Site fraction, definition

Definition of site fractions. The multiple sublattice model is an extension of earlier treatments of the two-sublattice models of Hillert and Steffansson (1970), Harvig (1971) and Hillert and Waldenstrom (1977). It allows for the use of many sublattices and concentration dependent interaction terms on these sublattices. To woiic with sublattice models it is first necessary to define what are known as site fractions, y. These are basically the fiactional site occupation of each of the components on the various sublattices where... 

As a simple example, consider the case of the adsorption of a gas-phase molecule, A, on a surface. The surface is composed of either open sites or adsorbed molecules. In this formalism, there are two surface species one corresponding to the adsorption location, the open site, designated O(s), and the adsorbed molecule, A(s). The site fractions of O(s) and A(s) surface species must sum to unity. There is one surface phase in this case. In this trivial example, such overhead and formal definitions are unnecessarily complicated. However, in complex systems involving many surface phases and dozens of distinct surface species, the discipline imposed by the formalism helps greatly in bookkeeping and in ensuring that the fundamental conservation laws are satisfied. 

The surface composition, usually represented by site fractions Z, must adjust itself to be consistent with the local gas-phase composition, temperature, and the heterogeneous reaction mechanism. When the surface composition is represented by site fractions, the definition requires that... 

Size fractionations of aquatic humic substances definitely need to be performed on-site to minimize changes in aggregation during sample preservation, transport, and storage if the size fractionation data are to be related to environmental conditions. If additional aggregation or precipitation or both occur after an on-site size fractionation, the sample should not be refractionated, but needs to be treated as if the on-site fractionation is valid. 

It is possible to justify Eq. (4) as follows The maximum number of contacts between a macromolecule and solvent molecules is given by the first portion of the far side of Eq. (4) [(z - 2)x/i2]- The coordination about a single unit of the macromolecule is given by z, and the -2 accounts for the two directions along which the macromolecule continues. This total number of macromolecular sites is to be multiplied by the site fraction on the macromolecules which is actually occupied by the smaller molecules. The site fraction is approximated by the volume fraction of small molecules v. The total number of contacts between macromolecules and small molecules must still be multiplied by some interaction parameter, Ah>i2- Equation (4), indicates that some simplifications are possible. The first one is that the product xn 2y can be replaced by the simpler product iV2. This can easily be seen from the definitions of the volume fractions. Next, the two constants, the coordination number (z - 2) and the interaction parameter (Am/j 2) be combined and expressed in units of RT. This new interaction parameter is commonly denoted by the letter %. It represents the total interaction energy per macromolecular volume element in units of RT. Making these substitutions leads to Eqs. (5) and (6). Note that AG has a quadratic... 

That is, terms of the form (1 — jr -I- jr< )/) appear in the denominator for all reactant sites having exchangeable protons and similarly in the numerator for all transition state sites. If there is no change in the fractionation factor for a site, its contribution cancels. If the solvent is a reactant, its term disappears because the solvent fractionation factor is unity by definition. 

Petroleum, natural gas, and synthetic fuels are excluded from the definition of a hazardous substance, and the definitions of pollutants and contaminants under CERCLA this is known as the Petroleum Exclusion. Although the EPA has the authority to regulate the release or threatened release of a hazardous substance, pollutant, or contaminant, the release of petroleum, natural gas, and synthetic fuels from active or abandoned pits or other land disposal units is currently exempt from CERCLA. Such sites cannot use Superfund dollars for cleanup, nor can the EPA enforce an oil and gas operator, landowner, or other individual to clean up a release under CERCLA. Substances exempt include such materials as brine, crude oil, and refined products (i.e., gasoline and diesel fuel) and fractions. 

There are conceivable a priori different functions determining the fraction of the total number of surface sites characterized by definite adsorption energy of a given substance, various combinations of these functions at simultaneous adsorption of two or more substances and, finally, various combinations of adsorption energy with kinetic characteristics of surface sites with respect to adsorption and elementary reactions. 

To reduce the number of parameters in the kinetic equations that are to be determined from experimental data, we used the following considerations. The values klt k2, and k4 that enter into the definition of the constant L, (236), are of analogous nature they indicate the fraction of the number of impacts of gas molecules upon a surface site resulting in the reaction. So the corresponding preexponential factors should be approximately the same (if these elementary reactions are adiabatic). Then, since k1, k2, and k4 are of the same order of magnitude, their activation energies should be almost identical. It follows that L can be considered temperature independent. 

When the crystal surface contains sites of different adsorption energies the adsorbate will condense area by area. According to Predali and Cases89) the adsorption isotherm will be steplike in relation to condensation of molecules on areas i, and each step i is compared with sites having the same energy 0 j. Developing the isotherm with condensation on inhomogenous surfaces they start with the definition of the fraction of sites a and /S on which condensation occurs between undersaturation Afi and dAft. When all the... 

In the first and second equation, E is the energy of activation. In the first equation A is the so-called frequency factor. In the second equation AS is the entropy of activation, the interatomic distance between diffusion sites, k Boltzmann s constant, and h Planck s constant. In the second equation the frequency factor A is expressed by means of the universal constants X2 and the temperature independent factor eAS /R. For our purposes AS determines which fraction of ions or atoms with a definite energy pass over the energy barrier for reaction. 

The percolation model suggests that it may not be necessary to have a rigid geometry and definite pathway for conduction, as implied by the proton-wire model of membrane transport (Nagle and Mille, 1981). For proton pumps the fluctuating random percolation networks would serve for diffusion of the ion across the water-poor protein surface, to where the active site would apply a vectorial kick. In this view the special nonrandom structure of the active site would be limited in size to a dimension commensurate with that found for active sites of proteins such as enzymes. Control is possible conduction could be switched on or off by the addition or subtraction of a few elements, shifting the fractional occupancy up or down across the percolation threshold. Statistical assemblies of conducting elements need only partially fill a surface or volume to obtain conduction. For a surface the percolation threshold is at half-saturation of the sites. For a three-dimensional pore only one-sixth of the sites need be filled. 

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