Reactive Inorganic Membranes for CO$_{2}$/N$_{2}$ separations: Ab-initio Density Functional Theory Calculations

The selectivity (CO$_{2}$/N$_{2})$ of mesoporous silica membranes can be enhanced by surface modification using APTS (3-aminopropyl-triethoxy silane). The hypothesized transport mechanism in such materialsis the reaction of CO$_{2}$ with surface amine groups to form a carbamate species and subsequent surface ``hopping'' of CO$_{2}$. DFT calculations were performed in order to elucidate the mechanism of CO$_{2}$ transport in APTS modified membranes, to compute the CO$_{2}$ diffusivity through the membrane, and to calculate its binding energy on an amine strand. The computed binding energy for docking one CO$_{2}$ molecule to an amine was calculated to be 15.5 kcal/mol (0.67 eV). The activation/barrier energy for a CO$_{2}$ molecule to hop from one amine strand (in form of carbamate) to another computed using Transition State Theory (TST) was 7.2 kcal/mol (0.31 eV) and compares well with our experimental data ($\sim $ 8kcal/mol; 0.35 eV). In the configuration studied, CO$_{2}$ hops from one strand to another in a zigzag fashion due to thermal motion of the strands; a strand with the CO$_{2}$ molecule undulates and eventually moves so that the CO$_{2}$ can be attracted by an adjacent strand. The CO$_{2}$ diffusivity calculated using the computed activation energy ranged from 1.1 X 10$^{-11}$m$^{2}$/sec (@ 25 C) to 5.7 X 10$^{-10}$m$^{2}$/sec (@100 C).