(113a) Dynamic Mean Field Theory Of Adsorption And Desorption In Porous Materials

Density functional theories have been an important tool in understanding the molecular level behavior of fluids confined in porous materials[1, 2]. These theories allow us to calculate the free energy and density distribution for fluids inside porous materials for equilibrium states of the system. They also allow us to study metastable states associated with hysteresis loops in adsorption/desorption isotherms. It is also of interest to study the dynamics in the approach to equilibrium and metastable equilibrium for fluids in pores. This has recently been done using molecular dynamics[3, 4] and dynamic Monte Carlo simulations[5]. In this paper we present a theoretical approach to studying the dynamics that makes use of a lattice gas treatment of the system. The theory yields the time evolution of the density distribution in the system. The equilibrium or metastable equilibrium states from mean field density functional theory emerge as the long time limit in the dynamics. A similar approach has been used to study phase separation in metal alloys[6] and diffusion in porous materials[7].

To illustrate the utility of this approach we present applications to two systems. A slit pore in contact with bulk fluid and an inkbottle pore geometry in contact with bulk fluid. We study the dynamics of the adsorption and desorption in the systems and compare the system behavior during reversible and irreversible adsorption and desorption processes.

1. Evans, R., Fluids Adsorbed in Narrow Pores - Phase-Equilibria and Structure. Journal of Physics-Condensed Matter, 1990. 2(46): p. 8989-9007. 2. Gelb, L.D., K.E. Gubbins, R. Radhakrishnan, and M. Sliwinska-Bartkowiak, Phase separation in confined systems. Reports on Progress in Physics, 1999. 62(12): p. 1573-1659. 3. Sarkisov, L. and P.A. Monson, Hysteresis in Monte Carlo and molecular dynamics simulations of adsorption in porous materials. Langmuir, 2000. 16(25): p. 9857-9860. 4. Sarkisov, L. and P.A. Monson, Modeling of adsorption and desorption in pores of simple geometry using molecular dynamics. Langmuir, 2001. 17(24): p. 7600-7604. 5. Woo, H.J. and P.A. Monson, Phase behavior and dynamics of fluids in mesoporous glasses. Physical Review E, 2003. 67(4): p. 041207. 6. Gouyet, J.F., M. Plapp, W. Dieterich, and P. Maass, Description of far-from-equilibrium processes by mean-field lattice gas models. Advances in Physics, 2003. 52(6): p. 523-638. 7. Aranovich, G.L. and M.D. Donohue, Diffusion equation for interacting particles. Journal of Physical Chemistry B, 2005. 109(33): p. 16062-16069.