spherical particles less than 1. im in diameter, sometimes referred to as combustion black (ASTM D-5061). 

Microspheres can be defined as solid, approximately spherical particles ranging in size from 1 to 1000 pm. 

Typical is microencapsulation , a method by which small portions of liquids, particulate solids, or gases are surrounded by a shell (membrane, capsule) to form approximate spherical particles. 

A stirred vertical cylindrical vessel contains a mixture of 12 parts polyethylene of mean molecular weight 21,5(X) and 100 parts of ethylene at 1,400 atm and 90 °C. The vessel is then cooled by a blast of cold compressed air to 30 °C, the pressure falling to 450 atm. The vessel is blown down to atmospheric pressure and opened. The upper part of the vessel is found to contain 1.2 parts of powdered polyethylene composed of loose aggregates of approximately spherical particles of average diameter below 0.01 mm. of molecular weight 9,000, while the bottom of the vessel contains a fused mass of 10.8 parts of ptolyethylene of molecular weight 23,000."... 

Fig. 1. Generalized structure of a lipoprotein particle. Lipoproteins are approximately spherical particles that consist of a neutral lipid core (triacylglycerols and cholesteryl esters) surrounded by a surface monolayer of amphipathic lipids (unesterified cholesterol and phospholipids) and specific apoproteins.

M is the molecular weight and p the density of the solid, d describes the particle size and a is a geometrical factor which depends on the shape of the particles. For approximately spherical particles with diameter d the geometry factor is a 6. According to Schindler [1967SCH] the mean free surface energy of the solid-liquid interface can be estimated by Eq. (VI1.44) ... 

HIPS polymers consist of a matrix of polystyrene containing approximately spherical particles of rubbery polybutadiene ranging in size from about 0.1 to 10 pm depending on the precise composition and method of polymerisation. The rubber particles may themselves contain small regions of PS as shown in fig. 12.7. Another series of rubber-toughened blends is the acrylonitrile-butadiene-styrene (ABS) terpolymers, which are basically... 

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