Revisiting Anisotropic Diffusion of Carbon Dioxide in the Metal - Organic Framework Zn2(dobpdc)

The diffusion of gases confined in nanoporous materials underpins membrane and adsorption-based gas separations, yet relatively few measurements of diffusion coefficients in the promising class of materials, metal-organic frameworks (MOFs), have been reported to date. Recently we reported self-diffusion coefficients for (CO2)-C-13 in the MOF Zn-2(dobpdc) (dobpdc(4-) = 4,4'-dioxidobiphenyl-3,3'-dicarboxylate) which has one-dimensional channels with a diameter of approximately 2 nm [Forse, A. C.; J. Am. Chem. Soc. 2018, 140, 1663-1673]. By analyzing the evolution of the residual C-13 chemical shift anisotropy line shape at different gradient strengths, we obtained self-diffusion coefficients both along (D-parallel to) and between (D-perpendicular to) the one-dimensional MOF channels. The observation of nonzero D-perpendicular to was unexpected based on the single crystal X-ray diffraction structure and flexible lattice molecular dynamics simulations, and we proposed that structural defects may be responsible for self-diffusion between the MOF channels. Here we revisit this analysis and show that homogeneous line broadening must be taken into account to obtain accurate values for D-perpendicular to. In the presence of homogeneous line broadening, intensity at a particular NMR frequency represents signal from crystals with a range of orientations relative to the applied magnetic field and magnetic gradient field. To quantify these effects, we perform spectral simulations that take into account homogeneous broadening and allow improved D(perpendicular to)values to be obtained. Our new analysis best supports nonzero D-perpendicular to at all studied dosing pressures and shows that our previous analysis overestimated D-perpendicular to.