(238b) A Theory of Adsorption/desorption Dynamics for Fluids In Porous Materials

Recent years have seen dramatic progress in the modeling the thermodynamics of adsorption and desorption for fluids in mesoporous materials based on density functional theories and molecular simulations. The occurrence of adsorption/desorption hysteresis in these systems is an indication of failure by the system to reach thermodynamic equilibrium during condensation and/or evaporation processes and it is important therefore to understand the dynamical behavior that underlies this hysteresis. In this paper we discuss an approach to modeling this dynamics.

We consider mean field kinetic equations describing the relaxation dynamics of a lattice model of a fluid confined in a porous material. The dynamical theory embodied in these equations can be viewed as a dynamical density functional theory, as a theory of diffusion, or as a mean field approximation to a Kawasaki dynamics Monte Carlo simulation of the system. The solutions of the kinetic equations for long times coincide with the solutions of the static mean field (density functional) theory for the inhomogeneous lattice gas. The approach can reveal very useful insights into the nature of dynamical processes in adsorption and desorption.

The approach is applied to a lattice gas model of a fluid confined in a finite length slit pore open at both ends and in contact with the bulk fluid at a temperature where capillary condensation and hysteresis occur. The states emerging dynamically during irreversible changes in the chemical potential are compared with those obtained from the static mean field equations for states associated with a quasistatic progression up and down the adsorption/desorption isotherm. In the capillary transition region the dynamics involves the appearance of undulates (adsorption) and liquid bridges (adsorption and desorption) which are unstable in the static mean field theory in the grand ensemble for the open pore but which are stable in the static mean field theory in the canonical ensemble for an infinite pore.