Regular Shapes

The most commonly met regular nano-fillers are silicas and titanias. These are generally made by controlled precipitation in the presence of surfactants, to prevent agglomeration and fusion of particles. Sol-gel processes starting from metal alkoxides are often utilised. Some very fine particles produced by more conventional gas phase processes are just within the definition used for this discussion. For example, fumed silicas, with diameters of under 10 nm are available. 

With the precipitation methods, organosilanes can be added during the precipitation, so that they become built into the surface layers. In order to obtain good dispersion, the precipitation is sometimes carried out in the host polymer, or its pre-cursor, such as a monomer. Another method of achieving the same result is to directly transfer (flush) a stabilised suspension, resulting from precipitation, into a liquid monomer. By the use of such methods, high loadings can be achieved in some polymers, such as poly(methyl methacrylate (PMMA). More details can be found in various publications [3-6]. 

In principle, similar things can be achieved with other materials that can be precipitated in fine form, such as calcium carbonate (PCC), although little seems to have been done 

One of the notable features of composites produced with such fillers is high transparency, as the particles are too small to scatter visible light. On present information, the applications for this type of nano-composite seem to be specialised, and they have not, so far, become of widespread interest. 

Part of the reason for their relative unimportance is their high cost. Their main potential applications to date seem to be at conventional (relatively high) loadings, where the amount of expensive surface modifier needed is very significant. Systems, such as the PCC-based ones, have the potential for significant cost reductions and could repay further investigation. 

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For skin packaging, ionomer films provide outstanding protection, especially for sharp objects. Films can be drawn down tightly around regular shapes without penetration. Characteristics of heat seals can be adjusted so that convenient peelable seals are obtained (31—35). 

Figure 1. Equivalent diameters of regular-shaped bodies.

In Figure 1, the equivalent diameter is related to regular shapes through equivalent volumes by the following formulas ... 

Colloidal suspensions are systems of small mesoscopic solid particles suspended in an atomic liquid [1,2]. We will use the term colloid a little loosely, in the sense of colloidal particle. The particles may be irregularly or regularly shaped (Fig. 1). Among the regular shapes are tiny spherical balls, but also cylindrical rods or flat platelets. As the particles are solid, fluctuations of their form do not occur as they do in micellar systems. Not all particles in a suspension will, in general, have the same form. This is an intrinsic effect of the mesoscopic physics. Of course in an atomic system, say silicon, all atoms are precisely similar. One is often interested in the con-... 

In general, a uniform distribution of potential over a regular-shaped passivated surface can be readily obtained by anodic protection. It is much more difficult to protect surface irregularities, such as the recessions around sharp slots, grooves or crevices since the required current density will not be... 

Products in regular-shaped packages, such as ice-cream in flat cartons, are pressed between horizontal, flat, refrigerated plates. These can... 

Ionic solids, such as lithium fluoride and sodium chloride, form regularly shaped crystals with well defined crystal faces. Pure samples of these solids are usually transparent and colorless but color may be caused by quite small impurity contents or crystal defects. Most ionic crystals have high melting points. 

The traditional methods for measuring the swelling degree [100] are, as a rule, limited due to the difficulties in quantitative separation of the swollen gel from the outer solution because of extremely low strength of the former. These difficulties can be avoided by measuring the dimensions of a regular shape sample directly in an excess of liquid [19, 101,102], The other example is the modified volumetric method recently developed by us especially for SAH [103],... 

Analytical solutions of equation 9.44 in the form of infinite series are available for some simple regular shapes of particles, such as rectangular slabs, long cylinders and spheres, for conditions where there is heat transfer by conduction or convection to or from the surrounding fluid. These solutions tend to be quite complex, even for simple shapes. The heat transfer process may be characterised by the value of the Biot number Bi where ... 

The effectiveness factor depends, not only on the reaction rate constant and the effective diffusivity, but also on the size and shape of the catalyst pellets. In the following analysis detailed consideration is given to particles of two regular shapes ... 

The relationship between effectiveness factor p and Thiele modulus < >l may be calculated for several other regular shapes of particles, where again the characteristic dimension of the particle is defined as the ratio of its volume to its surface area. It is found that... 

Today s massive efforts in nanotechnology will certainly provide more well-defined, regular-shaped particles in the submicron range, and mini fixed-bed technology wiU profit from that. 

Micro-flow processing is not an exclusive domain of micro-channel devices made by micro fabrication. This approach can be applied to any packing of regular-shaped objects which results in interstices of the same internal dimensions and the same precision as given for micro channels. Obviously, interstices made from extended, but thin objects resemble best the nature of micro channels. Hence the use of filaments for constituting a micro-flow assembly was recently described [8]. 

Kottmann, J. P., Martin, O. J. F Smith, D. R. and Schultz, S. (2001) Non-regularly shaped plasmon resonant nanopartide as localized light source for near-field microscopy. J. Microsc., 202, 60-65. 

Figure 9. TEM micrographs of nanocrystal superlattices of Au nanoparticles prepared by the inverse micelle method and digestive ripening, (a) and (b) low-magnification images (c (f) regularly-shaped nanocrystal superlattices (g) magnified image of a superlattice edge. Note the perfect arrangement of the Au nanoparticles. (Reprinted with permission from Ref. [30], 2003, American Chemical Society.)...

Mass can be determined by using a balance. If the object has a regular shape, such as a cube or a cylinder, volume can be calculated from length measurements. However, most objects have irregular shapes, and the volume must be determined indirectly. One way to measure the volume of an irregularly shaped item that does not dissolve in or react with water is by water displacement. An item that is entirely submerged in water will displace a volume of water equal to its volume. 

Supermarkets have a carcass specification for weight conformation and fat content, which ensures that the meat bought is commercially viable and provides the end product that the consumer requires. The supermarkets are able to insist on their own quality regulations for produce, because they are so dominant in the market place. Until such time as organic farmers can co-operate and become equally powerful, they will have to abide by the supermarket standards. At present, they seem to be under pressure to produce regularly shaped and sized, blemish-free products, on a mass scale, available all-year-round and often transported long distances. Despite these pressures, however, British organic farmers are not contract farmers to the extent that many conventional farmers are. 

Regular-shaped large area samples (Grimm sources)... 

On intuition, a minute amount of water was added to the solvent (ethyl acetate) in the first crystallization experiment containing a molar excess of imidazole corresponding to 1, Regularly shaped crystals were formed within one hour. Such a crystal, subjected to X-ray analysis, has the structure as shown in Fig. 41 U1). Apart from the formation of the expected salt-type associate (carboxylate-imidazolium ion pair, cf. Sect. 4.2.2), two water molecules are present in the asymmetric unit of the crystal structure. This fact called our attention again to the family of serine protease enzymes, where water molecules are reported as being located in the close vicinity of the active sites 115-120),... 

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