Multivariate analysis of disorder in metal–organic frameworks

Abstract

The rational design of disordered frameworks is an appealing route to target functional materials. However, intentional realisation of such materials relies on our ability to readily characterise and quantify structural disorder. Here, we use multivariate analysis of pair distribution functions to fingerprint and quantify the disorder within a series of compositionally identical metal–organic frameworks, possessing different crystalline, disordered, and amorphous structures. We find this approach can provide powerful insight into the kinetics and mechanism of structural collapse that links these materials. Our methodology is also extended to a very different system, namely the melting of a zeolitic imidazolate framework, to demonstrate the potential generality of this approach across many areas of disordered structural chemistry.

Modeling the Effect of Defects and Disorder in Amorphous Metal–Organic Frameworks

“…On the other hand, the distortion PDFs obtained from the series at the constant level of order (i.e., increasing proportion of defects) show a far more uniform envelope of the peaks in the 0–12 Å region, indicating that a similar extent of structural distortion occurs throughout the local structure. Two exceptions to this uniform shape are the high intensity peaks at 1.86 and 3.24 Å, which capture changes in the peak positions . The former captures changes in the Fe coordination sphere from the Fe–O bonds, while the latter captures changes in the peak dominated by Fe–Fe and Fe–Fe correlations.…”

“…This additional scattering can manifest as a low frequency oscillation of low intensity that modulates the fluctuating baseline of the PDF and can contribute to the overall increase/decrease of PDF peak intensities. 72,73 Incorporation of tetrahedral units also reduces the overall atomic number density of the system, which plays a role in the scaling of the PDF. 74 Figure 8b highlights the effect of changing the defect level when the disorder level is kept constant.…”

“…These fluctuations in atom density give rise to additional scattering at low- Q for tetrahedra-containing systems (Figure S15). This additional scattering can manifest as a low frequency oscillation of low intensity that modulates the fluctuating baseline of the PDF and can contribute to the overall increase/decrease of PDF peak intensities. , Incorporation of tetrahedral units also reduces the overall atomic number density of the system, which plays a role in the scaling of the PDF …”

Modelling the effect of defects and disorder in amorphous metal−organic frameworks

“…This additional scattering can manifest as a low frequency oscillation of low intensity that modulates the fluctuating baseline of the PDF and can contribute to the overall increase/decrease of PDF peak intensities. 72,73 Incorporation of tetrahedral units also reduces the overall atomic number density of the system, which plays a role in the scaling of the PDF. 74 Figure 8b highlights the effect of changing the defect level when the disorder level is kept constant.…”

“…As already seen for porosity and for PDF trends at constant defect levels, this result suggests that it is the level of disorder, and not defects, that has the strongest influence over the structure of the models. In order to better visualize the way in which defects and disorder affect the PDFs, we adopted our recently reported multivariate analytical approach 72 to probe our series of PDFs (details in SI section 1.3.5). Applying principal component analysis (PCA), a dimensionality reduction technique, on a series of PDFs, we can extract two statistically significant principal components from the series.…”