Transport in Nanostructured Materials: New Understanding through Theory and Simulation
The problem of transport in small pores and confined spaces is one of long standing interest in membrane separations, adsorption and catalysis, that is now receiving renewed attention due to its importance to the numerous applications of new nanomaterials being vigorously developed. Nevertheless, despite a long history dating back to the classical work of Knudsen, our understanding of the subject is still relatively rudimentary. Here we review recent work in our laboratory where the transport in small pores is successfully modeled by considering the momentum dissipation processes at the pore surface along with viscous transport in the pore, and describe an exact theory for the low-density transport coefficient in cylindrical nanopores, considering the molecular trajectories between diffuse wall reflections. Excellent correspondence between theory and simulation at all scales including the single file region is demonstrated, using as examples the transport of hydrogen, methane and carbon tetrachloride in cylindrical silica pores varying from the ultramicropore to the mesopore range, such as those in MCM-41 silicas, zeolites and related mesoporous and microporous materials..
As an application of the theory we discuss the relative importance of different contributions to transport of light gases in single walled carbon nanotubes, using atomistic simulation results for methane and hydrogen as examples. We also exploit our theory to estimate Maxwell coefficients for the wall reflection from the simulation results. It is found that reflection from the carbon nanotube wall is nearly specular, and the viscous contribution to transport is small. The reflection coefficient for hydrogen is 3-6 times as large as that for methane in tubes of 1.36 nm diameter, indicating less specular reflection for hydrogen and greater sensitivity to atomic detail of the surface. This reconciles results showing that transport coefficients for hydrogen and methane, obtained in simulation, are comparable in tubes of this size.