Microporous Materials
Organic Structure-Directing Agents in SAPO Synthesis: The Case
of 2-Ethyl-1,3,4-trimethylimidazolium
Paloma Vinaches
[a]and Sibele B. C. Pergher*
[a]Abstract: Structure direction is a key topic in zeolite synthesis.
In this work, the organic cation 2-ethyl-1,3,4-trimethylimid-azolium was studied for the first time in the synthesis of SAPO zeolite. Concentrated gels and fluoride media were chosen for the synthesis. To understand the formation of the main prod-ucts, CHA and LTA zeotypes, several statistical calculi were per-formed, and the results showed that the structure direction of the LTA zeotype was mainly caused by to the organic cation. For SAPO-CHA, the temperature and a combination of dilution and synthesis time also influenced the formation. The CHA zeo-type was studied thoroughly by other techniques such as
ther-Introduction
The search for new zeolites and the complete study of their synthesis parameters are hot topics.[1]Several aspects may in-fluence the different stages of zeolite synthesis, for example, the type of initial source, the solvents, the crystallization time, and the temperature. Among them, the use of organic struc-ture-directing agents (OSDAs) has been studied and treated as a strategy to aid the search for new zeolitic structures.[2] 2-Ethyl-1,3,4-trimethylimidazolium (2E134TMI) is an OSDA employed in the synthesis of pure silica zeolites.[3] This cation has already been used to synthesize a new chiral STW zeolite, named HPM-1. The space group of this zeolite is P6122 and it has a three-dimensional helicoidal channel system.[4]
Another parameter that influences zeolite synthesis is the mineralizing agent.[1b]Basic and fluoride media are used widely, and the pH of the synthesis gel varies from high basicity to neutrality. The main advantages of the use of fluoride media are that they lower the number of crystal defects after calcin-ation, reduce the quantity of solvent needed in the synthesis gel, and increases the silica-to-alumina ratio (SAR) of the result-ant products.[5]Fluoride media also enable the introduction of germanium into the zeolitic framework, for example, in the syn-theses of ITQ-24[6]and ITQ-37.[7]It is important to tailor proper-ties such as acidity and basicity to introduce a variety of hetero-atoms into zeolites,[8]for example, to enable their use in
cataly-[a] Laboratório de Peneiras Moleculares (LABPEMOL), Institute of Chemistry,
Federal University of Rio Grande do Norte (UFRN), Campus de Lagoa Nova, 59078-970 Natal, RN Brazil E-mail: [email protected]
Supporting information and ORCID(s) from the author(s) for this article are available on the WWW under https://doi.org/10.1002/ejic.201701002.
mogravimetry, high-power decoupled (HPDEC) magic-angle spinning (MAS) NMR spectroscopy, and nitrogen sorption. We calculated that this zeotype contains one cation per unit cell and observed that the fluoride medium also directs the struc-ture. The silicon atoms in SAPO-CHA are present in three states [SiO(4X), SiO(3X), and SiO(1X)], aluminium atoms were found in tetrahedral and octahedral coordination environments, and the phosphorus atoms also had tetrahedral geometries. Textural analysis confirmed the formation of a microporous material with a Brunauer–Emmett–Teller (BET) surface are of 510 m2g–1 and an external surface of 110 m2g–1.
sis, and these heteroatom-containing zeolites have an increas-ing importance in industry.[9]
The introduction of phosphorus was also studied in fluoride media. Some examples of the zeolites obtained are AlPO-16 and AlPO-5.[10]If other elements are introduced, AlPO materials with important catalytic properties are obtained. An example is the SAPO family. These materials can be applied to industrial reactions such as CO2/CH4separation or the methanol-to-olefin (MTO) process.[11]
For studies of the structure-directing factors, computational studies are usually employed to elucidate the role of the OSDAs.[12]In some studies, a priori statistical calculus was also performed to find the best synthesis conditions to obtain the most crystalline zeolite,[13]but what if these calculi were used to understand the factors that drive the formation of a certain zeolitic phase? This type of study performed a posteriori to study the effect of new OSDAs may help to elucidate the impor-tance of each parameter in the formation of each phase. This knowledge will lead to a better evaluation of what really occurs in the synthesis.
Therefore, the objective of this study is to evaluate the influ-ences of the structure-directing factors in the synthesis of SAPO zeolites in the presence of the organic cation 2-ethyl-1,3,4-tri-methylimidazolium and with the use of fluoride media and con-centrated gels, as such a study had not been performed previ-ously to the best of our knowledge. To evaluate these effects, statistical calculi and several characterizations will be used.
Results and Discussion
Initially, samples were obtained at 150 °C with various H2O quantities (x = 5.5, 8.2 and 13.2) and for different times (1–8 d).
The samples were characterized by X-ray diffraction, and the results are presented in Figures 1 and 2 and in the Supporting Information. Samples were also obtained at 135 °C and charac-terized by X-ray diffraction, and the results are shown in Fig-ures 3 and 4 and in the Supporting Information. The materials obtained in each experiment are summarized in Table 1. Several interesting studies in which the Si content of the SAPO-CHA zeolite was modulated have already been reported, for exam-ple, the studies performed by Tan et al.[14]Therefore, this pa-rameter was not evaluated in this research.
Figure 1. X-ray diffractograms of Samples 1–5 (150 °C).
Figure 2. X-ray diffractograms of Samples 10–13 (150 °C).
Two zeotypes were mainly obtained, that is, CHA and LTA.[21,22]The products obtained at both temperatures were ac-companied by a mixture of unknown lamellar phases, which were separated by decantation for SAPO-CHA. However, as the H2O proportion increased at 135 °C, it became very difficult to separate the phase by decantation owing to the low quantity of the other phase; therefore, for these samples, the lamellar phase was also represented in the diffractograms. From the syn-theses at 150 °C, it can be inferred the CHA zeotype coexisted with a LTA phase for higher dilutions. As the temperature de-creased, the LTA zeotype remained at every concentration
stud-Figure 3. X-ray diffractograms of Samples 14–17 (135 °C).
Figure 4. X-ray diffractograms of Samples 22–24 (135 °C).
Table 1. Summary of the syntheses.
Temperature [°C] x(H2O) Sample Time [d] Zeolitic type[21,22]
150 5.5 1 <1 (6.5 h) CHA 150 5.5 2 1 CHA 150 5.5 3 2 CHA 150 5.5 4 4 CHA 150 5.5 5 8 CHA 150 8.2 6 1 CHA 150 8.2 7 2 CHA 150 8.2 8 5 CHA 150 8.2 9 7 CHA 150 13.2 10 1 CHA, LTA 150 13.2 11 2 CHA, LTA 150 13.2 12 4 CHA, LTA 150 13.2 13 6 CHA, LTA 135 5.5 14 <1 (17 h) CHA, LTA 135 5.5 15 1 CHA, LTA 135 5.5 16 2 CHA, LTA 135 5.5 17 2.8 (68 h) CHA, LTA 135 8.2 18 >1 (16 h) lamellar 135 8.2 19 1 LTA, lamellar 135 8.2 20 2 LTA, lamellar 135 8.2 21 3 LTA, lamellar 135 13.2 22 >1 (19 h) LTA, lamellar 135 13.2 23 1 LTA, lamellar 135 13.2 24 2 LTA, lamellar
ied and, interestingly, the CHA phase disappeared if the gels were more diluted.
To isolate the SAPO-LTA, a synthesis test with LTA seeds was performed under the conditions that increased the quantity of LTA obtained, that is, at 135 °C and x = 13.2 (Supporting Infor-mation). The product obtained was a mixture of the unknown lamellar materials with no sign of the LTA phase.
The LTA framework density is 14.2 T/1000 Å3, whereas the CHA framework density is 15.1 T/1000 Å3.[15]The space group of the LTA framework reported in the International Zeolite Asso-ciation (IZA) database is Pm3
¯
m. LTA zeolites have athree-di-mensional channel system and their tiling arrangement is t-cub, which corresponds to the well-known D4R cages, t-toc (previ-ously called SOD), and t-gre, which is the corresponding tiling name of the LTA units. This structure is presented in Figure 5, for which the CIF file from the IZA database and the Mercury 3.5 program were used.[16]
Figure 5. LTA structure.
The space group of the CHA framework is R3
¯
m and, its tilingcomposition is t-hpr, related to D6R cages, and t-cha (the previ-ous CHA units). This structure is represented in Figure 6, which was prepared in the same way as Figure 5. For SAPO-CHA syn-thesized in hydrofluoric media, the symmetry can be triclinic
Figure 6. CHA structure.
owing to the presence of the fluoride in the framework.[17] Hydrofluoric media act as mineralizers and codirector in zeolite synthesis, and the fluoride anions are usually located in D4R cages, as reported by Camblor et al. and Vidal-Moya et al.[18]
The SAPO-CHA obtained through these syntheses was in-dexed before and after calcination. Thermogravimetric analysis was performed for the pure SAPO-CHA to define its calcination temperature, and then the cation/unit cell quantity was calcu-lated in combination with the inductively coupled plasma opti-cal emission spectroscopy (ICP-OES) data. The thermogravimet-ric (TG) curve (Figure 7) contains three main losses of 5.19 % to 161.7 °C, 1.8 % to 338.7 °C, and 18.4 % to 662.3 °C. The first and second losses are related to the zeolitic water, and the third loss is attributed to the decomposition of the cations and was used to calculate the quantity of cations occluded in the pores.
Figure 7. Thermogravimetric analysis and differential scanning calorimetry of the CHA zeotype (Sample 5).
On the basis of these results, the sample was calcined at 550 °C for 6 h. Indexing-quality X-ray diffractograms were re-corded before and after the calcination, and the DICVOL06 pro-gram[19]was used to calculate the unit-cell parameters (Table 2 and Supporting Information). The indexing data obtained be-fore and after calcination both resulted in triclinic symmetry, which confirmed the presence of fluoride in the framework. The calcined sample presented a distorted framework compared with that of the noncalcined sample owing to the liberation of at least some of the fluoride and the decomposition of the organic cation.
Table 2. Indexing results.
Parameters As-made Calcined
a [Å] 9.4017 8.7924 b [Å] 9.4097 9.6301 c [Å] 9.5228 9.8588 α [°] 94.468 86.3380 β [°] 95.399 81.365 γ [°] 94.989 73.271 Volume [Å3] 832.39 790.18 M (20 as-made/17 calcined) 17.9 20.8 F (20 as-made/17 calcined) 32.0 26.5 Refined zero-point shift 2θ [°] 0.0242 0.0049
Table 3. Input data for the statistical study.
Experiment Sample Temperature x(H2O) Time LTA CHA
[°C] [d] C1(10.50)[a] C2(21.20)[a] AC1[b] C3(15.90)[a] C4(20.50)[a] AC2[b]
1 15 135 5.5 1 16.44 1.16 8.80 1.51 1.32 1.41 2 16 135 5.5 2 16.44 10.32 13.38 4.38 3.59 3.98 3 23 135 13.2 1 30.74 14.77 22.76 0 0 0 4 24 135 13.2 2 45.05 74.91 59.98 0 0 0 5 2 150 5.5 1 0 0 0 24.36 23.24 23.80 6 3 150 5.5 2 0 0 0 14.07 12.69 13.38 7 10 150 13.2 1 51.01 48.17 49.59 4.29 2.41 3.35 8 11 150 13.2 2 83.11 70.70 76.91 46.90 50.03 48.46
[a] C = relative crystallinity. [b] AC = average relative crystallinity.
Statistical calculi were performed to achieve a better under-standing of these results. Firstly, the relative crystallinities of SAPO-LTA and SAPO-CHA obtained after 1 and 2 d at the higher and lower dilutions were calculated to build a 23factorial exper-iment,[20]as shown in Table 3. The concept of relative crystalli-nity employed in this study is used to provide a comparison between samples through the calculation of the intensities of the chosen peaks and then the transformation of the data to percentages. Secondly, the main effects and the combined ef-fects were obtained as described by Neto, Scarminio, and Bruns[20]and are presented in Table 4. Owing to the high error values of the SAPO-LTA statistical analysis, almost every effect studied was nondeterminant in the synthesis of this phase. In-terestingly, only the dilution [x(H2O)] had some effect in this case; therefore, the continuous dilution of the synthesis gel fa-vors the formation of the SAPO-LTA phase. These results indi-cated that the most important factor that influenced the ap-pearance of SAPO-LTA was the use of the OSDA. For the analysis of the statistical calculi of the SAPO-CHA, the errors were low; therefore, the data were ordered in a Pareto representation (Fig-ure 8). The p value obtained showed that every parameter had a statistical significance. Therefore, the SAPO-CHA synthesis was influenced by the use of the OSDA and also by the other three parameters. The temperature chosen seemed to have the big-gest influence, followed by the synthesis time. For combinations of two factors, the dilution and time had a bigger influence that any combination with temperature. This statistical analysis confirmed the observations made previously: SAPO-LTA is fa-vored at low temperatures, and SAPO-CHA appears preferably at higher temperatures.
Table 4. Main and combined effects.
LTA CHA
Average crystallinity for all samples 28.9 ± 12.3 11.8 ± 0.1 Main effects Temperature (T) 5.40 ± 24.7 20.9 ± 0.3 x(H2O) 46.8 ± 24.7 2.3 ± 0.3 Time (t) 17.3 ± 24.7 9.3 ± 0.3 Two-factor interactions T–x(H2O) 16.5 ± 24.7 5.0 ± 0.3 T–t –3.6 ± 24.7 8.0 ± 0.3 x(H2O)–t 15.0 ± 24.7 13.2 ± 0.3 Thee-factor interaction T–x(H2O)–t –1.3 ± 24.7 14.5 ± 0.3
Even though the SAPO-LTA was not obtained as a pure phase in the proposed experiments, it has been synthesized
Figure 8. Pareto chart for the synthesis of SAPO-CHA.
previously in the presence of the bulky organic cations 2,2-di-methyl-2,3-dihydro-1H-benzo[de]-isoquinoline-2-ium (DDBQ) and 4-methyl-2,3,6,7-tetrahydro-1H,5H-pyrido[3.2.1-ij]quinolin-ium (MTPQ),[21]which have higher C/N ratios (14 for DDBQ, 13 for MTPQ, and 4 for 2E134TMI). On the basis of these results and those presented in this article, SAPO-LTA may be obtained as a pure phase in more dilute syntheses and with lower Si content, which may be related to the C/N ratio of the organic cation.
The morphologies of zeotypes usually differ from those of pure silica or aluminosilicates owing to their different composi-tions (heteroatoms or even different structure-directing agents) and structural varieties. The obtained samples were observed by SEM, and two morphologies were found. The cubic-planar CHA zeotype can be seen clearly in Figure 9, and the morphol-ogy is similar to those reported previously.[22]The morphology of the LTA zeotype was octahedral, as shown in Figure 10, and also in agreement with that reported previously.[23]
The mapping of the sample by energy-dispersive X-ray spec-troscopy (EDS) coupled to field-emission scanning electron microscopy (FE-SEM, Figure 11) showed that both zeotypes con-tained the three elements (Si, Al, and P).
For the CHA zeotype, it was possible to obtain the composi-tion by ICP-OES. The calculated Si/Al and Al/P molar ratios were 0.06 and 1.04, respectively, which results in a composition of [Si0.03Al0.49P0.48]. As mentioned above, it is possible to estimate the quantity of cations per unit cell from the ICP-OES data and
Figure 9. SEM micrograph of SAPO-CHA (Sample 17).
Figure 10. SEM micrograph of SAPO-LTA (Sample 17).
Figure 11. EDS mapping of the SAPOs (Sample 17).
the thermogravimetric losses, and the estimated value is ap-proximately one cation per unit cell.
Infrared spectroscopy was used to characterize the as-made SAPO-CHA (Figure 12). The three bands between ν
˜
= 1600 and 1400 cm–1were attributed to aromatic C=C bending owing to the presence of organic molecules in the framework.[24] The asymmetric stretch of the internal tetrahedra (T–O–T) appeared at ν˜
= 1110 cm–1 with a shoulder at ν˜
= 1206 cm–1, and the symmetric stretch was related to the band at ν˜
= 732 cm–1.[25] The vibrations of the D6R cages were also located in the spec-trum at ν˜
= 641 and 566 cm–1.[25a]Finally, the T–O bend vibra-tions were assigned to the last three bands at ν˜
= 528, 482, and 439 cm–1.Figure 12. Infrared spectrum of the CHA zeotype (Sample 7).
The NMR spectra of the CHA zeotype are shown in Fig-ures 13, 14, and 15. To improve the resolution of the peaks, the high-power decoupled (HPDEC) pulse sequence was chosen. Initially, the29Si HPDEC magic-angle spinning (MAS) NMR
trum was obtained, and three signals at δ = –71.5, –89.1, and –106.8 ppm are related to SiO(4X), SiO(3X), and SiO(1X) respec-tively.[14,26]
Figure 14.27Al HPDEC MAS NMR spectrum of CHA zeolite (Sample 4).
Figure 15.31P HPDEC MAS NMR spectrum of CHA zeolite (Sample 4).
Two signals were observed in the 27Al HPDEC MAS NMR spectrum of the SAPO-CHA zeotype. The signal at δ = 42.2 ppm is related to the tetrahedral aluminium atoms, and that at δ = –10.3 ppm is attributed to hexacoordinate aluminium atoms, probably owing to interactions with the fluoride anions.[27]As reported previously, aluminium atoms in zeotypes can be in tetrahedral, pentahedral, or octahedral coordination environ-ments.[28]
To conclude the NMR spectroscopy study, the 31P HPDEC MAS NMR spectrum was obtained, and one signal was observed at δ = –26 ppm with a shoulder at δ = –17.4 ppm. These signals are attributed to the tetrahedral P atoms of the framework.[14]
Finally, the nitrogen sorption isotherm was obtained for the calcined CHA zeotype (see Supporting Information). The iso-therm was characteristic of a type IV microporous solid and had a small type H4 hysteresis, which is attributed to a small quan-tity of slit-shaped mesopores that probably formed through
particle agglomeration.[29] The surface area was calculated by the Brunauer–Emmett–Teller (BET) method in combination with the Keii–Rouquerol criteria.[30] The b point resulted in a p/p0 value of 0.009 and an SBETvalue of in 510 m2g–1with an error of 1.7 %. The α-plot methodology was used to calculate V0as well as the external and mesoporous surface.[31]The obtained
V0* value was 0.16 cm3g–1, and the external and mesoporous surface was 80 m2g–1. At p/p0 = 0.984, the Gurvich rule was applied.[30b]The total pore volume of 0.27 cm3g–1was used to calculate the mesopore volume from the data obtained in the
α-plot, and a value of 0.11 cm3g–1was obtained. All of these results are summarized in Table 5.
Table 5. Isotherm analysis (Sample 5).
Method Parameter Value
BET SBET[m2g–1] 510
BET b point 0.009
BET V0[cm3g–1] 0.16
α-plot external + mesoporous surface [m2g–1] 80
α-plot total pore volume [cm3g–1] 0.27
Gurvich rule mesopore volume [cm3g–1] 0.11
Conclusions
In this research, we studied the influence of the OSDA 2-ethyl-1,3,4-trimethylimidazolium in SAPO synthesis with HF as a min-eralizing agent. The synthesis resulted in two main products, namely, LTA and CHA zeotypes, which had octahedral and cubic-planar morphologies, respectively.
Several statistical calculi were performed to elucidate the main structure-direction factors that influenced the formation of each phase. The SAPO-LTA was obtained mainly because of the OSDA. For the formation of the SAPO-CHA phase, tempera-ture and a combination of dilution and synthesis time also influ-enced the formation.
The LTA zeotype could not be isolated under the conditions studied, but the SAPO-CHA was thoroughly characterized. It contained one cation per unit cell, and fluoride was also a struc-ture-directing agent. Through HPDEC NMR spectroscopy, the different framework T atoms were studied: the Si atoms were found in three environments [SiO(4X), SiO(3X), and SiO(1X)], the Al atoms were present in tetrahedral and octahedral coordina-tion environments, and the P atoms had tetrahedral environ-ments. The obtained SAPO-CHA was microporous with a BET surface area of 510 m2g–1 and an external surface of 110 m2g–1.
Finally, this study shows how several other factors influence zeolite synthesis and that it is also possible to evaluate their effects through statistical calculi represented in a Pareto chart.
Experimental Section
The reagents used in the synthesis were hydrofluoric acid (40 %, Sigma–Aldrich), tetraethylorthosilicate (TEOS, 98 %, Sigma–Aldrich), 2-ethyl-1,3,4-methyilmidazolium hydroxide (synthesized), ortho-phosphoric acid (85 %, Vetec), aluminium hydroxide (62.23 %, Synth), and distilled water.
Table 6. Conditions for the29Si,27Al, and31P HPDEC MAS NMR spectroscopy experiments.
Nucleus 29Si 31P 27Al
Reference kaolinite sodium monophosphate aluminium hexahydrate
Resonance frequency [MHz] 79.49 161.97 104.26
Rotation angle of the pulse [°] 90 90 90
Acquisition time [s] 0.08 0.04 0.03
Interval between pulses [s] 60 2 2
The cation 2E134TMI was synthesized as described previously.[4]The SAPOs were synthesized with the following synthesis-gel composi-tion: SiO2/Al2O3/P2O5/HF/OSDA/H2O 0.2:0.2:0.25:0.5:0.5:x.
Initially, all of the reagents except the hydrofluoric acid were weighed, and then the mixture was stirred for the time needed to hydrolyze the TEOS and to obtain the quantity of water desired (x = 5.5, 8.2, or 13.2). After this time passed, the hydrofluoric acid was added, and the mixture was mixed mechanically. The resulting gel was divided between Teflon autoclaves, which were then placed into steel autoclaves. The autoclaves were put into a rotatory oven at 135 or 150 °C for various times. The products were collected by filtration under vacuum and washed with distilled water several times. Afterwards, a test with the addition of LTA aluminosilicate seed to the synthesis gel was performed with x = 13.2 at 135 °C. The proportion of seeds added was 1 % of the gel weight. The products were characterized by X-ray diffraction (Bruker D2-Phaser with Lynxeye detector and Cu radiation, a divergent slit of 0.6 mm, a central slit of 1 mm, a measuring step of 0.02° and an acquisition time of 0.1 s; for the indexing analysis, the measuring step was 0.004°, and the acquisition time was 0.5 s), infrared spec-troscopy (IV-FTIR/ATR Spectrum 65, Perkin–Elmer, samples prepared in KBr from Merck); scanning electron microscopy (MIRA3 FE-SEM, Tescan) coupled to an EDS detector (Oxford instruments);29Si,31P, and 27Al HPDEC MAS NMR spectroscopy (Bruker Avance II+ 400 MHz HPDEC pulse sequence and the conditions listed in Table 6), ICP-OES [Thermo Fisher Scientific iCAP 6300 Duo spec-trometer with a simultaneous charge injection device (CID) de-tector, a Burgener Miramist nebulizer, and a cyclonic nebulization chamber; the samples (0.050 g) were dissolved in HNO3/HCl with the aid of a CEM Mars Xpress microwave digester], and thermograv-imetric analysis (TA instruments SDTQ600 simultaneous thermo-gravimetric and calorimetric analyzer, Pt sample holder, air atmos-phere, heating at 10 °C min–1from 25 to 900 °C, 0.005 g of sample). For textural analysis, some samples were calcined at 550 °C for 6 h. The calcined samples were pretreated at 200 °C under vacuum over-night in a Micromeritics Asap 2020 analyzer, and the measurements were performed with nitrogen as the probe molecule.
Acknowledgments
The authors acknowledge Programa de Pós-Graduação em Ciência e Engenharia de Materiais (PPGCEM), Universidade Fed-eral do Rio Grande do Norte (UFRN), and Coordenadoria de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for the facilities and financial support. The authors are also grateful to LABPEMOL (Laboratório de Peneiras Moleculares, UFRN) for the facilities for the synthesis, XRD, IR spectroscopy, and textural analysis techniques; UFRN Chemistry Department for the FE-SEM micrographs; NUPRAR (UFRN) for the ICP-OES analysis; the Institute of Chemistry (UFRN) for the TGA/DTG/DSC data; and Prof. Dr. H. O. Pastore and IQ-UNICAMP (Laboratório Multiusuário de Ressonância Magnética Nuclear) for the MAS NMR spectra.
Keywords: Structure-directing agents · Zeolites ·
Aluminosilicates · Microporous materials · Synthetic methods
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Microporous Materials For the synthesis of SAPO zeolites, the organic structure-directing agent
2-P. Vinaches, S. B. C. Pergher* ... 1–9
ethyl-1,3,4-trimethylimidazolium in Organic Structure-Directing Agents fluoride media and concentrated gels in SAPO Synthesis: The Case of 2- produced two zeolitic materials, Ethyl-1,3,4-trimethylimidazolium namely, SAPO-CHA and SAPO-LTA. The data obtained are studied through sta-tistical calculi to quantify the impor-tance of each directing factor.
