Langmuir 2003, 19, 8503-8510
8503
How Does ZrO2/Surfactant Mesophase Nucleate? Formation Mechanism F. Ne´,*,† F. Testard,† Th. Zemb,† and I. Grillo‡ DSM/DRECAM/SCM, CEA Saclay, Bat. 125, 91191 Gif sur Yvette, and DS/LSS, ILL, Bat. ILL 20, p 213, 6 rue Jules Horowitz, B.P. 156, 38042 Grenoble, France Received May 13, 2003. In Final Form: June 26, 2003 In situ time-resolved small-angle X-ray and neutron scattering have been used to investigate the mechanism of a bulk precipitation of a hexagonally ordered ZrO2/surfactant mesophase. Using hexadecyltrimethylammonium bromide (CTAB) as a structure-directing agent, the precipitation results from the addition of sulfate to an oxychloride zirconium/CTAB water solution. The precipitate obtained after a few seconds is organized in a 2D hexagonal network. There is no preexisting cylindrical micelle in the precursor solution, and the micelles act as a reservoir for monomer to feed the building grain. The precipitation occurs through a two-step mechanism: a random nucleation/growing process and a first-order reorganization from locally ordered cylinders to a hexagonal lattice in the grain at its final size.
Introduction 1
The mesoporous materials first synthesized in 1992 offer a significant potential in the field of catalysis, adsorption, and separation processes. Due to this potential, an interest in this field has increased in the last 10 years.2 The mesostructured materials are obtained by coprecipitation of an inorganic material (silica, aluminosilicate, or transition-metal oxides3) in an organic liquid crystal mesophase. The organic material is then calcined or washed to liberate the porous volume. The synthesis of such materials has been the subject of many mechanistic studies perfectly reviewed in two main review papers: the first one, by Ying et al.,4 concerns the publications until 1999, and the second one, by Patarin et al.,5 focuses on the advances since 1999. Beck and co-workers6 have initially proposed a liquid crystal templating (LCT) mechanism in which the surfactant liquid crystal acts as a template during polymerization. An interaction between silicate ions and surfactant molecules has been proposed in a cooperative template model3 (CTM) to complete the LCT mechanism. In the nucleation/growth mechanism7 proposed by Frasch and co-workers, colloidal silica “prepolymers” with a low degree of polymerization act as promoters. The silica prepolymers bind some free surfactants, and precipitation occurs when the silica polymers/ * To whom correspondence should be addressed. E-mail: ne@ drfmc.ceng.cea.fr. † CEA Saclay. ‡ ILL. (1) Kresge, C.; Leonowicz, M.; Roth, W.; Vartuli, J.; Beck, J. Nature 1992, 359, 710. (2) Schu¨th, F. Ordered mesoporous materials-state of the art and prospects; Studies in Surface Science and Catalysis 135; Elsevier: Amsterdam, 2001; p 1. (3) Monnier, A.; Schu¨th, F.; Huo, Q.; Kumar, D.; Margolese, D.; Maxwell, R. S.; Stucky, G. D.; Krishnamurty, M.; Petroff, P.; Firouzi, A.; Janicke, M.; Chmelka, B. F. Science 1993, 261, 1299. (4) Ying, J. Y.; Mehnert, C. P.; Wo,g, M. S. Angew Chem., Int. Ed. 1999, 38, 56. (5) Patarin, J.; Lebeau, B.; Zana, R. Curr. Opin. Colloid Interface Sci. 2002, 7, 107. (6) Beck, J. S.; Vartuli, J. C.; Roth, W. J.; Leonowicz, M. E.; Kresge, C. T.; Schmitt, K. D.; Chu, C.T-W, Olson, D. H.; Sheppared, E. W.; McCullen, S. B.; Higgins, J. B.; Schlenker, J. C. J. Am. Chem. Soc. 1992, 114, 10834. (7) Frasch, J.; Lebeau, B.; Soulard, M. Patarin, J.; Zana, R. Langmuir 2000, 16, 9049.
surfactant complexes reach a large size. In this mechanism the micelles act as a reservoir of monomers. The extrapolation of mechanisms established for silica to zirconia is not straightforward,8 and very few studies have been focused on zirconia mesostructrured materials.9 Ciesla et al.10 have proposed a templating mechanism by analogy with silica MCM-41. On the other hand, Knowles and Hudson11 consider the interaction between alkylamine and zirconia through a scaffolding phenomenon. Recently several papers have been focused on the mechanism of the formation of surfactant/silica12,13 or surfactant/zirconia14 films. Despite these studies on the mechanism of formation, it is still a matter of discussion, and few papers4,5,15,16 describe the very early stage of the formation of the bulky mesostructured materials. In a previous paper,17 we have shown that it is possible to characterize the early stage of the synthesis route proposed by Ciesla et al.10 by mixing a zirconium sulfate solution and a hexadecyltrimethylammonium bromide (CTAB) solution. We demonstrated by in situ small-angle X-ray scattering (SAXS) experiments that the 2D hexagonal mesostructure appears around 40 ms after the mixing. For the studied compositions, the reaction was too fast to analyze the transition from a micellar structure to a 2D hexagonal network. To follow the early stage of the formation of the zirconia/CTAB mesostructured material, the synthesis route has been modified to slow the precipitation. We mix a solution of zirconium oxy(8) Pacheco, G.; Zhao, E.; Sklyarov, A.; Fripiat, J. J. J. Mater. Chem. 1998, 8, 219. (9) Linden, M.; Blanchard, J.; Schacht, S.; Schunk, S. A.; Schu¨th, F. Chem. Mater. 1999, 11, 3002. (10) Ciesla, U.; Schacht, S.; Stucky, G.; Unger, K.; Schu¨th, F. Angew. Chem., Int. Ed. Engl. 1996, 35, 541 (11) Knowles, J. A.; Hudson, M. J. Chem. Commun. 1995, 2083 (12) Brennan, T.; Roser, S. J.; Mann, S.; Edler, K. J. Chem. Mater. 2002, 14, 4292. (13) Cagnol, F.; Grosso, D.; Soler-Illia, G. J.; Crepaldi, E. L.; Babonneau, F.; Amenitsch, H.; Sanchez, C. J. Mater. Chem. 2003, 13, 61. (14) Crepaldi, E. L.; Soler-Illia G. J. D. A.; Bouchara, A.; Grosso, D.; Durand, D.; Sanchez, C. Angew Chem., Int. Ed. 2003, 42, 347. (15) Sadasivan, S.; Fowler, C. E.; Khushalani, D.; Mann, S. Angew. Chem., Int. Ed. 2002, 41, 2151. (16) Ciesla, U.; Schu¨th, F. Microporous Mesoporous Mater. 1999, 27, 131-149. (17) Ne´, F.; Testard, F.; Zemb, Th.; Petit, J. M. ESRF Newsl. 1999, 33, 23.
10.1021/la034824g CCC: $25.00 © 2003 American Chemical Society Published on Web 09/03/2003
8504
Langmuir, Vol. 19, No. 20, 2003
chloride and CTAB with a solution of magnesium sulfate to obtain a 2D hexagonal mesostructure. In these conditions, the precipitation is visible on the macroscopic scale only after an induction period of a few seconds. This induction time allows the precipitation mechanism to be followed by in situ small-angle scattering experiments. However, as the characteristic time of our reaction is on the order of 1 s, it is essential to use a large instrument radiation beam (X-rays or neutrons) for reducing the acquisition time. Small-angle neutron scattering (SANS) and SAXS are complementary since SANS is mainly sensitive to the hydrogenated material while SAXS is more sensitive to the structure in the grain. The aim of this study is to investigate by in situ SAXS and SANS timeresolved experiments the transformation from zirconium and surfactant precursors to the final mesostructured network. Experimental Methods Materials. The following chemical products are used in the synthesis: zirconium oxychloride (ZrOCl2‚8H2O (OSI)), CTAB (Fluka), magnesium sulfate (Prolabo), and ammonium sulfate (Fluka). All chemicals are used as received. The water is purified using a Millipore apparatus (18.2 MΩ‚cm). Synthesis. Two precursor solutions are prepared. The first solution is obtained by dissolving CTAB (2.5 g, 6.8 mmol) and ZrOCl2‚8H2O (4.16 g, 13 mmol) in water (100 g). The second solution consists of MgSO4‚nH2O (3.25 g, 13 mmol) in water (15 g) or (NH4)2SO4‚nH2O (1.71 g, 13 mmol) in water (15 g). For this synthesis the molar ratios are CTAB/Zr ) 0.53 and Zr/SO4 ) 1. For the neutron scattering experiments, the solutions are prepared in D2O with the same concentrations. The two solutions are mixed together, and a white precipitate forms after a few seconds. These proportions and concentrations correspond to what we call from now on the “reference” synthesis. The resulting solution is stirred at room temperature for 15 min and then heated at 100 °C in a sealed Teflon vessel for 2 days (smooth hydrothermal conditions). Then, the solid is filtered and washed with pure water. Finally, the surfactant is removed by calcination at 500 °C for 5 h.18 In this study, we only focus on the first step and analyze what happens from a few seconds to a few minutes after mixing of the precursor solutions. Two other experimental conditions are used to study the influence of species concentration and CTAB/Zr molar ratio on the kinetics: (a) Keeping all other conditions equal, all the concentrations are divided by 2, keeping the molar ratios CTAB/Zr ()0.53) and Zr/SO4 ()1) constant. (b) The concentration of CTAB is decreased (0.029 mol‚L-1), keeping the other concentrations constant, to obtain a CTAB/Zr molar ratio of 0.26 with Zr/SO4 ()1) constant. Experimental Setup. The stopped-flow apparatus (BioLogic) is designed to mix together very low volumes (g20 µL) of solutions in a very short time (10-90 ms) with a good reproducibility. The solutions are contained in syringes, pushed by stepping motors. The vertical syringes are filled from the top to allow the evacuation of the bubbles formed during the filling. A spherical mixer ensures good mixing, and is open directly at the entry of a sample cell. The flow is from the bottom to the top. The syringes, tubes, and mixer are contained in a water-thermostated bath, so that the mixture entering the sample cell is at a controlled temperature. A “hard-stop” device is placed after the sample cell, to stop the flow of liquids at the end of the injection, and avoid turbulence. The sample cell is placed in the path of a beam, of either X-rays at ESRF on the ID02 beamline or neutrons at ILL19 on the D22 beamline. The sample cell is a 0.9 mm internal diameter quartz capillary at ESRF and a rectangular quartz Hellma cell of 0.2 mL volume with parallel sides at ILL, because the neutron beam is larger (defined by a 6 × 9 mm2 aperture) than the X-ray beam at ESRF (0.1 × 0.1 mm2). (18) Ne´, F. Thesis, Universite´ de Versailles St Quentin, 2001. (19) Internet site: Grillo, I., http://www.ill.fr, D22 experiment.
Ne´ et al. The electronics associated with the stopped-flow apparatus send a TTL signal (0-5 V) to the instrument workstation to start the acquisition sequence. At the ESRF, the detection is ensured with a 2D CCD camera, “FRELON” (fast readout low noise; BLISS group, ESRF), connected to a specific fast electronic device. This setup allows a 10 ms (minimum) acquisition time, and the camera needs a 400 ms readout time before the next acquisition. At the ILL, the scattered intensity is recorded on a 2D gas-filled detector. The acquisition card can store up to 200 acquisitions without any dead time between each spectrum. A kind of “movie” in the reciprocal space of the different states of the system as a function of time is obtained. The flux on the ID02 beamline (ESRF) is on the order of 1011 photons/s. To achieve a reasonable signal-to-noise ratio and good reproducibility, the acquisition time17 is fixed at 100 ms. For the experiments at ILL,18,19 the acquisition time is fixed at 200 ms, because the flux of neutrons is much lower (107 neutrons/s) than that of the synchrotron. Moreover, SANS experiments are done 10 times for each shot, and averaged to increase the signal-tonoise ratio. ILL: Three configurations are used (λ ) 6 Å, D ) 17.5, 5.8, and 1.4 m, collimation 17.6, 5.6, and 1.2 m) to cover a q range from 2.7 × 10-3 to 0.46 Å-1. Standard ILL data treatments are used for radial averaging and correction for the empty cell and electronic background. ESRF: The configuration used (λ ) 1 Å, D ) 1 m) allows a q range from 3.2 × 10-2 to 0.64 Å-1 to be covered. The 2D isotropic images are radially averaged and corrected for the empty cell and electronic background. To interpret the data, the intensity is modeled by eq 1, where A is the Porod limit at q tending to 0, P(q) the form factor, and S(q) the structure factor.
I(q) ) Aq-4 + P(q) S(q) + cst
(1)
Results Precursor Systems. Co¨lfen et al.20 recently summarized the literature on the zirconium salt solution for different anions such as chloride, nitrate, and sulfate. It has been proven by several techniques20,21 that tetramer species [Zr(OH)2‚4H2O]48+,8Cl- are present in zirconium oxychloride solution. The size of this tetramer has been determined by SAXS22-24 and is found to be between 0.35 and 0.5 nm. Our precursor solution contains both CTAB and zirconium oxychloride. By reference to several mechanisms proposed in the literature, it is important to know if there is any interaction between the zirconium clusters and the CTAB micelles before the addition of sulfate anions and, especially, if the micelles remain spherical, or if they become cylindrical. Ne´ et al.25 demonstrated by SANS experiments that the CTAB micelles (0.06 mol‚L-1) are still spherical at high zirconium oxychloride salt concentration (0.85 mol‚L-1) or at high magnesium sulfate concentration (2 mol‚L-1). This is illustrated in Figure 1, where the SANS patterns show that the shape of the micelles does not change with the addition of salts even at the high ionic strength used in the precipitation synthesis route. The fit is obtained with a micelle radius of 2.75 nm and scattering length densities of 6.34 × 1010 cm-2 for zirconium chloride/D2O solution and -2.10 × 109 cm-2 for CTAB surfactant. The results are concomitant (20) Co¨lfen, H.; Schnablegger, H.; Fisher, A.; Jentoft, F. C.; Weinberg, G.; Schlo¨gl, R. Langmuir 2002, 18, 3500. (21) Clearfield, A.; Vaughan, P. A. Acta Crystallogr., Sect. B 1956, 9, 555. (22) Singhal, A.; Toth, L. M.; Lin, J. S.; Affholter, K. J. Am. Chem. Soc. 1996, 118, 11529. (23) Singhal, A.; Toth, L. M.; Beaucage, G.; Lin, J. S.; Peterson, J. J. Colloid Interface Sci. 1997, 194, 470. (24) Toth, L. M.; et al. J. Phys. Chem. 1991, 95, 3106. (25) Ne´, F.; Zemb, Th. Submitted for publication.
How Does ZrO2/Surfactant Mesophase Nucleate?
Langmuir, Vol. 19, No. 20, 2003 8505
Figure 2. SAXS pattern of the water precursor solution containing ZrOCl2 (0.13 mol‚L-1) and CTAB (0.07 mol‚L-1). The continuous line is a fit of the intensity obtained by assuming a coexistence of 3.1 nm radius spherical CTAB micelles with 10 H2O per surfactant (pale gray line) and 0.5 nm clusters of zirconium (gray line).
Figure 1. (a) SANS pattern of precursor solutions: triangles, 0.06 mol‚L-1 CTAB micelle solution in D2O; circles, the same micelle solution with 2 mol‚L-1 MgSO4; squares, the same micelle solution with 0.2 mol‚L-1 ZrOCl2. The line is a fit of the form factor for 2.75 nm radius spherical micelles. As salt is added, the interactions between micelles are screened. (b) The same scattering pattern is zoomed, and the intensity is multiplied by q4; the position of the first minimum shows that the micelles remain spherical, even with a large amount of salt.
with those obtained by Glatter et al.26 in their systematic study of quaternary ammonium micelles versus ionic strength. The zirconium salt has no influence on the structure of the micelle aggregate in the precursor solution. In Figure 2, the experimental SAXS spectrum of the precursor solution and a modeled intensity are represented. Since in the low q range no “q-1” signal is visible, the intensity is modeled as the sum of the scattering produced by spherical CTAB micelles (in contrast with a water solution containing zirconium oxychloride, F ) 9.78 × 1010 cm-2) and the scattering produced by a tetramer cluster of zirconium in contrast with water. The general shapes of both modeled and experimental spectra are similar, showing that the CTAB micelles are not cylindrical and not coated with the zirconium clusters as found in some mechanisms suggested for the silica system.27,28 Precipitate after Mixing. A precipitate is obtained after the addition of the magnesium sulfate solution to the CTAB/ZrOCl2 solution. The product obtained after mixing and before heating and calcination is a 2D hexagonal mesostructured material, the SANS spectrum of the powder of which is represented in Figure 3a. The (26) Fritz, G.; Bergmann, A.; Glatter, O. J. Chem. Phys. 2000, 113, 9733. (27) Lee, Y. S.; Surjadi, D.; Rathman, J. F. Langmuir 1996, 12, 6202. (28) Chen, C. Y.; Burkett, S. L.; Li, H. X.; Davis, M. E. Microporous Mater. 1993, 2, 27.
Figure 3. (a) SANS pattern of a mesostructured zirconia/CTAB precipitate, obtained from the mixing of 115 g of a solution of CTAB (0.06 mol‚L-1) and ZrOCl2 (0.12 mol‚L-1) with 15 g of a solution of MgSO4 (0.86 mol‚L-1). From Porod law at low angle, the grain size is determined to be 0.6 µm, and the hexagonal lattice is evidenced by the presence of Bragg peaks, shown in linear scale on the right. (b) A direct image from an SEM photograph shows the same average size for the micrometersized grains. The bar represents 5 µm.
unit cell parameter deduced from the first Bragg peak (q ) 0.134 Å-1) is a ) 5.41 nm. In the low q range region the intensity follows a Porod29 law of q-4 characteristic of a well-defined and smooth interface of the grains at the observation scale. The specific surface area Σ can be (29) Prod, G. Kolloid K. 1951, 124, 83.
8506
Langmuir, Vol. 19, No. 20, 2003
Ne´ et al.
Figure 4. Variation of the square root of the intensity for some selected q values versus the volume fraction of D2O in the mixture D2O/H2O. In the spectra (not given here) obtained for the zirconia/CTAB precipitate the first-order Bragg peak is at q ) 0.134 Å-1.
calculated from the Porod law:
Σ)
lim I(q)q4 2π(∆F)2
(2)
where (∆F)2 is the contrast between the grain and the solvent.30 By matched contrast variation, the scattering length density of the precipitate is estimated to be 1.4 × 1010 cm-2, while it is equal to 6.4 × 1010 cm-2 for D2O. Therefore, the specific area obtained is 1900 cm2‚cm-3. Titration measurements show that less than 2 ppm carbon (due to the surfactant) and less than 4% of the initial zirconium are left in the supernatant after the precipitation. Therefore, all the initial precursors are in the final precipitate, and the grain volume fraction φ ) 0.04 can be calculated from the initial composition. Assuming a globular topology, the grain radius R ) 0.6 µm is given by eq 3, with φ the volume fraction and Σ the specific surface area. This value is coherent with the size of the grains observed by scanning electronic microscopy (SEM) as shown in Figure 3b.
R ) 3φ/Σ
(3)
In Situ SANS Experiments. Contrast Match Point. During the precipitation, to observe the transition from spherical micelles to cylinders in the mesophase, it is necessary to match the signal of the zirconia. A 5% (w/w) proportion of D2O in H2O is needed to match the negative scattering length density (-0.21 × 1010 cm-2) of the hydrogenated CTAB micelles. The scattering length density of the sulfated zirconia is estimated to be 3 × 1010 cm-2, and calculation gives 51% (w/w) D2O to contrast match the signal of sulfated zirconia. To experimentally determine this contrast match point in the precipitate, different syntheses are carried out in mixtures of D2O and H2O to achieve solutions ranging from 40% to 100% D2O. Figure 4 represents the square root of the intensity for a selected q value versus D2O volume fraction. There is no match point in the chosen concentration range. By extrapolation, a contrast-matched point is found to be around 27.5% D2O corresponding to a scattering length (30) Spalla, O. General theorems in small angle scattering. In Neutrons, X-rays and light, scattering methods applied to soft condensed matter; Lindner, P., Th. Zemb, Th., Eds.; North-Holland Delta Series; Elsiever: Amsterdam, 2002.
Figure 5. SANS patterns obtained during the first 10 s with a stopped-flow apparatus for the reference synthesis (CTAB/Zr ) 0.53, Zr/SO4 ) 1, and [CTAB] ) 0.06 mol‚L-1): (a) log-log scale centered on the micelles; (b) 3D view of the scattered intensity versus q and time.
density of F ) 1.4 × 1010 cm-2. This corresponds to the average scattering length density of the whole grain precipitating, containing both sulfated zirconia and CTAB. For this low q value, the observation scale is significantly larger than the size of the unit cell, so it is not possible to observe only the signal produced by the CTAB micelles. The signals produced by both the CTAB micelles and the whole grain are present in the spectra. Therefore, we choose to lead the experiments with precursor solutions prepared in D2O instead of H2O to increase the contrast between CTAB micelles and solvent even if the signal of zirconia grain cannot be matched. In this way it is possible to follow the behavior of the micelles in solution during precipitation. Edler et al.29 studied a contrast variation on CTAB/ silica mesostructured materials with similar results. It is only possible to obtain the scattering length difference at the interface between the particle and the solution. Kinetic Study: Consumption of Micelles and Growing of Grains. Figure 5 shows a series of SANS patterns obtained after the two precursor solutions of CTAB/ZrOCl2 and MgSO4 are mixed. Three features can be pointed out in these patterns: (i) The growing grains are detected at low angle, where their specific surface area can be measured using the Porod law (the final asymptotic value of this specific surface area is achieved 3 s after mixing). (ii) The signal due to the micelles in solution is visible in the medium q range (0.01-0.1 Å-1); the intensity of this signal decreases as a function of time. Since this signal
How Does ZrO2/Surfactant Mesophase Nucleate?
Langmuir, Vol. 19, No. 20, 2003 8507
Figure 6. An example of data treatment is taken for the 2 s after mixing pattern. An Iq4 function is subtracted (solid line) at low angle from the experimental data (triangles). The result is divided by a Guinier function (dashed line) to obtain the structure factor and reveal the Bragg peaks. The linear scale on the right is the one for this structure factor.
is proportional to the volume fraction of micelles in solution, this observation allows us to follow the consumption of the micelles. (iii) The first-order Bragg peak appears 0.8 s after mixing, and the second-order peak around 4 s after mixing. The data analysis (cf. eq 1) consists of subtracting a Porod function at low angle. The remaining scattered intensity cannot be fitted by a q-1 signal. This evidences that the micelles in solution are still spherical. The number of these micelles decreases with time, and their scattering intensity is fitted by a Guinier approximation for globular objects (eq 4, where A is proportional to the number of micelles in solution and RG is the radius of gyration of the micelles) representing the form factor of these micelles.31
(
P(q) ) A exp -
)
q2RG2 3
(4)
After subtraction of the Porod function, the intensity is divided by the Guinier function. The resulting curve is assumed to be the structure factor of the mesoscopic network (see Figure 6 for an example of the data treatment on the pattern obtained 2 s after mixing). Finally, three different values allow the quantifying of the patterns as a function of time: the specific area of the grains, the fraction of consumed micelles, and the area under the first Bragg peak. Kline32 has used a similar decomposition of the scattered intensity in three terms for polymerizing micelles. Figure 7a gives the results for the reference experiment, with a molar ratio CTAB/Zr ) 0.53. The micelles are completely consumed in about 5 s after mixing, while the specific area is at its maximum 3 s after mixing. This means that the continuous feeding of the grain by CTAB does not imply an increase of the specific area. Moreover, the Bragg peak is still growing while all the micelles are consumed. These two observations suggest a two-step mechanism. Another time-resolved experiment is carried out with the same CTAB/Zr ratio as the previous one (0.53), but the initial solutions are diluted by a factor of 2 (Figure 7b). In this case, the micelles are consumed in 3 s (compared to 5 s in the reference experiment), and the final specific area is now reached in 1 s (compared to 3 s (31) Ne´, F.; Zemb, Th. J. Appl. Crystallogr., in press. (32) Kline, S. J. Appl. Crystallogr. 2000, 66, 618.
Figure 7. SANS kinetics experiment (the evolution of the quantified parameters is drawn as a function of time to evaluate the kinetics): triangles: specific area of the grain (from Porod law); squares, consumed micelles; circles, area of the first Bragg peak (all these parameters are normalized to 1, and the lines are drawn to guide the eyes); (a) reference synthesis; (b) effect of dilution; (c) effect of changing the CTAB/Zr ratio (0.26 instead of 0.53 for reference synthesis).
in the reference experiment). Surprisingly, the lower the quantity of precursors per unit volume, the faster the reaction proceeds. However, in both conditions (“reference” and “diluted”), the peak position and intensity are the same in the final state. The same observation is made if the initial concentration of the CTAB solution is divided by 2 (CTAB/Zr ratio of 0.26), with all other conditions kept as in the reference synthesis (Figure 7c). Under these conditions, the equilibrium is now reached in 2 s after mixing, with respect to the quantity of consumed micelles, and around 1 s after mixing with respect to the specific surface area of the grains. Once again, the final state is the same as the previous experiments, and only the kinetics parameters are affected by the reduction of the initial quantity of precursors. This unexpected behavior
8508
Langmuir, Vol. 19, No. 20, 2003
Ne´ et al.
is usually interpreted as resulting from entanglement of cylindrical micelles. In our case, this explanation is inadequate since only spherical micelles are present in solution during the growth of the grain. Kinetic SAXS Experiments. The experimental conditions are almost the same as during the SANS experiments, especially from a chemical point of view, using the same CTAB/Zr ratio of 0.53 but with a Zr/SO4 ratio equal to 0.67. Moreover, the experiments at ESRF are carried out around 20 °C to be compared to 22 °C at ILL. So we will not compare the kinetics time of the synthesis between SAXS and SANS, but only analyze it to bring new elements to explain the mechanism. The experimental patterns are shown in a 3D view in Figure 8a, where the intensity is plotted as a function of q and time. Avrami Interpretation of the Data. The intensity of the first-order Bragg peak is used to quantify the kinetics of the precipitation (the baseline level of the peak is subtracted). For the diluted reaction, after a short latency time, this peak grows, even after 3 times the half-life of micelle consumption (Figure 8b). Clearly, the reaction is still evolving 14.5 s after mixing, showing that this reaction does not simply follow “n”-order kinetics. We treat this heterogeneous reaction with Avrami’s equation:33,34,35
I(t)/Imax(t) ) 1 - exp[-k(t - t0)n]
(5)
As we did not observe any asymptotic value for the intensity, we approximated Imax(t) as the maximum value obtained for the intensity at 14.5 s after mixing. k is the rate constant for the intensity growth, and n is related to the nucleation process, found from a fit of the log plot. The exponent n ) a + b represents both the nucleation process (a ) 0 for random nucleation, and a ) 1 for instantaneous nucleation) and the dimensions of the growing object (e.g., b ) 1 for cylinders, 2 for platelike objects, and 3 for spheres). In our case, n ) 1 (Figure 8c), and as b is strictly positive, the result is in good agreement with random nucleation of growing cylinders. Notice that this kind of ripening of solid grains, in equilibrium with themselves, has also been observed during the ripening of hexagonal crystalline polymers.36 Ordering of Surfactant Cylinders in the Growing Grain. At the shortest times after mixing, Figure 9 shows a broad “soft” peak, at lower q than the “sharp” Bragg peak resulting from the hexagonal order. This soft peak grows at lower q than the minimum value of the form factor of the micelles, and therefore can only be a structure peak. The peak shifts continuously toward higher q, until the appearance of the first-order Bragg peak from 7.8 to 6.3 nm in direct space for the reference synthesis. The soft peak then remains in coexistence with the sharp one, and does not shift in position during the hexagonal organization. Its intensity first remains stable as the Bragg peak grows in intensity, and then decreases during the hexagonal network organization. Since the Avrami analysis shows that cylindrical objects are growing, this broad peak is attributed to a soft order of cylindrical micelles in the grain, and only the average distance between the axes of neighboring cylinders can be deduced from the scattering pattern. These observations show that the cylindrical micelles are growing (in size and in number) with a soft order in the grain in the early stages of the reaction, before the hexagonal organization. The fact that the Bragg peak (33) Avrami, M. J. Phys. Chem. 1939, (34) Avrami, M. J. Phys. Chem. 1940, (35) Avrami, M. J. Phys. Chem. 1941, (36) Balsara, N.; Garetz, B.; Chang, Macromolecules 1998, 31, 5309.
7, 1103. 8, 212. 9, 177. M.; Dai, H.; Newstein, M.
Figure 8. Kinetics analysis for the diluted conditions (CTAB/ Zr ) 0.53, Zr/SO4 ) 0.67, and [CTAB] ) 0.029 mol‚L-1): (a) 3D view of the scattered intensity versus q and time; (b) intensity of the first-order Bragg peak versus time (the inflection point around 10 s shows that it is not a simple n-order reaction); (c) experimental Avrami plot y ) ln[1 - I(t)/Imax(t)] versus time and modeling plot y ) -k(t - t0)n versus t - t0; (d) SAXS pattern 14 s after mixing on a linear scale and zoomed in on the higher order Bragg peak during the precipitation. For clarity the spectra are moving out from the others in arbitrary units.
How Does ZrO2/Surfactant Mesophase Nucleate?
Figure 9. SAXS patterns obtained during the first seconds after mixing for the standard synthesis (CTAB/Zr ) 0.53, Zr/ SO4 ) 0.67, [CTAB] ) 0.06 mol‚L-1), showing the appearance of a broad peak before and during the growth of the first-order Bragg peak. The patterns are obtained with the precursor solution, and 0.5, 2, 4, and 6 s after mixing from the bottom to the top, respectively. The position of the broad peak moves from 7.8 to 6.3 nm in real space.
appears with a well-defined jump in “q” position is a direct proof of a sudden first-order transition of microstructure from unordered cylinders to hexagonal crystalline order. When a growing grain is large enough, interactions occur not only between nearest neighbors, but also between second nearest neighbors. We observe a cooperative effect, at the origin of the first-order transition, since this is not a gradual sharpening of the maximum in the structure factor of cylinders, but a jump in position and shape. The same scattering behavior is observed when a giant repulsive micelle system transforms in a hexagonal phase. Once again, the same experiments are carried out in diluted conditions (dilution by a factor of 2). The first Bragg peak appears 1.5 s after mixing, while it appears 4 s after mixing under reference conditions. The peak position is the same in both cases. As shown in Figure 8d, a second (11) and a third (20) order Bragg peak appear with increasing time. In diluted conditions, the third-order Bragg peak appears 2 s after mixing, instead of 10 s for the reference synthesis. The reaction goes faster in diluted conditions, confirming the conclusion on the dilution effect in the SANS experiment. The position of the soft peak gives an average distance between two cylinders before they organize into a 2D hexagonal network with long-range order. Again the peak shifts toward higher q until the appearance of the firstorder Bragg peak. This corresponds to a shift in direct space from 7.8 to 6.3 nm for the reference synthesis and from 6.5 to 5.8 nm under diluted conditions. Under diluted conditions, the nucleation step is faster and gives more compact grains. We can notice in Figure 8d that the (20) reflection line appears before the (11) reflection line, and the (20) intensity is higher than the intensity of the (11) reflection line at the beginning of the precipitation. Then the intensity ratio (11)/(20) increases with time. This has been observed by Ågren et al.37,38 for silica and by Linden et al. for zirconia9 mesophases at the initial time of the synthesis with CTAB surfactant and explained by a preferential increase of inorganic species (good scatters) along the (11) (37) Ågren, P.; Linde´n, M.; Rosenholm, J.; B.; Schwarzenbacher, R.; Kriechbaum, M.; Amentisch, H.; Laggner, P.; Blanchard, J.; Schu¨th, F. J. Phys. Chem. B 1999, 103, 5943. (38) Ågren, P.; Linde´n, M.; Rosenholm, J.; B.; Blanchard, J.; Schu¨th, F.; Amentisch, H. Langmuir 2000, 16, 8809.
Langmuir, Vol. 19, No. 20, 2003 8509
axis. Similar experimental trends have been observed for mesostructured materials obtained with pluronic copolymers (EOxPOyEOx) by Imperor-Clerc et al.39 This effect is explained by modeling the scattered intensity by the product of the structure factor S(q) (giving the position of the Bragg peak) and the form factor P(q) of the CTAB cylinders. This form factor depends on the radius of the core, r, on the electronic density of the core, and on the electronic density of the inorganic walls and a gradient between them. Since the scattering intensity is given by the product P(q) S(q), for certain values of r and the unit cell parameter a, a minimum of P(q) can be superimposed to a maximum of S(q), and in this case the (11) reflection is not (or is less) seen. A variation in the relative electronic densities induces a variation in the form factor and could also explain the experimentally relative variation of the (11)/(20) intensity reflection ratio. Discussion Ne´ et al.25 demonstrated that in the CTAB/water system the miscibility gap between the micellar phase and hexagonal phase increases dramatically with the ionic strength. The increase of the ionic strength allows nucleation and growth of the hexagonal phase in the solution due to the phase separation between the hexagonal and the micellar phases. The strong affinity between sulfate and zirconium leads to the formation of polynuclear complexes through different bridging mechanisms. Therefore, in the precipitation of the mesostructured sulfated zirconia phase, there is a cooperative process between the appearance of the CTAB hexagonal phase and the polymerization of the inorganic part. The precursor solution contains zirconium clusters and spherical CTAB micelles that coexist without interaction. This mechanism is different from the growth mechanism proposed by Chen et al.28 for silica MCM-41, where final ordering is initiated by the interaction between silicate and the organic micelles. In our case, there are no preexisting cylindrical micelles, and therefore, the precipitation cannot be initiated by elongated micelles coated with a zirconium shell. During precipitation, analysis of the underlying signal of the SANS data shows that the micelles remain spherical in solution and are continuously consumed. These micelles act as a surfactant monomer reservoir for feeding the grains, in agreement with the mechanism proposed by Frasch et al.7 for silica MCM-41, and by Sicard et al.40 for mesostructured hexagonal alumina. From SANS analysis, it has been observed that the specific area of the grains reaches an asymptotic value before total consumption of the spherical micelles in the solution, and before the final ordering of the grain, as indicated by the intensity of the Bragg peak. From SAXS analysis, the appearance of a broad peak in the spectra and the Avrami analysis permit us to conclude a random nucleation of cylindrical aggregates in the growing grain. To interpret the experimental data, a two-step mechanism is proposed: the first step is a nucleation/growth process, and the second is a reorganization of the cylinders from close-packed to a long-range hexagonal order when the grain reaches its final size. The nucleation/growth step consists of nucleation of the grains, which contain disordered cylinders of CTAB and clusters of zirconia. The broad peak seen during SAXS (39) Imperor-Clerc, M.; Davdison, P.; Davidson, A. J. Am. Chem. Soc. 2002, 122, 11925. (40) Sicard, L.; Lebeau, B.; Patarin, J.; Zana, R. Langmuir 2002, 18, 74.
8510
Langmuir, Vol. 19, No. 20, 2003
Ne´ et al.
Figure 10. Schematic drawing of the two-step mechanism proposed for the formation of the zirconia/CTAB mesophase, from precursor solutions to the building grain during ordering.
experiments gives the distance between these cylinders (from 7.3 to 6.3 nm before the appearance of the Bragg peak for the reference synthesis). This peak coexists with the first-order Bragg peak (5.41 nm for the reference synthesis), and the fact that it does not shift during the hexagonal organization step suggests that the nucleation is randomly distributed both in time and in space. In a second step (4 s after mixing in the case of the reference synthesis studied by SAXS), the intensity of the soft peak remains stable, and the Bragg peak grows in intensity. This observation suggests that the number of ripening grains is more or less the same as that of the nucleating ones during the beginning of the second step. Moreover, it explains why the specific area stops increasing rapidly (demonstrated by SANS experiments), while the number of spherical micelles consumed still decreases. Effectively, before the end of the ripening step, the intensity of the soft peak decreases while the intensity of the Bragg peak continues to increase. Each grain is progressively compact and organized into a hexagonal network by a first-order transition from a condensed fluid to a solid. At the level of observation, the specific area of the grain is the same either for grains with holes and short-range order or for grains without any holes and long-range order. A schematic view of the proposed mechanism is given in Figure 10. A disorder-order transition has been evidenced by Sadasivan et al.15 for a hexagonally ordered silica/ surfactant mesophase. By stopping the slower silica condensation reaction using a pH jump, they have shown an increase of ordering inside an already formed grain. The Solution Acts as a Reservoir of Monomers and Clusters. To interpret the first step of the mechanism, we can consider the solution like an ensemble of Voronoi cells, which pave the space. In those cells, monomers of surfactant and zirconia form micronic grains (Figure 11). After nucleation, the local concentration of monomer favors reorganization into cylinders. The clusters of zirconia grow in elementary units, which are trapped between the cylinders. This growth is induced by the presence of sulfate ions in the solution. The radius Rv of the Voronoi cells can be obtained from the initial volume fraction φ of zirconium clusters and CTAB (φ ) 0.04). The final radius 〈R〉 of the micronic grain is found by microscopy to be 1 µm. The relation between the two radii is given by Rv ) φ-1/3〈R〉, the application of which gives a radius Rv ) 3 µm. The diffusion coefficient of surfactant monomers is linked to both the characteristic reaction time (∼1 s) and the distance covered by the monomers: Dapp ) Rv2/t. We find an apparent diffusion coefficient Dapp ) 9 × 10-8 cm2‚s-1. Since the coefficient for free CTAB (3% w/w)41 is 6.6 × 10-6 cm2‚s-1, we can conclude that this reaction is (41) Smith D. J. Colloid Interface Sci. 1979, 68, 70.
Figure 11. Schematic drawing of the CTAB concentration profile during the precipitation. The micronic grains are formed at the center of a unitary volume cell of solution in which the precursors diffuse. Rv is the maximum distance covered by the precursors. The ordinate represents schematically the reactive concentration.
not limited by diffusion of the monomer. The solution after mixing acts as a reservoir, which continuously feeds the micronic grains. This is not in contradiction with the fact that the kinetics is faster for a diluted solution. Increasing the CTAB concentration is an obstacle to the diffusion of monomers in solution, and moreover, it prevents dissociation of the micelles because the concentration is too far from the critical micelle concentration.42 Conclusion The growth mechanism of a mesostructured hexagonal phase of zirconia/CTAB has been investigated by in situ time-resolved SANS and SAXS experiments. We determined that (i) there are no preexisting cylinders in the precursor solutions, (ii) there is a random nucleation of the grains, (iii) the micelles act as a reservoir to feed the grains, (iv) the early grains contain cylinders, (v) the reaction is not limited by the diffusion of monomers and clusters in the solution, and (vi) there is a first-order transition in the ripening grain from fluid to solid order. The mechanism through zirconium-coated cylinders is therefore excluded in our case. There is a progressive building up of the grain, which is compatible with the mechanism given by Patarin et al.5 Acknowledgment. We thank J. M. Petit and T. Naranayan, the local contacts on ID2 at ESRF, for the kinetics experiments, P. Lixon for the titration of supernatant solutions after precipitation, and O.Tache´ for data treatment software. LA034824G (42) Aniansson, E.; Wall, S.; Almgren, N.; Hoffmann, H.; Kielmann, L.; Ulbricht, W.; Zana, R.; Lang, J.; Tondre, C. J. Phys. Chem. 1976, 80, 905.
