Modeling and Simulation of Crystallization of Metal-Organic Frameworks

Metal-organic frameworks (MOFs) are the porous, crystalline structures made of metal-ligands and organic linkers that have applications in gas storage, gas separation, and catalysis. Several experimental and computational tools have been developed over the past decade to investigate the performance of MOFs for such applications. However, the experimental synthesis of MOFs is still empirical and requires trial and error to produce desired structures, which is due to a limited understanding of the mechanism and factors affecting the crystallization of MOFs. Here, we show for the first time a comprehensive kinetic model coupled with population balance model to elucidate the mechanism of MOF synthesis and to estimate size distribution of MOFs growing in a solution of metal-ligand and organic linker. The oligomerization reactions involving metal-ligand and organic linker produce secondary building units (SBUs), which then aggregate slowly to yield MOFs. The formation of secondary building units (SBUs) and their evolution into MOFs are modeled using detailed kinetic rate equations and population balance equations, respectively. The effect of rate constants, aggregation frequency, the concentration of organic linkers, and concurrent crystallization of organic linkers are studied on the dynamics of SBU and MOF formation. The results qualitatively explain the longer timescales involved in the synthesis of MOF. The fundamental insights gained from modeling and simulation analysis can be used to optimize the operating conditions for a higher yield of MOF crystals.