Molecular Orientation and Multilayer Formation of 1H,1H,8H,8H

Apr 14, 2009 - The surface tension of the aqueous solution of 1H,1H,8H,8H-perfluorooctane-1,8-diol (FC8diol) was measured as a function of temperature...
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J. Phys. Chem. B 2009, 113, 6305–6310

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Molecular Orientation and Multilayer Formation of 1H,1H,8H,8H-Perfluorooctane-1,8-diol at the Air/Water Interface Takanori Takiue,* Fumiya Nakamura, Daiki Murakami, Tsubasa Fukuda, Aya Shuto, Hiroki Matsubara, and Makoto Aratono Department of Chemistry, Faculty of Sciences, Kyushu UniVersity, Fukuoka 812-8581, Japan ReceiVed: January 14, 2009; ReVised Manuscript ReceiVed: March 17, 2009

The surface tension of the aqueous solution of 1H,1H,8H,8H-perfluorooctane-1,8-diol (FC8diol) was measured as a function of temperature and concentration under atmospheric pressure. The interfacial density and the entropy and energy of adsorption were evaluated and compared to those obtained for the adsorption of 1H,1H,10H,10H-perfluorodecane-1,10-diol (FC10diol) at the hexane solution/water interface. The surface tension curves show a break point corresponding to a phase transition of the adsorbed FC8diol film. The value of mean area per adsorbed molecule A just below the phase transition indicated the formation of a parallel condensed monolayer, and that above the phase transition suggested the spontaneous formation of a multilayer. The multilayer of FC8diol is less compressible and shows a smaller increase in layering with π compared to FC10diol. This is probably because the surface force is repulsive for the hexane/FC/water interface, while it is attractive for the air/FC/water interface. The partial molar entropy change of adsorption is positive in the condensed FC8diol film, while it is negative in the condensed FC10diol film, which is reasonably explained in terms of the difference in entropy change accompanied by desolvation around the hydrophobic chain. From the viewpoints of the energetic stabilization accompanied by adsorption for the FC8diol system, the contribution from the replacement of air/water contact with air/fluorocarbon and fluorocarbon/water contacts and that from the molecular ordering in the adsorbed film is almost equal in case of the condensed monolayer, while in the multilayer the latter is comparatively larger than the former due to the hydrogen bonding between hydroxyl groups and the dispersion interaction among the ordered hydrophobic chains. Introduction The fluorocarbon (FC) chain has various remarkable characteristics, such as (i) a rigid hydrophobic chain, (ii) a large polarization due to a strong electronegative nature of the fluorine atom, and (iii) a weak interaction with the hydrocarbon (HC) chain.1,2 These may cause unique behavior at soft interfaces, such as gas/liquid and liquid/liquid, and, therefore, it is very valuable to clarify the adsorption behavior of the FC alcohol in the basic sciences as well as in the industrial applications. In our previous study, the adsorbed FC alcohol films at the HC oil/water interface have been investigated by means of the interfacial tension measurement and analysis of thermodynamic data.3-7 It should be emphasized that the phase transitions take place among gaseous, expanded, and condensed states; especially FC alcohols with carbon numbers larger than eight form condensed films under atmospheric pressure, at which the molecules are closely packed. Furthermore, their molecular level structures of the adsorbed films were analyzed by synchrotron X-ray reflectivity measurement.8-10 Judging from the film thickness and electron density values, it was clearly demonstrated that 1H,1H,2H,2H-perfluorodecanol (TFC10OH) and 1H,1H,2H,2H-perfluorododecanol (TFC12OH) molecules are densely packed with almost perpendicular orientation to the hexane/water interface in the condensed state. Recently, the adsorption behavior of 1H,1H,10H,10H-perfluorodecane-1,10-diol (FC10diol), which has two hydroxyl groups at both ends of hydrophobic chain, at the hexane solution/ * Corresponding author: Telephone: +81 92 642 2578. Fax: +81 92 642 2607. E-mail: [email protected].

water interface has been investigated from the viewpoints of entropy and energy of adsorption.11 One of the important findings was that FC10diol molecules form a condensed monolayer arranged parallel to the interface. This is a striking contrast to the “wicket-like” conformation of bolaform surfactants with the HC chain, such as dodecane-1,12-bis(trimethylammonium bromide),12,13 at the air/water interface where the hydrophobic chain forms a loop and two head groups are anchored at the interface under saturated adsorption because of the flexible nature of the HC chain. Another noticeable finding was that FC10diol molecules pile spontaneously and successively form a multilayer at high concentrations and low temperatures. These novel adsorption behaviors are primarily attributable to the stiff nature of the FC chain in addition to the hydrogen bonding between the hydroxyl group and water and between the hydroxyl groups facing each other. Furthermore, the evaluation of partial molar entropy and the energy change of adsorption suggested that FC10diol molecules are not so densely packed in the upper layers due to the intercalation of hexane molecules into them. These results indicate appreciable participation not only of solute-solute interaction but also of solute-solvent interaction for the adsorption behavior of FC10diol. In this study, we employ 1H,1H,8H,8H-perfluorooctane-1,8diol (FC8diol) because it has a shorter FC chain length than FC10diol and is more soluble in water; the solubility of FC10diol in water is too small to measure precisely the surface tension of its aqueous solution as a function of concentration. Thus, the effect of solute-solvent interaction on the state of adsorbed film may be deduced by comparing the adsorption of FC10diol from the hexane phase to that of FC8diol from the water phase.

10.1021/jp900375q CCC: $40.75  2009 American Chemical Society Published on Web 04/14/2009

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We aim at clarifying the surface adsorption of FC8diol from the viewpoints of entropy and energy calculated from the temperature dependence of surface tension at the air/aqueous FC8diol solution. The interfacial density, entropy, and energy of adsorption are evaluated and compared to those of FC10diol at the hexane solution/water interface. Experimental Section Materials. FC8diol purchased from Lancaster Co Ltd. was purified by recrystallization in a chloroform-hexane (1/1 volume ratio) solution three times. Its purity was checked by observing no time dependence of surface tension of the aqueous FC8diol solution and by liquid/gas chromatography. Water was distilled three times; the second and third stages were done from a dilute alkaline permanganate solution. Surface Tensiometry. The surface tension γ of the aqueous FC8diol solution was measured as a function of temperature T and molality of FC8diol m1 (the subscript 1 denotes FC8diol) under atmospheric pressure by the shape analysis of pendant drops described elsewhere.14 The experimental error of the γ value was estimated within (0.05 mN m-1. Ellipsometry. Ellipsometric measurement was performed as a function of temperature at given concentrations by a Picometer Ellipsometer (Beaglehole Inst.) equipped with a He-Ne laser (632.8 nm) at the Brewster angle.15 In such a condition, the coefficient of ellipticity Fj is defined as the ratio between the Fresnel reflection coefficients for p- and s-polarized lights. The error in Fj was estimated to be within (2 × 10-5. To estimate the film thickness, the dielectric constant ε of the liquid state of 1H,1H,2H,2H-perfluorooctanol (TFC8OH) instead of FC8diol was evaluated through the measurement of refractive index n (ε ) n2) at given temperatures because of its high melting point (∼363.15 K). Results and Discussion Figure 1a shows the equilibrium surface tension γ vs temperature T curves under atmospheric pressure at given concentrations. The γ value decreases gradually with increasing temperature at all concentrations, except at high concentrations and low temperatures. In Figure 1b, the γ vs T curves are enlarged at high concentrations. It is clearly demonstrated that the curves have a distinct break point due to the phase transition of the adsorbed FC8diol film. The γ value increases with increasing temperature below the break point. The γ vs m1 curves at constant temperatures are shown in Figure 2a; the curves in a high concentration region are enlarged in Figure 2b. The curves at 288.15 and 293.15 K clearly show a break corresponding to the phase transition in the adsorbed film. By introducing the two dividing planes, which make the excess numbers of moles of air and water zero simultaneously, the total differential of surface tension γ is expressed as16

dγ ) -∆s dT + ∆V dp - ΓH1 (RT/m1) dm1

(1)

where the aqueous solution is assumed to be ideally dilute. Here ∆s and ∆V are the entropy and volume changes associated with the adsorption of FC8diol from the aqueous solution and defined by

∆y ) yH - ΓH1 yW 1 H

Γ1H,

(y ) s, V)

(2)

Figure 1. Surface tension vs temperature curves at constant molality: m1 ) (1) 0, (2) 0.060, (3) 0.100, (4) 0.249, (5) 0.499, (6) 0.701, (7) 1.002, (8) 1.497, (9) 1.999, (10) 2.999, (11) 3.999, (12) 4.990, (13) 5.998, (14) 6.404, (15) 6.635, (16) 6.682, (17) 6.749, (18) 6.999, (19) 7.055, (20) 7.104, (21) 7.202, and (22) 7.402 mmol kg-1.

Thus, the surface density, Γ1H, of FC8diol was calculated by applying the equation:

ΓH1 ) -(m1/RT)(∂γ/∂m1)T,p

(3)

to the γ vs m1 curves in Figure 2 and plotting against m1 in Figure 3. The Γ1H value increases with increasing m1 and is almost constant at 2.5 µmol m-2 below the phase transition point. At low temperatures, it increases discontinuously to around 14 µmol m-2 at the phase transition point. It should be noted that this value is much larger than the surface density (∼6 µmol m-2) expected for the condensed monolayer of FC alcohols such as 1H,1H,2H,2H-perfluorodecanol (TFC10OH) with a perpendicular orientation at the hexane/water interface.8-10 The surface pressure π vs the mean area per adsorbed molecule A curves are constructed by calculating them by

y1W

where y , and are, respectively, the surface excess thermodynamic quantity, the surface density of FC8diol per unit area, and the partial molar thermodynamic quantity of FC8diol in the aqueous phase.

π ) γ0 - γ and

(4)

Formation of 1H,1H,8H,8H-Perfluorooctane-1,8-diol

A ) 1/NAΓH1

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(5)

0

where γ is the surface tension of the pure water and NA is Avogadro’s number. In Figure 4 are shown the π vs A curves of FC8diol at 293.15 K together with the curve of FC10diol at the hexane/water interface.

Figure 4. Interfacial pressure vs mean area per adsorbed molecule curves at 293.15 K: (1) FC8diol at air/water interface; (2) FC10diol at hexane/water interface.

Figure 5. Coefficient of ellipticity vs temperature plot at m1 ) 7.40 mmol kg-1.

Figure 2. Surface tension vs molality curves at constant temperature: T ) (1) 288.15, (2) 293.15, (3) 298.15, (4) 303.15, and (5) 308.15 K.

Figure 3. Surface density vs molality curves at constant temperature: T ) (1) 288.15, (2) 293.15, (3) 298.15, (4) 303.15, and (5) 308.15 K.

The curve of FC8diol consists of two states connected by a discontinuous change. At a larger A region, the π value increases gradually with decreasing A, indicating a gradual packing of FC8diol molecules. Just below the phase transition, however, the π value rises quite steeply by only a small decrease of the area. This extremely low compressibility reveals a feature of the two-dimensional solid state of the FC8diol film. Basically the same situation as this was observed also in the adsorbed FC10diol film at the hexane/water interface (an intermediate region of the π vs A curve).11 Considering that the A value just below the transition pressure is larger than the cross-sectional area of fluorocarbon chain (0.28 nm2) and instead very close to the cross-sectional area along the major axis of FC8diol molecule (0.67 nm2), we concluded that the FC8diol molecules can form a condensed monolayer oriented parallel to the surface where both hydroxyl groups are anchored into the water. Above the phase transition point, the A value is around 0.19 nm2 and much smaller than the cross-sectional area for the perpendicular orientation given above 0.28 nm2. Therefore, FC8diol molecules are probably piled with parallel orientation to the surface and spontaneously form a multilayer. Three essential differences are realized between the π vs A curves of FC8diol and FC10diol. The first is that the A values in the parallel condensed monolayers are 0.66 nm2 for FC8diol and 0.82 nm2 for FC10diol, respectively, which assures the parallel orientation of the molecules. The second is that the multilayer state is less compressible for FC8diol than for

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FC10diol, which suggests that FC8diol molecules at the air/water surface are relatively closely packed even in the upper layer of the multilayer compared to FC10diol molecules at the hexane/ water interface. Furthermore, the decrease in A corresponding to the increase in layering with π is much larger for FC10diol than for FC8diol. This is probably due to the fact that the surface force is repulsive for the hexane/FC/water interface (Hamaker constant; 1022H ∼ -2.54 J), while attractive for the air/FC/ water interface (1021H ∼ +1.67 J). Here H values were calculated by17

( )( )

ε1 - ε3 ε2 - ε3 3 Η ) kT + 4 ε1 + ε3 ε2 + ε3 3hVe 4√2

kT

(n21 - n23)(n22 - n23) (n21 + n23)1/2(n22 + n23)1/2[(n21 + n23)1/2 + (n22 + n23)1/2]

(6)

where ε is the dielectric constant, n is the refractive index, and the subscripts 1, 2, and 3 show air (or hexane), water, and FC layer, respectively. The third is that the πeq between the condensed monolayer and multilayer states is higher for the FC8diol than for the FC10diol system. This is mainly due to the weaker dispersion interaction between hydrophobic chains of FC8diol molecules compared to that of FC10diol ones. In ellipsometry, the change in polarization of the reflected beam from the interface was measured. Figure 5 shows the coefficient of ellipticity Fj plotted against temperature at m1 ) 7.40 mmol kg-1 and a steep decrease around the phase transition point. For a thin isotropic film with dielectric constant ε on the air/water interface, Fj is expressed by18

Fj )

π √ε1 + ε2 η λ ε1 - ε2

(7)

where λ is the wavelength of the light, ε1 and ε2 are, respectively, the dielectric constant of air and water, and η is the ellipsometric parameter given as a function of thickness d by19

η)

(ε - ε1)(ε - ε2) d ε

(8)

The effect of surface roughness on Fj is included by an extra term from the capillary wave given by

T  72γ 298.15

F¯r ) (0.4 × 10-3)

(9)

Adopting that the ε value of FC8OH was ∼1.717 at 308.15 and ∼1.726 at 298.15 K from the measurements of refractive indexes, the thickness d of the adsorbed FC8diol film was ∼0.08 nm at 308.15 (condensed monolayer state) and ∼0.52 nm at 298.15 K (multilayer), respectively. Although 0.08 nm is smaller than the thickness of monolayer of 0.5 nm calculated from the CPK model, probably due to smaller ε for TFC8OH than for FC8diol, the ratio in d (0.52/0.08 ∼ 6.5) is similar to that in Γ1H (13.8/2.5 ∼ 5.5) and, thus, around six monolayers are piled just above the phase transition to the multilayer. We are planning to perform X-ray reflectivity and grazing incidence X-ray diffraction measurements in order to determine the structure of these films in detail. Next, the entropy change associated with adsorption was evaluated by applying the equation:

∆s ) -(∂γ/∂T)p,m1

(10)

to γ vs T curves, and the results are shown in Figure 6. Although the ∆s value decreases sharply at low concentrations with

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

increasing m1 and, thus, with increasing Γ1H, the value is still positive for a condensed monolayer with a parallel molecular orientation, which forms a striking contrast to a negative value (-0.31 mJ K-1 m-2 at 298.15 K) for the condensed monolayer with parallel molecular orientation of FC10diol at the hexane/ water interface.11 The phase transition from the condensed monolayer to the multilayer accompanies the discontinuous decrease in ∆s to a negative value. Why is such a large difference in ∆s generated between the condensed monolayer film of FC8diol at the air/water interface and that of FC10diol at the hexane/water interface? Since the partial molar entropy change associated with adsorption of FC8diol js1A/W - s1W and that of FC10diol js1O/W - s1O for the condensed monolayers are estimated approximately by6,16 H jsA/W - sW 1 1 ) ∆s/Γ1

(11)

jsO/W - sO1 ) ∆s/ΓH1 1

(12)

and

jsR/W 1

where (R ) A or O) and (β ) W or O) are, respectively, the partial molar entropies in the adsorbed films and in the bulk solutions. The ∆s in eqs 11 and 12 are estimated by eq 10, but the former is the entropy change associated with adsorption of FC8diol from the aqueous phase and the latter is that of FC10diol from the hexane phase, respectively. These equations show that the sign and magnitude of ∆s are directly correlated with the partial molar entropy change, at least in the condensed monolayer state. Therefore, the answer is that, considering the molecular orderings in condensed films at the interfaces are not so much different from each other, the entropies of desolvation accompanied by adsorption for FC8diol (release of water molecules) and FC10diol (release of hexane molecules) are influential on ∆s and probably opposite in their sign; dehydration of methane and fluoromethane accompanies an increase in entropy,20 and thus, the entropy accompanied by the dehydration around the hydrophobic chain (-CH2(CF2)6CH2-) of FC8diol molecule is expected to be positive, while, on the other hand, the desolvation of (-CH2(CF2)8CH2-) of FC10diol is expected to accompany a decrease in entropy, judging from the fact that the excess entropy of mixing of fluorocarbon and hydrocarbon oil is positive.21 The partial molar entropy changes are given as a function of - sW ΓH1 at 298.15 K in Figure 7. The jsA/W 1 1 of FC8diol is positive, sβ1

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Figure 7. Partial molar entropy change of adsorption vs interfacial density curves at 298.15 K: (1) FC8diol at the air/water interface; (2) FC10diol at hexane/water interface.

Figure 9. Partial molar energy change of adsorption vs interfacial density curves at 298.15 K: (1) FC8diol at air/water interface; (2) FC10diol at hexane/water interface.

as a function of m1 at constant temperatures in Figure 8. The ∆u value decreases with increasing m1 and changes discontinuously from positive to negative at the phase transition point. Examining the lowering in ∆u from the ∆u value of the bare air/water surface, ∆∆u, accompanied by adsorption in terms of the contributions of ∆γ ) π and ∆(T∆s) separately as

∆∆u ) π + ∆(T∆s)

Figure 8. Energy change associated with adsorption vs molality curves at constant temperature: T ) (1) 288.15, (2) 293.15, (3) 298.15, (4) 303.15, and (5) 308.15 K.

but the jsO/W - sO1 of FC10diol is negative. The difference between 1 them is around 0.15 kJ K-1 mol-1 and proved to be similar in value to the dehydration entropy of -CH2(CF2)6CH2-, as follows. Dehydration of methane and fluoromethane accompanies entropy increases by 0.067 and 0.088 kJ K-1 mol-1 as reported by Ben-Naim,20 and thus, the entropy increase accompanied by the dehydration around the hydrophobic chain of FC8diol molecule is estimated to be about 0.33 kJ K-1 mol-1 by assuming these values are proportional to the number of hydrogen and fluorine atoms being exposed by water molecules in the aqueous phase. Taking note that a part of the hydrophobic chain of the FC8diol molecule is still in contact with water in the condensed film because of parallel orientation at the interface, the increase in entropy of dehydration is probably less than 0.33 kJ K-1 mol-1. Next, let us discuss the adsorption behavior of FC8diol from the viewpoint of energy. The energy change associated with adsorption ∆u is evaluated by using the equation:

∆u ) γ + T∆s - p∆V ≈γ + T∆s

(13) (14)

where the p∆V term is negligibly small compared to the other two terms under atmospheric pressure. The results are shown

(15)

we note the totally different driving force of adsorption between the condensed monolayer and the multilayer. In case of interface parallel orientation of the condensed monolayer, π ∼ 29 mJ m-2 and ∆(T∆s) ∼ 34 mJ m-2, and thus, both contribute to the energetic stabilization (∆∆u) almost equally just before the transition to the multilayer. The former is mainly because the adsorption replaces the air-water contact (γA/W ∼ 72 mJ m-2) by the air-FC contact (γA/FC ∼ 18 mJ m-2), while the lower part of the monolayer keeps the water-FC contact (γW/FC ∼ 55 mJ m-2) at the interface. A rough estimation shows the fraction of the water-FC contact F to be about 0.44 from (γA/W - γA/FC) - γW/FCF. This value gives the entropy increase by dehydration around the hydrophobic chain of FC8diol molecule as 0.33F ) 0.15 kJ K-1 mol-1, which agrees well with the difference in the partial molar entropy change between FC8diol and FC10diol systems. With respect to the latter ∆(T∆s), the enforced ordering in the monolayer causes the entropy loss, but at the same time it accompanies the new formation of hydrogen bonding between hydroxyl groups facing each other in the monolayer and, thus, results in a decrease in ∆u. In the case of the multilayer, on the other hand, π ∼ 29 mJ m-2 and ∆(T∆s) ∼ 135 mJ m-2 at the transition point, and π ∼ 31 mJ m-2 and ∆(T∆s) ∼ 135 mJ m-2 at the highest surface density of the multilayer. Therefore, the contribution of π is not changed much even when monolayers are piled, while the energetic stabilization (∆∆u) is largely driven by the ∆(T∆s) term: the formation of hydrogen bonding between hydroxyl groups facing each other in the multilayer and the dispersion interaction among the ordered FC chains cause a loss in entropy, but a gain in energy. Here let us examine the difference of the condensed monolayer formations between FC8diol and FC10diol using the partial molar energy change of adsorption uj1A/W - u1W evaluated by7,16

ujA/W - uW jA/W - sW 1 1 ≈ γa1 + T(s 1 1 ) and uj1O/W - u1O by

(16)

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ujO/W - uO1 ≈ γa1 + T(sjO/W - sO1 ) 1 1

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(17)

where a1 is the partial molar area of solutes and is assumed to be 0.66 nm2 for FC8diol and 0.82 nm2 for FC10diol. The uj1A/W - u1W vs Γ1H curve at 298.15 K is shown together with the corresponding uj1O/W - u1O vs Γ1H curve of FC10diol in Figure 9; - uW jO/W the ujA/W - uO1 is negative. 1 1 value is positive, while the u 1 In the condensed film, the values of second terms of eqs 17 and 15 are +1.5 kJ mol-1 for FC8diol at the aqueous solution surface and -31.6 kJ mol-1 for FC10diol at the hexane solution/ water interface. Since the values of the first term are similar to each other (+18.2 for FC8diol and +17.1 kJ mol-1 for FC10diol), the difference in the partial molar energy change between both systems is primarily due to the difference in entropy change of adsorption as pointed out above. Acknowledgment. This work was supported in part by the Grant in Aid for Scientific Research (C) of the Japan Society for the Promotion of Science (No. 19550021) and the Asahi Glass Foundation. References and Notes (1) Kissa, E. Fluorinated Surfactants and Repellents; Surfactant Science Series, 2nd ed.; Marcel Dekker: New York, 2001; Vol 97. (2) Krafft, M. P.; Goldmann, M. Curr. Opin. Colloid Interface Sci. 2003, 8, 243. (3) Hayami, Y.; Uemura, A.; Ikeda, N.; Aratono, M.; Motomura, K. J. Colloid Interface Sci. 1995, 172, 142.

(4) Takiue, T.; Yanata, A.; Ikeda, N.; Motomura, K.; Aratono, M. J. Phys. Chem. B 1996, 100, 13743. (5) Takiue, T.; Uemura, A.; Ikeda, N.; Motomura, K.; Aratono, M. J. Phys. Chem. B 1998, 102, 3724. (6) Takiue, T.; Sugino, K.; Higashi, T.; Toyomasu, T.; Hayami, Y.; Ikeda, N.; Aratono, M. Langmuir 2001, 17, 8098. (7) Takiue, T.; Murakami, D.; Tamura, T.; Sakamoto, H.; Matsubara, H.; Aratono, M. J. Phys. Chem. B 2005, 109, 14154. (8) Tikhonov, A. M.; Schlossman, M. L. J. Phys. Chem. B 2003, 107, 3344. (9) Pingali, S. V.; Takiue, T.; Luo, G.; Tikhonov, A. M.; Ikeda, N.; Aratono, M.; Schlossman, M. L. J. Phys. Chem. B 2005, 109, 1210. (10) Pingali, S. V.; Takiue, T.; Luo, G.; Tikhonov, A. M.; Ikeda, N.; Aratono, M.; Schlossman, M. L. J. Dispersion Sci. Technol. 2006, 27, 715. (11) Takiue, T.; Fukuda, T.; Murakami, D.; Inomata, H.; Sakamoto, H.; Matsubara, H.; Aratono, M. J. Phys. Chem. C 2008, 112, 5078. (12) Abid, S. K.; Hamid, S. M.; Sherrington, D. C. J. Colloid Interface Sci. 1987, 120, 245. (13) Ikeda, K.; Yasuda, M.; Ishikawa, M.; Esumi, K.; Meguro, K.; Binana-Limbele, W.; Zana, R. Colloid Polym. Sci. 1989, 267, 825. (14) Sakamoto, H.; Murao, A.; Hayami, Y. J. Inst. Image Inf. TeleVision Eng. 2002, 56, 1643. (15) Wilkinson, K. M.; Lei, Q.; Bain, C. D. Soft Matter 2006, 2, 66. (16) Motomura, K. J. Colloid Interface Sci. 1978, 64, 348. (17) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1991; Chapter 11. (18) Drude, P. The Theory of Optics; Dover: New York, 1959. (19) Meunier, J. Light reflectivity and Ellipsometry. In Light Scattering by Liquid Surfaces and Complementary Techniques; Langevin, D., Ed.; Marcel Dekker: New York, 1992; p 333. (20) Ben-Naim, A. Y. , SolVation Thermodynamics; Plenum: New York, 1987; Chapter 2. (21) Rowlinson, J. S.; Swinton, F. L. Liquids and Liquid Mixtures; Butterworths Scientific Publications: London, 1982; Chapter 5.

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