Inhomogeneous Spherical Particles

A concise approach for the analysis of isotropic scattering curves of spherical and cylindrical particles with a radial density profile has been developed by Burger [207]. In practice it is useful for the smdy of latices and vesicles in solution. 

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Another controversial and evolving idea concerning casein micelle structure is the concept of the submicelle. That there is some substructure to the micelle can hardly be denied, because all of the appropriate techniques have revealed some inhomogeneities over distances of 5-20 nm. Proponents of submicellar models of casein micelle structure interpret this evidence in terms of spherical particles of casein, the submicelles, joined together, possibly, by the calcium... 

These imperfections have occasioned to review the spherical DFT approach with respect to a more correct description for fluids which consists of non-spherical particles. The paper applies a statistic thermodynamic approach [7, 8] which uses density functional formulation to describe the adsorption of nitrogen molecules in the spatial inhomogeneous field of an adsorbens. It considers all anisotropic interactions using asymmetric potentials in dependence both on particular distances and on the relative orientations of the interacting particles. The adsorbens consists of slit-like or cylinder pores whose widths can range from few particle diameters up to macropores. The molecular DFT approach includes anisotropic overlap, dispersion and multipolar interactions via asymmetric potentials which depend on distances and current orientations of the interacting sites. The molecules adjust in a spatially inhomogeneous external field their localization and additionally their orientations. The approach uses orientation distributions to take the latter into account. 

Two pellets, of porosities 0.41 and 0.48 respectively, were made by means of coaxial compaction of Alumina powder consisting of non porous spherical particles of size ca. 200A in diameter. Each pellet consists of 11 sections, and the compaction pressures of those sections were selected in such a way that no macroscopic porosity inhomogeneities would be present on the final pellet. The BET specific surface area of the pellets was calculated 100 15 m /gr. 

The ponderomotive force due to the inhomogeneity of the electric field in a direction perpendicular to the dust-covered surface can be determined for spherical particles by the formula... 

A small-angle X-ray scattering(SAXS) study of a model copolymer latex, based on styrene and pentabromobenzyl acrylate(PBBA, 40 wt %), was conducted. The contrast variation method used was shown to be a sensitive probe for inhomogeneity in the particles. The separation of the homogeneous function allowed direct calculation of the size distribution of the spherical particles. The SAXS analysis revealed a particle s inner structure which was a continuous copolymer phase, the composition of which was slightly richer in PBBA, within which domains of PS were randomly distributed. The volume fraction of the PS domains was estimated as 11 vol % and their characteristic length as 5.1 nm. 24 refs. 

It was shown that the phase-Doppler technique is a powerful tool for simultaneous measurements of diameters and velocities of spherical particles in application to optical absorbent homogeneous and inhomogeneous liquids. 

The electrodeposited gold was distributed randomly as small spherical particles, with an average diameter of 60 nm, and these nanoparticles were dispersed both at the grain boundaries and on the facets, as observed in SEM studies (Fig. 17.7 a b). The active sites for gold nucleation were inhomogeneously distributed on the surface of diamond. 

The Laplace-Young equation refers to a spherical phase boundary known as the surface of tension which is located a distance from the center of the drop. Here the surface tension is a minimum and additional, curvature dependent, terms vanish (j ). The molecular origin of the difficulties, discussed in the introduction, associated with R can be seen in the definition of the local pressure. The pressure tensor of a spherically symmetric inhomogeneous fluid may be computed through an integration of the one and two particle density distributions. 

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