Langmuir 2003, 19, 10803-10807
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Surface Density Measurement of the Bromide Ion by the Total-Reflection X-ray Absorption Fine Structure Technique at the Air/Aqueous Dodecyltrimethylammonium Bromide Solution Interface Takanori Takiue,* Yasuhiro Kawagoe, Soichiro Muroi, Ryo Murakami, Norihiro Ikeda, and Makoto Aratono Department of Chemistry, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan
Hajime Tanida,† Hideto Sakane,‡ Makoto Harada,§ and Iwao Watanabe| Experimental Facilities Division, Japan Synchrotron Radiation Research Institute, Sayo, Hyogo 679-5198, Japan, Center for Instrumental Analysis, Yamanashi University, Takeda, Kofu, Yamanashi 400-8511, Japan, Department of Chemistry, Graduate School of Science and Engineering, Tokyo Institute of Technology, Ookayama, Meguro, Tokyo 152-8551, Japan, and Faculty of Science, Osaka Women’s University, Daisen, Sakai, Osaka 590-0035, Japan Received February 18, 2003. In Final Form: September 30, 2003 The X-ray absorption fine structure technique was applied to the aqueous dodecyltrimethylammonium bromide solution surface under the total reflection condition at 275 K. The Br K-edge absorption jump (J) value was evaluated and compared to the surface density (ΓH 1 ) of surfactants calculated from the surface tension versus concentration curve at 275.15 K. An excellent correlation between the J and ΓH 1 values was found, and their dependences on concentration were not of a simple Langmuir type but of the Frumkin type. This should be indicative that a phase transition between the gaseous and expanded states takes place in the adsorbed film, claimed previously by us. Furthermore, the J value shows a stepwise increase at around the critical micelle concentration (cmc). This may be attributed to a change of the structure of the adsorbed film, such as staggered arrangement of surfactant ions close to the cmc to minimize the electric repulsion between their headgroups, or that of the electrical double layer. The results obtained in this study are compared to those evaluated from the radiotracer method applied to the aqueous tritiated sodium dodecyl sulfate solution surface.
Introduction The surface adsorption of surfactants at the liquid/vapor interface is of great concern because it is regarded as a good model for a biological membrane. Therefore, it has been used to know the mechanism of the interaction between lipids and proteins as well as to obtain fundamental information on the structure of the membrane. It is well-known that the surface density of surfactant adsorbed at interfaces can be evaluated by applying the Gibbs adsorption equation to the surface tension versus concentration curve.1,2 We have also discussed the state of the adsorbed film by measuring the surface tension with high accuracy and calculating the surface density in terms of our thermodynamics of interfaces.3-6 During our * Corresponding author: Dr. Takanori Takiue. Department of Chemistry, Faculty of Sciences, Kyushu University, Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan. Phone: +81 92 642 2580. Fax: +81 92 642 2607. E-mail:
[email protected]. † Japan Synchrotron Radiation Research Institute. ‡ Yamanashi University. § Tokyo Institute of Technology. | Osaka Women’s University. (1) Defay, R.; Prigogine, I. Surface Tension and Adsorption; Everett, D. H., Translator; Longmans: London, 1966. (2) Adamson, A. W. Physical Chemistry of Surfaces, 5th ed.; Wiley: New York, 1990. (3) Motomura, K. J. Colloid Interface Sci. 1978, 64, 348. (4) Motomura, K.; Iwanaga, S.; Hayami, Y.; Uryu, S.; Matuura, R. J. Colloid Interface Sci. 1981, 80, 32. (5) Motomura, K.; Iwanaga, S.; Uryu, S.; Matsukiyo, H.; Yamanaka, M.; Matuura, R. Colloids Surf. 1984, 9, 19.
systematic studies, we have found that the surface density versus concentration curves could not be regarded as a Langmiur type, which shows linear dependency of the surface density on concentration at a very low concentration region, but as a Frumkin type7 due to a phase transition from the gaseous to the expanded state.8 Because the surface tension method gives the surface density indirectly, it is desirable to have direct analytical methods to determine the surface density accurately. Tajima et al. measured directly the surface density of tritiated sodium dodecyl sulfate (TSDS) by using the radiotracer method to confirm the validity of the Gibbs adsorption equation.9 They have evaluated the surface density in a wide concentration range and found that it reaches a saturation value at a concentration close to the critical micelle concentration (cmc) and has an almost constant value above the cmc. Recently, some powerful techniques such as X-ray and neutron reflection were applied to the air/water interface to clarify the microscopic structure of the surface adsorbed film.10-12 Penfold et al. discussed the structure of the adsorbed film of alkyltrimethylammonium bromide and (6) Aratono, M.; Okamoto, T.; Motomura, K. Bull. Chem. Soc. Jpn. 1987, 60, 2361. (7) Frumkin, A. Z. Phys. Chem. 1925, 116, 466. (8) Aratono, M.; Uryu, S.; Hayami, Y.; Motomura, K.; Matuura, R. J. Colloid Interface Sci. 1984, 98, 33. (9) Tajima, K.; Muramatsu, M.; Sasaki, T. Bull. Chem. Soc. Jpn. 1970, 43, 1991. (10) Als-Nielsen, J.; Jacquemain, D.; Kjaer, K.; Leveiller, F.; Lahav, M.; Leiserowitz, L. Phys. Rep. 1994, 246, 251.
10.1021/la0300582 CCC: $25.00 © 2003 American Chemical Society Published on Web 11/22/2003
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Figure 1. Schematic diagram of the XAFS setup.
claimed the staggered structure of the headgroups (headgroups sit at the surface in a bumpy way, as in Figure 4a in ref 13) in the adsorbed film above the cmc.13,14 We have developed a new experimental system for observing the X-ray absorption spectra of ions at the air/water interface to know the hydration structure of the ions in the interfacial region.15,16 The X-rays are introduced onto the water surface at so small an incidence angle that they are totally reflected at the surface, and then the method becomes surface-sensitive X-ray absorption fine structure (XAFS). The preliminary experiments have shown that the jump value in the Br K-edge absorption spectrum for solutions containing bromide ions together with and without surface active ions was closely related to its amount spread at the solution surface, suggesting the possibility to obtain directly the amount of molecules or ions adsorbed at the air/solution interface.15,16 This method has another advantage over the other methods to determine surface density. It is element-sensitive, and, thus, the surface density of a specified single component can be determined even for the solution surfaces shared by several different elements competitively. It is also advantageous that the present method need not introduce any isotopes, compared to the works by Tajima et al. and Penfold et al. using radioactive tritium and deuterium, respectively. In this study, we aim to know if the surface density can be evaluated by this method reliably and accurately and to obtain direct evidence for the surface phase transition between the gaseous and expanded states at a low concentration, which has been found for the dodecyltrimethylammonium bromide (DTAB) solution by measuring its surface tension.8 It is also expected that the method can determine the surface density for a micellar solution surface because DTAB is known to form micelles in its bulk solution, and the surface tension experiment is not able to provide the surface density above the cmc. The possibility of the present method is important to obtain the surface density at any solution surface even for the solutions above the cmc. The bromide ion concentration at the air/water surface is estimated from the totalreflection XAFS measurement and compared to the surface density calculated by applying the thermodynamic relation to the surface tension data. Experimental Section Materials. DTAB was purchased from Tokyo Chemical Industry Co., Ltd., and purified by recrystallizing three times from the ethanol-acetone mixed solvent. Water was triply distilled, and the second and third stages were done from an alkaline permanganate solution.
Surface Tension Measurement. The surface tension γ of the aqueous solution of DTAB was measured by the drop volume technique4,17 at 275.15 K under atmospheric pressure. The temperature 275.15 K was chosen because the XAFS measurement, which favors a lower temperature, has been performed at that temperature. The temperature was kept constant within (0.01 K by immersing the measurement cell into the thermostated water. The density of pure water18 instead of that of the solution was used for the calculation of the interfacial tension because of the very dilute solution. The error in the γ value was estimated to be within (0.05 mN m-1. XAFS. The XAFS measurement was performed by using synchrotron radiation at BL-7C19 of the Photon Factory of the National Laboratory for High Energy Physics (Tsukuba, Japan). The experimental setup has been reported in detail16 and is shown schematically in Figure 1. The X-ray beam is monochromatized by a bouble-crystal monochromator [Si(111)] and is deflected to strike the solution surface at a 1-mrad incidence angle by using a mirror. The incidence angle is small enough for the total reflection condition at the aqueous solution surface. The X-ray beam is shaped as 6 mm × 0.05 mm by using a slit placed in front of the I0 (incident beam strength) gas-ionization detector filled with nitrogen gas. The total-conversion Helium-ion yield method is employed to obtain the I signal intensity, then I/I0 gives the XAFS spectrum. It was found that the I signal intensity depends on the incidence angle more than 10% per a 0.1-mrad difference in the incidence angle and that the mirror system at the station BL-7C is not stable enough for the present study. Therefore, before each scan of XAFS measurement the incidence angle was determined within a 0.01-mrad accuracy, and the I signal intensity has to be normalized as that of 1 mrad by using a calibration curve for the I signal intensity versus the incidence angle. The solution trough is placed on a floating boat to prevent the surface from being affected by the floor vibration. The solution temperature is kept constant at about 275 K to minimize the background current due to the photoionization of water vapor.
Data Analysis Evaluation of the J Value from the XAFS Spectrum. Figure 2 illustrates a typical XAFS spectrum (11) Schlossman, M.; Pershan, P. In Light Scattering by Liquid Surfaces and Complementary Techniques; Langevin, D., Ed.; Marcel Dekker: New York, 1991; Chapter 18. (12) Thomas, R. K.; Penfold, J. Curr. Opin. Colloid Interface Sci. 1996, 1, 23. (13) Lee, E. M.; Thomas, R. K.; Penfold, J.; Ward, R. C. J. Phys. Chem. 1989, 93, 381. (14) Lu, J. R.; Li, Z. X.; Thomas, R. K.; Penfold, J. J. Chem. Soc., Faraday Trans. 1996, 92, 403. (15) Watanabe, I.; Tanida, H. Anal. Sci. 1995, 11, 525. (16) Watanabe, I.; Tanida, H.; Kawauchi, S.; Harada, M.; Nomura, M. Rev. Sci. Instrum. 1997, 68, 3307. (17) Lando, L. J.; Oakley, T. H. J. Colloid Interface Sci. 1967, 25, 526. (18) Kell, G. S.; Whalley, E. Philos. Trans. R. Soc. London, Ser. A 1965, 258, 565. (19) Nomura, M.; Koyama, A.; Sakurai, M. KEK Report 1991, 91-1.
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ion concentration in the surface region as
J = kSP(0)Γ
(2)
where Γ is the surface concentration of Br ions per unit area. For surface-inactive salts such as potassium bromide (KBr), on the other hand, the distribution of the Br ion is assumed to be uniform from the bulk solution to the interfacial region, and, thus, we have
J ) kSP(0)Cλ
Figure 2. Total reflection XAFS spectrum for the 12.5 mmol kg-1 DATB aqueous solution.
obtained for the aqueous DTAB solution surface (m1 ) 12.5 mmol kg-1). The spectrum shows an absorption jump at around 13470 eV. The K-edge absorption jump value, J, is evaluated as follows. First, two best-fitted linear lines are determined by the least-squares method in the lower and higher energy regions, both far from the absorption edge. Then, the J value is determined as the vertical distance between the two lines at the absorption edge energy. Even after the correction for the incidence angle offset from 1 mrad, we have observed J value fluctuations from time to time for the same solution. Therefore, a standard solution, 12.5 mmol kg-1 DTAB, was measured every 10 or so samples. The J values from the standard were used for the sensitivity calibration purpose. Furthermore, a 100 mmol kg-1 potassium bromide (KBr) solution was also measured for subtracting the background intensity, which comes from the Br ions in the bulk solution, from the J value evaluated above. In this experiment, its contribution to the J value was negligibly small. The J value is correlated with the concentration profile of the Br ion C(z) and the intensity of the evanescent wave P(z), both of which are changed as a function of the distance z normal to the surface from the top of the surface (z ) 0), by
J ) kS
∫0∞C(z) P(z) dz ) kSP(0)∫0∞C(z) exp(-z/λ) dz
(1)
where k is a constant, S is the air/water surface area where the X-ray strikes, P(0) is the intensity of the incident beam, and λ is the penetration depth of the evanescent wave, which is defined as a length for reducing the intensity to 1/e times of the incedent beam. When the surfactant ions are adsorbed strongly at the surface from their dilute solutions, the concentrations of counter Br ions as well as surfactant ions in the surface region are estimated to be much higher compared to those in the bulk solution. For example, the surface excess concentration of ΓH 1 ) 3.5 µmol m-2 at the bulk concentration of m ) 15 mmol kg-1 (see Figure 4) yields the surface concentration of about 2.3 × 103 mmol kg-1 by assuming that the monolayer thickness of DTAB is about 1.5 nm.20 Therefore, the J value is reasonably assumed to be proportional to the Br (20) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: San Diego, 1991; Chapter 17.
(3)
where C is the concentration of KBr. By using the Γ value obtained from the surface tension measurement and J values evaluated from the XAFS spectra for the aqueous DTAB (12.5 mmol kg-1) and KBr (100 mmol kg-1) solution surface, we estimated λ as around 7 nm. Results and Discussion The surface tension γ of the aqueous solution of DTAB was measured as a function of the molality m1 at 275.15 K under atmospheric pressure. The results are shown in Figure 3. The γ value decreases with increasing m1 below the cmc, at which the γ versus m1 curve shows a distinct break and takes an almost constant value above the cmc. It is noted that the γ versus m1 curve has a narrow concentration region in which the slope of the curve changes rapidly at very low m1. Here, we briefly mention the thermodynamic relation used in this study. In the case of the three-component and two-phase system containing air, water, and cationic surfactant, the total differential of interfacial tension γ is given as a function of the temperature T, pressure p, and the electrochemical potential of ionic species µ˜ i (i ) + and -)
dγ ) -sH dT + vH dp - ΓH ˜ + - ΓH ˜+ dµ - dµ
(4)
where sH and vH are respectively the surface excess entropy and volume and ΓH i is the surface excess numbers of moles of species, which is defined with respect to the two dividing planes, making the surface excess numbers of moles of air and water zero simultaneously.3,21 The electrochemical potential is defined by
µ˜ i ) µi + ziFφ
(5)
where µi is the chemical potential of species i, F is the Faraday constant, φ is the electrical potential, and zi is the valence of the ion. In the present system, we have |z+| ) |z-| ) 1. When eq 5 is substituted into eq 4 and the electroneutrality condition given by H H ΓH 1 ≡ Γ+ ) Γ-
(6)
is used, eq 4 is rewritten as H dγ ) -sH dT + vH dp - ΓH 1 dµ+ - Γ1 dµ-
(7)
where ΓH 1 is the surface density of the surfactant. Because the degree of freedom is three, we employed T, p, and the molality of the aqueous DTAB solution m1 as independent variables. Assuming the solution to be ideally dilute and using the electroneutrality condition for the bulk solution, (21) Motomura, K.; Aratono, M. Langmuir 1987, 3, 304.
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Figure 3. Surface tension versus molality curve of the DTAB aqueous solution at 275.15 K.
Figure 4. Surface density versus molality curve of the DTAB aqueous solution at 275.15 K. (b) ΓH 1 at the cmc.
we obtain the equation
dγ ) -∆s dT + ∆v dp - ΓH 1 (2RT/m1) dm1
(8)
where ∆y is the thermodynamic quantity change associated with the adsorption of the surfactant defined by
∆y ) yH - ΓH 1 y1, y ) s and v
(9)
Now, we evaluate the surface density ΓH 1 of DTAB from thermodynamic analysis. The ΓH 1 value was calculated by applying the equation
ΓH 1 ) -(m1/2RT)(∂γ/∂m1)T,p
(10)
to the γ versus m1 curve in Figure 3, and the results are shown in Figure 4. The ΓH 1 value increases with increasing m1 and approaches a saturation value at around the cmc. It should be noted that the shape of the curve in the concentration region less than 3 mmol kg-1 is not of the Langmuir type, but the one suggesting the phase transition in the adsorbed film is the Frumkin type. The total-reflection XAFS spectra from the aqueous DTAB solution surface are presented at several concentrations in Figure 5, indicating that the K-edge absorption jump increases with increasing m1 and its increment decreases at a high concentration region. It also shows that the spectral shape varies with the concentration; the shift of the positions of the first maximum and minimum are observed. This suggests the change in the hydration structure of bromide ions in the surface region. Although it is very interesting to clarify this issue, we will focus on
Figure 5. Total reflection XAFS spectrum for the DTAB aqueous solution at given concentrations. m1 ) (1) 1.00, (2) 1.50, (3) 2.00, (4) 5.00, (5) 10.00, (6) 15.0, (7) 22.5, and (8) 25.0 mmol kg-1.
Figure 6. K-edge jump J value versus molality plot of the DTAB aqueous solution at 275 K.
the comparison of the dependency of the J value on m1 with that of ΓH 1 in this paper. The J values determined from the XAFS spectra are corrected for the incidence angle offset from 1 mrad and plotted against m1 in Figure 6. The J value increases with increasing m1 and reaches a saturation value at a high concentration. By comparing the plot of the J value against m1 to the ΓH 1 versus m1 curve, we realize that the dependency of J on m1 is very similar to that of ΓH 1 . This suggests that the J value is proportional to the surface density, and, therefore, it can be a good probe to know the amount of bromide ions in the surface region if we calibrate the J value with a known surface density evaluated from the surface tension measurement. To look at precisely the difference between the J value and the surface density of the DTAB system, the J value is shown together with in Figure 7. Here, the J values are multiplied by a factor for superposing them on the surface density. It is obvious that the J value traces almost perfectly the ΓH 1 versus m1 curve below the cmc. Especially, it is noteworthy that the J versus m1 plot is also of the Frumkin type representing a phase transition of the adsorbed film like the ΓH 1 versus m1 curve. This result should be indicative of our claim on the generality for the existence of a phase transition in the adsorbed film. An important additional observation is a discrepancy between the J value and the surface density at around the cmc; the J value starts to increase at 2-3 mmol kg-1 lower than the cmc. This may be caused by a change of
Surface Density Measurement of the Bromide Ion
Figure 7. Surface density and K-edge jump J values versus molality curves for the DTAB aqueous solution. The J value is multiplied by a factor to obtain the best fit between the two curves. (s) ΓH 1 ; (O) J value.
the Br ion concentration due to a structure change of the adsorbed film, such as a staggered arrangement of dodecyltrimethylammonium ions to minimize the electric repulsion between the headgroups, which is claimed by Penfold et al.,12,13 or due to that of the electrical double layer. Taking account of the fact that this stepwise increase takes place around the cmc, the micelle formation is supposed to be another factor to cause this increase. Here, let us examine shortly the latter possibility by estimating a concentration of micelle particles Cm as follows. At m1 ) 30 mmol kg-1, because the monomer concentration is regarded to be almost equal to the cmc (≈17 mmol kg-1) and the aggregation number of DTAB is reported about 50,22 Cm is estimated to be about 0.26 mmol L-1. Making the assumption that the micelle particles are distributed uniformly from the bulk solution to the interfacial region and the penetration depth of the X-ray in this XAFS (22) Hiemenz, P. C.; Rajagopalan, R. Principles of Colloid and Surface Chemistry, 3rd ed.; Marcel Dekker: New York, 1997.
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measurement is estimated to be about 7 nm, the concentration of the micelle particles per unit area is 1.8 × 10-3 µmol m-2. This leads to 0.09 µmol m-2 of Br ions, which is an upper limit, by assuming that the electrical double layer is formed around the micelle particle existing in the interfacial region and the Br ion concentraion is equal to that of the surfactant ions. It is realized from Figure 7 that the stepwise increase is about 0.4 µmol m-2. Thus, we can conclude that the micelle formation is not a main factor for causing the stepwise increase in the J value around the cmc. Tajima et al. have employed the radiotracer method for determining the surface density of TSDS and found that the adsorbed amount of TSDS does not change even beyond the cmc.9 The scintillation counter detected the radiation of a β ray from tritiated dodecyl sulfate ions both at the surface and in the bulk solution. However, only the contribution from the adsorbed film was extracted by counting the β ray from the dodecanol solution of tritiated dodecanol. Therefore, the surface concentration estimated is a surface excess one, and the results show that there is no detectable increase in the surface concentration close to the cmc for the TSDS system. On the other hand, the surface concentration obtained from the XAFS spectra is also the surface excess concentration whenever the penetration depth of the evanescent wave is long enough to reach the region showing a uniform distribution of ions. Thus, the different shape of the surface concentration versus concentration curve around the cmc between TSDS and DTAB systems should be regarded as a difference in their adsorption behavior. Acknowledgment. This work was supported in part by the Sumitomo Foundation. We thank Mr. Kazuhiko Fujiwara for his help during the XAFS measurements and writing the computer programs. This work has been performed under the approval of the Photon Factory Advisory Committee (Proposal Nos. 98G350 and 2000G099). LA0300582
