Thermodynamic and Kinetic Effects in the Crystallization of Metal–Organic Frameworks

The evolution of metal-organic frameworks (MOFs) has been one of the most exciting aspects of materials chemistry over the last 20 years. In this Account, we discuss the development during this period in our understanding of the factors that control the crystallization of MOFs from solution. Both classical porous MOFs and dense MOF phases are considered. This is an opportune time at which to examine this complex area because the experimental tools now available to interrogate crystallization processes have matured significantly in the last 5 years, particularly with the use of in situ synchrotron X-ray diffraction. There have also been impressive developments in the use of density functional theory (DFT) to treat not only the energies of very complex structures but also their entropies. This is particularly important in MOF frameworks because of their much greater flexibility compared with inorganic structures such as zeolites. The first section of the Account describes how early empirical observations on the crystallization of dense MOFs pointed to a strong degree of thermodynamic control, with both enthalpic and entropic factors playing important roles. For example, reactions at higher temperatures tend to lead to denser structures with higher degrees of framework connectivity and lower levels of solvation, and polymorphs tend to form according to their thermodynamic stabilities. In the case of metal tartrates, these trends have been validated by calorimetric studies. It has been clear for more than a decade, however, that certain phases crystallize under kinetic control, especially when a change in conformation of the ligand or coordination around a metal center might be necessary to form the thermodynamically preferred product. We describe how this can lead to time-dependent crystallization processes that evolve according to the Ostwald rule of stages and can be observed by in situ methods. We then consider the crystallization of porous MOFs, which presents additional challenges because of solvation effects. In spite of these problems, much has been learned about the energetics of the underlying frameworks, where the relationship between porosity and stability initially seemed to mirror the behavior of zeolites, with more porous structures being less stable. Recently, however, this simple relationship has had to be reconsidered with the emergence of some very flexible structures wherein the open structures are more stable than their denser analogues at finite temperatures because of their large vibrational entropies. In the final section we describe how the concepts developed in the MOF work have been extended into the closely related area of hybrid organic-inorganic perovskites. We describe recent studies on polymorphism in hybrid perovskites, which is amenable to total free energy calculations using a combination of DFT and lattice dynamics methods.