Miscibility and Distribution of Counterions of Imidazolium Ionic Liquid

Jul 27, 2009 - The miscibility and distribution of Br− and BF4− ions of imidazolium ... at the air/water surface were investigated by surface tens...
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Miscibility and Distribution of Counterions of Imidazolium Ionic Liquid Mixtures at the Air/Water Surface Kei Shimamoto,† Asuka Onohara,† Hiroki Takumi,† Iwao Watanabe,‡ Hajime Tanida,§ Hiroki Matsubara,† Takanori Takiue,† and Makoto Aratono*,† ‡

† Department of Chemistry, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan, SR Center, Ritsumeikan University, Shiga 525-8577, Japan, and §Experimental Facilities Division, Japan Synchrotron Radiation Research Institute, Hyogo 679-5198, Japan

Received March 30, 2009. Revised Manuscript Received July 3, 2009 The miscibility and distribution of Br- and BF4- ions of imidazolium ionic liquid mixtures, 1-hexyl-3-methylimidazolium bromide (HMIMBr) þ 1-hexyl-3-methylimidazolium tetrafluoroborate (HMIMBF4), at the air/water surface were investigated by surface tensiometry and the total-reflection XAFS (TRXAFS) method. Tensiometry showed that the surface density of BF4- was much larger than that of Br-, the adsorbed films of the HMIMBr-HMIMBF4 mixture were greatly enriched in BF4- at all surface tensions, and the excess Gibbs energy of adsorption was positive. However, TRXAFS revealed that the Br ions were all in the free-Br state solvated by six water molecules in the mixed adsorbed film. Entropy-originated nonideal mixing, where a kind of segregation of the counterion distribution takes place in the interfacial region, was suggested in the mixture.

Introduction Counterions of ionic amphiphiles change the properties and structure of amphiphile assemblies such as adsorbed films at air/ water surfaces, micelles, and vesicles. For example, the critical micelle concentration (cmc) of alkylsulfate salts is increased in the order of Na>K>Cs,1,2 and the surface density of alkylammonium halides is increased in the order of I>Br>Cl3 as the Hofmeister series suggests.4 Such an influence is closely related to the difference in counterion distribution at the surface, which comes from the difference in interaction between amphiphile ions and counterions. In past decades, amphiphiles with imidazolium cations have attracted much attention because many of 1-alkyl-3methylimidazolium salts are so-called room-temperature ionic liquid (RTIL) and are utilized as alternative solvents of the common organics,5-7 materials for electrochemical cells,8,9 triborogical materials,10,11 and so on. The adsorbed films at air/water surfaces are very concentrated and organized even at a low bulk concentration, thus their surface structures and properties obtained by spectroscopic and thermodynamic techniques provide information about molecular interactions, ion-ion interactions, and ion distributions. From these points of views, many papers have been published with respect to *To whom correspondence should be addressed. E-mail: aratono@chem. kyushu-univ.jp. (1) Rosen, M. J. Surfactants and Interfacial Phenomena, 2nd ed.; John Wiley & Sons: New York, 1989; p 122. (2) Aratono, M.; Ikeda, N. In Structure-Performance Relationships in Surfactants; Esumi, K., Ueno, M., Eds.; Marcel Dekker: New York, 1997; p 120. (3) Tamaki, K. Colloid Polym. Sci. 1974, 252, 547. (4) Evans, D.; Wennerstr€om, H. The Colloidal Domain, 2nd ed.; Wiley-VCH: New York; 1999; p 101. (5) Fry, S. C.; Pienta, N. J. J. Chem. Soc. 1992, 107, 9366. (6) Boon, J. A.; Levisky, J. A.; Pflug, J. L.; Wilkes, J. S. J. Org. Chem. 1986, 51, 480. (7) Earle, M. J.; Seddon, K. R. Pure Appl. Chem. 2000, 72, 1391. (8) Reiter, J.; Vondrak, J.; Michalek, J.; Micka, Z. Electrochem. Acta 2006, 52, 1398. (9) Quinn, B. M.; Ding, Z.; Moulton, R.; Bard, A. J. Langmuir 2002, 18, 1734. (10) Kamimura, H.; Kubo, T.; Minami, I.; Mori, S. Tribol. Int. 2007, 40, 620. (11) Yu, B.; Zhou, F.; Mu, Z.; Liang, Y.; Liu, W. Tribol. Int. 2006, 39, 879.

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the surface properties and structures of not only neat ionic liquids but also their aqueous solutions by a variety of methods,12-23 including surface tension measurements,14,20,21direct recoil spectrometry,12,13,16 sum-frequency generation spectroscopy,15,17,19 X-ray and neutron reflectivity techniques,18,22 molecular dynamics simulation,23 and so on. Nevertheless, research on the surface properties and structures of RTIL systems are not satisfactory but rather have just started in the last few years. Thus, this study focuses the counterion distribution of the imidazolium amphiphile mixtures at their aqueous solution/air surface, and for that purpose, surface tensiometry and total reflection X-ray absorption fine structure (TRXAFS) were employed.

Experimental Section Materials. The chemical structures of 1-hexyl-3-methylimidazolium tetrafluoroborate (HMIMBF4) and 1-hexyl-3-methylimidazolium bromide (HMIMBr) are shown in Figure 1 and were purchased from Wako Pure Chemical Industries, Ltd. and from Kanto Kagaku Co., Ltd., respectively. Organic impurities were removed by extracting them 10 times using hexane for HMIMBF4 and ethyl acetate for HMIMBr, and then both of them were dried under reduced pressure. Sodium tetrafluoroborate (NaBF4) was purchased from Kanto Kagaku Co., Ltd. (98%), recrystallized (12) Gannon, T. J.; Law, G.; Watson, P. R.; Carmichael, A. J.; Seddon, K. R. Langmuir 1999, 15, 8429. (13) Law, G.; Watson, P. R.; Carmichael, A. J.; Seddon, K. R. Phys. Chem. Chem. Phys. 2001, 3, 2879. (14) Dong, B.; Li, N.; Zheng, L.; Yu, L.; Inoue, T. Langmuir 2007, 23, 4178. (15) Baldelli, S. J. Phys. Chem. B 2003, 107, 6148. (16) Law, G.; Watson, P. R. Chem. Phys. Lett. 2001, 345, 1. (17) Iimori, T.; Iwahashi, T.; Ishii, H.; Seki, K.; Ouchi, Y.; Ozawa, R.; Hamaguchi, H.; Kim, D. Chem. Phys. Lett. 2004, 389, 321. (18) Slolutskin, E.; Ocko, B. M.; Taman, L.; Kuzmenko, I.; Gog, T.; Deutsch, M. J. Am. Chem. Soc. 2005, 127, 7796. (19) Rivera-Rubero, S.; Baldelli, S. J. Phys. Chem. B 2006, 110, 4756. (20) Matsuda, T.; Mishima, Y.; Saeid, A.; Mastubara, H.; Takiue, T.; Aratono, M. Colloid Polym. Sci. 2007, 285, 1699. (21) Aratono, M.; Shimamoto, K.; Onohara, A.; Murakami, D.; Tanida, H.; Watanabe, I.; Ozeki, T.; Matsubara, H.; Takiue, T. Anal. Sci. 2008, 22, 2511. (22) Bowers, J.; Vergara-Gutierrez, M. C.; Webster, J.R. P. Langmuir 2004, 20, 309. (23) Lynden-bell, R. M.; Del Popolo, M. Phys. Chem. Chem. Phys. 2006, 8, 949.

Published on Web 07/27/2009

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Article views of the methods were fully described in our previous papers.26-29

Results and Discussion

Figure 1. Chemical structures of HMIMBr and HMIMBF4. once from water, and then baked at 170 C for 7 h under reduced pressure. Sodium bromide (NaBr) purchased from Aldrich Chemical Co. Inc. (99.99%) was used without further purification. Their purities were confirmed by observing no time dependence of the equilibrium surface tension of aqueous solution. Water was distilled three times; the second and third stages were done from alkaline permanganate solution. Surface Tension Measurements. The surface tension γ of the aqueous solutions of NaBr and NaBF4 was measured by the drop ^ volume method24 as a function of the total molality of ions m defined by ^ ¼ mC þ mNa ¼ 2m m -

ð1Þ

BF4-

and m is the molality of where mC is the molality of Br or NaBr or NaBF4. The γ value was calculated by the following equation

Surface Tension and Thermodynamic Quantities. First, let us briefly summarize the thermodynamic equations employed in the analysis of the surface tension data of amphiphile mixtures with common ions such as the HMIMBr-HMIMBF4 mixture.30 The surface tension γ is expressed as a function of the total ^ defined by eq 3 and the mole fractions of the second molality m component in the mixture X^2 defined by eq 4 as ^ =2X^1 X^2 ÞðX^H -X^2 Þ dX^2 ð5Þ ^ =mÞ ^ dm ^ -RTðΓ dγ ¼ -RTðΓ 2 H

H

at constant temperature and pressure. Here the total surface density of ions Γˆ H and the surface composition of HMIMBF4, X^H 2 , are defined similarly to eqs 3 and 4 by ^ H ¼ ΓH þ ΓH þ ΓH þ ΓH ¼ ΓH þ ΓH þ ΓH Γ Br 1, Im BF4 2, Im Im Br BF4

ð6Þ

and γ ¼ VΔFgF=r

ð2Þ

where V is the volume of a drop, ΔF is the density difference between air and the aqueous solution, g is the local acceleration of gravity, r is the capillary radius, and F is the correction factor, respectively. However, γ of the aqueous solutions of HMIMBr, HMIMBF4, and the HMIMBr-HMIMBF4 mixture was measured by the pendant drop method based on the drop shape ^ analysis described elsewhere25 as a function of the total molality m ^ ¼ mBr þ m1, Im þ mBF4 þ m2, Im ¼ 2m -1 þ 2m2 m

ð4Þ

where m1,Im and m2,Im are the molality of imidazolium cations dissociated from HMIMBr and HMIMBF4. The experiments were done at 298.15 K under atmospheric pressure. The temperature of the experiments was kept constant at 298.15 K within (0.05 K under atmospheric pressure, and the estimated experimental error of γ was (0.05 mN m-1.

Total Reflection X-ray Absorption Fine Structure (TRXAFS). The XAFS experiments were performed by using the synchrotron radiation at beamline 7C of the Photon Factory of the National Laboratory for High Energy Accelerator Research Organization (Tsukuba, Japan). The XAFS method was applied to the air/water surface under the total-reflection condition. The X-ray beam monochromatized by a double-crystal monochromator [Si-(111)] hits the solution surface at about 1 mrad. The incident beam intensity I0 was measured by a gas ionization chamber filled with nitrogen, the signal intensity I was detected by the total-conversion helium ion yield method, and I/I0 versus photon energy plots were obtained. In the present study, the photon energy was scanned from 13 391 to 13 633 eV, which was enough to obtain the jump values at the K absorption edge and to extract the solvation structure because the oscillation of the spectra was greatly diminished at photon energies above 13 560 eV. The depth of the evanescent wave was estimated to be around 7 nm; therefore, TRXAFS is surface-selective. Details of the principle, procedures, and schematic (24) Lando, L. J.; Oakley, T. H. J. J. Colloid Interface Sci. 1967, 25, 526. (25) Murakami, R.; Sakamoto, H.; Hayami, Y.; Matsubara, H.; Takiue, T.; Aratono, M. J. Colloid Interface Sci. 2006, 295, 209.

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ð7Þ

Introducing the surface density of amphiphile i, ΓiH is defined by H H H H H ΓH 1 ¼ ΓBr ¼ Γ1, Im , Γ2 ¼ ΓBF4 ¼ Γ2, Im

ð8Þ

and we have

ð3Þ

and the mole fraction X^ 2 of the second component, HMIMBF4, ^ X^ 2 ¼ ðmBF4 þ m2, Im Þ=m

H ^H X^2H ¼ ðΓH BF4 þ Γ2, Im Þ=Γ

^ H ¼ 2ðΓH þ ΓH Þ Γ 1 2

ð9Þ

Thus, it should be noted that X^2 and X^H 2 defined by eqs 4 and 7 are equal to the mole fraction of BF4- ions in the bulk solution, X^2 = mBF 4/(mBr þ mBF4), and that in the adsorbed film, X^H 2= H H H ˆˆ H and X^H /(Γ þ Γ ), respectively. Γ are evaluated by ΓBF Br BF 2 4 4 applying ^ H ¼ -ðm=RTÞðDγ=D ^ ^ T , p, X^ 2 mÞ Γ

ð10Þ

^ m=D ^ X^2 ÞT , p, γ X^2H ¼ X^2 -ð2X^1 X^2 =mÞðD

ð11Þ

and

^ to the surface tension data. The diagram constructed from the m ^ versus X^2 curves at a given surface tension is versus X^H 2 and m called the phase diagram of adsorption (PDA) and provides the relation between the bulk and surface compositions at equilibrium. Furthermore, the mean activity coefficients of the amphiphiles in the adsorbed films are estimated from the surface compositions using the relation H ^ m ^ 0i Þ ¼ f^iH( ðX^i Þ1=2 ðX^i Þ1=2 ðm=

ð12Þ

(26) Watanabe, I.; Tanida, H. Anal. Sci. 1995, 11, 525. (27) Watanabe, I.; Tanida, H.; Kawauchi, S.; Harada, M.; Nomura, M. Rev. Sci. Instrum. 1997, 68, 3307. (28) Takiue, T.; Kawagoe, Y.; Muroi, S.; Murakami, R.; Ikeda, N.; Aratono, M.; Tanida, H.; Sakane, H.; Harada, M.; Watanabe, I. Langmuir 2003, 19, 10803. (29) Aratono, M.; Kashimoto, K.; Matsuda, T.; Muroi, S.; Takata, Y.; Ikeda, N.; Takiue, T.; Tanida, H.; Watanabe, I. Langmuir 2005, 21, 7398. (30) Aratono, M.; Villeneuve, M.; Takiue, T.; Ikeda, N.; Iyota, H. J. Colloid Interface Sci. 1998, 200, 161.

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Figure 2. (a) Surface tension and (b) surface density vs concentration curves: (1) NaBr and (2) NaBF4.

Figure 3. Surface tension vs total concentration of HMIMBrHMIMBF4 mixtures at constant bulk compositions: (1) X^ 2 = 0 (HMIMBr), (2) 0.05, (3) 0.1, (4) 0.2, (5) 0.5, (6) 0.8, and (7) 1 (HMIMBF4).

and thus the criterion of ideal mixing is written as ^ 01 Þ2 þ ½ðm ^ 02 Þ2 - ðm ^ 01 Þ2 X^2H ^ 2 ¼ ðm ðmÞ

ð13Þ

^ 0i is the total molality of at a given surface tension, where m amphiphile i that gives the surface tension in the respective single systems. Here f^H i ( is defined as the ratio of the mean activity H,0 coefficient in the mixture γH i ( to that in the single system γi ( by H, 0 f^iH( ¼ γH i ( =γi (

ð14Þ

and thus the excess Gibbs energy of adsorption per mole of ^H amphiphiles g^H,E is estimated from X^H i and f i ( by using g^ H, E ¼ RTðX^1H ln f^1H( þ X^2H ln f^2H( Þ

ð15Þ

The surface tension γ and the evaluated surface density Γˆ H= H H H ˆH ΓBr þ ΓH Na of NaBr and Γ = ΓBF4 þ ΓNa of NaBF4 at their aqueous solution/air interface are plotted against the total mol^ in Figure 2a,b, respectively. The surface tension of the ality m ^ and thus Γˆ H of NaBF4 NaBF4 system decreases with increasing m is positive whereas γ of the NaBr system increases and thus Γˆ H of NaBr is negative. Negative adsorption is usually observed for inorganic salts and is caused by repulsive image forces between ions in the solution and electrostatic images in the air phase as well as an ion-free layer formed by the hydration of ions.31 Although these are influential more or less also in the NaBF4 system, the positive adsorption of BF4- is attributable to the weaker hydration of BF4- as follows. Because BF4- is stabilized by the high electronegative nature of four fluorine atoms and also the surface charge density is lower because of its rather large geometrical size, the hydration of BF4- is expected to be weakened compared to that of bromide ions. The weaker hydration of BF4- was verified using IR spectroscopy, which yielded a BF4- hydration number of 3.8; this is much smaller than 6, the hydration number of Br-.32 The surface tension of the aqueous solution of the HMIMBr^ at seven fixed mole HMIMBF4 mixtures is plotted against m fractions of HMIMBF4 in the mixture X^2 in Figure 3. The total surface density Γˆ H evaluated by applying eq 10 to the γ versus ^ curves ^ curves is displayed in Figure 4. The γ and Γˆ H versus m m regularly change from that of HMIMBr to that of HMIMBF4 with increasing X^2. The surface pressure π versus the average area (31) Ohshima, H.; Matsubara, H. Colloid Polym. Sci. 2004, 282, 1044. (32) Kristansson, O.; Lindgren, J.; Villepin, J. D. J. Phys. Chem. 1988, 92, 2680.

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Figure 4. Total surface density vs total concentration of HMIMBr-HMIMBF4 mixtures at constant bulk compositions: (1) X^ 2 = 0 (HMIMBr), (2) 0.05, (3) 0.1, (4) 0.2, (5) 0.5, (6) 0.8, and (7) 1 (HMIMBF4).

per amphiphile A curves are shown for HMIMBr and HMIMBF4 in Figure 5. Here, π is the decrease in surface tension from that of the water/air surface γ0 given by π ¼ γ0 - γ

ð16Þ

A ¼ 1=NA ΓH 1

ð17Þ

and A is evaluated by

where NA is Avogadro’s number. The surface density of HMIMBF4 is evidently higher than that of HMIMBr at all concentrations, and the addition of a small amount of HMIMBF4 to the HMIMBr system largely increases the surface density of the imidazolium cations (e.g., Γˆ H at X^2=0.5 is very close to that of pure HMIMBF4). This is partially due to the fact that BF4- is adsorbed positively whereas Br- is adsorbed negatively, as demonstrated in Figure 2, and thus BF4- interacts more strongly with the imidazolium cation than does Br-. The latter is suggested from the π versus A curve in Figure 5 in which the surface compressibility κ  - (1/A)(∂A/∂π)T,p,X2 at the saturation adsorption of the HMIMBF4 system is very small compared to that of the HMIMBr system. Although the minimum area of HMIMBF4 is estimated to be about 0.7 nm2 from the smallest A of curve 2 in Figure 5 but larger compared to the expected total geometrical area (0.53 nm2) of the side-by-side arrangement of the dehydrated Langmuir 2009, 25(17), 9954–9959

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Figure 5. Surface pressure vs mean area of amphiphile: (1) HMIMBr and (2) HMIMBF4.

Figure 6. Total molality at given surface tensions vs bulk and surface compositions (phase diagram of adsorption): (1) γ/mN m-1=45, (2) 50, and (3) 55. (-O-) Bulk composition X^ 2, (---) surface composition X^ H 2 , ( 3 3 3 ) surface composition of ideal mixing, and (b) surface composition evaluated from TRXAFS.

imidazolium cation (0.36 nm2 and BF4- (0.17 nm2), the low compressibility may support the side-by-side, rather packed arrangement of partially dehydrated ions as reported on the basis of the sum frequency generation method.17,23 The difference in the tendency to form ion pairs with imidazolium cation between Br- and BF4- affects their distributions and thus miscibility in the surface. The phase diagram of adsorption (PDA) is beneficial and thus was constructed at several surface tensions. The representatives are demonstrated at γ = 55, 50, and ^ versus X^2, m ^ versus X^H 45 mN m-1 in Figure 6, where m 2 , and the criterion of the ideal mixing given by eq 13 are respectively drawn by solid, broken, and dotted curves. It is evident that the adsorbed films greatly abound in BF4- compared to the aqueous solution; for example, when X^2 is 0.2, X^H 2 is about 0.8, 0.85, and 0.92 at the three surface tensions, respectively. Although the enrichment in BF4- emerges even when two amphiphiles mix ideally as the dotted line demonstrates, it is clear that the adsorbed films become more enriched in BF4- over the ideal mixing state as the surface tension decreases. This certainly indicates the preferentiality of adsorption of BF4- ions over Br- ions. Figure 6 reveals that the mixing deviates positively from ideal mixing and thus Br- and BF4- are less miscible compared to the ideal mixture. This is estimated quantitatively in terms of the activity coefficients by eq 12 and then rationalized in terms of the Langmuir 2009, 25(17), 9954–9959

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Figure 7. Excess Gibbs energy of adsorption vs surface composition at given surface tensions: (1) γ/mN m-1=45, (2) 50, and (3) 55.

excess Gibbs energy of adsorption using eq 15. The evaluated g^H,E is plotted against the surface composition in Figure 7. It is seen that g^H,E is slightly negative (or virtually zero within the estimation error) at γ=55 mN m-1 but becomes definitely positive at lower surface tension. In other words, the mixing of one component with the other costs free energy compared with when the respective components form only adsorbed films. A positive deviation has been observed for combinations such as hydrocarbon surfactant þ fluorocarbon surfactant mixtures33,34 and cationic surfactant mixtures with different chain lengths but the same counterion30 and so on. In these cases, the positive deviation is attributable to the dispersion interaction between hydrophobic chains in the mixed adsorbed films is less effective than that in the respective pure adsorbed films. In the HMIMBr-HMIMBF4 mixture, however, the positive deviation inevitably comes from influences of mixing counterions. In our previous studies on the dodecyltrimethylammonium bromide (DTAB)- dodecyltrimethylammonium chloride (DTAC)29and decylammonium bromide (DeAB)-decylammonium chloride (DeAC)30 mixtures, their PDA demonstrated that bromide and chloride ions are ideally mixed in the adsorbed film at all concentrations below the cmc. Although the degree of counterion binding to surfactant cations and thus the ion distributions in the interfacial region are expected to be different from each other between Br- and Cl-, the ideal mixing observed suggested that the ion distributions of counterions are scarcely influenced by each other. Taking these findings into consideration, there are several possible causes for the positive deviation in the HMIMBrHMIMBF4 mixture. For example, because BF4- is expected to form ion pairs preferentially with imidazolium cations compared to Br-, the entropy of mixing of counteranions in the adsorbed film is probably lowered and thus the Gibbs energy rises from the corresponding ideal mixing at a given surface composition. This is closely related to the ion distribution in the interfacial region and may be more influential when HMIMBF4 is added to HMIMBr, that is, at lower X^2. Another possibility is that the electrostatic repulsive interaction between imidazolium cations is expected to be increased and thus also the Gibbs energy is increased by adding HMIMBr to HMIMBF4. This may be more influential at higher X^2. The former is entropy-originated nonideal mixing, but the latter is enthalpy-originated nonideal mixing. However, it should be noted that both entropy- and enthalpy-originated nonideal (33) Villeneuve, M.; Nomura, T.; Matsuki, H.; Kaneshina, S.; Aratono, M. J. Colloid Interface Sci. 2001, 234, 127. (34) Matsuki, H.; Ikeda, N.; Aratono, M.; Kaneshina, S.; Motomura, K. J. Colloid Interface Sci. 1992, 154, 454.

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Figure 8. TRXAFS spectra of HMIMBr-HMIMBF4 mixtures ^ at 60 mN m-1: (1) m/mmol kg-1 =205.73 and X^ 2 =0.05, (2) 179.30 and 0.1, (3) 147.55 and 0.2, (4) 104.76 and 0.5, and (5) 80.68 and 0.8. The I/I0 values at 13 392 eV for all of the spectra were moved to zero to visualize the differences in the jump values.

mixing come from the difference in interaction between the counterion and imidazolium cation between Br- and BF4-. Total-Reflection XAFS and Solvation Structure of Br-. The total-reflection XAFS (TRXAFS) method was employed for two reasons. The first was to estimate the surface excess concen, from the Br K-edge jump values and then tration of Br-, ΓXAFS Br through calculate the surface composition X^H,XAFS 2 H, XAFS ^H ¼1 -2ΓXAFS =Γ X^2 Br

ð18Þ

where Γˆˆ H is the total surface density evaluated by eq 10. The second was to investigate the solvation structure of Br- in the adsorbed films from the EXAFS analysis. The χ spectrum defined by χðkÞ ¼ ½μðkÞ - μ0 ðkÞ=μ0 ðkÞ

ð19Þ

is useful for this purpose, where the photoelectron wave vector k is defined by k ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2me ðE -E0 Þ=p2

ð20Þ

where E is the incident X-ray energy, E0 is the threshold energy for the K-edge absorption, μ(k) is the experimental absorption coefficient due to the K-shell excitation, and μ0(k) is that of a hypothetical isolated bromide atom. The extraction of the true threshold energy E0 and the determination of the absorption coefficient due to the K-shell excitation of a hypothetical isolated bromide atom, μ0(k), were important to obtaining sufficient fitting results. The detail procedure for this was demonstrated in our previous study.35 Typical examples of the TRXAFS spectra are shown in Figure 8, where the I/I0 values of all of the spectra are set to zero at 13 392 eV. The jump value J is correlated with the concentration profile of the Br ion C(z) and the intensity of the evanescent wave P(z), both of which change as a function of the distance z normal to the surface from the top of the surface at z = 0 by Z ¥ CðzÞ PðzÞ dz J ¼ kS 0

Z

¥

¼ kSPð0Þ

CðzÞ expð -z=λÞ dz

ð21Þ

0

(35) Harada, M.; Okada, M.; Watanabe, I. J. Phys. Chem. B 2002, 106, 34.

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Figure 9. EXAFS k3χ spectra of Br- of the HMIMBr-HMIMBF4 mixtures. Note that although eight curves at different ^ and X^ 2 are drawn, they almost overlap each combination of m other.

where k is a proportionality constant, S is the footprint of the air/ solution interface that is irradiated by X-rays, and P(0) is the intensity of the incident X-rays.26-29 Taking account of the fact that almost all surfactant ions are confined in the monolayer with a thickness of around 2 nm for usual surfactants and even almost all of their counterions exist in the electrical double layer with a thickness of several nanometers beneath the surfactant monolayers and the penetration depth of the evanescent wave is around 7 nm for ions in our experiment, the integral part of eq 21 is proportional to the surface excess concentration ΓXAFS Br evaluated from the surface tension measurements. Therefore, we have J ¼ kSPð0ÞΓXAFS Br

ð22Þ

It is evident from Figure 8 that ΓXAFS is strongly dependent on Br ^ and X^2 at a given surface tension. The X^H,XAFS values thus m 2 evaluated from eq 18 and the Γˆ H values given in Figure 4 are plotted by solid circles with error bars in the PDA in Figure 6. It coincides with X^H should be noted that X^H,XAFS 2 2 estimated from the surface tension measurement. This confirms that the experimental and evaluation processes of the surface compositions have performed appropriately using TRXAFS methods and that Brand BF4- are mixed nonideally in the surface. More importantly, in contrast to the significant change in the jump values, the oscillation structures of the XAFS spectrum virtually do not change with the sample solutions of the mixture ^ mmol within the present experiments (X^2=0.05-0.8, m=100-1000 kg-1); therefore, all of the spectra are assumed to be the same. This is clearly demonstrated by the k3χ versus k spectra in Figure 9, where the curves for eight different samples are written. This is also in striking contrast to the concentration dependence of the k3χ spectra of the DTAB and 1-decyl-3-methylimidazolium bromide (DeMIMBr) systems; for both systems, the amplitude of the k3χ spectra gradually becomes small with increasing bulk concentration and the spectra have isosbestic points, thus the k3χ spectrum at a concentration of m, χm, was expressed as a linear combination of the two representative spectra χ1 and χ2 as χm ¼ a1, m χ1 þ a2, m χ2

ð23Þ

where a1,m and a2,m are the weights of the respective spectra and change gradually with increasing m. To extract the structure parameters from the two representative spectra for the DTAB and DeMIMBr systems and the k3χ spectra Langmuir 2009, 25(17), 9954–9959

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and the subscript j is the coordination shell number and λ is the photoelectron mean free path. The parameters estimated from the fitting procedure are the distance r between absorbing and scattering atoms, the Debye-Waller-like factor σ, the amplitude factor B, and the absorption edge shift ΔE0. The back-scattering amplitude of photoelectron F and the total phase shift φ were generated by the computer program FEFF version 8.1038 for the distance between Br and O atoms rBr-O = 3.2 A˚. The anhamononicity C3 was fixed at 34.4  10-4 A˚3.39 The results of the fittings are summarized for the χ1 and χ2 spectra of the DeMIMBr system and the χ for the HMIMBr-HMIMBF4 mixtures in Table 1. Only one coordination shell number was extracted for χ1 and χ, whereas two were extracted for χ2. With regard to the results of the DeMIMBr system,21 because χ1 was similar in its shape to that of the KBr aqueous solution at low concentrations, the number of scattering atoms was assumed to be 6. Thus, the distance between the six scattering atoms and Br was determined to be 3.2 A˚. The analysis of χ2 yielded that there were about four scattering atoms at around 3.2 A˚ in the first shell and about three atoms at around 4 A˚ in the second shell. Referring to the results of χ1, therefore, the hydration number of χ2 was around four, and three atoms in the second shell are probably attributable to the atoms in the hydrophilic group of the imidazolium cation. The species corresponding to χ1 is referred to as free-Br because it is free from coordination to atoms except water molecules and that to χ2 is

referred to as bound-Br because it is partially bound to other atoms in addition to water molecules. However, the fitting result of the HMIMBr-HMIMBF4 mixtures undoubtedly revealed that the χ spectra at all concentrations within the present experiments are the same with χ1. That is, all Br are in the free-Br states and bound-Br was not observed in the mixture at least when the H H H mole fraction of Br in the adsorbed film, X^H 1 = ΓBr/(ΓBr þ ΓBF4), is smaller than around 0.5 judging from Figure 6. Nonideal Mixing and Distribution of Counterions. The tensiometry and the data analysis showed that the surface density of HMIMBF4 is much larger than that of HMIMBr, the adsorbed films of the HMIMBr-HMIMBF4 mixture are greatly enriched in BF4- at all surface tensions from the PDA, and the excess Gibbs energy of adsorption g^ H,E is positive. However, the TRXAFS revealed that Br ions are all in the free-Br state in the mixed adsorbed film, although they are in either the free-Br or bound-Br state and their ratio changes with the bulk concentration in the single-component system of amphiphiles with Br as their counterion. At the end of the first section in Results and Discussion, the hypothesis of the entropy-originated nonideal mixing for the positive deviation from the ideal mixing was provided as follows: because BF4- is expected to form ion pairs preferentially with imidazolium cations compared to Br-, the entropy of mixing of counteranions in the adsorbed film is probably lowered and thus the Gibbs energy rises from the corresponding ideal mixing at a given surface composition. Now the structure analysis of the TRXAFS certainly confirmed the hypothesis. On the basis of our results given above, let us provide a feasible situation for the adsorbed films of the HMIMBr-HMIMBF4 systems as follows. The adsorbed film of HMIMBF4 is hardly compressible at saturation adsorption and thus is densely packed similarly to the HMIMBF4 liquid/air surface, where a side-byside arrangement of the ion pair of BF4- and the imidazolium cation is suggested.17,23 This is due to the rather strong interaction between BF4- and the imidazolium cation and also the adsorption ability of BF4-. However, the adsorbed film of HMIMBr is comparatively compressible even at the saturation adsorption. The TRXAFS experiments showed that part of the Br- ions are in the bound-Br state, which forms ion pairs with cations, whereas the rest exist in the electrical double layer. In the mixture, the PDA shows that the surface compositions are on the ideal mixing line at higher surface tension and become enriched in BF4- over the ideal mixing as the surface tension decreases. However, TRXAFS revealed that Br- ions in the interfacial region are all in the free-Br state, which shows a kind of segregation in the counterion distribution in the mixture; BF4- ions are rather near the cationic group, and Br- ions are beneath the ion pairs between BF4- and the cation toward the aqueous phase.

(36) Watanabe, I.; Tanida, H.; Kawauchi, S. J. Am. Chem. Soc. 1997, 119, 12018. (37) Tanida, H.; Sakane, H.; Watanabe, I. J. Chem. Soc., Dalton Trans. 1994, 15, 2321. (38) Ankudinov, A. L .; Ravel, B.; Rehr, J. J.; Conradson, S. D. Phys. Rev. B 1998, 58, 7565. Rehr, J.; Albers, R. C. Rev. Mod. Phys. 2000, 72, 621. (39) Sawa, Y.; Miyanaga, T.; Tanida, H.; Watanabe, I. J. Chem. Soc., Faraday Trans. 1995, 91, 4389.

Acknowledgment. This work was supported by a Grant-inAid for Scientific Research on Priority Area (no. 20031020) from the Ministry of Education, Science, Sports and Culture. This work has been performed under the approval of the Photon Factory Advisory Committee (proposal no. 2008 G038), which is greatly appreciated.

Table 1. EXAFS Curve-Fitting Results shell

free bound

1 1 2

χ1 χ2

free

1

χ

N

r/A˚

σ/A˚

6 4.1 2.9

DeMIMBr 3.24 0.197 3.23 0.189 4.26 0.386

ΔE0

-1.41 -1.87 9.35

deviation (%)

5.31 4.18

HMIMBr-HMIMBF4 6

3.25

0.2

-1.56

3.66

in Figure 9 for the HMIMBr-HMIMBF4 mixtures, k3χ1, k3χ2, and k3χ spectra were fitted respectively by the equation36,37 k3 χ ¼ k3

X ½Bj Fj ðkj Þ=kj rj 2  exp½ -2rj =λ exp½ -2σj 2 kj 2  j

sin½2kj rj þ jj ðkj Þ - kj 3 C3j 

ð24Þ

kj ¼ ½k2 -ð2me =p2 ÞΔE0j 1=2

ð25Þ

where

Langmuir 2009, 25(17), 9954–9959

DOI: 10.1021/la901114e

9959