Axisymmetric drop shape analysis as a film balance

COLLOIDS AND ELSEVIER

Colloids and Surfaces A: Physicochemical and Engineering Aspects 88 (1994) 51-58

SURFACES

Axisymmetric drop shape analysis as a film balance D.Y. Kwoka, D. Vollhardtb, R . Miller', D . Lie, A.W. Neumann" 'Department of Mechanical Engineering, University of Toronto, 5 King's College Road, Toronto, Ont . M5S

I A4, Canada 'Max -Planck-Institut far Kolloid- and GrenzJlachenforschung, Rudower Chaussee 5, D-12489 Berlin-Adlershof, Germany `Department of Mechanical Engineering, University of Alberta, Edmonton, Alta . T6G 2G8, Canada

Received 3 August 1993 ; accepted 30 November 1993

Abstract A pendent drop experiment is used to demonstrate the possibility of using a surface tension measurement technique, axisymmetric drop shape analysis-profile (ADSA-P), as a film balance . Owing to the fact that both the values of the surface tension and the surface area are outputs of ADSA-P, a continuous measurement of the surface tension as a function of the surface area is possible using a motor-driven syringe to change the drop volume . In the case of an insoluble monolayer on the drop surface, the surface tension as a function of the surface area constitutes de facto film balance measurements . As an illustration, such "film-balance" measurements on a monolayer of octadecanol are presented and compared with conventional film balance measurements . It is shown that the results found by ADSA-P are in good agreement with those from the conventional film balance measurements . As a film balance, ADSA-P offers a range of possibilities which are discussed briefly . Keywords : Drop shape analysis ; Film pressure; Octadecanol ; Surface tension

1 . Introduction In this paper we propose to explore the possibility of using a technique called axisymmetric drop shape analysis (ADSA), which was developed originally for surface tension measurements, as a film balance. ADSA is a user-friendly methodology for determining the interfacial tension, contact angle, drop surface area and drop volume based on a drop profile . The methodology of ADSA consists of two parts : one is ADSA-P [1] and the other is ADSA-CD [2], where P and CD stand for profile and contact diameter of a drop respectively . The difference between the two approaches is that the numerical calculation by ADSA-P requires the profile of a * Corresponding author. 0927-7757,194/$07 .00 © 1994 Elsevier Science B .V. All rights reserved SSDI 0927-7757(94)02763-1

sessile or pendent drop, whereas ADSA-CD, which is a contact angle method, requires the contact diameter of a sessile drop; ADSA-CD was developed originally [2] for a sessile drop with a low contact angle, say below 20', because the precision of ADSA-P is limited as it is more difficult to acquire accurate coordinate points along the edge of a (sessile) drop profile . The modification [3] and various applications [4-6] of ADSA-CD have been described elsewhere. ADSA-P has been used to perform accurate measurements of the surface tensions and contact angles in a variety of situations . It can be used for both air-liquid and liquid-liquid systems; it is particularly suited for the study of the dependence on time [7], temperature [8] and pressure [9] of interfacial tensions and contact angles . Various surface tension and contact angle measurements



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using ADSA-P have been performed by other workers [10,11] . In addition, ADSA-P has been used in the study of film relaxation of surfactant adsorption layers [12] . The mechanics of this relaxation is performed by suddenly changing the drop volume and hence the drop surface area of a pendent drop while photographs of the drop profiles are taken. Thus the instantaneous response of these interfacial tensions to surface area changes can be obtained by ADSA-P after analyzing the drop profiles. This response of the interfacial tension provides information about the interfacial dilational elasticity of the interface and the exchange of surfactant between the bulk and the interface. Since interfacial tension and drop surface area are both outputs of ADSA, measurements corresponding to the film balance measurements can be performed by changing the drop volume in a controlled manner.

2. The principle of ADSA-P

3 . Measurements of surface pressure by ADSA-P

ADSA-P is a technique for determining liquid-fluid interfacial tensions and contact angles from the shape of axisymmetric menisci, i .e . from sessile as well as pendent drops. The strategy employed is to construct an objective function which expresses the deviation of the physically observed curve from a theoretical Laplacian curve, i.e . a curve satisfying the Laplace equation of capillarity :

4

1 1 _+_ =AP R, R2

1

Apart from local gravity and the densities of the liquid and the fluid phases, the only input information required by ADSA-P is several arbitrary but accurate coordinate points selected from the drop profile . Specifically, it is not necessary to identify the apex of the drop profile, or the drop width. To achieve rapid and accurate data acquisition and preprocessing, an automatic digitization technique utilizing recent developments in digital image acquisition and analysis has been developed [13,14] . Experience has shown that the accuracy of surface tension measurements can be improved with sub-pixel resolution of the drop profile coordinates . Further significant sources of error are optical distortion due to the camera and the lenses . These errors have been eliminated by ADSA-P, as is discussed in Ref. 14 . The output of the ADSA-P program will provide values of the surface tension, drop volume, surface area, and in the case of sessile drops, the radius of the three-phase contact line and the contact angle .

(1)

where y is the interfacial tension, R 1 and R 2 are the principal radii of curvature of the drop, and AP is the pressure difference across the curved interface . Experimental drop profiles are matched with the theoretical drop profiles, where the latter are calculated with the surface tension as one of the adjustable parameters. The best match identifies the correct, i .e. operative, surface tension . Details of these mathematical procedures can be found elsewhere [1,13] .

Owing to the fact that both surface tension and surface area are outputs of ADSA-P, the continuous measurement of surface tension as a function of surface area is possible using a motordriven syringe to change the drop volume (see later) . In this study, a pendent drop is used ; a sessile drop, grown from the bottom, can be employed, but the solid substrate used has to be perfectly smooth and homogeneous ; otherwise, the drop will not grow axisymmetrically . The possibility of using surface tension measurements to obtain the surface pressure depends on the well known relationship n = Yo - Y

(2)

where n is the surface pressure, y o is the surface tension of the pure liquid and y is the surface tension of the liquid covered with the monolayer . Clearly, the two types of measurement, film balance and ADSA-P, as explained above, are equivalent . As is well known (see Refs . 15 and 16), the film balance is used for measurements of the surface pressure n as a function of surface area . The film



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D. Y. Kwok et at /Colloids Surfaces A : Physicochent Eng. Aspects 88 (1994) 51-58

(a)

(b)

Fig. 1 . Pendent drops with an insoluble monolayer (octadecanol) as reproduced on a laser printer : (a) an initial drop before compression; (b) the same drop after compression .

balance contains pure water on one side and water covered with an insoluble monolayer on the other side . The two sides are separated by a floating barrier that can be used to compress and expand the film . The corresponding compression and expansion of the film by ADSA-P can be performed by decreasing and increasing the volume of the pendent drop continuously . This is accomplished by a motor-driven syringe which will be discussed later. The continuous change in the drop volume will, of course, lead to the change in the drop surface area . Figures la and lb show the compression analogue of the film, using ADSA-P. Figure la shows an initial drop of pure water with an insoluble monolayer and Fig. lb shows the same drop after some volume change.

4. Experimental set-up and procedure A block diagram of the original experimental set-up for ADSA-P is shown in Fig. 2 . As shown in the diagram, a Cohu 4800 monochrome camera d Run

O ::~_ I pelt fight -

~ algid

-

at

µ

, ms

mice ox

om,

W

Fig. 2 . Experimental set-up for pendent drop measurement by ADSA-P.



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D. Y. Kwok et al. /Colloids Surfaces A : Physicochem Eng. Aspects 88 (1994) 51-58

is mounted on a Wild-Heerbrugg M7S microscope . The video signal of the pendent drop is transmitted to a digital video processor, which performs the frame grabbing and digitization of the image with 256 gray levels for each pixel, where 0 represents black and 255 represents white. A SPARCstation 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 per second. Continuous measurement of the surface tension as a function of surface area can be performed by a minor modification of the original ADSA-P setup; the key element of the modification is a motordriven syringe. The motor drives a lead screw back or forth continuously, pulling or pushing the syringe plunger. This motion of the syringe will lead to a continuous change of volume of the pendent drop. The rate of volume change can be adjusted by the speed of the motor, by adjusting the voltage from a voltage controller . A crucial part of the experiment is the deposition of the insoluble surfactant onto the drop surface .

A few photographs of a pure water drop are taken before the deposition of the insoluble surfactant in order for ADSA-P to determine the surface tension of the pure water, y o. The desired amount of purified octadecanol is then weighed and dissolved in heptane as the solvent . The initial drop of pure water has to be small so as to prevent it from falling off due to the deposition of the solution . By using a digital micropipette, a known amount of the solution and hence of the insoluble surfactant can be deposited onto the surface of the small drop . After the deposition, the complete evaporation of the heptane on the drop surface takes place in approximately 20 s. This is shown in Fig. 3 where the surface tension ofpure water falls from 72.5 to 58 mJ m - 2 after the deposition of pure heptane, and then drifts back up again as the heptane evaporates . In the actual experiments, 5 min are allowed to elapse so as to ensure complete evaporation of the heptane before the actual experiment is started . The pendent drop, after deposition of the solution and evaporation of the solvent, carries an insoluble monolayer and can be slowly

75

o•

0*0*00 .006 . .0o 0

70

55 20

40 Time [sec]

60

80

Fig . 3. Surface tension as a function of time after the deposition of octadecanol dissolved in heptane .



D. Y. Kwok er al. /Colloids Surfaces A : Physicochem. Eng. Aspects 88 (1994) 51-58

lowered into the cuvette. The purpose of using a cuvette is to isolate the drop from the environment and to prevent contamination . The drop is now made as large as possible, in order to be in the gas-analogue state of the film . Photographs of the drop are then acquired while the drop volume is decreased continuously by the motor-driven syringe. Once the drop has become very small, the polarity of the voltage controller is reversed so that the motor turns in the opposite direction. Thus the drop volume and hence the drop surface area are increased . To check the reproducibility of the results, the same cycle of compression and expansion as described above can be repeated . 5. Results and discussion A typical result for the compression of a film of octadecanol on water, yielding the surface tension as a function of surface area at a rate of approximately 7 A' per molecule per minute is shown in Fig. 4. It can be seen that the surface tension starts

55

from about 72 .8 mJ m-2 and reaches a low value m"2 of 28 mJ as the film is compressed . This plot of the surface tension as a function of surface area can be transformed into the corresponding surface pressure as a function of area per molecule, by using Eq . (2) and a known amount of insoluble surfactant on the drop surface . The corresponding plot is shown in Fig . 5. To illustrate the reproducibility of the results, experiments were repeated at the end of the cycle ; circles and squares shown in Fig . 5 represent runs 1 and 2 respectively ; good reproducibility is observed . As shown in this figure, the surface pressure starts at 0 mJ m-2 and reaches about 45 mJ m-2 as the film is compressed. Owing to the limited range in the present voltage controller, in addition to the rate of approximately 7 A 2 per molecule per minute, only rates of approximately 5 and 9 A2 per molecule per minute have been studied . Results show that the n-A (where A is area per molecule) curves agree well with that obtained at approximately 7 A 2 per molecule per minute .

80.0

70.0

50.0 O--o Compression

30.0

0 .30

0 .35

0.40 Surface area (cm')

0 .45

0 .50

Fig. 4 . Surface tension as a function of surface area obtained by ADSA-P from the measurement of a pendent drop with an octadecanol monolayer (rate of compression, approximately 7 A2 per molecule per minute) .



D. Y. Kwok et allColloids Surfaces A : Physicochem . Eng. Aspects 88 (1994) 51-58

56 50 .0

40 .0 40.0€ 30 .0 E

E

E

N

30.0 -

G.

t 7 0,

20.0

10 .0 10.0 0 .0 Area per molecule (A' per molecule) Fig. 5 . A compression-expansion isotherm from the measurement of a pendent drop with an octadecanol monolayer (rate of compression, approximately 7 A' per molecule per minute, experimental technique, ADSA-P).

By using part of the same sample of octadecanol, and the same solvent, heptane, a plot of surface pressure as a function of area per molecule obtained from conventional film balance measurements at a rate of 5 A2 per molecule minute is shown in Fig. 6. Comparing Figs . 5 and 6, it is apparent that the results from ADSA-P are in good agreement with those from the conventional film balance measurements. The main limitation of ADSA-P as a film balance might well be the accuracy of the quantity of liquid and spreadable material delivered onto the drop surface : much smaller amounts of material need to be delivered onto the pendent drop than on the liquid surface in the film balance, possibly causing a larger relative error . Such errors would manifest themselves in errors in the limiting molecular areas, or, in other words, in an uncontrolled shift of the experimental curve along the x axis . With respect to the y axis, i.e . the surface pressure or the surface tension, there is no reason to believe that surface

I

24.0 26 .0 Area per molecule (A per molecule)

28 .0

Fig . 6. A compression-expansion isotherm for the a-A curve by using an insoluble surfactant monolayer (octadecanol) at a rate of 5 A2 per molecule per minute (technique, conventional film balance) .

tension measurement through ADSA is less accurate than film pressure measurement . However, as far as the present measurement is concerned, we note that both Figs . 5 and 6 yield, by means of the customary extrapolation, a limiting molecular area of approximately 23.2 A2. A further limitation of ADSA as a film balance might be expected to occur because of the indirect way in which the drop surface area is changed : a constant rate of drop volume change may not necessarily yield a constant rate of change in the drop surface area . In order to elucidate this point, changes in drop volume and drop surface area as a function of time are plotted in Fig. 7 for the data of Fig . 4. Circles and squares in Fig . 7 represent the drop volume and the surface area respectively . It is apparent that the rate of change in the drop volume is linear, . i .e. constant, as expected . Surprisingly, the rate of change in the drop surface



D . Y. Kwok et at /Colloids Surfaces A : Physicochem. Eng. Aspects 88 (1994) 51-58 0 .60

0 .040

6

57

0 .035

0 .55

0 .030

0 .50

0 0 .025 0 0 .020

0 .40

0 .015

0 .35

0 .010

50 .0

100 .0

150 .0

Time [Sec] Fig . 7 . Drop volume and drop surface area as a function of time obtained by ADSA-P from the measurement of a pendent drop with an octadecanol monolayer. 0, volume; D, surface area. Resulting rate of surface area change up to 100 s : 7 .2 per molecule per minute .

A2

area is also found to be perfectly linear up to about 100 s. Consequently, the precise rate of surface compression is 7 .2 A2 per molecule per minute . At approximately 100 s. the change in surface area with time undergoes a rather abrupt change . While the drop volume continues to change linearly, the surface area remains almost constant . For comparison purposes, the point corresponding to 100 s is marked "A" in Fig . 4 . Figure 7 indicates that, after approximately 100 s of compression, the film is fairly closely packed and has become essentially incompressible . The decrease in volume at constant surface area can, of course, only be accommodated by a very steep decrease in the surface tension . At this point, it is apparent that the surface tension measurements may provide an insight into the behaviour of closely packed films which cannot be readily achieved with a film balance ; the film balance changes the surface area a priori . The film may very quickly collapse. In the pendent drop technique, however, the compression is much more

gentle, occurring by means of a volume change which may or may not cause a surface area change but will certainly increase the surface pressure . The conventional determination of the limiting molecular area may have difficulties because of the presence of curvature in the rr-A curve, and there may be uncertainties in the results obtained . Langmuir and Schaefer [17] criticized the procedure on the basis that "there seems to be no theoretical reason for attaching particular significance" to the extrapolated limiting molecular area . From the perspective of Fig . 7, there is no reason to determine the limiting molecular area by means of an extrapolation; rather, the limiting area is given by the essentially constant limiting drop surface area and knowledge of the total number of molecules . This information yields a limiting molecular area for octadecanol of 22 .7 A2, i.e. a value which is approximately 0 .5 A2 smaller than that obtained by conventional extrapolation . Apart from the above differences between the



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V . Y. Kwok et aL,iColloids Surfaces A : Physicochem . Eng. Aspects 88 (1994) 51-58

conventional film balance and ADSA, it is to be expected that ADSA will have certain advantages . First, only small quantities of liquid and spreadable material are required . This is particular important if the materials are rare or expensive . Next, while conventional film balance measurements are restricted to liquid/gas interfaces, ADSA measurements can be, and have been, readily performed with liquid-liquid systems [9], i .e . films at liquidliquid interfaces can be studied . Furthermore, ADSA measurements are not restricted to insoluble films : soluble films can be studied as well [12] . Finally, environmental control (contamination, temperature and pressure) is a relatively straightforward matter; ADSA-P can be used to study the pressure-dependence [9] or the temperaturedependence [8] of the interfacial tension, and hence the surface pressure, by means of appropriate cells . Conventional film balance measurements with water can become difficult at temperatures above approximately 60'C because of evaporation . For such purposes, measurements in a pressure/ temperature cell at slightly elevated pressures might offer attractive alternatives . 6 . Acknowledgements This work was supported by a grant from the Medical Research Council of Canada (MT-5462) .

7. References [1]

Y. Rotenberg, L . Boruvka and A . W. Neumann, J . Colloid Interface Sci, 93, (1983) 169 . [2] F .K . Skinner, Y . Rotenberg and A.W . Neumann, J . Colloid Interface Sci ., 130(1) (1989) 25 . [3] E . Moy, P . Cheng, Z . Policova, S. Treppo, D. Kwok, D.R . Mack, P .M . Sherman and A .W . Neumann, Colloids Surfaces, 58 (1991) 215. [4] W.C. Duncan-Hewitt, Z. Policova, P. Cheng, E .I . VarghaButler and A .W . Neumann, Colloids Surfaces, 42 (1989) 391 . [5] B . Drumm, A.W. Neumann, Z . Policova and P.M . Sherman, Colloids Surfaces, 42 (1989) 289 . [6] B . Drumm, A.W . Neumann, Z . Policova and P .M . Sherman, J. Clin. Invest., 84 (1989) 1588 . [7] A. Voigt, 0 . Thiel, D . Williams, Z . Policova, W . Zingg and A .W . Neumann. Colloids Surfaces, 58 (1991) 315 . [8] J .K. Spelt, D.R . Absolom, and A .W. Neumann, Langmuir, 2 (1986) 620 . [9] S .S . Susnar, H .A. Hamza and A .W . Neumann, Colloids Surfaces A : Physicochem . Eng . Aspects, in press . [10] H .J. Busscher, W . van der Vegt, J . Noordmans, J .M . Schakenraad and H .C. van der Mei, Colloids Surfaces, 58 (1991) 229. [11] W. van der Vegt, H .C . van der Mei and H.J. Busscher, J . Colloid Interface Sci ., 156 (1993) 129. [12] R. Miller, R. Sedev, K.-H . Schano, C . Ng and A.W. Neumann, Colloids Surfaces, 69, (1993) 209 . [13] P . Cheng, D. Li, L. Boruvka, Y . Rotenberg and A.W . Neumann, Colloids Surfaces, 43 (1990) 151 . [14] P . Cheng . Ph .D . Thesis, University of Toronto, Canada, 1990. [15] A.W . Adamson, Physical Chemistry of Surfaces, 4th edn ., Wiley, New York, 1982 . [16] G.L . Gaines, Jr ., Insoluble Monolayers at Liquid-Gas Interfaces, Interscience, New York, 1966 . [17] 1. Langmuir and V .J . Schaefer, J . Am . Chem . See, 59 (1937) 2400.