Proposal for a material with negative thermal expansion

I propose a model of a material that exhibits negative thermal expansion (NTE) properties and criteria for the occurrence of linear and volumetric NTE. I derived the criteria for an arbitrary force between rigid units in the material. These criteria are also discussed specifically for the Lennard–Jones (6–12) potential and in more detail for metal–organic framework (MOF) materials comprising rigid units connected by organic linkers. Qualitatively, the model predictions can explain some observed results. Surprisingly, the model can produce equations for the transition temperature from NTE to positive thermal expansion (PTE), [Formula: see text] K, which is exactly the same as the temperature at which the glass transition begins to occur in most polymers, i.e., [Formula: see text] K.