Crystalline solids surface properties

Given the information above, the question remains as to the nature of the monolayer states responsible for the stereo-differentiation of surface properties in racemic and enantiomeric films. Although associations in the crystalline phases are clearly differentiated by stereochemical packing, and therefore reflected in the thermodynamic and physical properties of the crystals, there is no indication that the same differentiations occur in a highly ordered, two-dimensional array of molecules on a water surface. However, it will be seen below (pp. 107-127) that conformational forces that are readily apparent in X-ray and molecular models for several diastereomeric surfactants provide a solid basis for interpreting their monolayer behavior. 

The differences observed between the quasi-racetnic mixture and the mixture of enantiomers with the same configuration are analogous to the differences between the racemic and the optically active forms of the pure compounds. Thus, a kind of two-dimensional isomorphy exists between the molecular systems in question. The different properties of optically active and racemic forms in solid surface phases have been taken as evidence of an orderly arrangement of the molecules in some kind of two-dimensional crystalline lattice. 

Solid surfaces lie at the interface of two historically distinct regimes. On the one hand, a surface can be thought of as a perturbation on a crystalline solid. Hence ideas based on the properties of condensed matter can be used to develop interaction potentials. For example, in a bulk metal the concept of a free electron gas is well developed, and simple potentials based on these ideas have been extended to include surfaces Unfortunately, these ideas are... 

Clearly, the most prominent imperfection in a crystalline solid is its surface, since it represents a cutoff of the lattice periodicity. The surface can be defined as constituting one atomic-molecular layer. This definition is sometimes not particularly useful, however. lu certaiu cases the system or property of iuterest requires that additioual layers be cousidered as the surface. ... 

We turn now to the interaction energy e2/r12 between electrons and consider first its effect on the Fermi surface. The theory outlined until this point has been based on the Hartree-Fock approximation in which each electron moves in the average field of all the other electrons. A striking feature of this theory is that all states are full up to a limiting value of the energy denoted by F and called the Fermi energy. This is true for non-crystalline as well as for crystalline solids for the latter, in addition, occupied states in fc-space are separated from unoccupied states by the "Fermi surface . Both of these features of the simple model, in which the interaction between electrons is neglected, are exact properties of the many-electron wave function the Fermi surface is a real physical quantity, which can be determined experimentally in several ways. 

All of the other chapters in this book deal with the symmetries of finite (discrete) objects. We now turn to the symmetry properties of infinite arrays. The end use for the concepts to be developed here is in understanding the rules governing the structures of crystalline solids. While an individual crystal is obviously not infinite, the atoms, ions, or molecules within it arrange themselves as though they were part of an infinite array. Only at, or very close to, the surface is this not the case this surface effect does not, in practice, diminish the utility of the theory to be developed. 

To achieve a significant adsorptive capacity an adsorbent must have a high specific area, which implies a highly porous structure with very small micropores. Such microporous solids can be produced in several different ways. Adsorbents such as silica gel and activated alumina are made by precipitation of colloidal particles, followed by dehydration. Carbon adsorbents are prepared by controlled burn-out of carbonaceous materials such as coal, lignite, and coconut shells. The crystalline adsorbents (zeolite and zeolite analogues are different in that the dimensions of the micropores are determined by the crystal structure and there is therefore virtually no distribution of micropore size. Although structurally very different from the crystalline adsorbents, carbon molecular sieves also have a very narrow distribution of pore size. The adsorptive properties depend on the pore size and the pore size distribution as well as on the nature of the solid surface. 

The structures of the surfaces, the surface adsorption and the alkali-doped crystal and the atom diffusion path (cf. Section 4) were investigated by different quantum-chemical methods. We used foremost ab initio methodologies. The main computational tool utilized was the program CRYSTAL [54]. This program makes it possible to treat molecules and in particular crystalline solids and surfaces at an ab initio level of theory for surfaces and solids the periodic boundary conditions are applied in 2 or 3 dimensions [55]. The familiar Gaussian basis sets can be used for systems ranging from crystals to isolated molecules, which enables systematic comparative studies of chemical properties in different forms of matter. In our studies, split-valence basis sets were used [56]. 

Since the electronic properties of solids depend on the crystal structure, the transition from the crystalline to the amorphous state is expected to result in some modification of electronic (and surface) properties. Amorphous materials have first been used in catalysis [558-560] where some evidence for higher activity has been obtained [561]. In particular, hydrogenation reactions are catalyzed by this class of materials [562]. Studies on the H recombination reaction are also available [563]. However, the evidence that the amorphous state is really the origin of enhanced catalytic activity is not completely clear [562, 564]. These materials have the peculiarity that their surface is relatively homogeneous for a solid and in particular it is free from grain boundaries [565, 566]. Therefore, they have been suggested [562] as ideal model surfaces for studying elementary catalytic reactions, since they can be prepared with controlled electronic properties and controlled dispersion. Nevertheless, many prob-... 

Theoretical investigations of the modification phenomenon have been carried out by Roginskil and Vol kenshteln (342,418,419,420,421,423). Their work has been based upon the electronic theory of catalysis which utilizes greatly present-day knowledge of quantum chemistry and those theories of the solid state which deal with processes occurring within crystalline materials. On the basis of these concepts it is possible to treat the problems involved in the conversion of molecules adsorbed on a solid surface. The adsorbed molecule and the solid are treated as a unified system, the electrons of the lattice participating in bonding and subsequently chemical reaction. The velocity of the chemical reaction is dependent upon the electronic properties of the solid and reactants involved. 

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