Correlation functions solute-solvent pair

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 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... 

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). 

The thermodynamic properties are calculated from the ion-ion pair correlation functions 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 function If the... 

The K-B theory expresses the thermodynamic quantities such as the partial molar volume and the isothermal compressibility for a solution in terms of the pair correlation functions of constituent molecular species. The expressions in terms of the site-site pair correlation functions are obtained by coupling the K-B theory with the RISM theory. When we consider a two-component system (a solute with m-sites and a solvent with n-sites) and the infinite dilution limit, the partial molar volume of the solute Vm and the isothermal compressibility kt can be expressed as, respectively. 

Let us consider the following relaxational process. At times t < 0 the solvent is in equilibrium with the solute the average solvent structure around the solute is characterized by a set of solute-solvent site-site pair correlation functions... 

In this case, we also have p = 0.6 and A is very dilute in B. As can be seen from Fig. 4.38, the depth of the PMF increases considerably as we increase the temperature. Again, this lowering of the depth in Waa R) is not a result of the increase in the pair correlation function gAA(R) We can conclude that the strength of the PMF for the solute-solute increases considerably as we increase the temperature, and more dramatically than in the SW solvent. However, it is not clear whether these findings... 

Fig. 4.43 The four pair correlation functions for aqueous solutions of a solute (s) in water-like (w) solvent in a 2-D system. Parameters as in Eq. (4.10.1).

To conclude this section, I would like to add two sets of results on the pair correlation function (PCF) between two simple solutes in an L/ solvent. These results may or may not be relevant to the problem of Hhard-sphere (particles labeled A) solutes in an LJ solvent (particles labeled B) with varying strength of the energy parameter sbb- All the calculations for this and the subsequent demonstration were done by solving the Percus-Yevick integral equations with the following molecular... 

Fig. 4.45 The pair correlation function between two HS solutes in L/ solvent with different energy parameters. Parameters are as in Eq. (4.11.2).

The evaluation of the pair correlation functions of both the solvent molecules and the solutes is feasible but troublesome. For electrolyte solutions, however, averaging over the solvent effects yields reliable approximations, as shown by McMillan and Mayer, who considered the solution in osmotic equilibrium with the pure solvent (Fig. 2). They stressed that solutes can be treated as an imperfect gas, provided that one uses the potential of mean force at infinite dilution. The calculation yields the osmotic pressure Tl = P — Pq (see Fig. 2) from the virial equation [Eq. (69)] in terms of the forces among the particles for the solution state (p, T). The independent variables of... 

Figure 3.7. Pair correlation function of segments q[r) in dilute solutions (a single chain) in ideal (/) 2Uid good (S) solvent, and in semidilute solutions [3) (de Gennes, 1979) [Heprinted from Pierre-Gilles de Gennes Scaling Concepts in Polymer Physics. Copyright 1979 by Cornell University. Used by permission of the publisher, Cornell University Press]...

Relation (8.28) indicates a way to eliminate the direct pair potential U R), Suppose that we compare two solvents / and f and seek the pair correlation functions ghsW sisW for the same solute in the two solvents. From (8.28), we get... 

---