How can supercritical solvents be tuned to promote selective solvation and reactivity?

Brief Summary of research plans:

The common theme in my research plans is an understanding of the many-body, collective nature of fluids in the supercritical state. In supercritical fluids, the solvent dielectric constant can be tuned over a wide range by adjusting the thermodynamic conditions,1 thereby allowing one also to tune the selectivity of a reaction (Fig. 1). Figure 1: Enantioselectivity versus Pressure of the cyclopropanation of styrene in supercritical fluoroform (Ref. 2). The goal of this proposed project is to develop methods that allow us to predict conditions that will enhance selectivity in chemical reactions and separations. In doing so, we must account for the fact that the enantiomeric excess in Fig. 1 changes most rapidly in the so-called compressible regime of the solvent phase diagram, where proximity to the critical point requires that the fluid be more compressible than an ideal gas, and the fluid itself is inhomogeneous on a mesoscopic length scale. We must therefore address some fundamental statistical-mechanical issues about how short-ranged interactions lead to mesoscopic solvent inhomogeneities.

First stage: Survey of integral equations (numerical solutions); which one works "best" across the entire supercritical portion of the Lennard-Jones phase diagram (excluding the compressible regime)? Use numerical results to search for the optimal solvent conditions for separation of solute species (differential solvation). Examine the breakdown of conventional methods in the compressible regime. Compare all of these results with simulations. Ideally, a graduate student would handle the numerical work, while either another grad student or an undergrad would perform the simulations.

 Second stage: Focus on making the compressible regime accessible to theory, still considering simple liquids. Treat the compressible regime as an inhomogeneous fluid, essentially as a glass. At a minimum, compute the distribution of local environments numerically, and study how the thermodynamic state-point dependence of such distributions depends upon details of the potential. Compare with simulations. Concurrently develop simulation methodologies to sample local environments more efficiently. Search compressible regime for optimal selectivity. Several students (of any rank) can be employed in this work.

Third stage: Interpolate between the compressible regime and the "normal" supercritical fluid. Generalize to molecular solvents. Examine solute-solute effects (so-called "entrainer" effects).Study how diffusion works in an inhomogeneous, compressible fluid.

Funding possibilities: Because of the technological implications, funding has generally been available in this area. Besides the usual sources (NSF and PRF), a quick survey of research papers shows that DOE, EPA, Army, NIST, Air Force, and even a research consortium of over 30 companies have all contributed funding for supercritical-fluid research.

Introduction

Supercritical fluids are playing an increasingly important technological role in industrial reaction and separation processes as environmentally benign solvents.1 The principal advantage of working with a supercritical fluid is that the density of these fluids, and thus solvent properties which depend on density, such as the solvent dielectric constant and hence differential solvation, can be tuned over a broad range.1 Particularly important is the accessibility of states having densities which are intermediate between that of a gas and a liquid,1 since these densities are normally obscured by the vapor-liquid phase coexistence region (Fig. 2). Fig. 2: Experimental phase diagram for water (Ref. 15). It is here that anomalous spectroscopic1,3 (Fig. 3) Fig. 3: Fluorescence of anthracene in supercritical CO2 (Ref. 16). The dashed line is the expected behavior for a non-compressible fluid. The CO2 critical density is 0.46 kg/L. and dynamical4 results have been found for dilute solutes dissolved in compressible solvents, and it is in this compressible regime (notice the extremely flat isotherm just above the critical point in the water phase diagram) that one encounters solvent "clustering" — substantial, albeit labile, density inhomogeneities on a mesoscopic length scale.

Liquid Theories: Techniques and Applications

I plan to explore how liquid theoretic means, numerically solving the Ornstein-Zernike equation,6

with g(r) the radial distribution function and c(r) the direct correlation function, can be used to inexpensively predict supercritical fluid structure and dynamics. Because technological uses of supercritical fluids range over the entire supercritical region of the phase diagram,1 it is imperative that such methods be able to predict solvent (or solute) behavior regardless of the state point; in essence, one could search the phase diagram for a state point that optimizes the desired property (two obvious candidates would be to enhance selectivity in chemical separations or chemical reactions). Computer simulations are certainly an option, but even well away from the critical point such methods are inherently expensive — a knowledge of the position of every single particle in the system is clearly far too much information. Moreover, near the critical point MD simulations become problematic due to the system's large correlation length (see the next section), and considerable care is required to establish their validity. Integral equations and perturbation-theory techniques6 avoid (some of) these difficulties, and thus can serve as a useful counterpoint to simulation.

The principal difficulty in such a program is the fact that to date very little published work7 exists on finding effective liquid theories for the supercritical state, and those few studies that do consider only atomic systems which are not all that close to the critical point. My goal is to develop "closure relations", approximate solutions to Eq. (1), that are accurate throughout the supercritical state, especially within the compressible regime, where the presence of inhomogeneities will likely require the use of glass-like (replica) methods.8 Additionally, there is considerable need for the development of molecular theories that can be applied in the supercritical regime. Having found a successful theory, it is straightforward (and quick!) to use the structure predicted by the theory to compute fluid thermodynamics (compressibilities,6dielectric constants9, local properties (local density enhancements and distributions,5,10 spectral shifts11), and dynamics (vibrational relaxation,12 solvation dynamics13) under the thermodynamic conditions for which the theory is valid. These results then can be compared to experimental results. Moreover, in this fashion the relationship between fluid structure and the measurable observable is made clear. Furthermore, such techniques may well provide inroads into understanding how details of the inter- and intramolecular interactions translate into mesoscopic order in the compressible regime.

Development of new simulation techniques

Evaluating the success or failure of a particular closure requires comparison against accurate thermodynamic or dynamical results. Currently, the most accurate results are those obtained by molecular dynamics simulations. While simulations will play an important role in this work, the primary thrust is to develop theoretical methodologies that effectively build in the slow density fluctuations. The primary difficulty to be overcome in performing simulations in the compressible regime is that correlations in density fluctuations, which are necessarily large near the critical point, make simulations slow to converge and system-size dependent. As noted by Werthiem in reference to the difficulties involved in treating long-ranged forces, "the difficulties that arrive and the techniques used to overcome them involve questions that are quite properly problems of statistical mechanics rather than of computational technique".14 Here, density fluctuations become truculent through their many-body character; they extend over a mesoscopic length scale, thus requiring a simulation box that is much larger than the relevant mesoscopic distance. Furthermore, their collective dynamics are much slower than individual particle dynamics. In essence, a solute, or a tagged solvent molecule, that is found initially in a high-density region tends to stay there for a time that is long compared to the decay time of the velocity autocorrelation function in that environment. Thus, in a molecular dynamics simulation the tagged molecule essentially oversamples each local environment. Instead, we need a method that generates the appropriate local environments independently of the dynamics to be run in each environment.

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