Spheres surface roughness

A number of refinements and applications are in the literature. Corrections may be made for discreteness of charge [36] or the excluded volume of the hydrated ions [19, 37]. The effects of surface roughness on the electrical double layer have been treated by several groups [38-41] by means of perturbative expansions and numerical analysis. Several geometries have been treated, including two eccentric spheres such as found in encapsulated proteins or drugs [42], and biconcave disks with elastic membranes to model red blood cells [43]. The double-layer repulsion between two spheres has been a topic of much attention due to its importance in colloidal stability. A new numeri-... 

There is a convenient mathematical idealization which asserts that a cube of edge length, / cm, possesses a surface area of 6 f cm and that a sphere of radius r cm exhibits 4nr cm of surface. In reality, however, mathematical, perfect or ideal geometric forms are unattainable since under microscopic examinations all real surfaces exhibit flaws. For example, if a super microscope were available one would observe surface roughness due not only to the atomic or molecular orbitals at the surface but also due to voids, steps, pores and other surface imperfections. These surface imperfections will always create real surface area greater than the corresponding geometric area. 

The molecule is often represented as a polarizable point dipole. A few attempts have been performed with finite size models, such as dielectric spheres [64], To the best of our knowledge, the first model that joined a quantum mechanical description of the molecule with a continuum description of the metal was that by Hilton and Oxtoby [72], They considered an hydrogen atom in front of a perfect conductor plate, and they calculated the static polarizability aeff to demonstrate that the effect of the image potential on aeff could not justify SERS enhancement. In recent years, PCM has been extended to systems composed of a molecule, a metal specimen and possibly a solvent or a matrix embedding the metal-molecule system in a molecularly shaped cavity [62,73-78], In particular, the molecule was treated at the Hartree-Fock, DFT or ZINDO level, while for the metal different models have been explored for SERS and luminescence calculations, metal aggregates composed of several spherical particles, characterized by the experimental frequency-dependent dielectric constant. For luminescence, the effects of the surface roughness and the nonlocal response of the metal (at the Lindhard level) for planar metal surfaces have been also explored. The calculation of static and dynamic electrostatic interactions between the molecule, the complex shaped metal body and the solvent or matrix was done by using a BEM coupled, in some versions of the model, with an IEF approach. 

According to AFM micrographs, the surface roughness of porous spheres of DMN-DVB copolymer increases in the presence of methyl-containing silica. At the same time, the availability of methylsilyl and silicon hydride groups on the silica surface promotes surface smoothing upon filling, similar to an unfilled system. 

With respect to the preparation of die surface, a measurement of a surface property is obviously only as good as the preparation of the surface on which the measurement is made. Ideally one would desire to have a surface which was atomically flat on a crystallographically perfect and chemically pure crystal. After reliable information had been obtained chi such ideal surfaces, it would then be necessary to determine the influence of surface roughness, of impurities, and of crystal imperfections of various kinds on the oxidation process. Most of the measurements to be described in this paper, however, have been made on surfaces which were prepared by the best methods available at this time. A convenient method of determining the important faces of a metal for detailed study involves the initial use of the specimen in the form of a sphere exposing all possible crystal faces such methods have been previously described, it should be emphasized that much additional work... 

The adhesive force between a neutral particulate contaminant and the wafer is expected to be due to the attractive Van der Waal s interaction between molecules.This is a macroscopic force found by averaging over the force between all the molecules of a particle and the neighboring surface. For a spherical particle sitting on a flat wafer, it is known that surface roughness will cause the mean distance of separation between the particle and the wafer to be nonzero. The attractive force between these two entities acts along the normal between the sphere and the wafer, and is given by ... 

Surface roughness A is defined as the ratio of the geometric ( oeo) to the BET (5bet) surface areas (Helgeson, 1971). For a perfectly smooth surface, without internal porosity, the two surface area measurements should be the same, i.e., A = 1. For nonideal surfaces of geometric spheres, the roughness can be related directly to the particle diameter d and the mineral density p such that... 

The effect of surface roughness on the drag coefficient of a sphere. 

The fact that Na is the ratio of the molar volume to the atomic volume of any element provides a route to measuring its value, and several methods have been nsed to determine this ratio. A new method to refine the valne cnrrently is under development. Nearly perfectly smooth spheres of highly crystalline silicon (Si) can be prepared and characterized. The surface roughness of these spheres (which affects the determination of their volume) is 1 silicon atom. The molar volnme is determined by carefnlly measnring the mass and volume of the sphere, and the atomic volume is determined by measuring the interatomic distances directly nsing x-ray diffraction. (X-ray diffraction from solids is described in Chapter 21.) Avogadro s nnmber is the ratio of these two quantities. 

Figure 65. Van der Waals sphere/plane model with and without surface roughness...

Sphere-Flat Test Results. Kitscha [47] performed experiments on steady heat conduction through 25.4- and 50.8-mm sphere-flat contacts in an air and argon environment at pressures between 10 5 torr and atmospheric pressure. He obtained vacuum data for the 25.4-mm-diameter smooth sphere in contact with a polished flat having a surface roughness of approximately 0.13 pm RMS. The mechanical load ranged from 16 to 46 N. The mean contact temperature ranged between 321 and 316 K. The harmonic mean thermal conductivity of the sphere-flat contact was found to be 51.5 W/mK. The emissivities of the sphere and flat were estimated to be e, = 0.2 and e2 = 0.8, respectively. 

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