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Structure of AOT reverse micelles under shear
Journal of Colloid and Interface Science 288 (2005) 230–237 www.elsevier.com/locate/jcis
Structure of AOT reverse micelles under shear Hadas Gochman-Hecht, Havazelet Bianco-Peled ∗ Department of Chemical Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel Received 5 August 2004; accepted 25 February 2005 Available online 7 April 2005
Abstract Reverse micelles in the AOT/water/isooctane system, at various water contents (W0 ), were studied using rheometry and small angle X-ray scattering (SAXS) experiments under static conditions and under shear. The SAXS analysis confirmed the spherical shape of the micelles at low water content and revealed a transition into elongated micelles at higher water content. A population of spherical micelles was found to coexist with the cylindrical ones, even above the percolation threshold. The shape transformation was correlated with a viscosity leap observed in the rheometry measurements. Reverse micelles at low water content under shear act as a Newtonian fluid, without any detectable shape changes. In contrast, reverse micelles at high water content behave as a shear thinning fluid. SAXS measurements at high water content under shear force have shown that the shear forces induced alignment of the cylindrical micelles in the flow direction, without any other changes in the micelle dimensions. The anisotropy parameter, a measure of the degree of the spatial order, was found to increase with increasing water content and shear rate. 2005 Elsevier Inc. All rights reserved. Keywords: AOT reversed micelles; Small-angle X-ray scattering; Rheology; Shear-induced alignment; Shear thinning
1. Introduction Reverse micelles are thermodynamically stable surfactant aggregates having a polar core, which are formed spontaneously when dissolving certain types of surfactants in oil. A typical example is the ionic surfactant sodium di-2ethylhexylsulfosuccinate (AOT), which forms spherical reverse micelles in many organic solvents [1]. These micelles have the capability of solubilizing considerable amounts of water while maintaining their droplet-like structure (w/o microemulsion or L2 phase) up to moderately high values of the surfactant volume fraction and the molar ratio of water to surfactant, W0 [2]. In this isotropic liquid phase, addition of a small amount of water to a reverse micellar solution usually induces spherical growth of the micelles, with no significant changes of macroscopic quantities such as the viscosity. Small angle scattering experiments have shown that the micelles are polydisperse in size [3–5], with an av* Corresponding author. Fax: +972 4 8295672.
E-mail address: [email protected] (H. Bianco-Peled). 0021-9797/$ – see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2005.02.083
erage radius that depends linearly upon W0 [4] and is almost independent of surfactant concentration [6–8]. Reverse micelle solutions are also known to present a dynamic percolation phenomenon with increasing temperature or water volume fraction [9]. The percolation threshold corresponds to a considerable jump (2–3 orders of magnitude) in conductivity. Although extensive experimental results have been presented for droplet aggregation in this regime [10], it is still a matter of debate whether the increase in conductivity is a result of charge transfer between aggregated droplets or whether the aggregated droplets open, forming interconnected cylindrical structures [11]. Experimental [12] and theoretical [11] evidence that support the latter suggestion was only recently presented from studies that detected structural transition from spherical droplets to cylindrical structures in the single-phase w/o AOT system. Even though the structure of AOT/water/isooctane reverse micelles has been extensively studied by others, to the best of our knowledge, the influence of shear on the structure has never been investigated before. Yet it is well known that shear forces may induce significant structural changes in
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many surfactant systems. As an example, lecithin “polymerlike” reverse micelles exhibit shear thinning behavior under the effect of shear flow [13–15]. This phenomenon was attributed to shear-induced orientation, alignment, and elongation of micellar aggregates and their disentanglement along the flow direction. The main objective of this study was to characterize the behavior of the AOT/water/isooctane system under shear flow conditions and identify any shear-induced structural modifications. In addition to scientific interest, this study may have practical significance, since industrial utilization of reversed micelle solutions, for example as a solvent for liquid–liquid extraction of proteins or for enzymatic catalysis [16], is performed under stirring conditions.
2. Materials and methods 2.1. Materials AOT (Fluka) and isooctane (Carlo Erba or Scharlau) were used as received. For the preparation of reverse micelle solutions, Mili-Q water was injected into 10 or 100 mM solutions of AOT in isooctane using a Hamilton syringe to give a desired water content W0 = [H2 O]/[AOT]. 2.2. Rheology Rheology measurements were performed using a Rheometric Scientific (ARES) strain-controlled shear rheometer fitted with a bub-and-cup (Couette) fixture covered with an anti-evaporation cover. Steady rate sweep measurements were performed in a shear rate range of 1–250 Hz. Calculations and processing of the results were performed using the RSI Orchstator software package, version 6.5.1. 2.3. Small angle X-ray scattering Small angle X-ray scattering (SAXS) measurements under static conditions were performed with CuKα radiation using a compact Kratky camera having a linear-positionsensitive detector system (Raytech) with pulse-height discrimination and a multichannel analyzer (Nucleus). The entrance slit to the collimation block was 20 µm, and the slit length delimiters were set at 15 mm. The sample-to-detector distance was 26.4 cm. Reverse micelle solutions were placed in cylindrical quartz cells (A. Paar Co., 1 mm path length). The sample temperature was kept at 25 ◦ C by means of a temperature controller (A. Paar). Primary beam intensities were determined using the moving slit method of Kratky and Stabinger [17] and subsequently using a thin quartz monitor as a secondary standard. The scattering curves, as a function of the scattering vector h = 4π sin θ/λ (where 2θ and λ are the scattering angle and the wavelength, respectively), were corrected for counting time and for sample absorption. The
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background scattering (isooctane-filled capillary) was measured separately and subtracted from the scattering curve. The correction of the effect of the beam dimension (desmearing) was performed according to the indirect transformation method [18,19], using the program ITP. Data analysis was based on fitting the desmeared curve to an appropriate model using a least-square procedure. SAXS measurements under shear were performed at beam line ID02, European Synchrotron Radiation Facility, Grenoble, France. The wavelength of the incident photons was 1 Å, and the sample-detector distance was either 1 or 2 m. The measurements were performed using a twodimensional multiwire proportional gas counter. The samples were studied in a polycarbonate Couette cell having a 1 mm annular gap between the rotor-outer and stator-inner cylinders, mounted on motorized translation stages, which allow the sample to be aligned in both the radial and tangential positions [20]. In the radial configuration the incident beam was perpendicular to the flow direction but parallel to the velocity gradient. In the tangential configuration the incident beam was parallel to the flow direction or the shear velocity. The raw data were corrected to account for the transmission the response of the 2D detector.
3. Modeling of the SAXS intensities The analysis of scattered X-ray intensities requires taking into account the existence of an inherent polydispersity in the reverse micelles sizes, which arises from a balance between several contributions to the free energy of the micellar solution [21]. The scattered X-ray intensity, I (h), is expressed as [21–23] I (h) = np P s (h)S(h),
(1)
where np is the number of micelles per unit volume, Ps (h) is the average polydisperse form factor, which gives information on the internal structure of the reversed micelles (shape and size), and S(h) is the structure factor which provides information on the structural arrangement of the reversed micelles (intermicellar interaction). In dilute solutions, the structure factor is approximately equal to unity, due to negligible interparticle interference. At low water contents, AOT reverse micelles are commonly described using a model of spherical “core and shell” aggregates [22]. This model describes an aggregate with an outer diameter of R s , built on a core having a radius of Rc and electron density of ρc , surrounded by a thin spherical layer having an electron density of ρs . The form factor for such an aggregate is given by 4π 3 Ps (h) = R (ρs − ρm )Φ(hRs ) 3 s 2 4π 3 Rc (ρc − ρs )Φ(hRc ) + (2) 3
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with
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sin(hRs ) − hRs cos(hRs ) , (hRs )3 sin(hRc ) − hRc cos(hRc ) Φ(hRc ) = 3 , (hRc )3
Φ(hRs ) = 3
where ρm is the electron density of the medium. When all micelles have the same spherical core–shell structure but they differ in their size, the polydisperse form factor P s (h) can be obtained from Ps (h) by assuming a Gaussian (normal) size distribution of the core radius [23] with σ as the root-mean-square deviation from the mean water core radius Rc , and a constant shell thickness: 1 (Rc − Rc )2 (3) dRc . P s (h) = √ Ps (h) exp − 2σ 2 2πσ 2 In fitting Eqs. (1)–(3) to the experimental SAXS curves it was assumed that the shell had a constant thickness of 0.4 nm [21]. The electron densities of the shell, the water core, and the solvent were fixed as ρs = 550 e− /nm3 , ρc = 334.6 e− /nm3 , and ρm = 240.8 e− /nm3 , respectively. The fit was obtained by varying the values of Rc , σ , and np .
4. Results and discussion As already mentioned, our main objective was to characterize the structure of AOT/isooctane/water reverse micelles under shear conditions. As this system was never investigated before under shear, we measured first the flow characteristics and the viscosity using a rheometer, in an attempt to find indications to structural modification, if any. Fig. 1 shows the viscosity variations of reverse micelles solutions at two different surfactant concentrations, 10 mM and 100 mM AOT, as a function of the water content W0 . The data shown in this figure reveals that at low water content (up to about W0 ∼ = 70), the viscosity increases moderately with
Fig. 1. Viscosity of reverse micelles solution vs water content for (P) 10 mM AOT and (") 100 mM AOT.
an increase in the water content, whereas at higher water content, a sharp increase in the system viscosity is observed with further water addition. Huruguen et al. [24] have shown that a sharp leap in the viscosity of reverse micellar solution occurs at a water volume fraction equivalent to that of the percolation threshold. The viscosity increase with increasing water content was attributed to cluster formation by intermicellar interactions causing reverse micelles to connect and form temporary continuous and infinite structures. Steady rate sweep tests at low water content did not reveal any dependence of the viscosity on the shear rate; i.e., the solution acts as a Newtonian fluid. This observation suggests that the solution contains isotopic objects, as expected below the percolation threshold. In contrast, at higher water content (above the percolation threshold), the solution was found to act as a shear thinning fluid whose viscosity decreased with increasing shear rate (see an example in Fig. 2). Shear thinning behavior was previously observed in solutions of lecithin reverse micelles [13]. As lecithin was known to form cylindrical reverse micelles [14,15], the shear thinning was attributed to the alignment and disentanglement of these micelles along the flow direction. Despite the inherent differences between the polymeric lecithin micelles and the AOT micelles, the shear thinning behavior observed in our experiments may hint of the formation of larger, nonisotropic aggregates above the percolation threshold. Prior to an attempt to identify shear-induced structural changes using SAXS, reference measurements under static conditions were performed. As our main interest is to study the effect of shear, we have chosen to perform these experiments at very low surfactant concentration in order to minimize the effect of particle collision. Moreover, the analysis of the SAXS data is simplified since the effect of interparticle interference can be neglected and the value of the structure factor can be set to 1. The first series of SAXS experiments included reverse micelle solutions below the percolation threshold. The water content was varied in the range of W0 between 0 and 70,
Fig. 2. Viscosity changes in 100 mM AOT reverse micelle solution (W0 = 100) in shear rate sweep test.
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Table 1 Summary of best-fit parameters for 10 mM AOT solutions W0
np (aggregates/nm3 )
σ (nm)
Rc (nm)
0 10 20 30 40 50
3.73 × 10−6 1.07 × 10−5 3.11 × 10−6 2.27 × 10−6 1.42 × 10−6 1.04 × 10−6
2.80 0.68 1.71 1.24 1.25 1.67
0 1.59 3.25 3.52 5.16 5.74
Note. W0 : molar ratio of water to surfactant; np : number of micelles per unit volume; Rc : mean radius of the water core; σ : root-mean-square deviation from the mean water core radius. Table 2 Summary of best-fit parameters for 100 mM AOT solutions Fig. 3. Experimental scattering curves (symbols) for reverse micelles solutions containing 10 mM AOT at different W0 values indicated next to the curves. Solid lines were calculated from Eqs. (1)–(3) using the best-fit parameters summarized in Table 1. Successive curves are displaced upward by one logarithmic unit for better visualization.
W0
np (aggregates/nm3 )
σ (nm)
Rc (nm)
0 5 8 10 20 30 40 50 70
1.93 × 10−3 2.97 × 10−4 7.44 × 10−5 1.28 × 10−4 5.92 × 10−5 1.83 × 10−5 8.70 × 10−6 1.29 × 10−5 4.78 × 10−6
0.37 0.60 0.88 0.48 0.84 0.93 1.18 1.35 2.00
0 0.77 1.46 1.65 2.33 3.44 4.90 5.81 8.09
Note. W0 : molar ratio of water to surfactant; np : number of micelles per unit volume; Rc : mean radius of the water core; σ : root-mean-square deviation from the mean water core radius.
Fig. 4. Experimental scattering curves (symbols) for reverse micelles solutions containing 100 mM AOT at different W0 values indicated next to the curve. Solid lines were calculated from Eqs. (1)–(3) using the best-fit parameters summarized in Table 2. Successive curves are displaced upward by one logarithmic unit for better visualization.
keeping the concentration of AOT constant at either 10 mM (ca. 0.4% wt/vol) or 100 mM. As AOT reverse micelles at low water content are expected to have an isotropic, core– shell spherical shape, the experimental data were fitted to Eqs. (1)–(3), assuming S(h) = 1. The experimental SAXS curves are shown in Figs. 3 and 4 for AOT concentrations of 10 and 100 mM, respectively. The solid lines in these figures were calculated from the best-fit parameters given in Tables 1 and 2. As can be seen, the model gave a good fit to all the experimental scattering curves. It should be noted that in view of the recent analysis of Svergun et al. [12], the possibility of coexistence of cylindrical reverse micelles was examined. However, the symmetrical shape of the distance distribution function curves, as well as results of test calcu-
Fig. 5. Fits of the scattering data from 100 mM AOT with W0 of (!) 80, (P) 90, (") 100, and (E) 120 to a model of the cylindrical core–shell micelle (- - -) and to a model describing a mixture of cylindrical and spherical micelles (—). Successive curves are displaced upward by one logarithmic unit for better visualization.
lations, has shown that if such micelles exist in our system, their amount is very low and does not affect the scattering curves. At water content higher then W0 = 80, i.e., above the percolation threshold, the scattering patterns change considerably (Fig. 5). Accordingly, the model of “core–shell”
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spherical aggregates failed to give a reasonable fit to the experimental data. Huruguen et al. [25] suggested a model of cylindrical objects forming a network due to micelle entanglement to describe their SAXS data. The form factor Pc (h) of such an objects is given by [26] Pc (h) π/2 =
2J1 (hR sin α) sin(hL cos α/2) ρ hR sin α (hL cos α/2)
2 sin α dα, (4)
0
where ρ is the electron density difference between the cylinder and the medium, J1 is the first-order Bessel function, L is the cylinder length, and R is the radius of its cross-section. In the current work, we have followed the approach of Huruguen et al. [25], but used a form factor of core–shell cylindrical rodlike objects. Following preliminary calculations, we were able to justify the use of a simplified expression that is applicable in the limit of very long core– shell cylinders [27], 2J1 (hRs ) πL Pc (h) = (ρs − ρm )πRs2 h hRs 2J1 (hRc ) 2 (5) + (ρc − ρs )πRc2 , hRc where ρc and Rc are the electron density and the radius of the polar core of the cylindrical reverse micelles, Rs is the outer radius of the micelles, ρs is the electron density of the cylindrical shell surrounding the core, and ρm is the electron density of the medium. In addition, we have taken into account the polydispersity of the cylinder’s radius; i.e., it was assumed that all micelles had the same cylindrical core– shell shape but they varied in radius. The average form factor was calculated assuming a Gaussian size distribution by replacing Ps (h) with Pc (h) in Eq. (3). Finally, the scattering intensity was calculated from Eq. (1), assuming S(h) = 1 (as applying the structure factor given by Huruguen et al. [25] did not improve the fit). The best fits to this model, which were calculated from the best-fit parameters given in Tables 3 and are shown as solid lines in Fig. 5, agree well with the experimental data at small scattering angles. However, the fits at higher angles are rather poor, indicating the coexistence of smaller objects. Indeed, a good fit to the experimental data was obtained by suggesting a twocomponent model that takes into account the coexistence of small spherical micelles having a diameter of 1 nm (solid lines in Fig. 5). Interestingly, our results indicate that coexistence of cylindrical and spherical micelles seem to be found both not only below the percolation threshold [12], but also above it. Table 3 also lists the ratio of surfactant molecule forming cylindrical micelles to these forming spherical micelles, N c /N s . This value was calculated from the fit assuming an identical area per headgroup in both types of aggregates. It is evidence that most molecules are found in the cylindrical micelles.
Table 3 Summary of best-fit parameters for 100 mM AOT solutions at high water contents W0
Rc (nm)
σ (nm)
N c /N s
80 90 100 120
5.49 5.67 6.36 6.50
1.20 1.17 1.26 1.26
371 375 351 250
Note. W0 : molar ratio of water to surfactant; Rc : mean radius of the water core; σ : root-mean-square deviation from the mean water core radius; N c /N s : ratio of surfactant molecules forming cylindrical micelles to those forming spherical micelles.
Fig. 6. Two-dimensional scattering patterns from reverse micelles of 100 mM AOT; radial beam position vs shear rate and W0 .
Finally, we have measured the SAXS patterns of reverse micelle solutions in the dynamic state, while shearing the samples in a Couette flow cell at shear rates between 0 and 900 rpm. Experiments were performed using 100 mM AOT and water content W0 in the range between 0 and 120. The 2D scattering patterns of the different reverse micelle solutions in the radial beam position are shown on Fig. 6. In the static state (0 rpm), all scattering patterns seem to be spherical (Fig. 6), indicating that the samples are isotropic. At relatively low water content of W0 = 60 and 70, spherical patterns are still observed at all shear rates. Contrary, at higher water contents, a transition from spherical patterns to elongated ones, indicative to the development of anisotropy in the sample, may be observed. The anisotropy is more pronounced, and seen at a lower shear rate, as the water content increases. Scattering patterns of reverse micelles at low water content of W0 = 60 and 70 were circularly averaged and the resulting scattering curves were analyzed by fitting the experimental data to Eqs. (1)–(3), as described before. The
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scattering curves were almost identical to those obtained with the Kratky camera under static condition and therefore are not reported again. Moreover, the shear rate had no effect on the size of the spherical reverse micelles nor on any of the other fitted parameters. At higher shear rate and higher water contents, the scattering patterns show an increasing degree of anisotropy (Fig. 6). It was previously reported that cylindrical micelles under shear forces could go through shear-induced alignment [28], with an orientation distribution of the micelles respectively to the flow direction and the incident X-ray beam. The instantaneous angular velocity of the micelles is determined by their orientation relative to the local streamlines [29]. At the same time, Brownian motion, characterized by a rotational diffusion coefficient D, will tend to randomize the orientations. The relative importance of the two competing effects is characterized by the parameter Γ = G/D, where G is the shear rate. For very long cylinders D can be calculated from [29] D=
3kB T (s − t) , 8πη(L/2)3
s > 2,
(6)
where s = log(L/R), t = 1.57 − 7(0.28 − 1/s)2 , η is the solvent viscosity, k B the Boltzmann constant, and T the temperature. The scattered intensity, as a function of Γ , can be evaluated using the relation [29] 2π I (h) = C0
π f (φ, θ, Γ )
dφ0 0
0
× Pc (h, γ+ ) + Pc (h, γ+ ) sin θ dθ,
(7)
where C0 is a constant, cos γ± = sin θ cos φ cos ϑ0 ± cos θ · sin ϑ0 , f (φ, θ, Γ ) is a probability function calculated from f (φ, θ, Γ ) =
(1 − cos 2φ0 )(1 + sin2 θ cos 2φ0 ) 4π[1 − sin2 θ cos 2φ0 cos 2(φ − φ0 )]2
,
(8)
2φ0 = arctan(8/Γ ), and ϑ0 is defined as the angle between the micelle vertical axes in the laboratory coordinates system (z) and the scattering vector (h). The form factor Pc (h) was calculated from Eq. (4), modified to account for the core–shell structure of the micelle and for the radius polydispersity. Due to the complexity of this model, the length distribution was ignored. As previously described, the calculation of the scattering curve also took into account a second population of small (Rc = 1 nm) spherical micelles. The 2D scattering patterns, measured in the radial X-ray beam position, were cross-sectioned to get 1D scattering curves. The scattering intensities measured in the vertical and horizontal axes of the detector plane, Iv (h) (i.e., ϑ0 = 0) and IH (h) (i.e., ϑ0 = π/2), in which the scattering vector is perpendicular and parallel to the cylinder axes, were fit using Eq. (7). As an example, Fig. 7 demonstrates several fits for solutions with W0 = 80 at different shear rates. The most important observation that can be made based on the fits is that no change has occurred in the structural parameters of
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Table 4 Anisotropy parameter at high water content and its dependence on water content and shear rate W0
Shear rate 100 rpm
300 rpm
500 rpm
700 rpm
900 rpm
80 90 100 120
– 27 20.6 –
11.9 39.1 24.6 116.2
14.2 34.3 27.3 116.5
16.5 35.2 28.5 112.2
16.9 29 28.7 110.4
Note. W0 : molar ratio of water to surfactant.
the micelles: the core radius and polydispersity, the micelle length, and the cylinders/sphere ration remained practically constant with increasing shear rate. Following the work of Münch et al. [28], we have also calculated the anisotropy parameter A(h), defined as A(h) =
IV (h) . IH (h)
(9)
The anisotropy parameter was calculated for the maximum change in the ratio Iv (h)/IH (h) and is summarized in Table 4. These results are also illustrated in Fig. 8. The anisotropy degree indicates the degree of spatial order of the cylindrical reverse micelles in the flow direction due to induced shear force [28]. Table 4 and Fig. 8 show an increase in the anisotropy with water content increase, which might be due to an increase in the length of the cylindrical reverse micelles with increasing water content. Seemingly, there is a slight increase in the anisotropy parameter with increasing shear rate. This may suggest a better alignment of the cylinders in the flow direction at higher shear rates. This observation agrees well with the shear-thinning behavior that was found in the rheometry experiments, since better alignment in the flow direction results in less entanglement and therefore in lower viscosity. The scattering patterns shown in Fig. 6 were measured in the radial beam position, in which the incident beam is perpendicular to the flow direction. The results of measurements in this position are sensitive to ordering within the flow direction plane, and therefore alignment of the cylindrical micelles in the flow direction leads to anisotropic patterns. In contrast, measurement of the same solutions in the tangential position, in which the incident beam was parallel to the flow direction, showed isotropic scattering patterns at all water contents (data not shown). Since the results of measurements in this position are sensitive to ordering within the plane perpendicular to the flow direction, the isotropic pattern are indicative that there is no ordering in this plane.
5. Summary SAXS and rheometry experiments were used for the characterization of AOT reverse micelles in isooctane. At low water content the solution was found to behave as a Newtonian fluid. The structure was identified, using SAXS, as
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(a)
(b)
(c)
(d)
Fig. 7. Fit of Eq. (7), shown as solid lines, to experimental scattering intensities measured in the vertical and horizontal axes of the detector plane, Iv (h) (2) and IH (h) (!), at W0 = 80 and shear rates of (a) 300, (b) 500, (c) 700, and (d) 900 s−1 .
Fig. 8. Dependence of the anisotropy parameter on the shear rate at water content W0 of (") 80, (2) 90, (F) 100, and (Q) 120. Lines are guides to the eye.
spherical micelles, both under static conditions and under shear. At higher water content, a sharp viscosity increase occurs, which is probably associated with the percolation threshold. Viscosity measurements revealed that beyond this
point, the solution behaves as a shear-thinning liquid. SAXS analysis have shown that the reverse micelles at high water content have a cylindrical shape, but a population of small, spherical micelles coexists as well. The change in the micelle’s shape, which increases the aspect ratio of the micelle and therefore raises the resistance to shear, might be responsible for the sharp increase in viscosity observed in the rheometry experiments. SR-SAXS experiments under shear detected an alignment of the micelles in the flow direction; however, no other changes in the micelle dimensions were observed. The anisotropy parameter of the cylindrical reverse micelles solution, a measure of the degree of spatial order in the flow direction, increases with increasing water content and shear rate. The increase in the spatial order explains the shear-thinning phenomenon observed in the rheometry experiments.
Acknowledgments We acknowledge the European Synchrotron Radiation Facility for provision of synchrotron radiation facilities and
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we thank Dr. N. Theyencheri for assistance in using beamline ID02. This research was partly supported by the Technion V.P.R. Fund—Tobias and Reissman Research Fund in Chemical Engineering.
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Structure of AOT reverse micelles under shear Hadas Gochman-Hecht, Havazelet Bianco-Peled ∗ Department of Chemical Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel Received 5 August 2004; accepted 25 February 2005 Available online 7 April 2005
Abstract Reverse micelles in the AOT/water/isooctane system, at various water contents (W0 ), were studied using rheometry and small angle X-ray scattering (SAXS) experiments under static conditions and under shear. The SAXS analysis confirmed the spherical shape of the micelles at low water content and revealed a transition into elongated micelles at higher water content. A population of spherical micelles was found to coexist with the cylindrical ones, even above the percolation threshold. The shape transformation was correlated with a viscosity leap observed in the rheometry measurements. Reverse micelles at low water content under shear act as a Newtonian fluid, without any detectable shape changes. In contrast, reverse micelles at high water content behave as a shear thinning fluid. SAXS measurements at high water content under shear force have shown that the shear forces induced alignment of the cylindrical micelles in the flow direction, without any other changes in the micelle dimensions. The anisotropy parameter, a measure of the degree of the spatial order, was found to increase with increasing water content and shear rate. 2005 Elsevier Inc. All rights reserved. Keywords: AOT reversed micelles; Small-angle X-ray scattering; Rheology; Shear-induced alignment; Shear thinning
1. Introduction Reverse micelles are thermodynamically stable surfactant aggregates having a polar core, which are formed spontaneously when dissolving certain types of surfactants in oil. A typical example is the ionic surfactant sodium di-2ethylhexylsulfosuccinate (AOT), which forms spherical reverse micelles in many organic solvents [1]. These micelles have the capability of solubilizing considerable amounts of water while maintaining their droplet-like structure (w/o microemulsion or L2 phase) up to moderately high values of the surfactant volume fraction and the molar ratio of water to surfactant, W0 [2]. In this isotropic liquid phase, addition of a small amount of water to a reverse micellar solution usually induces spherical growth of the micelles, with no significant changes of macroscopic quantities such as the viscosity. Small angle scattering experiments have shown that the micelles are polydisperse in size [3–5], with an av* Corresponding author. Fax: +972 4 8295672.
E-mail address: [email protected] (H. Bianco-Peled). 0021-9797/$ – see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2005.02.083
erage radius that depends linearly upon W0 [4] and is almost independent of surfactant concentration [6–8]. Reverse micelle solutions are also known to present a dynamic percolation phenomenon with increasing temperature or water volume fraction [9]. The percolation threshold corresponds to a considerable jump (2–3 orders of magnitude) in conductivity. Although extensive experimental results have been presented for droplet aggregation in this regime [10], it is still a matter of debate whether the increase in conductivity is a result of charge transfer between aggregated droplets or whether the aggregated droplets open, forming interconnected cylindrical structures [11]. Experimental [12] and theoretical [11] evidence that support the latter suggestion was only recently presented from studies that detected structural transition from spherical droplets to cylindrical structures in the single-phase w/o AOT system. Even though the structure of AOT/water/isooctane reverse micelles has been extensively studied by others, to the best of our knowledge, the influence of shear on the structure has never been investigated before. Yet it is well known that shear forces may induce significant structural changes in
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many surfactant systems. As an example, lecithin “polymerlike” reverse micelles exhibit shear thinning behavior under the effect of shear flow [13–15]. This phenomenon was attributed to shear-induced orientation, alignment, and elongation of micellar aggregates and their disentanglement along the flow direction. The main objective of this study was to characterize the behavior of the AOT/water/isooctane system under shear flow conditions and identify any shear-induced structural modifications. In addition to scientific interest, this study may have practical significance, since industrial utilization of reversed micelle solutions, for example as a solvent for liquid–liquid extraction of proteins or for enzymatic catalysis [16], is performed under stirring conditions.
2. Materials and methods 2.1. Materials AOT (Fluka) and isooctane (Carlo Erba or Scharlau) were used as received. For the preparation of reverse micelle solutions, Mili-Q water was injected into 10 or 100 mM solutions of AOT in isooctane using a Hamilton syringe to give a desired water content W0 = [H2 O]/[AOT]. 2.2. Rheology Rheology measurements were performed using a Rheometric Scientific (ARES) strain-controlled shear rheometer fitted with a bub-and-cup (Couette) fixture covered with an anti-evaporation cover. Steady rate sweep measurements were performed in a shear rate range of 1–250 Hz. Calculations and processing of the results were performed using the RSI Orchstator software package, version 6.5.1. 2.3. Small angle X-ray scattering Small angle X-ray scattering (SAXS) measurements under static conditions were performed with CuKα radiation using a compact Kratky camera having a linear-positionsensitive detector system (Raytech) with pulse-height discrimination and a multichannel analyzer (Nucleus). The entrance slit to the collimation block was 20 µm, and the slit length delimiters were set at 15 mm. The sample-to-detector distance was 26.4 cm. Reverse micelle solutions were placed in cylindrical quartz cells (A. Paar Co., 1 mm path length). The sample temperature was kept at 25 ◦ C by means of a temperature controller (A. Paar). Primary beam intensities were determined using the moving slit method of Kratky and Stabinger [17] and subsequently using a thin quartz monitor as a secondary standard. The scattering curves, as a function of the scattering vector h = 4π sin θ/λ (where 2θ and λ are the scattering angle and the wavelength, respectively), were corrected for counting time and for sample absorption. The
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background scattering (isooctane-filled capillary) was measured separately and subtracted from the scattering curve. The correction of the effect of the beam dimension (desmearing) was performed according to the indirect transformation method [18,19], using the program ITP. Data analysis was based on fitting the desmeared curve to an appropriate model using a least-square procedure. SAXS measurements under shear were performed at beam line ID02, European Synchrotron Radiation Facility, Grenoble, France. The wavelength of the incident photons was 1 Å, and the sample-detector distance was either 1 or 2 m. The measurements were performed using a twodimensional multiwire proportional gas counter. The samples were studied in a polycarbonate Couette cell having a 1 mm annular gap between the rotor-outer and stator-inner cylinders, mounted on motorized translation stages, which allow the sample to be aligned in both the radial and tangential positions [20]. In the radial configuration the incident beam was perpendicular to the flow direction but parallel to the velocity gradient. In the tangential configuration the incident beam was parallel to the flow direction or the shear velocity. The raw data were corrected to account for the transmission the response of the 2D detector.
3. Modeling of the SAXS intensities The analysis of scattered X-ray intensities requires taking into account the existence of an inherent polydispersity in the reverse micelles sizes, which arises from a balance between several contributions to the free energy of the micellar solution [21]. The scattered X-ray intensity, I (h), is expressed as [21–23] I (h) = np P s (h)S(h),
(1)
where np is the number of micelles per unit volume, Ps (h) is the average polydisperse form factor, which gives information on the internal structure of the reversed micelles (shape and size), and S(h) is the structure factor which provides information on the structural arrangement of the reversed micelles (intermicellar interaction). In dilute solutions, the structure factor is approximately equal to unity, due to negligible interparticle interference. At low water contents, AOT reverse micelles are commonly described using a model of spherical “core and shell” aggregates [22]. This model describes an aggregate with an outer diameter of R s , built on a core having a radius of Rc and electron density of ρc , surrounded by a thin spherical layer having an electron density of ρs . The form factor for such an aggregate is given by 4π 3 Ps (h) = R (ρs − ρm )Φ(hRs ) 3 s 2 4π 3 Rc (ρc − ρs )Φ(hRc ) + (2) 3
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with
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sin(hRs ) − hRs cos(hRs ) , (hRs )3 sin(hRc ) − hRc cos(hRc ) Φ(hRc ) = 3 , (hRc )3
Φ(hRs ) = 3
where ρm is the electron density of the medium. When all micelles have the same spherical core–shell structure but they differ in their size, the polydisperse form factor P s (h) can be obtained from Ps (h) by assuming a Gaussian (normal) size distribution of the core radius [23] with σ as the root-mean-square deviation from the mean water core radius Rc , and a constant shell thickness: 1 (Rc − Rc )2 (3) dRc . P s (h) = √ Ps (h) exp − 2σ 2 2πσ 2 In fitting Eqs. (1)–(3) to the experimental SAXS curves it was assumed that the shell had a constant thickness of 0.4 nm [21]. The electron densities of the shell, the water core, and the solvent were fixed as ρs = 550 e− /nm3 , ρc = 334.6 e− /nm3 , and ρm = 240.8 e− /nm3 , respectively. The fit was obtained by varying the values of Rc , σ , and np .
4. Results and discussion As already mentioned, our main objective was to characterize the structure of AOT/isooctane/water reverse micelles under shear conditions. As this system was never investigated before under shear, we measured first the flow characteristics and the viscosity using a rheometer, in an attempt to find indications to structural modification, if any. Fig. 1 shows the viscosity variations of reverse micelles solutions at two different surfactant concentrations, 10 mM and 100 mM AOT, as a function of the water content W0 . The data shown in this figure reveals that at low water content (up to about W0 ∼ = 70), the viscosity increases moderately with
Fig. 1. Viscosity of reverse micelles solution vs water content for (P) 10 mM AOT and (") 100 mM AOT.
an increase in the water content, whereas at higher water content, a sharp increase in the system viscosity is observed with further water addition. Huruguen et al. [24] have shown that a sharp leap in the viscosity of reverse micellar solution occurs at a water volume fraction equivalent to that of the percolation threshold. The viscosity increase with increasing water content was attributed to cluster formation by intermicellar interactions causing reverse micelles to connect and form temporary continuous and infinite structures. Steady rate sweep tests at low water content did not reveal any dependence of the viscosity on the shear rate; i.e., the solution acts as a Newtonian fluid. This observation suggests that the solution contains isotopic objects, as expected below the percolation threshold. In contrast, at higher water content (above the percolation threshold), the solution was found to act as a shear thinning fluid whose viscosity decreased with increasing shear rate (see an example in Fig. 2). Shear thinning behavior was previously observed in solutions of lecithin reverse micelles [13]. As lecithin was known to form cylindrical reverse micelles [14,15], the shear thinning was attributed to the alignment and disentanglement of these micelles along the flow direction. Despite the inherent differences between the polymeric lecithin micelles and the AOT micelles, the shear thinning behavior observed in our experiments may hint of the formation of larger, nonisotropic aggregates above the percolation threshold. Prior to an attempt to identify shear-induced structural changes using SAXS, reference measurements under static conditions were performed. As our main interest is to study the effect of shear, we have chosen to perform these experiments at very low surfactant concentration in order to minimize the effect of particle collision. Moreover, the analysis of the SAXS data is simplified since the effect of interparticle interference can be neglected and the value of the structure factor can be set to 1. The first series of SAXS experiments included reverse micelle solutions below the percolation threshold. The water content was varied in the range of W0 between 0 and 70,
Fig. 2. Viscosity changes in 100 mM AOT reverse micelle solution (W0 = 100) in shear rate sweep test.
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Table 1 Summary of best-fit parameters for 10 mM AOT solutions W0
np (aggregates/nm3 )
σ (nm)
Rc (nm)
0 10 20 30 40 50
3.73 × 10−6 1.07 × 10−5 3.11 × 10−6 2.27 × 10−6 1.42 × 10−6 1.04 × 10−6
2.80 0.68 1.71 1.24 1.25 1.67
0 1.59 3.25 3.52 5.16 5.74
Note. W0 : molar ratio of water to surfactant; np : number of micelles per unit volume; Rc : mean radius of the water core; σ : root-mean-square deviation from the mean water core radius. Table 2 Summary of best-fit parameters for 100 mM AOT solutions Fig. 3. Experimental scattering curves (symbols) for reverse micelles solutions containing 10 mM AOT at different W0 values indicated next to the curves. Solid lines were calculated from Eqs. (1)–(3) using the best-fit parameters summarized in Table 1. Successive curves are displaced upward by one logarithmic unit for better visualization.
W0
np (aggregates/nm3 )
σ (nm)
Rc (nm)
0 5 8 10 20 30 40 50 70
1.93 × 10−3 2.97 × 10−4 7.44 × 10−5 1.28 × 10−4 5.92 × 10−5 1.83 × 10−5 8.70 × 10−6 1.29 × 10−5 4.78 × 10−6
0.37 0.60 0.88 0.48 0.84 0.93 1.18 1.35 2.00
0 0.77 1.46 1.65 2.33 3.44 4.90 5.81 8.09
Note. W0 : molar ratio of water to surfactant; np : number of micelles per unit volume; Rc : mean radius of the water core; σ : root-mean-square deviation from the mean water core radius.
Fig. 4. Experimental scattering curves (symbols) for reverse micelles solutions containing 100 mM AOT at different W0 values indicated next to the curve. Solid lines were calculated from Eqs. (1)–(3) using the best-fit parameters summarized in Table 2. Successive curves are displaced upward by one logarithmic unit for better visualization.
keeping the concentration of AOT constant at either 10 mM (ca. 0.4% wt/vol) or 100 mM. As AOT reverse micelles at low water content are expected to have an isotropic, core– shell spherical shape, the experimental data were fitted to Eqs. (1)–(3), assuming S(h) = 1. The experimental SAXS curves are shown in Figs. 3 and 4 for AOT concentrations of 10 and 100 mM, respectively. The solid lines in these figures were calculated from the best-fit parameters given in Tables 1 and 2. As can be seen, the model gave a good fit to all the experimental scattering curves. It should be noted that in view of the recent analysis of Svergun et al. [12], the possibility of coexistence of cylindrical reverse micelles was examined. However, the symmetrical shape of the distance distribution function curves, as well as results of test calcu-
Fig. 5. Fits of the scattering data from 100 mM AOT with W0 of (!) 80, (P) 90, (") 100, and (E) 120 to a model of the cylindrical core–shell micelle (- - -) and to a model describing a mixture of cylindrical and spherical micelles (—). Successive curves are displaced upward by one logarithmic unit for better visualization.
lations, has shown that if such micelles exist in our system, their amount is very low and does not affect the scattering curves. At water content higher then W0 = 80, i.e., above the percolation threshold, the scattering patterns change considerably (Fig. 5). Accordingly, the model of “core–shell”
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spherical aggregates failed to give a reasonable fit to the experimental data. Huruguen et al. [25] suggested a model of cylindrical objects forming a network due to micelle entanglement to describe their SAXS data. The form factor Pc (h) of such an objects is given by [26] Pc (h) π/2 =
2J1 (hR sin α) sin(hL cos α/2) ρ hR sin α (hL cos α/2)
2 sin α dα, (4)
0
where ρ is the electron density difference between the cylinder and the medium, J1 is the first-order Bessel function, L is the cylinder length, and R is the radius of its cross-section. In the current work, we have followed the approach of Huruguen et al. [25], but used a form factor of core–shell cylindrical rodlike objects. Following preliminary calculations, we were able to justify the use of a simplified expression that is applicable in the limit of very long core– shell cylinders [27], 2J1 (hRs ) πL Pc (h) = (ρs − ρm )πRs2 h hRs 2J1 (hRc ) 2 (5) + (ρc − ρs )πRc2 , hRc where ρc and Rc are the electron density and the radius of the polar core of the cylindrical reverse micelles, Rs is the outer radius of the micelles, ρs is the electron density of the cylindrical shell surrounding the core, and ρm is the electron density of the medium. In addition, we have taken into account the polydispersity of the cylinder’s radius; i.e., it was assumed that all micelles had the same cylindrical core– shell shape but they varied in radius. The average form factor was calculated assuming a Gaussian size distribution by replacing Ps (h) with Pc (h) in Eq. (3). Finally, the scattering intensity was calculated from Eq. (1), assuming S(h) = 1 (as applying the structure factor given by Huruguen et al. [25] did not improve the fit). The best fits to this model, which were calculated from the best-fit parameters given in Tables 3 and are shown as solid lines in Fig. 5, agree well with the experimental data at small scattering angles. However, the fits at higher angles are rather poor, indicating the coexistence of smaller objects. Indeed, a good fit to the experimental data was obtained by suggesting a twocomponent model that takes into account the coexistence of small spherical micelles having a diameter of 1 nm (solid lines in Fig. 5). Interestingly, our results indicate that coexistence of cylindrical and spherical micelles seem to be found both not only below the percolation threshold [12], but also above it. Table 3 also lists the ratio of surfactant molecule forming cylindrical micelles to these forming spherical micelles, N c /N s . This value was calculated from the fit assuming an identical area per headgroup in both types of aggregates. It is evidence that most molecules are found in the cylindrical micelles.
Table 3 Summary of best-fit parameters for 100 mM AOT solutions at high water contents W0
Rc (nm)
σ (nm)
N c /N s
80 90 100 120
5.49 5.67 6.36 6.50
1.20 1.17 1.26 1.26
371 375 351 250
Note. W0 : molar ratio of water to surfactant; Rc : mean radius of the water core; σ : root-mean-square deviation from the mean water core radius; N c /N s : ratio of surfactant molecules forming cylindrical micelles to those forming spherical micelles.
Fig. 6. Two-dimensional scattering patterns from reverse micelles of 100 mM AOT; radial beam position vs shear rate and W0 .
Finally, we have measured the SAXS patterns of reverse micelle solutions in the dynamic state, while shearing the samples in a Couette flow cell at shear rates between 0 and 900 rpm. Experiments were performed using 100 mM AOT and water content W0 in the range between 0 and 120. The 2D scattering patterns of the different reverse micelle solutions in the radial beam position are shown on Fig. 6. In the static state (0 rpm), all scattering patterns seem to be spherical (Fig. 6), indicating that the samples are isotropic. At relatively low water content of W0 = 60 and 70, spherical patterns are still observed at all shear rates. Contrary, at higher water contents, a transition from spherical patterns to elongated ones, indicative to the development of anisotropy in the sample, may be observed. The anisotropy is more pronounced, and seen at a lower shear rate, as the water content increases. Scattering patterns of reverse micelles at low water content of W0 = 60 and 70 were circularly averaged and the resulting scattering curves were analyzed by fitting the experimental data to Eqs. (1)–(3), as described before. The
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scattering curves were almost identical to those obtained with the Kratky camera under static condition and therefore are not reported again. Moreover, the shear rate had no effect on the size of the spherical reverse micelles nor on any of the other fitted parameters. At higher shear rate and higher water contents, the scattering patterns show an increasing degree of anisotropy (Fig. 6). It was previously reported that cylindrical micelles under shear forces could go through shear-induced alignment [28], with an orientation distribution of the micelles respectively to the flow direction and the incident X-ray beam. The instantaneous angular velocity of the micelles is determined by their orientation relative to the local streamlines [29]. At the same time, Brownian motion, characterized by a rotational diffusion coefficient D, will tend to randomize the orientations. The relative importance of the two competing effects is characterized by the parameter Γ = G/D, where G is the shear rate. For very long cylinders D can be calculated from [29] D=
3kB T (s − t) , 8πη(L/2)3
s > 2,
(6)
where s = log(L/R), t = 1.57 − 7(0.28 − 1/s)2 , η is the solvent viscosity, k B the Boltzmann constant, and T the temperature. The scattered intensity, as a function of Γ , can be evaluated using the relation [29] 2π I (h) = C0
π f (φ, θ, Γ )
dφ0 0
0
× Pc (h, γ+ ) + Pc (h, γ+ ) sin θ dθ,
(7)
where C0 is a constant, cos γ± = sin θ cos φ cos ϑ0 ± cos θ · sin ϑ0 , f (φ, θ, Γ ) is a probability function calculated from f (φ, θ, Γ ) =
(1 − cos 2φ0 )(1 + sin2 θ cos 2φ0 ) 4π[1 − sin2 θ cos 2φ0 cos 2(φ − φ0 )]2
,
(8)
2φ0 = arctan(8/Γ ), and ϑ0 is defined as the angle between the micelle vertical axes in the laboratory coordinates system (z) and the scattering vector (h). The form factor Pc (h) was calculated from Eq. (4), modified to account for the core–shell structure of the micelle and for the radius polydispersity. Due to the complexity of this model, the length distribution was ignored. As previously described, the calculation of the scattering curve also took into account a second population of small (Rc = 1 nm) spherical micelles. The 2D scattering patterns, measured in the radial X-ray beam position, were cross-sectioned to get 1D scattering curves. The scattering intensities measured in the vertical and horizontal axes of the detector plane, Iv (h) (i.e., ϑ0 = 0) and IH (h) (i.e., ϑ0 = π/2), in which the scattering vector is perpendicular and parallel to the cylinder axes, were fit using Eq. (7). As an example, Fig. 7 demonstrates several fits for solutions with W0 = 80 at different shear rates. The most important observation that can be made based on the fits is that no change has occurred in the structural parameters of
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Table 4 Anisotropy parameter at high water content and its dependence on water content and shear rate W0
Shear rate 100 rpm
300 rpm
500 rpm
700 rpm
900 rpm
80 90 100 120
– 27 20.6 –
11.9 39.1 24.6 116.2
14.2 34.3 27.3 116.5
16.5 35.2 28.5 112.2
16.9 29 28.7 110.4
Note. W0 : molar ratio of water to surfactant.
the micelles: the core radius and polydispersity, the micelle length, and the cylinders/sphere ration remained practically constant with increasing shear rate. Following the work of Münch et al. [28], we have also calculated the anisotropy parameter A(h), defined as A(h) =
IV (h) . IH (h)
(9)
The anisotropy parameter was calculated for the maximum change in the ratio Iv (h)/IH (h) and is summarized in Table 4. These results are also illustrated in Fig. 8. The anisotropy degree indicates the degree of spatial order of the cylindrical reverse micelles in the flow direction due to induced shear force [28]. Table 4 and Fig. 8 show an increase in the anisotropy with water content increase, which might be due to an increase in the length of the cylindrical reverse micelles with increasing water content. Seemingly, there is a slight increase in the anisotropy parameter with increasing shear rate. This may suggest a better alignment of the cylinders in the flow direction at higher shear rates. This observation agrees well with the shear-thinning behavior that was found in the rheometry experiments, since better alignment in the flow direction results in less entanglement and therefore in lower viscosity. The scattering patterns shown in Fig. 6 were measured in the radial beam position, in which the incident beam is perpendicular to the flow direction. The results of measurements in this position are sensitive to ordering within the flow direction plane, and therefore alignment of the cylindrical micelles in the flow direction leads to anisotropic patterns. In contrast, measurement of the same solutions in the tangential position, in which the incident beam was parallel to the flow direction, showed isotropic scattering patterns at all water contents (data not shown). Since the results of measurements in this position are sensitive to ordering within the plane perpendicular to the flow direction, the isotropic pattern are indicative that there is no ordering in this plane.
5. Summary SAXS and rheometry experiments were used for the characterization of AOT reverse micelles in isooctane. At low water content the solution was found to behave as a Newtonian fluid. The structure was identified, using SAXS, as
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(a)
(b)
(c)
(d)
Fig. 7. Fit of Eq. (7), shown as solid lines, to experimental scattering intensities measured in the vertical and horizontal axes of the detector plane, Iv (h) (2) and IH (h) (!), at W0 = 80 and shear rates of (a) 300, (b) 500, (c) 700, and (d) 900 s−1 .
Fig. 8. Dependence of the anisotropy parameter on the shear rate at water content W0 of (") 80, (2) 90, (F) 100, and (Q) 120. Lines are guides to the eye.
spherical micelles, both under static conditions and under shear. At higher water content, a sharp viscosity increase occurs, which is probably associated with the percolation threshold. Viscosity measurements revealed that beyond this
point, the solution behaves as a shear-thinning liquid. SAXS analysis have shown that the reverse micelles at high water content have a cylindrical shape, but a population of small, spherical micelles coexists as well. The change in the micelle’s shape, which increases the aspect ratio of the micelle and therefore raises the resistance to shear, might be responsible for the sharp increase in viscosity observed in the rheometry experiments. SR-SAXS experiments under shear detected an alignment of the micelles in the flow direction; however, no other changes in the micelle dimensions were observed. The anisotropy parameter of the cylindrical reverse micelles solution, a measure of the degree of spatial order in the flow direction, increases with increasing water content and shear rate. The increase in the spatial order explains the shear-thinning phenomenon observed in the rheometry experiments.
Acknowledgments We acknowledge the European Synchrotron Radiation Facility for provision of synchrotron radiation facilities and
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we thank Dr. N. Theyencheri for assistance in using beamline ID02. This research was partly supported by the Technion V.P.R. Fund—Tobias and Reissman Research Fund in Chemical Engineering.
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