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

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.