Two-structure model

The H NMR spectral changes of the abnormal ferric 0 chains of Hb M Milwaukee on oxygenation of the normal deoxy a chains are not compatible with a two-structure model for cooperativity and support the concept of direct ligand-linked interactions between subunits embodied in a sequential-type model (Fung et al., 1976, 1977). 

Figure 14.12 Two structural models of glass-like carbon heated to high temperature (a) network of ribbon stacking model (After Jenkins and Kawamura, 1971) (b) alternate model. (After, Shiraishi, 1984 ).

Fig. 13.10. Two structure models of the (100)(001) grain boundaries, (a) A (001) Cu02 plane of the upper grain faces a (100) Y—Ba—O plane of the lower grain, (b) A (001) BaO plane of the upper grain faces a (100) Cu—O plane in the lower grain. Broken lines mark the boundaries.

With the help of scalar relativistic DKH BP DF calculations, we examined the two structural models of Re(CO)3/MgO complexes at dehydroxylated and hydroxylated MgO surfaces (Fig. 4.8) Re(CO)3 and Re(CO)3 adsorbed on neutral and positively charged Vs centers (Mg defects) [264]. Our aim was (i) to justify the possibility that Re(CO)3/MgO complexes are formed, (ii) to determine their stmctural and spectroscopic parameters, and (iii) to investigate whether the Re-Osurf bonds are similar in strength and nature to common coordination bonds. That work [264] was the first high-level computational study to assess quantitatively stmcture and bonding parameters of an oxide-supported organometallic species. 

In Secs. 2.3 and 2.4, we turn to a thorough discussion of the MM approach to water. We shall start with some historical notes, present an example of a successful two-structure model, then proceed to the exact MM approach and some of its applications. 

To explain this we invoke once again the same two-structure model for water, and assume as before that the addition of a small amount of alcohol to water causes a shift in the equilibrium concentrations of the two components. (Note that small amount is important. This assumption is not valid for large amounts of alcohol.) The interpretation of this phenomenon is now simple. Take one mole of water this has a molar volume of about 18 cm mol h Add it to the mixture. Since the relative concentrations of the two water components now favor the ice-like structure, which is the... 

We describe here a simple two-structure model (TSM) for water which was published by Wada in 1961. This model is... 

In the next section, we shall discuss the application of an exact two-structure model based on the MM approach. 

The simplest version of the MM approach and the one that has most often been applied is the two-structure model (T5M). Again, we stress that the exact T5M does not involve any model... 

The pressure dependence of the compressibility is shown in Fig. 2.17. The HR system exhibits normal behavior, i.e. kt decreases monotonically with increasing pressure. However, for the water-like system the behavior is quite different. The compressibility increases with pressure, reaches a maximum value, and then decreases. The high value of the compressibility at low temperatures and the intermediate pressure of F 10 is a result of large fluctuations in the volume near the phase-transition-like pressure we saw in Fig. 2.15. This typical behavior is completely absent in the HR system. Note also that liquid water has a relatively small value of compressibility compared to other normal liquids. In the two-structure model, a negative contribution to the compressibility is obtained from structural rearrangement in the system induced by changes in the pressure (see Sec. 2.4). In the next section, we shall study the possible molecular mechanism that determines the value of the compressibility. 

In order to gain insight into the molecular mechanism underlying the anomalous behavior of liquid water (as well as of aqueous solutions, discussed in Chapter 3), we need to examine the temperature and the pressure derivatives of the quantity (Xhb). To see this, it is sufficient to consider a simple two-structure model for water. Let xhb be the HBed component (or the icelike species in the traditional mixture-model theories of water). 

Note that in whatever way we define the structure of the solvent, the contribution due to structural changes appearing in (3.4.7) or (3.4.10) also appears in the solvation entropy in either (3.4.5) or (3.4.9). Furthermore, when we form the combination of A — TAS, this term cancels out. We can now draw the general conclusion that structural changes in the solvent induced by the solute might affect A (or AH ) and AS but will have no effect on the solvation Helmholtz energy (or AG ). We shall see the analog of these quantities applied to a two-structure model in Secs. 3.5 and 3.6. 

Let Ni and Nh be the average number of L-cules and H-cules obtained by any classification procedure (Sec. 2.3). For the purpose of this section, we need not specify the particular choice of the two species therefore, our treatment will be very general. For concreteness, one may think of a two-structure model (TSM) constructed from the vector xcn (see Sec. 2.3), i.e. 

Examples of such studies are Frank and Quist (1961),Namiot (1961), Grigorovich and Samoilov (1962), Yashkiraga (1962), Ben-Naim (1965a), Mikhailov (1968), Mikhailov and Ponomareva (1968), and Frank and Franks (1968). We shall start in the next section with the two-structure model and then proceed with the more general MM approach. 

Fig. 3.15 Two possible distributions of xbe(v). In (a) one can find a value of V for the construction of a useful two-structure model. In (b) neither v nor V2 would be a good choice for v. ...

Within the two-structure model, we express the relaxation part of 8H R) as... 

Finally, we derive some general relations between the spatial pair correlation functions of the various quasi-components. We begin with the simplest case of a two-structure model. We denote Fy gafi R) the pair correlation function for the pair of species a and p. Then, Paga iR) is the local density of an a molecule at a... 

In this appendix, we use a very simple two-structure model to describe the effect of structural changes induced by a solute or by a co-solvent on the solubility of the solute. 

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