Reactions, colloidal model particles from

At the end of the precipitation reaction, the solid particles must be colloidally stable if a uniform particle-size distribution is to be observed. A question important to final uniformity is the particle size when this stability is achieved. The particles will always feel the long-range van der Waals attractive interactions. Interactions of an electrostatic or solvation origin can give rise to a repulsive barrier that can provide kinetic stabilization. At the end of the reaction, particles precipitated from TEOS and titanium alkoxides have final particle number densities, N , of 1016—1018 m-3. These particles are suspended in a solvent with an ionic strength of approximately 10-4 M and have surface potentials of 10-35 mV. Our studies indicate that the particles also feel a short-range repulsive interaction that we have modeled as a solvation interaction with decay... 

Conventional routes to ceramics involve precipitation from solution, drying, size reduction by milling, and fusion. The availability of well-defined mono-dispersed particles in desired sizes is an essential requirement for the formation of advanced ceramics. The relationship between the density of ceramic materials and the sizes and packing of their parent particles has been examined theoretically and modeled experimentally [810]. Colloid and surface chemical methodologies have been developed for the reproducible formation of ceramic particles [809-812]. These methodologies have included (i) controlled precipitation from homogeneous solutions (ii) phase transformation (iii) evaporative deposition and decomposition and (iv) plasma- and laser-induced reactions. 

One of the most important parameters in the S-E theory is the rate coefficient for radical entry. When a water-soluble initiator such as potassium persulfate (KPS) is used in emulsion polymerization, the initiating free radicals are generated entirely in the aqueous phase. Since the polymerization proceeds exclusively inside the polymer particles, the free radical activity must be transferred from the aqueous phase into the interiors of the polymer particles, which are the major loci of polymerization. Radical entry is defined as the transfer of free radical activity from the aqueous phase into the interiors of the polymer particles, whatever the mechanism is. It is beheved that the radical entry event consists of several chemical and physical steps. In order for an initiator-derived radical to enter a particle, it must first become hydrophobic by the addition of several monomer units in the aqueous phase. The hydrophobic ohgomer radical produced in this way arrives at the surface of a polymer particle by molecular diffusion. It can then diffuse (enter) into the polymer particle, or its radical activity can be transferred into the polymer particle via a propagation reaction at its penetrated active site with monomer in the particle surface layer, while it stays adsorbed on the particle surface. A number of entry models have been proposed (1) the surfactant displacement model (2) the colhsional model (3) the diffusion-controlled model (4) the colloidal entry model, and (5) the propagation-controlled model. The dependence of each entry model on particle diameter is shown in Table 1 [12]. 

The major distinction between the model of La Mer and that developed for uniform latex particles lies in the incorporation of colloidal stability of small particles. The La Mer model assumes that each nucleus is colloidally stable and survives at the end of the reaction at the center of a particle. The aggregation models argue that stabilizing primary small particles is difficult, but aggregation does not necessarily result in a broad particle-size distribution. When schemes for control of particle-size distribution are developed, the result of accepting the notion that colloidal stability can play an important role is that attention is focused away from the length of the nucleation period and towards the colloidal properties of the growing particles. 

The early models yielded approximate concentrations that reflected the understanding of the soil solution at the time. Later models have yielded better predictions of the soil solution s composition, but they are still only approximate. That reflects the complexity of the soil more than the inadequacy of modeling. The models predict ion interactions in the aqueous solution quite well. Reactions at the surface of colloidal particles are more complex, less understood, slower, and hence are more difficult to formulate. In addition, the models are forced to use the solubility products of pure, simple solids. Soil inorganic particles are far from pure compounds, are often poorly crystalline to amorphous, are not at internal equilibrium, and may not be in equilibrium with the aqueous phase. In addition, the reactions of soil organic matter are not known quantitatively aud soils are open systems, meaning that matter is continually being added and removed. 

Another method that introduces a very simplified dynamics is the Multi-Particle Collision Model (or Stochastic Rotation Model) [130]. Like DSMC particle positions and velocities are continuous variables and the system is divided into cells for the purpose of carrying out collisions. Rotation operators, chosen at random from a set of rotation operators, are assigned to each cell. The velocity of each particle in the cell, relative to the center of mass velocity of the cell, is rotated with the cell rotation operator. After rotation the center of mass velocity is added back to yield the post-collision velocity. The dynamics consists of free streaming and multi-particle collisions. This mesoscopic dynamics conserves mass, momentum and energy. The dynamics may be combined with full MD for embedded solutes [131] to study a variety of problems such as polymer, colloid and reaction dynamics. 

---