Quasi-chemical species

The concentrations of charged atomic defects—point defects—follow the law of mass action. The considerations of thermodynamic equilibria can be applied to disorder equilibria in solid crystalline compounds, the so-called ordered mixtures. Point defects can be regarded as quasi-chemical species with which chemical reactions can be formulated. This has led to the so-called imperfection chemistry. As an example, the disorder equilibrium between vacancies and interstitial particles—the so-called Frenkel equilibrium—will be regarded. 

It has been proposed that the evolution of transition aluminas (pure and doped) during the thermal treatment can be described as a single phase in which the stoichiometric concentrations of the quasi-chemical species vary. This evolution is consists of dehydroxylation by removal of water followed by the exothermic structural transformation to a-phase, which can be described in terms of an annihilation reaction between anionic and cationic vacancies ... 

All diversified point defects mentioned above, including intrinsic, impurity and electron defects, can be regarded as quasi-chemical species hke atoms or ions, which would exist or participate in chemical reactions as a composition of substance. 

When there is a large difference between ys(A) and ys(B) in the equation above, there must be signihcant deparmres from dre assumption of random mixing of the solvent atoms around tire solute. In this case tire quasi-chemical approach may be used as a next level of approximation. This assumes that the co-ordination shell of the solute atoms is hlled following a weighting factor for each of tire solute species, such that... 

Table II also demonstrates the discrepancy existing between E0/RTe calculated by the Yang-Li quasi-chemical theory and the experimental ratio. E0 is the energy difference between a fully ordered superlattice and the corresponding solid solution with an ideally random atom species distribution. It is a quantity that can only be estimated from existing experimental information, but the disparity between theory and experiment is beyond question.

By a statistical model of a solution we mean a model which does not attempt to describe explicitly the nature of the interaction between solvent and solute species, but simply assumes some general characteristic for the interaction, and presents expressions for the thermodynamic functions of the solution in terms of an assumed interaction parameter. The quasi-chemical theory is of this type, and we have noted that a serious deficiency is its failure to consider the vibrational effects in the solution. It is of interest, therefore, to consider briefly the average-potential model which does include the effect of vibrations. 

Whereas the quasi-chemical theory has been eminently successful in describing the broad outlines, and even some of the details, of the order-disorder phenomenon in metallic solid solutions, several of its assumptions have been shown to be invalid. The manner of its failure, as well as the failure of the average-potential model to describe metallic solutions, indicates that metal atom interactions change radically in going from the pure state to the solution state. It is clear that little further progress may be expected in the formulation of statistical models for metallic solutions until the electronic interactions between solute and solvent species are better understood. In the area of solvent-solute interactions, the elastic model is unfruitful. Better understanding also is needed of the vibrational characteristics of metallic solutions, with respect to the changes in harmonic force constants and those in the anharmonicity of the vibrations. 

Here we are considering the dynamic equilibrium between molecular species in the gas phase and the adsorbed gas species on a surface. Let us consider the following quasi-chemical equilibrium between the species B in the gas, Bg, and the available sites at the surface of the adsorbate ... 

Analyses of the defect chemistry and thermodynamics of non-stoichiometric phases that are predominately ionic in nature (i.e. halides and oxides) are most often made using quasi-chemical reactions. The concentrations of the point defects are considered to be low, and defect-defect interactions as such are most often disregarded, although defect clusters often are incorporated. The resulting mass action equations give the relationship between the concentrations of point defects and partial pressure or chemical activity of the species involved in the defect reactions. 

Fujii developed a method for detecting radical species in the gas phase with the use of lithium ion attachment to chemical species. Li ions have been chosen as reactant ions, because the affinity of the species is highest among all the alkah metal ions. The author also explored some of the unique properties of Li ion attachment in mass spectrometry. This technique provides mass spectra of quasi-molecular [R + Li]+ ions formed by lithium-ion attachment to the radical species under high pressure . ... 

Here <5gy — s j — e(y C" is the statistical weight of the configuration with n particles of A around the central particle / having the z neighboring sites. The ways of an approximate calculation of the functions 0, n) were discussed in Appendix B. In the quasi-chemical approximation, they are expressed in terms of the function 6, and 0y, where 6, — Nt/N, N, is the number of particles of species / on N total sites, and Oy — (1 + A y)NyjzN (Ny is the number of pairs of particles if). 

Transition-state theory allows details of molecular structure to be incorporated approximately into rate constant estimation. The critical assumption of transition-state theory is that quasi-equilibrium is established between the reactants and an activated complex, which is a reactive chemical species that is in transition between reactants and products. The application of transition-state theory to the estimation of rate constants can be illustrated by the bimolecular gas-phase reaction... 

The equilibrium concentrations of point defects can be derived on the basis of statistical mechanics and the results are identical to those obtained by a less fundamental quasi-chemical approach in which the defects are treated as reacting chemical species obeying the law of mass action. The latter, and simpler, approach is the one widely followed. 

Working out the historical quasi-chemical approximation in the present language for the two-dimensional Ising model of a binary solution will give perspective on the developments of this chapter. The model system is depicted in Fig. 7.15. Each site of the lattice possesses a binary occupancy variable, 5-, = —1,1 for the /th site. This will be interpreted so that Sj = 1 indicates occupancy of the /th site by one species, e.g. W (water), and = — 1 then indicates occupancy of that site by the other species, say O (oil). We write... 

Figure 7.15 Two-dimensional square lattice and figure for the development of a historical quasi-chemical theory. The model assumes that each lattice site will be occupied by either a black ( O ) or gray ( W ) square. Near-neighbor pairs of the same species contribute -7 < 0 to the net interaction energy. Near-neighbor pairs of the different species contribute 7 > 0 to the net interaction energy. Our calculation will focus on this five-site figure.

We normally use a full set of NS material balances, even though the number of independent balances is limited to the rank NK of the stoichiometric matrix u for the given reaction scheme as shown in Section 2.1. cmd in Aris (1969). Exceptions must be made, however, when one or more constraints are imposed, such as quasi-equilibrium for some reactions or pseudo-steady state (better called quasi-conservation) for some chemical species then each active constraint will replace a mass balance. By these procedures, we avoid catastrophic cancellations that might occur in subtractions performed to reduce the number of species variables from NS to NK. 

The Universal Quasi-chemical Theory or UNIQUAC method of Abrams and Prausnitz divides the excess Gibbs free energy into two parts. The dominant entropic contribution is described by a combinatorial part ( ). Intermolecular forces responsible for the enthalpy of mixing are described by a residual part ( ). The sizes and shapes of the molecule determine the combinatorial part, which is thus dependent on the compositions and requires only pure component data. Since the residual part depends on the intermolecular forces, two adjustable binary parameters are used to better describe the intermolecular forces. As the UNIQUAC equations are about as simple for multi-component solutions as for binary solutions, the UNIQUAC equations for multicomponent solutions are given below. Species are identified by subscript i, subscript j is a dummy index. Here, is a relative molecular surface area and r, is a relative molecular volume. Both of these quantities are pure-species parameters. 

It should be noted that a quasi-lattice, quasi-chemical theory of preferential solvation has been developed by Marcus (1983, 1988, 1989, 2002). In the author s opinion, this approach is not adequate to describe PS in liquid mixtures, especially when the different species have widely different sizes. 

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