Local solvent density enhancement

Previous experimental and theoretical studies have found what appears to be clear evidence for cluster formation, or local density enhancement, in near critical solutions (7t12t42-45). These include experimental optical absorption, fluorescence and partial molar volume measurements as well as theoretical simulation studies. These offer compelling evidence for local solvent density enhancement in near critical binary SCF systems. Theoretical models suggest that local density enhancement should be strongly dependent on the relative size and attractive force interactions strengths of the solute and solvent species as well as on bulk density and temperature (7,44). 

The simulations give information on the local solvent environment and structure of polymers at interfaces not currently available from experiments in supercritical fluids, as in Figure 5b. For example local solvent density enhancement observed in simulations and experiments of pure supercritical solvents near interfaces,[76] also occurs near Tc and pc in the simulations for grafted chain-solvent systems. The enhancement of solvent density persists out to large distances (6-7 G in Figure 5b) from the chains because of the intermolecular forces in the confined geometry and since the correlation length of the fluid increases near the critical point. 

This local solvent density enhancement raises the solvent quality in the thin film between the surfaces and resists flocculation even at bulk solvent densities below the UCSD. The enhancement is larger at pg = 0.35 where the solvent free volume and compressibility are larger than at pg = 0.45. Flocculation occurs, however, when the density of solvent in the thin film between surfaces equals the UCSD for the stabilizer chains. This result suggests that shorter stabilizers, with UCSDs close to may be able to stabilize latexes and emulsions near and p. Of course the stabilizer must be large enough to screen the Hamaker forces. These issues warrant further experimental studies. 

Section II provides a background discussion of local solvent density enhancements in SCFs. This discussion focuses on the origin of such density enhancements in order to highlight the relationship between two rather different, but not mutually exclusive, ways of understanding this phenomenon. The ways in which such enhancements can affect solute reaction are then presented in Section III, and conclusions follow. 

The origin of local solvent density enhancements in a compressible SCF can be understood from two different viewpoints. The more recently proposed viewpoint [10,12] ties the existence of local density enhancements directly to the presence of the solvent s critical, correlated density fluctuations, while the more common viewpoint bases the existence of local density enhancements upon the attractiveness of the solute-solvent interaction potential and the compressibility of the fluid [2,10,17,22,23,29-32]. These two viewpoints are described below. (Note that the effect of local density enhancements can also be understood within a purely thermodynamic framework through the Krichevskii parameter, lirrix- Q dP/dx)v r where x is the solute mole fraction. See Refs. [27], [28] and [33].)... 

A number of additional simulation studies have been directed towards understanding the relationship between the detailed solute-solvent interaction potentials and the local solvent density enhancements (or depletions). For example, Petsche and Debenedetti examined the sensitivity of clustering to the solute and solvent Lennard-Jones parameters. They found the intriguing result that Xe is an attractive solute in SC Ne, while Ne is a repulsive solute in SC Xe These authors also noted that this phenomena is in fact quite general. It follows from the fact that the Xe-Ne potential is more attractive than the Ne-Ne potential - causing Xe to be attractive in Ne - but less attractive than the Xe-Xe potential - causing Ne to be repulsive in Xe. 

These works have confirmed the importance of local solvent density enhancements in determining not only the rate of chemical reactions in SCFs, but also on the pressure and temperature dependence of these reactions. 

At present, the effect of local solvent density enhancements upon the rate of diffusion controlled reactions is not understood nor is it understood in which solvent-solute systems such effects, i.e., deviations form S/SE theory, are to be... 

From such spectroscopic studies it is also possible to infer the thermodynamic state dependence of the local density enhancement effects. For example, Carlier and Randolph examined the bulk-density dependence of the effective local-solvent-density, Pc, around di-tert-butyl nitroxide radicals in SC ethane via the spectroscopic method of electron paramagnetic resonance (EPR). These authors observed a maximum in local density enhancement (pc/p). Figure 6, to occur at p (l/2)pc consistent with the predictions of Chialvo and Cummings for the direct component of the density enhancement. While such spectroscopic studies are very suggestive, they do not actually allow for direct observation of local density enhancements. As a result, these methods can provide only cumulative, effective values of the local density enhancement and little information about the spatial distribution of these density effects. It is here that computer simulation and other computational techniques can contribute significantly to our understanding of SCF solvation. 

Another class of systems for which the use of the continuum dielectric theory would be unable to capture an essential solvation mechanism are supercritical fluids. In these systems, an essential component of solvation is the local density enhancement [26,33,72], A change in the solute dipole on electronic excitation triggers a change in the extent of solvent clustering around the solute. The dynamics of the resulting density fluctuations is unlikely to be adequately modeled by using the dielectric permittivity as input in the case of dipolar supercritical fluids. 

One aspect of the last set of experiments on W(CO)6 in supercritical ethane that we have not yet discussed involves the possible role of local density enhancements in VER and other experimental observables for near-critical mixtures. The term local density enhancement refers to the anomalously high solvent coordination number around a solute in attractive (where the solute-solvent attraction is stronger than that for the solvent with itself) near-critical mixtures (24,25). Although Fayer and coworkers can fit their data with a theory that does not contain these local density enhancements (10,11) (since in their theory the solute-solvent interaction has no attraction), based on our theory, which is quite sensitive to short-range solute-solvent structure and which does properly include local density enhancements if present, we conclude that local density enhancements do play an important play in VER and other spectroscopic observables (26) in near-critical attractive mixtures. 

In this paper, some recent experimental results regarding the density fluctuations in pure SCF are used to show that the local density enhancement in dilute SCR mixtures is mainly due to the near critical fluctuations in the solvent and an explanation is suggested for the negative partial molar volnme of the solute. This conclusion was also strengthened by a discussion, presented in the following section, based on the Kirkwood—Buff (KB) theory of solution. First, the problem will be examined in the framework of the Kirkwood—Buff theory of solution. Second, nsing experimental results about the near critical fluctuations in pure SCF, it will be shown that the density enhancement in dilnte SCR mixtures is mainly caused by the near critical density fluctuations in pure SCF. 

Density Enhancement in SCR Mixtures through the KB Theory of Solutions. Usually, the local densities in SCR mixtures were determined in very dilute solutions (molar fractions of solute between 10 and 10 ), in order to avoid the experimental and computational comphcations caused by solute—solute interactions. 45 jjje experimental data are provided in refs 24 and 25 as either the density augmentation ApU) around a solute molecule (the solvent is denoted as component 1 and the solute as component 2), or the local density pU) around a solute molecule. ... 

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