Modeling of deposit formation in mesoporous substrates via atomic layer deposition: insights from pore‐scale simulation

Atomic layer deposition (ALD) has been a promising technique in fabricating membranes and tuning their properties with a precision at the atomic level. Fabrication of zeolitic imidazolate framework (ZIF) membranes using the ligand-induced permselectivation (LIPS) method starts with the formation of an oxide in a mesoporous substrate by ALD and is followed by the transformation of this oxide to ZIF using imidazolate vapor treatment. The objective of the ALD step is to block the mesopores with a thin deposit, that is, one with small penetration depth and small thickness on the top surface of the substrate. Unlike typical ALD on nonporous substrates, where all available sites react per ALD cycle, thin deposit formation in a mesoporous substrate requires that only a small fraction of the available deposition sites (i.e., close to the substrate surface) is subjected to ALD. Consequently, reactant dosing and duration of pulses are important process variables which, together with diffusion and reaction kinetics determine the deposit structure. Quantitative understanding of the interplay of these variables and phenomena can enable the rational design of ALD within mesoporous substrates. Here, we extend our earlier modeling effort considering the coexistence of ALD both inside the pores and on the external surface of the substrate. Finite-volume based models were developed and validated to simulate the two distinct modes of deposition cycle by cycle. The total mass uptake of the substrate with ALD cycles can be predicted using the combined surface deposition and pore reaction-diffusion models as affirmed by in situ quartz crystal microbalance experimental data. The ALD reactor model combined with the deposition model can accurately capture the number of ALD cycles needed to block the pores of the substrate. Based on the model, we designed a modified ALD process and examined the performance of the corresponding LIPS membranes. The present modeling work provides a new understanding of the deposit formation via ALD within mesoporous substrates for a variety of membrane applications.