Modeling the Nucleation of Zeolite A - The Journal of Physical

Article pubs.acs.org/JPCC

Modeling the Nucleation of Zeolite A Chao-Shiang Yang,† José Miguel Mora-Fonz,‡ and C. Richard A. Catlow*,† †

Department of Chemistry, University College London (UCL), Gower Street, London, WC1E 6BT, United Kingdom DACB, Universidad Juárez Autónoma de Tabasco, A.P. 24 C.P. 86690, Cunduacán Tab., México

‡

ABSTRACT: The nucleation mechanism of zeolite A is investigated by means of Density Functional Theory (DFT) calculations. We calculated the Gibbs free energy change for the polymerization and cyclization reactions involved in the nucleation of zeolite A in the gas phase and solution between 298 and 450 K. Our analysis reveals that the four-ring species formed could be the most likely to participate in the nucleation of zeolite A, and its nucleation mechanism could proceed by a reaction route which involves the formation of the double-fourring.

the 6ring species that are not evident in the spectra.29,30 (iv) The use of atomic force microscopy (AFM), which detected the surface structure of zeolite A, found that the external structural units are predominantly the double-four-rings (D4Rs), which are suggested to be the key building unit for crystal growth. Similarly, the modeling of surface structures of zeolite A showed that the D4Rs are stable on the terminated surface of zeolite A.31,32 (v) In the synthesis of zeolite A, it is practicable to add cationic species (Na+ ions) as templates in synthesis media instead of organic templates.33,34 (vi) In the hydrothermal synthesis of zeolite A, the formation of zeolite A takes place as a batch process at temperatures ranging between 298 K (room temperature) and around 400 K.23,33 To summarize the above key points, from these studies, it appears that understanding the question of how the D4R unit is formed by means of the participation of the AlSiO(OH)6Na dimer or other 4ring species is one of the primary tasks in understanding the nucleation of zeolite A. In this paper, we present DFT/COSMO calculations aimed at determining the mechanism of formation of the D4Rs. To this end, in addition to employing the most stable aluminosilicate clusters (Si/Al = 1) as predicted in the previous papers,21,22 we investigate a series of proposed ring species with hanging dimers/tetramers (from the aluminous end of the chains) and multiple linked rings. Another key feature of this work is the role of the AlSiO(OH)6Na dimer that controls the two main competing condensation reactions, polymerizations or cyclizations. To elucidate the proposed reaction pathways, a schematic description showing the relations between each cluster is given in Figure 1, which can help us gain a better understanding of the whole reaction processes.

1. INTRODUCTION Understanding the nucleation and growth of zeolites is still a major challenge in the science of microporous materials despite extensive research using experimental and computational techniques.1−20 An effective approach to modeling polymerization reactions of silicates and aluminosilicates is provided by DFT (Density Functional Theory) together with COSMO (conductor-like screening model) methods, especially in the modeling of rings with the same Si/Al ratio as reported in our previous papers,17,21,22 in which we showed that the ends of the chain component of all the most stable aluminosilicate fused rings are likely to be aluminous and that the AlSiO(OH)6Na dimer plays a major role in condensation reactions. Building on our previous work which has provided valuable information regarding the polymerization reactions of aluminosilicates, here we address the subsequent condensation reactions of open aluminosilicate clusters as well as aluminosilicate rings, which is needed if we are to extend our understanding of the overall growth behavior of zeolites and gain detained knowledge of the nucleation and growth processes. Both experimental and computational techniques have given direct insights into the important characteristic features of the formation of zeolite A, and briefly the descriptions of the key proposed nucleation and growth mechanisms are as follows: (i) The thermodynamic modeling of condensation reactions strongly suggested that the AlSiO(OH)6Na dimer is a key species in cluster growth, as also indicated by experimental studies.23,24 (ii) The observation of the early nucleation stage of zeolite A revealed that the aluminosilicate species, which could produce the nuclei of zeolite A are present in solution; the precursors show short or medium range, but not long-range order.25−28 (iii) UV-Raman spectroscopy combined with XRD or NMR has been employed to analyze the crystallization of zeolite A and suggested that the four-ring (4ring) species are probably the main initial rings; but there is little evidence for © 2013 American Chemical Society

Received: May 21, 2013 Revised: September 24, 2013 Published: October 3, 2013 24796

dx.doi.org/10.1021/jp4050034 | J. Phys. Chem. C 2013, 117, 24796−24803

The Journal of Physical Chemistry C

Article

Figure 1. Clusters reactions; silicon in each corner and oxygen in the middle of each line. The relevant energies involved in these condensations are given in Tables 1−3.

2. METHODOLOGY As in our previous papers,21,22 our calculations have been performed using the DFT/COSMO method, which our earlier work has shown to be reliable for modeling aluminosilicate clusters. Geometry optimization for all relevant aluminosilicate species with the same Si/Al ratio (Si/Al = 1) and with charge balancing sodium ions is carried out using the DMol3 code35 based on DFT with a double numerical basis set plus polarization (DNP) and the BLYP exchange-correlation functional in this study. The treatment of the solvent effect on the optimized aluminosilicates is performed using the COSMO approach,36,37 in which the medium is treated as a dielectric continuum in a self-consistent procedure during the DFT calculation; the resulting structures are denoted the “solvated” clusters. Moreover, using the optimized structure obtained from the BLYP/DNP method as a starting point, a standard statistical mechanical method is employed to calculate the Gibbs free energy that combines zero-point energy, together with the rotational, vibrational, and translational contributions to the energy between 298 and 450 K for the gas phase and COSMO solvation. 3. RESULTS AND DISCUSSION All proposed reaction pathways related to the synthesis of the clusters are shown in Figure 1 and 11 structurally distinct optimized “solvated” aluminosilicate clusters and rings are shown in Figures 2 and 3, which also gives the terminology used in defining the clusters. Other clusters referred to in the figures have been studied in our previous papers.21,22 In Figure 1, each condensation reaction pathway of a polymerization reaction (the addition of the AlSiO(OH)6Na dimer or 4ring) or internal cyclization is defined by an arrow whose direction indicates the cluster produced (with the formation of water omitted for clarity). The calculated Gibbs free energy for each condensation reaction is presented in Tables 1−3. There are two main components of our results. First, the geometric features of the optimized aluminosilicate ring species are introduced and, second, we highlight the mechanisms and energetics involved in the D4R. To clarify general mechanistic

Figure 2. Optimized aluminosilicate four-ring species. In the abbreviation, “()” indicates the active atom at which the dangling species is attached. Color code: O, red (darker color); Si, pink; H, white; and Na, violet (nonbonded atoms).

aspects of the entire processes, the investigation for the successive condensation reactions can be divided into two main stages: (i) the initial linear polymerization and cyclization reactions and (ii) the subsequent multiple polymerization and cyclization reactions. Moreover, we will examine the question 24797



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Table 1. Calculated Free Energy (ΔG, kJ mol−1) Changes in the Gas Phase and COSMO Solvation at 298 and 450 K for Polymerization and Cyclization gas phase ΔG reactants dimerization Si tetramerization Si−Al hexamerization Si−Al−Si−Al

products

298 K

450 K

298 K

450 K

Al

Si−Al

−60

−54

−21

−23

Si− Al

Si−Al−Si−Al

−71

−63

−34

−30

Si− Al

Si−Al−Si−Al− Si−Al

−78

−70

−37

−35

4ring

16

−5

−33

−48

Al−(Si)3ring

12

−10

−30

−47

−12

−32

−23

−43

Al−(Si)5ring

−7

−32

−16

−38

Al−Si−(Al) 4ring clusters

−42

−71

−73

−95

4ring cyclization Si−Al−Si−Al Al-(Si)3ring cyclization Si−Al−Si−Al 6ring cyclization Si−Al−Si−Al− Si−Al Al-(Si)5ring cyclization Si−Al−Si−Al− Si−Al Al−Si−(Al)4ring cyclization Si−Al−Si−Al− Si−Al abbreviations

Figure 3. Optimized aluminosilicate four-ring species.

COSMO sol. ΔG

6ring

Si Al Al−Si Si−Al−Si−Al

Si(OH)4 Al(OH)4Na AlSiO7H6Na Al2Si2O13H10Na2

Si−Al−Si−Al− Si−Al

Al3Si3O19H14Na3

abbreviations 4ring 6ring Al−(Si)5ring Al−Si−(Al) 4ring

clusters Al2Si2O12H8Na2 Al3Si3O18H12Na3 Al3Si3O18H12Na3 Al3Si3O18H12Na3

To summarize this section, the geometrical aspects of the multiple rings studied will provide useful insights into the mechanism of self-assembly of the D4R , that is, the optimized multiple rings are curved, favoring direct condensation into the D4R structure, and the formation of the D4R according to the above analysis can probably be drawn as a simple route: 4ring → tri4ring → D4R, leading to growth of the zeolite A crystal. In the next section, on the basis of our preliminary work on selected cluster models, we will investigate the detailed mechanism of the whole condensation reactions in forming the D4R with emphasis on the calculated Gibbs free energy in order to ascertain which mechanism is favored. 3.2. Polymerization and Cyclization Reactions. In zeolite nucleation, polymerization and cyclization reactions are both essential, which means that the simultaneous occurrence of polymerization and cyclization reactions is inevitable. Under these circumstances, the competition between polymerization and cyclization reactions will have a large influence on the production of precursors in aluminosilicate solution, which can further control the conformational preference of zeolite structures. Ring species based on 4-, 5-, 6-, 8-, 10-, and 12-rings are the main constituents of zeolite structures. Hence, it is of vital importance to investigate the competitive position of cyclization relative to polymerization in zeolite nucleation. The oligomerization reactions of purely siliceous clusters have been modeled by the DFT/COSMO method with the results suggesting that the competing

of whether larger species especially in the multiple rings are formed by the condensation of the dimer or of the larger units such as the 4rings in the nucleation stage of zeolite A. The elucidation of these aspects will provide us with further insight into the nucleation mechanism of zeolite A. 3.1. Geometry Analysis of Multiple Ring Structures. As we have noted, experiment has suggested that during the nucleation of zeolite A, the 4ring species are the crucial species in solution. We consider all the multiple rings, the bi4ring, bi4ring with one dimer, tri4ring, 4−4ring, and openD4R, which could be involved in forming the D4R, as shown in Figures 1−3. The first multiple ring discussed is the bi4ring (Figure 2f), which can arise from two different routes: one is the internal condensation of the 4ring with one dimer and the other is the internal condensation of the 6ring. It is worth noting that the optimized geometry of the structure of the bi4ring is likely to be curved, not planar, due to the effect of the attractive interaction with the Na+ ions that are linked to three more oxygen atoms on the ring’s structure. Similarly, because of the force of attraction between the Na+ ions and ring structure, other clusters including the 4−4, and tri4rings (Figures 3b,c) are again likely to have “curved” configurations. The shape of the three configurations will facilitate the subsequent condensation reactions leading to the openD4R (Figure 3d)a key intermediate for the self-assembly of the D4R (Figure 3e). 24798



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the other two are the intramolecular cyclizations to produce the 4ring and Al-(Si) fused 3rings (Figure 2a). We first start with the formation of the Si−Al−Si−Al−Si−Al hexamer. Of particular importance is the observation that the free energy change is exergonic favoring the forward reaction in the gas phase and COSMO solvation, with the former being −41 (298 K) and −35 kJ mol−1 (450 K) more exergonic than the latter. Again, high temperature does not appear to facilitate this reaction thermodynamically and condensation at low temperature is more favorable.The prediction that the formation of the Si−Al−Si−Al−Si−Al hexamer is thermodynamically feasible is of critical importance, because the Si−Al− Si−Al−Si−Al hexamer itself can be directly involved in the relevant intramolecular condensations as an initiator for producing the ring clusters such as the 6ring or 3-, 4-, and 5rings with dangling monomers or dimers. The presence of the 6ring and 4ring with a dangling dimer leads to further possibilities for the building units of zeolite A and these internal condensations from the Si−Al−Si−Al−Si−Al hexamer will be analyzed later. Turning our attention to the intramolecular cyclization, the Al-(Si) fused 3- and 4rings are the initial products in the cyclization process. We initially consider the cyclization of the tetramer that proceeds with the formation of the Al-(Si) fused 3ring. In the gas phase, at 298 K, the formation of the Al-(Si) fused 3ring is an endergonic process with 12 kJ mol−1 in the free energy change, but at 450 K, it is an exergonic process with −10 kJ mol−1. In COSMO solvation, the Al-(Si) fused 3ring cyclization is predicted to be an exergonic process, which is driven by the moderate negative free energy of −30 (298 K) and −47 kJ mol−1 (450 K), indicating that the formation of the fused 3ring by cyclizations is thermodynamically feasible in COSMO solvation. However, if this is the case, there will be the question of whether the Al-(Si) fused 3ring can facilitate the nucleation of zeolite A because of the lack of the 3ring unit in zeolite A. This consideration suggests that perhaps the internal condensation reaction of the tetramer to provide the 4ring is a more likely process. Now let us consider the formation of the 4ring from the Si− Al−Si−Al tetramer. This reaction shows a similar trend to those for the Al-(Si) fused 3ring in the gas phase and COSMO solvation. In the gas phase, the condensation at 298 K is endergonic, inhibited by a thermodynamic force of 16 kJ mol−1 (ΔG), whereas the condensation at 450 K is slightly exergonic, possibly driven by a thermodynamic force of −5 kJ mol−1 (ΔG). However, when COSMO solvation is employed, the situation is reversed; the production of the 4ring is more likely to be a feasible exergonic process, driven by favorable thermodynamic force of −33 kJ mol−1 (ΔG) at 298 K and −48 kJ mol−1 (ΔG) at 450 K. Hence, for the 4ring cyclization, the role of solvation is more important, as it has lowered the free energy penalty found in the gas phase. Each of the reactions in the gas phase and COSMO solvation has already been reported in detail. We now consider how the hexamerization competes with the cyclization reaction to form the Al-(Si) fused 3- and 4rings. In the gas phase, the formation of the Al-(Si) fused 3- and 4rings does not compete with the hexamerization, which is the most favorable, and which will disfavor the cyclization reaction, especially in the 4ring species. In other words, the unfavorable cyclization reaction would hinder the nucleation of zeolite A, because the 4ring is the key and basic unit in the framework of zeolite A. However, the result for COSMO solvation is more significant, and, when

reactions of polymerization and cyclization reactions are primarily dependent on the variation of the silicate species, pH, temperature, and the effect of solvent.17 We now consider the competing reactions of polymerization and cyclization reactions of aluminosilicates, as shown in Figure 1. The key points highlighted are the role of aluminosilicate species, temperature, and the effect of solvent. To begin with, the synthesis is initiated by the condensation reaction of the Si(OH)4 and Al(OH)4Na monomers to produce the AlSiO(OH)6Na dimer, which in our previous work has been proposed as the main trigger in the subsequent condensation reactions of aluminosilicates.21 Following the initiation, some reactions continue with the step-by-step addition of the AlSiO(OH)6Na dimer; others with the addition of the 4ring or through an internal condensation reaction. 3.2.1. Dimer and Tetramer. As noted, the first stage of the nucleation process of zeolile A is the dimerization reaction (Table 1): following our earlier work, only one of the dimerization reactions is taken into consideration, where the Si(OH)4 monomer first undergoes condensation with the Al(OH)4Na monomer to generate the AlSiO(OH)6Na dimer. Comparison of the calculated energies of the dimerization reactions for three dimers formed showed that the AlSiO(OH)6Na dimer is more thermodynamically favorable than the other two (Si2O(OH)6 and Al2O(OH)6Na2).17,21 The next polymerization reaction is the tetramerization reaction (Table 1). The main tetramer, the Si−Al−Si−Al tetramer is formed by the condensation reaction of two AlSiO(OH)6Na dimers; the formation of the Si−Al−Si−Al tetramer is crucial as it is the direct precursor for the formation of the 4ring that is probably the main species involved in the nucleation of zeolite A. Its formation shows the same characteristic as the AlSiO(OH)6Na dimer: it is a thermodynamically feasible process in the gas phase and COSMO solvation. In the gas phase, the Si−Al−Si−Al tetramer formation has a large negative free energy (ΔG) of −71 (298 K) and −63 kJ mol−1 (450 K). As for COSMO solvation, a similar situation is found with the free energy changes of −34 (298 K) and −30 kJ mol−1 (450 K); due to the effect of solvent, the change in the free energy in COSMO solvation is reduced by almost a half compared to the gas phase. The free energy of reactions is slightly different between 298 and 450 K; the negative change in the free energy change is slightly decreased at the higher temperature, but will still not inhibit the formation of the Si−Al−Si−Al tetramer. In summary, an analysis of the calculated condensation energy of the above polymerization reactions reveals that the formation of the AlSiO(OH)6Na dimer and Si−Al−Si−Al tetramer is overall an exergonic process. Thus, we need next to ascertain the practical feasibility of the formation of the open clusters, which can become the principal pathway to the necessary subsequent internal condensation reactions (cyclizations). In next section, we will consider the hexamerization reaction and the formation of cyclic clusters from the direct condensation of these open clusters. 3.2.2. Hexamer, 4ring, and 3ring with One Dangling Monomer. Once the tetramer forms, it can grow further or condense internally. Here, the internal condensation of the tetramer is assisted by its almost circular structure, as mentioned already.21 Thus, three possible competing condensation reactions can occur involving the tetramer (Table 1): one is the further polymerization to produce the hexamer and 24799



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Moreover, it is also worth noting that the direct formation of a 6ring from a hexamer has a low probability in the nucleation of zeolite A. How can we explain the existence of the 6ring units in the framework of zeolite A? Perhaps the 6ring will be produced by other routes such as the condensation of three 4rings that form a larger cluster including the 6ring. Thus, overall, since the reactions take place through the 4ring species rather than other cases, the 4ring and 4ring with a dangling dimer are chosen to be the starting structures in the following reactions. 3.3. Dimer or 4ring Addition to the 4ring Species. The addition of oligomers to rings is commonly considered to be the main intermediate stage in the formation of multiple rings. Thus, in this section, there are two types of cases to be studied: first, a dimer or 4ring are added to the 4ring; second, one more dimer is added to the 4ring with a dangling dimer. 3.3.1. 4ring with a Dangling Dimer and 4ring with a Dangling 4ring. The formation of the Al−Si−(Al) fused 4ring via the internal condensation of a hexamer has been considered above. Here we consider the alternative route to form the Al− Si−(Al) fused 4ring proceeding through the addition of a dimer to a 4ring. According to Table 2, the addition of a dimer to a

latter is introduced, these two cyclization reactions become competitive with the hexamerization. At 298 K, the formation of the hexamer is slightly more favorable than the Al-(Si) fused 3- and 4rings, whereas at 450 K the condensation reaction prefers to form the two different ring species rather than continue with the hexamerization. As a result, changing temperature would result in a change in the relative distribution of the hexamer and rings. Of particular note is the very similar free energy of the Al-(Si) fused 3- and 4rings, which means that the Al-(Si) fused 3ring cyclization is as favorable as the 4ring cyclization. Interestingly, since the framework of zeolite A has no 3ring unit and the experimental spectra do not show the presence of the 3ring, the calculated thermodynamic feasibility of the Al(Si) fused 3ring cyclization prompts the questions both of its role if any in the nucleation of zeolite A and of the fate of this ring species? Perhaps the larger strain (the lower and narrower T−O b −T angles) in the 3ring might inhibit further combination with other rings during construction of zeolite A, or make the ring structure readily reopen.21 Possibly kinetic factors favor the 4ring cyclization rather than the 3ring cyclization, as supported by the experimental spectroscopic analysis showing that the 4ring species are the main initial rings in the nucleation of zeolite A. 3.2.3. 6ring and 5ring with a Dangling Monomer and 4ring with a Dangling Dimer. After formation of the hexamer in the condensation reaction, we need to consider its intramolecular cyclization to afford the 6ring, 5ring with a dangling monomer, 4ring with a dangling dimer, or the 3ring with monomers/dimer, although we do not study all these reactions in this section. The focus here is on the competing formation of the 6ring, Al-(Si) fused 5ring and the 4ring with a dangling dimer (Table 1); two of which (the 6ring and 4ring with a dangling dimer) are related to the framework of zeolite A. Considering first the formation of the 6ring from the Si−Al− Si−Al−Si−Al hexamer, the 6ring cyclization is exergonic in the gas phase and COSMO solvation (ΔG= −12/−32 kJ mol−1 (298/450 K) and ΔG = −23/−43 kJ mol−1 (298/450 K), respectively). The next ring formed is the Al-(Si) fused 5ring (Figure 2b), which does not appear in the framework of zeolite A. The free energy change has a similar pattern in the gas phase and COSMO solvation and is exergonic. In the gas phase and COSMO solvation, ΔG, is predicted to be −7/−32 (298/450 K) and −16/−38 kJ mol−1 (298/450 K), respectively. Following a similar trend to the previous considered cyclizations, this process is also favored at high temperature. Finally, we consider the formation of the Al−Si−(Al) fused 4ring (Figure 2c); for the gas phase and COSMO solvation, the Al−Si−(Al) fused 4ring cyclization is predicted to be highly exergonic with a free energy change of −42/−71 (298/450 K) and −73/−95 kJ mol−1 (298/450 K), respectively. Furthermore, the formation of this 4ring with a dangling dimer is at least 50 kJ mol−1 more favorable than that of the other two competing species. According to the calculations, a comparison of the three competing reactions shows that the 6ring and Al-(Si) fused 5ring cyclizations do not compete with the Al−Si−(Al) fused 4ring cyclization. Such a result could result in a low probability for the formation of the 6- and Al-(Si) fused 5rings; otherwise the Al−Si−(Al) fused 4ring is predominantly formed. This tendency is in good agreement with the experimental product ratio that the 4ring species favor the nucleation of zeolite A.

Table 2. Calculated Free Energy (ΔG, kJ mol−1) Changes in the Gas Phase and COSMO Solvation at 298 K and 450 K for Polymerization and Cyclization gas phase ΔG reactants Al−Si−(Al)4ring polymerization 4ring Si−Al

COSMO sol. ΔG

products

298 K

450 K

298 K

450 K

Al−Si−(Al) 4ring

−136

−135

−76

−82

−158

−146

−51

−74

−65

−49

−7

−3

−60

−47

11

10

4−4ring polymerization 4ring 4ring 4−4ring 2[Al−Si−(Al)]4ring polymerization Al−Si− Si−Al 2[Al−Si−(Al)] (Al)4ring 4ring Al−Si−Al−Si−(Al) 4ring polymerization Al−Si− Si−Al Al−Si−Al−Si− (Al)4ring (Al)4ring abbreviations 4−4ring 2[Al−Si−(Al)]4ring Al−Si−Al−Si−(Al)4ring

clusters Al4Si4O23H14Na4 Al4Si4O24H16Na4 Al4Si4O24H16Na4

4ring is a considerably exergonic reaction of −136/−135 kJ mol−1 (298/450 K) in the gas phase and −76/−82 kJ mol−1 (298/450 K) in COSMO solvation. In the latter, the free energy change is reduced significantly, but nonetheless the free energy change is still substantially negative. Moreover, a comparison of the reactions that add a dimer to form a tetramer, hexamer, and 4ring with a dangling dimer will give us a better understanding of which reaction involving the dimer addition to open clusters or ring is more energetically feasible. We find that the free energy will favor the Al−Si−(Al) fused 4ring cyclization over the tetramerization or hexamerization in the gas phase and COSMO solvation. Hence, in the light of the predicted preference for a dimer condensing on a 4ring rather than a dimer or tetramer, we suggest that the formation of long 24800



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Table 3. Calculated Free Energy (ΔG, kJ mol−1) Changes in the Gas Phase and COSMO Solvation at 298 and 450 K for Polymerization and Cyclization

chain clusters will be unfavorable in the nucleation process, which is a favorable route to zeolite formation. Turning now to the formation of a 4ring with a dangling 4ring (Figure 3b), we consider this reaction since the 4ring species are the predominant product in the prenucleation, resulting in a higher probability of 4ring species being condensed with each other. Thus, with the exception of a dimer adding to the 4ring, we should pose the question: does the 4ring grow by the addition of another 4ring? Indeed, a trend with a higher energy release of −158/−146 kJ mol−1 (298/450 K) and −51/−74 kJ mol−1 (298/450 K) in the gas phase and COSMO solvation is calculated(Table 2). Additionally, in contrast to a dimer condensing onto a dimer or tetramer in COSMO solvation, we find that as the temperature increases, there is a significant increase in exoergicity of the reaction. On comparing a 4ring condensation onto a dimer and onto a 4ring, the free energy of the former is more favorable in COSMO solvation, being greater by −25 kJ mol−1 at 298 K and −8 kJ mol−1 at 450 K. On the basis of this calculation, we assume that the Al−Si−(Al) fused 4ring is preferentially taken as the main reactant for the forward condensation reactions. We note that the 4−4ring cyclization leading to other ring species is quite possible since the corresponding free energies are significant especially at high temperature (−74 kJ mol−1). 3.3.2. 4ring with Two Dangling Dimers and 4ring with a Dangling Tetramer. According to the results in section 3.3.1, since the Al−Si−(Al) fused 4ring is a predominant product, it is, of course, involved in further growth or internal condensation. Let us first concentrate on cluster growth. As with the similar case in the previous section, the second dimer condensing with the Al−Si−(Al) fused 4ring forms the Al−Si− (Al) fused four and 2-[Al-Si-(Al)] fused 4rings (Figures 2d and 2e). From the results in Table 2, similar trends in the energetics of forming the two clusters can be observed. Starting with the gas phase, the 2-[Al-Si-(Al)] fused 4- and Al−Si−Al−Si−(Al) fused 4rings are thermodynamically favorable with calculated free energies of −65/−49 (298/450 K) and −60/−47 kJ mol−1 (298/450 K). In contrast to the gas phase, the addition of a dimer on the Al−Si−(Al) fused 4ring is not favored in COSMO solvation; the free energy change is −7/−3 kJ mol−1 (298/450 K) for the 2-[Al-Si-(Al)] fused 4ring reaction and 11/10 kJ mol−1 (298/450 K) for the Al−Si−Al−Si−(Al) fused 4ring, showing marginally exergonic and endergonic behaviour, respectively. Since the addition of a dimer does not appear to facilitate these reactions thermodynamically, we have to consider other alternative pathways or species to assist the nucleation. One route is through the internal cyclization of the Al−Si−(Al) fused 4ring to produce the bi4ring and the other is through the internal cyclization of the 4−4ring to produce the tri4ring. 3.4. Multiple Rings. In general, the framework of zeolites can be described as the integration of multiple rings, to understand whose formation is of key importance. Here, there are four different multiple rings formed: the bi4ring, tri4ring, openD4R, and D4R of relevance to in the nucleation of zeolite A. 3.4.1. Bi4ring and tri4ring. The free energy profile for the formation of the bi4ring and tri4ring is shown in Table 3; the intramolecular Si−O−Al bond formation is the step that determines whether the bi4ring and tri4ring (Figures 2f and 3c) are formed. As a start, the bi4ring cyclization via the Al−Si− (Al) fused 4ring is endergonic by 30/12 kJ mol−1 (298/450 K)

gas phase ΔG reactants

products

bi4ring cyclization Al−Si−(Al) 4ring 6ring Al−Si−(Al)bi4ring polymerization 2[Al−Si−(Al)] 4ring bi4ring Si−Al

298 K

450 K

COSMO sol. ΔG 298 K

450 K

bi4ring

30

12

5

−11

bi4ring

1

−26

−44

−63

Al−Si−(Al) bi4ring Al−Si−(Al) bi4ring

4

−16

−28

−43

−91

−77

−40

−36

tri4ring

−16

−39

−46

−62

tri4ring

0

−23

−39

−39

21

−3

−12

−32

tri4ring cyclization Al−Si−(Al) bi4ring 4−4ring openD4R cyclization tri4ring D4R cyclization openD4R abbreviations

D4R clusters

bi4ring Al−Si−(Al)bi4ring tri4ring

Al3Si3O17H10Na3 Al4Si4O23H14Na4 Al4Si4O22H12Na4

openD4R

34 14 abbreviations openD4R D4R

−52 −63 clusters Al4Si4O21H10Na4 Al4Si4O20H8Na4

in the gas phase and 5 kJ mol−1 (298 K) in COSMO solvation, but in COSMO solvation at 450 K the cyclization is slightly exergonic (−11 kJ mol−1). Thus, this reaction is unlikely to occur at low temperatures. It is also worth mentioning that the 6ring can further react internally to produce the bi4ring, The 6ring as the reactant leads to the bi4ring being thermodynamically feasible, with a free energy of 1/−26 kJ mol−1 (298/450 K) in the gas phase and −44/−63 kJ mol−1 (298/450 K) in COSMO solvation. This reaction pathway (see Figure 1) is considered to be a likely step in the nucleation of zeolite A, and such a route corresponds to the experimental result that the 4ring species rather than the 6ring species are the main intermediates in the nucleation processes. Considering now the formation of the tri4ring, there are two condensation routes: one is from the Al−Si−(Al) fused bi4ring and the other from the 4−4ring. We do not consider the internal condensation of the Al−Si−(Al) fused bi4ring to produce the tri4ring, as the 2-[Al-Si-(Al)] fused 4ring and bi4ring, which are the key reactants to produce the Al−Si−(Al) fused bi4ring, have unfavorable free energies of formation compared with the 4−4ring. In Table 3, we find that the internal condensation starting from the 4−4ring to afford the tri4ring is thermodynamically feasible especially with COSMO solvation; the free energy change is calculated as 0/−23 (298/ 450 K) and −39/−39 kJ mol−1 (298/450 K) in the gas phase and COSMO solvation. Clearly, there is a high probability for this internal condensation reaction; the tri4ring (via the 4− 4ring) could be one of the main intermediates to participate directly in the nucleation of zeolite A. 3.4.2. OpenD4R and D4R. Once the tri4ring is formed, its optimized “curved” structure would be expected to be very likely to make a direct internal condensation into the open D4R (Figure 3d). However, as shown in Table 3 in the gas phase, there is a thermodynamic penalty for the openD4R cyclization, 24801



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with a free energy of 21/−3 kJ mol−1 (298/450 K). Considering now the effect of solvent, the resulting free energy change is negative, with −12/−32 kJ mol−1 (298/450 K). This reaction is more favored at high temperature and can reasonably be extended to the next condensation reaction: the formation of the D4R. The D4R is supposed to be the final product in the first stage of the nucleation of zeolite A. Hence, to determine the formation of the D4R, the final condensation reaction of the open D4R to give the closed D4R is crucial. First, it is unlikely that the D4R is formed by the open D4R in the gas phase, which can be confirmed by the calculated positive free energy of 34/14 kJ mol−1 (298/450 K). However, when compared to the gas phase, this cyclization reaction in COSMO solvation is predicted to be exergonic by −52/−63 kJ mol−1 (298/450 K). To summarize, two distinct types of reaction pathways regarding the dimer or ring condensing onto the ring species (polymerizations), and the internal condensations of the ring species (cyclizations) have been investigated. The calculated energies show different trends in the gas phase and COSMO solvation. In the gas phase, a general trend is shown in the condensation reactions: polymerization reactions are more feasible than cyclization reactions. Most cyclization reactions are impractical (endergonic or less exergonic) especially at room temperature (298 K), with some exceptions such as the 6-, Al−Si−(Al) fused 4-, and Al-(Si) fused 5rings. Moreover, temperature has a significant effect on the polymerization and cyclization reactions; to increase temperature (to 450 K) will effectively make most cyclization reactions more exergonic, but most polymerization reactions less exergonic. When considering COSMO solvation, the free energy change for polymerization reactions is less favorable than in the gas phase, whereas cyclization reactions become feasible and almost all the reactions are exergonic. Again, when raising temperature to 450 K, cyclization reactions become relatively more favorable than at room temperature (298 K), but polymerization reactions become less exergonic except for the 4−4ring. Hence, the effect of temperature will influence which reactions or species are likely to proceed or be formed. Moreover, an interesting finding is that even at room temperature, almost all the reactions in COSMO solvation are thermodynamically favored, which corresponds to the experimental result of Mintova et al.33 and Smaihi et al.38 that synthesizing zeolite A is practical at room temperature.

form the ring species. (iii) Some condensation reactions are sensitive to temperature for controlling selectivity; for example, cyclization reactions become relatively more favorable at high temperature than at room temperature, but polymerization reactions become less exergonic. (iv) At room temperature, most condensation reactions can proceed successfully, corresponding to the experimental results. (v) Finally, according to the relative energies of these condensation reactions determined from COSMO solvation, it can be concluded that the fundamental mechanism of the nucleation of zeolite A is via dimer → tetramer → 4ring → 4−4ring → tri4ring → openD4R → D4R as shown in Figure 4. The mechanistic scenario shows similar behavior to the experimental results that the 4ring species dominate the early stages of the nucleation of zeolite A.

Figure 4. A proposed nucleation mechanism for the formation of a D4R.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to UCL for providing computational facilities. J.M.M.F. acknowledges the scholarship PROMEP-15-2012 UJAT PTC.

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4. SUMMARY AND CONCLUSIONS A comprehensive computational investigation of the nucleation of zeolite A has been presented by means of DFT/COSMO calculations although the mechanistic scenario is complex. To establish the possible nucleation mechanism of zeolite A, we examined and compared the free energy profile for the most competitive condensation reactions of polymerization and cyclization reactions that are related to the nucleation mechanism. On the basis of our energetic analysis, the highlights of this work can be summarized as follows: (i) Compared with polymerization reactions, COSMO solvation is very important in providing a favorable thermodynamic driving force for cyclization reactions, which means that cyclization reactions will become competitive with polymerization reactions. (ii) The formation of longer chain clusters, in COSMO solvation, will be less likely than that of rings. Such a result suggests that when small linear clusters or rings condense with the dimer, they will undergo internal condensations to

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Modeling the Nucleation of Zeolite A - The Journal of Physical

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