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Could Mesophases Play a Role in the Nucleation and Polymorph Selection of Zeolites? Abhinaw Kumar, Andrew H. Nguyen, Rita Okumu, Tricia D. Shepherd, and Valeria Molinero J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b06664 • Publication Date (Web): 31 Oct 2018 Downloaded from http://pubs.acs.org on October 31, 2018

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Journal of the American Chemical Society

Could Mesophases Play a Role in the Nucleation and Polymorph Selection of Zeolites? Abhinaw Kumar,1 Andrew H. Nguyen,1 Rita Okumu,2 Tricia D. Shepherd,2 and Valeria Molinero1* 1

Department of Chemistry, The University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112-0850, United States; 2 Department of Chemistry, Westminster College, 1840 South 1300 East, Salt Lake City, Utah 84105, United States * corresponding author, e-mail: [email protected]

Abstract: Zeolites and mesoporous silicas are porous materials with important applications in catalysis, gas storage, and separation. Zeolite crystals form in the presence of cationic surfactants that act as structure directing agents (SDAs). The way SDAs control the nucleation and polymorphs selection in zeolites is not fully understood. The formation of mesoporous silica is templated by liquid crystalline mesophases that result from frustrated attraction between silicates and long-chain SDAs. Experiments indicate that surfactants CnH2n+1(CH3)3N+ with n > 6 yield mesoporous silicas, and the one with n = 6 produces a zeolite. This suggests that the driving force towards mesophase formation is also present for small organocations, but is overcome by the ability of silica to wrap a crystal lattice around them. Here we use molecular dynamics simulations to investigate whether the existence of metastable mesophases can play a role in the nucleation and polymorph selection of zeolitic crystals. As a proof of concept, we investigate the phase behavior of simple mesogenic mixtures of SDAs and a network former T that favors tetracoordinated crystals. As a computationally efficient silica potential that would allow for the spontaneous nucleation of zeolites in molecular dynamics simulations is not yet available, we represent the network-former T by StillingerWeber models of water and silicon, in lieu of silica. The mixtures of T and SDA produce a rich phase diagram that encompasses the sII clathrate and at least six zeolites, including sigma-2 (SGT). We find that the nucleation of SGT is not assisted by a mesophase. The nucleation of the other five zeolites of this study, however, is facilitated by the existence of metastable mesophases that decrease the nucleation barriers and direct the selection of the crystal polymorph. Together with the experimental support for mesophases in mixtures of silicates and SDAs, our results for model systems suggest that metastable mesophases could play a prominent role in promoting the nucleation and polymorph selection of some zeolites.

KEYWORDS: crystallization, structure-directing agent, polymorphism, silica, water, silicon, clathrates

1. Introduction. Zeolites are crystalline materials with pores comparable to molecular dimensions, widely used in separations and catalysis.1-3 Topologically, zeolites are three-dimensional networks of corner-sharing tetrahedra. Silica zeolites consist of four-coordinated Si bridged by oxygen atoms.4 A variety of organic cations, typically tetraalkyammonium, are used as structure-directing agents (SDA) in the synthesis of zeolites, with the goal of producing specific crystal polymorphs.5-12 It has been proposed that the size and shape of SDAs direct the synthesis towards a given polymorph.5-6, 9, 13-17 Interestingly, the same SDA can lead to different zeolites under distinct synthetic conditions,18 and identical zeolites can be obtained with more than one SDA.19 The molecular mechanism by which cations direct the nucleation towards a specific zeolite structure has not yet been resolved.20

Experimental and simulation studies indicate that dense aggregates of amorphous silica and SDA of about 5 nm in diameter form before the nucleation of zeolites in hydrothermal and solution synthesis.21-24 It has been experimentally determined that these aggregates are the birthplace of the zeolite crystals.24-26 The aggregates evolve to well-defined sizes that depend on the pH, but are independent of the amount of silica in the solution.25, 27 While the size of the aggregates is stationary, experiments suggest that their composition and internal structure may change as they age:25 neutron diffraction experiments indicate that the structure of the amorphous phase evolves prior to crystallization, attaining local and medium-range order similar to that in the zeolite.28-29 The origin of this medium-range order in the precursors, and its impact on the pathway and nucleation barriers of zeolites has not been established.

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The formation of nanoaggregates of silicates and SDA is, in many ways, analogous to the aggregation of surfactants into micelles.27, 30 Aggregates with a narrow size distribution are typical of systems in which a combination of attractive and repulsive interactions leads to frustration.31-32 These encompass not only surfactants, but also block copolymers, molecules that combine short-range attraction and long-range repulsion, and systems with charge frustration.33-37 A commonality of all these systems is their ability to produce a wide range of stable and metastable mesophases in which the major component forms pores that can be filled by the minor component.36-40 Indeed, mesoporous silica materials are synthesized by calcination of aluminosilicate gels that produce hexagonal and gyroid mesophases in the presence of surfactants.39, 41 Interestingly, the tetraalkylammonium cationic surfactants CnH2n+1(CH3)3N+ with n > 6 produce mesoporous silicas, while the one with n = 6 produces a zeolite.42 These results suggest that the driving force towards mesophase formation is also present for the small organocations, but it is overwhelmed by the ability of silica to wrap a crystal lattice around them. It has been proposed that mesophases can act as stepping stones for the formation of complex crystals.43 Mesophases that become manifest in the formation of mesoporous silicas could be metastable with respect to the crystal polymorphs under the conditions of synthesis of zeolites. Metastable phase transitions, hidden below the envelope of the stable liquid to crystal transformation, have been found to facilitate the nucleation of crystals in systems as diverse as colloids,44-45 proteins,46-48 and clathrate hydrates.49-52 In those cases, a metastable phase segregation between dilute and concentrated solutions results in the formation of dense amorphous aggregates – not unlike those found in the nucleation pathway of zeolites – from which the crystals develop. Interestingly, studies of model systems indicate that transient clusters of the dense phase can facilitate crystal nucleation even when the dense phase is thermodynamically unstable, above the fluid-fluid critical point.47 This poses the question of whether the existence of metastable –or even unstable- mesophases that result from frustrated attraction in silicate/SDA mixtures could facilitate the formation of zeolite crystals and play a role in the selection of the polymorph. Here we investigate this possibility using molecular simulations. The formation of zeolites is a complex, multi-scale, problem, involving processes ranging from hydrolysis and polymerization of silica, to the formation of amorphous aggregates, and –finally- the nucleation and growth of the crystals.20-21 These processes cannot be addressed with a single computational approach.20, 53 Most computational studies have focused on the stability of the crystalline framework, their interactions with organic cations, and the polymerization and aggregation of silicates to produce amorphous precursors.14, 53-65 The formation of zeolitic

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order from amorphous mixtures of silicates and SDAs is arguably the most challenging to model, as this process can take up to a year at room temperature in the laboratory.25 A coarse-grained lattice simulation, powered by parallel tempering Monte Carlo (PTMC) provided the first spontaneous formation of zeolite analogs.26, 66 PTMC allows for very efficient sampling, revealing a wide range of ordered networks with similar stability.26 Enhanced replica exchange reactive Monte Carlo simulations (RE-RxMC) have also been recently used to construct zeolite frameworks.67-68 PTMC and RE-RxMC simulations, however, cannot provide insight on the mechanism by which the crystalline networks nucleate.26, 67 The computational cost of molecular dynamics simulations with fully atomistic reactive models has hampered the study of the pathway of crystallization of zeolites. Here we study the formation of zeolitic crystals using molecular dynamics simulations with a model that has only two species, the tetrahedral network former T – that represents the Si center of the silicate units – and the structure directing agent S. Our model of T and S experience frustrated attraction that leads to the formation of stable and metastable mesophases,69 while anisotropic interactions between T particles favor tetracoordinated crystals. Ideally, the interactions between T particles should reproduce the wide distribution of angles in silica crystals70 and the speciation of anionic silicate species.71 To date, the crystallization of silica crystals using molecular dynamics simulations has been achieved only for the nucleation of stishovite at very high driving forces,72 and – very recently- for the nucleation of b-cristobalite with advanced sampling methods.73 Porous crystals of silica have not yet been nucleated using molecular dynamics simulations. As a computationally efficient potential for silica that would allow for the spontaneous nucleation of zeolites in molecular dynamics simulations is not yet available, here we model T as a single particle that interacts with other T through a Stillinger-Weber (SW) potential, which favors tetrahedral order through three-body interactions.74 We use the SW parameterizations of silicon74 and mW water,75 because water, silicon and silica are tetrahedral substances that share the anomalies in the liquid phase and produce a common range of crystals.70, 75-80 In terms of coordination in the liquid and anomalies, silica is closer to water than to silicon.78-81 Water, nevertheless, has higher energy penalties than silica for the non-tetrahedral angles usually found in zeolites.70 An assessment of the energies of guest-free zeolitic frameworks optimized with the TIP4P/2005 water model revealed that a large number of zeolites made of water would have lower energy than sodalite,70 the highest energy hydrate isomorph of a zeolite realized in experiment.82 That analysis suggests that other water zeolites could be synthesized in the laboratory. In the present study we first use the simple model of T and S particles to investigate the


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formation of zeolitic crystals and the role of mesophases in their formation and polymorph selection, and then discuss the implications and significance of the results for the formation of silica zeolites as well as water zeolites.

2. Models and methods. 2.1. Model. In our quest for tractability, we model the tetrahedral network former as a single species, T. This assumes that the hydrolysis and reforming of bonds in silica is fast compared with the time scales involved in the development of crystallinity. It also neglects the distinction between neutral and anionic silicate species, and the explicit presence of solvent molecules. Our zeolite former model is a binary mixture of T and S that combines the non-additive size rules that lead to the formation of mesophases,69 with anisotropic interactions between T particles that favor the formation of four-coordinated crystals. We model T as a single particle that interacts through the Stillinger-Weber (SW) potential74 with the parameters of the mW water model,83 which has been extensively used to investigate the structure and crystallization of water.49, 83-103 We also investigate, for selected conditions, the phase behavior of mixtures in which T is modeled with the SW model of silicon74 keeping the size and energy scales of mW water, sTT = 2.3925 Å and energy eTT = 6.189 kcal mol-1, to allow for a direct comparison of the temperatures of formation and avoid reparameterization of the interactions with the solutes. This scaled model of silicon differs from mW only the weight l of the three-body term of the potential, which is 21 for silicon and 23.15 for mW water.83 The structure directing agent S is a single particle that interacts with other S and with T through the two-body term of the SW potential with parameters sSS = 4.5 Å, eSS = 0.34 kcal mol-1, sTS = 4.5 Å, and eTS ranging from 0.1 to 3.2 kcal mol-1. The parameters sSS = 4.5 Å, eSS = 0.34 kcal mol-1, sTS = 4.5 Å correspond to those of the interactions of mW water with the “extra-large” solute of ref. 104, previously shown to stabilize the sII clathrate.104 2.2. Simulation settings. We perform molecular dynamics simulation of the T+S mixtures in the isobaricisothermal ensemble using LAMMPS.105 The simulation cells are periodic in all directions. The equations of motion are integrated with the velocity-Verlet algorithm using a time step of 5 fs. Temperature and pressure are controlled with the Nose-Hoover thermostat and barostat with relaxation times 2.5 and 12.5 ps, respectively. The pressure is set to 1 bar in all simulations and is controlled independently in the three Cartesian directions. When a cooling or heating ramp is applied, the target temperature of the thermostat changes linearly at the indicated rate. 2.3. Phase diagram. We construct the phase diagram of the binary mixture of T and S at 300 K and 1 bar as a function of the strength of TS interaction eTS and the molar fraction of T, XT, using simulation cells that contain 64000

particles. All crystals and mesophases reported in this work nucleate and grow spontaneously from the isotropic liquid in at least one point of the phase diagram, or are obtained by cooling or heating other phases at a rate of 1 K ns-1. Section 3.1 details the structure of each phase. We build the phase-diagram of the binary system using the same procedure as in ref. 69, tracking the composition of coexisting phases as a function of eTS and XT at 300 K and 1 bar. This procedure defines the boundaries of the region of stability of each mesophase and crystal in the eTS-XT phase space. Within these regions, a single phase is stable. Outside of these regions, more than one phase coexist in a proportion determined by the lever rule. Most phases discussed in this work nucleate and grow spontaneously in their region of stability. An exception is the G2 gyroid-like mesophase (see section 3.1.D), which is not a stable mesophase of the mixture of isotropic particles with frustrated attraction.69 We have been, however, able to nucleate G2 at the interface between the hexagonal mesophase and liquid following two distinct protocols. In the first one, we start with hexagonal in contact with a ~2.5 nm slab of pure S liquid that is itself in contact with a T+S liquid mixture of composition XT = 0.77. We find that S slowly incorporates into the hexagonal phase in NpT simulations at 260 K, forming a connected hexagonal mesophase which, upon an adjustment in composition to yield a local molar fraction of T XT = 0.74, results in the nucleation and growth of the G2 gyroid-like mesophase. In the second protocol, the hexagonal mesophase is in contact with the liquid mixture with composition XT = 0.77 modeled with eTS = 1.0 kcal mol-1. This leads to connections between the cylinders of the minor (S) component of the hexagonal phase at the hexagonal/isotropic interface. On changing the composition of the isotropic phase to XT = 0.74 at 240 K, this two-phase system nucleates and grows of the Z2 zeolite (section 3.1.D), the nucleation of which we show in that section to be directed by the G2 gyroid– like mesophase. 2.4. Identification of rings in the zeolites. We compute the size of rings of connected T particles using the code of Matsumoto et al. 106. We consider two T particles as connected if they are within 3.5 Å, the first minimum in the water-water radial distribution function.75 2.5. Order parameters to identify mesophases and zeolite crystals. We identify the lamellar, hexagonal and gyroid mesophases with the order parameters presented and validated in ref. 107 and clathrates with the CHILL+ algorithm,108 which identifies recognizes eclipsed TTTT configurations. To identify the SGT zeolite we modify the range of Cij 108 used to identify eclipsed bonds in CHILL+ (Supp. Information 1A). To this end, we compute the distribution of Cij for the SGT crystal downloaded from the International Zeolite Association (IZA) database.109 We find that the Cij parameters that identify an eclipsed bond


3


in SGT range from -0.4 to 0.1 (Supplementary Figure S1), a shift from the range used for Frank-Kasper clathrates, 0.25 ≥ Cij ≥ −0.35.108 We distinguish the zeolite Z1 (section 3.1.E) from liquid using the bond-order parameter110 𝑞"# of the three-coordinated T particles in the zeolite, using with a cutoff of 11.5 Å (Supp. Information 1B). These order parameters are used to follow the nucleation and growth of mesophases and zeolites. 2.6. Diffusion coefficients. We compute the diffusion coefficient of T and S in the lamellar mesophase using Einstein’s relation between the displacement of the particles, the time and the diffusion coefficient = 2dDt, where d is the dimensionality (e.g. 2 for diffusion in a plane). We prepare a lamellar system that has the layers parallel to the xy plane and the z-axis is normal to the lamellar. We calculate the diffusion coefficients of T and S along the plane of the layers and in the direction perpendicular to it. 2.7. Melting temperatures. We compute the equilibrium melting temperatures of sII clathrate, SGT, Z1 and Z2 zeolites, lamellar, double gyroid (G1) and gyroidlike G2 mesophases. For the sII clathrate, SGT zeolite, and the mesophases, we compute the equilibrium melting transition to the disordered liquid phase. For Z1 and Z2 zeolites, we compute the equilibrium melting temperatures to their corresponding mesophases. We follow the protocol of ref. 69 to generate two-phase simulation cells with a slabs of the two phases of interest in coexistence and find the coexistence temperature by performing NpH simulations 3DS of the two-phase systems. The melting temperatures of the guest-free crystals are obtained from NpT simulations of the corresponding crystal in contact with vacuum, in which the temperature is increased at a rate of 1 K ns-1. The formation of a premelted layer at the crystal/vacuum interface ensures that this procedure does not result in superheating.111 2.8. Interaction energies per particle. We compute the contribution of the interactions between T particles (ETT) and between S particles (ESS) to the total potential energy by recomputing the energy the simulation trajectories of the corresponding zeolite or clathrate, turning off all but the TT and SS interaction potentials, respectively. In all these cases, the TS systems are evolved with eTS = 0.8 kcal mol-1 at 300 K and 1 bar, except for Z2, which is unstable at that temperature and is evolved at 260 K, turning off the TS interactions. Likewise, we compute the TS interaction energy (ETS) by turning off the TT and SS interactions in the analysis of the simulation trajectories. We present ETT – which includes the two- and three-body contributions – normalized by the moles of T, ESS normalized by the moles of S, and ETS by the total number of moles of T plus S. We compare the optimized energies of a variety of guestfree water zeolites modeled with the coarse-grained mW water model with values previously reported for the same structures optimized with the TIP4P/2005112 fully

atomistic water model in ref 70. To this end, we download the structures of the corresponding silica zeolites from the IZA database,109 from which we keep only the Si atoms and replace them by T sites modeled with mW, and generate superlattices with at least 512 T sites per cell by replication of the unit cell. We optimize the energy of the guest-free crystals with respect to cell dimensions and atom positions. We also compute the minimized energy of guest-free Z1 and Z2 zeolites, by removing the guests from these crystals formed in the simulations and then proceeding in the same manner as with the crystallographic structures.

3. Results and discussion. 3.1. T+S mixtures produce a wide range of zeolites. Figure 1 presents the phase diagram of the binary mixture of the tetrahedral network former T and structuredirecting agent S as a function of the strength of the TS attraction, eTS, and the mole fraction of T, XT, at 300 K and 1 bar. Note that the energy scale and melting temperatures are those of water, which are significantly lower than for silica: the melting point of mW ice is 273 K,113 while the experimental melting point of quartz is 1983 K.114 The first neighbor distance between T and S in the model is that of water with tetramethylammonium.115-116 As the distances between Si atoms in zeolites and other silica crystals are about 10 to 15% larger than between water molecules in ice and other water crystals, the structure directing agent S of this study could be considered to have a size intermediate between those of tetramethyl- and tetraethylammonium SDAs used for the formation of silica zeolites.

Z1 G2 HEX SGT

1.2

eTS (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 0.8 0.6 0.4 0.2 0.5

sII

lamellar 0.6

0.7

solution

XT

0.8

0.9

1

Figure 1. Phase diagram of binary mixtures of the T modeled with mW water and structure-directing agent S as a function of the strength of the TS interaction eTS and the mole fraction XT of T at 300 K and 1 bar. The colored shaded areas represent the regions of stability of the lamellar mesophase (red), zeolite Z1 (green), gyroid-like mesophase (blue), hexagonal mesophase (turquoise), SGT zeolite (magenta), clathrate sII (purple). The black line represents an incomplete mapping of the composition of liquid in stable or metastable coexistence with these phases. An S-rich hexagonal mesophase with one-dimensional chains of T particles forms at high T-S


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Journal of the American Chemical Society A

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B

C

attraction and XT = 0.25 region, outside of the composition range of this figure, and is discussed in Supporting Information 2A.

The T+S mixture stabilizes the lamellar, double gyroid, and hexagonal mesophases that result from frustrated attraction already in the absence of tetrahedral interactions,69 plus the known sII clathrate and several zeolites, including the well-known zeolite SGT117 and new ones described below which we call Z1, Z2 and Z3, Z4 and HX. The formation of these crystals is favored by the tetrahedral interactions between T particles. These phases nucleate and grow spontaneously in the simulations with the T and S model. The same phases are obtained when the network former is modeled with the parameters of SW silicon or mW water. To our knowledge this is the first report of the nucleation and grow of zeolitic crystals in molecular dynamics simulations. In this section we present and discuss each of the crystal phases in the phase diagram of the mixture of structure directing agent and tetrahedral network-former, from higher to lower T content, and the role of mesophases in directing or assisting their formation. Section 3.2 discusses the significance of the simulation results for silica zeolites and how can the model be improved to more accurately model them. Section 3.3 discusses the experimental feasibility of water zeolites. A. sII clathrate. Clathrates are a subset of zeolites in which the rings of the crystalline framework are too small to allow unimpeded transport of guest molecules throughout the crystal. sII clathrate is a known phase of many substances that favor tetrahedral coordination, including water,118 silicon,119 and silica.120 The T network in the sII clathrate is composed of two types of polyhedral cages, shown in Figure 2: dodecahedra (tiled by 12 pentagons, 512) and hexakaidecahedra (12 pentagons and 4 flat hexagons, 51264). sII clathrate with composition XT = 0.94 is the stable crystal of the T+S mixture at 300 K and 1 bar for eTS between 0.36 and 0.6 kcal mol-1. Only the large, 51264 cages of the sII clathrate are occupied by the S guest. sII is less stable than the liquid for eTS < 0.36 kcal mol-1 and less stable than SGT zeolite for eTS > 0.6 kcal mol-1, at 300 K and 1 bar. The stability, nucleation and growth of sII clathrates has been extensively studied in simulations with the mW water model,49, 104, 111, 121-123 as well as with fully atomistic models.50, 52, 124-126 MTN, the silica zeolite isostructural with sII has only recently been synthesized, with gas molecules in the large cages.127 To our knowledge, clathrates have not yet been nucleated and grown in molecular simulations with silica models.

51264

512

Figure 2. sII clathrate. Red sticks show bonds between T particles within 3.5 Å, blue spheres correspond to the S guest. A) shows the structure of a large simulation box of the sII clathrate, a zoom of which is shown in the panel B. C) shows the two types of cages of sII: 51264 (top) and 512 (bottom) The unit cell of sII has sixteen 512 and eight 51264 cages.

The guest-free sII clathrate is a metastable crystal phase of water111, 128 and silicon129 at room pressures, and it has been predicted to be the stable phase of these substances at negative pressures.111, 125, 130 The guest-free sII hydrate is close in energy to hexagonal ice70, 111, 125 (Table 1), the stable crystal of water at 1 bar. The weak interaction of the S guests with T compensates for the lower stability of the T framework, making guest-filled sII crystals stable for water, silicon, and silica at positive pressures.111, 131-132 The TS interaction contributes 9.2% of the cohesive energy of sII when eTS = 0.8 kcal mol-1 (Table 1). Stronger eTS further stabilizes the clathrate,121 but not as fast it stabilizes the SGT zeolite (Supp. Table S1), which becomes the stable crystal already at eTS = 0.6 kcal mol-1 (Figure 1). Table 1. Equilibrium melting temperatures and energy contributions of water zeolites, clathrates, and ice. The systems are modeled with mW as T and eTS = 0.8 kcal mol-1; the energy contributions, in kcal mol-1, are computed for the S-filled crystals at 300 K, except for those that melt below that temperature: Z2 is computed at 260 K, and ice Ih at 273 K. Crystal

XT

TmFilled

TmEmpt

ETT

ESS

ETS

%ETS

y

Z1

0.73

327

34

-8.97

1.29

-4.25

40.7

Z2

0.74

260

5

-9.12

1.25

-4.2

39.5

SGT

0.89

330

185

-10.76

2.17

-2.28

19.6

SGT

0.94

335

185

-10.73

0

-1.55

13.3

sII

0.94

320

252

-11.17

0

-1.07

9.2

Ice Ih

1.0

--

273

-11.46

--

--

0

Attempts to nucleate sII clathrate directly from supercooled mixtures result, here and in previous studies,4951 in amorphous clathrates – solids with Frank-Kasper cages (5126n with n = 0, 2, 3, and 4) and local order of clathrate polymorphs but no long-range order– that transform to crystalline hydrates upon heating or slow growth.49 51, 133


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B. Zeolite SGT. SGT is a known pure silica zeolite, also referred to as the sigma-2 phase.117 The T framework in SGT has two types of polyhedral cages, 51268 and 4356 (Figure 3); all T sites in SGT are four coordinated. Pure silica SGT has been synthesized with 1-aminoadmantane as structure directing agent that occupies the large cages in the crystal. The SGT zeolite is the stable crystal of the T+S mixture at 300 K and 1 bar for XT = 0.89 (two S per large cage) with eTS > 0.8 kcal mol-1 and for XT = 0.94 (one S per large cage) with eTS > 0.6 kcal mol-1 (Figure 1). The small cages of SGT are always empty. Guest-free SGT made of mW water is less stable than guest-free sII (Table 1 and Supp. Table S2), as is also the case for the TIP4P/2005 model.70 The energy gap between SGT and ice Ih for mW, however, is larger than for TIP4P/2005 (Supporting Figure S2),70 which we attribute to the lower stability of square rings in the Stillinger-Weber potential. Although the energy gap between guest-free water SGT and hexagonal ice decreases with increasingly negative pressures (because SGT is less dense than ice Ih), the guest-free SGT is not expected to become a stable form of ice under extension.134 Our calculations with mW and previous calculations with TIP4P/200570 (Supp. Table S2) concur that the water framework in SGT is more stable than in the sodalite water zeolite, which has been achieved in experiments with HPF6 as guest.82 We note that the large cage in SGT is the same as the large cage in sH clathrate135, which can be stabilized as a hydrate with tert-butyl methyl ether or medium size hydrocarbons in the 51268 cages and methane in the small and medium cages.135-136 Same as guest-free clathrates are metastable at positive pressures but can be stabilized with the proper guests S in the cages,111, 121 we expect that water SGT could be stabilized in experiments by proper selection of guests for the large cages. A

B

C

Figure 3. SGT zeolite. The left panel shows the simulation box with crystalline SGT zeolite with two S per large cage nucleated and grown in the simulations. Color codes as in Figure 2. The central panel zooms on the structure; the right panel shows the two types of cages: in SGT: 51268 and 4356. 51268 cages are filled with either one two S, depending on the composition, whereas 4356 cages are always empty. Cooling the XT = 0.94 and 0.89 mixtures wit eTS = 0.8 kcal mol-1 at 1 K ns-1 results in the nucleation of single and double occupied SGT, respectively, at 64 K below the corresponding Tm. The SGT crystals nucleated and grown NpT simulations of the

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mixture at a few degrees above these crystallization temperatures are quite perfect, with few defects.

The large cages in SGT can have single or double occupancy by the structure-directing agent S. The composition of SGT and sII with one S per large cage is the same, XT = 0.94. Although the water framework in SGT has higher energy than in sII hydrates, SGT has a more favorable contribution of the TS attraction (Table 1), that results in a crossover in stability from sII to SGT when eTS > 0.6 kcal mol-1 (Figure 1 and Supp. Table S1). SGT with two S per large cages (XT = 0.89) has lower melting point than the singly occupied one (Table 1). Nevertheless, it cannot be outcompeted by sII at any eTS, as the large cages of sII are too small to host two S molecules. We find that single- and double-occupied SGT zeolite nucleate spontaneously in cooling simulations of the T+S mixture with the corresponding composition (Figure 4). SGT nucleates from mixtures in which the network former is modeled with mW or SW silicon (Supp. Table S3). To our knowledge, the nucleation of SGT has never been achieved before in simulations of any substance. Cooling of the T+S liquid with XT = 0.94 and interaction potential close to the boundary between SGT and sII, eTS = 0.65 kcal mol-1, results in SGT zeolite mixed with 512 cages that disrupt the crystallinity. However, we find that the higher the TS attraction, the larger is the difference in stability between SGT and sII (Supp. Table S1), and the lower is the number of 512 cages that disrupt the SGT order. Mixtures with XT = 0.94 and eTS > 0.8 kcal mol-1 nucleate and grow singly occupied SGT with high crystallinity (Figure 3a). The formation of relatively perfect crystals distinguishes SGT from clathrate hydrates. The latter yield amorphous clathrates at the temperatures at which nucleation can be observed in times accessible to molecular dynamics simulations.49-50 We have not detected the formation of a mesophase preceding the nucleation of SGT. To test whether the high crystallinity of the SGT zeolites nucleated and grown in the simulations is favored by the existence of an underlying mesophase that never develops in the simulations, we prepare T+S mixtures with sSS = 5.9 Å (all other parameters same as before), which results in additive sizes and loss of the mesogenic character of the mixture.69 We find that SGT crystallizes, also quite perfect, from the nonmesogenic mixtures. Our results suggest that mesophases are not involved in the nucleation of SGT zeolite: the tetrahedral order favored by T, together with the size constraints imposed by the structure-directing agent, suffice to promote the formation of this relatively low energy zeolite crystal.


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predicted He-filled silicon crystal that has a hexagonal arrangement of 6-membered Si channels.131 The size of the channels in HX is larger because the ratio of sizes of S to T in this work is higher than for He to Si.131 The size of pores in the hexagonal crystal made by T and S is intermediate between the large pores of mesoporous silicas and the atomic pores that hold He in the silicon crystal. A

Figure 4. Nucleation of SGT zeolite from a T+S liquid at XT = 0.89, eTS = 0.8 kcal mol-1 at T = 273 K and p = 1 bar. The T sites are modeled with mW and shown with red sticks when identified as SGT; T in the liquid is shown with gray points. S is not shown, for clarity. The nucleation and growth of SGT clusters is shown in red. Panels A to D show the time sequence for the nucleation of SGT. The fully-grown SGT crystal that results from this simulation is shown in figures 3a-b.

C. Porous hexagonal crystal directed by hexagonal mesophase. A hexagonal mesophase directs the formation of mesoporous silicas, such as those of the MCM-41 family.42, 137 The synthesis of these mesoporous materials involves, first, the spontaneous formation of a hexagonal mesophase from a concentrated solution of silicate and CnH2n+1(CH3)3N+ SDA, followed by calcination to eliminate the organics.41 This procedure results in hexagonal arrays of cylindrical pores of diameter 2 to 20 nm, controlled by the length n of the surfactant chain, separated by ~1 nm wide walls of amorphous silica.41, 138-140 The T+S mixture of our study stabilizes a hexagonal mesophase (H) in which a triangular lattice of rows of S is surrounded by a three-dimensional sheath of T (Figure 5a) The hexagonal mesophase is stable in the T+S mixture at 300 K and 1 bar for eTS > 1 kcal mol-1 and 0.814 < XT < 0.841 (Figure 1), and nucleates spontaneously from amorphous mixtures of T and S with the proper composition. The nucleation is preceded by the formation of “hair-like” trains of solutes, reminiscent of the “entangled hair” pre-ordering found in the nucleation of the hexagonal mesophase from mesogenic mixtures of isotropic particles107 and from block copolymers.141 The mesogenic behavior of the T+S mixture is akin to that of the dense mixture of silicates and long-chain SDAs in experiments. Cooling the hexagonal mesophase results in its phase transition to a porous crystal that we here call HX, and could be considered a zeolite. The crystal is tiled with squares of T, connected in circular arrays to form 10membered ring channels about 9 Å in diameter filled with S (Figure 5b-c). HX bears some similarities to a recently

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Figure 5. Hexagonal mesophase and the crystal, HX, it forms on cooling. Colors as in Figure 2. A) Hexagonal mesophase B) HX crystal. C) Details of the HX crystal. The coordinates of a simulation box of HX are provided as Supporting File.

D. Zeolite Z2 directed by a gyroid-like mesophase. An excess of structure directing agent S in contact with the hexagonal mesophase at 300 K results in an increase in the connectivity of the S rows, and leads to the nucleation of a gyroid-like mesophase (here called G2) with molar fraction of T XT = 0.78. G2 forms through reconnection of S particles at the hexagonal/amorphous interface, a mechanism akin to the heterogeneous nucleation of double gyroid (which we here call G1) in the mixture of isotropic mesogenic particles in ref. 107. G2 very rarely nucleates from liquid mixtures of isotropic mesogenic particles, and its formation in the simulations with T+S can only be achieved when extra S are added to the hexagonal mesophase (see methods 2.3). We conjecture that G2 is a metastable mesophase of the T+S mixture. The minor component S in G2 forms two interpenetrated networks in which each S is 3-coordinated (Figure 6). Each strand of the two-interpenetrated S networks of G2 is similar to that of the minor component in the Fddd mesophase of block copolymers.142 Although the minor component in all G2, Fddd, and the double gyroid (G1) form networks with three-coordinated nodes, the angles between the arms that meet at each node is different in these three phases. The G2 mesophase nucleated and grown in equilibrium with the hexagonal mesophase is defective; not all its S are three-coordinated. A complete, perfect G2 is attained by increasing the fraction of structure directing agent S to reach XT = 0.74. We are not aware of any previous report of the gyroid-like G2 mesophase.


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Z2 from the liquid mixture with the same composition, however, does not occur in time scales accessible to our simulations. This indicates that the presence of a mesophase with structure related to the zeolite not only directs the formation of a specific polymorph, but also strongly diminishes the barrier required for the nucleation of the zeolite crystal. E. Zeolite Z1 directed by double gyroid mesophase.

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The T+S mixture stabilizes a zeolite crystal we here call Z1 in a broad range of compositions around XT = 0.72 (Figure 1). The T particles in zeolite Z1 tile a double gyroid surface (I4132 symmetry) that encloses two interpenetrated helical channels filled with S (Figure 7). We note that mesoporous silicas with gyroid pores and zeolitic crystals in which the framework encloses a gyroid surface are not uncommon. These include mesoporous silica MCM-48145 and KIT-6,146 germanosilicate zeolite ITQ-37,147 the metal organic frameworks ZIF-14,148 ZIF72,149 and FIR30,150 and zeolite UCSB-7 made with zinc and beryllium arsenates and gallium germanate.150-151 Zeolite Z1 has the same structure as the metal organic framework FIR-30:150 it is tiled with 4- and 5-membered rings of T connected to form 10-membered ring channels that converge into cavities with 12-member rings (Figure 7). The 4-, 5-, 10-, and 12-membered rings of Z1 occur in the proportions 6:4:1:2. 88% of the T’s in Z1 are fourcoordinated; the other 12% are three-coordinated. Same as in Z2, the three-coordinated T sites are about 1.5 kcal mol-1 higher in energy that the four-coordinated ones (Supp. Figure S5). The four-coordinated T sites in Z1 are in the positions of the zinc atoms in FIR-30 and the 3coordinated T of those of fluoride ions in the MOF. We expect that an aluminosilicate Z1 zeolite could be stabilized with Al in the three-coordinated sites. It is interesting to note that Z1 and Z2 form with the same structure-directing agent and at very similar conditions. Likewise, the same structure-directing agent with slightly different conditions results in the synthesis of different zeolites in laboratory experiments.18 The interactions of the S guests with the T crystal framework contribute 40% of the cohesive energy of Z1 (Table 1), same as for Z2 with which it shares the relatively low stability of the T framework (Tables 1 and 2). The energy of the empty Z1 evaluated with the mW model is 2.58 kcal mol-1 higher than the one of hexagonal ice, and 1.35 kcal mol-1 higher than the sodalite water zeolite (Supp. Table S2). This results in a very low melting point of the guest-free Z1 zeolite, just 34 K in the mW water model. We note that mW predicts an energy gap between ice Ih and sodalite almost twice larger than TIP4P/2005, 1.23 vs 0.72 kcal mol-1 (Supp. Table S2 and Supp. Figure S2). This reflects the higher penalty mW has for 4-member rings, abundant in zeolites, compared to the atomistic model.81, 152-153 We expect the Z1 framework of a water zeolite to be more stable than predicted by the mW model.

Figure 6. Structure of gyroid-like G2 and zeolite Z2. a) Detail of G2 gyroid-like mesophase and b) detail of Z2 zeolite, with colors as in Fig. 2. c) T sites in Z2, d) the two interpenetrated but not intersecting networks of S in Z2, shown one in green and other in blue. Supp. Figure S3 show the position of the 11- and 12-member rings in the zeolite. The coordinates of a simulation box of Z2 are provided as Supporting File.

The G2 mesophase melts to an isotropic liquid and freezes to a zeolite, which we call Z2 (Figure 6). These equilibrium transitions occur at 335 K and at 260 K for G2 of composition XT = 0.74 with eTS = 0.8 kcal mol-1. The phase transition from G2 to Z2 involves only the crystallization of T; the arrangement of the S-filled channels in zeolite Z2 is the same as in G2. The structuredirecting agent S has the same order and connectivity in G2 and Z2. The tetrahedral component T of zeolite Z2 forms a crystalline network with 4- and 5-membered rings that connect to produce 11-membered ring channels that converge into cavities that contain 12-membered rings. The 4-, 5-, 11-, and 12-membered rings of Z2 occur in ratios about 3:3:1:1. The 11th member rings are helical with 10 T per turn or twisted out of plane (Supp. Figure S3). We note that helical arrangements of hydrogen-bonded water molecules are also found in ice XII.143-144 80% of the T’s in Z2 are four-coordinated; the rest are three-coordinated and about 1.5 kcal mol-1 higher in energy than the tetracoordinated sites (Supp. Figure S4). The energy of the guest-free Z2 network is 2.4 kcal mol-1 higher than that of hexagonal ice, and 0.96 kcal mol-1 higher than water sodalite (Table 2), all evaluated with the mW model. However, Z2 is stabilized by a strong TS attraction, which contributes about 40% of the cohesive energy of the zeolite (Table 1). It is interesting to note that despite the complexity of the Z2 framework and its low intrinsic stability, Z2 nucleates easily from the G2 mesophase. Moreover, the nucleation occurs spontaneously with low supercooling, just 20 K below the Z2 to G2 equilibrium temperature, when G2 is cooled at 1 K ns-1. Nucleation of


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conditions, the formation of the zeolite involves two consecutive steps: first, the double gyroid G1 nucleates and grows from the amorphous mixture, and then the T framework of the gyroid crystallizes producing a zeolite with very few defects. The existence of a gyroid with stability intermediate between the zeolite and the mother liquid allows for the initial formation of the metastable mesophase, splitting the barrier from liquid to crystal and accelerating the nucleation of the complex crystal. Metastable gyroid mesophases that result from the frustrated attraction between silicates and SDAs may promote and direct the formation of gyroidal zeolites also in experiments.

Figure 7. Structure of the double gyroid and Z1 zeolite. A) double gyroid G1 with XT=0.73 and eTS = 0.8 kcal mol-1 showing T with red balls and S in blue balls, with bonds connecting T within 0.35 nm and S within 0.45 nm. b) network of T in zeolite Z1 shows the location of the threecoordinated T particles is at a point connecting three pentagons, c) adds further detail on the ordering of the 10member rings (shown in blue) and 12-member rings (in green) made by T as three channels converge into the largest cavity of Z1. The unit cell of Z1 consists of 132 T particles. d) S in Z1 forms two interpenetrated non-connected networks. The coordinates of a simulation box of Z1 are provided as Supporting File.

Z1 melts to a double gyroid mesophase with I4132 symmetry. The equilibrium transition between zeolite and gyroid occurs at 327 K for XT = 0.73 and eTS = 0.8 kcal mol1 . The order of S in the double gyroid and in zeolite Z1 is almost identical. The only difference is a subtle break in the symmetry between the two S networks in the zeolite, as one network fills cavities in which the T are bent inwards and the other fills cavities in which they are bent outwards and, hence, are slightly larger. The gyroid G1 mesophase with eTS = 0.8 kcal mol-1 is stable up to 352 K, when it melts to an isotropic liquid phase. Although amorphous zeolites and MOFs have been discussed in the literature,28-29, 154-156 even in the nucleation pathway of the zeolitic crystals,28-29, 156 the existence of a stable or metastable gyroid phase has not been investigated, to our knowledge, for any of the previously reported gyroidal zeolites or MOFs. Zeolite Z1 nucleates and grows spontaneously from the mixtures with either SW silicon or mW water as network former (Supp. Table S3). The nucleation of Z1 occurs even at a low degree of supercooling. Figure 8 shows snapshots along a trajectory in which Z1 nucleates and grows within a few hundred nanoseconds from the amorphous T+S mixture with XT = 0.73 at 318 K, just 9 K below its melting temperature to the gyroid mesophase. Under these

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Figure 8. Nucleation of Z1 zeolite from the amorphous mixture T+S facilitated by the formation of a double gyroid mesophase. The snapshots show that progression along the nucleation pathway of Z1 (shown in red) at 318 K and 1 bar from an amorphous liquid mixture (gray points) with XT = 0.73 and eTS = 0.8 kcal mol-1. Under these conditions the nucleation of the zeolite occurs via a two-step mechanism, which involves first the nucleation and growth of the double gyroid mesophase (blue) from the liquid, and then the nucleation of the zeolite from the gyroid. The fully-grown zeolite Z1 is shown in Figure 7. The mechanism of nucleation of zeolite Z1 is nonclassical at all temperatures: it occurs in two-steps at warmer temperatures and in one-step with a noncrystalline, gyroid critical nucleus at colder ones.157 It is quite possible that in silica zeolites the mesophases is always metastable with respect to the zeolites (i.e. the zeolites melt to an amorphous phase), see discussion in section 3.2 below. In that case, we expect the crystallization to occur in one classical step at warmer temperatures and through a two-step non-classical mechanism only at temperatures cold enough to be below the metastable gyroid to amorphous transition.157


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F. Zeolites Z3 and Z4 directed by lamellar mesophases. Lamellar is a common mesophase of surfactants and block copolymers,158-159 and a stable phase of the mesogenic mixture of particles from which the T+S model is derived.69 Lamellar precursors are used to prepare layered zeolites, such as MCM-22,160FER161 and OKO.162 Figure 1 shows that mixtures of T and S with eTS > 0.5 kcal mol-1 and XT around 0.6 stabilize a lamellar mesophase with alternating disordered layers of T and S (Figure 9a-c). The mobility of T and S in lamellar is highly anisotropic: particles diffuse within each layer about 100 times faster than between layers. Cooling down the lamellar mesophase with low T content, XT = 0.61, results in the formation of a crystalline layered crystal phase, LX (Figure 9d-e). An additional stable semicrystalline lamellar phase occurs between L and LX when the TS attraction is not very strong (e.g. eTS < 0.6 kcal mol-1), analogous to what is observed in the mesogenic mixtures of isotropic particles.69 S is fluid in the lamellar and semicrystalline phases and orders to a crystalline triangular lattice in the crystals –same as in LX formed by isotropic particles.69 T crystallizes into an unbuckled hexagonal lattice in the semicrystalline lamellar and layered crystal. The hexagonal order of T in the layered crystal is the one adopted by water monolayers in hard confinement,163 and by silicon in the CaSi2 layered Zintl crystal.164 A

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Figure 9. Lamellar mesophase and layered crystal LX. a) Lamellar mesophase –as well as LX- has alternate layers of T (red balls) and S (blue balls), b) disordered layer of T in the lamellar mesophase, c) disordered layer of S in lamellar mesophase, d) T in the crystalline layers of lamellar crystal adopts an unbuckled hexagonal structure, e) S in the layers of the lamellar crystal forms a triangular lattice.

The lamellar mesophase rich in T, XT = 0.675, is highly perforated (i.e. the S layer has holes transiently occupied by T, bridging the T layers) and crystallizes to a structure that has regions of LX and a distinct zeolite, which we call Z3 (Figure 10a). Consecutive layers of T in Z3 are connected by 6-6 units of T (i.e. two hexagons bound to form six squares, Figure 10b). Z3 is tiled by 4- and 5-membered rings of T, connected to form 10-member ring channels (Figure 10c-d). The channels run parallel to the plane of the layers, resulting in pores connected in two dimensions. Interestingly, even the T-poor lamellar seems to favor the

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formation of the Z3 motifs: we find that semicrystalline lamellar with XT = 0.61 slowly develops the Z3 motifs, a process that we interpret is driven by an increase in the fraction of four-coordinated T. Our results indicate that lamellar order can direct the formation of zeolitic crystals. A

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Figure 10. Zeolite Z3 forming within a perforated lamellar phase. Different from crystal LX, also derived from lamellar, Z3 has connection between layers of T. a) Detail of the structure of T in a partially formed zeolite Z3 formed by cooling the lamellar crystal with XT = 0.675 and eTS= 0.6 kcal mol-1. The structure-directing agent S is hidden, for clarity. The T connect between layers already at 300 K, as the lamellar is partially perforated, but do not order until about 150 K, b) zoom into the structure of a bridge that connects layers of T, c) 6-6 rings are connected to five pentagons in the upward as well as downward direction, effectively making two halves of the 51262 cage typical of sI clathrates; d) shows a top view of the motif formed by the two half-cages separated by the ring of four-member rings. The coordinates of a simulation box of Z3 interspersed with perforated lamellar are provided as Supporting File.

The width of the pores of the zeolites formed in the simulations can be controlled by tuning the size of the structure-directing agent, as is also the case in experiments.165 Zeolites Z1, and Z3, as well as HX, all have flat 10-member ring channels filled with the structuredirecting agent S. Z2 has twisted and helical 11-member rings that have the same diameter as flat 10-member rings. As the distances between neighboring T sites in the crystals are narrowly distributed, we use the relation between the side and radius of perfect polygons to forecast that increasing sTS from 4.5 to 5.5 Å would result in a change from 10- to 12-membered rings around S. To keep the nonadditivity of sizes that gives the mesogenic character to the T+S mixture, we concurrently increase sSS to 6.56 Å. Evolution of a mixture of T+S with these parameters at XT = 0.85 at 220 K results in the spontaneous formation of a zeolite, which we call Z4, with 13-membered ring channels connected in two directions (Figure 11). Although Z4 crystallizes with defects, it has well-defined medium and long-range order. The interaction energy between T particles in Z4 is ETT = -9.45 kcal mol-1, better than in Z1 and Z2, but not as favorable as in SGT (Table 1). This zeolite –which also forms when silicon is used as the


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network former (Supp. Table S3) – is built from perforated lamellar, same as Z3, and is very similar to the twodimensional zeolite OKO,166 but has alternated thin and thick layers of T (Figure 11). These results demonstrate how small variations in the size of the SDA and the composition of the mixture result in the formation of a rich variety of zeolitic polymorphs, several of them directed by underlying metastable mesophases of the mixture. A

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Figure 11. Structure of the zeolite Z4, in which both T and S adopt crystalline order. a) The T framework of Z4 is composed of alternating thick and thin layers of T connected by T bridges. The S layers –not shown- are parallel to the thin and thick layer of T and perpendicular to the plane of the figure, b) Detail of the order of S (blue) and T (red), c) detail of the connection between T in Z4. The coordinates of a simulation box of Z4 are provided as Supporting File.

3.2. Significance of the results of the model systems for the nucleation of silica zeolites. The coarse-grained model used in this study is computationally very efficient and appropriate to proof the concept that mesophases can assist in the nucleation and polymorph selection of zeolitic crystals. The model, however, lacks some elements needed for a quantitative prediction of the phase behavior and nucleation pathway of silica zeolites. Except for SGT, a known silica zeolite,117 the specific tiling of T in the other crystals of this study has not been found in silica zeolites. This is not unexpected, as the energy penalty to bend Si-Si-Si bonds in silica is quite different from that to bend O-O-O angles in water70 and SiSi-Si angles in silicon, which in terms of enforcement of tetrahedral order resembles water.79-81, 83, 153, 167 However, as discussed in section 3.1, zeolites with order based on gyroid or perforated lamellar mesophases have been obtained in the laboratory.147, 151, 166 The known mesogenic character of mixtures of silicates and tetraalkylammonium cations,30, 42 together with the results of this study for model systems suggest that the nucleation of these zeolites may be assisted by mesophases. Mesophases formed by SDAs and silicates could have a region of stability –as is the case for the long chain SDAs that produce mesoporous silicas and for the T+S systems of the present study– or be always metastable with respect to the amorphous and zeolite phases. The relative stability of zeolites and mesophases depends on the angular

dependence of the interaction potential between T particles, because the stability of the mesophases does not require anisotropic interactions,69 while the stability of the zeolites is strongly modulated by the form of the TTT three-body interaction. This implies that an interaction potential between T particles that favors the nontetrahedral angles typically found in zeolites would increase the stability of the zeolite crystals without changing the stability of the mesophases. That scenario, which we consider the most probable for silica zeolites, would result in a mesophase to amorphous transition that is always metastable with respect to the zeolite to amorphous transition. In that case, the role of mesophases on the nucleation of zeolites would be akin to that of metastable fluid-fluid transitions in the crystallization of protein and clathrate hydrates.46-52 Simulations of crystallization of patchy particles that have a metastable fluid-fluid transition indicate that even above the fluid-fluid critical point, where the dense fluid phase that promotes the nucleation of the crystal is unstable, fluctuations that lead to transient dense fluid order also promote crystallization.47 Moreover, that study suggests that crystals nucleated in the presence of the unstable dense fluid develop better crystallinity because the preferred anisotropic ordering of the particles dominates over the densification of the liquid. Likewise, it could be expected that mesogenic fluctuations above a metastable fluid-mesophase transition could be conductive to the development of crystal architectures that are less dominated by the order of the mesophase, resulting in a wider variety of crystal polymorphs. It would be interesting to investigate these possibilities with model systems and more realistic models of silica zeolites. To this end, in what follows we discuss some specific limitations of the T+S model used in this study and possible strategies to overcome them. First, the cosine quadratic form of the three-body term of the SW potential cannot represent the distribution of Si-SiSi angles in silica crystals. We consider this to be a central limitation for the reproduction of the phase behavior of silica, as the SW potential not only leads to a very low stability of the guest-free zeolites but is also unable to stabilize quartz, which has non-tetrahedral Si-Si-Si angles (91o, 107o, 124,o and 142o),168 also common in zeolites. This limitation may be surmounted within the framework of the coarse-grained model by either i) using a monatomic potential with a more flexible three-body form, or ii) introducing explicit Si and O atoms. A model that achieves the latter using short-range interactions could result in a good compromise of accuracy and computational cost. Second, the model could be improved by accounting for the speciation of the silicates in solution. This would account for the change in interaction strength between cationic SDAs and the silicates as these evolve from a highly charged to neutral by polymerization and crystallization. Although the interaction of SDAs with the


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fully crystallized silica framework is weak compared to the cohesive energy of the silica network,62-63, 169 the cationic SDAs may interact strongly with the anionic silicate precursors. The coarse-grained model could be improved by adopting the strategy of Monson, Auerbach and coworkers to account for speciation in silica models.56, 66, 71 Third, a coarse-grained model of silica and SDA could be further refined by tuning the mesogenic character of the mixture –which depends on the existence of watermediated interactions between the silicates and SDAs- or the introduction of explicit solvent as a third component in the mixture. The mesogenic character of the T-S interaction in the model systems implicitly accounts for the effect of solvent (if there were any) in the mixture, and can be tuned through the non-additivity of the T-S interaction.69 We note that in the simulations in which T is represented by mW, water is not playing the role of a solvent but of the network former. Fine resolution simulations with that account for all atomistic interactions between the silica species, SDA and solvent would be key to determine the regions of stability and metastability of mesophases in the hydrated silica/SDA mixtures. These results could be used to parameterize models that reproduce the initial formation of dense amorphous aggregates from dilute solutions and correctly represent the relative stability of amorphous mixture, mesophases, and zeolite crystals. Fourth, the models of SDA could be made more realistic by accounting for the specific interactions, shape, and conformational flexibility of the organic cations. It would be interesting to investigate in future studies how these variables impact the nucleation pathway and selection of crystal polymorph under conditions where mesophases direct the nucleation of the zeolites as well as for conditions where mesophases are not involved in the crystallization. The multiscale nature of zeolite crystallization probably requires a hierarchical modeling approach and the use of advanced sampling methods to identify the polymorphs and the barriers for their formation. Multiscale integration of the coarse-grained model of this work with finer and coarser resolution models would be key to achieve predictive capabilities for the design of SDAs that select for the desired polymorph. 3.3. How feasible are water zeolites? Molecular simulations have played an important role in predicting new crystals of water that have been later found in experiments.111, 125, 170 The guest-free sII clathrate structure was predicted to be a stable phase of water under extension111, 125 and metastable at room pressure,111 before it was produced in laboratory experiments.128 Several hypothetical water zeolites have been proposed from computational modeling.76, 134, 171-173 Of these, SGT, DDR, IRR, IWV have been considered the most promising candidates for realization of water zeolites in experiments.70, 134, 171 However, none of these water zeolites

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has been yet realized in the laboratory nor –to our knowledge- been nucleated and grown in simulations, except for SGT in the present study. The high density of four-member rings in zeolites set them apart from typical ice phases and makes them high in energy compare to other water crystals. There are three possible avenues to stabilize water zeolites in experiments: i) incorporation of attractive guests in the cavities and channels, ii) application of pressure, and iii) relief of the strain in the water network via incorporation of other hydrogen-bonded molecules or ions. The first avenue is illustrated by the formation of clathrate hydrates.174 Although guest-free water clathrates are metastable with respect to ice I,111 the van der Waals interactions of water even with hydrophobic guests such as methane- suffice to make clathrate hydrates more stable than ice I at moderate pressures. The second avenue, the application of high pressures, known to favor 4-membered rings in water crystals,175 should assist in this endeavor provided that the porous crystals are filled with stabilizing guests. The experimental realization of a water sodalite zeolite in semiclathrate form, with HF stabilizing the zeolitic water network,176 illustrates the third avenue for stabilization of high-energy water crystals. It may be possible to stabilize water zeolites with high density of four-member rings in semiclathrate form, by allowing HF or other hydrogen bonding molecules to relief the cost of forming water squares. A combination of the proper guests, pressure, and incorporation of HF, NH3 or other hydrogen-bonding molecules to the T network could be used to produce other water zeolites. Our calculations with the mW water model indicate that the crossover in stability from sII to SGT occurs with a guest that produces a melting temperature of 310 K for these crystals (Supporting Table 1). Melting temperatures higher than these have been reported for semi-clathrate hydrates; e.g. tetraisopentylammonium fluoride hydrate at 27 MPa melts at 320 K. 177 Use of a bulkier salt that could fit in the 51264 cages of SGT but not in the 51264 cages of sII could provide an avenue to stabilize SGT over sII. The other competitor to SGT is the sH clathrate. sH has three types of cages, 51268 , 43566, and 512 in 1:2:3 ratio. The largest cage of sH is the same as in SGT. TIP4P/2005 optimization of these crystals, indicates that guest-free SGT is about 1 kJ mol-1 higher in energy than guest-free sH.70 SGT, however, has twice as many large cages per water molecule as the former (1:16 vs 1:34). This suggests that SGT may outcompete sH if the only guest available is too large to fit the small and medium cages of sH and it has a hydration free energy in the large cage of 34 kJ mol-1, i.e. a modest 0.94 kJ mol-1 per water molecule in the cage. Future simulation studies could be used to identify which molecules –if any- satisfy these conditions and what is the stability of the resulting guest-filled SGT zeolites.


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The fast nucleation of guest-filled Z1, Z2, Z3, Z4 and HX water zeolites in our simulations zeolites relies on the existence of mesophases in the T+S mixture that decrease the crystallization barriers. Water-in-water mesophases form in the presence of double-hydrophilic block copolymers.178-179 It would be interesting to determine whether shorter versions of these polymers could produce metastable mesophases that facilitate the nucleation of water zeolites. The stability of the water zeolites Z1, Z2, Z3, Z4 and HX also requires relatively strong guest-host interactions that compensate for the existence of 3coordinated sites, which are higher in energy than the 4coordinated sites (Supporting Table 2 and Supporting Figures S4 and S5). Use of NH3 or other molecule to replace water on these sites may favor the formation of some of these water zeolites in semi-clathrate form. As the high penalty of mW towards four-member rings results in an overestimation of the cost of the zeolite frameworks compared to TIP4P/2005 (Supporting Table S2 and Supporting Figure S2), we expect that real water zeolites would require lower stabilization from water-guest interactions than predicted by the mW model.

4. Conclusions. In this work, we put forward the hypothesis that the experimentally supported mesogenic character of mixtures of silicates and SDAs30, 42 could play a role in facilitating the nucleation and polymorph selection of some zeolites. As proof of concept, we test this hypothesis using molecular dynamics simulations with coarse-grained models that capture two main elements of silicate/SDA mixtures: their mesogenic character, revealed in experiments by their formation of micelles and mesoporous silicas, and the strong preference of silica for tetracoordination, evident in the structure of its crystal and glass phases. As a computationally efficient model of silica that allows for the study of the nucleation pathway of zeolites with molecular simulations is not yet available, we model the tetracoordinated network former T of the zeolites with the Stillinger-Weber silicon or mW water models. We find that both silicon and water models nucleate and stabilize the same crystals. This may not be surprising, as both substances have a tetrahedral crystal as ground state.83, 167 The lower energy penalty for nontetrahedral angles in silica gives it a distinct advantage over water and silicon to stabilize zeolites,70 which typically have non-tetrahedral angles close to those found in quartz. We find that the interplay between mesogenic and tetracoordinated ordering results in a rich variety of zeolitic crystals in the model mixtures. The nucleation of some of these crystals is facilitated by the presence of metastable lamellar, gyroid, gyroid-like, and hexagonal mesophases. The results of this study indicate that metastable mesophases can direct the formation of zeolitic crystals, lowering the free energy barrier for the nucleation of these

complex structures and directing the order towards specific polymorphs. Among the zeolites spontaneously formed by the water and silicon models, it is the sigma-2 (SGT) crystal, a known silica zeolite that has been predicted to be an energetically accessible phase for water,70, 76, 171 but had not been previously nucleated for water or silicon in experiments and for any substance in simulations. We find that the nucleation of SGT does not rely on the existence of a mesophase. Our analysis suggests that water SGT could be stabilized in semi clathrate form. Except for SGT, the zeolites obtained in the simulations with silicon or water as network formers are not known to occur for silica. Nevertheless, there is experimental evidence for both the mesogenic character of mixtures of SDAs and silicates, and for zeolite crystals that have order consistent with known mesophases. For example, several gyroidal zeolites and MOFs have been synthesized in the last years.147-151 It would be interesting to investigate whether gyroid or gyroid-like medium range order can be detected in the nucleation pathway of gyroidal zeolites in experiments. Lamellar precursors are used to synthesize layered zeolites with two-dimensional (2D) channels.160-162 Metastable lamellar mesophases facilitate the nucleation of zeolites with 2D channels in the simulations. Same as in experiments,161 changing the size of the SDA in the simulations leads to the formation of different 2D zeolite polymorphs. One of the zeolitic crystals found in the simulations has a structure similar to that of the 2D zeolite OKO. These promising results suggest that molecular simulations with more accurate models could be used to elucidate the extent and type of mesogenic order in the precursors of zeolites and how does it interplay with the shape, size and interactions of SDAs to guide the selection of the zeolite polymorph. Although the minimalist model of this study does not account for the angular flexibility that allows silica to produce a large variety of zeolite polymorphs of comparable energy,70 nor does it represent the complex chemistry of bond breaking and creation involved in the formation of silica zeolites,21 it is to our knowledge the first that spontaneously nucleates a variety of zeolitic crystals in molecular dynamics simulations, paving the ground to investigate the pathway of nucleation and growth of model zeolites from dense silicate/SDA amorphous phases, and the role of metastable, or even unstable, mesophases in promoting and directing the formation of zeolite polymorphs. The tantalizing possibility that mesoscopic ordering of organic cations and silicates guides not only the structure of mesoporous silicas but also plays a significant role in polymorph selection of some zeolites, would –if confirmed through experiments– provide a unifying understanding of the formation of these widely used and investigated classes


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of porous silica materials, and a powerful route for designing materials with ordering at different length-scales.

ASSOCIATED CONTENT Supporting Information. Supporting Information is available free of charge on the ACS Publications website. It contains five text files that report configurations of the new crystals presented in this study, HX, Z1, Z2, Z3 and Z4, and a pdf file with supplementary methods for the identification of the SGT and Z1 zeolites, and supplementary results and discussion of the S-rich hexagonal mesophase, the crossover in stability between sII and SGT, the nucleation of SGT, comparison of the energies of zeolites optimized with the mW and TIP4P/2005 water models, a comparison of nucleation and melting temperatures of SW silicon and mW water model zeolites, details of the structure of the framework of Z2 zeolite, and the captions for the configuration files.

AUTHOR INFORMATION Corresponding Author [email protected]

Acknowledgements We gratefully acknowledge support for this work by the Camille and Henry Dreyfus Foundation through a Camille Dreyfus-Teacher-Scholar Award and by the American Chemical Society Petroleum Research Fund through a New Directions Award. We thank the Center for High Performance Computing at the University of Utah for technical support and a grant of computer time.

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Could Mesophases Play a Role in the Nucleation ... - ACS Publications

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