Void cubes

Moreover, by decreasing the shell thickness we can note (see Fig. 3.17) a red-shift of the piasmon peak and this in agreement with extinction spectroscopies measurements on Au core-shells [57, 73], In the quasi-static limit, where the size of the nanoshell is much smaller than the wavelength of light, the piasmon resonance energies are determined by the aspect ratio [78, 93]. As the aspect ratio is increased, the piasmon resonance shifts to longer wavelengths [94,95]. 

As previosly observed, the splitting of the plasmons appears only if the shell is thin enough. The two characteristic resonances which are the fingerprints of this kind of core-shell systems, can be identifted in several measured extinction spectra [34,57,69,70,72-76]. 

Here we consider cubically shaped void nanoparticles (see inset of Fig. 3.18), with external side /i and internal side Ij the thickness of the metallic wall is t = (/i — I2) /2. 

If by changing the effective volume and keeping t constant the spectra change only with a red-shift of the peaks (see Fig. 3.18), by changing t, we can observe important differences either in the profile of the curves or in the intensities of the resonances (see 

For the same dimensions of void Ag spheres, void Ag cubes show more separate peaks covering wider spectral ranges. 

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Figure 3.18 Absorption (a) and scattering spectra (b] of Ag void cubes with severai externai (/i) and internal (72] side dimensions but with the same wall-thickness (5 nm). The incident field polarization is directed along the y-axis.

Radius of wires distance from an atom or ion cube root of molecular volume radius of a void... 

Fond et al. [84] developed a numerical procedure to simulate a random distribution of voids in a definite volume. These simulations are limited with respect to a minimum distance between the pores equal to their radius. The detailed mathematical procedure to realize this simulation and to calculate the stress distribution by superposition of mechanical fields is described in [173] for rubber toughened systems and in [84] for macroporous epoxies. A typical result for the simulation of a three-dimensional void distribution is shown in Fig. 40, where a cube is subjected to uniaxial tension. The presence of voids induces stress concentrations which interact and it becomes possible to calculate the appearance of plasticity based on a von Mises stress criterion. 

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. 

A quantity obtained from the molar volume, ov = (6hi)V / NAv 1/3 is sometimes used in lieu of a better value of the molecular diameter. This has the drawback that it makes the diameter temperature-dependent, although much more moderately than is V itself because of the cube-root dependence, but mainly because it ignores the packing of the molecules in the liquid, i.e., the necessary existence of void volume in it. A packing factor, kv = 1.725, valid for the close packing of spheres obtained empirically... 

To start with, for simplicity, let us assume that all particles are of equal size in the oxide powder. If the radius of individual particles is 2r and if we take rr particles and pack them in a cube of each side 2m, then the total volume of the cube will be 8r n. The acmal volume occupied by the particles is, and hence the void space between the particles... 

To estimate the potential amount of surface area exposed by fracturing of the porous charcoal structure, we considered charcoal as a 3-dimensional matrix made up of elementary unit cells. Each cell consists of carbon and contains one void space within the cell to represent average structural quantities, like, porosity and reactive surface area. The imit cell has cubic symmetry, which is characterised by the cube length aceii. The void space located concentrically within each cell has also cubic symmetry with cube length avoid aceii)-... 

Void volume is the most critical parameter, as the flow rate is proportional to the cube of the void volume and inversely proportional to the square of one minus the void volume. As an example, if the void volume is increased from 0.4 to 0.6, the flow rate will increase by eight times. 

As discussed in Chapter 1, fluorite is a structure based on the close packing of spheres and it is not immediately obvious how the unit cell could accept extra oxygen. The biggest void in the structure is at the centre of the cube formed by the eight oxygen ions. 

A curious compromise is reached in many ionic crystals. The crystal NaCl,f or example, is based on two interpenetrating close-packed (fee) lattices. The positions of one lattice are occupied by positive ions, while those of the other are occupied by negative ions. Consider the unit cube of the fee structure in Fig. 27.7(a). There is a void, or hole, outlined by the octahedron, at the center of the cube. An identical octahedral hole is centered on each edge of the unit cube (Fig. 27.7b). Each hole is at the center of an octahedron, which has atoms at each of the six apices. The centers of the octahedral holes occupy the positions of an fee lattice, which interpenetrates the lattice on which the atoms are located. Small foreign atoms, such as H, B, C, N, can occupy these holes. Many carbides, hydrides, borides, and nitrides of the metals are interstitial compounds formed in this way. 

The mass of outfall particulates emitted annually into the ocean by the five major Southern California municipal waste dischargers is about 2.9 X 10 metric tons, dry weight. Since this mass may seem immense, certain perspectives aid its conceptualization. At a compaction density of 1 g cm" and no void volume, this dry mass has a volume equal to that of a cube 66 m on a side if this volume of material were spread over the seabottom in a layer 1 mm thick it would constitute a blanket equal to a square 16 km on a side. However, the particles are neither dry nor without porosity. For example, if the particles constituting the above dry... 

The materials which have been mentioned here so far are predominantly shaped in planar films of hierarchical order. However, the synthesis of hierarchically structured particles is also highly desirable, as they might be further processed and used for the preparation of composite porous materials. Wu et al. showed the synthesis of raspberry-like hollow silica spheres with a hierarchically structured, porous shell, using individual PS particles as sacrificial template [134]. In another intriguing approach by Li et al. [135], mesoporous cubes and near-spherical particles (Fig. 10) were formed by controlled disassembly of a hierarchically structured colloidal crystal, which itself was fabricated via PMMA latex and nonionic surfactant templating. The two different particle types concurrently generated by this method derive from the shape of the octahedral and tetrahedral voids, which are present in the template crystal with fee lattice symmetry. 

Notice that the chloride ions are not closest-packed, but instead are stacked in a square arrangement within a layer and in a neat cubic arrangement in 3-dimensions. This means that the voids between the layers are cubic, with eight chloride ions forming the comers of the cube. The large cesium ion occupies these voids. 

Placing and compacting of concrete are extremely important with regard to durability. Excessive voids left after compaction, due to segregation or insufficient vibration, affect the permeability of the structure. Obviously, proper surrounding of the rebars is essential for their corrosion protection. It should be borne in mind that this regards the actual structure, but it cannot be detected by tests on cubes or cylinders made from samples of fresh concrete. 

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