Unified Roadmap for ZIF-8 Nucleation and Growth: Machine Learning Analysis of Synthetic Variables and Their Impact on Particle Size and Morphology

Metal–organic frameworks (MOFs) have settled in the scientific community over the last decades as versatile materials with several applications. Among those, zeolitic imidazolate framework 8 (ZIF-8) is a well-known MOF that has been applied in various and diverse fields, from drug-delivery platforms to microelectronics. However, the complex role played by the reaction parameters in controlling the size and morphology of ZIF-8 particles is still not fully understood. Even further, many individual reports propose different nucleation and growth mechanisms for ZIF-8, thus creating a fragmented view for the behavior of the system. To provide a unified view, we have generated a comprehensive data set of synthetic conditions and their final outputs and applied machine learning techniques to analyze the data. Our approach has enabled us to identify the nucleation and growth mechanisms operating for ZIF-8 in a given sub-space of synthetic variables space (chemical space) and to reveal their impact on important features such as final particle size and morphology. By doing so, we draw connections and establish a hierarchy for the role of each synthetic variable and provide with rule of thumb for attaining control on the final particle size. Our results provide a unified roadmap for the nucleation and growth mechanisms of ZIF-8 in agreement with mainstream reported trends, which can guide the rational design of ZIF-8 particles which ultimately determine their suitability for any given targeted application. Altogether, our work represents a step forward in seeking control of the properties of MOFs through a deeper understanding of the rationale behind the synthesis procedures employed for their synthesis.


Methodology and database generation
As schematized in Figure S1, the data set for this work was generated by collecting research articles from Scopus using different combinations of keywords: ZIF-8, Zeolitic,Framework, and MOF, giving a total of 3440 entries.After this, duplicates and Review articles were identified and deleted, for a final 2248 entries.A total of 165 articles were hand-picked by title+abstract analysis, starting with the highest cite score.
One by one, the following parameters were extracted: Zinc source and the amount employed for the synthesis in mmol (milli-moles); 2-methylimidazole in mmol (hereinafter HmIm); solvent and quantity employed (in mmol).Then, temperature, time, and stirring conditions during synthesis; quiescent synthesis, (parametrized as 0) was discriminated from stirring conditions; stirring used just at the beginning (parametrized as 1) or during the entire synthetic time (parametrized as 2) was also classified.Finally, it was also registered if the article was systematic (39.24 %); i.e., whether or not the authors explored systematically the effects of any variable over the ZIF-8 characteristics.After these, features of the obtained materials were extracted.Given that not every work analyzed simultaneously all textural characteristics (size, crystallinity, morphology, porosity, etc.) from the synthesized particles, only particle size, morphology, and porosity (in terms of BET area) were extracted.Particle size was discriminated according to the technique employed; DLS, TEM, SEM, SAXS, or Crystalline size (by Scherrer equation).To establish a common base of comparison, only TEM/SEM information was employed in the analysis.From the initial 165 articles, only 79 reported any information about particle sizes (47.88 %) and were included in the curated database, representing a total of 254 entries (i.e., 254 individual sets of synthetic conditions with information about the resulting particles analysis).The data set is openly available in Zenodo.S1 For those works where SEM/TEM images were available but no information about particle size distribution was reported by authors (13.78 %), ImageJ software was employed to extract the information from the reported images, assuming they were representative of the Figure S1c shows histograms of the individual parameters extracted.The curated database (i.e., the database composed of 79 documents, with a total of 254 synthetic conditions) is presented as supplementary material.
Figure S2: Reference for morphology assignment of ZIF-8 particles as (a) Faceted particles.Adapted with permission from ref. S2 Copyright 2011 American Chemical Society; Poorfaceted and Quasispherical particles.Reproduced from ref. S3 with permission from the Royal Society of Chemistry.(b) Aggregative growth example.Adapted with permission from ref. S4 Copyright 2020 American Chemical Society.
To describe the morphology of the particles, three categories were applied, namely: (i) faceted particles (particles with well-defined edges, with rhombic dodecahedral shape or truncated rhombic dodecahedral); (ii) poor-faceted particles (particles with visible edges yet poorly defined); (iii) quasispherical particles (round particles with no visible edges).
Additionally, particles forming aggregates were also classified and analyzed separately.All these categories are exemplified in Figure S2.

Overview on nucleation and growth mechanisms
The following is a compendium of different sources, where nucleation and growth are addressed from different points of view.S40-S44 The goal of this section is to link them together, highlighting the differences between them and underlying the driving force of each of them and thus providing a minimal common ground for the discussion throughout this manuscript.
Nucleation is considered as the initial process for the formation of a crystal and is typically explained in terms of the supersaturation.The condition of chemical equilibrium in a homogeneous system is given by the equality of chemical potentials of every chemical species present.In a heterogeneous system, the role of chemical potentials is the driving force in all phenomena dealing with molecular transport, from the phase with higher chemical potential µ ′ to the phase with the lower one, µ ′′ .The resulting chemical work gained by the molecular transport, is typically called supersaturation, and it can be written as ∆µ = µ ′ − µ ′′ .In ideal solutions, supersaturation can be written in terms of concentrations, as given by: where γ is the surface tension of the new particle.CNT predicts the existence of a critical radius r * : If a nucleus radius is smaller than r * , it dissolves; nuclei that reach r * become stable and continue to grow by a given mechanism.This process is schematized in S3a.The previous considerations are based on a free-standing particle growing in a homogeneous phase.When a crystal nucleates on preexisting nuclei of the same material, nucleation is called Secondary nucleation and is considered a different phenomenon than growth (see later).When a crystal is formed on a foreign surface, it is called heterogeneous nucleation.Also, CNT implicitly assumes that any nucleation leads directly to the formation of the most thermodynamically stable phase, with no amorphous intermediates nor polymorphous, which might not be true for every system, such as Zeolites.
It is commonly accepted that nucleation in Zeolites is based on the generation/breaking of Si/Al − O bonds.The differences between models are how this happens and which intermediates are involved.In the zeolites monomer model, for example, there is an initial formation of an amorphous gel-like phase that evolves by local-restructuring into a crystalline phase.It is important to separate this model from the CNT monomer model, which predicts that nucleation takes place at the interface between a homogeneous solution and the growing particle, by the addition of individual units.Rather than individual units, nucleation can also take place by the addition of the so-called Secondary Building Units (SBU), which are the S-8 minimum structural units of the crystal.Zeolite formation by the SBU model also involves the formation of the amorphous gel-like phase, but here it acts as either a reservoir of SBUs or as a heterogeneous nucleation site.The nuclei grow then, maintaining the final crystalline phase, without any intermediate phase, like in CNT nucleation.CNT also considers the process of an SBU attaching homogeneously on a surface, following the crystalline structure of the most thermodynamically stable phase.
Somewhere between the accepted limit of nucleation and growth, it falls under the proposed Nanoslab model for zeolites; here, crystalline particles are formed by the internal reorganization of pre-existing nanoparticles.Nanoslab resembles an aggregative process, where nanoparticles aggregate in an oriented fashion and the final crystal is defined as the aggregate of monocrystalline domains with well-defined sizes and orientations.
Once stable nuclei are formed by any of the above-discussed mechanisms, those nuclei must grow.Classical growth models consider the addition of a given entity to the growing nuclei, and how this addition is taking place.From the thermodynamic point of view, crystal growth is favorable at supersaturation conditions and proceeds to yield morphologies that minimize the total Gibbs surface free energy.From the kinetic point of view, individual units must reach the surface of the growing crystal and then attach to it.According to the limiting process, crystalline growth will be dominated either by diffusion or by the interaction between the individual units and the crystal's surface, as summarized in S3b.
When the limiting process is not the diffusion but the attachment on the crystal's surface, there are mainly three different scenarios, according to the supersaturation degree.At low supersaturations, the resulting crystalline surface is smooth.Individual units adsorb onto energetically favorable points, what is typically known as mononuclear regime (different from zeolites' mononuclear mechanism).Here, each "layer" has enough time to complete its growth before the next layer starts to grow.Because of this, particles with well-defined edges are obtained, favoring the most dense crystalline planes.For moderate-supersaturated regimes, small units can adsorb on steps or kink sites by "birth and spread" mechanisms.
Surface attachment here is so fast that atomic layers are not complete before the next one starts to grow, which is known as polynuclear growth.However, at high supersaturation regimes, crystalline growth driving forces increase, and so units attach at the surface at any available site.This mechanism is typically known as adhesive growth and yields crystals with fractal, dendritic, or spherulitic shapes.
The classical mechanisms described so far, consider the growth as an amplification process, in which a stable nucleus increases its size without any structural change, either in bulk or in the crystal's surface.Classical models also assume that during growth, no change in crystalline phase will take place; and that the growth proceeds by the addition of small and individual units.However, under a given condition these assumptions might not hold, specially if the system is under kinetic control.One of the models that accounts for nonclassical growth is Ostwald's Step Rule.Ostwald's rule is typically seen for polymorphic materials, where molecules can adopt different arrangements, either amorphous or crystalline, each of which will have a different energetic barrier, as shown in S3c.Under these conditions, crystallization of the same final crystal can take place by successive precipitations; the phase with the lower energetic barrier is the one that appears first, instead of the thermodynamically favorable phase.Later, this phase will suffer a transformation, for instance, dissolution-recrystallization or solid-phase reorganizations.The latter requires the initial and final phases to be structurally related and to have identical construction units.These mechanisms are highly sensitive to reaction parameters, such as the solvent, temperature, modulators, etc.
Finally, crystals can grow by an aggregative mechanism.Here, pre-formed construction units aggregate to form a crystal.This aggregation is typically oriented and it is influenced by the morphology of the original particles.The Nanoslab mechanism proposed for Zeolites nucleation is sometimes considered an aggregative growth mechanism.
It is important to highlight at this point the following.Across the manuscript, we have employed the word "particle" understanding that a particle can be amorphous, polycrys-S-10 talline, or even a single crystal.Then, if we consider the particle formation (nucleation and growth), this can take place either with the utmost control thus ultimately leading to the formation of single crystals, where no grain boundaries are present and the entire extent of the solid (whichever it´s dimensioned) can be considered as a continuous repetition of unit cells in the three dimensions; or by a kinetic control, where polycrystalline and irregular particles are obtained.Between these two extremes, we can encounter all kinds of mechanisms, which is what we aim to summarize and show at the beginning of our manuscript.Where to set the limit between a single crystal and a nanoparticle with a high degree of crystallinity is, to the best of our knowledge, a matter of discussion today.Due to the limited data reported across the reviewed manuscripts, to discern whether or not the particles are indeed single crystals when the authors did not provide a deep analysis in those lines is far from trivial, and we can only attempt to classify those particles as either crystalline or not (first) and then obtain some insight based on the morphology of the particle, understanding that a faceted particle with well-defined facets will be closer to the single crystal case.At this point, it is necessary to include the ongoing discussion in the community on which nucleation and growth mechanisms operate for the formation of ZIF-8.As we tried to postulate at the beginning of our manuscript, the individual reports are only proving a limited section of the chemical space that leads to the obtention of ZIF-8, and it is only until those reports are discussed together that we can have a clearer vision of the processes taking place.Figure S7a shows a pair plot constructed with different synthetic variables, such as Zn and HmIm concentration, their molar ratio, time, and final diameter of the particles.The upper half of the pair plot, classifies the data according to the morphology of the particle, while the bottom part of the plot, classifies the data according to the solvent employed.Both halves are mirror images.To take advantage of this, two pair plots are shown at once, where the upper part classifies the data points based on the particle shape, while the bottom part classifies them by solvent employed during the synthesis.The diagonal of the pair plots was extracted and is presented in S7b for clarity.

Violin plots
Figure S8 shows the same pair plot arrangement, yet classified according to the counterion employed.As can be seen, the synthesis reported employs mainly nitrate as counterion, followed by some reports using acetate and then other counterions to a very low extent.BET area trends and Diameter-shape correlation From the 254 entries after filtering the data set as described above, only 101 reported a value for the surface area.From this sub-set, reported values below 1000 m 2 g −1 (which represents about 50% of the estimated crystallographic porosity value of 1947 m 2 g −1 ) S45 were discarded.The remaining 83 entries were classify according to the morphology of the particles.Figure S9 cross-references the reported BET surface areas with particles' diameter.that the feature has a more complex effect on the prediction.

Figure S1 :
Figure S1: Schematic representation of database construction, curation, and extracted data.

For
1) were k B is the Boltzmann constant, T is the absolute temperature, and c and c 0 are the concentration of a supersaturated and saturated solutions.Nucleation and growth models can be grouped into classic and non-classic mechanisms, each of them taking place under different supersaturation conditions: Surface reaction-limited, which includes (i) Mononuclear growth.(ii) Polynuclear growth (iii) Adhesive or spherulitic growth.Theory (CNT), the formation of crystal nuclei occurs after the constituent atoms and/or molecules of the crystal have come together and positioned into a fixed lattice.Under supersaturation conditions, crystallization is thermodynamically favored, and nucleation of a particle with radius r generates a change in free energy ∆G c , associated with an interfacial free energy per unit area ∆G a and the energy required to form the bulk of the particle, in terms of volume unit ∆G v :

Figure S3 :
Figure S3: Schematics of the (a) formation of nuclei with critical radii according to Classical Nucleation Theory.(b) Diffusion-limited and attachment-limited growth processes.(c) Ostwald's Step Rule.

Figure
Figure 2b in the main manuscript showcases the distribution of ZIF-8 particles with the different morphologies, based on the concentration ratio C HmIm /C Zn , separated by waterand methanol-based synthesis.This graph gives a quick view of the main trends and concentration ranges explored in each case, by including all the reported values included in our dataset after curation, except for flagrant outliers, individually represented.For analyzing each subcase (i.e., water-and methanol-based synthesis), Figure S4 presents the data in a shorter range, excluding outliers.Here, it can be easily seen by analyzing the median of the distribution, that as the molar ratio increases, the obtained particles shift from faceted to poor-faceted and ultimately quasispherical morphologies, thus supporting the progression of nucleation and growth mechanisms proposed.

Figure S4 :
Figure S4: Violin plot distribution of ZIF-8 particles with faceted, poor-faceted, and quasispherical morphologies for (a) methanol-and (b) water-based synthesis.The width of plots in (b) is magnified x3 for better showcasing of the distribution.

Figure S6 :
Figure S6: Contour plot for particle morphology according to HmIm and Zn concentrations.

Figure S7 :
Figure S7: (a) Pair plot for different synthetic variables, classify according to particle morphology (upper half) and solvent (bottom half).(b) The pair plot's diagonal is extracted for clarity.

Figure S8 :
Figure S8: Pair plot for different synthetic variables, classify according to the counterion employed.

Figure S9 :
Figure S9: BET surface area cross dependence with particle diameter, classify by morphology.Box plots on the right represent the distribution of surface area values by morphology, considering all sizes.

Figure S10 :
Figure S10: Exemplification of obtaining an average predicted response with a confidence interval based on predicted curves in partial dependence plots.

Table S1 :
References for Figure 1 in the main manuscript