Computer Simulation of the Growth of a Metal-Organic Framework Proto-crystal at Constant Chemical Potential

TL;DR

This work tackles the lack of molecular-level understanding of MOF growth by simulating the solvothermal growth of ZIF-8 from a pre-formed proto-crystal under constant chemical potential conditions. The authors couple constant chemical potential MD (CµMD) with a particle-insertion scheme to maintain steady Zn^{2+} and MIm^- concentrations at the proto-crystal surface, across multiple concentrations and temperatures. They find non-classical growth mediated by oligomer attachment, an amorphous growth front with defect-rich ring statistics, and a shift toward larger rings at higher concentration and temperature, indicating adsorption-controlled growth rather than diffusion-limited processes. The methodology and insights into ring statistics and growth kinetics provide a general computational framework for studying MOF growth under realistic synthesis conditions and can guide experimental protocol design.

Abstract

Designing metal-organic frameworks (MOFs) synthesis protocols is currently largely driven by trial-and-error, since we lack fundamental understanding of the molecular level mechanisms that underlie their self-assembly processes. Previous works have studied the nucleation of MOFs, but their growth has never been studied by means of computer simulations, which provide molecular level detail. In this work, we combine constant chemical potential simulations with a particle insertion method to model the growth of the ZIF-8 MOF at varying synthesis temperatures and concentrations of the reactants. Non-classical growth mechanisms triggered by oligomer attachments were detected, with a higher predominance in the most concentrated setups. The newly formed layers preserve the pore-like density profile of the seed crystal but contain defective sites characterized by the presence of 3, 5 and 7 membered rings, typical of amorphous phases. Compared to the amorphous intermediate species obtained at the nucleation part of the self-assembly process previously investigated in our group [Chem. Mater., doi: 10.1021/acs.chemmater.5c02028, 2025], larger-sized rings are more common in the grown layer. Moreover, these are favored by increasing reactant concentration and temperature, as is the degree of deviation with respect to the original crystal structure. We computed growth rates for the steady-state regime, and the non-linear tendency with respect to concentration leads us to hypothesize that in these conditions the growth is controlled by the adsorption rather than by the diffusion processes.

Figures (10)

• Figure 1: Schematic representation of the simulation system showing a symmetric box containing a ZIF-8 proto-crystal slab at its center. Red diamonds represent solvent molecules, cyan spheres represent Zn$^{2+}$ ions, and the ball-and-stick model corresponds to the MIm$^{-}$, with carbon atoms shown in gray, nitrogen in blue, and hydrogen in white. The transition region (TR), control region (CR), and reservoir (Res) are highlighted in transparent purple, orange, and white, respectively. The red dashed line indicates the position where the external force is applied. DCR= size of TRs, CRSIZE = size of the CRs, DF = DCR + CRSIZE.
• Figure 2: Snapshots illustrating (A) the initial and (B) the final configurations of one of the independent simulations for the [Zn$^{2+}$]= 0.4 M and T=298 K system. Zn$^{2+}$ ions are shown as cyan spheres, ligands are represented as blue lines connecting their two nitrogen atoms, DMSO molecules are displayed with carbon in grey, hydrogen in white, oxygen in red and sulfur in yellow.
• Figure 3: (a) Ionic density as a function of the $z$ coordinate for each of the systems studied at the end of the simulation. Only ions connected to the central cluster are considered. One out of the three independent simulations is shown in each case. The densities are normalized to integrate to one. (b) Maximum $z$-distance of the grown layer with respect to the original proto-crystal slab as a function of the total number of ions that were added ($N$). Each plot corresponds to an average over six surfaces (three independent simulations that contain two external surfaces each). Color code: [Zn$^{2+}$] = 0.1 M, T = 298 K (red), [Zn$^{2+}$] = 0.2 M, T = 298 K (black), [Zn$^{2+}$] = 0.4 M, T = 298K (green) [Zn$^{2+}$] = 0.2 M, T = 320 K (orange).
• Figure 4: a) Snapshots of the growth on the ZIF-8 proto-crystal surface at several ion concentrations and temperatures. Red sticks indicate newly formed bonds, cyan spheres show newly coordinated Zn$^{2+}$ ions, and blue spheres represent the N atoms of newly attached ligands. The underlying crystal surface is shown in the background as blue sticks and cyan balls. The uppermost plots depict a side view of the surface while the rest show the top view for each system. b) Snapshots of the surface density of the added ions in the $xy$ plane at the end of one of the independent simulations for each system. The density color scale goes from blue to red as the density increases. Densities are normalized to integrate to one. Throughout the figure, each system is noted as (I) [Zn$^{2+}$] = 0.1 M, T = 298 K, (II) [Zn$^{2+}$] = 0.2 M, T = 298 K, (III) [Zn$^{2+}$] = 0.2 M, T = 320 K and (IV) [Zn$^{2+}$] = 0.4 M, T = 298 K. c) Kullback–Leibler divergence between the ion surface density distribution and the reference distribution as a function of the amount of ions (N) added to the surface. Each curve corresponds to an average of the six simulated surfaces. Systems (I), (II), (III) and (IV) correspond to red, black, orange and green curves respectively.
• Figure 5: Time evolution of the average number of rings of different sizes ranging from 3 to 8 Zn$^{2+}$ ions for systems with concentrations of ([Zn$^{2+}$]= 0.1, 0.2 and 0.4 M at T=298 K as well as for the system with [Zn$^{2+}$]= 0.2 at T=320 K. Each data point represents the average from three independent simulations.