[ACS Symposium Series] Surfactant Adsorption and Surface Solubilization Volume 615 || Determination...

Chapter 24

Determination of Ultralow Interfacial Tension by Axisymmetric Drop-Shape Analysis

D. Y. Kwok1, P. Chiefalo1, B. Khorshiddoust1, S. Lahooti1, M. A. Cabrerizo-Vilchez2, O. del Rio1, and A. W. Neumann1

1Department of Mechanical Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario M5S 1A4, Canada

2Departamento de Fisica Aplicada, Universidad de Granada, Campus de Fuentenueva, 18071 Granada, Spain

It is shown that Axisymmetric Drop Shape Analysis (ADSA) is well-suited to study ultra-low interfacial tensions down to at least the order of 10-3 mJ/m2: The technique is not restricted to equilibrium interfacial tensions, it is also suitable for measuring the time dependence of ultra-low interfacial tensions in the presence of surface active materials. The capability of ADSA to measure ultra-low interfacial tensions is shown by forming inverted sessile drops for two liquid-liquid surfactant systems: Oleic acid in olive oil with aqueous solution of NaCl and NaOH and Dioctyl Sulfosuccinate (AOT) in aqueous solution of NaCl/water and n-heptane.

Many techniques have been developed to measure interfacial tensions and detailed descriptions of the methods can be found in Padday (7), Ambwani and Fort (2), Adamson (3), and Neumann and Good (4). Among the commonly used methods for interfacial tensions, drop shape methods are very promising; they are based on the idea that the shape of a sessile or pendant drop is determined by a combination of surface tension and gravity effects. When gravitational and surface tension effects are comparable, one can, in principle, determine the surface tension from the measurements of the shape of the drop or bubble. A general procedure is to form the drop or bubble under static conditions and then to make certain measurements of its dimensions, for example, from a photograph.

The advantages of using pendant and sessile drop methods are as follows. First, only small quantities of liquid are required. Second, they can be used to study both liquid-vapour and liquid-liquid interfacial tensions. The methods have been applied to materials ranging from organic liquids to molten metals and from

0097-6156/95/0615-0374$12.00/0 © 1995 American Chemical Society

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In Surfactant Adsorption and Surface Solubilization; Sharma, R.; ACS Symposium Series; American Chemical Society: Washington, DC, 1996.

24. KWOKETAL. Determination of Ultralow Interfacial Tension by ADSA 375

pure solvent to concentrated solutions. Equally satisfactory, both methods have been applied at low and high temperatures, at high pressures and under vacuum conditions. Since the profile of the drops can be rapidly recorded, these methods are used to determine the surface tension of aging systems, i.e., systems where the properties are changing with time.

Despite the experimental simplicity in using sessile and pendant drops for determining interfacial tension and contact angle, there are doubts remaining whenever high precision and consistency are needed. Usually, the cases of sessile and pendant drops are treated separately, and the experimental information has to be interpreted with different sets of tables. Such tables are those of Bashforth and Adams (5) for sessile drops, and of Foidham (6) for pendant drops, as well as other tables (7). The use of the tables is limited to drops of a certain size range and drops of a certain shape range. Hardand and Hartley collected numerous solutions for determining the interfacial tensions of axisymmetric liquid-fluid interfaces of different shapes and presented the results in tabulated form (8). A serious and perhaps major source of error in these methods is connected with input data selection. The description of the whole surface of the drop is reduced to the measurements of a few preselected critical points which are compatible with the use of the tables. These points are critical since they must be determined with high precision.

More recently, Rotenberg et al (9) have developed a drop shape technique called Axisymmetric Drop Shape Analysis (ADSA). It relies on a numerical integration of the Laplace equation of capillarity (see below). This numerical procedure unifies both the method of the sessile drop and the method of the pendant drop. There is no need for any table nor is there any restriction on the applicability of the method. It is a powerful and versatile methodology in interfacial energetics; it has been applied to drop size dependence of contact angles and line tension (70), contact angle measurements with an accuracy exceeding other methods by an order of magnitude (11), the pressure dependence of liquid/liquid interfacial tensions (72), film balance experiments with insoluble films (75) and a variety of studies on the time dependence of liquid/fluid interfacial tensions in the presence of surface active materials (14-16). ADSA has also been employed by other laboratories (17,18).

Theoretically, a drop profile can be generated from a known interfacial tension value, by numerical integration of the Laplace equation of capillarity. This procedure can be thought of as the reverse of ADSA, where ADSA determines the interfacial tension based on a given drop profile. It should be noted that determining the interfacial tension from a given drop profile by using ADSA is more complicated: it requires both numerical integration of the Laplace equation and least square optimization between the theoretical and experimental drop profiles (see later).

The purpose of this paper is to illustrate the applicability of ADSA to study ultra-low interfacial tensions. We began by looking for a system with very low interfacial tension from Adamson (3). It was found in the literature (79) that the interfacial tension of oleic acid in olive oil and aqueous solution of NaCl and

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376 SURFACTANT ADSORPTION AND SURFACE SOLUBILIZATION

NaOH should be very low, approximately in the order of 10*3 mJ/m2. However, using A D S A as the experimental technique, we found that the interfacial tension of this system appears to be two order of magnitude larger than that published by Harkins and Zollman (79). Doubts arose on whether A D S A can be used to measure ultra-low interfacial tensions. To investigate this further, we tried to find other independent means to estimate an interfacial tension based on another drop shape analysis, proposed by Malcom and Elliott (20). The interfacial tensions calculated from the scheme given by Malcom and Elliott (20) are of the same order of magnitude as our interfacial tension values.

As an alternative to an experimental test, we have generated a mathematically computed drop profile based on a given low interfacial tension; coordinates points were then taken from this profile as input data for ADSA. The output interfacial tension was found to be in excellent agreement with the input interfacial tension (see later). We, therefore, concluded that A D S A can be used to measure ultra-low interfacial tensions and that the interfacial tension values reported by Harkins and Zollman (79) are incorrect. More interfacial tension measurements were performed on Dioctyl Sulfosuccinate (AOT) in aqueous solution of NaCl/water and Λ-heptane for three different concentrations.

Theory of Axisymmetric Drop Shape Analysis

Axisymmetric Drop Shape Analysis (ADSA) is a technique to determine liquid-fluid interfacial tensions and contact angles from the shape of axisymmetric menisci, i.e., from sessile as well as pendant drops (9). The strategy employed is to fit the shape of an experimental drop to a theoretical drop profile according to the Laplace equation:

ΔΡ = γ (1)

where 7?j and R2 are the principal radii of curvature of the drop, and ΔΡ is the pressure difference across the curved interface. The surface tension γ is then computed from the best numerical fit to the Laplacian curve using non-linear least-squares optimization techniques. Figure 1 shows a typical theoretical sessile drop profile with a number of coordinates from an experimental profile. As described above, A D S A determines the operative surface tension by finding a best fit between the two profiles.

Apart from local gravity and densities of liquid and fluid phases, the only information required by A D S A is several arbitrary but accurate coordinate points selected from the drop profile. To achieve rapid and accurate data acquisition and preprocessing, an automatic digitization technique utilizing recent developments

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24. K W O K E T A L . Determination of Vltralow Interfacial Tension by ADSA 377

in digital image acquisition and analysis has been used (21J22). Computer software has been developed to implement this method and computational results provide the values of interfacial tension, drop volume, surface area, radius of curvature at the apex and, in the case of a sessile drop, contact angle and the radius of the three phase contact line.

Materials and Experimental Set-Up

Materials. Oleic Acid in Olive Oil and Aqueous Solution of NaCl and NaOH.

Oleic acid and olive oil were supplied from Sigma Co. with 99% purity and with a "highly refined" purity (Cat. No. 015000), respectively. A concentration of 1 mM of oleic acid in olive oil was used to form an inverted sessile drop in 0.15 M of NaCl, (Fisher Sci. Co.) and 1 mM of NaOH, (BDH Chem. Ana.).

Dioctyl Sulfosuccinate (AOT) in Aqueous Solution of NaCl/Water and it-Heptane. Dioctyl Sulfosuccinate (AOT) was supplied by Aldrich Co. with 98% purity. A stock solution (0.001 mole/litre) of AOT in aqueous solution of 0.0513 M NaCl/water was always used. Three different AOT concentrations were used: 0.415 mM, 0.410 mM and 0.420 mM in aqueous solution of NaCl/water were produced by dilution from the stock solution and subsequently used to form inverted sessile drops in n-heptane (Aldrich Co., 99% purity). Pendant drops or inverted pendant drops are very difficult to work with at very low interfacial tensions because the drops detach very easily from the capillary. The advantage of using an inverted sessile drop is that it is easier to manipulate than a sessile drop when the interfacial tension is very low.

Experimental Set-Up. A block diagram of the experimental set-up for ADSA is shown in Figure 2. As shown in this diagram, a Cohu 4800 monochrome camera is mounted on a Wild-Heerbrugg M7S microscope. The video signal of the pendant drop is transmitted to a digital video processor, which performs the frame grabbing and digitization of the image with 256 gray levels for each pixels, where 0 represents black and 255 represents white. A SPACRstation 10 computer is used to acquire images from the image processor and to perform the image analysis and computation. The rate of image acquisition for the present experiment is one image every two to five seconds.

Figure 3 shows the experimental apparatus for ultra-low interfacial tension measurements. As can be seen, an inverted sessile drop of liquid 1 with lower density can be formed from a steel capillary onto a glass surface inside a quartz cuvette containing liquid 2 with higher density. For the AOT system, AOT in aqueous solution of NaCl/water is liquid 1 and /i-heptane is liquid 2; for the oleic acid system, oleic acid in olive oil is liquid 1 and aqueous solution of NaCl and NaOH is liquid 2.

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x

Figure 1. A schematic sessile drop profile (solid line) with a number of coordinates from an experimental drop profile (circles). The best fit between the two profiles identifies the operative interfacial tension. a\ is the perpendicular distance between the experimental and theoretical coordinates.

ADSA-P Pendant Drop digitizer

diffuscr

light \ pendant drop

computer •<=— terminal

microscope and video camera

ADSA-P Sessile Drop

diffuser

light source

sessile drop

microscope and video camera

digitizer monitor digitizer monitor

A

computer terminal computer terminal computer

Figure 2. A schematic of an experimental set-up for pendant drop and sessile drop experiments.

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KWOK ET AL. Determination of Ultralow Interfacial Tension by ADSA

Liquid 2

* \ I , Liquid 1

1. Inverted Pendant Drop 2. Inverted Sessile Drop 3. Steel Capillary 4. Glass Surface 5. Teflon Screw 6. Teflon Support 7. Quartz Cuvette

System 1: Liquid 1: AOT in Solution of NaCl/Water Liquid 2: n-Heptane

System 2: Liquid 1: Oleic Acid in Olive Oil Liquid 2: Solution of NaCl and NaOH

Figure 3. A schematic of an apparatus to form inverted sessile drops for ultra-low interfacial tension measurements.

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Results and Discussion

Oleic Acid in Olive Oil and Aqueous Solution of NaCl and NaOH. Figure 4 shows the results of 1 mM oleic acid in olive oil with 0.15 M of NaCl and 1 mM of NaOH. A picture of an inverted sessile drop for this experiment is shown in Figure 5. As can be seen in Figure 4, the interfacial tension decreases from about 0.8 mJ/m2 to 0.2 mJ/m2 in 10 minutes. It should be noted that this time dependent behaviour cannot be readily studied by the conventional ultra-low interfacial tension technique, i.e., the spinning drop method.

The result of this experiment was compared with the interfacial tension values in the literature (79). It was found that our interfacial tension values are two orders of magnitude larger than those published by Harkins and Zollman (79). We, therefore, investigated an alternative, independent means to estimate the interfacial tension from the drop shape: The scheme proposed by Malcolm and Elliott (20) to estimate interfacial tension requires knowledge of the height and diameter of the sessile drop with a contact angle of 180°. It was found that the interfacial tensions calculated from the scheme given by Malcolm and Elliott (20) are of the same order of magnitude as our interfacial tension values shown in Figure 4, with a discrepancy ranging from 9% to 27%: the interfacial tensions calculated from the scheme of Malcolm and Elliott tends to decrease as the contact angle decreases from 180°; the interfacial tensions obtained from ADSA are very consistent and, of course, independent of the contact angle values.

We have also calculated a mathematically computed sessile drop profile based on a low interfacial tension value. Figure 6 shows such computed sessile drop profile generated by the numerical integration of the Laplace equation of capillarity, using an interfacial tension value of 0.001 mJ/m2 and a density difference Ap between the liquid and fluid phases of 0.05 g/cm3. Using drop profile coordinates from Figure 6 as input parameters, ADSA yielded an output interfacial tension value of 0.001 mJ/m2, which is, of course, in perfect agreement with the input value of interfacial tension used for the mathematical generation of the drop. In view of this, ADSA should, in principle, be able to measure ultra-low interfacial tensions. We concluded that the interfacial tension values reported by Harkins and Zollman (79) are incorrect.

Dioctyl Sulfosuccinate (AOT) in Aqueous Solution of NaCl/Water and it-Heptane. Figure 7 shows the interfacial tension results of 0.410 mM of AOT in aqueous solution of 0.0513 M NaCl/water and n-heptane. As shown in this figure, the interfacial tension decreases from about 0.25 mJ/m2 to 0.06 mJ/m2 in 3 minutes. It can be seen that an equilibrium of the interfacial tension cannot be reached in this period. A picture of an inverted sessile drop for 0.41 mM of AOT in aqueous solution of NaCl/water and n-heptane is shown in Figure 8.

The same type of experiment was performed for 0.415 mM of AOT in aqueous solution of NaCl/water and w-heptane. Figure 9 shows the result of this experiment: The interfacial tension decreases from about 0.05 mJ/m2 to an equilibrium value of 0.01 mJ/m2 in 12 minutes.

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Figure 4. Interfacial tension vs. time for 1 mM of oleic acid in olive oil in the aqueous solution of 0.15 M of NaCl and 1 mM of NaOH.

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Figure 5. A picture of an inverted sessile drop for 1 mM of oleic acid in olive oil in the aqueous solution of 0.15 M of NaCl and 1 mM of NaOH. The upper part of the picture is a reflection of the actual drop due to minor image effect of the glass surface. The contact diameter of this drop is 0.150 cm.

-0.05

1 0.00 N

0.05

Y= 0.001 mJm Ap = 0.05 g cm

-0.10 -0.05 0.00 X(cm)

0.05 0.10

Figure 6. A theoretical sessile drop profile generated by using an interfacial tension of 0.001 mJ/m2 and a density difference of 0.05 g/cm3.

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0.25

100 150 Time [Sec]

Figure 7. Interfacial tension vs. time for 0.410 mM of AOT in aqueous solution of 0.0513 M of NaCl/water and n-heptane.

250

Figure 8. A picture of an inverted sessile drop for 0.410 mM of AOT in aqueous solution of 0.0513 M of NaCl/water and n-heptane. The upper part of the picture is a reflection of the actual drop due to mirror image effect of the glass surface. The contact diameter of this drop is 0.035 cm.

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0.00 1 1 1 • 1 • 1 • 1

200 400 600 800 Time [Sec]

Figure 9. Interfacial tension vs. time for 0.415 mM of AOT in aqueous solution of 0.0513 M of NaCl/water and n-heptane.

Figure 10 shows the results of 0.420 mM of AOT in aqueous solution of NaCl/water and n-heptane. It can be seen that the interfacial tension decreases from about 0.026 mJ/m2 to 0.006 mJ/m2 in 2 minutes: Increasing the AOT concentration decreases both the interfacial tension value and the time required to reach equilibrium.

The above results suggest that not only can ADSA be used to determine ultra-low interfacial tension down to the order of 10"3 mJ/m2, it can also be employed to study time dependent behaviour of such systems in the presence of surface active materials. Since the results shown in Figure 7 did not reach equilibrium, only the results shown in Figures 9 and 10 could be compared with those published by Aveyard et al (23) who used the spinning drop technique: The interfacial tension values reported by Aveyard et al (23) were estimated from their graph to be = 0.01 mJ/m2 and « 0.003 mJ/m2, respectively, for 0.415 mM and 0.420 mM of AOT in the aqueous solution of 0.0513 M NaCl/water and n-heptane, in good agreement with the results shown in Figures 9 and 10.

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24. KWOK ET AL. Determination of Ultralow Interfacial Tension by ADSA 385

0.030

0.000 80

Time [Sec]

Figure 10. Interfacial tension vs. time for 0.420 mM of AOT in aqueous solution of 0.0513 M of NaCl/water and w-heptane.

Conclusions

Axisymmetric Drop Shape Analysis (ADSA) is a novel experimental technique which can be used to study ultra-low interfacial tensions. We have shown that ADSA can be used to determine ultra-low interfacial tension down to the order of 103 mJ/m2. Not only the equilibrium values, but also the time dependence of ultra-low interfacial tensions in the presence of surface active materials can be studied.

Acknowledgments

This research was supported by the Natural Science and Engineering Research Council of Canada (No. A8278), and a University of Toronto Open Fellowship (D.Y.K). One of the authors (M.A.C) would like to thank the Direcci6n General de Investigaci6n Cientifica y Tdcnica (DGICYT) PR 94-047 for financial support

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Literature Cited

1. Padday, J.F., In Surface and Colloid Science, Editor, Matijevic, E., Ed.; Wiley, New York, 1986, Vol. 1; p.101. 2. Ambwani, D.S. and Fort, Jr. T., In Surface and Colloid Science, Editor, Good, R.J. and Stromberg, R.S., Eds.; Plenum Press, New York, 1979, Vol. 11; p.93. 3. Adamson, A.W., In Physical Chemistry of Surfaces, John Wiley & Sons, New York, 1990, 5th Ed. 4. Neumann, A.W. and Good, R.J., In Surface and Colloid Science, Editor, Good, R.J. and Stromberg, R.S., Eds.; Plenum Press, New York, 1979, Vol. 11, p.31. 5. Bashforth, F. and Adams, J.C., In An Attempt to test the Theories of Capillary Action, Cambridge Univ. Press and Deighton Bell & Co, Cambridge, 1883. 6. Fordham, S., Proc. Ro. Soc. London, 1948, 194A, p.1. 7. Padday, J.F., In Surface and Colloid Science, Editor, Matijevic, E. and Eirich, F.R., Eds; Wiley-Interscience, New York, 1969, Vol. 1, p.151. 8. Hartland, S. and Hartley, R.W., In Axisymmetric Fluid-Liquid Interfaces, Elsevier, Amsterdam, 1976. 9. Rotenberg, Y., Boruvka, L., and Neumann, A.W., J. Colloid Interface Sci., 1983, 93, pp.l69-183. 10. Gaydos, J.A., and Neumann, A.W., J. Colloid Interface Sci., 1987, 120, pp.76-86. 11. L i , D., and Neumann, A.W., J. Colloid Interface Sci., 1992, 148, pp.190-200. 12. Susnar, S.S., Hamza, H.A., and Neumann, A.W., Colloids & Surfaces A: Physicochemical and Engineering Aspects, 1994, 89, pp.169-180. 13. Kwok, D.Y., Vollhardt, D., Miller, R., L i , D., and Neumann, A.W., Colloids & Surfaces A: Physicochemical and Engineering Aspects, 1994, 88, pp. 51-58. 14. Voigt, A., Thiel, O., Williams, D., Policova, Z., Zingg, W., and Neumann, A.W., Colloids & Surfaces, 1991, 58, pp.315-326. 15. Miller, R., Sedev, R., Schano, K-H., Ng, C., and Neumann, A.W., Colloids & Surfaces, 1993, 69, pp.209-216. 16. Miller, R., Policova, Z., Sedev, R., and Neumann, A.W., Colloids & Surfaces A: Physicochemical and Engineering Aspects, 1993, 76, pp.179-185. 17. Busscher, H.J., van der Vegt, W., Noordmans, J.M., Schakenraad, J.M., and van der Mei, H.C., Colloids & Surfaces, 1991, 58, p.229. 18. van der Vegt, W., van der Vegt, H.C., and Busscher, H.K., J. Colloid Interface Sci., 1993, 156, p.129. 19. Harkins, W., and Zollman, H., Amer. Chem. Soc., 1926, 48, pp.69-80. 20. Malcolm, J.D., and Elliott, C.D., Can. J. Chem., 1980, 58, pp.151-153. 21. Cheng, P., L i , D., Boruvka, L., Rotenberg, Y., and Neumann, A.W., Colloids & Surfaces, 1990, 43, pp.151-167. 22. Cheng, P., Ph. D. Thesis, University of Toronto, Toronto, Canada, 1990. 23. Aveyard, R., Binks, B.P., Lawless, T.A., and Mead, J., Can. J. Chem., 1988, 66, pp.3031-3037. RECEIVED May 3, 1995

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