Monodisperse spherical particle systems

For monodisperse spherical particle systems, the total scattering intensity, I(q), is simply be given as... 

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. 

Zirconia has been synthesized by hydrolysis of zirconium tetrabutoxide in the water pools of reverse microemulsions . Kawai et al. investigated the relationship between particle formation and the solubilized states of water in the reaction system. The results indicate that monodisperse, spherical particles are more easily obtained in reverse and swollen micelles than in a w/o microemulsion. Crystalline Zr02 particles were achieved after calcination at 800 °C. The use of zirconium oxynitrate as precursor is also reported in the literature By reacting a microemulsion containing this precursor with a microemulsion containing aqueous ammonia as water phase, the calcination temperature for obtaining crystalline zirconia could be reduced to 362 °C. 

SUica particles can be coated by the silane coupling agent APS in the reaction medium to obtain stable colloids. These systems can be used to further bind relevant groups to the particle surface [48,51,52]. Quantitative Si NMR spectroscopy appears to be a valuable tool in characterizing a new kind of stable colloidal particles synthesized from a mixture of the alkoxides APS and TES. These monodisperse, spherical particles can aheady be prepared with a low polydispersity and contain APS molecules distributed through an important part of the bulk of the particle. It would be interesting to see whether this method is also applicable to other mixtures of alkoxides. More work concerning the characterization of these new systems has to be done [50]. 

During the past few decades the increase in activity in polymer colloids [100-104] and with it methods for the formation of veiy monodisperse spherical particles has provided a variety of polymeric substrates for adsorption or chemical attachment of polymers or surfactants. They have also provided quite well-defined systems for investigating the effects of these molecules on colloidal stability. Added to this has been a complementaiy growth in the synthesis of various type of surfactants and macromolecules in well-defined, often pure, form. On the theoretical front the rapid development of computers has also provided ways of simulating both molecular structures in solution and at surfaces. This has meant a rapid growth of the literature on adsorption of various molecules on polymer colloids and on the effects of this adsorptioi colloid stability. Much of this is now summarized in review articles, conferences and books [105-107] which are too extensive to discuss in this chapter hence rally the salient points will be covered. 

K. Ichiki, M. Asano, A. Kawasaki, R. Watanabe, M. Miyajima Preparation of monodisperse spherical particles of Bi-Sb system for thermoelectric microdevices, J. Jpn. Soc. Powder Powder Metall. 44, 700-705 (1997) (in Japanese). 

Modern synthetic methods allow preparation of highly monodisperse spherical particles that at least approach closely the behavior of hard-spheres, in that interactions other than volume exclusion have only small influences on the thermodynamic properties of the system. These particles provide simple model systems for comparison with theories of colloidal dynamics. Because the hard-sphere potential energy is 0 or 00, the thermodynamic and static structural properties of a hard-sphere system are determined by the volume fraction of the spheres but are not affected by the temperature. Solutions of hard spheres are not simple hard-sphere systems. At very small separations, the molecular granularity of the solvent modifies the direct and hydrodynamic interactions between suspended particles. 

Generally, alkoxide-derived monodisperse oxide particles have been produced by batch processes on a beaker scale. However, on an industrial scale, the batch process is not suitable. Therefore, a continuous process is required for mass production. The stirred tank reactors (46) used in industrial process usually lead to the formation of spherical, oxide powders with a broad particle size distribution, because the residence time distribution in reactor is broad. It is necessary to design a novel apparatus for a continuous production system of monodispersed, spherical oxide particles. So far, the continuous production system of monodisperse particles by the forced hydrolysis... 

Several monodisperse, spherical oxide particles were produced from the hydrolysis of metal alkoxide in ethanol or emulsion solution using the CTTR system. 

Monodisperse spherical oxide particles were prepared by the hydrolysis of metal alkoxide in homogeneous alcohol in an emulsion state. The formation mechanism from homogeneous alcohol and emulsion state was discussed by chronomal analysis and in situ observation using laser photo scattering. Two types of continuous systems for the industrial production of monodispersed oxide powders were also offered. 

This equation again demonstrates that particle size and solubility are the main parameters affecting dissolution kinetics of drug powders, which, in turn, could affect the release profile of dosage forms if dissolution is the rate-limiting step of in vivo absorption. Table 5.1 demonstrates several examples of dissolution times of spherical particles (assuming monodispersed systems) as a function of solubility and particle size. 

Equation (14) also provides a satisfactory description of the II-A isotherm for monodisperse spherical polystyrene particles 2.6 pm in diameter at the water/octane interface.40,41 For this system, fitting parameters using Eq. (14)... 

Lee and Lightfoot [229] developed the theoretical basis of Fl-FFF. This theory has been confirmed by numerous works on the fractionation of model systems, including monodisperse spherical polystyrene latexes and a number of proteins [41,228,229,240], some polydextrans [229], viruses [241], and other spherical particles and macromolecules [242,243]. 

Another important method for photonic crystal fabrication employs colloidal particle self-assembly. A colloidal system consists of two separate phases a dispersed phase and a continuous phase (dispersion medium). The dispersed phase particles are small solid nanoparticles with a typical size of 1-1000 nanometers. Colloidal crystals are three-dimensional periodic lattices assembled from monodispersed spherical colloids. The opals are a natural example of colloidal photonic crystals that diffract light in the visible and near-infrared (IR) spectral regions due to periodic modulation of the refractive index between the ordered monodispersed silica spheres and the surrounding matrix. 

Monodisper.se, spherical polystyrene latex particles in aqueous su.spension are available commercially in sizes ranging from 0.088 to about 2 m. Relative standard deviations in panicle size are usually less than 0% and sometimes less than 1%. The suspensions are manufactured industrially by emulsion polymerization. Monodisperse polyvinylioluene particles of somewhat larger diameter, up to 3.5 im. are also available. The properties of these systems are reviewed by Mercer (1973). 

For the sedimentation of rarefied monodisperse systems of spherical particles, drops, or bubbles, the mean Sherwood number can be calculated by using formulas (4.6.8) and (4.6.17), where the Peclet number must be determined on the basis of the constrained flow velocity. 

Let us consider mass and heat transfer for a monodisperse system of spherical particles of radius a with volume density of the solid phase. We use the fluid velocity field obtained at low Reynolds numbers from the Happel cell model (see Section 2.9) to find the mean Sherwood number [74,76 ... 

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