The Music Model

The much more realistic multisite surface complexation (music) model recognizes that different kinds of oxo-/hydroxo-groups are developed on the surface of the oxidic supports [18], Thus, single MO(H), double M20(H) and/or triple MjO coordinated oxo-/hydroxo-groups may be developed on the surface. Moreover, this model provides a very simple formula for estimating the surface charge of the surface oxo-/hydroxo-groups. 

It is obvious that the surface charge of an oxo-group differs by one unit charge from the surface charge of the corresponding hy dr oxo-group. 

Finally, the music model provided the following empirical equation for calculating the protonation constants of the oxo- and hydroxo-groups. 

In principle, a more reliable value for the charge of an oxo/hydroxo-group could be obtained by performing ab-initio calculations in the frame of the density Junctional theory. The first example of catalytic interest, recently reported, concerns the oxo/hydroxo-groups developed on anatase (23). 

The third subregion, called diffuse part of the interface, is charged because in this region the counterions are accumulated. The size of the diffuse part depends strongly on the ionic strength of the impregnating solution. Assuming a planar sohd/water interface, its thickness (L) may be approximately estimated by the formula 

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Hiemstra et al.1617 applied this concept of local neutralization of charge and geometrical considerations to develop the MUSIC model, which permits estimation of the intrinsic protonation constant of various surface groups. The model was proposed to explain the reactivity of surface groups in metal oxides, but it can also be applied to evaluate the reactivity of groups belonging to clay surfaces. Indeed, Pauling s concepts, on which the MUSIC model is based, were developed for minerals and clays. 

This problem was solved as follows. The original version of the MUSIC model assumed the charge of the central ion to be equally distributed over the ligands. In the refined model the bond valence is calculated from the empirical formula... 

In view of the discussed above discrepancies, some spectroscopic evidence of particular surface species used in the MUSIC model would be much desired. Connor et al. [51] studied internal reflection infrared spectra of Ti02 (amorphous + anatase) films, and obtained the following speciation. The (=Ti)20H species is formed at pH < 4.3, and =TiOH2 at pH < 5. The =TiOH species was detected at pH 4.3-10.7 (maximum abundance at pH 8) and =TiOH2 species at pH < 10.7. 

Lo S (1996) Application of the MUSIC model to bubbly flows. AEAT-1096, AEA Technology, June 1996... 

The MUSIC model with counterion binding has been tested against a large set of data two types of goethite, at different concentrations of NaCl and NaNO, [759]. 

Another objective in the study of the application of CFD in crystallization is to simulate the particle size distribution in crystallization. In order to solve this problem, the simulation should take into account the population balance. The internal coordinates of the population balance make it difficult to utilize it in the CFD environment. In addition, different-sized particles have different hydrodynamics, which causes further complications. Wei and Garside [42] used the assumption of MSMPR and the moments of population balance to avoid the above difficulties in the simulation of precipitation. In the CFX commercial application, the MUSIC model offers a method for solving the population balance equation in CFD and defines the flow velocity of different-sized particles... 

Since we can write no surface reactions with Se04 (using neutral or positively charged surface sites) which release less than one hydroxyl, these results suggest that some selenate sorption may be non-specific or outer-sphere. Alternative surface complexes can be written using the sites defined by the MUSIC model (25), FeOrf, FejO, FejOH, and FejO. Consideration of alternative sites does not change the interpretation of the titration and EM data. 

When experimental methods to measure proton affinity distribution spectra (PADs) from potentiometric titration data became available [54a], it was found by Contescu et al. [58] that the apparent values of proton binding constants identified from PADs were in semiquantitative agreement with log K values for binding predicted by the MUSIC model (Table 1). The characteristic PADs for several oxides are shown in Fig. 2. 

Data predicted theoretically by the MUSIC model and measured experimentally by PAD and other techniques. 

It is worth emphasizing that the arguments leading up to the construction of the MUSIC model are gas-phase arguments based on ionic concepts such as Pauling bond order. This essential physics is present in both approaches. It cannot be argued that the MUSIC model is accounting for subtle quantum mechanical effects not present in ionic model because the MUSIC model rests entirely on an ionic framework. 

At present the MUSIC (MUlti Site Complexation) model [13,14] can, in principle, explain differences in PZC values for different samples however, for goethite, the variation shown in Fig. 1 is too laige to be explained by the MUSIC model alone based on the current knowledge. 

Applied to the cerium oxide particles, the MUSIC model predicts the following values for the elementary pKs ... 

Since the acidity of a group increases with increasing positive formal charge, the MUSIC model allows a simple calculation of acidity constants, starting from electrostatic considerations. 

This is of course a very general approach applicable only in the case of a two-pK system (two protons involved per surface group, see Section 7.1.2). A more refined analysis such as the MUSIC model shows that, in most cases, a single protonation equilibrium must be considered per surface group. The pH at which the net charge... 

The quantities accessible to the experiment are the surface chaige ao as a function of pH, the potential of the diffuse layer assimilated to the electrokinetic potential and the total density of reactive sites N. The equilibrium constants K and K are determined graphically or numerically (see Section 7.3.2.) from the pH, (To and Nj for various electrolyte concentrations and types. The MUSIC model (see Section 7.1.1) allows simplification in the calculation of the intrinsic constants and K. ... 

In the previous models, the surface acidity constants are obtained by fits of experimental data. Let us look at what happens when the intrinsic acidity constants are obtained using the MUSIC model (see Section 7.1.1). 

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