Bulk Electronic Properties

Perhaps of greater interest to us are results derived by the same authors71 that relate surface and bulk electronic properties of jellium. Considering two jellium slabs, one extending from —L to -D and the other from D to L, they calculated the force per unit area exerted by one on the other. According to the Hellmann-Feynman theorem, this is just the sum of the electric fields acting... 

Melle-Franco M, Marcaccio M, Paolucci D et al (2004) Cyclic voltammetry and bulk electronic properties of soluble carbon nanotubes. J Am Chem Soc 126 1646-1647... 

There have been many attempts to relate bulk electronic properties of semiconductor oxides with their catalytic activity. The electronic theory of catalysis of metal oxides developed by Hauffe (1966), Wolkenstein (1960) and others (Krylov, 1970) is base d on the idea that chemisorption of gases like CO and N2O on semiconductor oxides is associated with electron-transfer, which results in a change in the electron transport properties of the solid oxide. For example, during CO oxidation on ZnO a correlation between change in charge-carrier concentration and reaction rate has been found (Cohn Prater, 1966). 

In the apparent absence of a correlation between hydrogenation activity and the bulk electronic properties of alloys, Sachtler et al. [321,322,... 

The oxidation of carbon monoxide on nickel oxide has often been investigated (4, 6, 8, 9, II, 16, 17, 21, 22, 26, 27, 29, 32, 33, 36) with attempts to correlate the changes in the apparent activation energy with the modification of the electronic structure of the catalyst. Published results are not in agreement (6,11,21,22,26,27,32,33). Some discrepancies would be caused by the different temperature ranges used (27). However, the preparation and the pretreatments of nickel oxide were, in many cases, different, and consequently the surface structure of the catalysts—i.e., their composition and the nature and concentration of surface defects— were probably different. Therefore, an explanation of the disagreement may be that the surface structure of the semiconducting catalyst (and not only its surface or bulk electronic properties) influences its activity. 

The electronic structure of a solid metal or semiconductor is described by the band theory that considers the possible energy states of delocalized electrons in the crystal lattice. An apparent difficulty for the application of band theory to solid state catalysis is that the theory describes the situation in an infinitely extended lattice whereas the catalytic process is located on an external crystal surface where the lattice ends. In attempting to develop a correlation between catalytic surface processes and the bulk electronic properties of catalysts as described by the band theory, the approach taken in the following pages will be to assume a correlation between bulk and surface electronic properties. For example, it is assumed that lack of electrons in the bulk results in empty orbitals in the surface conversely, excess electrons in the bulk should result in occupied orbitals in the surface (7). This principle gains strong support from the consistency of the description thus achieved. In the following, the principle will be applied to supported catalysts. 

These questions lead on to further fundamental questions concerning the shapes and properties of small metal particles. For example, what is the stable shape for a small metal particle How is this affected by size, method of preparation, temperature, gaseous environment, precursor compound, support morphology, etc. Do small metal particles have different electronic properties from bulk metal Do surface electronic properties depend on particle size, and if so, do they vary in the same way as bulk electronic properties When, indeed, is a particle small enough to have unusual properties ... 

Bulk electronic properties are observed for particles containing about 150 atoms, corresponding to diameters in the range 1.5-2.0 nm. On the other hand, surface electronic properties typical of bulk metal are observed with much smaller particles. Only about 25 atoms are required in a particle for the adsorption to the be characteristic of the bulk metal. 

Functionalized N-triethylene glycol pyrrolidino-CNTs (Fig. 1.10a) allowed electrochemistry and quantum chemical calculations to be carried out to investigate the bulk electronic properties [167]. Functionalization obviously modified the electronic state of pristine CNTs however, some of the metallic character was retained and the overall electron density of states (DOS) was not strongly affected [167]. Pyrrolidino-SWCNTs and -MWCNTs bearing a free amino-terminal N-oligoethy-lene glycol moiety formed supramolecular associates with plasmid DNA through ionic interactions. The complexes were able to penetrate within cells. SWCNTs... 

The bulk electronic properties of extrinsic semiconductors are largely determined by the level of doping that is used to make the materials n-type or p-type. For non-degenerate semiconductors, the electron concentration in the conduction band and the hole concentration in the valence band are related to the Fermi energy EF and to the effective densities of states in the conduction and valence bands (Nc and Ny respectively) by... 

Surface activity (a) strength and mode of adsorption (b) adsorption isotherms (c) adatom formation (d) substrate-catalyst interactions (e) surface diffusion (f) adsorbate spillover (g) bulk electronic properties (h) surface electronic properties. 

Proportions of atoms having unusually low CN will change relatively little as size is increased beyond about 2 nm (ca. 60 % dispersion). (2) Bulk electronic properties are not likely to be shown by particles having less than about 150 atoms (1.7 nm, 70 % dispersion) (3) Typical surface electronic properties are however probably shown by particles with only 25-30 atoms (90 % dispersion). (4) Unusual crystallographic structures are rare. (5) Since the heat released by chemisorption is enough to convert one structure into another, metastable stmctures are unlikely to survive under reaction conditions, and surface reconstruction may occur frequently. (6) A small metal particle may comprise a solid core and a semi-fluid surface layer. 

Effect of Surface Structure on Bulk Electronic Properties... 

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