Quasi-components distribution

Swaminathan S, Beveridge DL (1977) A theoretical study of the structure of liquid water based on quasi-component distribution functions. J Am Chem Soc 99 8392-8398... 

Figure 2. (a) Geometrical parameters used in the hydrogen bond deflnition. (b) Quasi-component distribution functions for the parameter R ST2 water at lO C. (From Mezei and Beveridge 1981. )... 

P.K. Mehrotra and D.L. Beveridge. Structural analysis of molecular solutions based on quasi-component distribution functions. Application to [H2CO]aq at 25 oC. J. Am. Chem. Soc. 102 (1980) 4287-94. 

In section 2.7, we introduced the generalized molecular distribution functions GMDFs. Of particular importance are the singlet GMDF, which may be re-interpreted as the quasi-component distribution function (QCDF). These functions were deemed very useful in the study of liquid water. They provided a firm basis for the so-called mixture model approach to liquids in general, and for liquid water in particular (see Ben-Naim 1972a, 1973a, 1974). 

Studying the MM approach based on a quasi-component distribution function had led to the formulation of what I shall refer to as the principal molecular property of water, or for short, the principle. While the importance of the structure of water and the underlying hydrogen bonds were recognized long ago, the new and more fundamental aspect of the intermolecular interactions which can explain both the structure and the outstanding properties of water were recognized much later. 

As a second example, consider the quasi-component distribution function based on the concept of binding energy (BE). We recall that the vector (or the function) xbe gives the composition of the system when viewed as a mixture of molecules differing in their BE. Thus, XBE( )dv is the mole fraction of molecules with BE between v and v + dv. A possible TSM constructed from this function is... 

The above examples illustrate the general procedure by which we construct a TSM from any quasi-component distribution function. From now on, we assume that we have made a classification into two components, L and H, without referring to a specific example. The arguments we use will be independent of any specific classification procedure. We will see that in order for such a TSM to be useful in interpreting the properties of water, we must assume that each component in itself behaves normally (in the sense discussed below). The outstanding properties of water are then interpreted in terms of structural changes, i.e. redistribution of the molecules into various species that take place in the liquid. 

At the molecular level, the condition (2.3.58) can be formulated in terms of the quasi-component distribution function xbe,cn(v,K). For a normal liquid, we expect that the average binding energy of species having a fixed coordination number will be a decreasing function of K (see Fig. 2.5a). On the other hand, in water we expect that this function will increase... 

In Sec. 2.3, we have seen that any quasi-component distribution function can be used as a basis for constructing an exact... 

We now briefly mention a similar treatment of the partial molar volume of the solute. Consider the quasi-component distribution function based on the volume of the Voronoi polyhe-dra (VP) (Sec. 2.3). Let Nu)() and Ns((f>) be the corresponding singlet distribution functions. The total volume of the system is written as... 

In this appendix, we present the generalized Euler theorem for homogeneous functions of order one. We first write the Euler theorem for a discrete quasi-component distribution function QCDF) and then generalize by analogy for a continuous QCDF. A more detailed proof is available. ... 

P. K. Mehrota and D, L. Beveridge,/. Am. Chem. Soc., 102,4287 (1980). Structural Analysis of Molecular Solutions Based on Quasi-Component Distribution Functions. Application to [HjCO], at 25 °C. 

Note that equation (5.1) follows immediately from Fick s laws on the assumption of a quasi-stationary distribution of the concentration of components within the diffusion boundary layer. Indeed, if in this layer cAl t 0, then the second Fick law yields cA x const. It means that the distribution of the concentration of component A within this layer is close to linear (Fig. 5.1). Anywhere outside of this layer, the concentration of A is assumed to be the same and equal to an instantaneous value, c. This implies sufficiently intensive agitation of the liquid. In such a case, the flow of A atoms across the diffusion boundary layer under the condition of constancy of the surface area of the dissolving solid is... 

The presence of non-interacting components in a macromrriecular system of different molecular weight or density, or both. Quasi-continuous distribution of mucin molecular weights arising from variability in carbohydrate side-chain composition. 

We can now re-interpret the quantity Um)s — Um)o oti the right-hand side of (3.4.7) in terms of structural changes. A more appropriate term would be redistribution of quasi-components. We shall do it in two steps. First, we use the binding energy distribution function xbe introduced in Sec. 2.3. Second, we shall reformulate this quantity in terms of structure as defined in Sec. 2.7.4. Finally, we shall use the same quantity to apply to a two-structure mixture-model approach to water. 

Fantazzini and co-workers discussed the quasi-continuous distributions of spin-lattice relaxation times in porous media, with examples from the biological materials articular cartilage and hydrated collagen. They argued that negative amplitude components in such distributions could arise as a result of magnetization exchange between the solid- and liquid-like proton pools. 

In the following, we restrict ourselves to quasi two-dimensional current distributions invariant along the z direction, for simplicity [51], Under such conditions we have jz = 0 and dByjdz = dBx/dz = 0. The only finite current density components are then... 

Liquid chromatography (LC) and, in particular, high performance liquid chromatography (HPLC), is at present the most popular and widely used separation procedure based on a quasi-equilibrium -type of molecular distribution between two phases. Officially, LC is defined as a physical method... in which the components to be separated are distributed between two phases, one of which is stationary (stationary phase) while the other (the mobile phase) moves in a definite direction [ 1 ]. In other words, all chromatographic methods have one thing in common and that is the dynamic separation of a substance mixture in a flow system. Since the interphase molecular distribution of the respective substances is the main condition of the separation layer functionality in this method, chromatography can be considered as an excellent model of other methods based on similar distributions and carried out at dynamic conditions. 

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