Langmuir 1997, 13, 4995-5000
4995
Evaluation of Micellar Overlapping Parameters for a Drag-Reducing Cationic Surfactant System: Light Scattering and Viscometry Yuntao Hu† and Eric F. Matthys*,‡ Materials Research Laboratory and Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, California 93106 Received August 19, 1996. In Final Form: June 18, 1997X The equilibrium micellar structure in a tris(2-hydroxyethyl)(tallowalkyl)ammonium acetate (TTAA)/ sodium salicylate (NaSal) surfactant system has been studied using light scattering and low-shear viscometry methods. Scattered light intensity autocorrelation functions were measured and the hydrodynamic correlation lengths were obtained for solutions with surfactant concentrations ranging from 1 to 5 mM and NaSal/TTAA ratios from 0.6 to 5 at temperatures from 10 to 80 °C. From the temperature dependence of the hydrodynamic correlation length, the concentration, counterion/surfactant ratio, and temperature at which the free micelles begin to overlap were inferred. The overlapping surfactant concentration decreases with increasing counterion/surfactant ratio, and the overlapping ratio decreases with increasing surfactant concentration. The overlapping temperature increases with increasing surfactant concentration and counterion/surfactant ratio. “Zero shear rate” viscosities of these solutions at 25 °C were measured to estimate the overlapping concentrations, and the results are compared to light scattering results.
1. Introduction The surfactant tris(2-hydroxyethyl)(tallowalkyl)ammonium acetate (TTAA) with added sodium salicylate (NaSal) as the counterion has good drag-reducing abilities and has been studied as a potential additive for drag reduction applications in industrial systems.1 (Drag reduction is a phenomenon characterized by much reduced wall friction in turbulent flow of high-molecular weight polymers and self-assembling surfactant solutions.) This surfactant system also shows rheological characteristics typical of shear-induced structures (“SIS”),2-4 which are found in surfactant drag-reducing systems. There have been a few rheological studies on this surfactant system, but most of the studies were carried out under strong shear flow conditions where shear-induced structures are present. Indeed, the flow in practical industrial situations is usually rather strong and drag reduction is seen only in strong (turbulent) flow regimes. It is also suspected that shear-induced structures play a very important, and perhaps necessary, role in the drag reduction effect. However, as more information on the drag reduction and rheology of this surfactant system became available, we realized that the micellar structures at rest might be more relevant than was thought previously in accounting for the drag reduction and rheological behavior of the solutions. It was observed that there is usually good drag reduction in solutions where micelles appear to be overlapping. In a few cases during our simultaneous studies on drag reduction and rheology, we observed drag reduction in micellar solutions for which we were not able to observe any obvious sign of shear-induced structures with our rheometers. It might indeed be possible that the original micelles or micellar structures may be capable of generating drag reduction without any subsequent shearinduced structure formation. Furthermore, in a study of the effect of counterion salt on the rheological behavior of this surfactant solution,3 we found that the buildup of †
Materials Research Laboratory. Department of Mechanical and Environmental Engineering. X Abstract published in Advance ACS Abstracts, August 15, 1997. ‡
(1) Gasljevic, K.; Matthys, E. F. Energy Buildings 1993, 20, 45. (2) Hu, Y.; Matthys, E. F. Rheol. Acta 1995, 34, 450. (3) Hu, Y.; Matthys, E. F. Rheol. Acta 1996, 35 (5), 470. (4) Hofmann, S.; Stern, P.; Myska, J. Rheol. Acta 1994, 33, 419.
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shear-induced structures can be greatly facilitated or even become quasi-instantaneous if there are preexisting large micelles or micellar structures, giving us more evidence that the micellar structure at rest may be more directly responsible for the nonlinear flow behavior. It is therefore desirable to have more information about the equilibrium micellar structures in this drag-reducing surfactant system. Obtaining such information was a goal of the present study. Light scattering has been used extensively to probe micellar systems at the equilibrium state,5-16 but a common difficulty encountered in the light scattering studies of micellar systems is that both the intermicellar interactions and the micellar size may change with changing surfactant concentration. This coupling makes it difficult to obtain quantitatively accurate data on the dimensions of the micelles, since it becomes then questionable to extrapolate data to zero micellar concentration in order to correct for the effect of intermicellar interactions. Some valuable information was nevertheless obtained on the equilibrium micellar structures, and especially so in the semidilute region. Candau et al., for example, studied micellar solutions of cetyltrimethylammonium bromide (CTAB) in H2O and KBr.5,6 They found that both the scattered intensity and the collective diffusion coefficient depend on the concentration in a fashion analogous to that for semidilute polymer solutions in good solvent. The effect of NaSal on the diffusion coefficient of micelles in CTAB was studied by Nemoto et al. and shows a complicated relationship with a maximum followed by a minimum.8 The issue of micellar overlapping (5) Candau, S. J.; Hirsch, E.; Zana, R. J. Phys. 1984, 45, 1263. (6) Candau, S. J.; Hirsch, E.; Zana, R. J. Colloid. Interface Sci. 1985, 105, 521. (7) Makhloufi, R.; Hirsch, E.; Candau, S. J.; Binana-Limbele, W.; Zana, R. J. Phys. Chem. 1989, 93, 8095. (8) Nemoto, N.; Kuwahara, M. Langmuir 1993, 9, 419. (9) Nemoto, N.; Kuwahara, M. Colloid Polym. Sci. 1994, 272, 846. (10) Nemoto, N.; Kuwahara, M.; Yao, M. L.; Osaki, K. Langmuir 1995, 11, 30. (11) Ng, S. C.; Gan, L. M.; Chew, C. H. Colloid Polym. Sci. 1992, 270, 64. (12) Koike, A.; Yamamura, T.; Nemoto, N. Colloid Polym. Sci. 1994, 272, 955. (13) Imae, T. J. Phys. Chem. 1990, 94, 5953. (14) Imae, T.; Ikeda, S. J. Phys. Chem. 1986, 90, 5216. (15) Imae, T. Langmuir 1989, 5, 205. (16) Imae, T. Colloid Polym. Sci. 1989, 267, 707.
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in both nonionic and cationic surfactant solutions was studied by Imae et al.13-16 There are few light scattering studies on the TTAA/ NaSal micellar system. Myska measured the hydrodynamic radius of micelles at different surfactant concentrations.17 The data were extrapolated to zero concentration and a value of 19.5 nm was obtained for a TTAA/ NaSal ratio of 1.5. The validity of this value relies on the assumption that the micellar size remains constant at varying concentrations, however, which is uncertain. In addition to the light scattering approach, intrinsic viscosity measurements have also been used for probing the equilibrium molecular conformation and structures in dilute polymer solutions.18 In this method, the zero shear rate viscosity at different polymer concentrations is measured and extrapolated to zero concentration. For micellar solutions, however, the extrapolations are again of unclear validity because of the same problem associated with the light scattering technique, i.e., the fact that the micellar structures change with concentration, Even such qualitative information is very useful, however. In this work we studied the equilibrium micellar structures for the TTAA/NaSal surfactant system over the temperature, surfactant concentration, and counterion/surfactant ratio ranges within which drag reduction applications are contemplated and rheological studies have been performed. Considering our practical motivations and the limitations in interpreting the light-scattering results and low shear rate viscosity measurements, rather than attempting a fundamental study, we have focused here on realistic qualitative information, which may help to improve our understanding of the drag-reducing and rheological behavior of this surfactant system. 2. Experimental Section 2.1. Materials. The surfactant used is tris(2-hydroxyethyl)(tallowalkyl)ammonium acetate or “TTAA” [CH3(CH2)nN(C2H4OH)3CH3COO-] from AKZO Chemicals (a.k.a. Ethoquad T/1350). This surfactant is a mixture with two dominant alkyl chain lengths of 16 and 18. The average molecular weight is 454. The master fluid is in liquid form with 50% of surfactant and 36% of 2-propanol by weight in water. 2-Hydroxylbenzoate (sodium salicylate) from Aceto, Inc. was used as the counterion. The solvent was ultrapure water produced with a Milli-Q ultrapure water system. All the materials were used as received. The solution was kept at room temperature for at least 12 h after preparation. The samples for light scattering studies were filtered using 0.2 µm Nalgene filters (Nalge Co.). The filtered solutions were then kept for at least 24 h before measurements. 2.2. Instrumentation. The dynamic light scattering measurements (photon correlation functions) were performed using a Brookhaven BI-2330AT digital correlator system with 72 channels. The light source was a vertically polarized He-Ne laser with a wavelength of 632.8 nm and an output of 30 mW. All the data reported were collected at a scattering angle of 30° and with a detector pinhole of 200 µm unless otherwise indicated. Data were analyzed using the cumulant software provided by the company. The temperature was controlled by a water bath and kept stable within 0.5 °C. Low shear rate viscosities were measured with a Rheometrics ARES controlled rate rheometer with a cocylinder geometry (gap outer diameter, 34 mm; gap inner diameter, 32 mm; height, 33 mm) and a DSR controlled stress rheometer with a cocylinder geometry (outer cup diameter, 32 mm; inner bob diameter, 29.5 mm; height, 44 mm).
3. Results and Discussion 3.1. Light Scattering. Analysis of the Intensity Autocorrelation Function. The parameter measured directly in the dynamic light scattering experiments was (17) Myska, J.; Stern, P. Colloid Polym. Sci. 1994, 272, 542. (18) Ait-Kadi, A.; Carreau, P. J.; Chauveteau, G. J. Rheol. 1987, 31, 537.
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Figure 1. Hydrodynamic correlation length and scattered light intensity vs surfactant concentration. [NaSal/TTAA ) 1. T ) 25 °C.]
the time autocorrelation function g(t) of the scattered light intensity. From g(t) we may obtain the average decay rate Γ using the cumulants method19 to account for the polydispersity of the micelles. The average decay rate Γ is related to the apparent diffusion coefficient D of micelles by Γ/q2 ) D, where q is the scattering vector given by q ) 4πnλ0 sin(θ/2), with n the refractive index of the solvent and λ0 the wavelength of the incident light in vacuum. From the apparent diffusion coefficient D the so-called hydrodynamic correlation length ξH can be calculated through the Stokes-Einstein relation ξH ) kBT/(6πηsD), where kB, T, and ηs are the Boltzmann constant, temperature, and solvent viscosity, respectively. How ξH is related to the actual micellar size is not a simple issue, however. If the micelles are in the singular state and ξH , λ0, then ξH is equivalent to the hydrodynamic radius of the micelles. Even in this case, one should be cautious when relating ξH to the micellar length. Doi and Edwards20 predict that D ) kBT ln(L/d)/3πηsL for rigid polymer chains, where L and d are the length and diameter of the rod, respectively. From this equation and the Stokes-Einstein relation we find that L ) 2ξH ln(L/d). Evidently, L could be much larger than ξH, since L/d is usually very large for cylindrical micelles. For example, Imae obtained a contour length of 2500 nm16 and a ξH of 169 nm15 for a cationic surfactant. In this paper we will use ξH as a qualitative parameter to monitor the change of micellar size with changing environment such as temperature. On the other hand, if the micelles are overlapping with each other, then the diffusion coefficient corresponds to the collective movement of the micelles and ξH represents the meshsize and should be independent of the length of the single micelles.21,22 Therefore, from the dependence of ξH on the micellar length one may be able to tell whether the micelles are in free or overlapping state. Effects of Surfactant Concentration. Figure 1 shows the hydrodynamic correlation length ξH and scattered light intensity as a function of the surfactant concentration at (19) Brookhaven Instruments Corp. Digital correlator operator’s manual; 1986. (20) Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Oxford University Press: Oxford, U.K., 1986. (21) Cates, M. E.; Candau, S. J. J. Phys: Condens. Matter 1990, 2, 6869. (22) de Gennes, P. G. Scaling concepts in polymer physics; Cornell University Press: Ithaca, NY, 1979.
Micellar Overlapping Parameters for a Surfactant Solution
a constant NaSal/TTAA ratio of 1. Most measurements were performed at least at three different angles. However, the angle dependence was found to be insignificant for surfactant concentrations above 1 mM. The goal of the work was to study the overlapping condition by measuring the correlation length and scattering intensity as a function of temperature. The absolute value of these parameters is therefore not as important as their variation with temperature. For these reasons, we only present here results measured at an angle of 30°. The monotonic increase in the scattered light intensity may be due to both the increase in surfactant concentration and the growth of the micelles. To understand the nonmonotonic change of the hydrodynamic correlation length of the micelles, we should bear in mind that increasing the surfactant concentration may lead to conflicting effects on the hydrodynamic correlation length. On the one hand, the micellar length increases with surfactant concentration,23 which would lead at low concentration (i.e., before overlap) to a larger ξH, but on the other hand, intermicellar interactions also increase, which speeds up the diffusion rate of the micelles and results in a lower measured value of the hydrodynamic correlation length. At low surfactant concentrations, the increase in intermicellar interactions may dominate the growth of micelles and the overall result is a decreasing ξH with increasing concentration. On the other hand, when the surfactant concentration is above a certain level (1.5 mM here), the growth of micellar length may begin to dominate and the hydrodynamic correlation length begins to increase, as it reflects more the growth of the micelles. When the concentration is above 2.5 mM, however, ξH levels off and even appears to decrease slightly when the concentration exceeds 4 mM. It is thought that above a surfactant concentration of 2.5 mM the micelles begin to overlap and the micellar diffusion quantified becomes more reflective of the collective motion of the overlapping micelles. Therefore, the overlapping surfactant concentration for the equimolar solution of NaSal/ TTAA is estimated to be around 2.5 or 3 mM in this case. The crossover of micelles from the free state to an overlapped state is further suggested by the different dependence of the micellar size on temperature in the low- and high-concentration ranges. Figure 2 shows the hydrodynamic correlation length and the scattered light intensity as a function of temperature for a 1/1 mM NaSal/ TTAA solution. The monotonic decrease of both quantities is expected for micelles in the free state since the micellar length and weight usually decrease with increasing temperature. On the other hand, if the micelles are in the overlapped state, the hydrodynamic correlation length should not change very much with increasing temperature up to the point at which they begin to disentangle. This is indeed the case for the 5/5 mM solution, as seen in Figure 3. Up to 35 °C there is no significant change in the hydrodynamic correlation length. Above 35 °C, ξH begins to decrease, likely due to the fact that the micelles become too short to overlap with each other. The scattered light intensity shows the same trend. Therefore we may take the temperature at which the hydrodynamic correlation length begins to decrease as the crossover point between the free and overlapped micelles, and in this case for a 5/5 mM solution, about T ) 35 °C. Effects of Counterion/Surfactant Ratio. The counterion/ surfactant ratio has been shown to be an important factor (23) Israelachvili, J. N. In Physics of amphiphiles: micelles, vesicles and microemulsions, Degiorgio, V., Corti, M., Eds.; North-Holland: Amsterdam, 1985.
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Figure 2. Hydrodynamic correlation length and scattered light intensity vs temperature for a 1/1 mM NaSal/TTAA solution.
Figure 3. Hydrodynamic correlation length and scattered light intensity vs temperature for a 5/5 mM NaSal/TTAA solution.
in both the drag-reducing ability of the solution24 and its rheological properties,3 and we also studied the effect of this ratio on micellar overlap. Figure 4 shows the hydrodynamic correlation length as a function of the NaSal/TTAA ratio for solutions of various concentrations at 25 °C. It appears that ξH has a stronger dependence on the NaSal/TTAA ratio than on the surfactant concentration. Indeed, it is known that the optimum shape and size of the micelle depends on the effective packing geometry among the surfactant molecules.23 TTAA is a cationic surfactant with positive hydrophilic charges on the head, resulting in large electrostatic repulsion forces. The introduction of Sal- nullifies the positive charges and directly changes the effective geometric packing parameters, which may greatly promote micellar growth. On the other hand, the influence of concentration on the micellar length is only of thermodynamic origin and may be less significant.23 The scattered light intensity of these solutions also generally increases with increasing sur(24) Lu, B.; Talmon, Y.; Zakin, J. L. Proc. ASME Fluids Engineering Div. Summer Mtg 1996, 2, 169-175.
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Figure 4. Hydrodynamic correlation length vs NaSal/TTAA ratio for solutions of various TTAA concentrations. [T ) 25 °C.]
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Figure 6. Hydrodynamic correlation length vs temperature for 3.3 mM TTAA solutions with various NaSal concentrations.
Figure 5. Hydrodynamic correlation length vs temperature for 1 mM TTAA solutions with various NaSal concentrations.
Figure 7. Crossover temperature between free micelles and overlapped micelle states vs NaSal/TTAA ratio for solutions of various TTAA concentrations.
factant concentration and counterion/surfactant ratio, possibly due to more and longer micelles. To ascertain the effect of the surfactant and counterion concentrations on the state of the micelles and their stability with temperature, we measured the hydrodynamic correlation length as a function of temperature for solutions of various surfactant and counterion concentrations. Figure 5 shows such data for the 1 mM TTAA solution with different NaSal/TTAA ratios. In the temperature range covered (15-70 °C), ξH decreases continuously with increasing temperature for solutions with up to 2.5 NaSal/TTAA ratio, suggesting that micelles may be in the free state over this entire temperature range. For the solution with a 3.5 NaSal/TTAA ratio, ξH does not decrease until the temperature is above 35 °C, suggesting that the micelles stay overlapped below 35 °C. At a NaSal/ TTAA ratio of 5, the transition temperature increases to about 50 °C. The temperature dependence of ξH and scattered light intensity has been studied for other surfactant concentrations ranging from 2.5 to 5 mM. They show trends similar to those of the data in Figure 5 and are not all shown here
for brevity. However, the transition temperature shifts up for solutions of higher concentrations. For example, at 3.3 mM surfactant concentration, the solution with a NaSal/TTAA ratio of 3.5 appears to remain overlapped up to above 70 °C, as seen in Figure 6. In Figure 7, the estimated transition temperature from the overlapped regime to the free micelles regime is plotted against the NaSal/TTAA ratio for solutions of various concentrations. We see that for solutions of a given surfactant concentration, the transition temperature increases with NaSal/ TTAA ratio. For solutions with a given NaSal/TTAA ratio, the transition temperature increases with increasing surfactant concentration. Conversely, from the temperature dependence of ξH, we may obtain by interpolation or extrapolation an estimate of the NaSal/TTAA ratio at overlapping for a given surfactant concentration at any temperature. For example, in Figure 7 we see that at a temperature of 40 °C, micelles in the 3.3 mM solution start to overlap at a NaSal/TTAA ratio of about 1.7. The overlapping NaSal/ TTAA ratio decreases with increasing surfactant concentration at a given temperature. This may be due to the
Micellar Overlapping Parameters for a Surfactant Solution
Figure 8. Relative zero shear rate viscosity vs surfactant concentration for solutions of unit NaSal/TTAA ratio at 25 °C.
increasing micellar length for increasing surfactant concentrations, as it is conceivable that the overlap would occur more readily for longer micelles. 3.2. Viscosity Measurements. Data Interpretation. An estimate of the overlapping concentration C* in polymer solutions is given by C*[η] ) 1,25 with [η] the intrinsic viscosity. In the dilute regime, as a first approximation, we have η ) ηs(1 + c[η]),20 and therefore, η ) 2ηs at C*. This is a criterion often used to estimate overlapping for polymers. We use here the same criterion for characterizing the overlapping of micelles. It should be noted, however, that unlike polymer molecules, the micellar length in surfactant solutions may change with concentration and that the usage of intrinsic viscosity becomes less straightforward. The overlapping criterion η ) 2ηs should nevertheless still be useful in first approximation. In order to probe micellar structures in the equilibrium state, the viscosity should be obtained from the upper Newtonian plateau or from oscillation measurements in the linear region, where the structure is not disturbed. The viscosity obtained this way is called “zero shear rate viscosity” or η0. Concentration Effect. Figure 8 shows the relative zero shear rate viscosity ratio η0/ηs as a function of the surfactant concentration at a unit NaSal/TTAA ratio and 25 °C. These data were obtained by frequency sweep tests. Normally, the complex viscosity reaches a plateau at sufficiently low frequencies and the plateau viscosity is taken as the zero shear rate viscosity. Based on the η0 ) 2ηs criterion, the overlapping concentration appears to be around 3.4 mM for these equimolar solutions. Effects of Counterion/Surfactant Ratio. Figure 9 shows the relative zero shear rate viscosity ratio η0/ηs as a function of the NaSal/TTAA ratio for solutions of various surfactant concentrations at 25 °C. The overlapping NaSal/TTAA ratios were estimated as being those corresponding to a viscosity ratio of 2. The estimates are plotted as a function of concentration in Figure 10. As expected, the overlap ratio decreases with increasing surfactant concentration. It is also seen that the ratios obtained from these viscosity measurements are in reasonable agreement with the values obtained by extrapolation from the light scattering data at the same (25) Macosko, C. W. Rheology: principles, measurements, and applications; VCH: New York: 1994; p 483.
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Figure 9. Relative zero shear rate viscosity vs NaSal/TTAA ratio for solutions of various surfactant concentrations at 25 °C.
Figure 10. NaSal/TTAA ratio at overlapping obtained from both light scattering data and zero shear rate viscosity data at 25 °C vs surfactant concentration.
temperature. The latter were estimated from Figure 7 and are also shown in Figure 10 for comparison. 4. Summary and Conclusions The crossover temperature, surfactant concentration, and counterion/surfactant ratio at which the free micelles begin to overlap have been investigated for a cationic surfactant system that is being studied as a potential additive for drag reduction applications. These parameters can be inferred from the temperature dependence of the hydrodynamic correlation length since the latter decreases for free micelles but remains unchanged for overlapped micelles as the temperature increases. The crossover temperature thus obtained increases with increasing counterion/surfactant ratio and increasing surfactant concentration. At a given temperature, the overlapping surfactant concentration decreases with increasing counterion/surfactant ratio and the overlapping ratio decreases with increasing surfactant concentration. The overlapping surfactant concentration and counterion/
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surfactant ratio were also estimated from zero shear rate viscosity measurements. These data map out the overlapping range in terms of surfactant concentration, counterion/surfactant ratio, and temperature. Such information should be useful to determine the most efficient concentration and ratio for drag reduction applications over the desired temperature range, since drag reduction may be enhanced when micelles are in the overlapped state.
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Acknowledgment. The authors acknowledge gratefully the financial support of the MRL Program of the U.S. National Science Foundation under MRL Award No. DMR-9123048 (Prof. A. Cheetham, MRL Director); the donation of Ethoquad samples by AKZO chemicals; and the access to equipment provided by Prof. G. Leal (UCSB) and Prof. F. Lange (UCSB). LA960829K
