### Structure and Dynamics in Supercritical Fluids

Supercritical fluids (SCFs) are currently receiving much industrial and scientific interest as a result of their unique physical properties. The most characteristic features of SCFs are liquid-like densities, gas-like viscosities, and diffusivities that are intermediate between typical gas and liquid values. The resulting combination of high dissolving power and enhanced mass-transfer rates makes SCFs attractive alternatives to liquid solvents for a variety of industrial applications, such as extraction, separation and reaction processes. In addition, the high compressibility of SCFs in the near-critical region allows one to tune their properties to desired values by applying small changes in pressure, which in turn makes it possible to tailor the rates and selectivities of chemical processes. Since the aforementioned applications of SCFs generally involve dilute solutions, it is essential to develop a microscopic understanding of the structure and dynamics of a supercritical solvent in the vicinity of a solute.

We use the methods of classical statistical mechanics, such as integral equation theory and mode coupling theory, to study structural and dynamical properties of supercritical solutions. Some of the problems we address are as follows. How does the solvent-solute and solute-solute clustering affect the rates and equilibrium constants of chemical reactions in SCFs? How does the proximity to the critical point affect the transport properties and what are the ramifications for diffusion controlled chemical reactions? How is preferential solvation manifested in local composition effects in dilute supercritical solutions? The answers to these questions should help us shed further light on fundamental properties of SCFs and their practical applications.

### Quantum and Semiclassical Many-Body Dynamics

Numerous problems in chemical physics involve calculations of quantum time correlation functions (TCFs) in many-body systems. Particular examples include: medium-induced electron transfer, dissipative tunneling, radiationless processes, and electronic spectroscopy of chromophores in crystals and in liquids. While certain systems require a fully quantum mechanical treatment, there exists a large class of systems of chemical interest for which classical mechanics provides a reasonably good approximation. An appealing approach to the calculation of TCFs for such systems involves using semiclassical methods, which are generally based on the assumption that quantum effects can be taken into account by introducing relatively small corrections to the classical results. However, the shorter the time scale on which the behavior is analyzed, the more important quantum corrections may become, even for systems which are classical as far as their static and low-frequency dynamical properties are concerned. One of the research projects in our group involves developing a systematic procedure for including quantum effects into the results for TCFs obtained from classical simulations.

An alternative approach to study quantum dynamics in condensed phases involves calculating imaginary-time correlation functions using path integral Monte Carlo (PIMC) method and performing analytic continuation to the real-time axis. Unfortunately, analytic continuation is numerically unstable, and therefore leads to uncontrollable amplification of statistical noise unavoidable in PIMC simulations. In our group we employ the information theory and the methodology from the field of inverse problems in order to develop various techniques, such as Maximum Entropy and Singular Value Decomposition, for stabilizing the procedure of analytic continuation of quantum imaginary-time TCFs.

### Recent Publications

Insertion of nanoparticles into polymer brush under variable solvent conditions. Egorov SA. *J. Chem. Phys.* 137:134905 (2012).

Microphase separation of mixed polymer brushes physisorbed on cylindrical surfaces. Egorov SA. *Soft Matter*. 8:3971 (2012).

Anomalous nanoparticle diffusion in polymer solutions and melts: A mode-coupling theory study. Egorov SA. *J. Chem. Phys. *134:084903 (2011).

Sterically stabilized lock and key colloids: A self-consistent field theory. Egorov SA. *J. Chem. Phys.* 134:194901 (2011).

Hydrophobic interactions with coarse-grained model for water. Egorov SA. *J. Chem. Phys.* 134:234509 (2011).

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