Fragmented cluster model

The Fragmented Cluster Model proposed above is also Consistent with the IR results of Luck, et. al. for porous glass (X), and Toprak, et., for cellulose acetate (2). Indeed, the IR results confirm the original model of Belfort al. fo " explaining the desalting mechanism of porous glass desalination membranes... 

Figure 5. Fragmented cluster model of adsorbed water showing hydrogen-bonded proton clusters in a porous glass pore...

The present Fragmented Cluster Model predicts a priori the size range of the pore diameter below which bulk water is not able to establish itself. Above this size range, porous glass and dense cellulose acetate desalination membranes have not shown significant salt rejection. 

Based on these results, a hydration model - The Fragmented Cluster Model for adsorbed water in porous glass (and possibly cellulose acetate) membranes is proposed. It predicts a priori, that for glass pore sizes above 32 to 52 A, bulk water structure can be established. Observations from the literature indicate that above this pore size range significant desalting is not expected. 

The parameters of Hamiltonians (1) and (2) are determined in our approach by pure theoretical way using different quantum chemical models and calculations unlike the traditional fitting the experimental thermodynamic and dielectric data. Our method of the many-pseudospin clusters [ 1,4] seems to be the most reliable way of determination. The latter are obtained in this case within the static approximation from the system of equations for a typical crystal fragment (cluster) for all possible proton distributions on H-bonds. The left-hand side of any equation expresses the cluster total energy in terms of Jy, while the right-hand side is determined by means of the quantum chemical calculation of this energy. 

In cluster models, a surface site is modeled using a surface fragment (cluster) that contains the surface site of interest and its nearest environment. The further procedure depends on the substrate type. 

Figure 5.11 Representation ofthe double helix of crystalline starch after modeling a branching point between two strands. Schematic cluster model of amylopectin molecule incorporating the double helical fragments. (Reproduced with permission from reference 45)...

It therefore seems quite natural to choose silica, silica aluminas, and aluminium oxide as the objects of the first systematical quantum-chemical calculations. These compounds do not contain transition elements. They are built of the individual structural fragments primary, secondary, etc. This enables one to find the most suitable cluster models for quantum-chemical computations. The covalent nature of these structures again makes quite efficient a comparatively simple method of taking into account the boundary conditions in the cluster calculations. Finally, these systems demonstrate clearly defined Bronsted and Lewis acidity. This range of questions comprises the subject of the present review. This does not by any means imply that there are no quantum-chemical computations on the cluster models of the surface active sites of transition element oxides. It would be more proper to say that the few works of this type represent rather preliminary attempts, being far from systematic studies. Also, many of them unfortunately include some disputable points both in the statement of the problem and in the procedure of calculations. In our opinion, the situation is such that it is still unreasonable to try to summarize the results obtained, and therefore this matter is not reviewed in the present article. 

Cluster modeling of possible chemisorption states and of possible intermediate states in surface reactions can to a first approximation be useful in guiding experiments or interpretations of experimental data for surface reactions (23-25). One important and enlightening result (6, 26, 27) in metal carbide cluster chemistry will be used here to illustrate this particular point because it bears directly on the importance of multicenter C-H-M bonding for hydrocarbon fragments in metal chemistry. 

In light of the utility of spectroscopic comparisons between surface adsorbed species and cluster models, it is surprising that so few of the more unique cluster-bound hydrocarbyl ligands have been spectroscopically characterized. Given the exceptional stabilities of structures such as /xs-jj -RCCR CR" in cluster systems, it is to be expected that such fragments are also to be found on metal surfaces. 

According to the assumption we have made the change in the density matrix, ARX, due to the coulombic interaction between fragments will be more or less localized. It is tempting to set ARX = XL. By doing that, however, one is forced [8] to split off the local space from the remainder of the system to satisfy the idempotency condition. This results in an ordinary cluster model which does not allow electron transfer to or from the surroundings and, as we will see in Sect. 5, is unsuitable for our purposes. In order to properly embed the cluster we take advantage of the fact that the sum of the occupied and unoccupied molecular orbital (MO) spaces is identical to the total AO space. So, instead of ARX = XL, we write... 

Merrill GN, Gordon MS. Study of small water clusters using the effective fragment potential model. J Phys Chem A 1998 102 2650-2657. 

Both the lack of freezing and the inability of ions to enter the pores containing motionally restricted water can be explained by the existence of fragmented clusters such as monomors, dimers etc. Thus, the presence of these fragmented clusters prevent the necessary aggregation and co-operative expansion needed for an ice-like structure to exist, while at the same time they are less able to hydrate ions resulting in low solubilities and consequently low rejections in the desalination sense (1,2 ). This could be the microscopic mechanistic basis for the solution-diffusion model so... 

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