Modeling the Relaxation Dynamics of Fluids in Nanoporous Materials

Mesoporous materials are being widely used in the chemical industry in various environmentally friendly separation processes and as catalysts. Our research can be broadly described as an effort to understand the behavior of fluids confined in such materials. More specifically we try to understand the influence of state variables like temperature and pore variables like size, shape, connectivity and structural heterogeneity on both the dynamic and equilibrium behavior of confined fluids. The dynamic processes associated with the approach to equilibrium are largely unexplored. It is important to look into the dynamic behavior for two reasons. First, confined fluids experience enhanced metastabilities and large equilibration times in certain classes of mesoporous materials, and the approach to the metastable/stable equilibrium is of tremendous interest. Secondly, understanding the transport resistances in a microscopic scale will help better engineer heterogeneous catalysts and separation processes. Here we present some of our preliminary studies on dynamics of fluids in ideal pore geometries. The tool that we have used extensively to investigate the relaxation dynamics of fluids in pores is the dynamic mean field theory (DMFT) as developed by Monson[P. A. Monson, J. Chem. Phys., 128, 084701 (2008) ]. The theory is based on a lattice gas model of the system and can be viewed as a highly computationally efficient approximation to the dynamics averaged over an ensemble of Kawasaki dynamics Monte Carlo trajectories of the system. It provides a theory of the dynamics of the system consistent with the thermodynamics in mean field theory. The nucleation mechanisms associated with confined fluid phase transitions are emergent features in the calculations. We begin by describing the details of the theory and then present several applications of DMFT. First we present applications to three model pore networks (a) a network of slit pores with a single pore width; (b) a network of slit pores with two pore widths arranged in intersecting channels with a single pore width in each channel; (c) a network of slit pores with two pore widths forming an array of ink-bottles. The results illustrate the effects of pore connectivity upon the dynamics of vapor liquid phase transformations as well as on the mass transfer resistances to equilibration. We then present an application to a case where the solid-fluid interactions lead to partial wetting on a planar surface. The pore filling process in such systems features an asymmetric density distribution where a liquid droplet appears on one of the walls. We also present studies on systems where there is partial drying or drying associated with weakly attractive or repulsive interactions between the fluid and the pore walls. We describe the symmetries exhibited by the lattice model between pore filling for wetting states and pore emptying for drying states, for both the thermodynamics and dynamics. We then present an extension of DMFT to mixtures and present some examples that illustrate the utility of the approach. Finally we present an assessment the accuracy of the DMFT through comparisons with a higher order approximation based on the path probability method as well as Kawasaki dynamics