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 ¹³CO₂ in the MOF, Zn₂(dobpdc), (dobpdc^4– = 4,4′-dioxidobiphenyl-3,3′-dicarboxylate) that has one-dimensional channels with a diameter of approximately 2 nm. By analyzing the evolution of the residual ¹³C chemical shift anisotropy lineshape at different gradient strengths, we obtained self-diffusion coefficients both along (D_||) and between (D_⊥) the one-dimensional MOF channels. The observation of non-zero D⊥ 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⊥. 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⊥ values to be obtained. Our new analysis best supports non-zero D⊥ at all studied dosing pressures and shows that our previous analysis overestimated D⊥.