Long Chain

The dihedral angle of an alcohol lens floating on the air/water interface and the three kinds of interfacial tensions of air/1-undecanol/water and ...
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Langmuir 1998, 14, 7313-7320

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Dihedral Angle of Lens and Interfacial Tension of Air/Long Chain Alcohol/Water Systems. 2† Takayuki Toyomasu,* Takanori Takiue, Norihiro Ikeda,‡ and Makoto Aratono Department of Chemistry, Faculty of Science, Kyushu University 33, Fukuoka 812-8581, Japan Received April 14, 1998 The dihedral angle of an alcohol lens floating on the air/water interface and the three kinds of interfacial tensions of air/1-undecanol/water and air/1-dodecanol/water systems were measured as a function of temperature under atmospheric pressure. By applying the thermodynamics of interfaces to the experimental results of the interfacial tension measurement, it was found that the phase transitions between the expanded and the condensed states take place in the interfaces. It was found that there are break points on the dihedral angle versus temperature curves corresponding to the phase transitions of the interfacial films. The mutual relation among the states and the phase transition of the interfacial film, the wetting behavior, and the intruding phenomenon of the water phase on the air/alcohol interface was discussed. It was shown that the dihedral angles measured coincide with those calculated by Neumann’s equation with a satisfactory accuracy except at very low temperatures. The discrepancy at the low temperatures was proved to be attributable to the meniscus of the air/water interface.

Introduction Studies on the wetting behavior of a system consisting of three liquid phases and that of one with one gas and two liquid phases are very important because of not only theoretical interests but many industrial applications such as environmental, oil, and chemical industries. Therefore, many researchers have studied the wetting behavior from the theoretical and experimental points of view.1-11 Moldover and Cahn observed the curious phenomenon that the lower phase intruded between the upper and middle phases2 (intruding phenomenon). Chen et al. have reported the various patterns of the wetting behavior on the basis of the values of interfacial tension.6 Few works, however, have appeared on the measurement of the dihedral angle of the liquid lens of the middle phase with sufficient accuracy, although the dihedral angle is a useful property making the wetting behavior of the middle phase * To whom correspondence should be addressed. Mailing address: Takayuki Toyomasu, Department of Chemistry, Faculty of Science, Kyushu University 33, Hakozaki 6-10-1, Higashiku, Fukuoka812-8581,Japan.E-mailaddress: [email protected]. † Dihedral Angle of Lens and Interfacial Tension of Air/Long Chain Alcohol/Water Systems, which appeared in Langmuir 1997, 13, 2158-63, should be regarded as the first part of this series. ‡ Present address: Department of Environmental Science, Faculty of Human Environmental Science, Fukuoka Women’s University, Higashiku, Fukuoka 813-8529, Japan. (1) Cahn, J. W. J. Chem. Phys. 1977, 66, 3667. (2) Moldover, M. R.; Cahn, J. W. Science 1980, 207, 1073. (3) Costas, M. E.; Varea, C.; Robledo, A. Phys. Rev. Lett. 1983, 51, 2394. (4) Kahlweit, M.; Busse, G. J. Chem. Phys. 1989, 91, 1339. (5) Aratono, M.; Kahlweit, M. J. Chem. Phys. 1991, 95, 8578; 1992, 97, 5932(E). (6) Chen, L.-J.; Yan, W.-J. J. Chem. Phys. 1993, 98, 4830. (7) Pe´rez, C.; Roquero, P.; Talanquer, V. J. Chem. Phys. 1994, 100, 5913. (8) Chen, L.-J.; Hsu, M.-C.; Lin, S.-T.; Yang, S.-Y. J. Phys. Chem. 1995, 99, 4687. (9) Carrillo, E.; Talanquer, V.; Costas, M. J. Phys. Chem. 1996, 100, 5888. (10) Dussaud, A.; Vignes-Adler, M. Langmuir 1997, 13, 581. (11) Lucht, R.; Bahr, C.; Heppke, G.; Goodby, J. W. J. Chem. Phys. 1998, 108, 3716.

clear. It has been shown in our previous paper12 that the new apparatus and procedure for the dihedral angle measurement of the air/1-octanol/water and air/1-decanol/ water systems afford accurate values of the dihedral angle of an alcohol lens floating on the air/water interface. It has also been shown that the three kinds of interfacial tensions give important information that the alcohol phase forms a thermodynamically stable lens for both systems at all the temperatures examined and, furthermore, that the intruding phenomenon may possibly occur in the air/ 1-decanol/water system.12 In this study we employed the longer chain alcohols 1-undecanol and 1-dodecanol for the following reasons. First the intruding may occur more probably, because it is expected that the values of γAO and γAW + γOW approach each other with increasing hydrocarbon chain length of the alcohol, judging from our previous results given in ref 12, where γAO, γAW, and γOW denote the interfacial tensions of the air/alcohol (A/O), air/water (A/W), and alcohol/water (O/W) interfaces, respectively. Second, it has been proved that the 1-undecanol/water and 1-dodecanol/water interfacial films exhibit the phase transition between the expanded and condensed states.13,14 The interfacial tension and dihedral angle were measured as a function of temperature. Then the states and phase transition of the interfacial films, the wetting behavior, the intruding phenomenon, and the mutual relation among them are discussed thoroughly. Experimental Section 1. Materials. 1-Undecanol (C11OH) and 1-dodecanol (C12OH) were the highest grade (Tokyo Kasei Kogyo Co., Ltd) and distilled fractionally under reduced pressure. Their boiling points were 107-108 °C at 3.8 mmHg and 114-115 °C at 2.5 mmHg, respectively, and their purities were estimated to be more than 99.9% by gas-liquid chromatography. Water was distilled three times; the (12) Aratono, M.; Toyomasu, T.; Shinoda, T.; Ikeda, N.; Takiue, T. Langmuir 1997, 13, 2158. (13) Aratono, M.; Takiue, T.; Ikeda, N.; Nakamura, A.; Motomura, K. J. Phys. Chem. 1992, 96, 9422. (14) Aratono, M.; Takiue, T.; Ikeda, N.; Nakamura, A.; Motomura, K. J. Phys. Chem. 1993, 97, 5141.

10.1021/la9804233 CCC: $15.00 © 1998 American Chemical Society Published on Web 11/19/1998

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second and third distillations were done from alkaline permanganate solution. 2. Interfacial Tension. Interfacial tensions were measured by the pendant drop technique15 within (0.05 mN m-1 as a function of temperature from 287.50 K (mp of the C11OH phase) to 313.15 K for the C11OH system and from 298.25 K (mp of the C12OH phase) to 318.15 K for the C12OH system under atmospheric pressure. It should be noted that the lower limits of the experimental temperature were the melting points of each alcohol phase. 3. Dihedral Angle. The dihedral angle θO interposing the alcohol phase was measured by the drop shape analysis16,17 based upon the Young-Laplace equation of capillarity as a function of temperature under atmospheric pressure. There are two available methods called β-γ and β- methods: the latter was proved to be more trustworthy than the former,12 and therefore the values obtained from the β- method are employed in this paper. The experimental procedure of dihedral angle measurements is given in detail in our previous paper.12 Here, it should be kept in mind that the two angles θUO and θLO are measured separately by using an alcohol lens floating on the water surface being convex upward (Type I) and by using one being convex downward (Type II), where θUO is defined as the angle between the A/O interface and the plane containing the three-phase contact line and θLO is the one between the O/W interface and the plane, respectively. The dihedral angle θO was calculated as the sum of θUO and θLO. Additionally it should be noted that the size of the alcohol lens is large (about 4-6 mm in diameter) enough for the influence of the line tension on the magnitude of a dihedral angle to be considered negligible. Results and Discussion According to the Gibbs phase rule, the degree of freedom of these systems is two, since the systems consist of three components (water, alcohol, and air) and consist of three phases. We adopted temperature T and pressure p as the independent variables. The interfacial tension and dihedral angle were measured as a function of temperature under atmospheric pressure. 1. Interfacial Tension. Figure 1a shows the interfacial tension versus temperature curves of the C11OH system. It is seen that the γAO value increases almost linearly at low temperatures but decreases almost linearly at high temperatures. Then the curve has a sharp break at 288.50 K, which is higher than the mp of the C11OH phase by about 1 K. The γAW and γOW versus T curves also have a break point at 300.50 and 293.65 K, respectively, although they have a positive slope at all temperatures. Let us designate the temperatures of the breaks on the γAO, γAW, and γOW versus temperature curves by TAO, TAW, and TOW, respectively. The corresponding curves of the C12OH system are shown in Figure 1b: the γAO, γAW, and γOW versus T curves are similar in shape to those in Figure 1a and exhibit a break point at TAO ) 299.50 K, TAW ) 312.45 K, and TOW ) 305.35 K, respectively. We have shown previously that the O/W interfacial films of C11OH and C12OH exhibit the phase transition between the expanded and condensed states at the break points of the γOW versus T curves.13,14 Therefore, the break point of the γAO and γAW versus T curves suggests the phase transition of the A/O and A/W interfacial films. The break point of the γAO versus T curve has been observed for the surface (15) Matubayasi, N.; Motomura, K.; Kaneshina, S.; Nakamura, M.; Matuura, R. Bull. Chem. Soc. Jpn. 1977, 50, 523. (16) Maze, C.; Burnet, G. Surf. Sci. 1969, 13, 451. (17) Maze, C.; Burnet, G. Surf. Sci. 1971, 24, 335.

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Figure 1. Interfacial tension versus temperature curves: (a) C11OH; (b) C12OH; (1) γOW; (2) γAW; (3) γAO.

of higher n-alkanes18-21 and alcohols22,23 and considered to be the surface freezing phenomenon by Deutsch et al. The phase transition will be examined below from the viewpoint of the entropy and energy. Moreover, it is noted that the γAO and γAW curves intersect with each other at about 303.5 and 311 K for the C11OH and C12OH systems, respectively. This point also will be examined later in connection with the intruding phenomenon of the water phase into the A/O interface. Now let us develop the thermodynamic equations to evaluate the quantities associated with the surface formation and then examine the state of the interfacial film by using the thermodynamic quantities. By defining the interfacial excess quantities with regard to the two dividing planes chosen so as to make the excess numbers of moles of water and air be zero, the total differential of γAW is expressed as24

dγAW ) -sAW dT + vAW dp - ΓAW dµo o

(1)

Here sAW, vAW, and ΓAW represent the interfacial excess o entropy, volume, and number of moles of alcohol per unit area (interfacial density) at the A/W interface, and µo represents the chemical potential of alcohol, respectively. Substituting the total differential of µo in the water phase into eq 1, we have the total differential of γAW expressed as a function of T, p, and xW o :

dγAW ) W W -∆AWs dT + ∆AWv dp - ΓAW o (∂µo/∂xo )T,p dxo (2) where ∆AWy is the thermodynamic quantity associated (18) Wu, X. Z.; Ocko, B. M.; Sirota, E. B.; Sinha, S. K.; Deutsch, M.; Cao, B. H.; Kim, M. W. Science 1993, 261, 1018. (19) Wu, X. Z.; Sirota, E. B.; Sinha, S. K.; Ocko, B. M.; Deutsch, M. Phys. Rev. Lett. 1993, 70, 958. (20) Pfohl, T.; Beaglehole, D.; Riegler, H. Chem. Phys. Lett. 1996, 260, 82. (21) Hayami, Y.; Findenegg, G. H. Langmuir 1997, 13, 4865. (22) Deutsch, M.; Wu, X. Z.; Sirota, E. B.; Sinha, S. K.; Ocko, B. M.; Magnussen, O. M. Europhys. Lett. 1995, 30, 283. (23) Gang, O.; Ocko, B. M.; Wu, X. Z.; Sirota, E. B.; Deutsch, M. Phys. Rev. Lett. 1998, 80, 1264. (24) Motomura, K. J. Colloid Interface Sci. 1978, 64, 348.

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with the A/W interface formation defined by

∆AWy ≡ yAW - ΓAW yW o o , y ) s, v

(3)

W W and sW o , vo , and xo are the partial molar entropy, volume, and mole fraction of alcohol in the water phase, respectively. Since T and p are the independent variables adopted for the systems in this paper, the entropy and volume associated with the A/W interface formation are calculated by

R(∂ ln xW ∆AWs ) -(∂γAW/∂T)p - ΓAW o o /∂ ln T)p (4) and

RT(∂ ln xW ∆AWv ) (∂γAW/∂p)T + ΓAW o o /∂p)T

(5)

where the water phase is assumed to be an ideal dilute solution. Furthermore the corresponding energy is given by

∆AWu ) γAW + T∆AWs - p∆AWv

(6)

Since the experiments showed that the ln xW o versus ln T curve is almost flat,25,26 the second term on the right hand side of eq 4 is negligibly small and then the entropy ∆AWs is evaluated by

∆AWs ≈ -(∂γAW/∂T)p

Figure 2. Entropy of interface formation versus temperature curves: (a) C11OH; (b) C12OH; (1) ∆OWs; (2) ∆AWs; (3) ∆AOs.

(7)

Similarly the entropies of the O/W and A/O interface formation, ∆OWs and ∆AOs, are estimated by

∆OWs ≈ -(∂γOW/∂T)p

(8)

∆AOs ≈ -(∂γAO/∂T)p

(9)

and

where it was taken into account that the value of ∂ ln xwO/∂ ln T is very small, as shown in the literature;25,26 also the ΓAO value is expected to be small, judging from the w finding that the γAO value is very close to that in the absence of water,27 and the presence of air may not influence appreciably the property of the O/W interface. Here xwO is the mole fraction of water in the alcohol phase and ΓAO w is the interfacial density of water at the A/O interface, respectively. Furthermore, the corresponding energy associated with the R/β interface formation ∆Rβu is evaluated approximately by

∆Rβu ) γRβ + T∆Rβs

(10)

where the p∆Rβν term has been proved to be negligibly small at atmospheric pressure.13,14,28 The ∆Rβs and ∆Rβu values were evaluated by applying eqs 7-10 to the curves in Figure 1, and they are plotted against temperature in Figures 2 and 3, respectively. First we note that the phase transition accompanies discontinuous changes of ∆Rβs and ∆Rβu from a more negative value of the condensed state to a less negative or even positive one of the expanded state. This suggests that (25) Stephenson, R.; Stuart, J.; Tabak, M. J. Chem. Eng. Data 1984, 29, 287. (26) Stephenson, R.; Stuart, J. J. Chem. Eng. Data 1986, 31, 56. (27) Jasper, J. J. J. Phys. Chem. Ref. Data 1972, 1, 841. (28) Motomura, K.; Aratono, M.; Matubayasi, N.; Matuura, R. J. Colloid Interface Sci. 1978, 67, 247.

Figure 3. Energy of interface formation versus temperature curves: (a) C11OH; (b) C12OH; (1) ∆OWu; (2) ∆AWu; (3) ∆AOu.

alcohol molecules are in the more restricted but energetically favorable orientation at each interface in the condensed state. The remarkable point is that the ∆AOs and ∆AOu values are much more negative than the corresponding quantities of the O/W and A/W interfaces, while the γAO value is highest in the condensed state. This finding explains why the thinning of a water lens intruded on the A/O interface is stopped by the transition of the A/O interface, as described later. Now let us summarize the formation of the three kinds of interfaces on the basis of the interfacial tension, entropy, and energy for the 1-octanol (C8OH), 1-decanol (C10OH), C11OH, and C12OH systems. They are given in Figures 4-6. With respect to the A/O interface in its expanded state, the γAO value decreases with increasing temperature and decreasing hydrocarbon chain length. This observation is similar to that for the A/O interfaces in the absence of water and to that for the hydrocarbon liquid/water interfaces.27 The ∆AOs and ∆AOu values of the four systems are not so different from each other except at temperatures

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Figure 4. Interfacial tension versus temperature curves: (a) γAO; (b) γAW; (c) γOW; (1) C8OH; (2) C10OH; (3) C11OH; (4) C12OH.

Figure 5. Entropy of interface formation versus temperature curves: (a) ∆AOs; (b) ∆AWs; (c) ∆OWs; (1) C8OH; (2) C10OH; (3) C11OH; (4) C12OH.

very near to TAO. It is obvious that the transition temperature TAO becomes higher and the entropy and energy in the condensed state become more negative as the chain length is increased. This suggests that alcohol molecules are highly ordered at the A/O interface and the transfer of alcohol molecules from the interior of the bulk phase to the A/O interface becomes energetically more favorable for the longer chain. With respect to the A/W and O/W interfaces, it is noted that both ∆Rβs and ∆Rβu values decrease significantly with increasing hydrocarbon chain length in both the expanded and condensed states. This suggests that the A/W and O/W interface formation is governed predominantly by the orientation of and the energetically favorable interaction between hydrocarbon chains. 2. Dihedral Angle. Figure 7 shows the values of θO, θUO, and θLO for the C11OH and C12OH systems as a function of temperature. It is seen that the θOL and hence

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Figure 6. Energy of interface formation versus temperature curves: (a) ∆AOu; (b) ∆AWu; (c) ∆OWu; (1) C8OH; (2) C10OH; (3) C11OH; (4) C12OH.

O Figure 7. Angle versus temperature curves: (1) θO U; (2) θ L; (3) O θ ; (O) C11OH; (b) C12OH. Arrows represent the phase transition temperatures: (dotted arrows) C11OH; (solid arrows) C12OH.

the θO values decrease greatly with increasing temperature and are considerably different from each other for both systems, while the θUO values increase very slightly with increasing temperature and are not so different from each other. It is clear that the break points on the θLO, θUO, and θO versus T curves correspond to the break points on the interfacial tension versus T curves. By comparing the θ versus T curves of the four systems shown in Figure 8, it is said that the θLO and θO values and their temperature dependence are larger for the longer hydrocarbon chain. On the other hand, the θUO values are not very different from each other. 3. Dihedral Angle and Interfacial Tension. By applying Neumann’s equation describing the relation between the interfacial tension and the dihedral angle29,30

Dihedral Angle of an Alcohol Lens

Figure 8. Angle versus temperature curves: (a) θO; (b) θLO; (c) θUO; (1) C8OH; (2) C10OH; (3) C11OH; (4) C12OH.

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Figure 10. Interfacial tension versus temperature curves for the C11OH system: (1) γOW; (2) γAW; (3) γAO; (4) γAW + γOW; (5) γOW + γAO; (6) γAO + γAW.

Figure 9. Dihedral angle versus temperature curves: (O) θO O for the C11OH system; (b) θO for the C12OH system; (s) θCal .

cos θO ) {(γAW)2 - (γOW)2 - (γAO)2}/2γOWγAO (11) to the γ values given in Figure 1, the dihedral angle interposing the alcohol lens can be calculated and is O O . The values of θO and θCal are compared denoted by θCal each other for the C11OH and C12OH systems in Figure 9. It is seen that the θO values are sufficiently close to the O θCal values except in the much lower temperature range. Considering that the interfacial tension has been measured independently with good accuracy, this result proves also that the dihedral angles for the C11OH and C12OH systems have been measured accurately except in the lower temperature range. The discrepancy between the O values was observed to be maximally apθO and θCal proximately 15° at lower temperatures, and its cause will be discussed later. Now let us investigate the wetting behavior of a middle alcohol phase between the air and water phases and the intruding of a heavy phase into a light phase by closely examining the interfacial tensions between the three coexisting phases. When the inequalities given by30 (29) Princen, H. M. Surf. Colloid Sci. 1968, 2, 1. (30) Rowlinson, J. S.; Widom, B. Molecular Theory of Capillarity; Oxford University Press: Oxford, 1982.

Figure 11. Interfacial tension versus temperature curves for the C12OH system: (1) γOW; (2) γAW; (3) γAO; (4) γAW + γOW; (5) γOW + γAO; (6) γAO + γAW.

γAO < γAW + γOW, γAW < γOW + γAO, γOW < γAO + γAW (12) hold and the amount of the middle phase is small enough, the middle phase contracts to form a lens. In Figures 10 and 11 are shown the variations of the interfacial tensions and the sum of the two of them with temperature for the C11OH and C12OH systems, respectively. Since all the inequalities in eq 12 are satisfied, a lens of the alcohol phase is thermodynamically stable on the A/W interface at all the temperatures. In our previous paper,12 it was pointed out with respect to the C10OH system that a small amount of the water phase may intrude into the A/O interface and it may be contracted to a small lens at a temperature below about 295 K, where the γAO value is larger than the γAW value but eq 12 still holds. Therefore, as Figures 10 and 11 suggest, the intruding phenomenon

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Figure 12. Images of the alcohol lens with an intruded water lens in the C12OH system at 298.25 K. Arrows point to the intruded water lens. The diameter of the intruded water lens is about 0.54 mm: (a) the raw image; (b) the enlarged image processed by using Adobe Photoshop version 1.0 (High Pass filter 10 pixel).

Figure 13. Dihedral angle versus temperature curves: (1) C11OH; (2) C12OH.

may take place at a temperature below about 303.5 and 311 K for the C11OH and C12OH systems, respectively. Actually a small lens of the water phase was sometimes observed on the A/O interface. The example image of the lens is shown in Figure 12. In Figures 10 and 11, it should be noted that the values of γAW + γOW and γAO approach each other with decreasing temperature. It was found, however, that the γAO value starts to decrease rapidly with decreasing temperature at the phase transition temperature of the expanded to the condensed state of the A/O interface. This happens at the temperature just before the γAW + γOW and γAO versus T curves may cross each other. This situation is closely related to the wetting behavior of a water lens intruding into the A/O interface and is manifested in Figure 13, where the dihedral angle of the intruding lens θW Cal was computed by applying

cos θW ) {(γAO)2 - (γAW)2 - (γOW)2}/2γAWγOW

(13)

to the interfacial tension and was plotted against temperature. It is seen that the θW Cal value decreases very rapidly with decreasing temperature at the temperatures of the expanded state of the A/O interface. However, the θW Cal value is almost constant where the A/O interface is

in the condensed state: the condensed state prevents the lens from thinning. Figure 14 illustrates qualitatively the aspects of the relation between the states of the interfacial film and the wetting behavior of an alcohol lens, and the intruding phenomenon of the water phase on the A/O interface for the C11OH system. At T > TAW ≈ 300.5 K (Figure 14e), the three interfaces are in the expanded states and a small lens of the lower water phase may intrude into the A/O interface at a temperature of about 303 K, where the value of γAO is equal to that of γAW. At T ) TAW, the A/W interface transforms its state from the expanded one to the condensed state. Because of this more energetically favorable A/W interface compared to the A/O interface, the intruding of the water phase is expected to take place more plausibly and replace the A/O interface by the A/W interface (Figure 14d). At T ) TOW ) 293.65 K, the O/W interface is also transformed into the condensed state. This is also advantageous for the intruding, and the lens intruded becomes much more stable (Figure 14c). At T ) TAO ) 288.50 K, the A/O interface in the expanded state is transformed eventually into the condensed state. Since the A/O interface in the condensed state becomes energetically much more stable than the A/W and the O/W interfaces in the condensed state, the water lens is prevented from thinning and keeps its size small on the A/O interface (Figure 14a and b). The behavior of the C12OH system is similarly described. Finally, let us look at the causes for the discrepancy O values at the low temperature between the θO and θCal shown in Figure 9. One of them may be the water phase intruded near the three-phase contact line, which distorts really the shape and/or the video image of the lens. The second one may be ascribed to the meniscus of the A/W interface near the three-phase contact line. There are three typical types of the shape of the A/W interface at the three-phase contact line, as schematically shown in Figure 15: (a) the convex upward meniscus, (b) the flat surface, and (c) the convex downward meniscus. Here let θUO be smaller than and θLO larger than 90°, as is the case of

Dihedral Angle of an Alcohol Lens

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Figure 14. Schematic diagram for the relation between states of the interfacial film and wetting behavior: (i) alcohol lenses floating on the A/W interface; (ii) water lenses intruded in the A/O interface. The unshaded and darkly, medium, and lightly shaded areas represent air, solid alcohol, liquid alcohol, and water phases, respectively. The solid and broken lines represent the condensed and expanded states, respectively. See text for details.

Figure 15. Schematic diagram of the three types of the shape of the A/W interface near the three-phase contact line and the A O O definition of the angles θW Cal + θL and θCal + θU. The shaded portion represents the blind portion of the lens, owing to the meniscus of the A/W interface. See text for details.

present system at low temperatures. Let R, ΘUO, and ΘLO represent the radius of the circle and the upper and lower part of the dihedral angle ΘO at the three-phase contact line, respectively. As described in the experimental section, θUO is measured from the Type I experiments and θLO from the Type II experiments. When the A/W surface is in state b, both the radius rU and angle θO U obtained from the Type I experiment and the rL and θO L from the Type II experiment coincide with O R, ΘO U, and ΘL, respectively, where rU and rL are the experimental values of the radius of the circle at the threephase contact line obtained from the experiments of Type I and Type II, respectively. In this case, therefore, ∆r ) A O rL - rU is expected to be zero and both θW Cal + θL and θCal

+ θO U are equal to 180°: the experiments will give the correct values of the radius and angles, rU ) rL ) R, θO U ) ΘUO, and θLO ) ΘLO. When the A/W surface is in state a, the A/W meniscus surrounding the alcohol lens may hide a small part of the lens (shaded portion in Figure 15a) and therefore the three-phase contact line is not correctly taken into the video image. In this case, ∆r is expected to be O positive and θW Cal + θL larger than 180°. Only the Type II experiments give the correct values, and the Type I experiments give lower values of the radius and angles, O O O rL ) R, θO L ) ΘL, rU < R, and θU < ΘU. In the case of c, A ∆r is expected to be positive and θCal + θO U larger than 180°. Only the Type I experiments give the correct values,

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Figure 16. Difference of radii of the upper and lower parts of an alcohol lens versus temperature plot: (a) C8OH; (b) C10OH; (c) C11OH; (d) C12OH.

and the Type II experiments give higher values of radius O and lower ones of angles, rU ) R, θO U ) ΘU, rL > R, and θLO < ΘLO. A O O The values of ∆r, θW Cal + θL, and θCal + θU are plotted against temperature in Figures 16 and 17, where θW Cal and θACal were calculated by using Neumann’s equations, eq 13 and

cos θA ) {(γOW)2 - (γAO)2 - (γAW)2}/2γAOγAW

(14)

and the interfacial tensions shown in Figure 4. It is seen that the ∆r values are definitely positive at low temperatures for the C11OH and C12OH systems, while they are close to zero for the C8OH and C10OH systems and the C11OH and C12OH systems at higher temperatures.

Figure 17. Angle versus temperature curves: (a) θACal + θO U; O (b) θW Cal + θL ; (1) C8OH; (2) C10OH; (3) C11OH; (4) C12OH. O Furthermore it is clear that the θW Cal + θL value is smaller A O and θCal + θU is larger than 180° at lower temperatures for the C11OH and C12OH systems, while they are close to 180° at all the experimental temperatures for the C8OH and C10OH systems and at higher temperatures for the C11OH and C12OH systems. These findings show that the A/W interface forms a convex downward meniscus near the three-phase contact line, that is, case c. Therefore O the θO L and hence θ values were underestimated. This explains the gap between the θO and θO Cal values at lower temperatures in Figure 9.

Acknowledgment. The present research was supported by Kurata Foundation (1997), which is greatly acknowledged. LA9804233