Embedded sphere

Figure 6.34 Schematically presented embedded sphere morphology of the particles of hybrid dispersions prepared according to method 2 (diluting the prepolymer-ionomer with monomers, emulsifying it in water, crosslinking with polyamine and polymerisation)...

The morphology of dispersed particles revealed by TEM appeared to be very interesting. It was found that the method of hybrid synthesis had a substantial influence on the particle morphology and that usually core-shell or englued morphologies described earlier in the literature were observed. However, in one case the unusual embedded sphere morphology was seen. In these particles, the core made of polyurethane-urea is surrounded by a 25-40 nm thick sphere made of acrylic/styrene polymer and covered by a 15-20 nm thick outer layer of polyurethane-urea. The structure of film made from such dispersions is very interesting since it is a two-phase structure where nanospheres of acrylic/styrene polymer are suspended in a polyurethane-urea matrix. 

Let 5 C fa be a smoothly embedded sphere, such that its sufficiently small tubular neighbourhood NgS of radius e > 0 be represented as the direct product 5 X where is a normal disk of dimension n — A and radius e. Then... 

The interiors of rhodopseudomonad bacteria are filled with photosynthetic vesicles, which are hollow, membrane-enveloped spheres. The photosynthetic reaction centers are embedded in the membrane of these vesicles. One end of the protein complex faces the Inside of the vesicle, which is known as the periplasmic side the other end faces the cytoplasm of the cell. Around each reaction center there are about 100 small membrane proteins, the antenna pigment protein molecules, which will be described later in this chapter. Each of these contains several bound chlorophyll molecules that catch photons over a wide area and funnel them to the reaction center. By this arrangement the reaction center can utilize about 300 times more photons than those that directly strike the special pair of chlorophyll molecules at the heart of the reaction center. 

Baumgartner and coworkers [145,146] study lipid-protein interactions in lipid bilayers. The lipids are modeled as chains of hard spheres with heads tethered to two virtual surfaces, representing the two sides of the bilayer. Within this model, Baumgartner [145] has investigated the influence of membrane curvature on the conformations of a long embedded chain (a protein ). He predicts that the protein spontaneously localizes on the inner side of the membrane, due to the larger fluctuations of lipid density there. Sintes and Baumgartner [146] have calculated the lipid-mediated interactions between cylindrical inclusions ( proteins ). Apart from the... 

The first detailed model of the atom, proposed by J. J. Thomson in 1898, was based upon the expectation that the atom was a sphere of positive electricity in which electrons were embedded like plums in a pudding. This picture of the atom was not particularly satisfying because it was not useful in predicting or explaining the chemical properties of the atom. Finally, in 1911, a series of experiments performed in the McGill University laboratory of Ernest Rutherford showed that Thomson s picture of the atom had to be abandoned. 

Carnie and Chan and Blum and Henderson have calculated the capacitance for an idealized model of an electrified interface using the mean spherical approximation (MSA). The interface is considered to consist of a solution of charged hard spheres in a solvent of hard spheres with embedded point dipoles, while the electrode is considered to be a uniformly charged hard wall whose dielectric constant is equal to that of the electrolyte (so that image forces need not be considered). 

An attempt has been made by Spiering et al. [39,40] to relate the magnitude of the interaction parameter F(x) as derived from experiment to the elastic interaction between HS and LS ions via an image pressure [47]. To this end, the metal atoms, inclusive of their immediate environments, in the HS and LS state are considered as incompressible spheres of radius /"h and Tl, respectively. The spheres are embedded in an homogeneous isotropic elastic medium, representing the crystal, which is characterized by specific values of the bulk modulus K and Poisson ratio a where 0 < a < 0.5. The change of molecular volume A Fas determined by X-ray diffraction may be related to the volume difference Ar = Ph — of the hard spheres by ... 

In order to derive an expression for the interaction parameter T on the basis of elasticity theory, the elastic energy of a single sphere of volume F( is considered which is embedded in a spherical hole of volume Fq in the elastic medium ... 

In the theoretical section above, the nonlinear polarization induced by the fundamental wave incident on a planar interface for a system made of two centrosymmetrical materials in contact was described. However, if one considers small spheres of a centrosymmetrical material embedded in another centrosymmetrical material, like bubbles of a liquid in another liquid, the nonlinear polarization at the interface of a single sphere is a spherical sheet instead of the planar one obtained at planar surfaces. When the radius of curvature is much smaller than the wavelength of light, the electric field amplitude of the fundamental electromagnetic wave can be taken as constant over the whole sphere (see Fig. 7). Hence, one can always find for any infinitely small surface element of the surface... 

Both investigated systems are melts of polybead chains at a temperature of 473 K. Configurations of chain length ranging from 24 beads to 100 beads at a density of 0.75 g/cm3 (this corresponds to a comparable real system of polyethylene at a pressure of 1 bar) have been successfully embedded. The hard-sphere radius was 2.2 A, corresponding approximately to a van-der-Waals ra-... 

Figure 3. Temporal and Spatial Evolution of Reaction Rates in the Liquid Phase Reaction Zone. Rates were calculated as a function of time and distance from the bubble surface assuming only conductive heat transport from a sphere with radius 150ym at 5200K, embedded in an infinite matrix at 300K.

Figure 3. Various type of SERS active metallic nanostructures (a) metal-island films (b) metal-coated nanospheres (semi-nanoshells) (c) metal-coated random nanostructures and (d) polymer coatings embedded with metal nanoparticles. Inset An SEM image of silver-coated polystyrene spheres.

This simplified representation of the morphology shows spheres of polystyrene embedded in a continuous soft elastomeric polybutadiene phase. Here the polystyrene domains act as pseudo crosslinks and the polybutadiene conveys elasticity to the material. When heated above the Tg of polystyrene, the domains soften, disassociate, and the material can be made to flow. When cooled, the polystyrene domains reform and elastomeric behaviour returns. 

Apparently, the direct transition from vapor to solid is less common than the double transition vapor — liquid — solid, see, e.g., Refs.158-160). From the rate of solidification of metal droplets (average diameter near 0.005 cm) at temperatures 60° to 370° below their normal melting points, the 7sl was concluded158) to be, for instance, 24 for mercury, 54 for tin, and 177 erg/cm2 for copper. For this calculation it was necessary to assume that each crystal nucleus was a perfect sphere embedded in the melt droplet the improbability of this model was emphasized above. 

Si spheres embedded in a vacuum with 45% nominal porosity [Kol5], micro PS shows a significantly lower absorption in the visible than expected from a calculation for 72% nominal porosity. After [Ko4]. 

---