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

• Published in: Physical review letters Vol. 113; no. 3; p. 038301
• Main Authors: Wang, Chi-Jen, Ackerman, David M, Slowing, Igor I, Evans, James W
• Format: Journal Article
• Language: English
• Published: United States 18.07.2014
• Subjects: Diffusion; Models, Chemical; Nanopores
• ISSN: 1079-7114
• DOI: 10.1103/PhysRevLett.113.038301

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.