Langevin and fOkker-Planck analyses of inhibited molecular passing processes controlling transport and reactivity in nanoporous materials

Phys Rev Lett. 2014 Jul 18;113(3):038301. doi: 10.1103/PhysRevLett.113.038301. Epub 2014 Jul 14.

Abstract

Inhibited passing of reactant and product molecules within the linear pores of nanoporous catalytic materials strongly reduces reactivity. The dependence of the passing propensity P on pore radius R is analyzed utilizing Langevin dynamics to account for solvent effects. We find that P ∼ (R-R(c))(σ), where passing is sterically blocked for R≤R(c), with σ below the transition state theory value. Deeper insight comes from analysis of the corresponding high-dimensional Fokker-Planck equation, which facilitates an effective small-P approximation, and dimensional reduction enabling utilization of conformal mapping ideas. We analyze passing for spherical molecules and also assess the effect of rotational degrees of freedom for elongated molecules.

Publication types

  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Diffusion
  • Models, Chemical*
  • Nanopores*