Surface Adsorption and Aggregate Formation of Cationic Gemini

Jun 11, 2009 - We measured the surface tension of aqueous solutions of octanol−butandiyl-1,4-bis(decyldimethylammonium bromide) using the drop-volum...
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J. Phys. Chem. B 2009, 113, 8847–8853

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Surface Adsorption and Aggregate Formation of Cationic Gemini Surfactant and Long-Chain Alcohol Mixtures H. Matsubara,*,† T. Eguchi, H. Takumi,† K. Tsuchiya,# T. Takiue,† and M. Aratono† Department of Chemistry, Faculty of Sciences, Kyushu UniVersity, Japan, and Department of Pure and Applied Chemistry, Faculty of Science and Technology, Tokyo UniVersity of Science, Japan ReceiVed: December 8, 2008; ReVised Manuscript ReceiVed: April 20, 2009

We measured the surface tension of aqueous solutions of octanol-butandiyl-1,4-bis(decyldimethylammonium bromide) using the drop-volume technique at 298.15 K under atmospheric pressure as a function of the total molality and bulk composition. The results of the surface tension measurements, which were analyzed by originally developed thermodynamic equations, suggested that octanol molecules filled the spaces among the hydrophobic chains of gemini surfactants and formed a densely packed monolayer with them in the adsorbed film. The turbidity of aqueous solutions was also measured to construct the concentration-composition diagram with the surface tension data. A transmission electron microscope was used to determine the aggregate morphology in the aqueous solutions. Disc-like micelle and microemulsion regions were found on the diagram prior to the spherical micelle formation; nevertheless, the butandiyl-1,4-bis(decyldimethylammonium bromide) itself formed only spherical (or small ellipsoid) micelles in the concentration range measured. We also studied the relationship between synergism and molecular packing in the aggregates. Introduction In a previous study, the molecular packing in the surfactant aggregates was explained as the balance between the opposing tendencies of the head groups to minimize hydrocarbon-water contact and to spread apart as a result of electrostatic, hydration, and steric repulsions.1 In addition, recent experimental observations indicated that the geometrical matching of the surfactant molecules appreciably influenced the effective packing and resultant aggregate formed in the surfactant mixed systems. For example, the addition of a small amount (less than 0.5% in the relative ratio) of the single-chain cationic surfactant dodecyltrimethylammonium bromide (DTAB) into the aqueous solution of the double-chain cationic surfactant didodecyldimethylammonium bromide (DDAB) reduced the critical vesicle concentration from 1 to 0.01 mmol kg-1.2,3 The authors mentioned that the preferential mixing of the DTAB molecules in the outer layer of vesicles stabilizes a negative curvature of the monolayer and then induces the small size vesicle formation from the composition dependence of vesicle size observed by dynamic light scattering and cryogenic transmission electron microscope. In addition, Bain et al. studied the mixed adsorption of dodecanol and alkyltrimethylammonium bromides at the air/ water interface using sum frequency spectroscopy and found that the dodecanol molecules filled the spaces among the hydrocarbon chains of alkyltrimethylammonium ions, which then led to a surface crystallization.4 In this study, we examined the role of molecular geometry and the effective packing of different molecules in the surfactant aggregates by using the mixture of butandiyl-1,2-bis(decyldimethylammonium bromide) and long-chain alcohol (octanol). The former is simply called “gemini surfactant” because it has two identical amphiphilic moieties connected at the level of the polar * To whom correspondence should be addressed. E-mail: h.matsubarascc@ chem.kyushu-univ.jp. † Kyushu University. # Tokyo University of Science.

head groups by a spacer alkandiyl chain. An important advantage of using the gemini surfactant instead of the corresponding single-chain surfactant is the lower entropic cost to form ordered aggregates such as condensed monolayers, vesicles, microemulsions, and liquid crystals. The other important point is that the length of the spacer group can control the separation between two hydrophobic chains. From the CPK model, the spacer chain with four methyl carbons provided better space to be filled by octanol molecules in the planar geometries than the other gemini surfactants. Experimental Section Materials. Butandiyl-1,4-bis(decyldimethylammonium bromide) was synthesized by refluxing 1-bromodecane (SigmaAldrich Corporation, St. Louis, MO) and N,N,N′,N′-tetramethyltetramethylenediamine (Sigma-Aldrich) with ethanol. It was then recrystallized six times from acetone. The purity of the surfactant was checked with a differential scanning calorimeter, elemental analysis, and surface tension measurements. 1-Octanol (Nacalai Tesque, Inc.) was distilled under reduced pressure, and the purity was confirmed by gas-liquid chromatography to be >99.9%. The water used by all experiments was distilled three times. Surface Tension Measurement. The surface tension of aqueous solutions was measured using the drop-volume technique at 298.15 K under atmospheric pressure.5,6 The temperature was kept constant within (0.05 K by immersing the measurement cell in the water bath. The error of the surface tension measurement was within 0.05 mN m-1. Turbidity Measurement. Turbidity was measured using a HACH 2100P turbidimeter (Hach Company, Loveland, CO) and the ratio nephelometric method.7,8 Samples were left for 24 h in an air-conditioned room before measurement to remove the bubbles in the sample solutions. The experimental error of the turbidity measurement was less than 1% of the reading. Transmission Electron Microscopy. The aggregate morphologies were determined by using a transmission electron

10.1021/jp8109034 CCC: $40.75  2009 American Chemical Society Published on Web 06/11/2009

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m ) m1 + m2

(3)

X2 ) m2 /m

(4)

and

was that the total differential of the surface tension at the constant temperature and pressure Η Η dγ ) -ΓΗ 1 dµ1 - Γ2 dµ2+ - 2Γ2-dµ2-

(5)

could be simplified with the chemical potentials of each species

Figure 1. Surface tension vs molality curves at constant composition: Xˆ2 ) 0 (O), 0.30 (3), 0.50 (∆), 0.75 ([), 0.90 (]), 0.95 (2), 0.98 (0), and 1 (b). At Xˆ2 ) 0.75 and 0.90, the sample solution became turbid and showed the Tyndall phenomenon at concentrations below the break point on the surface tension versus molality curves, reflecting the formation of a large aggregate instead of the generally observed spherical micelle.

microscope (H7650; Hitachi High-Technologies Corporation, Tokyo, Japan) with the cryotransfer attachment (CT-3500; Oxford Instruments, Oxfordshire, U.K.). The sample solutions were held on the hydrophilic microgrid charged in the vacuum and then rapidly refrigerated by liquid ethane after the excess solutions were removed by a filter paper. All experiments were performed in cooled air (less than -170 °C) provided in a copper cell that had been thermostatted by liquid nitrogen. Results and Discussion The results of surface tension measurements are shown in Figure 1 as a function of concentration and composition of the gemini surfactant in the aqueous solution defined, respectively, as9,10

m ˆ ) m1 + 3m2

(1)

µ1 ) µθ1 + RT ln m ˆ (1 - Xˆ2)

(6)

θ µ2+ ) µ2+ + RT ln(1/3)m ˆ Xˆ2

(7)

θ µ2- ) µ2+ RT ln(2/3)m ˆ Xˆ2

(8)

dγ ) -(RTΓˆ Η /m ˆ )dm ˆ - (RTΓˆ Η /Xˆ1Xˆ2)dXˆ2

(9)

and

to

where the Xˆ2H is the composition of the gemini surfactant in the adsorbed film in equilibrium with the bulk solution defined by

ˆΗ Xˆ2H ) 3ΓΗ 2 /Γ

and Γˆ H is the total surface density defined in a manner similar to m ˆ in eq 1 by using the surface density of each component as Η Γˆ Η ) ΓΗ 1 + 3Γ2

and

Xˆ2 ) 3m2 /m

(2)

The factor 3 arose because the gemini surfactant dissociated into a divalent cation and two counterions. The surface tension value dropped dramatically when we added a small amount of octanol in the aqueous solution. As explained later in this paper, the break points on the surface tension curves at Xˆ2 ) 0.95, 0.98, and 1 corresponded to the spherical micelle formation; those at Xˆ2 ) 0.50, 0.75, and 0.90 are related to the disk-like micelle formation followed by the change in the composition of the aggregates. The other curves had no distinctive break point. Although, in general, the surface tension of a single surfactant system would become constant if the aggregate formed in the aqueous solution was sufficiently large, the decrease (or increase) in γ of the binary mixture after aggregate formation is thermodynamically feasible when the composition in the aggregate changes (see the Appendix). The advantage of using the definitions in eqs 1 and 210 instead of the normal definitions

(10)

(11)

From eq 9, one can find that the slope of the m ˆ versus Xˆ2 curves H ˆ at a given γ gives X2 by applying

XˆH2 ) Xˆ2 - (Xˆ1Xˆ2 /m ˆ )(∂m ˆ /∂Xˆ2)T,p,γ

(12)

We plotted the results of the calculation in the form of the phase diagram of adsorption shown in Figure 2. The compositions of the bulk solution and adsorbed film were represented, respectively, by the solid and dash-dotted curves. The end points of the horizontal line connecting these curves show the compositions of the bulk solution and the adsorbed film when they were in equilibrium. With our treatment, all thermodynamic quantities were obtained by means of the overall surface density including the counterions, which were obtained as realized from eq 11. However, the determination of the surface density of the gemini surfactant ion individually from the surface tension measurements was rather complex. From the comparison of the surface density obtained by the neutron reflectivity to that obtained by

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ΓΗ 2 ) -(m2 /nRT)(∂γ/∂m2)T,p

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(13)

the constant n should be 2, indicating that one gemini surfactant ion binds one counterion in submicellar concentrations.11 On the other hand, no experimental evidence of the ion pairing was found by the electrical conductivity measurements.12 Thus, the possibility of the ion pairing of the gemini surfactants seems to be realistic in some cases, but it is still open for further investigation. The straight lines connecting the molalities of pure components express the ideal mixing criterion in the adsorbed film given by

m ˆ )m ˆ 01 + (m ˆ 02 - m ˆ 01)XˆH2

(14)

The deviation from the ideal mixing line can be evaluated quantitatively by referring to the excess Gibbs energy of adsorption determined from the equation H H gˆH,E ) RT(XˆH1 ln ˆf1( + XˆH2 ln ˆf2( )

(15)

where ˆfHi( is the mean activity coefficient of components i in the adsorbed film and is evaluated by H ˆfi( ) (m ˆ /m ˆ i0)(Xˆi /XˆiH)1/2

(16)

The gˆH,E versus Xˆ2H curves at γ ) 40, 45, and 50 mN m-1 are shown in Figure 3. Two observations can be noted, (A) the excess Gibbs energies are obviously negative at all compositions in the adsorbed film, and (B) the excess Gibbs energies decrease

Figure 3. Excess Gibbs energy of adsorption versus composition curves at constant surface tension: (1) γ ) 50, (2) 45, and (3) 40 mN m-1. The decrease in the excess Gibbs energy caused by the thermodynamic decrease in the surface tension indicates that molecules tend to occupy a smaller surface area compared to that of the ideal mix generated by the effective packing of molecules in the adsorbed film.

with decreasing surface tension. The former observation indicates that the mutually attractive interaction between octanol and gemini surfactant molecules in the adsorbed film was stronger than interactions between the same species. The latter observation indicates that the packing of the molecules became more favorable in the mixed adsorbed films compared to that for the respective single surfactant systems because the surface excess area per molecule given by13,14

aˆH.E ) -[∂(gˆH,E /NA)/∂γ]T,p,XˆH2

Figure 2. Total molality versus composition curves at constant surface tension: (1) γ ) 50, (2) 45, and (3) 40 mN m-1. The compositions of the bulk solution and adsorbed film were represented by the solid and dash-dotted curves, respectively. The straight lines connecting the molalities of pure components express the ideal mixing criterion in the adsorbed film. The end points of the horizontal line connecting the solid and dash-dotted curves give the compositions of the bulk solution and the adsorbed film in equilibrium with each other, and the negative deviation from the ideal mixing line means the existence of the net attractive interaction between the different components in the adsorbed film.

(17)

was negative in the present case. We deduced the following interaction mechanism between octanol and gemini surfactant molecules in the adsorbed film by comparing gˆH,E and aˆH.E values with those obtained from previous studies. Our interpretations are consistent with the results from turbidity and cryo-TEM experiments shown later; however, it is noteworthy to mention that there may be alternative interpretations which also suit the experimental data. The absolute value of the excess Gibbs energy in the present system was considerably larger than the value in other nonionic-cationic surfactant systems. For example, the excess Gibbs energy of adsorption observed in the dodecylammonium chloride-tetraethylene glycol monooctyl ether system was -0.4 kJ mol-1 at 50 mN m-1, but it increased with decreasing surface tension to -0.2 kJ mol-1 at 35 mN m-1, and thus, aˆH.E was positive.10 Such a combination of negative gˆH,E and positive aˆH.E was also observed for the sodium dodecyl sulfate-tetraethylene glycol monooctyl ether system.15 In these cases, the energetic stabilization due to the ion-dipole interaction between head groups overcame a decrease in the dispersion interaction between hydrophobic chains and/or an energetic loss due to the increase in the water-hydrocarbon contact area. On the other hand, several mixtures had the combination of negative gˆH,E and negative aˆH.E. Some of them were the dodecyltrimethylammonium halides-nonionic surfactant mixtures;16 the negative aˆH.E was attributable to the fact that the nonionic surfactant

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Figure 4. Pictures of sample solutions at Xˆ2 ) 0.60 and m ˆ ) 6, 8, 10, 12, 15, 20, 40, and 60 mmol kg-1 (left to right). Picture B shows the Tyndall phenomenon observed at m ˆ ) 6, 8, 10, 12, and 15 mmol kg-1.

molecules were effectively packed into the spaces among hydrocarbon chains of cationic surfactants. This yielded not only an energetically favorable ion-dipole interaction but also denser packing. Another example is the hexadecyltrimethylammonium bromide (HTAB)-DTAB system. In this case, the synergism in the adsorbed film (-0.4 kJ mol-1) was attributable to the dispersion interaction between the hydrophobic chains because both surfactants had the same head groups.17-19 On the basis of the neutron reflectivity measurement of the pure DTAB adsorbed film near the cmc, Penfold et al. proposed that the head groups of these molecules took the staggered configuration to reduce the electrical and/or hydration repulsion between trimethylammonium groups.20 This allowed the surfactant molecules to be packed more closely compared with the normal adsorbed film and led to the negative excess Gibbs energies of the HTAB-DTAB system in which the hydration diameter of the trimethylammonium groups was matched with the difference in the length between the hydrocarbon chains. Comparing these experimental findings with those obtained in the present study, it may be concluded that the attractive ion-dipole interaction between the octanol and gemini surfactant and the shielding of the electric repulsion between the gemini surfactants by the octanol molecules contributed to the negative excess Gibbs energies in the adsorbed film. However, the effective packing between surfactant molecules in the adsorbed film also worked in a way similar to the HTAB-DTAB system as the surface density increased. Filling the space among hydrophobic chains of the gemini surfactants with octanol molecules led to a decrease in the occupied area and an increase in the dispersion interaction between hydrocarbon chains compared with the ideal mixing. It also simultaneously led to the large packing parameter favoring the planar geometry. Our preliminary experiments concerned with the mixture of ethandiyl1,2-bis(decyldimethylammonium bromide) and octanol only showed that the magnitude of negative excess Gibbs energy was less than half of that of the present system. Therefore, we concluded that the spacer chain with four methyl carbons provided more proper space to be filled by alcohol molecules in the adsorbed film and promoted the ion-dipole interaction between hydrophilic groups and the dispersion interaction between hydrophobic chains cooperatively. Next, we discuss the aggregate formation in the aqueous solutions. At compositions below Xˆ2 ) 0.90, sample solutions became turbid and showed the Tyndall phenomenon before concentrations reached the break points on the γ versus m ˆ curves as shown in Figure 4. The turbidity was more sensitive to the change of radius than the number of particles in the solution, as one can see from the following equation. Thus, we applied

the turbidity measurement to determine the phase boundaries between the different aggregates

τ ) (128π5a6N/3λ4)(n2 - 1)/(n2 + 1)

(18)

where a is the particle radius, N the number of particles per unit volume, λ the wavelength of incident light, and n the refractive index of particles relative to the surrounding medium. The turbidity measured at Xˆ2 ) 0.50, 0.85, and 0.95 is shown in Figure 5. The turbidity at Xˆ2 ) 0.95 was almost 0 within the concentration region measured, reflecting the fact that the surfactant molecules dispersed as monomers (m) or small micelles represented the spherical and ellipsoid micelles (M). However, the turbidity started to increase at a certain concentration in the other compositions. At Xˆ2 ) 0.85, the turbidity decreased again from m ˆ ) 33.0 mmol kg-1, and then, it became almost 0 at m ˆ ) 56.0 mmol kg-1. The increase in turbidity corresponded with the formation of a large aggregate (D) compared with the micelles (M), and the following decrease in turbidity corresponded with the coexistence of the large aggregate and the micelle (D + M). The shape of the turbidity curve at Xˆ2 ) 0.50 was similar to the one belonging to the m f D f D + M f M region, but the turbidity increased again before the coexisting region ended and reached a much larger value compared with the D region. Hence, the coexisting region in this curve consisted of D and another kind of large aggregate instead of the micelles. If we use the symbol E for this aggregate, the sequence would be m f D f D + E f E. To determine the aggregate morphologies formed in the D region and E region, the cryo-TEM observation was performed ˆ ) ) (a) 0.95, 50 mmol kg-1, (b) 0.80, 30 mmol kg-1, at (Xˆ2, m (c) 0.60, 30 mmol kg-1, and (d) 0.60, 60 mmol kg-1 (Figure 6). Points (a), (b), (c), and (d) are marked in the concentrationcomposition diagram determined from the surface tension and turbidity measurements in Figure 7. At point (a), a large number of small dots (several nanometers in diameter) were observed that were consistent with the fact that point (a) belongs to the M region in the concentration-composition diagram. On the other hand, at point (b), the aggregates up to 50 nm in diameter were mainly observed. Because the silhouette of these aggregates, which overlapped with another one, could be recognized in the picture, these micelles were probably relatively thin. Therefore, one of the possible structures of these aggregates is the disk-like micelle, which is also suitable for the surfactant molecules to be packed in the planar geometry. In the E region (points (c) and (d)), we found the large spherical aggregates, which had a diameter ranging from 30 to 200 nm. For the

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Figure 5. Turbidity vs molality curves at constant compositions: (a) Xˆ2 ) 0.95, (b) 0.85, and (c) 0.50. Monomers (m) and small aggregates (micelles: M) do not scatter the incident light and have no influence on the turbidity values. Therefore, the detected turbidity values come from the larger surfactant aggregates, which were assigned as the disk-like micelle (D) and emulsion droplet (E) in this study.

Figure 6. Cryo-TEM images of surfactant aggregates taken at (Xˆ2, m ˆ ) ) (a) 0.95, 50 mmol kg-1, (b) 0.80, 30 mmol kg-1, (c) 0.60, 30 mmol kg-1, and (d) 0.60, 60 mmol kg-1. Small micelles observed in the bulk compositions rich in the gemini surfactant (a) transform to disk-like micelles (b) and then to emulsion droplets (c) as the octanol molecules were added to the solution. The change from (c) to (d) shows the growth of the emulsion droplet at constant bulk composition. The bar shows 200 nm.

aqueous solutions of surfactants, the electron density in a unit volume of the hydrocarbon chains self-assembled in the aggregates was much larger than that of the surrounding monomer solution. This resulted in the ring-like dark patterns for the vesicle particles in the cryo-TEM pictures. In the present case, the transmission of the electron beam was suppressed near the center of the aggregates. Therefore, the droplet microemulsion was the more plausible structure. Judging from the fact that small emulsions observed at point (c) disappeared at point

(d) and larger emulsions increased, it is likely that the average size of the microemulsions increased with increasing m ˆ . In actual practice, the emulsions may be much larger; however, such emulsions are unable to enter the grid and are thus sucked by a filter paper or broken in the grid because the thickness of the aqueous film formed in the grid is approximately 300 nm. Such uncertainness involved in the sample preparation of the cryoTEM experiment can not be eradicated completely. Hence, it is desirable to confirm the morphologies expected in the present

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Matsubara et al. Acknowledgment. The authors are grateful to Prof. Masahiko Abe and Associate Prof. Hideki Sakai at Tokyo University of Science for the cryo-TEM observation. H.M. is also pleased to acknowledge financial support from the Japan Society for the Promotion of Science (Grant in Aid for Young Scientists [B], No. 19750117). Appendix

Figure 7. Concentration-composition diagram for octanol-butandiyl1,4-bis(decyldimethylammonium bromide) mixtures. Symbols m, M, D, and E, respectively, refer to monomer, spherical micelle, disk-like micelle, and microemulsion regions; (a)-(d) refer to the (Xˆ2, m ˆ ), of which cryo-TEM pictures are shown in Figure 6.

studies with other experimental techniques such as the X-ray or neutron scattering, especially in region D where the unusual surfactant aggregate, the disk-like micelle, was observed. The present study demonstrated that there are four typical sequences of phase changes with increasing m ˆ at fixed composition, (1) m f M, (2) m f D f D + M f M, (3) m f D, and (4) m f D f D + E f E. The disk-like micelle and microemulsion could have been formed prior to the normal small micelles and remained stable over wide concentration and composition ranges. Because the gemini surfactant itself only formed micelles in the concentration range measured, the appearance of D and E regions on the diagram was clearly attributable to the change in packing parameter caused by the addition of octanol. Zana, et al. previously showed that the aggregate morphology of gemini surfactants changed from the thread-like micelle, to the spherical micelle, and then to the vesicles as the spacer chain increased;21 however, such aggregates were observable only in the high-concentration region compared with the cmc. Therefore, the mixing of gemini surfactants with other components was quite useful for bringing out the potential performance of surfactants. Considering the fact that the microemulsion phase boundary had a minimum at around Xˆ2 ) 0.60 and that the size of the microemulsion rapidly increased with increasing m ˆ , the microemulsion was stabilized by the monolayer in which the relative ratio between octanol and gemini surfactant was 2:1, which was suitable for the close-packed monolayer. Conclusions In this study, we proposed the idea that the average packing parameter could be controlled to form planar surfactant aggregates by filling the spaces among the spacer chains of the gemini surfactant using other surface active agents such as octanol. The most important result identified a concentration range in which the disk-like micelle and droplet microemulsions appeared prior to the normal spherical (or ellipsoid) micelles with increasing concentration from the phase diagram determined by surface tension and turbidity measurements. Our work built on previous experimental results that were concerned with the preferential vesicle formation in the double-chain-single chain cationic surfactant mixtures and the synergetic adsorption in the homologous cationic surfactants. Our strategy was based on the geometry of surfactant molecules and their combinations, which seemed to be a useful option for the application of the surfactant self-assembling systems.

Thermodynamic Explanation of the Change in Surface Tension after Aggregate Formation. The surface tension of the binary surfactant system was measured as a function of the concentration and composition at constant temperature and pressure. One degree of freedom remained even after the micelle formation, which means that the surface tension generally varied as the m ˆ increased. The change in γ after the micelle formation could be realized from the composition relationship when the adsorbed film and micelle were in equilibrium. If we define the physical properties of the micelles by using the reference to the surrounding aqueous solution phase indicated by excess thermodynamic quantities, the micelle particles can be treated as an apparent phase, and the Gibbs-Duhem equation that is analogous to eq 5 also holds22 M M NM 1 dµ1 + N2+dµ1 + 2N2-dµ2- ) 0

(A1)

where NM i is the excess number of molecules of species i in a micelle particle. This formulation also compelled us to rewrite m ˆ on the right side of eqs 6-8 by the cmc, Cˆ, in a limited concentration range near the cmc. Equation A1 then led to

ˆ ˆ (RT/Cˆ)dCˆ + (RT/Xˆ1Xˆ2)(XˆM 2 - X2)dX2 ) 0

(A2)

ˆ ˆ ˆ ˆ ˆ ˆ XˆM 2 ) X2 - (X1X2/C)(∂C /∂X2)T,p

(A3)

and

where the composition in the micelle is defined by M M M XˆM 2 ) 3N2 /(N1 + 3N2 )

(A4)

On the other hand, because eq 9 is applicable to the adsorbed film even at the cmc, we have

ˆ - (RTΓˆ Η,C /Xˆ1Xˆ2)(XˆH,C dγC ) -(RTΓˆ Η,C/Cˆ)dC - Xˆ2)dXˆ2 2 (A5) where the superscript is used to designate the thermodynamic quantities at the cmc. Substituting eq A2 into eq A5, the composition relationship between the micelle and adsorbed film is obtained as

ˆ ˆ ˆ H,CRT)(∂γC /∂Xˆ2)T,p XˆH,C ) XˆM 2 2 - (X1X2 /Γ

(A6)

The results of this calculation are plotted in Figure A. (For simplicity, Figure A shows a smooth plot of Cˆ values against Xˆ2; however, the transition from spherical micelles to disk-like ones, as in the present case, should produce a discontinuity in the graph.) For example, when the composition of the bulk

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J. Phys. Chem. B, Vol. 113, No. 26, 2009 8853 References and Notes

Figure A. Surface tension at cmc versus composition curves. The compositions of the bulk solution, adsorbed film, and micelle were represented by the solid, dotted, and chained curves, respectively.

solution was Xˆ2 ) 0.50, the surface tension at cmc was γC ) 24.9 mN m-1, and the composition of the micelle was Xˆ2M ) 0.22. If the phase separation model is applied to the micelle formation, the composition of micelle must approach that of the bulk solution as the concentration increases. Accordingly, in the process when the micelle composition changed, the adsorbed film also changed composition. Then, the surface tension decreased from 24.9 to 23.2 mN m-1. Applying the same explanation to the micelle formed at Xˆ2 ) 0.9, the surface tension increased with increasing m ˆ after the cmc. Hence, the surface tension remains constant when different aggregates coexist in the solution or when the composition of the aggregate is independent of m ˆ in the binary surfactant systems.

(1) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes; John Wiley & Sons Inc: New York, 1980. (2) Aratono, M.; Onimaru, N.; Yoshikai, Y.; Shigehisa, M.; Koga, I.; Wongwailikhit, K.; Ohta, A.; Takiue, T.; Lhoussaine, B.; Strey, R.; Takata, Y.; Villeneuve, M.; Matsubara, H. J. Phys. Chem. B 2007, 111, 107. (3) Aratono, M.; Mori, A.; Koga, I.; Shigehisa, M.; Onimaru, N.; Tsuchiya, K.; Takiue, T.; Mastubara, H. J. Phys. Chem. B 2008, 112, 12304. (4) Bain, C. D.; Casson, B. D. J. Phys. Chem. B 1999, 103, 4678. (5) Lando, L. J.; Oakley, T. H. J. Colloid Interface Sci. 1967, 25, 526. (6) Motomura, K.; Iwanaga, S.; Hayami, Y.; Uryu, S.; Matuura, R. J. Colloid Interface Sci. 1981, 80, 32. (7) Sadar, M. Technical Information Series, Booklet No. 11; Hach Company: Loveland, CO, 1998. (8) Hunter, R. J. Introduction to Modern Colloid Science; Oxford University Press: Oxford, U.K., 1993. (9) Aratono, M.; Villeneuve, M.; Takiue, T.; Ikeda, N.; Iyota, H. J. Colloid Interface Sci. 1998, 200, 161. (10) Matsubara, H.; Ohta, A.; Kameda, M.; Ikeda, N.; Aratono, M. Langmuir 2000, 16, 7589. (11) Li, Z.; Dong, C. C.; Thomas, R. K. Langmuir 1999, 15, 4392. (12) Zana, R. J. Colloid Interface Sci. 2002, 246, 182. (13) Iyota, H.; Todoroki, N.; Ikeda, N.; Motomura, K.; Ohta, A.; Aratono, M. J. Colloid Interface Sci. 1999, 216, 41. (14) Aratono, M.; Ohta, A.; Minamizawa, H.; Ikeda, Takiue, T. J. Colloid Interface Sci. 1999, 217, 128. (15) Matsubara, H.; Muroi, S.; Kameda, M.; Ikeda, N.; Ohta, A.; Aratono, M. Langmuir 2001, 17, 7752. (16) Matsuda, T.; Asoh, Y.; Villeneuve, M.; Matsubara, H.; Takiue, T.; Aratono, M. Colloid Polym. Sci. 2004, 282, 324. (17) Matsubara, H.; Nakano, T.; Matsuda, T.; Takiue, T.; Aratono, M. Langmuir 2005, 21, 8131. (18) Kashimoto, K.; Matsubara, H.; Takahara, H.; Nakano, T.; Takiue, T.; Aratono, M. Colloid Polym. Sci. 2004, 283, 3. (19) Matsubsara, H.; Nakano, T.; Matsuda, T.; Takiue, T.; Aratono, M. Langmuir 2006, 22, 2511. (20) Lee, E. M.; Thomas, R. K.; Penfold, J.; Ward, R. C. J. Phys. Chem. B 1989, 93, 381. (21) Danino, D.; Talmon, Y.; Zana, R. Langmuir 1995, 11, 1448. (22) Motomura, K.; Yamanaka, M.; Aratono, M. Colloid Polym. Sci. 1984, 262, 948.

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