Temperature Effect on the Adsorption of Fluorooctanols at the Hexane

The interfacial tensions of the hexane solution of fluorooctanols (1,1,2,2-tetrahydrotridecafluorooctanol, TFC8OH, and 1,1-dihydropentadecafluorooctan...
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Langmuir 2001, 17, 8098-8103

Temperature Effect on the Adsorption of Fluorooctanols at the Hexane/Water Interface Takanori Takiue,* Koichi Sugino, Taketo Higashi, Takayuki Toyomasu, Yoshiteru Hayami,† Norihiro Ikeda,‡ and Makoto Aratono Department of Chemistry, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan Received September 19, 2000. In Final Form: August 31, 2001 The interfacial tensions of the hexane solution of fluorooctanols (1,1,2,2-tetrahydrotridecafluorooctanol, TFC8OH, and 1,1-dihydropentadecafluorooctanol, DFC8OH) against water were measured as a function of temperature and molality under atmospheric pressure. By drawing the interfacial pressure π vs mean area per adsorbed molecule A curves, it was concluded that the adsorbed film of TFC8OH exhibits a first-order phase transition between the gaseous and expanded states and that of DFC8OH shows the two types of phase transitions from the gaseous to the expanded state and from the expanded to the condensed one at the hexane/water interface. The comparison of the π vs A curve between TFC8OH and DFC8OH shows that the intermolecular interaction is enhanced by the substitution of fluorine for hydrogen on the β-carbon of TFC8OH. Furthermore, the difference in the transition pressure between DFC8OH and TFC10OH (1,1,2,2-tetrahydroheptadecafluorodecanol) is explained by the differences in London dispersion force between hydrophobic chains and the dipole moment of their hydroxyl group. The partial molar entropy sjsH - ssO and energy u j sH - usO changes of adsorption were evaluated and compared to those of TFC10OH. The sjsH - ssO value is negative and therefore alcohol molecules have smaller entropy at the interface than in the solution, which is attributable to the orientation of the molecules at the interface. The phase transition from the expanded to the condensed state in the adsorbed TFC10OH film causes larger decrease in partial molar entropy than that in the DFC8OH one. This may arise from the larger partial molar entropy of TFC10OH molecules due to the larger entropy of mixing of longer fluorocarbon chain with hexane in the expanded state and the smaller entropy of TFC10OH due to the stronger attractive interaction in the j sH - usO value is less negative for DFC8OH than condensed state than that of DFC8OH molecules. The u for TFC10OH and therefore the energetical stabilization of DFC8OH accompanied by the adsorption from the solution is less than that of TFC10OH. Furthermore, it was concluded that the DFC8OH molecules are stabilized by forming the condensed film at the interface because of the strong molecular interaction between them, and the TFC8OH molecules form mainly tetramers in the hexane solution to lower the energetical state of the system.

Introduction Fluorocarbon (FC) compounds exhibit unique properties compared to hydrocarbon (HC) compounds:1 very high thermal stability, stiffer and more hydrophobic chains, and so on. It is well-known that perfluoroalkanecarboxylic acid is a stronger acid than the corresponding alkanoic acid because of the strong electronegativity of the fluorine atom. Henn et al. investigated the shielding effect of one methylene group between the FC chain and the carboxylic group from the viewpoint of acidity and concluded that even two methylene groups cannot shield completely the electronegative induction effect of the FC chain.2,3 Thus far, we have studied thoroughly the adsorption of fluoroalkanols at the hexane/water interface by measuring the interfacial tension and evaluating the thermodynamic quantities of adsorption in terms of our thermodynamics * To whom correspondence should be addressed. Mailing address: Takanori Takiue, Department of Chemistry, Faculty of Sciences, Kyushu University, Hakozaki, Higashi-ku, Fukuoka 8128581, Japan. Tel: +81 92 642 2580. Fax: +81 92 642 2607. E-mail: [email protected]. † Present address: Department of Human Life Science, Chikushi Jogakuen Junior College, Dazaifu, Fukuoka 818-0192, Japan. ‡ Present address: Department of Environmental Science, Faculty of Human Environmental Science, Fukuoka Women’s University, Fukuoka 813-8529, Japan. (1) Fluorinated Surfactants; Kissa, E., Eds.; Marcel Dekker: New York, 1994; Chapter 3. (2) Henn, A. L.; Fox, C. J. J. Am. Chem. Soc. 1951, 73, 2323. (3) Henn, A. L.; Fox, C. J. J. Am. Chem. Soc. 1953, 75, 5750.

of interfaces.4-7 In these studies, we employed 1,1,2,2tetrahydrofluoroalkanol, CF3(CF2)i-3(CH2)2OH (TFCiOH), with different FC chain length (i ) 8, 10, 12), and discussed the effect of the difference in the FC chain length on the adsorption behavior of TFCiOH from the viewpoint of the thermodynamic quantity change of adsorption. We found that the longer the FC chain length is, the more negative the partial molar volume (entropy) change of adsorption becomes because of the larger increase in the partial molar volume (entropy) in the bulk solution with increasing FC chain length compared to the corresponding increase in the adsorbed film. Now it is very interesting to know the effect of the fluorination of β-carbon in the hydrophobic chain of TFCiOH, in other words, the effect of the difference in the number of methylene group between the FC chain and hydroxyl group on the adsorption behavior of fluoroalkanol, as well as to know the effect of the difference in the FC chain length. So we chose two kinds of fluoroalkanols, 1,1,2,2-tetrahydrotridecafluorooctanol (CF3(CF2)5(CH2)2OH; TFC8OH) and 1,1-dihydropentadecafluorooctanol (CF3(CF2)6CH2OH; DFC8OH), as materials. The reasons why we employed them are as follows: (1) Their total (4) Hayami, Y.; Uemura, A.; Ikeda, N.; Aratono, M.; Motomura, K. J. Colloid Interface Sci. 1995, 172, 142. (5) Takiue, T.; Yanata, A.; Ikeda, N.; Motomura, K.; Aratono, M. J. Phys. Chem. 1996, 100, 13743. (6) Takiue, T.; Yanata, A.; Ikeda, N.; Hayami, Y.; Motomura, K.; Aratono, M. J. Phys. Chem. 1996, 100, 20122. (7) Takiue, T.; Uemura, A.; Ikeda, N.; Motomura, K.; Aratono, M. J. Phys. Chem. B 1998, 102, 3724.

10.1021/la001345y CCC: $20.00 © 2001 American Chemical Society Published on Web 11/28/2001

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carbon numbers are the same, while the number of methylene group between the FC chain and the hydroxyl group is different. (2) The adsorption behavior of TFC8OH has been already clarified from the viewpoint of the pressure dependence of interfacial tension.8 (3) TFC8OH is in liquid state and DFC8OH is a solid at room temperature and therefore we can expect to obtain a large difference in their adsorption behavior. The interfacial tensions of the hexane solution of fluorooctanols against water were measured as a function of temperature and molality under atmospheric pressure. The interfacial density and the entropy and energy of adsorption were evaluated by analyzing the experimental results thermodynamically and compared to discuss the effect not only of the difference in the FC chain length but of the difference in the number of methylene group on the adsorption behavior of fluorooctanols. Experimental Section 1,1,2,2-Tetrahydrotridecafluorooctanol (TFC8OH) and 1,1dihydropentadecafluorooctanol (DFC8OH), purchased from PCR Inc., were purified before use. The procedure of purification of TFC8OH was as follows. At first, the mixture of TFC8OH and hexane (50:50 wt %) was stirred vigorously at 40 °C for 2 h and then allowed to stand for a few hours to separate completely into two transparent phases. The upper phase (hexane-rich phase) was exchanged several times to fresh hexane in order to extract impurities. Finally, the lower phase (TFC8OH rich phase) was dried under reduced pressure at room temperature to remove the hexane dissolved. DFC8OH was purified by recrystallization from its hexane solution several times. The purities of these alcohols were estimated as more than 99% by gas-liquid chromatography and confirmed by observing no time dependence of interfacial tension between their hexane solution and water. The interfacial tension γ of the hexane solution of alcohol against water was measured as a function of temperature T and molality of the solution ms under atmospheric pressure by the pendant drop method.9 The densities of pure water and hexane10,11 were used for the calculation of interfacial tension. The error in the γ value was estimated to within (0.05 mN m-1.

Results The interfacial tension γ of the TFC8OH system is plotted against temperature T at constant concentration ms in Figure 1a. The γ value of the pure hexane/water interface decreases slightly, while that of the solution increases with increasing T. At an intermediate concentration, the γ vs T curve has a break at which the slope of the curve changes abruptly. The point to be noted is that the γ value at a very high concentration increases almost linearly with T. A similar temperature dependence of the γ value was found in the DFC8OH system (Figure 1b), but another series of break point was observed on the γ vs T curves at low interfacial tensions. The γ value at a high concentration increases linearly with T and its increment is greater than that of the TFC8OH system. In Figure 2 are plotted the γ values read from Figure 1 against ms at 298.15 K, together with the γ vs ms curve of the TFC10OH (1,1,2,2-tetrahydroheptadecafluorodecanol) system.7 It is seen that the γ value decreases gradually with increasing concentration and the γ vs ms curve of TFC8OH has one break point and that of the (8) Hayami, Y.; Ono, S.; Ikeda, N.; Takiue, T.; Aratono, M. Langmuir 2000, 16, 7006. (9) Motomura, K.; Matubayasi, N.; Aratono, M.; Matuura, R. J. Colloid Interface Sci. 1978, 64, 356. (10) Kell, G. S.; Whally, E. Philos. Trans. R. Soc. London A 1965, 258, 565. (11) Orwoll, R. A.; Flory, P. J. J. Am. Chem. Soc. 1967, 89, 6814.

Figure 1. (a) Interfacial tension vs temperature curves of the TFC8OH system at constant molality: (1) ms ) 0, (2) 0.501, (3) 1.000, (4) 1.504, (5) 2.003, (6) 2.500, (7) 3.004, (8) 3.501, (9) 4.000, (10) 5.004, (11) 6.002, (12) 7.001, (13) 8.001, (14) 9.003, (15) 10.00, (16) 11.00, (17) 12.00, (18) 13.00, (19) 15.00, (20) 17.00, (21) 18.51, (22) 22.03, (23) 24.94, (24) 28.76, (25) 32.43, (26) 37.02, (27) 40.00, (28) 43.00, (29) 46.83, (30) 54.89, (31) 60.73, (32) 75.64, (33) 82.83 mmol kg-1. (b) Interfacial tension vs temperature curves of the DFC8OH system at constant molality: (1) ms ) 0, (2) 0.102, (3) 0.254, (4) 0.504, (5) 0.754, (6) 1.003, (7) 1.302, (8) 1.562, (9) 2.001, (10) 2.200, (11) 2.501, (12) 3.004, (13) 3.504, (14) 4.003, (15) 4.503, (16) 5.002, (17) 5.601, (18) 6.303, (19) 7.004, (20) 7.801, (21) 8.800, (22) 10.00, (23) 11.20, (24) 12.50, (25) 13.74, (26) 15.00, (27) 17.00, (28) 19.50, (29) 21.15, (30) 25.00, (31) 27.48, (32) 30.00, (33) 33.86, (34) 38.70, (35) 43.55 mmol kg-1.

DFC8OH has two, which are shown by the arrows. Judging from the slope of the curve, the surface activity of these alcohols at the hexane/water interface decreases in the following order: TFC10OH > DFC8OH > TFC8OH. By plotting the interfacial tension γeq and the molality mseq values at the break point against T, we obtained Figure 3. The γeq value decreases and the corresponding mseq value increases with increasing temperature. Taking our previous results4,7,12 into account, these break points on the γ vs T and ms curves are responsible for the phase transition in the adsorbed film. (12) Matubayasi, N.; Motomura, K.; Aratono, M.; Matuura, R. Bull. Chem. Soc. Jpn. 1978, 51, 2800.

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dγ ) -∆s dT + ∆v dp - ΓsH(RT/ms) dms

(2)

Here ∆y is the thermodynamic quantity change associated with adsorption defined by

∆y ) yH - ΓsHysO y ) s, v

(3)

where ysO is the partial molar thermodynamic quantity of alcohol in the hexane solution. To make clear the state of the adsorbed film, we first evaluated the interfacial density ΓsH by applying the equation

ΓsH ) -(ms/RT)(∂γ/∂ms)T,p Figure 2. Interfacial tension vs molality curves at 298.15 K: (1) TFC8OH; (2) DFC8OH; (3) TFC10OH.

(4)

to the γ vs ms curves in Figure 2. The results are shown as ΓsH vs ms curves at 298.15 K together with the curve of TFC10OH in Figure 4. The ΓsH value increases with increasing ms and changes discontinuously at the phase transition points. It should be noted that the saturated value of DFC8OH is almost equal to that of TFC10OH. Furthermore, it is noted that the ΓsH vs ms curve of TFC8OH has a shallow maximum at a high concentration. This apparently anomalous behavior comes from that the assumption of ideal dilute solution is no longer adequate for calculating ΓsH in a very high concentration region. Next, we calculated the interfacial pressure π and the mean area per adsorbed molecule A values by using

π ) γ0 - γ

(5)

A ) 1/NAΓsH

(6)

and

Figure 3. (a) Equilibrium interfacial tension vs temperature curves: (1) gaseous-expanded transition for TFC8OH; (2) gaseous-expanded transition for DFC8OH; (3) expandedcondensed transition for DFC8OH. (b) Equilibrium molality vs temperature curves: (1) gaseous-expanded transition for TFC8OH; (2) gaseous-expanded transition for DFC8OH; (3) expanded-condensed transition for DFC8OH.

Discussions Now let us evaluate the thermodynamic quantities of adsorption for the two systems. The fundamental equation describing the interfacial tension γ is given by

dγ ) -sH dT + vH dp - ΓsH dµs

(1)

where sH, vH, and ΓsH are respectively the interfacial excess entropy, volume, and the number of moles of solute per unit interfacial area defined with respect to the two dividing planes, which make the excess number of moles of water and hexane zero simultaneously.13 By assuming an ideal dilute solution and adopting temperature T, pressure p, and molality ms as independent variables, the total differential of interfacial tension γ is expressed by (13) Motomura, K. J. Colloid Interface Sci. 1978, 64, 348.

respectively, where γ0 is the interfacial tension of the pure hexane/water interface and NA is Avogadro’s number. In Figure 5 are shown the π vs A curves at 298.15 K for three fluoroalkanols. It is seen that the curves of DFC8OH and TFC10OH consist of three parts and that of TFC8OH two parts connected by discontinuous changes. The A value in the almost vertical region found in the DFC8OH and TFC10OH systems is about 0.3 nm2, which is very close to the cross-sectional area of the fluorocarbon (FC) chain. Taking note of our previous conclusion5,7 that the adsorbed film of TFC10OH exhibits two kinds of phase transitions from the gaseous to the expanded state and from the expanded to the condensed one, we concluded that the same types of phase transitions as those of TFC10OH take place in the adsorbed film of DFC8OH and the phase transition between the gaseous and the expanded states occurs in the adsorbed TFC8OH film at the hexane/water interface. Here we will briefly mention some experimental evidence on the gaseous-expanded phase transition. One is the volume change of adsorption ∆v calculated from the pressure dependence of interfacial tension of the TFC8OH system.8 We have examined the first-order phase transition based on the discontinuous change in the ∆v value at low concentration. In the case of DFC8OH, essentially the same results were obtained from the pressure dependence of interfacial tension.14 The other is the results for the adsorption behavior of mixed fluoroalkanol systems: TFC8OH-TFC12OH and DFC8OHTFC10OH.15 The interfacial tension γ of the hexane solution (14) Takiue, T.; Kajiwara, E.; Ikeda, N.; Aratono, M., unpublished data. (15) Takiue, T.; Sugiyama, T.; Ikeda, N.; Aratono, M., to be submitted.

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Figure 4. Interfacial density vs molality curves at 298.15 K: (1) TFC8OH; (2) DFC8OH; (3) TFC10OH.

Figure 5. Interfacial pressure vs mean area per adsorbed molecule curves at 298.15 K: (1) TFC8OH; (2) DFC8OH; (3) TFC10OH.

of these mixtures against water was measured as a function of the total molality m and the composition of the mixture X2 at 298.15 K under atmospheric pressure. By plotting the interfacial tension γeq at the break points on the γ vs m curves against X2, we found that the extrapolation of the γeq vs X2 curve representing the gaseous-expanded phase transition in the mixed system gives the γeq value for the gaseous-expanded transition of the pure TFC8OH and DFC8OH systems asserted here. Figure 5 gives some important information on molecular interaction. Comparing the curve of DFC8OH to that of TFC8OH, it is said that the intermolecular interaction is strengthened by substituting fluorine for two hydrogen atoms on the β-carbon of the TFC8OH molecule. This comes from two factors. The first is that the substitution accompanies the increase in the molecular weight and then an increase in London dispersion force between hydrophobic chains.16 Second, taking into account that only the R-carbon atom is hydrogenated in the DFC8OH molecule and therefore the electronegative induction effect of the fluorocarbon chain on the hydroxyl group is larger in the DFC8OH molecule than in TFC8OH,17 the hydroxyl groups of DFC8OH are expected to have stronger dipole moments and interact more strongly with each other than those of TFC8OH. The differences observed among three alcohol systems are also attributable essentially to these (16) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1992; Chapter 6. (17) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1992; Chapters 4 and 8.

Figure 6. Entropy change associated with adsorption vs molality curves of at constant temperature: (a) TFC8OH, (b) DFC8OH; (1) T ) 288.15, (2) 293.15, (3) 298.15, (4) 303.15, (5) 308.15 K.

two factors. The first factor is a relatively short range force and is expected to influence mainly the expandedcondensed phase transition; TFC10OH molecules having longer fluorocarbon chains transform their film state from the expanded to the condensed one at a lower interfacial pressure compared to DFC8OH molecules. The finding that the DFC8OH molecules form a condensed film but TFC8OH does not is also mainly due to this factor. On the other hand, the second factor acts even at a relatively long distance between molecules and then influences also the gaseous-expanded phase transition; DFC8OH molecules having higher dipole moments can take an orientation which is favorable for dipole-dipole interactions and eventually transform their film state from the gaseous to the expanded one at a lower interfacial pressure compared to TFC8OH and TFC10OH molecules. Now, let us consider the adsorption behavior of these fluorooctanols from the viewpoint of entropy. For doing this, we evaluated the entropy change associated with adsorption ∆s by using the equation

∆s ) -(∂γ/∂T)p,ms

(7)

The results are shown as the ∆s vs ms plots in Figure 6. It is seen that the ∆s value of both alcohols decreases from positive to negative with increasing adsorption and changes discontinuously at the phase transition points. In the condensed state of DFC8OH, the ∆s values are largely negative and independent of temperature. Also in the expanded state of the TFC8OH system, it is found that the ∆s values above 40 mmol kg-1 are almost

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Figure 7. Partial molar entropy change of adsorption vs molality curves at 298.15 K: (1) TFC8OH; (2) DFC8OH; (3) TFC10OH.

Figure 8. Partial molar energy change of adsorption vs molality curves at 298.15 K: (1) TFC8OH; (2) DFC8OH; (3) TFC10OH.

independent of temperature and concentration. However, the constancy of ∆s in the TFC8OH system does not stem from a property of adsorbed film but does come from that of oil solution. This behavior will be discussed in the latter part of this paper, coupled with the results of interfacial density at high concentration (Figure 4). Furthermore, we estimated the partial molar entropy change of adsorption sjsH - ssO by using the relation13

sjsH - ssO ) [∆s + (1 - ΓsHas)(∂γ/∂T)p,ΓsH]/ΓsH (8) where ssO is the partial molar entropy of alcohol in the hexane solution, sjsH the mean partial molar entropy inherent in the interface, and as the partial molar area of alcohol molecule. The sjsH - ssO value of the expanded and condensed states was estimated at 298.15 K by assuming the as value to be 0.3 nm2 and plotted against ms in Figure 7. The sjsH - ssO value is negative and changes discontinuously from a less negative to a more negative value at the phase transition points. Hence it is realized that the alcohol molecule has smaller entropy in the adsorbed film than in the bulk solution and in the condensed state than in the expanded state because of the orientation of alcohol molecules at the interface. Figure 7 also shows the effect of the difference in FC chain length on the partial molar entropy change associated with phase transition. At the transition point, the magnitude of the discontinuous change in the sjsH - ssO value gives the difference in the partial molar entropy between the expanded and condensed states sjsH,c - sjsH,e. It is found that the magnitude of the sjsH,c - sjsH,e value is larger for TFC10OH than for DFC8OH. This may arise from the larger value of sjsH,e of TFC10OH due to the larger entropy of mixing of a longer fluorocarbon chain with hexane molecules in the expanded state and the smaller value of sjsH,c of TFC10OH due to the stronger attractive interaction in the condensed film compared to those of DFC8OH. Now, it is very informative to discuss the adsorption behavior of DFC8OH and TFC8OH from the viewpoint of energy. The partial molar energy change of adsorption u j sH - usO was calculated at 298.15 K by using

u j sH - usO ) γas + T(sjsH - ssO) - p(vj sH - vsO)

(9)

where vj sH - vsO is the partial molar volume change of adsorption, which was estimated from the pressure dependence of interfacial tension14 in a similar manner for the estimation of the sjsH - ssO value. The results are shown as u j sH - usO vs ms curves in Figure 8 together with that of TFC10OH. The u j sH - usO value is negative and therefore the adsorption of DFC8OH and TFC8OH is

Figure 9. Values of coefficient of dT of eqs 10 and 11 vs temperature curves: (O) eq 10; (s) eq 11; (1) gaseous-expanded transition for TFC8OH, (2) gaseous-expanded transition for DFC8OH, (3) expanded-condensed transition for DFC8OH.

caused by the decrease in energy that exceeds the disadvantage of the decrease in entropy. Furthermore, the u j sH - usO value of DFC8OH is larger than that of TFC10OH. It means that the energetical stabilization of DFC8OH accompanied by the adsorption is less than that of TFC10OH. Now, we examined the order of phase transitions found in this study. When two phases R and β coexist in the adsorbed film, the equilibrium interfacial tension is given by

dγeq ) -[(∆sβ/ΓsH,β - ∆sR/ΓsH,R)/ (1/ΓsH,β - 1/ΓsH,R)] dT + [(∆vβ/ΓsH,β - ∆vR/ΓsH,R)/ (1/ΓsH,β - 1/ΓsH,R)] dp (10) Since γeq is also determined by temperature and pressure, we have

dγeq ) (∂γeq/∂T)p dT + (∂γeq/∂p)T dp

(11)

The coefficient of dT of eq 10 was calculated by using the ΓsH and ∆s values at the phase transition points and that of eq 11 was evaluated from the slope of the γeq vs T curve in Figure 3a. By comparing both values in Figure 9, it is found that the agreement is good enough to substantiate the first-order phase transitions. Let us consider the apparently anomalous behavior found at high concentrations in the TFC8OH system in Figure 4. Since it was more evident at lower temperatures, we show the ΓsH vs ms curves at 288.15 K in Figure 10. It is clearly seen that the ΓsH value in the expanded state once increases and takes a maximum value, and then it

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ΓsH ) Γ1H + N h 1ΓaH

(13)

where Γi (i ) 1, a) represents the interfacial density of species i, N h 1 the mean aggregation number, and subscripts 1 and a the monomer and aggregate species, respectively. Assuming that the solution is an ideal dilute associated one and the dependence of N h 1 on ms is negligibly small within the experimental concentration range, we obtain the relation18 H

dγ ) -∆s dT + ∆v dp - ΓsH{(RT/ms)/ [1 + (N h 1 - 1)]} dms (14) where  is the fraction of alcohol molecules in aggregates to the total number of alcohols given by Figure 10. Interfacial density vs molality curves of TFC8OH system at 288.15 K: (----) ΓsH,mx.

decreases gradually with ms. In a previous study,18 we observed similar behavior for the hexane solution of oleyl alcohol (cis-9-octadecen-1-ol)-water system and concluded that it results from the aggregate formation of oleyl alcohol in hexane solution. Furthermore, Aveyard et al. reported that organic alcohol forms oligomers in nonpolar solvent at high concentrations.19,20 Taking these results into account, the apparently anomalous behavior found in this study is probably attributable to the self-aggregation of TFC8OH molecules in the hexane solution. On the basis of our experimental finding, the micelle formation of surfactants in aqueous solution is accompanied by a discontinuous change in the ∆s value at the critical micelle concentration. The self-aggregation of TFC8OH is not as critical as micelle formation and therefore it is plausible that the ∆s values converge continuously into one value in a narrow concentration range (ms ) 40-43 mmol kg-1). Now let us try to estimate roughly the mean aggregation number of TFC8OH in the hexane solution. Since the chemical potential of solute component µs is equal to that of monomer species µ1 under the equilibrium condition between the aggregate and monomer species,21,22 eq 1 is rewritten as

dγ ) -sH dT + vH dp - ΓsH dµ1

(12)

Here ΓsH is the total interfacial density defined by (18) Aratono, M.; Murakami, R.; Ohta, A.; Taura, J.; Ikeda, N.; Suzuki, M.; Takiue, T. J. Colloid Interface Sci., to be submitted for publication. (19) Aveyard, R.; Briscoe, B. J.; Chapman, J. J. Chem. Soc., Faraday Trans. 1 1973, 1772. (20) Aveyard, R.; Briscoe, B. J.; Chapman, J. J. Colloid Interface Sci. 1973, 44, 282. (21) Aratono, M.; Ohta, A.; Ikeda, N.; Takiue, T. J. Colloid Interface Sci., to be submitted for publication. (22) Prigogine, L.; Defay, R. Chemical Thermodynamics; Everett, D. H., Translator; Longmans: London, 1954; Chapter 26.

 ) (ms - m1)/ms

(15)

Therefore, the total interfacial density is calculated by

ΓsH ) -[1 + (N h 1 - 1)](ms/RT)(∂γ/∂ms)T,p

(16)

In the following, let us express the ΓsH value calculated by using eq 4 as ΓsH,id because this value was obtained on the basis of the assumption of ideal dilute solution. By comparing eq 16 to eq 4, we obtain the relation which enables us to estimate the N h 1 value from the ratio of ΓsH to ΓsH,id

h 1 - 1) ΓsH/ΓsH,id ) 1 + (N

(17)

According to the procedure employed in our previous study,18 the monomer concentration m1 is assumed to be 43 mmol kg-1, at which the ∆s value ceases to depend on temperature in Figure 6a, and the ΓsH value is given by the maximum one ΓsH,mx read from Figure 10. The N h1 values estimated at ms ) 60 mmol kg-1 is 3.44. This may suggest that the TFC8OH molecules form mainly cyclic tetramers and a small fraction of dimers in the hexane solution due to the intermolecular hydrogen bonding between their hydroxyl groups. Summing up briefly the results obtained in this study, it is found that the fluorination of the β-carbon of tbe TFC8OH molecule causes a large difference in the adsorption behavior between TFC8OH and DFC8OH. We conclude that the DFC8OH molecules are stabilized by forming the condensed film at the interface because of the strong molecular interaction between them. On the other hand, although the adsorbed film of TFC8OH does not transform to the condensed state, the TFC8OH molecules forms mainly tetramer in the hexane solution to lower the energetical state of the system. 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). LA001345Y