Size regimes

Fig. 28. The optical spectra of the products of the decomposition of CutiCiH, ) (A)-(C) wanned from 50 to 100 K from pure CjH< matrices (D)-(G) warmed from 45 to 70 K from concentrated CjH Ar = 1 10 matrices, showing the temperature-time evolution of "growing copper clusters in the size regime less than 1.0 nm (122).

The term nanosized cluster or nanocluster or simply cluster is used presently to denote a particle of any kind of matter, the size of which is greater than that of a typical molecule, but is too small to exhibit characteristic bulk properties. Such particles enter the size regime of mesoscopic materials. 

As was demonstrated in the preceding sections, structure-sensitivity phenomena are mostly confined to particle size regimes smaller than 3-4 nm. A process of industrial relevance was investigated by de Jong et al. [127] in their study on cobalt particle size effects in the Fischer-Tropsch reaction. Earlier works noted distinct drop in activity for Co particles smaller than lOnm and ascribed this phenomenon to either a partial oxide or carbide formation which should be enhanced for particles in this size regime [128-139]. In order to avoid similar effects, de Jong used... 

Because the size regime of n=l-6 atoms is of great practical significance to the spectroscopic, chemical and catalytic properties of supported metal clusters in both weakly and strongly interacting environments (28), it is important to study very small metal clusters in various types of substrate as well as in the gas phase. In this way, one can hope to develop a scale of metal cluster-support effects (guest-host interactions) and evaluate the role that they play in diverse technological phenomena. 

Pore Size Regimes and Pore Growth Rates... 

The average pore size of PS structures covers four orders of magnitude, from nanometers to tens of micrometers. The pore size, or more precisely the pore width d, is defined as the distance between two opposite walls of the pore. It so happens that the different size regimes of PS characterized by different pore morphologies and different formation mechanisms closely match the classification of porous media, as laid down in the IUPAC convention [Iu2]. Therefore the PS structures discussed in the next three chapters will be ordered according to the pore diameters as mostly microporous (d<2 nm), mostly mesoporous (2 nm50 rim). Note that the term nanoporous is sometimes used in the literature for the microporous size regime. 

The smallest pores that can be formed electrochemically in silicon have radii of < 1 nm and are therefore truly microporous. However, confinement effects proposed to be responsible for micropore formation extend well into the lower mesoporous regime and in addition are largely determined by skeleton size, not by pore size. Therefore the IUPAC convention of pore size will not be applied strictly and all PS properties that are dominated by quantum size effects, for example the optical properties, will be discussed in Chapter 7, independently of actual pore size. Furthermore, it is useful in some cases to compare the properties of different pore size regimes. Meso PS, for example, has roughly the same internal surface area as micro PS but shows only negligible confinement effects. It is therefore perfectly standard to decide whether observations at micro PS samples are surface-related or QC-related. As a result, a few properties of microporous silicon will be discussed in the section about mesoporous materials, and vice versa. Properties of PS common to all size regimes, e.g. growth rate, porosity or dissolution valence, will be discussed in this chapter. 

Fig. 6.10 Pore density versus silicon electrode doping density for PS layers of different size regimes. The broken line shows the pore density of a triangular pore pattern with a pore pitch equal to twice the SCR width for 3 V applied bias. Note that only macropores on n-type substrates may show a pore spac-...

While for macroporous structures the inner surface can be calculated from the geometry, meso and micro PS layers require other methods of measurement First evidence that some PS structures do approach the microporous size regime was provided by gas absorption techniques (Brunauer-Emmet-Teller gas desorption method, BET). Nitrogen desorption isotherms showed the smallest pore diameters and the largest internal surface to be present in PS grown on low doped p-type substrates. Depending on formation conditions, pore diameters close to, or in, the microporous regime are reported, while the internal surface was found to... 

The conductivity of porous structures depends on the size of the conducting filaments making up the silicon skeleton [An5] and will therefore be discussed for each of the three size regimes separately. 

These same general templating strategies are extended into the mesopore size regime with the use of self-assembled supramolecular arrays, a topic which has been extensively reviewed elsewhere. 

R. Although expressions for this parameter exist, they are derived by a hybrid of molecular mechanical and thermodynamic arguments which are not at present known to be consistent as droplet size decreases (8). An analysis of the size limitation of the validity of these arguments has, to our knowledge, never been attempted. Here we evaluate these expressions and others which are thought to be only asymptotically correct. Ve conclude, from the consistency of these apparently independent approaches, that the surface of tension, and, therefore, the surface tension, can be defined with sufficient certainty in the size regime of the critical embryo of classical nucleation theory. 

While f determines the radiative lifetime of an exciton at low temperature limit, fN determines the light absorption coefficient, hence the exciton absorption band will get stronger with decreasing nanoparticle size in the R< ae size regime. 

A 750 nm, the first case corresponds to particles with D 0.03 yarn and the third to particles with D 10 fjum. Particles with sizes between these two extremes fall in the second category where D A as we have seen, this is the most important size regime for atmospheric particles. 

---