Anomalous Mechanical Behaviour Arising From Framework Flexibility

This chapter describes in detail the framework of anisotropic elasticity to introduce exotic elastic and thermoelastic properties that are often prevalent and extreme in MOFs: negative linear compressibility (NLC), negative thermal expansion (NTE) and negative Poisson's ratio (NPR). The complete elastic tensors of 56 MOFs are collated and analysed to reveal that NPR is very common in non-cubic MOF structures, but the mechanisms are not yet clear. This is in contrast to NLC and NTE, which derive from the interplay between rigid, stiff building blocks and compliant joint flexing in ‘wine-rack’ type motions and dynamic equivalents. As the existence of flexible mechanisms seems to allow large and unusual framework deformations, several potential measures of materials and framework flexibility are considered, from ad hoc elastic anisotropy metrics to graph-theoretical and group-theoretical analyses, including physical models.