Solute-solvent pair correlation

We see that after a rapid initial decay the components evolve slowly in time and that Sbft) falls to a negative value and stays negative over much of the interval depicted. Study of the time evolution of the solvent structure aroimd the solute can help explain the behavior of S f) and of its components. We have examined solute-solvent pair correlations involving the solute C sites that change their partial charges. Fig. 11 shows some of these results, specifically the pair correlations g+jvW and g+c (r) for the solute site that increases its charge by e/2 with an acetonitrile N site and a benzene C site, respectively. 

Figure 2 Solute-solvent pair correlation function at T = 1.37 and p = 0.40, 0.50, and 0.60. a) Short range structure b) long range structure (note change of axes).

First, consider the case of a simple LJ solute, say, neon or argon, denoted A, very diluted in water w. The solute-solvent pair correlation function should have a first peak at about Ri mainly due to the solute-solvent direct inter-... 

For a simple solute A diluted in water w, we assume that the direct solute-solvent interaction is spherically symmetrical, that is, Uaw R) is a function of R only. Therefore, the solute-solvent pair correlation function for this pair is written as... 

The conclusion (8.146) can be summarized with the help of the schematic drawing in Fig. 8.22. We assume that each solute has a radius of influence Rf which may be defined as the distance at which the solute-solvent pair correlation function is practically unity. In this region, we know that the concentration of the L form is larger than its bulk concentration, a fact which has been referred to as the stabilization of the L form by the solute. When the two solute particles come close to each other, the spheres of influence of the two solutes must overlap. It is therefore likely that the total excess of L-cules in the union of the two spheres of influence is smaller than the excess of L-cules in the two spheres when they do not overlap. If we identify the L form as the more structured species, then we conclude that the structure of water decreases as a result of the HI process. 

The solute-solvent pair correlation function r ) gives the probability... 

One of the most important applications of the theory of PS is to biomolecules. There have been numerous studies on the effect of various solutes (which may be viewed as constituting a part of a solvent mixture) on the stability of proteins, conformational changes, aggregation processes, etc., (Arakawa and Timasheff 1985 Timasheff 1998 Shulgin and Ruckenstein 2005 Shimizu 2004). In all of these, the central quantity that is affected is the Gibbs energy of solvation of the biomolecule s. Formally, equation (8.26) or equivalently (8.28), applies to a biomolecule s in dilute solution in the solvent mixture A and B. However, in contrast to the case of simple, spherical solutes, the pair correlation functions gAS and gBS depend in this case on both the location and the relative orientation of the two species involved (figure 8.5). Therefore, we write equation (8.26) in an equivalent form as ... 

The thennodynamic properties are calculated from the ion-ion pair correlation fimctions by generalizing the expressions derived earlier for one-component systems to multicomponent ionic mixtures. For ionic solutions it is also necessary to note that the interionic potentials are solvent averaged ionic potentials of average force ... 

Assuming that additive pair potentials are sufficient to describe the inter-particle interactions in solution, the local equilibrium solvent shell structure can be described using the pair correlation fiinction g r, r2). If the potential only depends on inter-particle distance, reduces to the radial distribution fiinction g(r) = g... 

With a few exceptions solvent dependent coupling constants have been observed only in non-ionic compounds. As a result no data are available concerning correlations of coupling constant changes and heats of solvation, heats of solution, ion pairing, etc. 

As before, the modified pair correlation has one factor which is the same as the vacuum pair correlation, and a second contribution which has the same/orm as the solute-solute pair correlation in a solvent. It is not identical, however, to the solute-solute pair correlation in a solvent, due to the presence of the adsorbent molecule. Therefore, this factor has been referred to as a conditional pair correlation. The exact statistical-mechanical expression for the conditional pair correlation is quite complicated. We shall not discuss this aspect here. The reader can understand the qualitative difference between the two factors on the rhs of Eq. (9.3.5) from the following considerations. 

The second case is when the reservoir is a solution of the ligand in a solvent, say water. The form of the BI is the same, except for areinterpretation of the quantity G . In Eq. (D.7), G is an integral over the pair correlation function of the ligands in vacuum, i.e., in Eq. (D.9) is the ligand-ligand pair potential. In the case... 

This method is to be used to estimate the activity coefficient of a low molecular weight solvent in a solution with a polymer. This procedure, unlike the other procedures in this chapter, is a correlation method because it requires the Flory-Huggins interaction parameter for the polymer-solvent pair which must be obtained from an independent tabulation or regressed from experimental data. In addition, the specific volumes and the molecular weights of the pure solvent and the pure polymer are needed. The number average molecular weight of the polymer is recommended. The method cannot be used to estimate the activity of the polymer in the solution. 

There have been a number of modeling efforts that employ the concept of clustering in supercritical fluid solutions. Debenedetti (22) has used a fluctuation analysis to estimate what might be described as a cluster size or aggregation number from the solute infinite dilution partial molar volumes. These calculations indicate the possible formation of very large clusters in the region of highest solvent compressibility, which is near the critical point. Recently, Lee and coworkers have calculated pair correlation functions of solutes in supercritical fluid solutions ( ). Their results are also consistent with the cluster theory. 

Figures 2a and 2b show how the predicted solvent-solute pair correlation function, gAB varies with density. At the highest density (p = 0.6) the structure is liquid-like with hrst, second, third,. .. maxima/minima oscillating about 1.0. The size of the solvent-solute cluster for this state was calculated to be about —1 solvent molecule the presence of one solute molecule at this state excludes about one solvent molecule.

Figures 6a and 6b show the solute-solute pair correlation function at the same conditions as the solvent-solute functions in Figures 2a and 2b. The aggregation of the solute molecules is quantitatively stronger than the solvation structure shown in Figure 2. A quantitative interpretation in terms of the local density of solute molecules surrounding a given solute molecule has not been given for the band attributed to a solute-solute excimer dimer in the fluorescence spectra of Brennecke and Eckert (2) nevertheless, their qualitative interpretation suggesting a significant solute-solute aggregation near the CP appears to be supported by these results.

One may, for example, regfnd the (planar) substrate(s) of a slit-pore as the surface of a spherical particle of infinite radius. The confiniKl fluid plus the substrates may then be perceived as a binary mixture in which macro-scopically large (i.e., colloidal) particles (i.e., the substrates) are immersed in a sea of small solvent molecules. The local density of the confined fluid may then be interpreted as the mixture (A-B) pair correlation function representing correlations of solvent molecules (A) caused by the presence of the solute (B). 

They refer to Eq. (3.4.3) as the proper integral equation in view of the fact that the direct correlation function so defined does correspond to the sum of the nodeless diagrams in the interaction site cluster expansion of the total correlation function. Following Lupkowski and Monson, we shall refer to Eq. (3.4.3) as the Chandler-Silbey-Ladanyi (CSL) equation. Interestingly, the component functions have a simple physical interpretation. The elements of Ho correspond to the total correlation functions for pairs of sites at infinite dilution in the molecular solvent. The elements of the sum of Hq and //, (or H ) matrices are the solute-solvent site-site total correlation functions for sites at infinite dilution in the molecular solvent. 

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