Thermodynamic Study on Phase Transition in Adsorbed Film of

Jan 6, 2001 - 8. Phase Transition and Miscibility in the Adsorbed Film of Fluoroalkanol Mixture ... This suggests that the difference in the magnitude...
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J. Phys. Chem. B 2001, 105, 789-795

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Thermodynamic Study on Phase Transition in Adsorbed Film of Fluoroalkanol at the Hexane/Water Interface. 8. Phase Transition and Miscibility in the Adsorbed Film of Fluoroalkanol Mixture Takanori Takiue,* Takenori Fukuta, Hiroki Matsubara, Norihiro Ikeda,† and Makoto Aratono Department of Chemistry, Faculty of Sciences, Kyushu UniVersity, Fukuoka 812-8581, Japan ReceiVed: April 3, 2000; In Final Form: October 16, 2000

The interfacial tension γ of the hexane solution of a mixture of 1,1,2,2-tetrahydroheptadecafluorodecanol (FC10OH) and 1,1,2,2-tetrahydrohenicosafluorododecanol (FC12OH) against water was measured as a function of the total molality m and composition of FC12OH X2 at 298.15 K under atmospheric pressure. The γ vs m curve has one or two distinct break points depending on X2. By plotting the γ and m values at the break points and drawing the interfacial pressure π vs mean area per adsorbed molecule A curves, it was suggested that the triple point of adsorbed film, at which the three kinds of states (gaseous, expanded, and condensed states) coexist simultaneously, exists at a middle composition. The phase diagrams of adsorption (PDA) were constructed and the excess Gibbs energy of adsorption gH,E was calculated to examine the miscibility of FC10OH and FC12OH molecules in the adsorbed film. It was found that these alcohols mix almost ideally both in the gaseous and expanded states and nonideally in the condensed state. Furthermore, the mixing of FC10OH and FC12OH in the condensed film was accompanied by a positive gH,E value. This suggests that the difference in the magnitude of mutual interaction between the same species affects appreciably the miscibility of molecules in the condensed state where the adsorbed molecules are assumed to be closely packed and arranged regularly.

Introduction The study on the binary surfactant systems1-3 is indispensable to understand the structures and properties of molecular organized systems such as microemulsion, vesicle and so on. Thus far, we have explored the adsorption of various surfactant mixtures at air/water interface by measuring the interfacial tension with high accuracy and analyzing the experimental results thermodynamically.4 Among them, we have discussed quantitatively the miscibility in the adsorbed film by constructing the phase diagram of adsorption (PDA) and calculating the excess thermodynamic quantities of adsorption.5-8 However, few studies of the mixed adsorption at oil/water interfaces have been reported in this field. In this series, we have discussed systematically the states, properties, and the phase transitions of the adsorbed film of the mixed alkanol-fluoroalkanol system9-12 at the hexane/water interface as well as those of single component systems.13-15 For example, in the study of the binary FC10OH (1,1,2,2tetrahydroheptadecafluorodecanol) and C20OH (1-icosanol) system, we found the phase transition from the FC10OH condensed to the C20OH condensed state at a narrow composition range, in addition to the phase transition between the expanded and condensed states. Furthermore, the PDA changes its shape from the positive azeotrope, at which these alcohols are miscible with each other, to the heteroazeotrope, at which they are almost * To whom correspondence should be addressed. Mailing address: Takanori Takiue, Department of Chemistry, Faculty of Sciences, Kyushu University, Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan. E-mail: [email protected]. † Present address: Department of Environmental Science, Faculty of Human Environmental Science, Fukuoka Women’s University, Fukuoka 813-8529, Japan.

immiscible, as the interfacial tension decreases. Furthermore, the analysis by employing thermodynamic equations have revealed that the mixing of FC10OH and C20OH in the expanded film is accompanied by a positive excess Gibbs energy because of the very weak mutual interaction between the different alcohol molecules compared to those between the same species, and by a positive excess volume due to the increase in the occupied area at the interface. This mixture is one of the typical examples which shows nonideal mixing or demixing of components in the adsorbed film. On the basis of our previous studies,7,16 the homologous compounds tend to mix almost ideally at the air/water interface because of their similar chemical and physical properties. However, it should be remembered that the adsorbed films are in the expanded state in these cases. To examine the miscibility in the condensed state in addition to those in the gaseous and expanded states, therefore, we expected the mixture of two homologous fluoroalkanols, FC10OH and FC12OH (1,1,2,2tetrahydrohenicosafluorododecanol) to be a good candidate because we have already clarified the properties and types of phase transitions in the adsorbed film of these alcohols. Furthermore, it is also interesting to know how the phase transition points vary with composition of the mixture because the adsorbed film of FC10OH exhibits the two kinds of phase transitions from the gaseous to the expanded state and from the expanded to the condensed one, while that of FC12OH makes only one transition between the gaseous and condensed states. The interfacial tension of the hexane solution of a FC10OHFC12OH mixture against water was measured as a function of the total molality and composition of FC12OH of the mixture at 298.15 K under atmospheric pressure. The interfacial pressure

10.1021/jp0012855 CCC: $20.00 © 2001 American Chemical Society Published on Web 01/06/2001

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π vs mean area per adsorbed molecule A curves were drawn and the phase diagrams of adsorption (PDA) were constructed in order to make clear the state and the miscibility of alcohol molecules in the adsorbed film. Experimental Section 1,1,2,2-Tetrahydroheptadecafluorodecanol (FC10OH) was recrystallized two times from the hexane solution and 1,1,2,2tetrahydrohenicosafluorododecanol (FC12OH) was done once from the chloroform solution.13,14 Their purities were checked and confirmed by gas-liquid chromatography and no time dependence of interfacial tension between the hexane solution and water. Water was distilled three times from dilute alkaline permanganate solution and hexane once in the presence of metallic sodium particles. The interfacial tension γ of the hexane solution of FC10OH and FC12OH mixture against water was measured as a function of the total molality m and the composition of FC12OH X2 defined respectively by

m ) m 1 + m2

(1)

X2 ) m2/m

(2)

and

at 298.15 K under atmospheric pressure by the pendant drop method.11,17 Here m1 and m2 are the molalities of FC10OH and FC12OH, respectively. Results and Discussion The γ values measured in this study are plotted against the total molality m at constant X2 in Figure 1a. Some of the curves in a low concentration region were magnified in Figure 1b to see the break points on the γ vs m curves clearly. The experimental points were traced by the more appropriate solid lines within experimental errors. The γ value decreases gradually with increasing concentration and the γ vs m curve has one or two distinct break points, at which the slope of the curve changes abruptly, depending on X2. As we have already clarified in the previous studies, there are two break points on the γ vs m curve of the pure FC10OH system and they correspond to the two kinds of phase transitions from the gaseous to the expanded state and from the expanded to the condensed one in the adsorbed film.13 On the other hand, the curve of pure FC12OH system shows one break due to the phase transition between the gaseous and condensed states.14 Looking at the curves at the compositions between the pure component systems, we found two breaks on the γ vs m curve at low X2 and only one at high X2. To realize the way how these two X2 regions are connected, the interfacial tension γeq and total molality meq values at the break points are plotted against X2 in Figure 2. The γeq value increases and the corresponding meq value decreases with increasing X2. The noticeable point is that these curves meet at the middle composition X2 ) 0.542. Therefore, it is suggested that there exist three kinds of states (shown by A, B, and C) in the adsorbed film of the FC10OH and FC12OH mixture and all the three states coexist simultaneously at X2 ) 0.542. In this sense, let us call this point as a triple point of adsorbed film.

Figure 1. (a) Interfacial tension vs total molality curves at constant composition: (1) X2 ) 0, (2) 0.100, (3) 0.200, (4) 0.275, (5) 0.350, (6) 0.425, (7) 0.500, (8) 0.652, (9) 0.801, (10) 1. (b) Interfacial tension vs total molality curves at constant composition: (1) X2 ) 0, (2) 0.275, (3) 0.625, (4) 1.

To make clear the state of the adsorbed film, we first calculated the total interfacial density ΓH by applying the equation

ΓH ) -(m/RT)(∂γ/∂m)T,p,X2

(3)

to the γ vs m curves and then evaluated the interfacial pressure π and the mean area per adsorbed molecule A values by using

π ) γ0 - γ

(4)

A ) 1/NAΓH

(5)

and

respectively. The results are shown as the ΓH vs m curves in Figure 3 and as the π vs A curves in Figure 4. The ΓH value increases with increasing concentration and changes discontinuously at the phase transition points. It is seen from Figure 4 that the π vs A curves at low X2 consist of three parts and those at high X2 two parts connected by discontinuous changes. Taking account of our previous results obtained for the pure component systems, it is concluded that the two break points on the γ vs m curves below X2 ) 0.542 correspond to the two types of phase transitions from the gaseous to the expanded state and from

Phase Transition in Adsorbed Film of Fluoroalkanol

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Figure 4. Interfacial pressure vs mean area per adsorbed molecule curves at constant composition: (1) X2 ) 0, (2) 0.100, (3) 0.200, (4) 0.275, (5) 0.350, (6) 0.425, (7) 0.500, (8) 0.652, (9) 0.801, (10) 1.

Figure 2. (a) Equilibrium interfacial tension vs composition curves: (1) gaseous-expanded transition, (2) expanded - condensed, (3) gaseous - condensed; (b) Equilibrium total molality vs composition curves: (1) gaseous - expanded transition, (2) expanded - condensed, (3) gaseous - condensed.

Figure 5. Total molality vs composition curves at constant interfacial tension: (1) γ ) 49 mN m-1, (2) 48, (3) 46, (4) 44, (5) 42, (6) 40, (7) 35, (8) 30.

Figure 3. Total interfacial density vs total molality curves at constant composition: (1) X2 ) 0, (2) 0.100, (3) 0.200, (4) 0.275, (5) 0.350, 0.425, (7) 0.500, (8) 0.652, (9) 0.801, (10) 1.

the expanded to the condensed one and a break point above X2 ) 0.542 corresponds to the phase transition between the gaseous and the condensed states. According to this conclusion, the three states A, B, and C, shown in Figure 2, correspond to the gaseous, expanded, and condensed states, respectively. In both gaseous and expanded states, the A value changes regularly with X2 and therefore the FC10OH and FC12OH molecules are expected to be miscible with each other in the adsorbed film. The A value of the condensed state converges into about 0.3 nm2 which is very close to the cross sectional area of fluorocarbon chain. However, we cannot judge whether FC10OH and FC12OH molecules are miscible in the condensed state only by drawing the π vs A curves.

The A values at the triple point, Atp were evaluated by plotting the A value at the phase transition point, Aeq against X2 and extrapolating the Aeq vs X2 curve to X2 ) 0.542. In Figure 4 are also shown the three Atp values by solid circles. We can recognize the coexistence of three kinds of states (gaseous, expanded, and condensed states) having different A values at π ≈1.6 mN m-1. Now, let us discuss the miscibility of FC10OH and FC12OH molecules in the adsorbed film. For doing this, we first illustrated the total molaity m vs composition X2 curves at given interfacial tensions γ in Figure 5. The m value decreases with increasing X2 and the m vs X2 curve shows break at a point where the curve intersects the meq vs X2 curve shown by the broken lines. Then we evaluated the composition of adsorbed film XH2 defined by

XH2 ) ΓH2 /ΓH

(6)

by applying the thermodynamic relation4

XH2 ) X2 -(X1X2/m)(∂m/∂X2)T,p,γ

(7)

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Figure 6. Phase diagram of adsorption at constant interfacial tension: (a) γ ) 49 mN m-1, (b) 48.7, (c) 48, (d) 45; (s) m vs X2, (- - -) m vs XH2 , (- - -) meq vs X2 curves.

to the m vs X2 curve in Figure 5. The results are shown as phase diagrams of adsorption (PDA) which give the quantitative relation between the bulk composition X2 and the film one XH2 . In Figure 6 are illustrated the PDA at high interfacial tensions. Now, let us look closely at the PDA at various interfacial tensions. Figure 6a shows the PDA at γ ) 49.0 mN m-1 at which the adsorbed film is in a gaseous state at all compositions. It is seen that the m vs XH2 curve is almost horizontal and therefore the composition of the adsorbed film is nearly equal to that in the bulk solution (XH2 ≈ X2). At 48.7 mN m-1 (Figure 6b), the m vs X2 curve shows a break on the meq vs X2 curve at a composition larger than the triple point. The condensed state appears at X2 above the break point and is found to be enriched by the FC12OH molecules compared with the bulk solution. In the PDA at 48.0 mN m-1 (Figure 6c), the m vs X2 curve breaks on the meq vs X2 curve corresponding to the gaseousexpanded transition at low X2 (≈ 0.2) in addition to the break on the curve corresponding to the expanded-condensed transition at high X2 (≈ 0.5). It is noted that the m vs XH2 curves of both gaseous and expanded states seem to be linear. Decreasing further the interfacial tension down to 45 mN m-1 (Figure 6d), the gaseous state disappears and the condensed state extends in a wide composition range. It is clearly seen that the m vs XH2 curve of the expanded state is almost linear and that of the condensed state shows convex upward. On the basis of our thermodynamic treatment,16 the criterion of ideal mixing of surfactants in the adsorbed film with respect to the PDA gives the straight m vs XH2 line connecting each pure m values at a given γ,

m ) m01 + (m02 - m01) XH2

(8)

Therefore, it is suggested that the FC10OH and FC12OH molecules mix almost ideally both in the gaseous and expanded states.

Figure 7. Phase diagram of adsorption at constant interfacial tension: (1) γ ) 40 mN m-1, (2) 35, (3) 30; (s) m vs X2, (- - -) m vs XH2 .

Concerning the PDA in the condensed state shown in Figure 7, it is found that the FC10OH and FC12OH molecules are miscible with each other and the m vs XH2 curve deviates slightly from the straight line given by eq 8. It means that the FC10OH and FC12OH molecules mix nonideally in the condensed state even though they are homologous molecules with different chain length by only two. To examine the nonideal mixing of FC10OH and FC12OH molecules in the condensed state more quantitatively, we estimated the activity coefficient f Hi by applying5,7

f Hi ) Xim/XHi m0i , i ) 1, 2

(9)

Phase Transition in Adsorbed Film of Fluoroalkanol

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Figure 8. Excess Gibbs energy of adsorption vs film composition curves at constant interfacial tension: (1) γ ) 40 mN m-1, (2) 35, (3) 30.

Now, let us elucidate the relation of the compositions between the coexisting three phases at the triple point as well as those at the phase transition points. With the aid of the PDA in Figure 6 and the analogous ones at the other γ values, the film composition XH2 in the three states are estimated at the transition points. The values are plotted against the equilibrium total molality meq in Figure 9a. The diagram looks to be composed of three bamboo leaves and each of them represents the equilibrium of the two different states. It is realized that the gaseous state is located in the region below the meq vs XH,g 2 curve, the condensed state is above the meq vs XH,c 2 curve, and the region of the expanded state sits between the two meq vs H eq XH,e 2 curves. In the similar way, we constructed the γ vs X2 curves at the phase transition points in Figure 9b. It is seen that the state in which the molecules are more densely arranged, is enriched by more surface-active FC12OH molecules. Furthermore, we realize from this diagram that the three states having different compositions coexist with each other at the triple point of adsorbed film. In the case of the coexistence of two phases at the interface, we have

dγeq ) -∆sψdT + ∆Vψdp - ΓH,ψ(RT/meq)dmeq - X2)dX2, ψ ) R and β (11) ΓH,ψ(RT/X1X2)(XH,ψ 2 where ∆s and ∆V are respectively the entropy and volume changes associated with adsorption and superscripts R and β represent the coexisting two phases. By eliminating dmeq from two equations for R and β phases, the following equation is obtained:

dγeq ) -[(∆sR/ΓH,R - ∆sH,β/ΓH,β)/(1/ΓH,R - 1/ΓH,β)]dT + [(∆VR/ΓH,R - ∆Vβ/ΓH,β)/(1/ΓH,R - 1/ΓH,β)]dp H,R H,β - 1/ΓH,β)]dX2 (12) [(RT/X1X2)(XH,R 2 - X2 )/(1/Γ Since γeq is described as a function of T, p, and X2, we have

dγeq ) (∂γeq/∂T)p,X2 dT + (∂γeq/∂p)T,X2 dp + Figure 9. (a) Equilibrium total molality vs film composition curves: H,e H,c eq eq (1) meq vs XH,g 2 , (2) m vs X2 , (3) m vs X2 curves; (b) Equilibrium eq interfacial tension vs film composition curves: γeq vs XH,g 2 , (2) γ vs eq vs XH,c curves. XH,e , (3) γ 2 2

to the PDA and then calculated the excess Gibbs energy of adsorption gH,E by using

gH,E ) RT(XH1 ln f H1 + XH2 ln f H2 )

(10)

The results are shown as the gH,E vs XH2 curve at given γ in Figure 8. It is seen that the gH,E value is positive over the whole composition range and therefore the mutual interaction between the same kind of alcohols is stronger than that between the different species. However, it is noted that the gH,E value is not so large compared with that obtained in the expanded state of the FC10OH-C20OH (1-icosanol) mixture,10 which exhibits typical positive deviation from the ideal mixing. It is reasonably assumed that the fluoroalkanol molecules are closely packed in the condensed film and the mean distance between the molecules is very close to the diameter of the rod of hydrophobic chain. Therefore, we suggest that the difference in the magnitude of intermolecular interaction between the same species affects appreciably the miscibility of molecules in the condensed state.

(∂γeq/∂X2)T,p dX2 (13) The value of coefficient of dX2 of eq 12 was calculated by using the ΓH and XH2 values at the phase transition points and that of eq 13 was obtained from the γeq vs X2 curve in Figure 2a. If the values of both coefficients agree well with each other within experimental errors, we can claim that the first-order phase transition takes place in the adsorbed film. This is one of the strategies to substantiate phase transition as well as those based on the surface equation of state such as Frumkin’s equation.19 The results are shown in Figure 10. We found that the agreement of both coefficients is good enough to claim that the first-order phase transition occurs in the adsorbed film. This also supports the adequacy for tracing the experimental points by solid lines as given in Figure 1. Furthermore, according to the phase rule of the system with interfaces,18 the degrees of freedom are two when the three phases coexist with each other in the adsorbed film and therefore the interfacial tension γtp and total molality mtp at the triple point are functions of temperature T and pressure p. Denoting the three coexisting phases by R, β, and δ in eq 11 and eliminating dmtp and dX2 from the three equations, we obtain

794 J. Phys. Chem. B, Vol. 105, No. 4, 2001

Figure 10. Values of coefficient of d X2 of eqs 12 and 13 vs composition curves: (O) eq 12, (s) eq 13; (1) gaseous-expanded transition, (2) expanded-condensed, (3) gaseous-condensed.

the total differential of γtp as H,R H,β dγtp ) -{[∆sR(XH,δ + 2 - X2 )/Γ H,δ H,R H,β H,δ + ∆sδ (XH,β ]/ ∆sβ (XH,R 2 - X2 )/Γ 2 - X2 )/Γ H,R H,β H,β H,δ + (XH,R + [(XH,δ 2 - X2 )/Γ 2 - X2 )/Γ H,δ H,R H,R H,β ]}dT + {[∆VR(XH,δ + (XH,β 2 - X2 )/Γ 2 - X2 )/Γ H,δ H,R H,β H,δ + ∆Vδ (XH,β ]/ ∆Vβ (XH,R 2 - X2 )/Γ 2 - X2 )/Γ H,R H,β H,β H,δ + (XH,R + [(XH,δ 2 - X2 )/Γ 2 - X2 )/Γ H,δ H,R ]}dp (14) (XH,β 2 - X2 )/Γ

We see that the temperature and pressure dependence of γtp are closely related to the entropy and volume of adsorption in one phase combined with the difference in the composition between the other two phases, respectively. To substantiate the existence of the triple point of adsorbed film, we should measure the interfacial tension of the present system as a function of T and p at given m and X2 and evaluate ∆s and ∆V values at the triple point. Finally, we summarize this series for the better understanding the phase transitions and miscibility in the adsorbed film of fluoroalkanol. Adsorbed Film of Pure Component Systems.13-15 We measured the interfacial tension of the hexane solution of FCiOH (i ) 10, 12) against water as a function of pressure p, temperature T, and concentration of the solution m1. The interfacial density ΓH1 , volume ∆V, entropy ∆s, and energy ∆u changes associated with adsorption were evaluated and the interfacial pressure π vs mean area per adsorbed molecule A curves were drawn in order to discuss thoroughly the state and property of the adsorbed fluoroalkanol film. (1) The adsorbed film of FC10OH exhibits the two types of first-order phase transitions from the gaseous to the expanded state and from the expanded to the condensed one and that of FC12OH exhibits a phase transition between the gaseous and condensed states. (2) The values of ∆V, ∆s, and ∆u decrease with increasing concentration and change discontinuously at the phase transition points. (3) The partial molar volume, entropy, and energy changes of adsorption decrease with increasing adsorption and are largely negative in the condensed state. This means that the alcohol

Takiue et al. molecules have a smaller volume and entropy, and lower energy at the interface than in the bulk solution. (4) The longer the fluorocarbon chain length is, the more negative the partial molar volume (entropy) change of adsorption becomes. This relies upon the larger increase in the partial molar volume (entropy) in the bulk solution with increasing fluorocarbon chain length compared to the corresponding increase in the adsorbed film. (5) The energetical stabilization of the FC12OH molecule accompanied by adsorption is larger than that of the FC10OH molecule. (6) The partial molar volume change associated with the phase transition from the expanded to the condensed state is larger for fluoroalkanol than for alkanol. This suggests that the microscopic circumstance in the adsorbed film affects appreciably the volume change of adsorption. (7) The pressure and temperature dependencies of the π vs A curves are related to the partial molar volume and entropy changes of adsorption, respectively. By estimating the pressure and temperature coefficients of A at given π, it was found that a temperature increase of only 1 K is sufficient to keep π and A constant upon a decrease of pressure by 1 MPa. Adsorbed Film of Binary Alcohol Systems.9-12 The interfacial tensions of the hexane solutions of C20OH-FC10OH and FC10OH-FC12OH mixtures against water were measured as a function of pressure p, total molality m, and composition of the mixture X2 at 298.15 K. The total interfacial density ΓH and ∆V values were evaluated and π vs A curves were drawn to make clear the state of the adsorbed film. By constructing the phase diagram of adsorption (PDA) and calculating the excess thermodynamic quantities of adsorption, we discussed the miscibility of alcohols in the adsorbed film quantitatively. (1) In the case of the C20OH-FC10OH system, the adsorbed films at all compositions exhibit the first-order phase transition from the expanded to the condensed state. (2) It was found that the phase transition from the FC10OH condensed to the C20OH condensed state takes place in a narrow composition region. (3) Furthermore, it was shown that the phase transition from the C20OH condensed to the FC10OH condensed state cannot occur because the cross sectional area of fluorocarbon chain is larger than that of the hydrocarbon chain and the condensed film is constructed by the individual alcohol molecules. (4) The PDA of C20OH-FC10OH system changes its shape from a positive azeotrope in the expanded state, where the two alcohols are miscible with each other, to a hetroazeotrope in the condensed state, where they are practically immiscible in the adsorbed film as interfacial tension decreases. (5) The excess Gibbs energy gH,E and area AH,E of adsorption calculated in the expanded state are largely positive because of the very weak mutual interaction between the different kind of alcohols compared with that between the same kind. (6) The criterion of the ideal mixing in the adsorbed film with respect to the volume change of adsorption was constructed and used to examine the nonideal mixing of FC10OH and C20OH in the adsorbed film. The mixing of these alcohols in the adsorbed film causes a positive excess volume VH,E due to the increase in the occupied area of alcohol molecules at the interface. (7) By constructing the PDA at high pressures, it was suggested that the FC10OH and C20OH molecules become less miscible in the expanded state as pressure rises and are practically immiscible in the condensed state also at high pressure.

Phase Transition in Adsorbed Film of Fluoroalkanol (8) In the case of the binary fluoroalkanol mixture (FC10OH-FC12OH), we found a triple point of the adsorbed film in a middle composition region, at which the three kinds of states (gaseous, expanded, and condensed states) coexist with each other at the interface. (9) The PDA shows that the FC10OH and FC12OH molecules mix almost ideally in the gaseous and expanded states and nonideally in the condensed state. The mixing of these alcohols in the condensed film was accompanied by a positive gH,E, and therefore the mutual interaction between the same kind of alcohols is stronger than that between the different species. (10) Above result suggests that the difference in the magnitude of the mutual interaction between the same alcohols affects appreciably the miscibility of molecules in the condensed film at which the mean distance between the molecules is very close to the diameter of the rod of hydrophobic chain. Acknowledgment. This work was supported in part by the Grant-in Aid for Encouragement of Young Scientists of The Ministry of Education, Science, Sports and Culture (No. 10740326). References and Notes (1) Scamehorn, J. F., Ed. Phenomena in Mixed Surfactant Systems; ACS Symposium Series 311; American Chemical Society: Washington, DC, 1986. (2) Holland, P. M., Rubingh, D. N., Eds. Mixed Surfactant Systems; ACS Symposium Series 501; American Chemical Society: Washington, DC, 1992.

J. Phys. Chem. B, Vol. 105, No. 4, 2001 795 (3) Ogino, K., Abe, M., Eds. Mixed Surfactant Systems; Surfactant Science Series 46; Marcel Dekker: New York, 1993. (4) Motomura, K.; Aratono, M. In Mixed Surfactant Systems; Ogino, K., Abe, M., Eds.; Marcel Dekker: New York, 1993; Vol. 46, p 99. (5) Iyota, H.; Aratono, M.; Motomura, K. J. Colloid Interface Sci. 1996, 178, 53. (6) Villeneuve, M.; Sakamoto, H.; Minamizawa, H.; Ikeda, N.; Motomura, K.; Aratono, M. J. Colloid Interface Sci. 1997, 194, 301. (7) Aratono, M.; Villeneuve, M.; Takiue, T.; Ikeda, N.; Iyota, H. J. Colloid Interface Sci. 1998, 200, 161. (8) Aratono, M.; Ohta, A.; Minamizawa, H.; Ikeda, N.; Iyota, H.; Takiue, T. J. Colloid Interface Sci. 1999, 217, 128. (9) Takiue, T.; Matsuo, T.; Ikeda, N.; Motomura, K.; Aratono, M. J. Phys. Chem. B 1998, 102, 4906. (10) Takiue, T.; Matsuo, T.; Ikeda, N.; Motomura, K.; Aratono, M. J. Phys. Chem. B 1998, 102, 5840. (11) Takiue, T.; Toyomasu, T.; Ikeda, N.; Aratono, M. J. Phys. Chem. B 1999, 103, 6547. (12) Takiue, T.; Ikeda, N.; Toyomasu, T.; Matsubara, H.; Aratono, M. J. Phys. Chem. B 2000, 104, 7096. (13) Takiue, T.; Yanata, A.; Ikeda, N.; Motomura, K.; Aratono, M. J. Phys. Chem. 1996, 100, 13743. (14) Takiue, T.; Yanata, A.; Ikeda, N.; Motomura, K.; Aratono, M. J. Phys. Chem. 1996, 100, 20122. (15) Takiue, T.; Uemura, A.; Ikeda, N.; Motomura, K.; Aratono, M. J. Phys. Chem. B 1998, 102, 3724. (16) Todoroki, N.; Tanaka, F.; Ikeda, N.; Aratono, M.; Motomura, K. Bull. Chem. Soc. Jpn. 1993, 66, 351. (17) Matubayasi, N.; Motomura, K.; Kaneshina, S.; Nakamura, M.; Matuura, R. Bull. Chem. Soc. Jpn. 1977, 50, 523. (18) Defay, R.; Prigogine, I. Surface Tension and Adsorption; Everett, D. H.; Translator; Longmans: London, 1966; Chapter 6. (19) Frumkin, A. Z. Z. Phys. Chem. 1925, 116, 466.