Surfactant Adsorption and Surface Solubilization - American Chemical

Chapter 24

Determination of Ultralow Interfacial Tension by Axisymmetric Drop-Shape Analysis 1

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Downloaded by UNIV MASSACHUSETTS AMHERST on October 11, 2012 | http://pubs.acs.org Publication Date: May 5, 1996 | doi: 10.1021/bk-1995-0615.ch024

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D. Y. Kwok , P. Chiefalo , B. Khorshiddoust , S. Lahooti , M. A. Cabrerizo-Vilchez , O. del Rio , and A. W. Neumann 1

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Department of Mechanical Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario M5S 1A4, Canada Departamento de Fisica Aplicada, Universidad de Granada, Campus de Fuentenueva, 18071 Granada, Spain 2

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 mJ/m : 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. -3

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


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KWOKETAL.

Determination of Ultralow Interfacial Tension by ADSA

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

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

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NaOH should be very low, approximately in the order of 10* mJ/m . 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 A D S A . 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 R 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 2


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KWOKETAL.

Determination of Vltralow Interfacial Tension by ADSA

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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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

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light

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pendant drop

computer

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Surfactant Adsorption and Surface Solubilization - American Chemical

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