Soret Effect of Nonionic Surfactants in Water Studied by Different

Aug 8, 2008 - Forschungszentrum Jülich GmbH, IFF - Weiche Materie, D-52428 Jülich, Germany, Institut für Physikalische Chemie, Universität zu Köln, ...
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J. Phys. Chem. B 2008, 112, 10927–10934

10927

Soret Effect of Nonionic Surfactants in Water Studied by Different Transient Grating Setups Hui Ning,† Sascha Datta,‡ Thomas Sottmann,‡ and Simone Wiegand*,† Forschungszentrum Ju¨lich GmbH, IFF - Weiche Materie, D-52428 Ju¨lich, Germany, Institut fu¨r Physikalische Chemie, UniVersita¨t zu Ko¨ln, Luxemburger Str. 116, D-50939 Ko¨ln, Germany ReceiVed: January 31, 2008; ReVised Manuscript ReceiVed: April 10, 2008

We studied the thermal diffusion behavior of the nonionic surfactant solutions C12E6/water and C12E5/water at different concentrations and temperatures using thermal diffusion forced Rayleigh scattering (TDFRS). Two different types of TDFRS setups have been applied. In the classical TDFRS, we use an argon laser to write the optical grating into the sample by using a small amount of ionic dye to convert the optical grating into a temperature grating. In the other setup, called IR-TDFRS, we use an infrared laser as the writing beam, which utilizes the water absorption band to convert the optical grating into a temperature grating. The measurements by IR-TDFRS show a one-mode signal for all concentrations and temperatures, while the signal in the classical TDFRS consists of two modes for higher temperatures and lower surfactant concentrations (Ning, H.; et al. J. Phys. Chem. B 2006, 110, 10746). We find good agreement between the Soret coefficient determined in the IR-TDFRS and the one derived from the first fast mode in the previous studies. The Soret coefficient of the nonionic solutions is positive and enhanced at the critical point. In general, the Soret coefficient of the micelles tends to increase with temperature. We found that the presence of the second mode observed in the classical TDFRS is related to the addition of the ionic dye, but even with the ionic dye it is not possible to observe a second mode in the IR-TDFRS. The origin of the second mode is discussed in terms of charged micelles and an inhomogenous dye distribution in the temperature gradient. I. Introduction Surfactant molecules, which show amphiphilic properties due to their hydrophilic and hydrophobic part, form micelles in water, when the concentration of the monomer is beyond a critical micelle concentration (cmc). The size and structure of the micelles depend on concentration and temperature. Surfactant solutions are of great interest due to their ample phase behavior, rich physical properties, and extensive applications in industry, agriculture, biology, and daily life.1–3 In the simple case of binary mixtures, thermal diffusion describes the mass diffusion of the components induced by a temperature gradient. As a result of this process, a concentration gradient builds up. In the steady state when the mass flux vanishes, the concentration gradient is given by

∇w ) -STw(1 - w)∇T

(1)

where ST ) DT/D is the Soret coefficient, DT is the thermal diffusion coefficient, D is the translational diffusion coefficient, and w is the weight fraction of the surfactant. Due to the fact that the Soret coefficient is inversely proportional to the translational diffusion coefficient, ST is a few orders of magnitude larger for slow diffusing systems such as heavy and large polymers and colloids compared to low molecular weight mixtures. In contrast, the size and shape dependence of DT is not so pronounced; for instance, it is well-known that for diluted solutions of polymers DT is independent of the molecular mass and shape.4 A similar tendency has already been observed for higher alkanes.5 * To whom correspondence should be addressed. E-mail: s.wiegand@ fz-juelich.de. † Forschungszentrum Ju ¨ lich GmbH. ‡ Universita ¨ t zu Ko¨ln.

Figure 1. The adsorption of aqueous basantol yellow solution and water in dependence of the wavelength.

Several experimental techniques have been used to study the thermal diffusion behavior of surfactant systems. Using a beam deflection and thermal lens setup, Piazza et al. investigated an ionic surfactant, sodium dodecyl sulfate (SDS), in water.6,7 The Soret coefficient of SDS shows an exponential dependence on the temperature and 1/ST scales linearly with the concentration. Further ST of SDS shows a quadratic dependence on the Debye length. For a mixture of SDS and the nonionic surfactant β-dodecyl-maltoside (DM), a sign change of the Soret coefficient was observed with increasing temperature.7 Ning et al. studied a series of nonionic surfactants in water in a wide temperature and concentration range using the classical thermal diffusion forced Rayleigh scattering (TDFRS).8,9 For their measurements, a small amount of ionic dye, basantol yellow (the absorption curve is shown in Figure 1), is added in order to create a sufficient temperature gradient. At higher temperatures and lower concentrations, the concentration part of the signal consists

10.1021/jp800942w CCC: $40.75  2008 American Chemical Society Published on Web 08/08/2008

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Figure 2. Sketch of the IR-TDFRS setup. The shaded region in the figure marks the part of the setup which is used for simultaneous illumination of the sample cell from the backside.

of two modes. Although it turned out that the two-mode signal can be suppressed by the addition of a simple salt, such as sodium chloride (NaCl), the origin of the second mode is still an open question. Several theoretical approaches by Dhont,10 Braun,11 and Wu¨rger12 have been applied to describe the salinity dependence of the Soret coefficient of the ionic surfactants or charged colloids in the dilute regime. All theories describe the Debye length dependence of the Soret coefficient for low Debye lengths reasonably well.13 The Soret coefficient of SDS can also be described by the Ruckenstein approach,14 which has been carried out by Piazza. In the investigated Debye length range, they found a good agreement. The objective of this work is to get a better understanding of the origin of the second concentration mode, which has been observed recently.9 Therefore, we study the thermal diffusion behavior of C12E6 by the IR-TDFRS setup, which avoids the addition of the dye. In order to separate the contributions stemming from the charge of the ionic dye and its absorption at the writing wavelength, we perform also measurements of C12E6 + SDS in water. From the previous study, we also know that the distance to the two-phase boundary plays an important role; therefore, we perform also a few additional measurements for the system C12E5/water, which has a much lower phase boundary compared to C12E6/water. The paper is organized as follows: In section II, we will simply elucidate the principle of the IR-TDFRS setup. In section III, we will address the preparation of the sample and experimental details. The phase behavior and thermal diffusion behavior of the studied aqueous surfactant solutions will be presented in section IV. The measurements by TDFRS and IRTDFRS are compared in section V, and we will suggest a model to explain the mechanism of the two-mode signal. II. Instrument and Working Equations A. IR-TDFRS. The IR-TDFRS setup has been described elsewhere in detail.15 Two intersecting laser beams at λ ) 980 nm create an optical grating into the sample. Due to the weak absorption of the infrared beam by the water molecules, the optical intensity grating is converted into a temperature grating, which results in a refractive index grating. This is probed by the diffraction of a He-Ne laser beam, operating at λ ) 633 nm.

As can been seen in Figure 1, water has a weak absorption at 975 nm, while at 633 nm there is almost no absorption. In contrast to the classical TDFRS, no dye is needed for the aqueous system in the IR-TDFRS setup. Especially in the case of the micellar systems, the experiment is simplified, because for those systems the phase behavior is influenced by the addition of the dye. In general, the addition of a dye disturbs the system more, because many water soluble dyes change their absorption behavior with pH or temperature. The diffraction signal ζhet is fitted by

ζhet(t) ) 1 +

-1

∂n ( ∂T∂n ) ( ∂w ) w,p

STw(1 - w)(1 - e-q Dt ) (2) 2

T,p

where w is the weight fraction of the surfactant, D is the translational diffusion coefficient, and q is the scattering vector. The refractive index increments (∂n/∂w) and (∂n/∂T) have to be measured by an Abbe refractometer and interferometer in separate experiments, respectively. Figure 3a presents the refractive index depending on the weight fraction of C12E5 at room temperature. We get (∂n/∂w) from the slope as 0.1329 ( 0.0004. Figure 3b shows (∂n/∂T) of the C12E5 solution as a function of the surfactant content at 20, 24, and 28 °C. It can be seen that (∂n/∂T) decreases linearly with increasing C12E5 content. For the refractive index increments of C12E6 in water, we refer to our previous work.9 We found that the addition of a small amount of dye almost has no influence on the refractive index increments. In the case of a two-mode signal, which occurs in the classical TDFRS for surfactant systems, the analytical equation can be found in our previous publication.9 III. Experiment A. Sample Preparation. C12E6 (hexaethylene glycol monododecyl ether; purity g98%), C12E5 (pentaethylene glycol monododecyl ether; purity g98%), and SDS (sodium dodecyl sulfate; purity g98.5%) were ordered from SIGMA-Aldrich. All surfactants were used without further purification. We used deionized Milli-Q water. The dye, basantol yellow, was donated by BASF. All solutions were prepared by weighting. Before the measurements, the solutions were stirred at least for 1 h. For all samples containing dye, the dye/water solution was prepared in advance and later the surfactant was added. The optical density (OD) is measured by the absorption of the sample at the wavelength λ ) 488 nm using a Carry 50 spectrometer.

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Figure 3. (a) The refractive index of C12E5 in water as a function of the weight fraction measured at room temperature. (b) (∂n/∂T) for the same mixture as a function of the weight fraction at 20, 24, and 28 °C. The lines represent linear fits to the data.

Figure 4. The phase diagram of C12E6 in water (a),16 mixture of C12E6 and SDS in water17 (b), and C12E5 in water (c).18 Measurements by IRTDFRS (×) and by classical TDFRS, which show a one-mode signal (b) and two-mode signal (O), respectively. The different phases in the phase diagram are indicated as follows: diluted surfactant phase (L1′), concentrated surfactant phase (L1′′), hexagonal phase (H1), lamellar phase (LR), and isotropic sponge phase (L3). cmc is the abbreviation of critical micellar concentration. The lines in the figures are guides to the eye.

The measurements use a baseline correction by a measurement cell containing pure water. For IR-TDFRS and classical TDFRS measurements, the surfactant solutions were directly filtered into the sample cell by a polyNylon (Spartan) filter with a mesh size of 0.45 µm. B. TDFRS and IR-TDFRS Measurement. For all experiments, the thickness of the sample cell is 0.2 mm. The sample cell is thermally equilibrated in a brass or copper holder for at least half an hour. The temperature is controlled by a circulating water bath with an accuracy of (0.02 K. The IR-TDFRS measurements are performed for C12E6 solutions in the concentration range wC12E6 ) 0.0025-0.1 and at T ) 20, 25, 30, and 40 °C and for C12E5 solutions in the concentration range wC12E5 ) 0.0025-0.025 and at T ) 20, 24, and 28 °C. In some of the IR-TDFRS experiments, we illuminated the sample additionally with an argon-ion laser operating at a wavelength of λ ) 488 nm from the backside. The purpose of this experiment was to gain a better understanding of the second mode as it was observed in the classical TDFRS. In order to clarify the mechanism, we varied the optical density between 1 and 20 cm-1 and the illuminating power between 0 and 220 mW. In order to study the influence of the basantol yellow, we performed additional measurements for various amounts of dye (OD ) 1-20 cm-1) at a weight fraction of C12E6 of w ) 0.025 and a temperature of T ) 25 °C using the classical TDFRS setup. The chosen point in the phase diagram designates the boundary between one-mode and two-mode behavior. The

purpose of this measurement was to see whether a second mode could be initiated by increasing the amount of dye. IV. Results A. Phase Behavior. Figure 4 shows the phase diagrams of the aqueous surfactant systems. All our TDFRS measurements are performed in the isotropic L1 phase. Both C12E6 and C12E5 in water show a two-phase region (denoted as L1′ + L1′′) at high temperatures. Here, L1′ represents the more diluted surfactant phase and L1′′ the more concentrated one. According to the literature, the critical points are wc ) 0.025 at Tc ) 51.3 °C and wc ) 0.015 at Tc ) 32.0 °C for C12E6 and C12E5, respectively.19 Using the C12E6 ordered from SIGMA-Aldrich, we found a critical concentration of wc ) 0.021 ( 0.001 at a critical temperature of Tc ) 51.53 ( 0.02 °C. It is known that C12E6 forms small spherical micelles in the L1 phase at low surfactant concentrations and low temperatures, while with increasing concentration and temperature large cylindrical micelles are found.18 In Figure 4a, we can see that the addition of the dye shifts the two-phase boundary toward higher temperatures. If the dye content is kept constant (OD ) 2 cm–1, ∆), the shift of the two-phase boundary to higher temperatures is more pronounced in the low surfactant region. On the other hand if we fix the weight fraction δ of the dye in the mixture of dye and surfactant to δ ) 0.0444 (∇) (implying that the dye acts as a cosurfactant), the two-phase boundary shifts parallel by ∆T ) 25 °C. If we quench the system into the L1′ + L1′′ region, we find that the color of the surfactant rich region is

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Figure 5. (a) IR-TDFRS and TDFRS heterodyne signals measured for C12E6 in water with wC12E6 ) 0.025 at different temperatures. (b) IR-TDFRS signals for C12E6/water, C12E6/SDS/water, and C12E6/dye/ water at different temperatures. The weight fraction of C12E6 is 0.025, and the ratio of SDS molecules to C12E6 molecules is 9.8 × 10-5. (c) IR-TDFRS and TDFRS signals measured for C12E5 in water with wC12E5 ) 0.025.

dark orange, while the water rich phase is almost colorless. This indicates a preference of the dye in the surfactant phase which suggests that the dye is incorporated in the micelles. The temperature shift of the two-phase boundary in the presence of basantol yellow is probably caused by the electrostatic repulsion between the micelles, which get charged by the incorporation of the ionic dye molecules in the micelles. Figure 4b shows the phase behavior of C12E6 + SDS in water. The addition of SDS shifts the two-phase boundary also toward higher temperatures.17 From the literature, it is known that SDS acts as a cosurfactant and is incorporated into the nonionic C12E6 micelles. Therefore, the micelles get charged. Comparing the effect of SDS and basantol yellow on the phase behavior of the C12E6/water system strongly supports the presumption that basantol yellow acts as cosurfactant. For comparison, we present in Figure 4c the phase diagram of C12E5 in water. At low temperatures, the system shows a similar behavior as C12E6 in water. The main difference between the two systems is that the phase boundary between L1 and L1′ + L1′′ is roughly 25 K lower compared to the system C12E6 in water and the existence of a diluted anisotropic lamellar (LR) and an isotropic sponge (L3) phase which both intrude into the upper miscibility gap.18 B. IR-TDFRS and TDFRS Measurements. Figure 5 shows typical diffraction signals obtained for both surfactant systems

Ning et al. at different temperatures with the classical TDFRS and the IRTDFRS. The rapid increase of ζhet(t) is due to the establishment of the temperature gradient, and the slower growth reflects the formation of a concentration gradient due to the thermal diffusion process. In many experiments, the concentration mode measured in the classical TDFRS consists of two modes, while in IR-TDFR in all cases a monoexponential increase has been observed. Considering the positive increase of the concentration signal and the signs of (∂n/∂T) and (∂n/∂w), we can conclude that the micelles move to the cold side of the temperature gradient. Figure 5a shows the signal for C12E6 in water at w ) 0.025 for different temperatures obtained by the classical TDFRS and IR-TDFRS. At a low temperature of T ) 20 °C, the signals from both setups agree. At higher temperatures of T ) 30 and 40 °C, the signal obtained by classical TDFRS shows a double exponential decay in the concentration part, while the concentration part of the signal in the IR-TDFRS experiment is monoexponential. By comparing the signals measured at the same temperature by both setups, we find that the initial slope of the concentration part of the signal agrees. In Figure 5b, we compare the signals from C12E6, C12E6 + SDS, and C12E6 + dye in water obtained by the IR-TDFRS setup. None of the measured diffraction signals in the IR-TDFRS shows a second mode, even not if basantol yellow is added. At a low temperature of T ) 20 °C, the addition of SDS and dye has almost no influence on the signal, but at a high temperature of T ) 40 °C, the signals of the C12E6 + SDS and C12E6 + dye in water show a pronounced smaller amplitude than the system C12E6 in water. In Figure 5c, we present the signals for the C12E5 solution. Similar to the C12E6 solution, C12E5 shows a two-mode signal in the classical TDFRS measurement. We also noticed that the second mode of the two-mode signal for C12E5 is so strong that it eventually reaches a negative plateau. This means the refractive index grating is completely inverted. The Soret coefficients of C12E6 and C12E5 measured by the IR-TDFRS setup are displayed in Figure 6. All Soret coefficients are positive, which means that the micelles migrate to the cold side. For the system C12E6 at 40 °C, the Soret coefficient ST reaches a maximum. The strong increase in ST close to the critical concentration wc ) 0.021 is a consequence of the critical slowing down.20 For the lower temperatures at 25 and 20 °C, we observe an ambiguous minimum around wc ) 0.005 and 0.025, respectively, while at higher surfactant concentrations ST increases monotonically, which might be related to the increasing viscosity. The variations at lower concentrations are probably a consequence of structural changes in the surfactant solution. In this concentration and temperature range lies, for instance, the boundary between globular and cylindrical micelles. Only in the very low concentration regime (wC12E6 ) 0.0025 and 0.005), the ST value of C12E6 decreases with increasing temperature between T ) 20 and 25 °C, while ST generally increases with temperature. This particular temperature dependence at low concentrations was also observed in the previous experiments.9 The temperature dependence of ST for C12E6 in water is also displayed in Figure 7. For the C12E5 system, we performed only a few measurements. It turned out that the equilibrium times were very long. Nevertheless, we observe the same trend. The Soret coefficient increases with increasing temperature. Figure 8 shows the concentration dependence of D and DT for the C12E6/water mixture at different temperatures. In Figure 8a, we can see that the translational diffusion coefficient D decreases with increasing temperature in the low concentration regime (when w < 0.075). At higher concentrations when w >

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Figure 6. (a) The dependence of the Soret coefficient of C12E6 in water on the surfactant content at different temperatures T ) 20 °C (9), 25 °C (O), 30 °C (2), and 40 °C ()) measured by IR-TDFRS. (b) The dependence of the Soret coefficient of C12E5 in water on the surfactant content at different temperatures T ) 20 °C (9), 24 °C (b), and 28 °C (2).

Figure 7. The Soret coefficient of C12E6 measured by IR-TDFRS as a function of the temperature for various concentrations wC12E6 ) 0.0025 (9), 0.005 (O), 0.015 (2), 0.025 (3), 0.05 ((), and 0.1 (]). The lines connect the data points.

Figure 8. Diffusion coefficient D (a) and thermal diffusion coefficient DT (b) measured by the IR-TDFRS as a function of the weight fraction of C12E6.

0.075, D slightly increases with increasing temperature. This is the same tendency we observed already for ST. As expected, D reaches a minimum close to the critical concentration. This was also measured previously by dynamic light scattering experiments.20 In contrast, DT seems to be less affected by the presence of the critical point (cf. Figure 8b). In the entire investigated temperature and concentration range, we find a positive DT

Figure 9. Soret coefficient of C12E6 in water as a function of the content of the dye. The inset shows the Soret coefficient as a function of the power of the illuminating beam. 9, O, 2, 1, ), and f are measurements for the sample with optical density 0, 1, 2, 5, 10, and 20, respectively. The solid lines are guides to the eye.

value. At higher temperature, DT increases monotonically with concentration, while for the two lower temperatures an ambiguous minimum at w ) 0.035 and 0.015 can be observed. This minimum seems to shift toward lower concentrations with increasing temperature. At T ) 30 and 40 °C, the thermal diffusion coefficient becomes concentration independent for higher concentrations of w > 0.05 and w > 0.01. According to our data analysis (c.f. eq 2), the diffraction signal has a low contrast, when one of the factors (∂n/∂w)T,p, ST, or w becomes small. This is the reason that the error bars at low surfactant content become large. Figure 9 shows the Soret coefficient in dependence of the dye content using the IR-TDFRS. All measurements have been performed at the temperature T ) 40 °C for solutions with a surfactant content of wC12E6 ) 0.025. Under the same conditions, we found a strong second mode in the classical TDFRS experiment, while the measurements with the IR-TDFRS show only one mode. The Soret coefficient decreases with increasing dye content. This can be expected because the two-phase boundary is shifted toward higher temperature, so that the critical slowing down becomes less pronounced at high dye content, which leads to a decay of ST. In another experiment, we illuminated these samples with an argon laser with λ ) 488 nm, at which the dye strongly absorbs. We expected the following scenario: Due to the thermal diffusion, the surfactant molecules are enriched in the cold region, because the dye molecules move with the surfactant. Therefore, the dye content should be higher in the cold region.

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Figure 10. Diffraction signal at T ) 25 °C measured with the classical TDFRS for different amounts of basantol yellow. The weight fraction of C12E6 in water is 0.025.

If we now illuminate the sample with the argon-ion laser, the inhomogeneous distribution of the dye should lead to a strong heating in the cold region, which consequently reduces the temperature gradient produced by the IR laser. With increasing illuminating power, the effect should become stronger, and on the other hand, the thermal plateau should not be influenced by the additional illumination, so that we expected a decreasing Soret coefficient with increasing illumination power. The inset in Figure 9 shows that the measured Soret coefficient is within the error bars independent of the illuminating power. Obviously, the effect is not strong enough to get observed. With the classical TDFRS, we performed systematic measurement of C12E6 in water using a small amount of dye necessary to reach an optical density between 1.5-2 cm-1 at 488 nm. Under these conditions, we found for wC12E6 ) 0.025 at a temperature of T ) 25 °C a one-mode signal. From the phase diagram in Figure 4a, it can be seen that a slightly lower concentration or higher temperature results in two-mode behavior. As can be seen in Figure 10, an increase of the dye content leads to a second mode, which becomes stronger if the dye content is further increased. The addition of the dye influences significantly the second mode, but the initial slope of the first mode remains the same for all signals. The initial slope of the concentration signal correlates with DT.21 V. Discussion A. Thermal Diffusion Behavior of Aqueous Surfactant Solutions. As observed in Figure 6, the Soret coefficient for both surfactants C12E6 and C12E5 in water is enhanced close to the critical point. The signature of the critical slowing down is also reflected in the diffusion coefficient D displayed in Figure 8a. As expected, DT is less sensitive to the critical point, and we observe only a vague minimum for C12E6 around 20 °C at the critical concentration. Ko¨hler et al. studied a polymer blend mixture close to the critical temperature.22 For the polymer blend mixtures, they found a power law for the Soret coefficient as a function of the distance to the critical temperature. In the present publication, the database is not sufficient to determine the critical exponent. In general, the Soret coefficient of C12E6 in water increases with increasing temperature (c.f. Figure 7). Only for low temperatures and concentrations deviations are found. As can be seen in Figure 4a, the transition boundary between globular and large cylindrical micelles falls in the same region.18 It can be expected that ST is influenced by the change of micelles in shape and size, because many other experimental and theoretical studies show that the Soret coefficient of colloids and microemulsions depends on the particle size.11,23,24

Ning et al.

Figure 11. The Soret coefficient of C12E6 (9), C12E6/basantol yellow (b, OD ) 5), C12E6/SDS (2, wSDS ) 9.8 × 10-5), and C12E6/SDS/ NaCl (4, wSDS ) 1.0 × 10-4; wNaCl ) 1.38 × 10-3) in water. The weight fraction of C12E6 is 0.025. Further details can be found in the text.

We have strong evidence that the charged basantol yellow is incorporated in the micelles. In order to study the influence of the charging of the micelles more systematically, we performed IR-TDFRS measurement on a mixture of C12E6/SDS in water. We add a small amount of SDS (wSDS ) 9.8 × 10-5) into a C12E6 solution with w ) 0.025. This corresponds to δ ) mSDS/ (mSDS + mC12E6) ) 3.9 × 10-3. SDS is an ionic surfactant and will be incorporated in the micelles. The number ratio of the SDS molecules to C12E6 molecules is 6.1 × 10-3; therefore, the micelles will be only slightly charged. According to the literature, the C12E6 micelles (w ) 0.025, T ) 40 °C) consist of roughly 2000-2500 molecules,25 so that each micelle contains approximately 12-15 SDS molecules. A precise determination of the shape by scattering data is difficult because the measurements are disturbed due to the vicinity of the critical point. As discussed in section IV.A, the addition of SDS shifts the two-phase boundary in the same way as basantol yellow. Also, the influence on the diffraction signal (c.f. Figure 5b) is similar. At lower temperatures, the effect is minor, but with increasing temperature, the amplitude of the concentration part of the signal becomes smaller. The main reason for this behavior is the shift of the two-phase boundary toward higher temperatures. As can be seen in Figure 11, the reduced amplitude leads to a smaller Soret coefficient for the two systems containing SDS or bansantol yellow. If we add a sufficient amount of sodium chloride to the solution, the values obtained for the pure system C12E6/water are restored. Piazza et al. investigated also mixtures of a nonionic and ionic surfactant.7 The nonionic surfactant β-dodecyl-maltoside (DM) in water shows a negative Soret coefficient, and SDS shows a positive Soret coefficient. For the equimolar mixture of both, one finds a ST for the mixed micelles which changes sign from negative to positive with increasing temperature. Whether the observation that for this particular ternary mixture the value of the Soret coefficient of the mixed micelles in the equimolar mixtures lies between those of the binary mixtures is an accident or might also be valid for other systems is an open question. From gaseous systems, it is know that there is no link between binary and ternary mixtures,26 but in the case of mixed micelles, where the system continously changes, the situation might be different. This question needs to be investigated in further studies. For both, C12E6/SDS mixtures and DM/SDS mixtures, the Soret coefficient increases with increasing temperature. Estimating the Soret coefficient of SDS in water from Piazza’s work, we find for a weight fraction of wSDS ) 0.025 at 40 °C that ST ∼ 0.014. This is 1 order of magnitude smaller than ST of C12E6 under the same

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Figure 13. Ordinary and dye-infected micelles move in a temperature gradient. (A) Both micelles move to the cold side. (B) Ordinary micelles move to the cold side, while dye-infected micelles move to the warm side. Figure 12. Soret coefficient of C12E6 in water in dependence of the weight fraction of C12E6 measured by IR-TDFRS (small solid symbols) and classical TDFRS (large open symbols).

a dynamic equilibrium between dye-infected micelles and dye molecules in solution

cmicelle with dye H cmicelles + cdye in solution conditions. The Soret coefficient of the mixture C12E6/SDS in water lies in between the values of the two binary mixtures. In Figure 12, we plot the Soret coefficient of C12E6 in water obtained by both TDFRS setups at the temperatures 20, 30, and 40 °C. In general, the Soret coefficients obtained from the first mode of the classical TDFRS agree with those measured by the IR-TDFRS. At the two temperatures of 30 and 40 °C, the Soret coefficients are sometimes larger than those calculated from the IR-TDFRS especially at a weight fraction of 0.05. The reason could also be a data analysis problem. In our previous work,9 the two-mode signals were analyzed by a double exponential decay model, which becomes unreliable if the time constants for the two modes are similar. B. Origin of the Two-Mode TDFRS Signal. As mentioned already in section IV.B, we observe two-mode signals in the classical TDFRS, while we find only one mode in the IRTDFRS. Even if we add basantol yellow in the IR-TDFRS experiment, we observe only one mode (c.f. Figure 5). Previously, we had assumed that the second mode is solely caused by the charged micelles, because it could be suppressed by adding a sufficient amount of a simple salt.9 The new measurements with the IR-TDFRS setup with and without illumination show clearly that it is not only the presence of the charged dye but also its inhomogeneous distribution in the interference grating which causes the second mode. The pure charge effect by basantol yellow, which is mainly a shift of the two-phase boundary toward higher temperatures can also be obtained by adding SDS to the nonionic surfactant C12E6 in water. From our previous study, we had concluded that basantol yellow acts such as SDS as a cosurfactant and is incorporated in the C12E6 micelles.9 This assumptions is justified if we compare the measurements of C12E6 + basantol yellow and C12E6 + SDS in water with the IR-TDFRS setup. As long as the system is not additionally heated due to the strong absorption of blue light by basantol yellow, both systems behave similar. Additionally, we observed (c.f. Figure 10) that an increase in the dye concentration can induce a second mode, even if at lower dye concentration no second mode is visible. Also, for the system C10E8 in water, which did not show a second mode in the previous study,9 we found a second mode when we increased the amount of dye by a factor of 5. Apparently, the dye concentration but probably also the microstructure of the system and the solubility of the dye are important for the formation of the second mode. The strength of the second mode varies for various nonionic surfactant systems, but the mechanism seems to be the same. In the experiment exists certainly

(3)

Here, one has to keep in mind that not every micelle contains a dye molecule. In the TDFRS measurements, we fix the dye concentration to an optical density of OD ) 2. This implies that the ratio of cdye to cmicelle will be higher at lower surfactant concentrations compared to higher surfactant concentrations. As a consequence, the equilibrium will move toward the left side with decreasing surfactant content, and this means there will be more dye-infected micelles at low surfactant concentrations. This is also reflected in the phase diagram in Figure 4a. We see that if we fix the concentration of the dye in solution (OD ) 2, ∆), the two-phase boundary shifts higher at the low C12E6 content. In contrast, if we fix the ratio of dye to C12E6 content (∇), the two phase boundary is shifted parallel. Furthermore, we found in our previous work that the addition of salt suppresses the second mode.9 The addition of the salt leads to a decrease of the two-phase boundary to its original position in the pure C12E6/water system, which implies that the structure of the L1 phase is the same or similar. Also, the Soret coefficients of C12E6/basantol yellow/water and C12E6/SDS/water agree with the one for the pure system, if we add a sufficient amount of salt to the mixtures. The strength of the second mode depends also on the magnitude of the Soret coefficient. Therefore, a certain concentration gradient and also dye content is required in order to create the second mode. Measurements indicate that basantol yellow moves with the surfactant, which implies that in the case of a strong concentration gradient per temperature gradient (Soret coefficient) in the order of 0.1-0.2 K-1 also a strong dye gradient is achieved in the classical TDFRS. From the IR-TDFRS measurement, we know that the Soret coefficient of C12E6 in water is positive, which means that the ordinary micelles move to the cold side. An open question is whether the dye-infected micelles migrate also to the cold side or to the warm side. The two possible scenarios are sketched in Figure 13. In model A, we assume both micelles move to the cold side, while in model B dye-infected micelles move to the warm side. This assumption might be justified, because we observe in Figure 11 that the addition of the SDS and basantol yellow decreases the Soret coefficient, which means that charged micelles are more thermophilic. In model A, due to absorption of the blue light by basantol yellow, a temperature grating is formed and then both kinds of micelles move to the cold side. Due to the enrichment of the dye in the cold region, the temperature gradient is weakened, which results in a weakening of the concentration gradient, and a backward motion of part of the micelles starts. This can cause a second mode. Under these conditions, the strongest second

10934 J. Phys. Chem. B, Vol. 112, No. 35, 2008 mode would occur, if the temperature grating vanishes and the diffraction signal goes to zero. In model B, the dye-infected micelles move to the warm side, as shown in Figure 13. After equilibration of the temperature grating, the ordinary micelles move to the cold side, while at the same time the dye-infected micelles migrate to the warm side. This movement is reflected in the first mode. Due to the enrichment of the dye in the warm regions of the grating, the temperature gradient is strengthened and again a feedback mechanism starts, and more dye-infected micelles will move to the warm side which leads to the negative second mode. Although both models explain qualitatively the appearance of a second mode, the first model fails in the case of some surfactants such as C16E8 and C12E5. In these cases, the second mode is so strong that the diffraction signal efficiency becomes negative, which means the refractive index grating is reversed (see Figure 5c). As shown in Figure 5b, we observe only one mode with the IR-TDFRS, even if we add basantol yellow. The difference is that the amplitude of the grating is not changed due to absorption of the blue laser light and that we do not have a feedback mechanism in the IR-TDFRS. VI. Conclusion In this work, we present the thermal diffusion behavior of C12E6 and C12E5 measured by the recently developed IR-TDFRS setup.15 In this setup, the temperature gradient is achieved due to a weak absoprtion band of water in the near-infrared. Therefore, we do not need to add a dye, which leads in systems with a complex behavior often to artifacts. Both nonionic surfactants C12E6 and C12E5 show positive Soret coefficients in water, which indicates that the micelles move to the cold side. The Soret coefficient is enhanced close to the critical point, which is due to the slowing down of the diffusion. The Soret coefficient increases with increasing temperature when w > 0.01, while at lower surfactant content the Soret coefficient decreases in the temperature range 20-25 °C and increases with temperature when T > 25 °C. The reversion of the temperature dependence is close to the boundary between globular micelles and larger network structures; therefore, this might be an indication that the thermal diffusion behavior is influenced by structural changes in the micellar solution. However, the IRTDFRS measurements become very difficult in this concentration range. The addition of the ionic surfactant SDS as well as basantol yellow shifts the two-phase boundary toward higher temperatures. In both cases, the measured Soret coefficient becomes smaller. Due to the vicinity of the two-phase boundary in the

Ning et al. pure system, this effect is especially pronounced at higher temperatures. A comparison of the measurements with SDS or basantol yellow as a third component leads us to the conclusion that both molecules are incorporated into the micelles. The occurrence of a second mode in the classical TDFRS and the absence of this mode in the IR-TDFRS can be explained by some sort of feedback mechanism, which leads to a modulation of the grating in the case of the blue writing laser. It is not exclusively a charge effect as we thought in the beginning. Acknowledgment. The authors thank Reinhard Strey for his constant interest in this work and his support. We also appreciate the technical support of Hartmut Kriegs. This work was partially supported by the Deutsche Forschungsgemeinschaft grants So 913 and Wi 1684. References and Notes (1) Quintero, L.; Disper, J. Sci. Technol. 2002, 23, 393. (2) Knoche, M. Weed Res. 1994, 34, 221. (3) Ezrahia, S.; Tuvala, E.; Aserinb, A. AdV. Colloid Interface Sci. 2006, 128-130, 77. (4) Schimpf, M. E.; Giddings, J. C. Macromolecules 1987, 20, 1561. (5) Blanco, P.; Polyakov, P.; Bou-Ali, M. M.; Wiegand, S. J. Phys. Chem. B 2008, 112, 8340. (6) Piazza, R.; Guarino, A. Phys. ReV. Lett. 2002, 88, 208302. (7) Iacopini, S.; Rusconi, R.; Piazza, R. Eur. Phys. J. E 2006, 19, 59. (8) Ning, H.; Kita, R.; Wiegand, S. Prog. Colloid Polym. Sci. 2006, 133, 111. (9) Ning, H.; Kita, R.; Kriegs, H.; Luettmer-Strathmann, J.; Wiegand, S. J. Phys. Chem. B 2006, 110, 10746. (10) Dhont, J. K. G.; Wiegand, S.; Duhr, S.; Braun, D. Langmuir 2007, 23, 1674. (11) Duhr, S.; Braun, D. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 19678. (12) Fayolle, S.; Bickel, T.; Wu¨rger, A. (2007),arXiv:0709.0384v1 [condmat.soft]. (13) Ning, H.; Dhont, J. K. G.; Wiegand, S. Langmuir 2008 24, 2426. (14) Ruckenstein, E. J. Colloid Interface Sci. 1981, 83, 77. (15) Wiegand, S.; Ning, H.; Kriegs, H. J. Phys. Chem. B 2007, 111, 14169–14174. (16) Strey, R.; Pakusch, A. In Proceedings of the 5th International Symposium on Surfactant in Solution; Mittal, K., Bothorel, P., Eds.; Plenum: New York, 1986; pp 465-472. (17) De Salvo Souza, L.; Cantu, L.; Degiorgio, V. Chem. Phys. Lett. 1986, 131, 160. (18) Strey, R. Ber. Bunsen-Ges. Phys. Chem. 1996, 100, 182. (19) Schubert, K.-V.; Strey, R.; Kahlweit, M. J. Colloid Interface Sci. 1991, 141, 21. (20) Wilcoxon, J. P.; Schaefer, D. W.; Kaler, E. W. J. Chem. Phys. 1989, 90, 1909. ¨ ohler, W. Macromolecules 1996, 29, 3203. (21) Rossmanith, P.; K ¨ ohler, W. Phys. Chem. Chem. Phys. 2004, 6, 2373. (22) Enge, W.; K (23) Duhr, S.; Brauna, D. Phys. ReV. Lett. 2006, 96, 168301. (24) Vigolo, D.; Brambilla, G.; Piazza, R. Phys. ReV. E 2007, 75, 040401. (25) Youshimura, S.; Shirai, S.; Einaga, Y. J. Phys. Chem. B 2004, 108, 15477–15487. (26) Firoozabadi, A.; Ghorayeb, K.; Shukla, K. AIChE J. 2000, 46, 892.

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