Dispersion particles model

Abstract The structure and surface pressure of compressed monolayers consisting of silica nanoparticles at the water-air interface have been studied by means of molecular dynamics computer simulations. The simple hexagonal array of mono-disperse particles model overestimates the range of the repulsive interparticle potentials between the nanoparticles in a monolayer. On the basis of the results of the simulation we proposed a method to assess the error of the estimation. We also investigated the relevance of... 

Friis and Hamielec (48) offered some comments on the continuous reactor design problem suggesting that the dispersed particles have the same residence time distribution as the dispersing fluid and the system can be modeled as a segregated CSTR reactor. 

Because XPS is a surface sensitive technique, it recognizes how well particles are dispersed over a support. Figure 4.9 schematically shows two catalysts with the same quantity of supported particles but with different dispersions. When the particles are small, almost all atoms are at the surface, and the support is largely covered. In this case, XPS measures a high intensity Ip from the particles, but a relatively low intensity Is for the support. Consequently, the ratio Ip/Is is high. For poorly dispersed particles, Ip/Is is low. Thus, the XPS intensity ratio Ip/Is reflects the dispersion of a catalyst on the support. Several models have been reported that derive particle dispersions from XPS intensity ratios, frequently with success. Hence, XPS offers an alternative determination of dispersion for catalysts that are not accessible to investigation by the usual techniques used for particle size determination, such as electron microscopy and hydrogen chemisorption. 

The physicochemical forces between colloidal particles are described by the DLVO theory (DLVO refers to Deijaguin and Landau, and Verwey and Overbeek). This theory predicts the potential between spherical particles due to attractive London forces and repulsive forces due to electrical double layers. This potential can be attractive, or both repulsive and attractive. Two minima may be observed The primary minimum characterizes particles that are in close contact and are difficult to disperse, whereas the secondary minimum relates to looser dispersible particles. For more details, see Schowalter (1984). Undoubtedly, real cases may be far more complex Many particles may be present, particles are not always the same size, and particles are rarely spherical. However, the fundamental physics of the problem is similar. The incorporation of all these aspects into a simulation involving tens of thousands of aggregates is daunting and models have resorted to idealized descriptions. 

We present an improved model for the flocculation of a dispersion of hard spheres in the presence of non-adsorbing polymer. The pair potential is derived from a recent theory for interacting polymer near a flat surface, and is a function of the depletion thickness. This thickness is of the order of the radius of gyration in dilute polymer solutions but decreases when the coils in solution begin to overlap. Flocculation occurs when the osmotic attraction energy, which is a consequence of the depletion, outweighs the loss in configurational entropy of the dispersed particles. Our analysis differs from that of De Hek and Vrij with respect to the dependence of the depletion thickness on the polymer concentration (i.e., we do not consider the polymer coils to be hard spheres) and to the stability criterion used (binodal, not spinodal phase separation conditions). 

These block copolymers can act as effective steric stabilizers for the dispersion polymerization in solvents with ultralow cohesion energy density. This was shown with some polymerization experiments in Freon 113 as a model solvent. The dispersion particles are effectively stabilized by our amphi-philes. However, these experiments can only model the technically relevant case of polymerization or precipitation processes in supercritical C02 and further experiments related to stabilization behavior in this sytem are certainly required. 

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. 

Fig. 2 (a) 2D image of oil-extended PP/EPDM TPVs. Crosslinked EPDM particles are separated by circle, (b) 3D model of blend showing EPDM dispersed particles... 

Stokes s law and the equations developed from it apply to spherical particles only, but the dispersed units in systems of actual interest often fail to meet this shape requirement. Equation (12) is sometimes used in these cases anyway. The lack of compliance of the system to the model is acknowledged by labeling the mass, calculated by Equation (12), as the mass of an equivalent sphere. As the name implies, this is a fictitious particle with the same density as the unsolvated particle that settles with the same velocity as the experimental system. If the actual settling particle is an unsolvated polyhedron, the equivalent sphere may be a fairly good model for it, and the mass of the equivalent sphere may be a reasonable approximation to the actual mass of the particle. The approximation clearly becomes poorer if the particle is asymmetrical, solvated, or both. Characterization of dispersed particles by their mass as equivalent spheres at least has the advantage of requiring only one experimental observation, the sedimentation rate, of the system. We see in sections below that the equivalent sphere calculations still play a useful role, even in systems for which supplementary diffusion studies have also been conducted. 

In general, a dispersed particle is free to move in all three dimensions. For the present, however, we restrict our consideration to the motion of a particle undergoing random displacements in one dimension only. The model used to describe this motion is called a onedimensional random walk. Its generalization to three dimensions is straightforward. 

The Adsorption of Hydrolyzed Al(III). O Melia and Stumm (12) have shown that specific adsorption of hydrolyzed Fe(III) species accounts for the observed coagulation and restabilization of silica dispersions. A model was formulated on the basis of the Langmuir adsorption isotherm and was shown to explain the observations adequately. The authors derive a relationship between the surface area concentration of the dispersed phase S (in meter2/liter and the applied coagulant ion concentration Cte (in M) necessary to reach a certain fraction of surface coverage. The extent of destabilization or of restabilization can be concluded from the amount of surface coverage on the colloidal particle ... 

Virtually every textbook states that (all) wave packets disperse and therefore cannot serve as a serious particle model. 

The knowledge of the surface potential for the dispersed systems, such as metal oxide-aqueous electrolyte solution, is based on the model calculations or approximations derived from zeta potential measurements. The direct measurement of this potential with application of field-effect transistor (MOSFET) was proposed by Schenk [108]. These measurements showed that potential is changing far less, then the potential calculated from the Nernst equation with changes of the pH by unit. On the other hand, the pHpzc value obtained for this system, happened to be unexpectedly high for Si02. These experiments ought to be treated cautiously, as the flat structure of the transistor surface differs much from the structure of the surface of dispersed particle. The next problem may be caused by possible contaminants and the surface property changes made by their presence. 

For colloidal semiconductor systems, Albery et al. observed good agreement between the value of the radial dispersion obtained from dynamic light scattering and the value found from application of the above kinetic analysis to flash photolysis experiments [144], It should be remembered that this disperse kinetics model can only be applied to the decay of heterogeneous species under unimolecular or pseudo-first order conditions and that for colloidal semiconductors it may only be applied to dispersions whose particle radii conform to equation (37), i.e., a log normal distribution. However, other authors [145] have recently refined the model so that assumptions about the particle size distribution may be avoided in the kinetic data analysis. 

Dynamic light scattering (DLS) techniques measure the fluctuations in the scattered light intensity caused by the random Brownian motion of the dispersed particles. The use of a theoretical model of particle Brownian motion enables us to extract particle size from DLS data. Other dynamic light scattering techniques such as electrophoretic light scattering (ELS) study collective particle motions. Theoretical interpretation of ELS data leads to other particle properties such as electrophoretic mobility fi and zeta potential f. These techniques will be discussed in more detail in subsequent sections. 

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