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Line Tension and Wetting Behavior of an Air/ Hexadecane/Aqueous Surfactant System Youichi Takata,*,† Hiroki Matsubara,† Yoshimori Kikuchi,† Norihiro Ikeda,‡ Takashi Matsuda,† Takanori Takiue,† and Makoto Aratono† Department of Chemistry and Physics of Condensed Matter, Graduate School of Sciences, Kyushu University, Fukuoka 812-8581, Japan, and Department of Environmental Science, Faculty of Human Environmental Science, Fukuoka Women’s University, Fukuoka 813-8529, Japan Received July 13, 2004 The line tension of an air/hexadecane/aqueous solution of an dodecyltrimethylammonium bromide (DTAB) system was measured as a function of the molality of DTAB at 298.15 K by means of a newly constructed apparatus. It was estimated to be on the order of 10-10-10-12 N, which is comparable to the theoretical estimation. Furthermore, its sign was reversed from positive to negative in the vicinity of the wetting transition concentration. The reversal of the sign was examined on the basis of our experimental findings on the wetting transition and the theory of Indekeu.
Line tensions may be classified as mechanical or thermodynamic tensions of three types: one in a 2D heterogeneous systems, one at the three-phase contact line, and the effective one on deformable solids.1 The first is regarded as the 1D analogue of the interfacial tension between two macroscopic phases in the respect that it never becomes negative. Because the second can be either positive or negative, it should be noted that it is essentially different from the first and not regarded as the 1D analogue of the interfacial tension, although it may be similar to the interfacial tension in the respect that both interfacial and line tensions can be explained as a kind of excess thermodynamic quantity.2 Its magnitude is theoretically estimated to be on the order of 10-11-10-12 N, and thus it plays an important role in the phenomena observed in microscopic bodies or regions smaller than several micrometers (eq 1) (e.g., heterogeneous nucleation,3,4 domain shape in insoluble monolayers,5-7 particle wettability at liquid/fluid interfaces,8,9 and so on). Furthermore, negative line tension deserves special attention because it promotes the fusion of cells10 and the coalescence of an emulsion.11,12 Some groups have measured line tension using various techniques3-9,13-17 and often reported quite different results even for identical systems. This may partly arise * To whom correspondence should be addressed. E-mail:
[email protected]. † Kyushu University. ‡ Fukuoka Women’s University. (1) Rusanov, A. I. Colloids Surf., A 1999, 156, 315. (2) Rowlinson, J. S.; Widom, B. Molecular Theory of Capillarity; Oxford University Press: Oxford, U.K., 1982. (3) Scheludko, A.; Chakarov, V.; Toshev, B. J. Colloid Interface Sci. 1981, 82, 83. (4) Toshev, B. V.; Platikanov, D.; Scheludko, A. Langmuir 1988, 4, 489. (5) Siegel, S.; Vollhardt, D. Thin Solid Films 1996, 284-285, 424. (6) Miranda, J. A. J. Phys. Chem. B 1999, 103, 1303. (7) Wurlitzer, S.; Steffen, P.; Wurlitzer, M.; Khattari, Z.; Fischer, Th. M. J. Chem. Phys. 2000, 113, 3822. (8) Aveyard, R.; Clint, J. H. J. Chem. Soc., Faraday Trans. 1996, 92, 85. (9) Faraudo, J.; Bresme, F. J. Chem. Phys. 2003, 118, 6518. (10) Karatekin, E.; Sandre, O.; Brochard-Wyart, F. Polym. Int. 2003, 52, 486. (11) Churaev, N. V.; Starov, V. M. J. Colloid Interface Sci. 1985, 103, 301. (12) Denkov, N. D.; Petsev, D. N.; Danov, K. D. J. Colloid Interface Sci. 1995, 176, 189.
from adopting an air/liquid/solid system instead of an air/ liquid/liquid system. As pointed out by some authors,18-20 it is very difficult to prepare a molecularly smooth solid surface, and the heterogeneity and/or roughness significantly affects the nature of line tension. Recently, this problem was improved theoretically by taking into account the effect of surface roughness on line tension21,22 or experimentally by using the silicon wafer as an ideally smooth and homogeneous surface.19,23-25 However, it is indispensable to perform experiments on molecularly smooth liquid surfaces to elucidate the nature of line tension. We have investigated the wetting behavior of the air/ hexadecane lens/aqueous solution of ionic surfactant systems and obtained the following results:26,27 (1) The wetting transition of the oil phase on the aqueous solution occurs concurrently with the phase transition in the adsorbed film of a surfactant at the air/water surface. (2) The oil lens exists even at surfactant concentrations where Neumann’s triangle relation does not hold and is in equilibrium with the molecularly thin film composed of surfactant and oil molecules. During these studies, we have paid special attention to the relationship between line tension and wetting behavior because the contact line (13) Nikolov, A. D.; Kralchevsky, P. A.; Ivanov, I. B. J. Colloid Interface Sci. 1986, 112, 122. (14) Kralchevsky, P. A.; Nikolov, A. D.; Ivanov, I. B. J. Colloid Interface Sci. 1986, 112, 132. (15) Li, D.; Cheng, P.; Neumann, A. W. Adv. Colloid Interface Sci. 1992, 39, 347. (16) Dussaud, A.; Vignes-Adler, M. Langmuir 1997, 13, 581. (17) Sto¨ckelhuber, K. W.; Radoev, B.; Schulze, H. J. Colloids Surf., A 1999, 156, 323. (18) Chen, P.; Susnar, S. S.; Amifazli, A.; Mak, C.; Neumann, A. W. Langmuir 1997, 13, 3035. (19) Wang, J. Y.; Betelu, S.; Law, B. M. Phys. Rev. E 2001, 63, 031601. (20) Checco, A.; Guenoun, P.; Daillant, J. Phys. Rev. Lett. 2003, 91, 186101. (21) Lin, F. Y. H.; Li, D.; Neumann, A. W. J. Colloid Interface Sci. 1993, 159, 86. (22) Li, D. Colloids Surf., A 1996, 116, 1. (23) Wang, J. Y.; Betelu, S.; Law, B. M. Phys. Rev. Lett. 1999, 83, 3677. (24) Pompe, T.; Herminghaus, S. Phys. Rev. Lett. 2000, 85, 1930. (25) Pompe, T. Phys. Rev. Lett. 2002, 89, 076102. (26) Aratono, M.; Kawagoe, H.; Toyomasu, T.; Ikeda, N.; Takiue, T.; Matsubara, H. Langmuir 2001, 17, 7344. (27) Matsubara, H.; Ikeda, N.; Takiue, T.; Aratono, M.; Bain, C. D. Langmuir 2003, 19, 2249.
10.1021/la040098l CCC: $30.25 © 2005 American Chemical Society Published on Web 08/13/2005
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Figure 1. Schematic illustration of an oil droplet (O) floating on the interface between air (A) and aqueous solution (W) phases: γab, interfacial tension of the a/b interface; R (β), lens angle between the A/O (O/W) interface and the plane containing the three-phase contact line; r, lens radius; τ, line tension. In this case, the water surface was effectively planar up to the contact line (i.e., the angle ψ = 0).
is always concerned with the wetting behavior and, moreover, the wetting transition may cause an abrupt change in line tension. The principle of the line tension measurement employed in this study is simple. A balance of forces acting on the contact line is described by the Neumann-Young equation1,4,28,29
γAO cos R + γOW cos β ) γAW -
τ r
(1)
where γAO, γOW, and γAW represent interfacial tensions, R and β represent the lens angles, r represents the lens radius, and τ represents the line tension, respectively (Figure 1). Furthermore, for sufficiently small angles, by taking the forces normal to the air/water surface at the contact line into account as proposed by Aveyard et al.,30 eq 1 is rewritten as follows:
(
γAO cos
)
(
)
γOWδ γAOδ τ OW + γ cos ) γAW r γOW + γAO γOW + γAO (2)
Here the dihedral angle is δ ) R + β. Thus, the slope of a straight line best fitted to the plots of the value of the left-hand side against r-1 yields a line tension. The γAO and γOW values were measured by the pendant drop method31 and are shown in ref 27. The accuracy of the pendant drop method was within (0.05 mN m-1. When we take advantage of the straightforward approach using eq 1, three interfacial tensions have to be measured with considerable accuracy on the order of micronewton. According to the method employed in this study, however, this problem was resolved by using the slope of a straight line drawn by eq 2 instead of the absolute values of γ. The δ and r values were estimated by interferometry for the simultaneous determination of their values, which Aveyard et al. have already applied to dodecane lenses containing dodecanol on a water surface with satisfactory precision.30 The line tension was estimated as a function of the molality of the surfactant at 298.15 K in the air/ hexadecane/aqueous solution of the dodecyltrimethylammonium bromide (DTAB) system. All materials for the experiments were thoroughly purified by the appropriate method as described elsewhere.26,27 We employed a BX60F microscope and an LMPlan FL 20 × BD reflectance objective with a working distance of 12 mm (Olympus Optical Co. Ltd.). A measurement cell for interferometry was newly and specially designed to prevent the evapora(28) Pethica, B. A. Rep. Prog. Appl. Chem. 1961, 46, 14. (29) Boruvka, L.; Neumann, A. W. J. Chem. Phys. 1977, 66, 5464. (30) Aveyard, R.; Clint, J. H.; Nees, D.; Paunov, V. Colloids Surf., A 1999, 146, 95. (31) Motomura, K.; Matubayasi, N.; Aratono, M.; Matuura, R. J. Colloid Interface Sci. 1978, 64, 356.
Figure 2. Plots of the left-hand side of eq 2 vs the reciprocal of the lens radius: (a) 0.505 and (b) 1.013 mmol kg-1. The solid line denotes the best fit due to the least-squares method for all of the data. Table 1. Values of the Line Tension at Various Molalities of the Surfactant molality (mmol kg-1)
line tension (10-12 N)
0.505 0.677 0.699 0.734 0.912 1.013 1.106
+8.04 +24.0 +10.1 +3.30 -24.8 -19.7 -138
tion of materials and to keep the three-phase equilibrium. A monochromatic light (546 nm) for the illumination was separated out from a mercury lamp through an interference filter. The lens image was processed and analyzed using Scion Image (Scion Corp.). Figure 2a shows the value of the left-hand side of eq 2, y, versus r-1 plots at 0.505 mmol kg-1. It is noted that the y values are inclined to decrease with increasing r-1. From the best-fitted linear equation for all of the data, the line tension was estimated to be +8.04 × 10-12 N at this concentration, of which the order coincides very well with the theoretical estimation (ca. 10-11-10-12 N). At 1.013 mmol kg-1, however, the y values increase with increasing r-1 as shown in Figure 2b. Consequently, we acquired a negative line tension of -19.7 × 10-12 N. All of the values at different molalities are summarized in Table 1 and plotted against molality in Figure 3. It should be noted that the line tension changes its sign from positive to negative around 0.8 mmol kg-1. A similar dependence
Figure 3. Plots of line tension vs molality.
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Figure 4. Image of hexadecane lenses left for 3 h on an aqueous solution: (a) 0.505 and (b) 1.013 mmol kg-1. A white bar equals 50 µm.
was reported by Toshev et al., although the experimental system was foam film.4 The reversal of sign was also supported by the following phenomenological observation. Figure 4 displays the image of lenses 3 h after some droplets of hexadecane were placed on the water surface. At 0.505 mmol kg-1 (Figure 4a), the smaller lenses gradually disappeared, and the larger lenses increased with time. At 1.013 mmol kg-1 (Figure 4b), however, the larger lenses were inclined to split into smaller ones. Because the line tension is regarded as a kind of free energy for making a unit length of the contact line,2 the positive one is expected to bring about the coalescence of the lens, and the negative one is expected to bring about the fission (or deformation) of the lens. Thus, the phenomenological observation of the clear
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change from coalescence to fission around 0.8 mmol kg-1 is consistent with the change in the sign of line tension around this concentration given in Table 1 and Figure 3. In our previous studies on wetting behavior of the same system,26,27 the transition from partial to the pseudopartial wetting was observed around 0.5 mmol kg-1. We expect that the transition from positive to negative line tension is attributable to this wetting transition, though there is a little gap between the transition concentrations. In 1992, Indekeu32 developed the theory of line tension from various aspects of wetting based on de Gennes’ review.33 In his theory, the line tension corresponds to the excess free energy caused by the deviation between the observed and idealized profile of the lens, where the latter obeys the Young-Laplace equation, near the contact line. The prediction of this theory was in agreement with the experiments on the line tension approaching a first-order wetting transition from partial to complete wetting on solid surfaces.19,23-25 The change in the sign of line tension at a first-order wetting transition concentration from partial to pseudo-partial wetting in our system was qualitatively explained by this theory. Further consideration will certainly reveal a close relationship between line tension and wetting behavior, and a more quantitative discussion using the refined theoretical studies34,35 should shed light on the origin of line tension from the viewpoint of intermolecular interaction near the contact line. In summary, we constructed a new apparatus and measured the line tension as a function of the molality of the surfactant at 298.15 K in the air/hexadecane/aqueous solution of a DTAB system. The experimental values of line tension were estimated to be 10-10-10-12 N and coincided with the theoretical estimation. Furthermore, it was found that the line tension changes its sign from positive to negative at around 0.8 mmol kg-1. The inversion of its sign was supported by the phenomenological observation of coalescence and fission of the lens. Taking our previous studies and theory by Indekeu into account, it was suggested that the reversal of the sign of line tension is attributable to the wetting transition. Thus, we could demonstrate clearly by means of our experiments the close relationship between line tension and the wetting transition. Currently, we are performing experiments in another system exhibiting wetting behavior similar to that in this system in order to confirm such a relationship. Acknowledgment. This work was supported by Grant-in-Aid for Scientific Research B(2) no. 16350075 from the Japan Society for the Promotion of Science. LA040098L (32) Indekeu, J. O. Physica A 1992, 183, 439. (33) de Gennes, P. G. Rev. Mod. Phys. 1985, 57, 827. (34) Getta, T.; Dietrich, S. Phys. Rev. E 1998, 57, 655. (35) Bauer, C.; Dietrich, S. Eur. Phys. J. B 1999, 10, 767.
