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 co-valent organic frameworks (2D COFs) call for a crystallization model capable of capturing exper-imental time and size scales. However, accurately describing their crystallization process remains a significant challenge due to the presence of non-classical pathways. Here, we demonstrate the implementation of a machine-learning approach, overcoming the difficulties associated with bot-tom-up model derivation. The resulting model, referred to as NEgen1, establishes correlations among the induction time, nucleation rate, growth rate, material parameters, and common solu-tion synthesis conditions for 2D COFs that belong to the nucleation-elongation category. NEg-en1 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 elu-cidate the detailed competition between the nucleation and growth dynamics 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 opti-mizing the synthesis conditions, which has predominantly relied on empirical knowledge to date. The identification of conditions superior to those routinely used experimentally reveals a promis-ing 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 systemati-cally improving the crystal quality of 2D COFs for wider applications.