Study on the formation of mesoporous molecular sieves in the presence of various anions

Study on the formation of mesoporous molecular sieves in the presence of various anions

Microporous and Mesoporous Materials 32 (1999) 211–228 www.elsevier.nl/locate/micmat Study on the formation of mesoporous molecular sieves in the pre...

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Microporous and Mesoporous Materials 32 (1999) 211–228 www.elsevier.nl/locate/micmat

Study on the formation of mesoporous molecular sieves in the presence of various anions Heloise O. Pastore a, *, Marcello Munsignatti a, Diomar R.S. Bittencourt b, Ma´rcia M. Rippel a a Micro- and Mesoporous Molecular Sieves Group, Instituto de Quı´mica – Universidade Estadual de Campinas, CP 6154, CEP 13083-970, Campinas SP, Brazil b Instituto de Fı´sica, Universidade de Sa˜o Paulo, CP 66318, CEP 05315-970, Sa˜o Paulo, Brazil Received 7 December 1998; received in revised form 22 March 1999; accepted for publication 17 May 1999

Abstract This work describes the mesophases obtained when mesoporous silicates are synthesized in the presence of hydrofluoric, hydrochloric, hydroiodic, acetic or nitric acids. The results show that when the silicate precursor is varied different phases or mixture of phases can be obtained. Thus pure-silica MCM-41 is obtained from sodium silicate or [(TMA)SiO ] and cetyltrimethylammonium bromide in the presence of acetic, hydrofluoric and 2.5 8 hydrochloric acids. Hydroiodic acid affords a mixture of phases from both sources of silica after either mild thermal (347–349 K ) or hydrothermal (423 K ) treatments. Upon removal of the organic counterpart, MCM-41 is formed from tetramethylammonium silicate and magadiite from sodium silicate. The presence of nitric acid yields MCM-41, for sodium silicate and when HNO is used, for tetramethylammonium silicate, after mild thermal treatment. Upon 3 hydrothermal treatment, MCM-41 converts to magadiite. The presence of aluminosilicate anions causes the appearance of phases mixture for nitric and hydrofluoric acids in high surfactant:silicon molar ratios. These results show that the mesophase formation might be the product of competition reactions involving the surfactant, silicate anions and the acid anions present in the reaction mixture. There seems to be a compromise between silicate and aluminosilicate charge density and basicity on the process of assembling and polymerizing (alumino)silicates species on CTA+ arrangements. Charge density is likely to direct the choice of species that are drawn to the organo-inorganic interface: the highly charged silicate species or the aluminosilicate ones are the first assembled. The polymerization process affects the basicity of species, turning them more or less capable of competing with acid anions for the CTA+ molecules. When acid anions bind more effectively with CTA+, they displace silicate or aluminosilicate species and might remain in the solid as contaminating phases. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Influence of inorganic anions; Liquid crystals; Mesoporous materials; Molecular sieves; Supramolecular assemblies; Surfactants

* Corresponding author. Tel.: +55-19-788-3095; fax: +55-19-788-3023. E-mail address: [email protected] (H.O. Pastore) 1387-1811/99/$ – see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S1 3 8 7 -1 8 1 1 ( 9 9 ) 0 0 10 8 - 0

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1. Introduction The initial reports [1–3] on the syntheses and characterization of mesoporous molecular sieves, the M41S family, indicated that, while using the same surfactant (cetyltrimethylammonium bromide, CTAB), the nature of mesophases obtained depended upon the surfactant:silicon molar ratio (CTA/Si). Thus, MCM-41, with a hexagonal arrangement of monodimensional tubes, appears when the CTA/Si molar ratio is lower than 1.0. The cubic mesophase, tridimensional MCM-48, is obtained when CTA/Si is within 1.0 and 1.5, while for CTA/Si between 1.2 and 2.0, a layered phase, later called MCM-50, is observed. It has also been shown [4,5] that by maintaining very low CTA/Si, typically between 0.06 and 0.12, it is possible to obtain all three mesophases by varying the pH (basic or highly acidic), and the nature and shape of surfactant molecules. In that sense, surfactant molecules with one or two hydrophobic tails on nitrogen atom or two nitrogen atoms bound through a (CH ) spacer were 2n studied. Using sodium silicate and HF, only one mesophase could be obtained in any CTAB/Si molar ratio from 0.5 to 2.0 [6 ], contrary to what had been previously reported [1–3]. Until that moment, however, attempts were not made to evaluate effectively the influence of silicate precursor basicity and hapticity upon maintenance, nature and stability of mesophases, even though some of the reports [4,5] comment on precursor basicity based on pK values. The role played by a anions different from bromide, chloride or sulphate remains not evaluated as well. The multidentate character of [(TMA)SiO ] has been elegantly 2.5 8 studied by Firouzi et al. [7] using several physical techniques and they introduced the concept of silicatropic liquid crystals. This paper shows that by using certain acids to lower the pH of a silicate solution, in the place of sulphuric acid, as in the previous reports [1], it is possible to obtain the same mesophase all through the range of CTA/Si molar ratio, even though one expects other mesophases to appear. The influence of precursor hapticity on the maintenance of meso-

phases in the presence of other anions is also investigated.

2. Experimental section 2.1. Syntheses Reaction mixtures were prepared by dissolving the required amount of either sodium silicate ( Vetec, 25.90 wt.% SiO , 26.59 wt.% Na O, 2 2 47.26 wt.% H O, Na/Si=2.0) or [(TMA)SiO ] · 2 2.5 8 xH O, x=35–50, TMA/Si=1.00–1.05 (by thermo2 gravimetric analysis), prepared in the laboratory by procedures already reported [8], in distilled water to give a 1.5 mol l−1 solution. To this clear solution, a 33 wt.% aqueous suspension of cetyltrimethylammonium bromide, aged for 12 h at room temperature, was added. The mixture was stirred for 30 min and the pH was slowly lowered from 13.40–13.60 (for sodium silicate) or from 12.6– 12.5 (for tetramethylammonium silicate) to 10.80– 10.90 with the addition of 48.0 wt.% hydrofluoric, 99.7 wt.% acetic, 37.0 wt.% hydrochloric, 57.0 wt.% hydroiodic or 63.0 wt.% nitric acid. HCl, HF, CH COOH (HOAc) and HNO , from Merck, 3 3 were used as received. HI, also from Merck, was distilled in the presence of hypophosphoric acid, under argon and in the absence of light, to eliminate I [9]. The suspension was then stirred for 2 4 h at 347–349 K. The final gel compositions were SiO · x(CTA) O · 100H O, where x was calculated 2 2 2 in order to obtain CTA+/Si4+ molar ratios of 0.5, 1.0, 1.5, and 2.0. In the preparation of aluminosilicates, aluminium isopropoxide (Alfa Æsar, 99.999%) was added before the CTABr suspension. The final composition of the reaction mixture was 60SiO · Al O · x(CTA) O · 6000H O, 2 2 3 2 2 where x was adjusted to give CTA/Si=0.5, 1.0, 1.5 and 2.0. For the preparartion of aluminosilicates, the source of silicon was the tetramethylammonium silicate. Half of the total reaction mixture volume was transferred to a Teflon-lined acid digestion bomb and placed in an oven pre-heated to 423 K, for a period of 66 h. The other half of the reaction mixture was filtered and thoroughly washed with distilled water (minimum 3 l or until foaming stops). These samples are referred to as

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precursors or P. After the hydrothermal treatment, the samples were isolated by washing, as described for the P samples, and named 00. All of them were air dried, sieved to 200 mesh and stored in a desiccator over a saturated CaCl solution. To 2 eliminate the organic part from these materials a solvent extraction was performed in a Soxhlet system with a 0.15 mol l−1 HCl solution in 50/50 ethanol/heptane, at 353 K. Twelve discharges over 1 week were enough to obtain the inorganic matrix free of organics as indicated by thermogravimetric analysis. The samples were also calcined by heating from room temperature to 773 K with a rate of 1 K min−1, under dry argon and then maintained at that temperature for 6 h under dry oxygen. 2.2. Techniques 2.2.1. Powder X-ray diffraction (PXRD) Samples were analysed as hand-pressed wafers, except for the precursor and as-synthesized samples, obtained with HI, P and 00 samples, respectively. These were spread over a thin layer of vacuum grease to avoid effects from preferential orientation. The equipment used was a Shimadzu ˚ , at 35 kV XD3, using Cu Ka radiation (1.54 A and 25 mA, with a scan rate of 2° 2h min−1. 2.2.2. Small-angle X-ray scattering (SAXS) Measurements were made using a Kratky camera, 70 mm slit, a conventional radiation generator equipped with a copper tube operating at 40 kV and 30 mA, both from Rigaku. The scattering profiles were registered by a sensitive position detector. Cu Ka radiation was filtered with a nickel filter and an electronic X-ray energy selection. The sample–detector distance was 46 cm with a 12 mm size of the X-ray spot on the sample. The profiles were normalized by the counting time and no further corrections were made. 2.2.3. Thermogravimetry (TGA) and differential thermogravimetric analyses (DTGA) Samples were heated under argon, at a rate of 20 K min−1 from room temperature to 1273 K, the equipment used was a TA Instruments Hi-Res TGA 2950 thermogravimetric analyser.

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2.2.4. Differential scanning Calorimetry Samples were analysed in a Thermal Analyst 200, TA Instruments, with a DSC 910 module, from Du Pont Instruments, from 303 to 773K, at a heating rate of 20K min−1, in an aluminium pan. 2.2.5. Liquid-state 29Si nuclear magnetic resonance (29Si NMR) Aqueous 1.5 mol l−1 sodium silicate and tetramethylammonium silicate were analysed as well as the liquid part of these solutions after the addition of a 33 wt.% aqueous solution of CTAB (CTA+/Si=1.0), in the presence or absence of aluminium isopropoxide in varied concentrations. The equipment used was a 7.05T Bruker AC300/P at 59.68 MHz with inverse decoupling, without nuclear Overhouser effect to allow integration, acquisition time of 0.688 s, recycle delay of 60 s, 90° flip angle, 32 K data points were used and a line broadening of 10. 2.2.6. Elemental analyses The samples were analysed for silicon, aluminium, bromide, iodide and chloride by energydispersive X-ray fluorescence in a Tracor X-ray Spectrace 5000, and compared with calibration curves for each of these elements. The analyses were performed under vacuum with radiation generated at 15 kV and 0.05 mA, and filtered with cellulose. Fluoride was determined with a selective electrode Orion model 96-09 (combined) on the residue of the extraction. The analysis of nitrate was performed with the cadmium method [10]. The samples were dissolved in HF (48 wt.%, Merk) and the nitrate reduced to nitrite in a cadmium metal column. The nitrite was analysed by UV– vis spectroscopy at 538 nm after the addition of sulphanilamide-hydrochloric acid and N1-naphthylethylenediamine dihydrochloride which forms an azo dye absorbing at that wavelength.

3. Results The samples obtained, syntheses conditions and mesophases isolated are listed in Tables 1 and 2. The overall chemical analysis of as-synthesized samples are given in Tables 3–5. Typical powder

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Table 1 Mesophases obtained from pure silica sources with CTA/Si from 0.5 to 2.0a Source

Acid

P

00

01

Sodium Silicate

HF, HCl, HOAc HNO 3 HI

MCM-41 MCM-41 Mixture

MCM-41 Magadiite Mixture

MCM-41 Magadiite Magadiite

TMA Silicate

HF, HCl, HOAc and HNO 3 HI

MCM-41 Mixture

MCM-41 Mixture

MCM-41 MCM-41

a TMA=tetramethylammonium; P=samples obtained after 4 h at 347–349 K; 00=samples after hydrothermal treatment; 01= samples where the organic part has been removed; mixture=mixture of phases composed of the layered surfactant and an unidentified silicate.

Table 2 Mesophases obtained from aluminosilicates with CTA/Si from 0.5 to 2.0a CTA/Si

Acid

P

00

01

0.5

HF, HCl, HOAc and HNO 3 HI

MCM-41 Mixture

MCM-41 Mixture

MCM-41 MCM-41

1.0

HF, HNO 3 HCl HOAc HI

MCM-41 Tubes MCM-41 Mixture

Tubesb Tubes MCM-41 Mixture

Tubes Tubes MCM-41 MCM-41

1.5

HF HCl, HOAc HNO 3 HI

Mixture Tubes MCM-41 Mixture

Mixture MCM-41 Tubes Mixture

MCM-41 MCM-41 Tubes MCM-41

2.0

HF, HNO 3 HCl HOAc HI

Mixture MCM-41 MCM-41 Mixture

Tubes Tubes MCM-41 Mixture

Tubes Tubes MCM-41 MCM-41

a See footnote to Table 1. b Tubes=monodimensional rods, non-organized in a hexagonal arrangement, as mentioned by Chen et al. [11].

X-ray diffraction and scattering at small angles for the samples prepared in this work are presented in Figs. 1–3. The first point to mention is that, when using the same acid to promote silicate polymerization, namely HCl, HI, HNO , HF or HOAc, the silica 3 mesophases obtained are the same, regardless of the CTA+/Si4+ molar ratio. This is not true for aluminosilicates, where at CTA/Si=2.0, for instance, and with the use of nitric or hydrofluoric acids, a mixture of phases is obtained while for the other CTA/Si molar ratios and the same acids, MCM-41 is the observed mesophase. With nitric

acid and sodium silicate, phase transitions do occur on hydrothermal treatment. For HCl and HOAc, the samples are always MCM-41, regardless of the silicon source, CTA/Si molar ratio and composition of the inorganic part in the reaction. The surfactant retained in the pores of silica mesophases after hydrothermal treatment for MCM-41, non-organized tubes or magadiite is usually between 6 and 20 mol.% of the silicon present, again, independently of initial CTA/Si molar ratio and the acid used (see CTA/Si in Tables 3 and 4).

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Table 3 Elemental analyses of silicates prepared from sodium silicatea %SiO

2

%CTA( T )

%CTA(S)

%CTABr

%CTAX

CTA/Si

HI 0.5 1.0 1.5 2.0

8.46 6.09 3.84 3.45

91.8 94.38 96.17 96.56

77.72 87.27 92.37 94.13

0.02 0.08 0.08 0.39

14.06 7.03 3.72 2.04

1.94 3.03 5.08 5.76

HF 0.5 1.0 1.5 2.0

50.77 53.84 50.02 56.93

39.67 37.39 40.66 31.35

39.67 37.30 37.87 22.89

– – 2.64 8.20

– 0.09 0.15 0.26

0.16 0.15 0.16 0.08

HCl 0.5 1.0 1.5 2.0

56.46 58.89 45.24 58.24

33.58 35.26 43.36 33.08

28.58 33.54 42.07 30.74

– – 0.33 0.25

5.00 1.72 0.96 2.09

0.11 0.12 0.20 0.11

HOAc 0.5 1.0 1.5 2.0

55.58 62.54 70.67 67.14

36.59 31.27 25.05 26.86

36.59 31.27 25.05 21.07

– – – 5.79

na na na na

0.14 0.11 0.07 0.07

HNO 3 0.5 1.0 1.5 2.0

66.27 71.33 90.87 60.47

20.33 23.37 4.87 32.90

20.33 23.37 4.87 32.90

– – – –

0.83 – – –

0.06 0.07 0.01 0.12

a CTA(T )=CTA(S)+CTABr+CTAX, CTA(S )=CTA+ in the solid, CTA/Si=molar ratio in the solid after hydrothermal crystallization, X=F−, OAc−, Cl−, NO− I −; na=not analysed. 3

When HI is used, with silicic or aluminosilicic gels, after thermal treatment at 347–349 K or 423 K, a mixture of phases composed of the layered surfactant mesophases, CTAI and CTABr, and a very small amount, usually 3.0 to 14.5% of an unidentified silicate is obtained independently of silicon source (Fig. 1(c) and (d)). The removal of the organic part by solvent extraction or by calcination in these HI-prepared phases, yields different phases for the two starting materials: sodium silicate affords magadiite (Fig. 1(g)), probably aided by the massive presence of sodium (Na/Si=2.0), while the tetramethylammonium silicate yields MCM-41 (Fig. 2(d)). In all the compositions, the HI-prepared samples show CTA/Si molar ratios higher than the unit in the samples after hydrothermal treatment ( Tables 3–5). Nitric acid affords MCM-41 in any step of the

synthesis procedure when the starting material is the tetramethylammonium silicate. However, for sodium silicate, the reaction gives MCM-41 as a precursor sample (Fig. 2(c)) and intercalated magadiite ( Fig. 1(e)) as the product after hydrothermal treatment; the removal of organics causes the collapse of the expanded structure yielding H,Na-magadiite ( Fig. 1(f ))

4. Discussion Since the different phases were observed only after mild thermal treatment in silicate and aluminosilicate systems, with a variety of acids and at different CTA/Si molar ratios, it seems necessary to understand the organic–inorganic assemblage

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Table 4 Elemental analyses of silicates prepared from tetramethylammonium silicatea %SiO

2

%CTA( T )

%CTA(S)

%CTABr

%CTAX

CTA/Si

HI 0.5 1.0 1.5 2.0

13.61 5.39 3.90 5.06

82.93 92.54 94.70 93.37

75.64 88.37 92.08 90.33

0.23 0.90 1.01 1.34

10.34 5.08 2.65 2.89

1.17 3.46 4.99 3.77

HF 0.5 1.0 1.5 2.0

49.62 50.87 58.45 56.34

45.16 44.72 38.31 39.60

45.16 43.69 38.26 38.89

– 0.40 0.06 –

– 0.05 – 0.05

0.19 0.18 0.14 0.15

HCl 0.5 1.0 1.5 2.0

51.88 57.57 53.89 52.06

41.44 37.32 38.43 42.54

40.02 35.58 36.32 41.20

– – – 0.44

1.60 1.96 2.36 1.12

0.16 0.13 0.14 0.17

HOAc 0.5 1.0 1.5 2.0

50.62 53.80 56.45 50.72

32.00 42.18 37.00 37.03

31.87 42.10 37.00 36.87

0.18 0.11 – 0.21

HNO 3 0.5 1.0 1.5 2.0

53.10 53.27 50.42 57.76

41.52 38.80 43.76 33.76

39.62 37.72 41.36 33.55

1.84 0.85 3.07 0.27

na na na na 0.56 0.50 0.003 0.003

0.13 0.17 0.14 0.15 0.16 0.15 0.17 0.12

a See footnote to Table 3.

under each reaction condition that leads, finally, to the mesoporous materials. 4.1. Formation of organic supermolecular assemblies and the role of counterions The molecular description of surfactant organization is based on the concept of the local effective parameter, v/a l [12,13], which describes the rela0c tion between the total volume of the hydrocarbon core, v, and the volume of a cylinder with the area of the polar head, a , and the height of the 0 hydrophobic tail, also known as the critical length, l , roughly equal, but less than, the fully extended c length of the hydrocarbon chain. When v and a l are the same, the lamellar mesophase will be 0c favoured over any other curved surface, because the volume of the hydrophobic chain is exactly

described by the product of the polar area times the length of the extended, or almost extended, hydrocarbon chain. When the surfactant molecule is defined, l is c constant and only a and v are variable parameters. 0 The area of the polar head, a , can be freely varied 0 through the change in the nature of the surfactant counterion. The polar head area, a , is defined, to a large 0 extent, by the interaction of the polar head with the anions, in the case of cationic surfactants [12– 15]. When the anion effectively compensates the polar head positive charge, a diminishes and the 0 hydrophilic parts of the molecules are allowed to approach each other, yielding flat surfaces and layered organic mesophases. On the other hand, when the anion does not interact as effectively with the cationic polar head, the repulsive effects

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H.O. Pastore et al. / Microporous and Mesoporous Materials 32 (1999) 211–228 Table 5 Elemental analyses of aluminosilicates prepared from tetramethylammonium silicate SiO

2

Al O 2 3

CTA(T )a

CTA(S )b

CTABr

CTAXe

SARc

CTA/Sid

15.01 10.75 4.55 2.62

88.2 37.1 37.3 31.4

1.01 1.67 2.64 3.78

39.0 77.2 27.3 72.7

0.14 0.08 0.60 0.08

2.60 1.17 5.98 10.01

36.3 95.3 43.2 22.4

0.13 0.13 0.15 0.09

HI 0.5 1.0 1.5 2.0

14.52 10.17 6.89 5.30

0.28 0.45 0.31 0.29

80.54 85.87 91.14 93.47

70.06 77.80 86.30 89.75

0.21 0.86 2.19 2.23

HF 0.5 1.0 1.5 2.0

55.38 67.33 22.19 66.40

2.41 1.48 1.38 1.55

36.99 28.86 74.66 29.79

36.83 26.76 62.99 25.71

0.14 0.68 13.39 1.58

HCl 0.5 1.0 1.5 2.0

53.09 58.38 44.35 61.35

2.48 1.04 1.74 4.65

37.31 37.73 47.06 29.58

33.64 35.57 30.60 19.19

1.73 1.43 14.28 1.91

HNO 3 0.5 1.0 1.5 2.0

53.92 60.30 52.74 68.62

3.96 2.26 1.27 1.28

36.80 28.96 45.81 27.50

36.80 27.80 38.41 27.28

– 1.49 7.48 0.29

na na na na

23.1 45.0 70.5 91.0

0.21 0.10 0.15 0.08

HOAc 0.5 1.0 1.5 2.0

55.75 56.78 65.71 55.83

2.13 1.60 2.11 2.27

39.41 32.49 30.79 37.65

38.27 30.96 29.91 26.55

1.45 1.96 1.14 14.22

na na na na

44.3 60.0 52.8 41.7

0.14 0.12 0.10 0.10

0.061 0.11 0.05 0.20

a CTA(T )=CTA(S)+CTABr+CTAX. b CTA(S)=CTA+ in the solid after hydrothermal treatment. c SAR=SiO /Al O 2 2 3 d CTA/Si=molar ratio in the solid after hydrothermal treatment. e X=F−, OAc−, Cl−, NO− I −; na=not analysed. 3

on the hydrophilic part are important, making a 0 large and forcing the polar heads apart. This would favour curved surfaces and hexagonal or cubic mesophases. Israelachvili et al. [12] mentioned that the surface repulsive terms are not amenable to a rigorous analysis owing to the many terms and interactions involved. A phenomenological approach was, however, attempted by Tanford [14,15] who showed that surface repulsive forces, dependent on a , 0 would arise from a double layer of charge similar to a capacitor. The surfactant counterions would be found in the space between the capacitor planes. Having defined a surfactant cation, the variation of concentration and temperature might cause

mesophase transition [16 ]; however, mixtures of cationic and anionic surfactant [17] or of an ionic surfactant and a long-chain alcohol [18] might cause the appearance of lamellar aggregates even in low concentrations, where only hexagonal phases would be expected. Some surfactant molecules in aqueous solution are transformed from micelles to lamellar arrays in the presence of high slat concentrations [19]. This aspect was shown by Sein and Engberts [20] where sodium dodecylbenzenesulphonate micelles transform to lamellar aggregates upon the addition of salts whose cations exchange for Na+ in NaDoBS. Blackmore and Tiddy [21] have shown that the

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Fig. 1. Representative powder X-ray diffractograms of (a) CTABr, Aldrich, analysed as received, (b) CTAI prepared by neutralization of CTAOH by HI, (c) mixture of phases prepared with tetramethylammonium silicate, HI, CTA/Si=2.0, as-synthesized (sample 00), (d ) mixture of phases, sodium silicate, HI, CTA/Si=1.0, as-synthesized (sample 00), (e) CTAintercalated magadiite, sodium silicate, HNO , CTA/Si=0.5, 3 as-synthesized (sample 00), (f ) magadiite obtained from the organic extraction of sample (e) (sample 01), and (g) magadiite obtained from the organic extraction of sample (d ) (sample 01).

counterion binding influences the nature of the LC mesophase formed through the increase or decrease of the surfactant polar head area, a . 0 Thus iodide ions favour lamellar mesophases while bromide or chloride ions induce a change to rodshaped micelles. In the case of complex reaction mixtures, where more than one counterion is present, some other aspects of liquid crystal chemistry have to be taken into account: surfactant counterions might be exchanged by others if the interaction with the entering counterion is favoured. This preference is described by the specificity or exchange constants, K [22,23]. Table 6 displays the K values for ex ex ordinary anions. The order of K is also the order of decrease ex in a , i.e. the more strongly or the more specific is 0

Fig. 2. Representative powder X-ray diffractograms of (a) silica MCM-41, from sodium silicate, HOAc, CTA/Si=0.5, precursor (sample P), (b) silica MCM-41, from tetramethylammonium silicate, HF, CTA/Si=0.5, as-synthesized (sample 00), (c) silica MCM-41, from sodium silicate, HNO , precursor, CTA/Si= 3 0.5 (sample P), and (d) silica MCM-41 obtained from organics extraction from the sample of Fig. 1(b) (sample 01).

Fig. 3. Powder X-ray diffractograms of aluminosilicates: (a) HF, CTA/Si=0.5, calcined (sample 01); (b) HOAc, CTA/Si= 1.0, as-synthesized (sample 00); (c) HNO , CTA/Si=1.0, 3 as-synthesized (sample 00)

H.O. Pastore et al. / Microporous and Mesoporous Materials 32 (1999) 211–228 Table 6 Specificity constants X−OCTAX+Br−

for

the

reaction:

219

CTABr+

X−

KX ex, Br

F− Cl− OAc− NO− 3 I−

0.044 0.098 0.20 1.10 5.60

the interaction of a counterion with the surfactant molecule, the smaller is a and the more favoured 0 is a flat surface. The opposite is also valid: less specific counterions favour curved surfaces and therefore the rod-shaped micelles or mesophases. Firouzi et al. [24] have shown that, under reaction conditions where silicate polymerization is avoided, the cubic octamer, Si O8− , is a 8 20 very specific anion, reducing a and producing a 0 lamellar organic–inorganic composite that precipitates. However, the influence of the presence of other anions besides chloride or bromide, as well as the use of aluminosilicate, on the (alumino)silicate mesophase formation is not yet clear. Other than the work by Firouzi et al. [24], no work has been reported on the dynamics of anion exchange on the hydrophobic–hydrophilic interface and the influence of (alumino)silicate polymerization on the inorganic mesophases formed. 4.2. Sodium silicate as source of silicon Table 1 shows that, when the synthesis is performed with sodium silicate as silicon source, the use of HF (Fig. 2(b)), HCl or HOAc (Fig. 2(a)) yields good quality MCM-41, regardless of the CTA/Si molar ratio used in the range of 0.5 to 2.0. Fig. 4(a) shows the solution 29Si NMR of a 1.5 mol l−1 sodium silicate solution, at pH= 13.40–13.60, Na/Si molar ratio of 2.0. The silicon species present are the monomer (Q0, −71.2 ppm), dimer (Q1Q1, −79.1 ppm), linear and cyclic trimers (Q1Q2Q1, Q1 at −78.7 ppm, Q2 at −87 ppm and Q2 , at −80.9 ppm), linear and cyclic tetra3 mers (Q1Q2Q , Q1 at −78.7 ppm, Q2 at 2 1

Fig. 4. 29Si NMR of (a) 1.5 mol l−1 sodium silicate solution, Na O/SiO =1.0, (b) solution in (a) after addition of a CTAB 2 2 33 wt.% suspension, CTA/Si=1.0. The rising baseline above −100 ppm is due to the NMR glass tube.

−87.2 ppm and Q2 at −86.7 ppm), and trigonal 4 prism (Q3 at −88.8 ppm) [25]. 6 The addition of the CTABr suspension, at CTA/Si=1.0, at this pH, does not cause extensive solid formation. The 29Si NMR spectrum of the solution, Fig. 4(b), indicates that there is no strong preference for precipitation of any particular species. Species Q1 and Q2 are those whose intensities diminish in solution, probably because of the small uptake of dimer and linear trimer and tetramer (Table 7). Small silicate species do not fully neutralize the CTA+ polar head, so there is still some electrostatic repulsion between polar heads, which try to be as far apart as possible (see Section 4.1), and favour hexagonal arrangements. The pH adjustment to 10.8–10.9 with acetic, hydrofluoric and hydrochloric acids causes the polymerization of silicate species entrapping CTA+ in the same hexagonal mesostructure previously existing. When nitric acid is used, MCM-41 is obtained only after mild thermal treatment, in sample P ( Fig. 2(c)). After hydrothermal crystallization the product is CTA+-intercalated magadiite [26 ], independent of the CTA/Si molar ratio used in the reaction. Table 6 [22,23] indicates that nitrate binds strongly to the CTA+ micelles, displacing bromide. If the model discussed above, involving competition and displacement of one anion by another, can be applied to the system under study, competition is settled between nitrate and silicate anions by CTA+. Bromide anions, even when in excess, at CTA/Si=1.5 and 2.0, are not capable of

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Table 7 Silicate species from sodium silicate as indicated by 29Si NMR Solution

(a) Sodium silicate, 1.5 mol l−1, Na/Si=2.0 (b)+CTABr, CTA/Si=1.0

Species

Percentage Proportiona Percentage Proportion

Q3 6

Q2+Q1

Q0

30 1 35 1

42 2 34 1

28 1 31 1

a Normalized to the percentage of monomer.

displacing nitrate and probably nor silicates. Thus, in the precursor sample the silicate species bound to CTA+ are interspaced by nitrate anions in the micelles, creating a heterogeneous interface. The presence of these nitrate ions bound to CTA+ makes it difficult for the silicate anions to polymerize. Thus, when the precursors samples are extracted, they collapse. This lack of extensive CTA-directed polymerization, in the presence of Na+ even at pH 10.8, allows the reconstruction of the silicate part to yield CTA+-magadiite. During the hydrothermal crystallization, that is with the higher temperature, the silicate polymerization is reinforced and the lower oligomers are neutralized by CTA+ and by Na+. These Na+ are in a 2:1 molar ratio in relation to silicon (Na/Si molar ratio of 2.0) and direct the polymerization to magadiite while CTA+ ions act only as spacers between layers. Upon extraction or calcination, the organic part is eliminated and the material turns to H,Na-magadiite (Fig. 1(f )). With hydroiodic acid and sodium silicate, one obtains, after mild thermal treatment, the mixture of the lamellar phases of CTAI and CTABr, and a small amount of silicate. Iodide ion displaces bromide more efficiently than nitrate ion (see Table 6) and is probably capable, as well, of displacing small silicate anions. This can explain why the yield in siliceous material obtained by these procedures, is low. CTAI has low solubility in water, so remains precipitated in the samples, after either mild thermal or hydrothermal treatment. The nature of the siliceous phase is revealed only after the surfactant extraction or calcination. In these cases, the product is magadiite, but it is not possible to indicate the prior formation of an

intercalated material, as was observed with nitric acid. 4.3. Tetramethylammonium silicate as source of silicon All the processes in the organic–inorganic interface change when the silicon source is tetramethylammonium silicate. The 29Si NMR of a 1.5 mol l−1 aqueous solution of this silicon source, with TMA/Si molar ratio of 1.0, in pH 12.4–12.6, in the absence of added stabilizers, is shown in Fig. 5(a). The species formed in this solution are the same as for sodium silicate with the addition of the cubic octamer, Q3 , at −99.8 ppm [25,26 ]. 8 The addition of a 33 wt.% aqueous suspension of CTABr, with CTA/Si=1.0, causes the immediate precipitation of a white solid. The solution 29Si NMR of the supernatant solution, Fig. 5(b), indicates that the cubic octamer is precipitated preferentially together with approximately 20% Q3 and 27% of species Q1 and Q2, remaining in 6 solution, mainly the monomer ( Table 8).

Fig. 5. 29Si NMR of (a) a 1.5 mol l−1 tetramethylammonium silicate solution ( TMA/Si=1.0) without additives, and (b) solution in (a) after addition of a CTABr 33 wt.% suspension, CTA/Si=1.0.

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H.O. Pastore et al. / Microporous and Mesoporous Materials 32 (1999) 211–228 Table 8 Silicate species from tetramethylammonium silicate as indicated by 29Si NMR Solution

(a) Tetramethylammonium silicate, 1.5 mol l−1, TMA/Si=1.0 (b)+CTABr, CTA/Si=1,0

Species

Percentage Proportiona Percentage Proportion

Q3 8

Q3 6

Q2+Q1

Q0

50 3 0 0

15 1 12 0.1

19 1 14 0.2

16 1 74 1

a Normalized to the percentage of monomer.

The pK values of solution species indicate that a the higher oligomers, Q3 and Q3 , are mainly 8 6 unprotonated in the pH of the reaction, their pK is around 6.5 [27], while the monomer and a dimer, with pK of 9.5 and 10.7, respectively, are a partially protonated. The silicate interaction with CTA+ presents a strong ionic character, so the preferred interaction of the double rings, with a higher charge density, with the organic arrangement is not unexpected. Fig. 6 shows that these species appear in the solid, either in lower ( Fig. 6(a)) or higher (Fig. 6(b)) CTA+ concentration. The fact that smaller species are not evident in the spectrum of solid is probably due to their low concentration in the solid when compared with D4R and D3R. The addition of HF, HOAc or HCl accelerates polymerization and MCM-41 is obtained after

hydrothermal crystallization, organics extraction or calcination of these samples. Another difference between the system prepared with tetramethylammonium silicate and the sodium silicate one appears in the use of nitric acid. When the pH is adjusted with this acid, the final product, sample 00, is MCM-41 and not magadiite, as previously observed. This is attributed to the absence of Na+, which would favour magadiite, and to the fact that the species preferentially precipitated are polidentated ones that display the same type of stabilization as quelate ligands [28]. The samples P and 00 obtained with HI and tetramethylammonium silicate resemble very closely those obtained with sodium silicate and HI Fig. 1(c) and (d)). These results indicate that, even when the interaction between the inorganic phase

Fig. 6. 29Si MAS NMR of the solids obtained from addition of a 33 wt.% CTABr suspension to the 1.5 mol l−1 tetramethylammonium silicate solution ( TMA/Si=1.0), with (a) CTA/Si=1.0, and (b) CTA/Si=2.0. The negative peak, marked with an asterisk is the centre of the frequency range measured.

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and the CTA+ assemblies is strong ( Table 6), the I − anion is able to displace the silicon species, yielding CTAI and an unidentified silicate. The synthesis from aluminosilicate systems The introduction of aluminium in this system causes a series of modifications that are more or less important depending upon the amount of aluminium added. The only aluminium species present at pH 12.4– 12.6 is Al(OH )− [29] which, as an anion, will 4 probably react faster with species with lower charge density, i.e. the dimer. The monomer at that pH has a charge density of –2, SiO (OH )2− . 2 2 Since more polymerized species have lower pK a values, the linear and cyclic trimer [30] would be partially protonated and could also react with aluminium. Thus, these small polymeric species react preferentially with Al(OH )− to yield alumi4 nosilicate anions [29]. The more polymerized species, D4R and D3R, and the monomer, Q0, have lower probability of reaction. Fig. 7(a), (c) and (e) shows the 29Si NMR spectra of aqueous 1.5 mol l−1 tetramethylammonium silicate where aluminium isopropoxide was added to obtain SiO /Al O ratios of 20, 60 and 2 2 3 120 in the solution. No solid formation was observed. The general observation is that the aluminium addition causes enlargement of the lines attributed to monomer, dimer, trimers and tetramers; the peak assigned to the cubic octamer remains reasonably unchanged. The substitution of one aluminium ion in any of these species would generate one new signal, 5 ppm to the lower field of the unsubstituted peak [25]. This was only observed when SiO /Al O =20 ( Fig. 7(a)) for the cubic octamer 2 2 3 signal: a very weak signal was observed at −93 ppm. The enlargement of peaks and the absence of definite peaks for Al-substituted species indicate that silicon exchange between species might be very fast [29]. The addition of a 33 wt.% aqueous suspension of CTABr to these solutions, with varied SiO /Al O molar ratios, keeping CTA/Si=1.0, 2 2 3 causes again the immediate formation of a white solid. Fig. 7(b), (d ) and (f ) show the 29Si NMR

of the solutions after the solid has been filtered off. These solution composition in terms of siliceous species varies according to the concentration of aluminium, as shown in Table 9. When SiO /Al O is 120, in the lowest alumin2 2 3 ium concentration, Fig. 7(f ), all siliceous species are taken in the solid, none of them quantitatively. Even the cubic octamer, which in the absence of aluminium is completely precipitated, remains in the solution as a residue. The organic–inorganic interface might be heavily populated and therefore not able to take the cubic octamer species completely. An increase in the aluminium concentration, at SiO /Al O =60, Fig. 7(d ), causes the quantitative 2 2 3 precipitation of the cubic octamer, trigonal prism and Q3 species. The Q1 and Q2 species, dimer, linear trimer and tetramer are also taken to the solid but not quantitatively; a part of these species remain in solution together with a part of monomer. A further increase in the aluminium relative concentration, at SiO /Al O =20, Fig. 7(b), pre2 2 3 cipitates all species, except part of the monomer, which remains in solution. Bearing in mind that the substitution of one silicon (IV ) ion by aluminium (III ) generates negative charge in the framework, and that the interaction of silicon species with CTA+ is strongly ionic, it is not unexpected that the higher the concentration of aluminium in the system, the more the oligomers are drawn to the organic– inorganic interface. Summarizing, the CTA+ supramolecular arrangement precipitates with siliceous species that have high charge density and/or with aluminosilicate species. Fig. 8 shows the 29Si MAS NMR of the solids obtained from solutions of tetramethylammonium silicate/aluminium isopropoxide with SiO / 2 Al O =60, and different amounts of CTABr to 2 3 afford CTA/Si=1.0 (Fig. 8(a)) and 2.0 (Fig. 8(b)). When the CTA/Si molar ratio is 2.0 (Fig. 8(b)), i.e. with an excess of CTA+, all species are taken into the solid, the cubic octamer and the trigonal prism, particularly, but also dimer, linear trimer and tetramer (ca. −80 ppm) and even a small amount of monomer (ca. −71 ppm). A reduction

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Fig. 7. 29Si NMR of supernatant solutions from the reactions of a 1.5 mol l−1 tetramethylammonium silicate solution with aluminium in different concentrations: (a) SiO /Al O =20; (b) sample from (a) after CTABr addition; (c) SiO /Al O =60; (d) sample from (c) 2 2 3 2 2 3 after CTABr addition; (e) SiO /Al O =120; (f ) sample from (e) after CTABr addition. 2 2 3

Table 9 Silicate species from tetramethylammonium silicate, with aluminium isopropoxide, before and after the addition of CTABr, as indicated by 29Si NMR Tetramethylammonium silicate solution, 1.5 mol l−1, TMA/Si=1.0

(a) SiO /Al O =20 2 2 3 (b)+CTABr, CTA/Si=1.0 (c) SiO /Al O =60 2 2 3 (d)+CTABr, CTA/Si=1.0 (e) SiO /Al O =120 2 2 3 (f )+CTABr, CTA/Si=1.0

a Normalized to the percentage of monomer.

Species Q3 8

Q3 6

Q2+Q1

Q0

Percentage Proportiona Percentage Proportion

34 2 0 0

23 2 0 0

29 2 0 0

14 1 100 1

Percentage Proportiona Percentage Proportion

53 4 0 0

19 1 0 0

15 1 34 0.5

13 1 66 1

Percentage Proportiona Percentage Proportion

63 9 6 0.1

15 2 7 0.2

15 2 41 0.9

7 1 46 1

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Fig. 8. 29Si MAS NMR of the solids obtained from addition of a 33 wt.% CTABr suspension on the 1.5 mol l−1 tetramethylammonium silicate solution (TMA/Si=1.0), SiO /Al O =60, with (a) CTA/Si=1.0, and (b) CTA/Si=2.0. 2 2 3

in the amount of CTA+, to CTA+/Si=1.0, Fig. 8(a), again causes the precipitation of cubic octamer, trigonal prism, and, in smaller amounts, also dimer, linear trimer and tetramer, which appear in the spectra at ca. −82 ppm. The comparison of Fig. 6(a) and Fig. 8(a) shows that substitution favours a better interaction of aluminosilicate oligomers with CTA+ than with pure silicate oligomers. After the assembling, it is possible that polymerization begins, since the interaction with the interface has collected the oligomers in a restricted environment. The polymerization of small aluminosilicate oligomers is fast; as they grow, the polymerization slows down [31]. Thus, at the interface the polymerization and retention of aluminium is fast and expressive, reducing charge density on silicate and aluminosilicate species. As charge density is reduced, less CTA+ is necessary to neutralize (alumino)silicate anions. When the pH is lowered to 10.8–10.9 there is protonation of dimer, particularly, but also monomer. The D4R and D3R, if still in solution, remain deprotonated. At that pH, the polymerization of interface species is again accelerated, aiding to entrap aluminium in the solid. The charge density on the inorganic species is even lowered and less CTA+ is needed to stabilize these species.

At this lower pH and later with mild heating, the cubic octamer begins to decompose [32,33], generating monomer, dimer and trimers that return to the solution. Since the presence of aluminium in these double ring is minimum, the solution is enriched in silicate species. These charge density decrease and polymerization processes explain why phase mixtures are not obtained at CTA/Si=0.5 in the aluminosilicate gels, with any of the acids: in that lowered surfactant concentration, all the organic part is necessary to keep the hexagonal arrangement and direct polymerization. Only when the acid used is HI does one observe phases mixtures and, even then, it is caused by the more favoured interaction of CTA+with iodide [22,23] and the fact that CTAI is only slightly soluble in water. This process is a true displacement of silicate species by iodide ions. At CTA/Si=2.0, the addition of nitric acid causes the formation of a phase mixture: the lamellar phase of surfactant and a non-organized aluminosilicate ( Table 2). Nitrate is an anion with a specificity constant of 1.3 ( Table 6) in relation to bromide, i.e. it binds more effectively with CTA+ than does bromide, displacing the anions that have not already been displaced by (alumino)silicate. The difference in the case of nitrate as compared with acetate or chloride is that it binds strongly to CTA+ and is probably not displaced

H.O. Pastore et al. / Microporous and Mesoporous Materials 32 (1999) 211–228

by the aluminosilicate that grows on the interface. Therefore, as discussed for sodium silicate, it generates a heterogeneous surface. Its presence might also hinder any polymerization of adjacent aluminosilicate units that are simultaneously on the interface, forcing them to react with species that are in solution which are the protonated monomer, dimer and trimers from double ring decomposition, and therefore richer in silicon. This CTA+ bound to nitrate is a neutral species and might be expelled from the organic–inorganic composite [22,23]. There is probably a synergistic effect in that aspect that favours polymerization of silicate when the surfactant is expelled from the organic– inorganic composite, and forces the CTA+ ions out of the organic arrangement with further polymerization. This effect of polymerization with solution species will probably increase the SiO /Al O , since, with the decomposition of cubic 2 2 3 octamers, it has been enriched in the siliceous species. The chemical analysis shows that, when phases mixtures are formed, the incorporation of silicon in the framework is higher ( Table 10). Thus, the SiO /Al O molar ratios for precursor samples, 2 2 3 which are mixtures, are ca. 50 while in pure hexagonal phases, where the CTA+ remains in the composite, this molar ratio is close to 30. Besides nitric acid, the other acid that produces phases mixture is hydrofluoric acid. The fluoride, unlike nitrate, is not efficient in displacing bromide from CTA+ ( Table 6), so its effect should operate in the inorganic phase. Fluoride ions are capable of binding to silicon, displacing O− [34]. If that really occurs, then the charge density of the growTable 10 SiO /Al O molar ratios in precursor samplesa 2 2 3 Acid

CTA/Si 0.5

HF HCl HNO 3

1.0

1.5

2.0

P

00

P

00

P

00

P

00

34

39

37

77

50

27

36

71

51 37 50

73 22 91

a The values for samples 00 were taken from Table 5.

225

ing inorganic chain diminishes without the need for extensive polymerization. For each SiO− converted to SiF, one CTA+ can be released to solution to bind to bromide and afford the phases mixture. This effect, with fluoride, is more important than that occurring for nitrate ions since it is already observed at a CTA/Si molar ratio of 1.5. In that case, the polymerization with solution species is accelerated with the release of surfactant and the SiO /Al O molar ratios are also close to 2 2 3 50 ( Table 10). The higher incorporation of aluminium in samples after mild thermal treatment was also observed by Holmes et al., who prepared gels with SiO /Al O =74, heated at 313, 323, 333, and 2 2 3 343 K, and obtained solids with SiO /Al O #30 2 2 3 [35]. All the polymerization and double ring decomposition described above are more important during the hydrothermal crystallization, although the outcome of the reaction is difficult to foresee based on these processes. This is reinforced by the behaviour of the SiO /Al O molar ratio after the 2 2 3 crystallization, as shown in Table 10: there are samples that incorporate more silicon and samples that release silicon to the solution. 4.5. Energetics of (alumino)silicate interaction The differential scanning calorimetry shows that the energetics of interaction of CTA+ with the precursors, purely silicic, from sodium and tetramethylammonium silicate, or aluminosilicic, is different. Fig. 9 shows the DSC profile of the silicate precursor prepared with tetramethylammonium silicate, with CTA/Si=1.5, before the addition of any acid. The curve shows two important endothermic events: one at 343.7 K due to water release and the other at 557.3 K assigned to organics decomposition. The profile is the same for all samples synthesized in this work with variations in the temperature where each event occurs and the enthalpy involved. The enthalpy of organics decomposition as a function of CTA/Si molar ratio in each synthesis, for silicates prepared with sodium and tetramethylammonium silicate and for aluminosilicate, is

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Fig. 9. Differential scanning calorimetry profile of the sample prepared from tetramethylammonium silicate and CTABr at CTA/Si=1.5.

plotted in Fig. 10. It is possible to observe three behaviours: for aluminosilicates at CTA/Si=0.11 and 0.5, region 1, for silicates prepared from sodium silicate at CTA/Si=1.5 and 2.0, region 3, and for silicates prepared from sodium and tetramethylammonium silicate at CTA/Si=0.11, 0.5

and 1.0 together with silicates prepared from tetramethylammonium silicate at CTA/Si≥1.0, region 2. These types of behaviour are limited by dashed lines in Fig. 10. For aluminosilicates at low CTA/Si molar ratios (region 1 in Fig. 10), the enthalpy involved in organics release is the lowest among all samples. The NMR discussion showed that the majority of silicate species in the solid at these low CTA/Si molar ratios are D4R and D3R, already polymerized and less basic. With the lower CTA+ concentration, the aluminosilicate is probably more polymerized than in the other samples, forming species that are less basic than all the others and therefore, bind weakly to CTA+. When the concentration of CTA+ is increased to CTA/Si≥1.0 (region 2 in Fig. 10), the species collected in the solid are, on the average, less polymerized than when CTA/Si is lower (see Fig. 8(b)). Less polymerized species are more basic, so the enthalpy involved in organics decomposition is higher. It is not possible to differentiate between the DH values for silicates prepared with tetramethylammonium silicate at CTA/Si=0.11–1.0 from the values for silicates and aluminosilicates prepared with CTA/Si≥1.0, region 2 in the graph of Fig. 10. In the absence of aluminium, at CTA/Si≤1.0, the species drawn to the solid are mainly D4R and D3R (see Fig. 6(a)) the polymerization of silicate is less extensive (as discussed before) and the species in the solid are of a more basic nature, on the average. For silicates prepared from sodium silicate (regions 2 and 3 in Fig. 10, empty squares), the presence of sodium ions has to be taken into account. Sodium ions neutralize charge from the silicate framework, aiding in keeping the precursors less polymerized and more basic, thus involving a higher enthalpy for organics release.

5. Conclusions Fig. 10. Enthalpy of organics release from solid samples as a function of the CTA/Si molar ratios used in the syntheses: %, silicates prepared from sodium silicate; +, silicates prepared from tetramethylammonium silicate; $, aluminosilicates.

A subtle compromise seems to exist between charge density and basicity on the process of assembling and polymerizing inorganic moieties

H.O. Pastore et al. / Microporous and Mesoporous Materials 32 (1999) 211–228

on the interface of CTA+ supramolecular arrangements. The first effect to take place is a reflex of charge density: the species drawn preferentially to the interface are the larger and more highly charged ones, D4R and D3R, and aluminosilicates when present, because of the higher charge density imposed by aluminium substitution. The second effect comes from the different basicity of each species: the larger ones are less basic and are weakly bound, particularly when the polymerization has initiated by the presence of aluminium or by the lower concentration of CTA+. When iodide is used, the effectiveness of its interaction with CTA+ surpasses that of any silicate species and therefore it displaces silicate anions from the majority of organic molecules yielding CTAI and a very small amount of hexagonal material. Anions such as nitrate, which bind to CTA+ more effectively than bromide, but are not as effective as iodide in displacing silicate, may hamper the polymerization of species simultaneously present in the interface; thus they react with solution species causing a variation of SiO /Al O molar ratio. 2 2 3 When the charge density has become small, either because the degree of polymerization has increased or because fluoride substitution on the framework has occurred, CTA+ ions are expelled from the composite and might interact with either bromide or anions from acids, generating mixtures of phases as a final solid product.

Acknowledgements The Fundac¸a˜o de Amparo a` Pesquisa no Estado de Sa˜o Paulo is gratefully acknowledged for the financial support to this work (Grant number 96/9900-7). This work was also supported, in its initial part, by the Fundo de Apoio ao Ensino e a` Pesquisa ( FAEP, UNICAMP). H.O.P. and M.M.R. acknowledge the Conselho Nacional de Desenvolvimento Cientı´fico e Tecnolo´gico (CNPq) for fellowships. The authors wish to express their gratitude to Drs. Dilson Cardoso, Frank Quina, and Pedro L. O. Volpe for very helpful discussions

227

and to Prof. Carol H. Collins for her careful reading of the manuscript.

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[31]

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