Spherical particles homogeneous

Fig. 35 Crystallization of non-spherical particles homogeneously coated with DNA. (a, b) Schematic of a hexagonal close-packed 2D layer in assemblies of gold nanorods and corresponding structure factor S(q) obtained from SAXS measurements (blue line) and simulations (red line), (c, d) Schematic of ID columnar assembly of gold triangular nanoprisms and corresponding SAXS patterns, (e, f) Schematic of the 3D fee assembly of gold rhombic dodecahedra (the lines indicate the fee unit cell) and corresponding SAXS patterns. Adapted with permission from [152]...

Because enzymes can be intraceUularly associated with cell membranes, whole microbial cells, viable or nonviable, can be used to exploit the activity of one or more types of enzyme and cofactor regeneration, eg, alcohol production from sugar with yeast cells. Viable cells may be further stabilized by entrapment in aqueous gel beads or attached to the surface of spherical particles. Otherwise cells are usually homogenized and cross-linked with glutaraldehyde [111-30-8] to form an insoluble yet penetrable matrix. This is the method upon which the principal industrial appHcations of immobilized enzymes is based. 

It follows from general considerations that the role of the shape of the filler particles during net-formation must be very significant. Thus, it is well-known that the transition from spherical particles to rod-like ones in homogeneous systems results in such radical structural effect as the formation of liquid-crystal phase. Something like that must be observed in disperse systems. 

This case can also be approached using Kolmogoroff s (K9, H15) theory of local isotropic turbulence to predict the velocity of suspended particles relative to a homogeneous and isotropic turbulent flow. By examining this situation for spherical particles moving with a constant relative velocity, varying randomly in direction, Levich, (L3) has demonstrated that... 

Neal and Nader [260] considered diffusion in homogeneous isotropic medium composed of randomly placed impermeable spherical particles. They solved steady-state diffusion problems in a unit cell consisting of a spherical particle placed in a concentric shell and the exterior of the unit cell modeled as a homogeneous media characterized by one parameter, the porosity. By equating the fluxes in the unit cell and at the exterior and applying the definition of porosity, they obtained... 

Neale, GH Nader, WK, Prediction of Transport Processes Within Porous Media Diffusive Flow Processes Within a Homogeneous Swarm of Spherical Particles, AIChE Journal 19, 112, 1973. 

Particle Size Laser Refractometiy is based upon Mie scattering of particles in a liquid medium. Up until about 1985, the power of computers supplied with laser diffraction instruments was not sufficient to utilize the rigorous solution for homogeneous spherical particles formulated by Gustave Mie in 1908. Laser particle instrument manufacturers therefore used approximations conceived by Fraunhofer. 

Bartle et al. [286] described a simple model for diffusion-limited extractions from spherical particles (the so-called hot-ball model). The model was extended to cover polymer films and a nonuniform distribution of the extractant [287]. Also the effect of solubility on extraction was incorporated [288] and the effects of pressure and flow-rate on extraction have been rationalised [289]. In this idealised scheme the matrix is supposed to contain small quantities of extractable materials, such that the extraction is not solubility limited. The model is that of diffusion out of a homogeneous spherical particle into a medium in which the extracted species is infinitely dilute. The ratio of mass remaining (m ) in the particle of radius r at time t to the initial amount (mo) is given by ... 

The pH is thus slowly raised in the solution by the gradual release of ammonia basic carbonates are precipitated. Although very uniform spherical particles are obtained (Figure 2), they do not have a homogenous cation distribution since upon the slow increase of pH, Cu is precipitated first as the nucleus of these particles, then Y (32). Ba can be precipitated only if large amounts of urea are used (31). Another procedure is to first precipitate Y Cu particles then disperse them in a solution containing Ba(NOs)2 and urea in order to, by the... 

In 1968, Stober et al. (18) reported that, under basic conditions, the hydrolytic reaction of tetraethoxysilane (TEOS) in alcoholic solutions can be controlled to produce monodisperse spherical particles of amorphous silica. Details of this silicon alkoxide sol-gel process, based on homogeneous alcoholic solutions, are presented in Chapter 2.1. The first attempt to extend the alkoxide sol-gel process to microemul-sion systems was reported by Yanagi et al. in 1986 (19). Since then, additional contributions have appeared (20-53), as summarized in Table 2.2.1. In the microe-mulsion-mediated sol-gel process, the microheterogeneous nature (i.e., the polar-nonpolar character) of the microemulsion fluid phase permits the simultaneous solubilization of the relatively hydrophobic alkoxide precursor and the reactant water molecules. The alkoxide molecules encounter water molecules in the polar domains of the microemulsions, and, as illustrated schematically in Figure 2.2.1, the resulting hydrolysis and condensation reactions can lead to the formation of nanosize silica particles. 

Spherical particles of various metal phosphate particles can be prepared by precipitation using urea as a homogeneous precipitation agent. Surface-active agents, such as SDS and CTAC, are effective in preparation of uniform-size spherical particles. The formed spherical particles are amorphous and contain OH- and H20, except cobalt phosphate particles with layered structure. These panicles are agglomerates of primary particles, and have pores of different sizes ranging from ultramicropore to mesopore. 

At low water content from vv = 2 to 5.5, a homogeneous reverse micellar solution (the L2 phase) is formed. In this range, the shape of the water droplets changes from spheres (below ir = 4) to cylinders. At tv — 4, the gyration radius has been determined by SAXS and found equal to 4 nm. Syntheses in isolated water-in-oil droplets show formation of a relatively small amount of copper metallic particles. Most of the particles are spherical (87%) with a low percentage (13%) of cylinders. The average size of spherical particles is characterized by a diameter of 12 nm with a size polydispersity of 14%. 

Work with a neighbor. Consider Eq. (3.34), which describes the free energy change associated with the homogeneous nucleation of a solid, spherical particle of radius, r, from a parent liquid phase ... 

One way to deal with heterogeneous materials is to assume that the composite has an effective thermal conductivity, kgff, which can tlien be used in heat transport expressions as previously performed for homogeneous materials. There are several expressions for k ff that have been developed, depending upon the type and amount of reinforcing material. For spherical particles of small volume fractions, (p, we have... 

We note that (5.36) implies that a homogeneous spherical particle will be invisible (i.e., a = 0) if it is coated with a material such that the numerator in... 

Predicting optical properties of atmospheric aerosols from calculations for homogeneous, spherical particles leaves much to be desired. Mie theory may be a gross oversimplification. In addition, there may not be accurate optical constants for the constituents, even those that are known and they may not all be known. Yet even minor constituents can be major contributors to absorption. 

Whatever the nature of the template, among possible applications such as catalysts, grafting supports, or filtration medium, the use of MTS for chromatography applications has been claimed for years. However, this latter application requires the ability to synthesize homogeneous batches of spherical particles with a mean diameter at least equal to 5 pm. Such particles were observed only once, in a pH-dependent synthesis of MCM-41 particles, performed by Yang, Ozin and co-workers [1], Most of the time, the synthesis of submicrometer-size particles of MCM-41 or MCM-48 materials was only reported [2-4], We present the synthesis of MSU-X silica with perfectly controlled size and shape suitable for chromatography applications. 

In order to obtain a reliable mathematical apparatus there has to be a reasonably simple, yet accurate, model of the structure of a syntactic foam. Attempts to extend the known models of monolithic plastics to syntactic structures filled with solid spherical particles have not proved successfull 8,76). Models which rely on close microsphere packing 157,158> have not been very accurate either. For example, Krzhechkovsky et al.,59) showed that syntactic foams can be treated as homogeneous uniform materials with small Ks (up to 20%) only if there is no stress field in the polymer matrix around the microspheres (see Sect. 3.5). 

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