Machine-Learning Discovered Crystallization Model for Two-Dimensional Covalent Organic Frameworks: Towards Precise Control of the Crystal Quality

The rational molecular design and experimental condition optimizations for two-dimensional covalent organic frameworks (2D COFs) call for a crystallization model capable of capturing experimental time and size scales. However, accurately describing their crystallization process remains a significant challenge due to the presence of non-classical pathways. Here, we demon-strate the implementation of a machine-learning approach, overcoming the difficulties associ-ated with bottom-up model derivation. The resulting model, referred to as NEgen1, establishes correlations among the induction time, nucleation rate, growth rate, material parameters, and common solution synthesis conditions for 2D COFs that belong to the nucleation-elongation category. NEgen1 represents the emergence of practical crystallization models for 2D COFs, enabling the direct calculation of their crystallization processes in both experimental times and sizes. The results elucidate the detailed competition between the nucleation and growth dynam-ics in solution, which has been inappropriately apprehended via classical, empirical models with assumptions invalid for 2D COFs. Importantly, we demonstrate the potential application of the NEgen1 model in optimizing the synthesis conditions, which has predominantly relied on empirical knowledge to date. The identification of conditions superior to those routinely used experimentally reveals a promising strategy of gradually increasing monomer addition speed for growing large 2D COF crystals while maintaining a reasonable synthesis time. These results highlight the potential for systematically improving the crystal quality of 2D COFs for wider applications.