Gas adsorption in the topologically disordered Fe-BTC framework SUPPLEMENTARY INFORMATION

Disordered metal–organic frameworks are emerging as an attractive class of functional materials, however their applications in gas storage and separation have yet to be fully explored. Here, we investigate gas...


Surface Area Analysis
Brunauer-Emmett-Teller (BET) surface areas were calculated from N2 adsorption isotherms at 77 K according to the following procedure. 1 The isotherm region where (1 − / ! ) increases versus / ! , where is the amount of N2, was identified. Within this isotherm region, sequential data points that led to a positive intercept in the plot of (#/# ! ) &('(#/# ! ) against / ! were found. This plot yields a slope and a positive intercept . The BET surface area was then calculated according to the following equation: where A is Avogadro's constant and ! is the cross-sectional area of a N2 molecule, which is 16.2 Å 2 .

Non-Local Density Functional Theory Analysis
Pore size distributions were extracted from the N2 adsorption isotherms at 77 K using a non-local density functional theory (NL-DFT) approach. 2 Within NL-DFT, classical fluid density functional theory is used to construct adsorption isotherms in ideal pore geometries and then solve the adsorption integral equation. The main limitation of NL-DFT as applied here is the absence of a specific kernel designed for MOFs. 3 Instead, kernels for activated carbons are often used given the majority of accessible surface within a MOF is organic in nature -that is the 1,3,5-benznetricabolate anion in the case of MIL-100 and Fe-BTC. 4,5 Furthermore, while the use of NL-DFT methods on amorphous MOFs has proven valuable, it cannot be scrutinised with the same quantitative level of detail as for crystalline systems. 3 NL-DFT methods have also been reported to underestimate the pore dimensions, compared to the expected van der Waals dimensions. 6,7 Pore size distributions were calculated within the SAIEUS software employing a carbon-N2, 2D heterogenous kernel and a regularisation parameter (λ) of 1.75. 8

Virial Analysis
Isosteric heat of adsorption, Qst, values were calculated from adsorption isotherms measured at 273 and 293 K for CO2, CH4 and C3H6. 9 The isotherms were fit via global optimisation to the virial equation: where P is pressure, N is the amount of gas adsorbed, a and b are the virial coefficients, m and n are the number of coefficients required to model the isotherm. Qst values were then derived using the parameters obtained from the virial fits using the following equation: The heat of adsorption at near-zero coverage were approximated using the following equation:

Ideal Adsorbed Solution Theory Analysis
Thermodynamic gas selectivities for equimolar mixtures of CO2/N2, CH4/N2 and CO2/CH4 at 273 K were calculated using ideal adsorbed solution theory (IAST) in the IAST++ software package. 10 ( ) is the number of moles of gas adsorbed on the surface when in equilibrium with a pure gas phase as a function of its pressure . These parameters were used afterwards to carry out IAST calculations. The selectivity, $ % ⁄ , was calculated using the following equation: is the mole fraction in the adsorbed phase and is the mole fraction in the gas phase.

Pawley Refinement of MIL-100
Figure S1 Experimental data (black), calculated diffraction pattern (red), difference function (grey) and symmetry-allowed reflections (blue tick marks). Symmetry-allowed reflections were calculated from the reported crystallographic information file in Ref. 12. Data reproduced from Ref. 13.       Carbon Dioxide Isotherms