Solvent-separated minimum

Note that one feature of Figure 11.12 is a solvent-separated minimum for the X-Y pair. Insofar as solvent-separated minima involve intervening solvent molecules that typically differ significantly in their behavior from normal bulk solvent as a consequence of being isolated between the two solutes, such situations are unlikely to be handled accurately by continuum models in general. 

Figure 30.8 illustrates the main features of the pmf. First, the test molecules may come into contact if they are attracted to each other. This separation can be the position of the deepest well in the pmf. The second well in the pmf is called the solvent-separated minimum. This is where the two test particles are separated by a single layer of solvent. Each test particle protects the near side of the other particle from collisions with the solvent that would otherwise drive two solute molecules apart. So it is more probable that solvent collisions will drive two nearby solute particles together than that they will drive them apart. This means that there is an apparent solvent-driven attraction of the test particles even when they are solvent-separated by one solvation shell. The system is unstable when two particles that are too close together for a solvent molecule to fit between them. 

Modeling by Pratt and Chandler [14], Zichi and Rossky [9, 15], Watanabe and Andersen [16], and Ravishanker et al. [17, 18] shows that the solvent-separated minimum can sometimes be most stable. For example. Figure 30.10 shows the krypton-krypton pair correlation function in water computed by Watanabe and Andersen [16] the second small peak represents a population of solvent-separated pairs. This state is stable because each nonpolar molecule is surrounded by a clathrate cage. Solvent-separated states are most likely to occur when the solutes are small [19]. 

The most noteworthy prediction of the PC theory was the potential of mean force for model methane pairs in water (Figure 5). This was the first molecularly realistic prediction of a potential of mean force between hydrophobic spheres in water. It showed structural oscillations that are natural features of these functions in simpler liquids a solvent-separated minimum free energy configuration, a thermally substantial barrier to desolvation, and a free energy minimum at contact of the two methane molecules. These qualitative features of the potential of mean force between spherical hydrophobic solutes have subsequently been observed in simulation many times. The result shown in Figure 5 was produced with the two-moment ITM, is substantially the same as the prediction of PC, and is in good agreement with the available computer simulation data. 

The sohd can be contacted with the solvent in a number of different ways but traditionally that part of the solvent retained by the sohd is referred to as the underflow or holdup, whereas the sohd-free solute-laden solvent separated from the sohd after extraction is called the overflow. The holdup of bound hquor plays a vital role in the estimation of separation performance. In practice both static and dynamic holdup are measured in a process study, other parameters of importance being the relationship of holdup to drainage time and percolation rate. The results of such studies permit conclusions to be drawn about the feasibihty of extraction by percolation, the holdup of different bed heights of material prepared for extraction, and the relationship between solute content of the hquor and holdup. If the percolation rate is very low (in the case of oilseeds a minimum percolation rate of 3 x 10 m/s is normally required), extraction by immersion may be more effective. Percolation rate measurements and the methods of utilizing the data have been reported (8,9) these indicate that the effect of solute concentration on holdup plays an important part in determining the solute concentration in the hquor leaving the extractor. 

Solvent-separated ion pairs, in which the first solvation shells of both ions remain intact on pairing may be distingnished from solvent-shared ion pairs, where only one solvent molecule separates the cation and the anion, and contact ion pairs, where no solvent separates them (Fig. 2.6). The parameter a reflects the minimum distance by which the oppositely charged ions can approach each other. This eqnals the sum of the radii of the bare cation and anion pins 2, 1, and 0 diameters of the solvent, respectively, for the three categories of ion pairs. Since a appears in Eq. (2.49), and hence, also in Q(b), it affects the value of the equilibrium constant, K s- The other important variable that affects K ss is the product T and, at a given temperature, the value of the relative permittivity, e. The lower it is, the larger b is and, hence, also K s-... 

The water content of furfural is critical and must be kept to a minimum. In order to dehydrate the solvent a pair of distillation columns is utilized. Condensed wet solvent separates into two layers in a settling drum. The top layer, which is lean in furfural, is separated into saturated solvent vapor and solvent-free water in the furfural-from-water stripper. The solvent-rich layer is separated in the water-from-furfural stripper into wet solvent vapor and dry furfural. 

Contact and solvent-separated ion pairs can be distinguished in anionic systems the interionic distance of the former is usually 1-3 A, which increases to 4 or even 7 A in solvent-separated ion pairs [21]. There is apparently no further minimum in the potential energy diagram. The reactivity of solvent-separated ion pairs and free ions in anionic systems are similar, being a few orders of magnitude more reactive than contact ion pairs. In contrast, contact ion pairs in cationic systems are separated by 4-6 A, and therefore resemble the solvent-separated species of anionic systems in terms of structure, as well as their relative reactivity and ability to dissociate. The existence of solvent-separated ion pairs in cationic polymerization is questionable and has not yet been proven spectroscopically. 

The propagating anion and its counterion exist in relatively nonpolar solvents mainly in the form of associated ion pairs. Different kinds of ion pairs can be envisaged, depending on the extent of solvation of the ions. As a minimum, an equilibrium can be conceived between intimate (contact) ion pairs, solvent-separated ion pairs, and solvated unassociated ions. The nature of the reaction medium and counterion strongly influences the intimacy of ion association and the course of the polymerization. In some cases the niicrostructure of the polymer that is produced from a given monomer is also influenced by these variables. In hydrocarbon solvents, ion pairs are not solvated but they may exist as aggregates. Such inter-molecular association is not important in more polar media where the ion pairs can be solvated and perhaps even dissociated to some extent. 

The initiation and propagation processes are influenced by equilibria between various degrees of association of the active center and its counterion. As a minimum, it is necessary to conceive of the existence of contact (associated) ion pairs, solvent-separated ion pairs, and free solvated ions. A simplified reaction scheme [3] is presented in reaction (9-37). 

In particular, the relative stability of contact and solvent-separated ion pairs has been the object of much debate in the literature. This was started from a striking finding by Pettitt et al. [239] who observed an attractive minimum for contact Cl pairs in water by extended RISM calculations. 

On the other hand, if one is interested in separating out thermodynamic properties such as enthalpy change (AH) and entropy change (A5), a solvent with minimum mutual solubility with water (such as cyclohexane or heptane) is preferable. 

E.xample problems are included to highlight the need to estimate the entire set of products that can be reached for a given feed when using a particular type of separation unit. We show that readily computed distillation curves and pinch point cur es allow us to identify the entire reachable region for simple and e.xtractive distillation for ternary mixtures. This analysis proves that finite reflux often permits increased separation we can compute exactly how far we can cross so-called distillation boundaries. For extractive distillation, we illustrate how to find minimum. solvent rates, minimum reflux ratios, and, interestingly, ma.xinnim reflux ratios. 

Both the initiation and propagation processes are, moreover, influenced by equilibria between various degrees of association of the active center and its counterion. As a minimum, it is necessary to consider the existence of solvent-separated ion pairs, and free solvated ions. A simplified scheme [20] is shown in Fig. 8.7. The existence of contact (associated) ion pairs [as in Eq. (8.1)] is neglected in this scheme because the dielectric constants of the solvents usually used for cationic polymerizations are high enough (9-15) to render concentrations of intimate ion pairs negligible compared to those of solvated ion pairs. The observed kp in these simplified reactions will thus be composed of contributions from the ion pairs and free solvated ions ... 

Figure 15.4. Potential of mean force (PMF) between two methane molecules in water. This shows a first deeper minimum corresponding to the contact geometry of the two methane molecules. Another second (less deep) minimum is also observed in the PMF, corresponding to the solvent separated minimmn. Adapted from thesis entitled Molecular dynamics simulations of hydrophobic solutes in hquid water by Andy Hsu, Institute of Atomic and Molecular Sciences, Academia Sinica. (http //w3.iams.sinica.edu.tw/lab/jlli/thesis andy/%5d.)...

In the same figure we also show the distance dependence of the effective interaction energy between the two spheres. The results have been obtained by eomputer simulations where the spheres are methane molecules. Note the pronounced minimum between the two spheres at contact and then the maximum at intermediate distances. The interaction energy falls off to zero as the two spheres move away. In some cases, one finds a second minimum at a distance beyond the maximum [10]. Such a minimum at a larger separation is referred to as a solvent separated pair and arises due to the structuring around the hydrophobic spheres. 

Figure 12.3. Global minimum energy structures determined by full optimization at the B3LYP/6-31G level of a trifluoromethanesulfonic acid molecule (a) and apara-toluene sulfonic acid molecule (b) each with 6 water molecules. Both acids show the dissociated proton exists as a solvent separated pair consisting of what resembles an Eigen cation and sulfonate ion. The 0-0 and 0-H (in brackets) distances for each acid reveal that aromatic anion is the stronger base. First presented in Ref. [23],...

Theoretical calculations support the existence of discrete ion pair intermediates in solvolysis reactions. Figure 8.11 shows a reaction coordinate diagram, and Figure 8.12 shows calculated structures for the solvolysis of f-butyl chloride in water. The (CH3)3C CD contact ion pair and the solvent-separated ion pair are distinct species, with calculated energies indicating that each is a local minimum. The more widely separated ion pair Figure 8.12(c) is similar in energy to the solvent-separated ion pair. ... 

This solution-induced intercalation process has the novelty to swell and disperse clays into a polymer solution. This process is difficult to carry out commercially because of the high cost factor of the solvents. In addition, phase separation in this process is quite tedious for solvent separation from the phase. There are also health and safety concerns associated with the application of this technology. However, this technology is exclusively applicable to water soluble polymers. As the solvent used in this process is water, which is a low-cost as well as an eco-friendly solvent with minimum... 

Illustration 11. A solution containing 50% n-hcptane (A), 50% cyclohexane (C) (on a solvent-free basis) is to be separated into a raffinate containing 95% heptane and an extract containing 95% cyclohexane (both percentages on a solvent-free basis), with aniline (B) as the extracting solvent at 25 C., in a countercurrent multiple contact system with reflux. Feed, reflux, and product streams are to be saturated with solvent, and pure solvent will be added at the mixer and removed from the extract solvent separator. Determine the minimum number of stages and the minimum reflux ratio. 

Figure 6 shows the potential of mean force (PMF) between a sodium ion and a chloride ion in water, at infinite dilution of the two ions, obtained from classical atomistic simulations [75]. The first minimum of the potential corresponds to the contact ion pair (CIP) distance, the second minimum corresponds to the solvent-shared ion pair (SIP) distance, and the third minimum to the solvent-separated ion pair (2SIP) distance. Figure 7a shows an example of a SIP in aqueous NaCl [75]. The infinite dilute potential of mean force in Fig. 6 can be used as an effective pah-potential in implicit solvent simulations. The osmotic coefficient (j) (ps) = nilpJc- T (with n the osmotic pressure and ps the salt number density) can be obtained through the virial route. For the case of a binary mixture of components i and j and pairwise additive, density-independent pair potentials, the virial equation can be expressed as... 

For water to form the solvent-separated pair, let l , be the minimum distance to be accommodated in the aqueous core region of the reverse micelle. From the pair correlation function between methane and the oxygen, the location of the first minima is observed (Rao et al. 2007) at a distance of Iso = 5.6 k. Fet Ir be the distance between atomic centers of the solute atoms in the solvent-separated configuration, hence the minimum distance, l , = l, + 24. For the case of methane in the solvent-separated configuration in free water, 1 = 1 k and = 18.2 A. For the contact pair, 4 = 3.95 A and the corresponding value of = 15.15 A. From the water density distributions in the reverse micelle. 

The first solvation shell of the methyl cation in water and HF can satisfactorily be represented by five and that of the fluorine anion—by six solvent molecules, i.e., the total number of the solvent molecules included in the supermolecular approximation is 11. The C—X distance was taken as the reaction coordinate and all other geometry parameters, includingg those of the solute environment, were optimized. The most important result of the calculations of Eq. (5.7) by the CNDO/2 and ab initio (STO-3G basis set) methods is the detection of three minima along the MERP. The first of these characterized by the distance r( p= 1.388 A corresponds to the hydrated undissociated molecule CH3F. The second minimum corresponds to rcp = 3.480 A. There are no solvent molecules between the ions CHj and F , hence they are located in one cage and may be structurally described as a contact ion pair of type IV. The third minimum corresponds to a completely dissociated system (r< p = 5.463 A), i.e., the solvent-separated ion pair V with each ion surrounded by its own solvation shell with n = 11, j = 5, and k = 6 in Eq. (5.7). 

Upon going to solution in methane (w = 9)—a model of nonpolar and nonpolarizable solvent—the minima on the PES, which are associated with the ion pairs, vanish. The effect of the solvent is felt only in some lowering of the calculated dissociation energy. So as to assess the role of a nonpolar but readily polarizable solvent, the authors of Ref. [67] chose H2(n = 11). The calculation revealed, apart from solvated undissocated CH3F, only one additional minimum at r p = 2.92 A, = 5, /c = 6. In this structure, one H2 molecule is incorporated into the cavity between the ions, and this sytem may be represented as a solvent-separated ion pair in which one solvent molecule is shared by two solvation shells formed upon ionic dissociation. 

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