- Email: [email protected]
Rheological behavior of surfactant-based precursors of silica mesoporous materials
Journal of Colloid and Interface Science 320 (2008) 290–297 www.elsevier.com/locate/jcis
Rheological behavior of surfactant-based precursors of silica mesoporous materials L.D. Mendoza a , M. Rabelero a , J.I. Escalante a,∗ , E.R. Macías a , A. González-Álvarez a , F. Bautista b , J.F.A. Soltero a , J.E. Puig a a Departamento de Ingeniería Química, Universidad de Guadalajara, Boul. M. García-Barragán # 1451, Guadalajara, Jal. 44430, México b Departamento de Física, Universidad de Guadalajara, Boul. M. García-Barragán # 1451, Guadalajara, Jal. 44430, México
Received 20 September 2007; accepted 17 December 2007 Available online 23 December 2007
Abstract The linear and non-linear viscoelastic behaviors of polymer-like micellar solutions of cetyltrimethylammonium tosilate (CTAT) with added NaOH and tetraethyl orthosilicate (TEOS) to produce precursors of mesoporous materials are studied. The effect of TEOS/CTAT (T/C) ratio at fixed CTAT concentration, CTAT concentration at fixed T/C and aging time are reported. The systems show increasingly larger deviations from near-Maxwell behavior upon increasing T/C ratio, CTAT concentration and aging. Moreover, in steady and unsteady shear-flow, shear banding develops between two critical shear rates, which tend to fade as the T/C ratio and aging increase. The Granek–Cates model is employed to analyze linear viscoelastic behavior. The Bautista–Manero–Puig (BMP) model is used here to reproduce the steady and transient nonlinear rheology of these systems. We explain these results in terms of the changes in inter-macromolecular interactions that arise out of the presence of colloidal additives in the viscoelastic gel. The ordered mesoporous materials were identified by X-ray diffractometry (XRD) and high-resolution transmission electron microscopy. © 2008 Elsevier Inc. All rights reserved. Keywords: Polymer-like micelles; Colloidal additives; Inter-macromolecular interactions; Viscoelastic behavior
1. Introduction Cetyltrimethylammoniun tosilate (CTAT) is a cationic surfactant that forms polymer-like micelles in water in a concentration range from ca. 1 to 25 wt% at room temperature [1]. These polymer-like solutions exhibit near Maxwell behavior in linear oscillatory flow and shear thinning as well as shear banding in steady shear flow [2–4]. This complex behavior is related to the relaxation mechanisms in this kind of systems, mainly, i.e., kinetic-controlled and diffusion-controlled relaxation mechanisms [5–8]. The ratio of the breaking time to the reptation time (ζ = τbreak /τrep ) controls the relaxation of the system: for very small values of ζ , a single relaxation time dominates and near-Maxwell behavior follows whereas for larger values of ζ , a spectrum of relaxation times and deviations from * Corresponding author.
E-mail address: [email protected] (J.I. Escalante). 0021-9797/$ – see front matter © 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2007.12.024
Maxwell behavior are observed, similar to polymers solutions with wide molecular weight distributions [9]. Moreover, shearbanding flow, characterized by the coexistence of two bands supporting different shear rates at a fixed stress, is commonly observed in the fast-breaking (kinetic-controlled mechanism) regime and this flow vanishes as the diffusion-controlled mechanism becomes dominant [10–12]. The rheology of polymer-like micelles networks can be altered by addition of cosurfactants, electrolytes, organic salts with strongly hydrophobic counter-ions and submicron-sized colloidal particles, because they modify the inter-micellar interactions and the micellar packing and in some cases, it may even result in phase transitions and the formation of novel complexes [12–18]. Ordered mesoporous materials are typically made using surfactant-based self-organized media as templates over which silicate or other inorganic material is added [19–25]. The mechanism of formation of this kind of materials is still under debate.
L.D. Mendoza et al. / Journal of Colloid and Interface Science 320 (2008) 290–297
Moreover, with the exception of the recent report of Bandyopadhyay and Sood [26], the rheology of the precursors of this kind of materials has not been reported, in spite of the rich features that it possesses. In this paper we address the linear and non-linear rheology of CTAT micellar solutions in basic media and the effect of adding a template silica material, mainly tetraethyl orthosilicate (TEOS). We examine the effects of varying TEOS/CTAT (T/C) molar ratio at fixed CTAT concentration (5 wt%) and TEOS/NaOH molar ratio (= 2), varying the surfactant concentration at fixed T/C and TEOS/NaOH = 2, and of aging of the sample. The system was studied over wide frequency and shear rate ranges. 2. Experimental CTAT (99+% pure from Aldrich) was used as received. TEOS was 98% pure (Aldrich). NaOH was 98% pure (Productos Químicos Monterrey). Doubly distilled and de-ionized water was employed. Samples were prepared by weighing the appropriate amount of CTAT and water, and the sample was homogenized and equilibrated at room temperature for a week. Then the TEOS and NaOH (in a molar ratio of 2) were added, shaken by hand and allowed the sample to rest for 15 min (these samples are referred as “fresh” or “freshly-made” in the rest of the text, other wise the aging is indicated in the text) before starting the rheological tests. To examine the effect of the hydroxide ion in the absence of TEOS, CTAT solutions (5 wt%) containing varying amounts of NaOH were also prepared. Steady and transient simple shear as well as small-amplitude oscillatory shear measurements were performed at 30 ◦ C in a Rheometrics Dynamic Stress Rheometer RS-5 having a coneand-plate geometry with diameter of 40-mm and angle of 0.0384 radian (2.2◦ ) and in a Rheometrics RDS-II dynamical spectrometer using also a cone-and-plate geometry of 0.1 radian and 50 mm in diameter. An environmental control unit was used during the measurements to prevent solvent evaporation. The structural properties of the CTAT/TEOS materials were studied in a Siemens D-500 X-ray diffractometer (XRD) fitted with a copper tube and a monochromator for Kα radiation (λ = 1.541 Å). The silica-templated samples were observed in a CM-200 TWIN Philips high-resolution transmission electron microscope. 3. Theoretical The linear viscoelastic data were fitted with a simplified Poisson renewal model proposed by Granek and Cates [9]. The best fitting of this model to Cole–Cole plots, i.e., G (ω) versus G (ω), yields the ratio of the characteristic micellar breaking time to the reptation time (ζ = τbreak /τrep ) that allows to discriminate between kinetic-controlled flow (fastbreaking regime when ζ 1) and diffusion-controlled flow (slow-breaking regime when ζ ca. 0.1). The steady and transient nonlinear flow regimes were fitted with the BMP model that consists of the upper convected Maxwell equation coupled to a shear stress-dependent kinetic
291
equation that accounts for the effect of flow on the breaking and reformation of micelles [4,27,28]. For simple shear, the model reads: 1 dσ12 γ˙12 1 − γ˙12 σ22 = , (1) G0 ϕ dt G0 ϕ ϕ dϕ (ϕ0 − ϕ) (2) = + k0 (1 + ϑ γ˙12 )(ϕ∞ − ϕ)σ12 γ˙12 . dt λ Here σ12 is the shear stress, γ˙12 is the shear rate, σii (i = 1, 2, 3) are the normal stresses, ϕ(≡ η−1 ) is the fluidity, η is the shear viscosity, ϕ0 and ϕ∞ are the fluidities at zero- and at infiniteshear rate, G0 is the high frequency elastic plateau modulus, λ is a structure relaxation time, k0 is a kinetic constant for structure breakdown, and ϑ can be interpreted as a shear-banding intensity parameter. Because σ22 is negligible for CTAT micellar solutions [27], the third term on the left-hand side of Eq. (1) will be droped for the rest of the paper. As detailed elsewhere [27], the parameters of this model can be estimated from independent rheological experiments and then use to fit other experimental data. For steady simple-shear flow, Eqs. (1) and (2) with their time derivatives set to zero give:
σ12 +
2 ϕ 2 − ϕ0 ϕ − k0 λ(ϕ∞ − ϕ)γ˙12 (1 + ϑ γ˙12 ) = 0.
(3)
4. Results 4.1. Linear rheology As discussed above, the stress relaxation in polymer-like micellar solutions is governed by the breaking-and-reformation time, τbreak , and the reptation time, τrep , of the micelles [7]. In the limit where τbreak τrep , the resulting single exponential stress relaxation can be fit to the Maxwell model with a disentanglement or main relaxation time τd {= (τrep · τbreak )1/2 } [5]. A good indication of single exponential stress relaxation is the semicircular form of the so-called Cole–Cole plot. Fig. 1 depicts normalized Cole–Cole plots, i.e., G /G0 versus G /G0 , for 5 wt% CTAT micellar solutions containing different T/C molar ratios. For T/C ca. 0.4, Cole–Cole data can be fitted accurately by a semicircle of radio G0 /2 (dotted line in Fig. 1), up to moderately high frequencies, which demonstrates that the solutions follow closely the Maxwell model with a single relaxation time; the fitting of the Granek–Cates model to these curves (continuous lines in Fig. 1) yields ζ -values smaller than 0.05 (Table 1), indicating that these solutions are in the fast-breaking regime. At higher frequencies, departures from the semi-circle are evident, which can be associated to the breaking time (τbreak ) of the micelles and to Rouse and breathing modes [6]. For T/C > 0.4, deviations from the semicircle at increasingly lower frequencies are detected as this ratio increases, implying a distribution of relaxation times, possibly arising out of competing processes, such as comparable breakage and reptation times, which is typical of the transition from the fast- to the slow-breaking regime. The fitting of the Cates and Granek model to these data gives increasingly larger ζ -values (Table 1), corroborating the transition into the
292
L.D. Mendoza et al. / Journal of Colloid and Interface Science 320 (2008) 290–297
Table 1 Parameters obtained from the oscillatory measurements and the best fit to the Granek–Cates model for a micellar solution containing 5 wt% CTAT as function of the ratio T/C T/C
τd (s)
G0 (Pa)
η0 (Pa s)
ζ (–)
0.00 0.10 0.20 0.40 0.50 0.65 1.00 1.50 2.00
0.410 0.588 0.487 0.293 0.228 0.205 0.101 0.068 0.035
70.19 64.94 60.69 69.98 72.88 99.91 87.79 85.12 83.02
17.75 35.85 28.18 19.61 15.92 29.93 8.65 6.15 4.02
0.1143 0.0143 0.0290 0.0410 0.1433 0.1520 0.2866 1.4330 14.330
Fig. 1. Normalized Cole–Cole plot at 30 ◦ C for CTAT 5 wt% micellar solutions containing different molar relationship of T/C: (1) 0, (2) 0.1, (!) 0.2, (Q) 0.5, (E) 1.0, (e) 1.5, (F) 2.0. The solid lines represent the best fit from the Cates–Granek model while the dotted line is the Maxwell model. The inset shows the influence of the NaOH on the preparation of the samples for different molar ratios of NaOH/CTAT: (P) 0 with ζ = 0.2866, (!) 0.25 with ζ = 0.0286, and (× + ) 1 with ζ = 0.0028.
slow-breaking regime. The values of τd , G0 , the zero-shear dynamic viscosity (η0 ) and ζ are reported in Table 1. Notice that G0 does not depend strongly on T/C, although it increases steadily as the T/C ratio is increased, whereas η0 and τd decrease abruptly with increasing the concentration of TEOS in the solution. To examine the effect of NaOH in the absence of TEOS, measurements were performed with 5 wt% solutions containing no TEOS and varying NaOH/CTAT ratios (see inset). Contrary to the trend observed upon increasing T/C ratio, departures from Maxwell behavior occur at higher frequencies in the TEOS-free CTAT solutions that contain NaOH, i.e., ζ diminishes (see caption in Fig. 1). Evidently, this is a result of the electrostatic screening caused by the addition of OH− that modifies the curvature of the micelles and promotes further growth and larger entanglement density. In the absence of CTAT, concentrated TEOS/NaOH dispersions exhibit weak viscoelasticity with a nearly frequency-independent complex viscosity with values ranging from 0.08 to 0.3 Pa s as TEOS concentration is increased (not shown). Fig. 2 shows normalized Cole–Cole plots at 30 ◦ C for micellar solutions containing T/C molar ratio of 0.2 (Fig. 2A), 0.5 (Fig. 2B) and 0.8 (Fig. 2C) as a function of surfactant concentration. For the lower T/C ratio (Fig. 2A), the experimental data follow again the Maxwell semicircle (dotted line) up to moderately high frequencies after which deviations are observed that become more severe as the surfactant concentration increases. Similar features are depicted for the higher T/C ratios (Figs. 2B and 2C), but deviations take place at lower surfactant concentrations and lower frequencies. The best fitting of the Cates and Granek model (solid lines) again reveals increasing larger ζ -values as the T/C molar ratio and the CTAT concentration are increased (Table 2). This implies again that the micellar solution evolves from a single relaxation time system
Fig. 2. Normalized Cole–Cole plot at 30 ◦ C for micellar solutions containing a ratio of T/C constant at different CTAT concentration in wt%: (1) 3, (!) 5, (P) 15, (× + ) 30. The solid lines represent the best fit from the Cates–Granek model while the dotted line is the Maxwell model. (A) T/C = 0.2, (B) T/C = 0.5 and (C) T/C = 0.8.
(fast-breaking) to a wide relaxation time distribution system (slow-breaking), akin to polymer solutions with a wide molecular weight distribution, with increasing surfactant concentration and increasing T/C ratio. Notice that the data for the 30 wt% sample do not follow the semicircle even at lower frequencies regardless of the T/C ratio because at this concentration, CTAT forms a hexagonal phase in water [1]. The values of τd , G0 , η0 and ζ are reported in Table 2. Fig. 3 shows the effect of the aging on the linear viscoelastic response of a 5 wt% CTAT micellar solution and a T/C = 0.8. The elastic modulus follows the Maxwell model, G = G0 ω2 τd2 / 1 + ω2 τd2 , immediately after the addition of TEOS (solid line in Fig. 3). However, deviations from Maxwell behavior appear after a few minutes of aging, which become more severe as the aging time
L.D. Mendoza et al. / Journal of Colloid and Interface Science 320 (2008) 290–297
293
Table 2 Parameters obtained from the oscillatory measurements and the best fit to the Granek–Cates model, for a micellar solution—with different contain of CTAT and a constant ratio of T/C = 0.2, 0.5 and 0.8 η0 (Pa s)
T/C
CTAT (wt%)
τd (s)
G0 (Pa)
0.2 0.2 0.2 0.2
3 5 15 30
1.7473 0.4875 0.1593 0.0450
21.42 60.69 745.6 1460
36.86 28.18 118.7 65.74
0.014 0.028 0.286 1.433
0.5 0.5 0.5 0.5
3 5 15 30
0.7312 0.2284 0.0631 0.008
22.7 72.8 495.1 1140
16.55 15.92 31.24 9.12
0.014 0.043 1.433 –
0.8 0.8 0.8
3 5 15
0.2930 0.1861 0.0303
17.6 83.5 719.3
5.15 15.53 21.86
0.286 0.143 1.433
ζ (–)
Fig. 4. Flow curves for a micellar solutions containing CTAT 5 wt% as function of the molar ratio of T/C: (") 0, (2) 0.1, (!) 0.2, (Q) 0.5, (E) 1.0, (e) 1.5, (F) 2.0. The solid lines represent the best fit from the BMP model. The inset shows the influence of the NaOH on the preparation of the samples for different molar ratios of NaOH/CTAT: (P) 0, (!) 0.25 and (× + ) 1.
Fig. 3. Rheograms at 30 ◦ C for CTAT 5 wt% micellar solutions that shown the effect of the aging maintained a T/C constant of 0.8: (1) 0, (!) 2, (P) 3.5, (E) 28, (× + ) 52 h. The solid lines represent the best fit from the Maxwell model.
increases. After one day of aging, the system behaves like a solution of wide size-distribution rigid polymer molecules. For larger aging times, only small changes are detected (compare data indicated with E and × + in Fig. 3). 4.2. Nonlinear rheology Fig. 4 depicts plots of normalized shear stress (σ/G0 ) versus normalized shear rate (γ˙ τd ) for freshly made 5 wt% CTAT solutions that contain increasing amounts of TEOS. In the absence of TEOS, CTAT micellar solutions exhibit Newtonian behavior at low shear rates up to γ˙ τd = 1 and then a wide stress plateau or shear banding flow for higher values of γ˙ τd in the concentration range from ca. 3 to 25 wt% at 30 ◦ C [2]; this shear banding region extends from two critical shear rates, γ˙c1 and γ˙c2 . Here, the second critical shear rate is not observed but the wide stress plateau for the TEOS-free CTAT solutions is evident (data indicated by "); also the transition from the Newtonian region to the shear-banding region is quite abrupt. Upon addition of
small amounts of TEOS, the low shear rate Newtonian region is still detected up to γ˙ τd ≈ 0.5, followed by a shear thinning region up to γ˙ τd ≈ 2 and then by a quasi-plateau region. Notice that in these normalized plots, all the Newtonian data overlap regardless of the T/C ratio and that the transition into the stress plateau is not sharp but rather smooth. The stress plateau decreases slightly with increasing amounts of TEOS and reaches σ/G0 values around 1. These values are larger than that (0.67) predicted by the Cates model [5,6]. Also, the reduced shear rate interval for the stress plateau is larger and better defined at lower T/C ratios. However, as this ratio is increased, the stress plateau tends to vanish and it disappears completely at T/C ca. 0.6. Notice that the stress of the sample with T/C = 2 follows a nearly straight line with increasing shear rate (in this log–log plot), i.e., it behaves like a Newtonian fluid in the whole γ˙ -range examined. The predictions of our model (solid lines) with the parameters obtained experimentally, reported in Table 3, reproduce nicely the experimental data. Again, to determine the role of NaOH, steady shear flow measurements were done in the absence of TEOS in 5 wt% CTAT solutions made with NaOH (samples are the same as those reported in the inset of Fig. 1). Regardless of the NaOH content, the solutions exhibit the same steady shear rheological features, mainly a Newtonian region at low shear rates followed by a well-defined stress plateau above a critical shear rate; however, the value of σPlateau /G0 is the smallest in the NaOH-free CTAT solution; then it increases upon addition to NaOH (NaOH/CTAT = 0.25) and it diminishes again at the largest NaOH/CTAT (=1) ratio employed here. Samples of TEOS/NaOH (molar ratio = 2) without CTAT, on the other hand, are Newtonian in a wide shear rate range and they shear thin weakly at high shear rates but no stress plateau is detected (not shown). Fig. 5 discloses plots of σ/G0 versus γ˙ τd for a 5 wt% CTAT solution with T/C = 0.8 as a function of the aging of the sample.
294
L.D. Mendoza et al. / Journal of Colloid and Interface Science 320 (2008) 290–297
Table 3 Parameters obtained from the best fit to the BMP model (k0 λ and ν) for a micellar solution containing 5 wt% CTAT as function of the ratio T/C, here ϕ0 , ϕ∞ , γ˙c1 and γ˙c2 were obtained from independent rheological measurements
Table 4 Parameters obtained from the best fit to the BMP model (k0 λ and ν) for a micellar solution containing 5 wt% CTAT—and a ratio of T/C = 0.8—as function of the aging from the sample
T/C
γ˙c1 (s−1 )
γ˙c2 (s−1 )
ϕ0 (Pa−1 s−1 )
ϕ∞ (Pa−1 s−1 )
k0 λ (s)
ν (s Pa−1 )
taging (h)
γ˙c1 (s−1 )
γ˙c2 (s−1 )
ϕ0 (Pa−1 s−1 )
ϕ∞ (Pa−1 s−1 )
k0 λ (s)
ν (s Pa−1 )
0.00 0.10 0.20 0.40 0.50 0.65 1.00 2.00
1.07 2.98 2.87 5.14 11.6 7.47 11.2 71.4
477.5 241.3 286.2 306.9 53.1 52.1 21.5 –
0.018 0.018 0.021 0.035 0.037 0.052 0.071 0.80
6.0 6.0 4.0 2.3 2.1 1.9 1.75 1.75
1.0E–5 6.0E–5 1.0E–4 1.5E–4 1.5E–4 1.8E–4 6.0E–4 0.80
0.280 0.050 0.035 0.020 0.017 0.012 0 0
0 2 28 120 290
1.252 3.112 3.178 5.015 0.413
20.08 43.98 19.21 38.50 –
0.059 0.059 0.059 0.059 0.059
6.0 4.45 3.08 2.42 1.80
3.0E–4 2.6E–4 2.3E–4 2.1E–4 2.0E–4
0.040 0.004 4.2E–4 1.3E–4 5.0E–5
Fig. 5. Flow curves for a micellar solutions containing CTAT 5 wt% and a molar ratio of T/C = 0.8 as function of the aging: (2) 0, (!) 2, (P) 28, (F) 120, and (× + ) 290 h. The solid lines represent the best fit from the BMP model.
Once more, regardless of aging, the rheological data overlap in the Newtonian region, which ends at γ˙ τd ≈ 0.1 to 0.2. For higher normalized shear rates, a well defined plateau stress is observed for the sample freshly mixed with TEOS; this plateau stress develops between two critical shear rates and for shear rates larger than γ˙c2 , another Newtonian region appears. The stress plateau vanishes in the sample aged for two hours; instead, a shear-thinning region (with a power-law slope smaller than one) and a Newtonian region at high shear rates are apparent. This behavior becomes more evident as the aging increases and the slope of the shear-thinning region diminishes. Again, the model (solid lines) reproduces quite well the experimental data. Table 4 contains the parameters of the model for the data in this figure. Fig. 6 displays normalized stress growth (σ/σss , being σss , the stress achieved when steady state has been reached) curves after inception of shear flow for 5 wt% CTAT solutions containing different TEOS concentrations for shear rates within the low-shear Newtonian region, γ˙ = 0.03 s−1 (Fig. 6A), and within the shear-banding region, γ˙ = 100 s−1 (Fig. 6B). When the applied shear rate falls within the low-shear Newtonian region, the steady-state stress is reached very rapidly and no overshoots are observed (Fig. 6A). Moreover, the stress growth
Fig. 6. Step rate flow curves for micellar solutions containing CTAT 5 wt% at constant shear rate of (A) 0.026 s−1 and (B) 100 s−1 as function of the molar ratio of T/C: (2) 0, (P) 0.2, (E) 0.5, (× + ) 1.0; solid lines represent the prediction of Maxwell model. Inset: Magnification of (B).
is reproduced with the Maxwell model (solid lines) using τd and G0 obtained from oscillatory measurements (Table 1). On the other hand, when the applied shear rate is within the shearbanding region, stress overshoots and oscillations are detected and longer times are required to achieve steady state (Fig. 6B). The inset in Fig. 6B depicts enlargements of the stress growth curves at short time to observe in more detail the magnitude and position of the overshoots. Notice that the magnitude of the overshoots diminishes and the overshoot maximum shifts to longer times with increasing TEOS content. Moreover, oscillations are detected at longer times that last tens of relaxation times in the TEOS-free sample, which is typical of wormlike micelles undergoing shear-banding flow [3,29,30]. With increasing TEOS, the oscillations damp down quite rapidly and at high T/C ratios, no oscillations are observed and the steady state is achieved quite rapidly.
L.D. Mendoza et al. / Journal of Colloid and Interface Science 320 (2008) 290–297
Fig. 7. Relaxation flow curves for micellar solutions containing CTAT 5 wt% at constant shear rate of (A) 0.026 s−1 and (B) 100 s−1 as function of the molar ratio of T/C: (2) 0, (P) 0.2, (E) 0.5, (× + ) 1.0.
Fig. 7 depicts stress relaxation for 5 wt% CTAT solutions containing different TEOS concentrations after cessation of steady shear flow at applied shear rates of 0.03 (Fig. 7A) and 100 s−1 (Fig. 7B). When the applied shear rate is within the Newtonian region (see Fig. 4), a single relaxation mechanism is detected in the absence and presence of TEOS (Fig. 7A). Notice here that the relaxation becomes faster (steeper slope) as the TEOS concentration is increased. When the applied shear rate is within the shear-banding region (see Fig. 4), the stress exhibits two main relaxation mechanisms in the absence of TEOS and at low T/C ratios: one fast and another slow with a transition region between them (Fig. 7B), which are similar to those observed in the relaxation behavior of micellar solution after been sheared at shear rates within the shear-banding region [10,30]. Notice that the slopes of the fast and slow relaxation mechanisms become steeper, indicating faster relaxation processes as the T/C ratio increases. In fact, for the higher T/C ratio (=1), the relaxation is nearly single-exponential. 5. Discussion and conclusions In this paper we showed that upon addition of TEOS to CTAT solutions, a transition from the fast- to the slow-breaking regime occurs at the T/C molar ratio (Figs. 1 and 2) and aging (Fig. 3) are increased. This transition occurs at increasingly lower frequencies as the T/C ratio (Fig. 1) and the CTAT concentration are raised (Fig. 2), and with aging (Fig. 3). The fitting of the Granek–Cates model discloses increasingly larger ζ -values indicating that reptation becomes increasingly dominant as the TEOS concentration and aging increase. From these data one has to conclude that the system evolves from a kinet-
295
ically dominant wormlike micellar solution to a polymer-like solution with a spectra of relaxation times. One possible explanation to this behavior is the micellar-template role and the polymerization of the silicate groups of TEOS over the micellar surface catalyzed by the presence of a basic medium. In fact, the addition of NaOH increases the dissociation of the surface silanol groups and enhances the interactions with the positively charged micellar surface. All these combined effects should produce shorter and more rigid polymer-like tubular structures, which, of course cannot relax by breaking and recombination like the original wormlike micelles. Of course, the addition of NaOH also screens the electrostatic interactions of the micelles and modifies the curvature and the interface; however, this effect is the opposite to that observed upon addition of both TEOS and NaOH (see inset in Fig. 1). Bandyopadhyay and Sood [26] studied the effect of adding silica particles on the linear rheology of more dilute CTAT solutions (1.4 to 2.6 wt%) in the absence or presence of NaOH (0.178 mM) and found the opposite results to the ones reported here. In fact, they found strong departures from Maxwell behavior in the CTAT solution that did not contained SiO2 particles and increasing approach to Maxwell behavior as the SiO2 amount (keeping fixed the CTAT concentration) was increased. They observed an increase in the values of η0 and G0 upon addition of SiO2 , which they explained by an enhanced screening of the electrostatic interactions that leaded to an increasingly entangled wormlike micellar network. They also reported that η0 and G0 diminish as the SiO2 particle concentration was increased, and explained these trends with the formation of surfactant bilayers due to adsorption of CTA+ ions into the negatively charged silica. However, no evidence of the formation of these bilayers was presented. Yang and co-workers [31, 32] studied by scanning electron microscopy (SEM) the flowinduced silica structure formed during the in situ gelation of wormlike micellar solutions of CTACl and sodium salycilate (NaSal), using tetramethyl orthosilicate (TMOS) and HCl as gelatin substrate. Similar to our hypothesis, these authors observed wormlike micelles of different lengths and orientations depending on the amount of TMOS and on shear rate, but no bilayers. In steady shear measurements, a Newtonian region followed by a wide plateau stress region between two critical shear rates were observed in the TEOS-free CTAT micellar solution (Fig. 4), at low T/C molar ratios (Fig. 4) and in freshly prepared samples (Fig. 5). All these samples follow Maxwell behavior with a single relaxation time. By contrast, at higher T/C (>0.5 for the 5 wt% CTAT sample) (Fig. 4) and after a few hours of aging (Fig. 5), the shear-banding region vanishes; instead a slowly rising (not a plateau) stress with shear rate is observed. The power-law exponent of this shear-thinning region diminishes as the T/C (Fig. 4) or aging (Fig. 5) increases. Escalante et al. [10] reported that wormlike micelles of CTAB and NaSal shifted from kinetic- to reptation-controlled relaxation by increasing the NaSal/CTAB molar ratio and noticed that the shear-banding region tends to vanish as the solutions evolve from the fast- to the slow-breaking regime in agreement with our findings.
296
L.D. Mendoza et al. / Journal of Colloid and Interface Science 320 (2008) 290–297
Results from transient shear flow experiments are also consistent with the disappearance of fast-breaking flexible wormlike micelles. Upon inception of shear flow on freshly mixed CTAT and TEOS samples, the stress growth follows Maxwell behavior regardless of the TEOS content when the applied shear rate is within the Newtonian region (γ˙ = 0.03 s−1 ); this growth is faster as the T/C ratio augments indicating a more elastic structure (Fig. 6A). In fact, τd diminishes and G0 increases as the T/C ratio increases (Table 1), in agreement with these data. At larger shear rates, i.e., γ˙ = 100 s−1 , overshoots are detected in all samples, the maximum of which decreases as the amount of TEOS becomes larger (Fig. 6B). Moreover, the long transients and oscillations, typical of wormlike micelles undergoing shear banding, tend to vanish as the TEOS concentration augments (Fig. 6B). These results support a transition from entangled flexible micelles to rigid polymer-like elongated-rod solutions with wide size distributions. This conclusion is further backed up by the stress relaxation data (Fig. 7). When the applied shear rate is within the Newtonian region (see Fig. 4), a single relaxation behavior is observed in all samples, however, the relaxation becomes faster (again due to the shorter relaxation time) as the TEOS concentration in the sample increases (Fig. 7A). By contrast, when the applied steady shear rate prior to cessation of flow is within the shear-banding region (in the absence of TEOS or in freshly prepared samples of T/C < 0.4), slow and fast relaxation mechanisms are detected. The presence of two relaxation mechanisms have been associated to the different structures that coexist within the shear-banding region in wormlike micellar solutions: one due to the quiescent wormlike solution and another associated to a highly aligned structure induced by flow [10–12]. We proposed that these structures remain in freshly make solutions of CTAT and TEOS. However, as the TEOS content is increased, the behavior tends to a single-relaxation mechanism, which becomes faster as the concentration of TEOS augments. Again, this result is consistent with a typical polymer solution that does not undergo breaking and recombination. In fact, those freshly-made CTAT solutions containing small TEOS contents (T/C 0.4) that exhibit two relaxation times, tend to relax single-exponential as the aging time increases, indicating the disappearance of the fast breaking-and-recombining wormlike micelles and the formation of rigid and shorter elongated polysiloxanes macromolecules over the original micelles that served as templates. The analysis of the variations of the linear-oscillatory parameters and those of the BMP model with T/C ratio (see Fig. SM1 in supporting material) provides further support to our hypothesis. This figure reveals that all the parameters (G0 , τd , λ and ϑ ) exhibit a change in slope in log–log plots against the T/C ratio at values of the T/C (0.5–0.8) where the transition from fast-to-slow breaking occurs as indicated by the plot for ζ versus T/C. The shear banding intensity parameter ϑ tends to zero in this interval, indicating the fading of shear banding, in agreement with previous reports on polymer-like micellar systems that shift into the slow breaking regime [10]. Concurrently, G0 increases monotonically with T/C ratio but, after the transition to slow breaking, it reaches a nearly constant value in-
Fig. 8. XRD of a micellar solutions containing CTAT 5 wt% and T/C of 0.8 as a function of aging after preparation: (A) 0.33 h; (B) 4 h; (C) 24 h; (D) 72 h.
dicating that the structure remains practically unchanged above this T/C ratio. More importantly, τd diminishes whereas the structure relaxation time λ increases as the T/C ratio augments; this suggests that a more rigid structure forms inasmuch as λ increases and the disentanglement time diminishes above the transition to slow breaking. Similar trends in the rheological parameters are observed as the sample age (not shown). To prove conclusively our hypothesis, the structural modifications in the samples with aging were probed by XRD (Fig. 8). Freshly made samples are amorphous as demonstrated by the absence of peaks (diffractogram A). However, after three hours, peaks begin to develop but no well-defined ordered structure has developed yet (diffractogram B); at longer times, several peaks become sharper as time increases. After ca. 24 h, an ordered structure that corresponds to the laminar phase, identified by the position of the three observable peaks (1:2:3), is evident (diffractogram C) and no further changes in peak intensities are noticeable after this time (diffractogram D), in agreement with the aging determined by rheology (Fig. 5). It is noteworthy that XRD measurements to determine the kinetics of formation of ordered mesophases from non-calcinated samples made at room temperature, i.e., without hydrothermal treatment (as in this work), has been reported elsewhere [33,34]; these researchers report similar aging (on the order of hours) for the formation of ordered mesoporous materials. Upon calcination, these TEOS-covered CTAT solutions form a variety of mesoporous materials, depending on the T/C ratio, pH conditions and treatment temperature. The high resolution TEM photograph, shown in the supporting material (Fig. SM2) depicts a section of an elongated rod-like structure, where the laminar mesophase is observed. It is interesting that originally the images in the TEM photographs were identified as the hexagonal MCM-41 phase. However, XRD revealed that instead a laminar phase forms. Kruk et al. [35] reported that interpretation of TEM data is not unambiguous because of the many possible alignments of the order mesoporous sample with respect to the direction of the electron
L.D. Mendoza et al. / Journal of Colloid and Interface Science 320 (2008) 290–297
beam. XRD analysis of the sample examined here demonstrates un-disputably that an ordered laminar mesoporous material forms. Acknowledgments The work was supported by the National Council of Science and Technology of Mexico (CONACyT) through Grant # 48169-Y. Supplementary material Supplementary material associated with this article can be found, in the online version, at DOI: 10.1016/j.jcis.2007.12.024. References [1] J.F.A. Soltero, J.E. Puig, O. Manero, P.C. Schulz, Langmuir 11 (1995) 3337. [2] J.F.A. Soltero, J.E. Puig, O. Manero, Langmuir 12 (1996) 2654. [3] J.F.A. Soltero, F. Bautista, J.E. Puig, O. Manero, Langmuir 15 (1999) 1604. [4] F. Bautista, J.F.A. Soltero, J.H. Pérez-López, J.E. Puig, O. Manero, J. NonNewtonian Fluid Mech. 94 (2000) 57. [5] M.E. Cates, Macromolecules 20 (1987) 2289. [6] M.E. Cates, S.J. Candau, J. Phys. Condens. Matter 2 (1990) 6869. [7] M.E. Cates, M.S. Turner, Eur. Phys. Lett. 7 (1990) 681. [8] M.E. Cates, S. Fielding, in: R. Zana, E.W. Kaler (Eds.), Giant Micelles. Properties and Applications, Marcel Dekker, Boca Raton, 2007, chap. 4. [9] R. Granek, M.E. Cates, J. Chem. Phys. 96 (1992) 4758. [10] J.I. Escalante, E.R. Macías, F. Bautista, J.H. Pérez-López, J.F.A. Soltero, J.E. Puig, O. Manero, Langmuir 19 (2003) 6620. [11] J.-F. Berret, in: R.G. Weiss, P. Terech (Eds.), Molecular Gels. Materials with Self-Assembled Fibrillar Networks, Springer, Secaucus, 2006. [12] J.E. Puig, F. Bautista, J.F.A. Soltero, O. Manero, in: R. Zana, E.W. Kaler (Eds.), Giant Micelles. Properties and Applications, Marcel Dekker, Boca Raton, 2007, chap. 9.
297
[13] J. Rädler, I. Koltovich, T. Salditt, C.R. Safinya, Science 275 (1997) 810. [14] M. Zapotocky, L. Ramos, P. Poulin, T.C. Lubensky, D.A. Weiys, Science 283 (1999) 209. [15] G. Basappa, K.V. Sunnel, P.R. Nott, S. Ramaswamy, V.M. Naik, D. Rout, Eur. Phys. J. B 12 (1999) 269. [16] I. Koltover, J. Rädler, C.R. Safinya, Phys. Rev. Lett. 82 (1999) 1991. [17] M.J. Solomon, T. Saeki, M. Wan, P.J. Scales, D.V. Boger, H. Usui, Langmuir 15 (1999) 20. [18] S.P. Meeker, W.C.K. Poon, J. Crain, E.J. Terentjev, Phys. Rev. E 61 (2000) R6083. [19] J.S. Beck, C. Vartuli, W.J. Roth, M.E. Leonowicz, C.T. Kresge, K.D. Schmitt, C.T.-W. Chu, D.H. Olson, E.W. Sheppard, S.B. McCullen, J.B. Higgins, J.L. Schlenker, J. Am. Chem. Soc. 114 (1992) 10834. [20] C.T. Kresge, M.E. Leonowicz, W.J. Roth, J.C. Vartuli, J.S. Beck, Nature 359 (1992) 710. [21] A. Monnier, F. Schüth, Q. Huo, D. Kumar, D. Margolese, R.S. Maxwell, G.D. Stucky, M. Krishnamurthy, P. Petroff, A. Firouzi, M. Janicke, B.F. Chmelka, Science 261 (1993) 1299. [22] J.S. Beck, C. Vartuli, G.J. Kennedy, C.T. Kresge, W.J. Roth, S.E. Schramm, Chem. Mater. 6 (1994) 1816. [23] P. Yang, D. Zhao, D.L. Margolese, B.F. Chmelka, G.D. Stucky, Nature 396 (1998) 152. [24] A. Sellinger, P.M. Weiss, A. Nguyen, Y. Lu, R.A. Assink, W. Gong, C.J. Brinker, Nature 394 (1998) 256. [25] J. Esquena, C. Rodríguez, C. Solans, H. Kunieda, Microporous Mesoporous Mater. 92 (2006) 212. [26] R. Bandyopadhyay, A.K. Sood, J. Colloid Interface Sci. 283 (2005) 585. [27] F. Bautista, J.F.A. Soltero, E.R. Macías, J.E. Puig, O. Manero, J. Phys. Chem. B 106 (2002) 13018. [28] O. Manero, J.H. Pérez-López, J.I. Escalante, J.E. Puig, F. Bautista, J. NonNewtonian Fluid Mech. 146 (2007) 22. [29] J.-P. Decruppe, E. Cappelare, R. Cresseley, J. Phys. II 7 (1997) 257. [30] J.-F. Berret, G. Porte, Phys. Rev. E 60 (1999) 4268. [31] D.-G. Choi, W.J. Kim, S.-M. Yang, Korea–Australia Rheol. J. 12 (2000) 139. [32] W.J. Kim, S.-M. Yang, Langmuir 16 (2000) 4761. [33] M. Bandyopadhyay, Ph.D. thesis, Bochum Ruhr-University (2004). [34] E. Terrés, Master in Science thesis, Universidad Nacional Autónoma de México (2000). [35] M. Kruk, M. Jaroniec, Y. Yang, A. Sayari, J. Phys. Chem. B 104 (2000) 1581.
Rheological behavior of surfactant-based precursors of silica mesoporous materials L.D. Mendoza a , M. Rabelero a , J.I. Escalante a,∗ , E.R. Macías a , A. González-Álvarez a , F. Bautista b , J.F.A. Soltero a , J.E. Puig a a Departamento de Ingeniería Química, Universidad de Guadalajara, Boul. M. García-Barragán # 1451, Guadalajara, Jal. 44430, México b Departamento de Física, Universidad de Guadalajara, Boul. M. García-Barragán # 1451, Guadalajara, Jal. 44430, México
Received 20 September 2007; accepted 17 December 2007 Available online 23 December 2007
Abstract The linear and non-linear viscoelastic behaviors of polymer-like micellar solutions of cetyltrimethylammonium tosilate (CTAT) with added NaOH and tetraethyl orthosilicate (TEOS) to produce precursors of mesoporous materials are studied. The effect of TEOS/CTAT (T/C) ratio at fixed CTAT concentration, CTAT concentration at fixed T/C and aging time are reported. The systems show increasingly larger deviations from near-Maxwell behavior upon increasing T/C ratio, CTAT concentration and aging. Moreover, in steady and unsteady shear-flow, shear banding develops between two critical shear rates, which tend to fade as the T/C ratio and aging increase. The Granek–Cates model is employed to analyze linear viscoelastic behavior. The Bautista–Manero–Puig (BMP) model is used here to reproduce the steady and transient nonlinear rheology of these systems. We explain these results in terms of the changes in inter-macromolecular interactions that arise out of the presence of colloidal additives in the viscoelastic gel. The ordered mesoporous materials were identified by X-ray diffractometry (XRD) and high-resolution transmission electron microscopy. © 2008 Elsevier Inc. All rights reserved. Keywords: Polymer-like micelles; Colloidal additives; Inter-macromolecular interactions; Viscoelastic behavior
1. Introduction Cetyltrimethylammoniun tosilate (CTAT) is a cationic surfactant that forms polymer-like micelles in water in a concentration range from ca. 1 to 25 wt% at room temperature [1]. These polymer-like solutions exhibit near Maxwell behavior in linear oscillatory flow and shear thinning as well as shear banding in steady shear flow [2–4]. This complex behavior is related to the relaxation mechanisms in this kind of systems, mainly, i.e., kinetic-controlled and diffusion-controlled relaxation mechanisms [5–8]. The ratio of the breaking time to the reptation time (ζ = τbreak /τrep ) controls the relaxation of the system: for very small values of ζ , a single relaxation time dominates and near-Maxwell behavior follows whereas for larger values of ζ , a spectrum of relaxation times and deviations from * Corresponding author.
E-mail address: [email protected] (J.I. Escalante). 0021-9797/$ – see front matter © 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2007.12.024
Maxwell behavior are observed, similar to polymers solutions with wide molecular weight distributions [9]. Moreover, shearbanding flow, characterized by the coexistence of two bands supporting different shear rates at a fixed stress, is commonly observed in the fast-breaking (kinetic-controlled mechanism) regime and this flow vanishes as the diffusion-controlled mechanism becomes dominant [10–12]. The rheology of polymer-like micelles networks can be altered by addition of cosurfactants, electrolytes, organic salts with strongly hydrophobic counter-ions and submicron-sized colloidal particles, because they modify the inter-micellar interactions and the micellar packing and in some cases, it may even result in phase transitions and the formation of novel complexes [12–18]. Ordered mesoporous materials are typically made using surfactant-based self-organized media as templates over which silicate or other inorganic material is added [19–25]. The mechanism of formation of this kind of materials is still under debate.
L.D. Mendoza et al. / Journal of Colloid and Interface Science 320 (2008) 290–297
Moreover, with the exception of the recent report of Bandyopadhyay and Sood [26], the rheology of the precursors of this kind of materials has not been reported, in spite of the rich features that it possesses. In this paper we address the linear and non-linear rheology of CTAT micellar solutions in basic media and the effect of adding a template silica material, mainly tetraethyl orthosilicate (TEOS). We examine the effects of varying TEOS/CTAT (T/C) molar ratio at fixed CTAT concentration (5 wt%) and TEOS/NaOH molar ratio (= 2), varying the surfactant concentration at fixed T/C and TEOS/NaOH = 2, and of aging of the sample. The system was studied over wide frequency and shear rate ranges. 2. Experimental CTAT (99+% pure from Aldrich) was used as received. TEOS was 98% pure (Aldrich). NaOH was 98% pure (Productos Químicos Monterrey). Doubly distilled and de-ionized water was employed. Samples were prepared by weighing the appropriate amount of CTAT and water, and the sample was homogenized and equilibrated at room temperature for a week. Then the TEOS and NaOH (in a molar ratio of 2) were added, shaken by hand and allowed the sample to rest for 15 min (these samples are referred as “fresh” or “freshly-made” in the rest of the text, other wise the aging is indicated in the text) before starting the rheological tests. To examine the effect of the hydroxide ion in the absence of TEOS, CTAT solutions (5 wt%) containing varying amounts of NaOH were also prepared. Steady and transient simple shear as well as small-amplitude oscillatory shear measurements were performed at 30 ◦ C in a Rheometrics Dynamic Stress Rheometer RS-5 having a coneand-plate geometry with diameter of 40-mm and angle of 0.0384 radian (2.2◦ ) and in a Rheometrics RDS-II dynamical spectrometer using also a cone-and-plate geometry of 0.1 radian and 50 mm in diameter. An environmental control unit was used during the measurements to prevent solvent evaporation. The structural properties of the CTAT/TEOS materials were studied in a Siemens D-500 X-ray diffractometer (XRD) fitted with a copper tube and a monochromator for Kα radiation (λ = 1.541 Å). The silica-templated samples were observed in a CM-200 TWIN Philips high-resolution transmission electron microscope. 3. Theoretical The linear viscoelastic data were fitted with a simplified Poisson renewal model proposed by Granek and Cates [9]. The best fitting of this model to Cole–Cole plots, i.e., G (ω) versus G (ω), yields the ratio of the characteristic micellar breaking time to the reptation time (ζ = τbreak /τrep ) that allows to discriminate between kinetic-controlled flow (fastbreaking regime when ζ 1) and diffusion-controlled flow (slow-breaking regime when ζ ca. 0.1). The steady and transient nonlinear flow regimes were fitted with the BMP model that consists of the upper convected Maxwell equation coupled to a shear stress-dependent kinetic
291
equation that accounts for the effect of flow on the breaking and reformation of micelles [4,27,28]. For simple shear, the model reads: 1 dσ12 γ˙12 1 − γ˙12 σ22 = , (1) G0 ϕ dt G0 ϕ ϕ dϕ (ϕ0 − ϕ) (2) = + k0 (1 + ϑ γ˙12 )(ϕ∞ − ϕ)σ12 γ˙12 . dt λ Here σ12 is the shear stress, γ˙12 is the shear rate, σii (i = 1, 2, 3) are the normal stresses, ϕ(≡ η−1 ) is the fluidity, η is the shear viscosity, ϕ0 and ϕ∞ are the fluidities at zero- and at infiniteshear rate, G0 is the high frequency elastic plateau modulus, λ is a structure relaxation time, k0 is a kinetic constant for structure breakdown, and ϑ can be interpreted as a shear-banding intensity parameter. Because σ22 is negligible for CTAT micellar solutions [27], the third term on the left-hand side of Eq. (1) will be droped for the rest of the paper. As detailed elsewhere [27], the parameters of this model can be estimated from independent rheological experiments and then use to fit other experimental data. For steady simple-shear flow, Eqs. (1) and (2) with their time derivatives set to zero give:
σ12 +
2 ϕ 2 − ϕ0 ϕ − k0 λ(ϕ∞ − ϕ)γ˙12 (1 + ϑ γ˙12 ) = 0.
(3)
4. Results 4.1. Linear rheology As discussed above, the stress relaxation in polymer-like micellar solutions is governed by the breaking-and-reformation time, τbreak , and the reptation time, τrep , of the micelles [7]. In the limit where τbreak τrep , the resulting single exponential stress relaxation can be fit to the Maxwell model with a disentanglement or main relaxation time τd {= (τrep · τbreak )1/2 } [5]. A good indication of single exponential stress relaxation is the semicircular form of the so-called Cole–Cole plot. Fig. 1 depicts normalized Cole–Cole plots, i.e., G /G0 versus G /G0 , for 5 wt% CTAT micellar solutions containing different T/C molar ratios. For T/C ca. 0.4, Cole–Cole data can be fitted accurately by a semicircle of radio G0 /2 (dotted line in Fig. 1), up to moderately high frequencies, which demonstrates that the solutions follow closely the Maxwell model with a single relaxation time; the fitting of the Granek–Cates model to these curves (continuous lines in Fig. 1) yields ζ -values smaller than 0.05 (Table 1), indicating that these solutions are in the fast-breaking regime. At higher frequencies, departures from the semi-circle are evident, which can be associated to the breaking time (τbreak ) of the micelles and to Rouse and breathing modes [6]. For T/C > 0.4, deviations from the semicircle at increasingly lower frequencies are detected as this ratio increases, implying a distribution of relaxation times, possibly arising out of competing processes, such as comparable breakage and reptation times, which is typical of the transition from the fast- to the slow-breaking regime. The fitting of the Cates and Granek model to these data gives increasingly larger ζ -values (Table 1), corroborating the transition into the
292
L.D. Mendoza et al. / Journal of Colloid and Interface Science 320 (2008) 290–297
Table 1 Parameters obtained from the oscillatory measurements and the best fit to the Granek–Cates model for a micellar solution containing 5 wt% CTAT as function of the ratio T/C T/C
τd (s)
G0 (Pa)
η0 (Pa s)
ζ (–)
0.00 0.10 0.20 0.40 0.50 0.65 1.00 1.50 2.00
0.410 0.588 0.487 0.293 0.228 0.205 0.101 0.068 0.035
70.19 64.94 60.69 69.98 72.88 99.91 87.79 85.12 83.02
17.75 35.85 28.18 19.61 15.92 29.93 8.65 6.15 4.02
0.1143 0.0143 0.0290 0.0410 0.1433 0.1520 0.2866 1.4330 14.330
Fig. 1. Normalized Cole–Cole plot at 30 ◦ C for CTAT 5 wt% micellar solutions containing different molar relationship of T/C: (1) 0, (2) 0.1, (!) 0.2, (Q) 0.5, (E) 1.0, (e) 1.5, (F) 2.0. The solid lines represent the best fit from the Cates–Granek model while the dotted line is the Maxwell model. The inset shows the influence of the NaOH on the preparation of the samples for different molar ratios of NaOH/CTAT: (P) 0 with ζ = 0.2866, (!) 0.25 with ζ = 0.0286, and (× + ) 1 with ζ = 0.0028.
slow-breaking regime. The values of τd , G0 , the zero-shear dynamic viscosity (η0 ) and ζ are reported in Table 1. Notice that G0 does not depend strongly on T/C, although it increases steadily as the T/C ratio is increased, whereas η0 and τd decrease abruptly with increasing the concentration of TEOS in the solution. To examine the effect of NaOH in the absence of TEOS, measurements were performed with 5 wt% solutions containing no TEOS and varying NaOH/CTAT ratios (see inset). Contrary to the trend observed upon increasing T/C ratio, departures from Maxwell behavior occur at higher frequencies in the TEOS-free CTAT solutions that contain NaOH, i.e., ζ diminishes (see caption in Fig. 1). Evidently, this is a result of the electrostatic screening caused by the addition of OH− that modifies the curvature of the micelles and promotes further growth and larger entanglement density. In the absence of CTAT, concentrated TEOS/NaOH dispersions exhibit weak viscoelasticity with a nearly frequency-independent complex viscosity with values ranging from 0.08 to 0.3 Pa s as TEOS concentration is increased (not shown). Fig. 2 shows normalized Cole–Cole plots at 30 ◦ C for micellar solutions containing T/C molar ratio of 0.2 (Fig. 2A), 0.5 (Fig. 2B) and 0.8 (Fig. 2C) as a function of surfactant concentration. For the lower T/C ratio (Fig. 2A), the experimental data follow again the Maxwell semicircle (dotted line) up to moderately high frequencies after which deviations are observed that become more severe as the surfactant concentration increases. Similar features are depicted for the higher T/C ratios (Figs. 2B and 2C), but deviations take place at lower surfactant concentrations and lower frequencies. The best fitting of the Cates and Granek model (solid lines) again reveals increasing larger ζ -values as the T/C molar ratio and the CTAT concentration are increased (Table 2). This implies again that the micellar solution evolves from a single relaxation time system
Fig. 2. Normalized Cole–Cole plot at 30 ◦ C for micellar solutions containing a ratio of T/C constant at different CTAT concentration in wt%: (1) 3, (!) 5, (P) 15, (× + ) 30. The solid lines represent the best fit from the Cates–Granek model while the dotted line is the Maxwell model. (A) T/C = 0.2, (B) T/C = 0.5 and (C) T/C = 0.8.
(fast-breaking) to a wide relaxation time distribution system (slow-breaking), akin to polymer solutions with a wide molecular weight distribution, with increasing surfactant concentration and increasing T/C ratio. Notice that the data for the 30 wt% sample do not follow the semicircle even at lower frequencies regardless of the T/C ratio because at this concentration, CTAT forms a hexagonal phase in water [1]. The values of τd , G0 , η0 and ζ are reported in Table 2. Fig. 3 shows the effect of the aging on the linear viscoelastic response of a 5 wt% CTAT micellar solution and a T/C = 0.8. The elastic modulus follows the Maxwell model, G = G0 ω2 τd2 / 1 + ω2 τd2 , immediately after the addition of TEOS (solid line in Fig. 3). However, deviations from Maxwell behavior appear after a few minutes of aging, which become more severe as the aging time
L.D. Mendoza et al. / Journal of Colloid and Interface Science 320 (2008) 290–297
293
Table 2 Parameters obtained from the oscillatory measurements and the best fit to the Granek–Cates model, for a micellar solution—with different contain of CTAT and a constant ratio of T/C = 0.2, 0.5 and 0.8 η0 (Pa s)
T/C
CTAT (wt%)
τd (s)
G0 (Pa)
0.2 0.2 0.2 0.2
3 5 15 30
1.7473 0.4875 0.1593 0.0450
21.42 60.69 745.6 1460
36.86 28.18 118.7 65.74
0.014 0.028 0.286 1.433
0.5 0.5 0.5 0.5
3 5 15 30
0.7312 0.2284 0.0631 0.008
22.7 72.8 495.1 1140
16.55 15.92 31.24 9.12
0.014 0.043 1.433 –
0.8 0.8 0.8
3 5 15
0.2930 0.1861 0.0303
17.6 83.5 719.3
5.15 15.53 21.86
0.286 0.143 1.433
ζ (–)
Fig. 4. Flow curves for a micellar solutions containing CTAT 5 wt% as function of the molar ratio of T/C: (") 0, (2) 0.1, (!) 0.2, (Q) 0.5, (E) 1.0, (e) 1.5, (F) 2.0. The solid lines represent the best fit from the BMP model. The inset shows the influence of the NaOH on the preparation of the samples for different molar ratios of NaOH/CTAT: (P) 0, (!) 0.25 and (× + ) 1.
Fig. 3. Rheograms at 30 ◦ C for CTAT 5 wt% micellar solutions that shown the effect of the aging maintained a T/C constant of 0.8: (1) 0, (!) 2, (P) 3.5, (E) 28, (× + ) 52 h. The solid lines represent the best fit from the Maxwell model.
increases. After one day of aging, the system behaves like a solution of wide size-distribution rigid polymer molecules. For larger aging times, only small changes are detected (compare data indicated with E and × + in Fig. 3). 4.2. Nonlinear rheology Fig. 4 depicts plots of normalized shear stress (σ/G0 ) versus normalized shear rate (γ˙ τd ) for freshly made 5 wt% CTAT solutions that contain increasing amounts of TEOS. In the absence of TEOS, CTAT micellar solutions exhibit Newtonian behavior at low shear rates up to γ˙ τd = 1 and then a wide stress plateau or shear banding flow for higher values of γ˙ τd in the concentration range from ca. 3 to 25 wt% at 30 ◦ C [2]; this shear banding region extends from two critical shear rates, γ˙c1 and γ˙c2 . Here, the second critical shear rate is not observed but the wide stress plateau for the TEOS-free CTAT solutions is evident (data indicated by "); also the transition from the Newtonian region to the shear-banding region is quite abrupt. Upon addition of
small amounts of TEOS, the low shear rate Newtonian region is still detected up to γ˙ τd ≈ 0.5, followed by a shear thinning region up to γ˙ τd ≈ 2 and then by a quasi-plateau region. Notice that in these normalized plots, all the Newtonian data overlap regardless of the T/C ratio and that the transition into the stress plateau is not sharp but rather smooth. The stress plateau decreases slightly with increasing amounts of TEOS and reaches σ/G0 values around 1. These values are larger than that (0.67) predicted by the Cates model [5,6]. Also, the reduced shear rate interval for the stress plateau is larger and better defined at lower T/C ratios. However, as this ratio is increased, the stress plateau tends to vanish and it disappears completely at T/C ca. 0.6. Notice that the stress of the sample with T/C = 2 follows a nearly straight line with increasing shear rate (in this log–log plot), i.e., it behaves like a Newtonian fluid in the whole γ˙ -range examined. The predictions of our model (solid lines) with the parameters obtained experimentally, reported in Table 3, reproduce nicely the experimental data. Again, to determine the role of NaOH, steady shear flow measurements were done in the absence of TEOS in 5 wt% CTAT solutions made with NaOH (samples are the same as those reported in the inset of Fig. 1). Regardless of the NaOH content, the solutions exhibit the same steady shear rheological features, mainly a Newtonian region at low shear rates followed by a well-defined stress plateau above a critical shear rate; however, the value of σPlateau /G0 is the smallest in the NaOH-free CTAT solution; then it increases upon addition to NaOH (NaOH/CTAT = 0.25) and it diminishes again at the largest NaOH/CTAT (=1) ratio employed here. Samples of TEOS/NaOH (molar ratio = 2) without CTAT, on the other hand, are Newtonian in a wide shear rate range and they shear thin weakly at high shear rates but no stress plateau is detected (not shown). Fig. 5 discloses plots of σ/G0 versus γ˙ τd for a 5 wt% CTAT solution with T/C = 0.8 as a function of the aging of the sample.
294
L.D. Mendoza et al. / Journal of Colloid and Interface Science 320 (2008) 290–297
Table 3 Parameters obtained from the best fit to the BMP model (k0 λ and ν) for a micellar solution containing 5 wt% CTAT as function of the ratio T/C, here ϕ0 , ϕ∞ , γ˙c1 and γ˙c2 were obtained from independent rheological measurements
Table 4 Parameters obtained from the best fit to the BMP model (k0 λ and ν) for a micellar solution containing 5 wt% CTAT—and a ratio of T/C = 0.8—as function of the aging from the sample
T/C
γ˙c1 (s−1 )
γ˙c2 (s−1 )
ϕ0 (Pa−1 s−1 )
ϕ∞ (Pa−1 s−1 )
k0 λ (s)
ν (s Pa−1 )
taging (h)
γ˙c1 (s−1 )
γ˙c2 (s−1 )
ϕ0 (Pa−1 s−1 )
ϕ∞ (Pa−1 s−1 )
k0 λ (s)
ν (s Pa−1 )
0.00 0.10 0.20 0.40 0.50 0.65 1.00 2.00
1.07 2.98 2.87 5.14 11.6 7.47 11.2 71.4
477.5 241.3 286.2 306.9 53.1 52.1 21.5 –
0.018 0.018 0.021 0.035 0.037 0.052 0.071 0.80
6.0 6.0 4.0 2.3 2.1 1.9 1.75 1.75
1.0E–5 6.0E–5 1.0E–4 1.5E–4 1.5E–4 1.8E–4 6.0E–4 0.80
0.280 0.050 0.035 0.020 0.017 0.012 0 0
0 2 28 120 290
1.252 3.112 3.178 5.015 0.413
20.08 43.98 19.21 38.50 –
0.059 0.059 0.059 0.059 0.059
6.0 4.45 3.08 2.42 1.80
3.0E–4 2.6E–4 2.3E–4 2.1E–4 2.0E–4
0.040 0.004 4.2E–4 1.3E–4 5.0E–5
Fig. 5. Flow curves for a micellar solutions containing CTAT 5 wt% and a molar ratio of T/C = 0.8 as function of the aging: (2) 0, (!) 2, (P) 28, (F) 120, and (× + ) 290 h. The solid lines represent the best fit from the BMP model.
Once more, regardless of aging, the rheological data overlap in the Newtonian region, which ends at γ˙ τd ≈ 0.1 to 0.2. For higher normalized shear rates, a well defined plateau stress is observed for the sample freshly mixed with TEOS; this plateau stress develops between two critical shear rates and for shear rates larger than γ˙c2 , another Newtonian region appears. The stress plateau vanishes in the sample aged for two hours; instead, a shear-thinning region (with a power-law slope smaller than one) and a Newtonian region at high shear rates are apparent. This behavior becomes more evident as the aging increases and the slope of the shear-thinning region diminishes. Again, the model (solid lines) reproduces quite well the experimental data. Table 4 contains the parameters of the model for the data in this figure. Fig. 6 displays normalized stress growth (σ/σss , being σss , the stress achieved when steady state has been reached) curves after inception of shear flow for 5 wt% CTAT solutions containing different TEOS concentrations for shear rates within the low-shear Newtonian region, γ˙ = 0.03 s−1 (Fig. 6A), and within the shear-banding region, γ˙ = 100 s−1 (Fig. 6B). When the applied shear rate falls within the low-shear Newtonian region, the steady-state stress is reached very rapidly and no overshoots are observed (Fig. 6A). Moreover, the stress growth
Fig. 6. Step rate flow curves for micellar solutions containing CTAT 5 wt% at constant shear rate of (A) 0.026 s−1 and (B) 100 s−1 as function of the molar ratio of T/C: (2) 0, (P) 0.2, (E) 0.5, (× + ) 1.0; solid lines represent the prediction of Maxwell model. Inset: Magnification of (B).
is reproduced with the Maxwell model (solid lines) using τd and G0 obtained from oscillatory measurements (Table 1). On the other hand, when the applied shear rate is within the shearbanding region, stress overshoots and oscillations are detected and longer times are required to achieve steady state (Fig. 6B). The inset in Fig. 6B depicts enlargements of the stress growth curves at short time to observe in more detail the magnitude and position of the overshoots. Notice that the magnitude of the overshoots diminishes and the overshoot maximum shifts to longer times with increasing TEOS content. Moreover, oscillations are detected at longer times that last tens of relaxation times in the TEOS-free sample, which is typical of wormlike micelles undergoing shear-banding flow [3,29,30]. With increasing TEOS, the oscillations damp down quite rapidly and at high T/C ratios, no oscillations are observed and the steady state is achieved quite rapidly.
L.D. Mendoza et al. / Journal of Colloid and Interface Science 320 (2008) 290–297
Fig. 7. Relaxation flow curves for micellar solutions containing CTAT 5 wt% at constant shear rate of (A) 0.026 s−1 and (B) 100 s−1 as function of the molar ratio of T/C: (2) 0, (P) 0.2, (E) 0.5, (× + ) 1.0.
Fig. 7 depicts stress relaxation for 5 wt% CTAT solutions containing different TEOS concentrations after cessation of steady shear flow at applied shear rates of 0.03 (Fig. 7A) and 100 s−1 (Fig. 7B). When the applied shear rate is within the Newtonian region (see Fig. 4), a single relaxation mechanism is detected in the absence and presence of TEOS (Fig. 7A). Notice here that the relaxation becomes faster (steeper slope) as the TEOS concentration is increased. When the applied shear rate is within the shear-banding region (see Fig. 4), the stress exhibits two main relaxation mechanisms in the absence of TEOS and at low T/C ratios: one fast and another slow with a transition region between them (Fig. 7B), which are similar to those observed in the relaxation behavior of micellar solution after been sheared at shear rates within the shear-banding region [10,30]. Notice that the slopes of the fast and slow relaxation mechanisms become steeper, indicating faster relaxation processes as the T/C ratio increases. In fact, for the higher T/C ratio (=1), the relaxation is nearly single-exponential. 5. Discussion and conclusions In this paper we showed that upon addition of TEOS to CTAT solutions, a transition from the fast- to the slow-breaking regime occurs at the T/C molar ratio (Figs. 1 and 2) and aging (Fig. 3) are increased. This transition occurs at increasingly lower frequencies as the T/C ratio (Fig. 1) and the CTAT concentration are raised (Fig. 2), and with aging (Fig. 3). The fitting of the Granek–Cates model discloses increasingly larger ζ -values indicating that reptation becomes increasingly dominant as the TEOS concentration and aging increase. From these data one has to conclude that the system evolves from a kinet-
295
ically dominant wormlike micellar solution to a polymer-like solution with a spectra of relaxation times. One possible explanation to this behavior is the micellar-template role and the polymerization of the silicate groups of TEOS over the micellar surface catalyzed by the presence of a basic medium. In fact, the addition of NaOH increases the dissociation of the surface silanol groups and enhances the interactions with the positively charged micellar surface. All these combined effects should produce shorter and more rigid polymer-like tubular structures, which, of course cannot relax by breaking and recombination like the original wormlike micelles. Of course, the addition of NaOH also screens the electrostatic interactions of the micelles and modifies the curvature and the interface; however, this effect is the opposite to that observed upon addition of both TEOS and NaOH (see inset in Fig. 1). Bandyopadhyay and Sood [26] studied the effect of adding silica particles on the linear rheology of more dilute CTAT solutions (1.4 to 2.6 wt%) in the absence or presence of NaOH (0.178 mM) and found the opposite results to the ones reported here. In fact, they found strong departures from Maxwell behavior in the CTAT solution that did not contained SiO2 particles and increasing approach to Maxwell behavior as the SiO2 amount (keeping fixed the CTAT concentration) was increased. They observed an increase in the values of η0 and G0 upon addition of SiO2 , which they explained by an enhanced screening of the electrostatic interactions that leaded to an increasingly entangled wormlike micellar network. They also reported that η0 and G0 diminish as the SiO2 particle concentration was increased, and explained these trends with the formation of surfactant bilayers due to adsorption of CTA+ ions into the negatively charged silica. However, no evidence of the formation of these bilayers was presented. Yang and co-workers [31, 32] studied by scanning electron microscopy (SEM) the flowinduced silica structure formed during the in situ gelation of wormlike micellar solutions of CTACl and sodium salycilate (NaSal), using tetramethyl orthosilicate (TMOS) and HCl as gelatin substrate. Similar to our hypothesis, these authors observed wormlike micelles of different lengths and orientations depending on the amount of TMOS and on shear rate, but no bilayers. In steady shear measurements, a Newtonian region followed by a wide plateau stress region between two critical shear rates were observed in the TEOS-free CTAT micellar solution (Fig. 4), at low T/C molar ratios (Fig. 4) and in freshly prepared samples (Fig. 5). All these samples follow Maxwell behavior with a single relaxation time. By contrast, at higher T/C (>0.5 for the 5 wt% CTAT sample) (Fig. 4) and after a few hours of aging (Fig. 5), the shear-banding region vanishes; instead a slowly rising (not a plateau) stress with shear rate is observed. The power-law exponent of this shear-thinning region diminishes as the T/C (Fig. 4) or aging (Fig. 5) increases. Escalante et al. [10] reported that wormlike micelles of CTAB and NaSal shifted from kinetic- to reptation-controlled relaxation by increasing the NaSal/CTAB molar ratio and noticed that the shear-banding region tends to vanish as the solutions evolve from the fast- to the slow-breaking regime in agreement with our findings.
296
L.D. Mendoza et al. / Journal of Colloid and Interface Science 320 (2008) 290–297
Results from transient shear flow experiments are also consistent with the disappearance of fast-breaking flexible wormlike micelles. Upon inception of shear flow on freshly mixed CTAT and TEOS samples, the stress growth follows Maxwell behavior regardless of the TEOS content when the applied shear rate is within the Newtonian region (γ˙ = 0.03 s−1 ); this growth is faster as the T/C ratio augments indicating a more elastic structure (Fig. 6A). In fact, τd diminishes and G0 increases as the T/C ratio increases (Table 1), in agreement with these data. At larger shear rates, i.e., γ˙ = 100 s−1 , overshoots are detected in all samples, the maximum of which decreases as the amount of TEOS becomes larger (Fig. 6B). Moreover, the long transients and oscillations, typical of wormlike micelles undergoing shear banding, tend to vanish as the TEOS concentration augments (Fig. 6B). These results support a transition from entangled flexible micelles to rigid polymer-like elongated-rod solutions with wide size distributions. This conclusion is further backed up by the stress relaxation data (Fig. 7). When the applied shear rate is within the Newtonian region (see Fig. 4), a single relaxation behavior is observed in all samples, however, the relaxation becomes faster (again due to the shorter relaxation time) as the TEOS concentration in the sample increases (Fig. 7A). By contrast, when the applied steady shear rate prior to cessation of flow is within the shear-banding region (in the absence of TEOS or in freshly prepared samples of T/C < 0.4), slow and fast relaxation mechanisms are detected. The presence of two relaxation mechanisms have been associated to the different structures that coexist within the shear-banding region in wormlike micellar solutions: one due to the quiescent wormlike solution and another associated to a highly aligned structure induced by flow [10–12]. We proposed that these structures remain in freshly make solutions of CTAT and TEOS. However, as the TEOS content is increased, the behavior tends to a single-relaxation mechanism, which becomes faster as the concentration of TEOS augments. Again, this result is consistent with a typical polymer solution that does not undergo breaking and recombination. In fact, those freshly-made CTAT solutions containing small TEOS contents (T/C 0.4) that exhibit two relaxation times, tend to relax single-exponential as the aging time increases, indicating the disappearance of the fast breaking-and-recombining wormlike micelles and the formation of rigid and shorter elongated polysiloxanes macromolecules over the original micelles that served as templates. The analysis of the variations of the linear-oscillatory parameters and those of the BMP model with T/C ratio (see Fig. SM1 in supporting material) provides further support to our hypothesis. This figure reveals that all the parameters (G0 , τd , λ and ϑ ) exhibit a change in slope in log–log plots against the T/C ratio at values of the T/C (0.5–0.8) where the transition from fast-to-slow breaking occurs as indicated by the plot for ζ versus T/C. The shear banding intensity parameter ϑ tends to zero in this interval, indicating the fading of shear banding, in agreement with previous reports on polymer-like micellar systems that shift into the slow breaking regime [10]. Concurrently, G0 increases monotonically with T/C ratio but, after the transition to slow breaking, it reaches a nearly constant value in-
Fig. 8. XRD of a micellar solutions containing CTAT 5 wt% and T/C of 0.8 as a function of aging after preparation: (A) 0.33 h; (B) 4 h; (C) 24 h; (D) 72 h.
dicating that the structure remains practically unchanged above this T/C ratio. More importantly, τd diminishes whereas the structure relaxation time λ increases as the T/C ratio augments; this suggests that a more rigid structure forms inasmuch as λ increases and the disentanglement time diminishes above the transition to slow breaking. Similar trends in the rheological parameters are observed as the sample age (not shown). To prove conclusively our hypothesis, the structural modifications in the samples with aging were probed by XRD (Fig. 8). Freshly made samples are amorphous as demonstrated by the absence of peaks (diffractogram A). However, after three hours, peaks begin to develop but no well-defined ordered structure has developed yet (diffractogram B); at longer times, several peaks become sharper as time increases. After ca. 24 h, an ordered structure that corresponds to the laminar phase, identified by the position of the three observable peaks (1:2:3), is evident (diffractogram C) and no further changes in peak intensities are noticeable after this time (diffractogram D), in agreement with the aging determined by rheology (Fig. 5). It is noteworthy that XRD measurements to determine the kinetics of formation of ordered mesophases from non-calcinated samples made at room temperature, i.e., without hydrothermal treatment (as in this work), has been reported elsewhere [33,34]; these researchers report similar aging (on the order of hours) for the formation of ordered mesoporous materials. Upon calcination, these TEOS-covered CTAT solutions form a variety of mesoporous materials, depending on the T/C ratio, pH conditions and treatment temperature. The high resolution TEM photograph, shown in the supporting material (Fig. SM2) depicts a section of an elongated rod-like structure, where the laminar mesophase is observed. It is interesting that originally the images in the TEM photographs were identified as the hexagonal MCM-41 phase. However, XRD revealed that instead a laminar phase forms. Kruk et al. [35] reported that interpretation of TEM data is not unambiguous because of the many possible alignments of the order mesoporous sample with respect to the direction of the electron
L.D. Mendoza et al. / Journal of Colloid and Interface Science 320 (2008) 290–297
beam. XRD analysis of the sample examined here demonstrates un-disputably that an ordered laminar mesoporous material forms. Acknowledgments The work was supported by the National Council of Science and Technology of Mexico (CONACyT) through Grant # 48169-Y. Supplementary material Supplementary material associated with this article can be found, in the online version, at DOI: 10.1016/j.jcis.2007.12.024. References [1] J.F.A. Soltero, J.E. Puig, O. Manero, P.C. Schulz, Langmuir 11 (1995) 3337. [2] J.F.A. Soltero, J.E. Puig, O. Manero, Langmuir 12 (1996) 2654. [3] J.F.A. Soltero, F. Bautista, J.E. Puig, O. Manero, Langmuir 15 (1999) 1604. [4] F. Bautista, J.F.A. Soltero, J.H. Pérez-López, J.E. Puig, O. Manero, J. NonNewtonian Fluid Mech. 94 (2000) 57. [5] M.E. Cates, Macromolecules 20 (1987) 2289. [6] M.E. Cates, S.J. Candau, J. Phys. Condens. Matter 2 (1990) 6869. [7] M.E. Cates, M.S. Turner, Eur. Phys. Lett. 7 (1990) 681. [8] M.E. Cates, S. Fielding, in: R. Zana, E.W. Kaler (Eds.), Giant Micelles. Properties and Applications, Marcel Dekker, Boca Raton, 2007, chap. 4. [9] R. Granek, M.E. Cates, J. Chem. Phys. 96 (1992) 4758. [10] J.I. Escalante, E.R. Macías, F. Bautista, J.H. Pérez-López, J.F.A. Soltero, J.E. Puig, O. Manero, Langmuir 19 (2003) 6620. [11] J.-F. Berret, in: R.G. Weiss, P. Terech (Eds.), Molecular Gels. Materials with Self-Assembled Fibrillar Networks, Springer, Secaucus, 2006. [12] J.E. Puig, F. Bautista, J.F.A. Soltero, O. Manero, in: R. Zana, E.W. Kaler (Eds.), Giant Micelles. Properties and Applications, Marcel Dekker, Boca Raton, 2007, chap. 9.
297
[13] J. Rädler, I. Koltovich, T. Salditt, C.R. Safinya, Science 275 (1997) 810. [14] M. Zapotocky, L. Ramos, P. Poulin, T.C. Lubensky, D.A. Weiys, Science 283 (1999) 209. [15] G. Basappa, K.V. Sunnel, P.R. Nott, S. Ramaswamy, V.M. Naik, D. Rout, Eur. Phys. J. B 12 (1999) 269. [16] I. Koltover, J. Rädler, C.R. Safinya, Phys. Rev. Lett. 82 (1999) 1991. [17] M.J. Solomon, T. Saeki, M. Wan, P.J. Scales, D.V. Boger, H. Usui, Langmuir 15 (1999) 20. [18] S.P. Meeker, W.C.K. Poon, J. Crain, E.J. Terentjev, Phys. Rev. E 61 (2000) R6083. [19] J.S. Beck, C. Vartuli, W.J. Roth, M.E. Leonowicz, C.T. Kresge, K.D. Schmitt, C.T.-W. Chu, D.H. Olson, E.W. Sheppard, S.B. McCullen, J.B. Higgins, J.L. Schlenker, J. Am. Chem. Soc. 114 (1992) 10834. [20] C.T. Kresge, M.E. Leonowicz, W.J. Roth, J.C. Vartuli, J.S. Beck, Nature 359 (1992) 710. [21] A. Monnier, F. Schüth, Q. Huo, D. Kumar, D. Margolese, R.S. Maxwell, G.D. Stucky, M. Krishnamurthy, P. Petroff, A. Firouzi, M. Janicke, B.F. Chmelka, Science 261 (1993) 1299. [22] J.S. Beck, C. Vartuli, G.J. Kennedy, C.T. Kresge, W.J. Roth, S.E. Schramm, Chem. Mater. 6 (1994) 1816. [23] P. Yang, D. Zhao, D.L. Margolese, B.F. Chmelka, G.D. Stucky, Nature 396 (1998) 152. [24] A. Sellinger, P.M. Weiss, A. Nguyen, Y. Lu, R.A. Assink, W. Gong, C.J. Brinker, Nature 394 (1998) 256. [25] J. Esquena, C. Rodríguez, C. Solans, H. Kunieda, Microporous Mesoporous Mater. 92 (2006) 212. [26] R. Bandyopadhyay, A.K. Sood, J. Colloid Interface Sci. 283 (2005) 585. [27] F. Bautista, J.F.A. Soltero, E.R. Macías, J.E. Puig, O. Manero, J. Phys. Chem. B 106 (2002) 13018. [28] O. Manero, J.H. Pérez-López, J.I. Escalante, J.E. Puig, F. Bautista, J. NonNewtonian Fluid Mech. 146 (2007) 22. [29] J.-P. Decruppe, E. Cappelare, R. Cresseley, J. Phys. II 7 (1997) 257. [30] J.-F. Berret, G. Porte, Phys. Rev. E 60 (1999) 4268. [31] D.-G. Choi, W.J. Kim, S.-M. Yang, Korea–Australia Rheol. J. 12 (2000) 139. [32] W.J. Kim, S.-M. Yang, Langmuir 16 (2000) 4761. [33] M. Bandyopadhyay, Ph.D. thesis, Bochum Ruhr-University (2004). [34] E. Terrés, Master in Science thesis, Universidad Nacional Autónoma de México (2000). [35] M. Kruk, M. Jaroniec, Y. Yang, A. Sayari, J. Phys. Chem. B 104 (2000) 1581.