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Invasive and Noninvasive Measurements of Dynamic Surface Tensions Samantha Manning-Benson and Colin D. Bain* Physical & Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, U.K.
Richard C. Darton Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, U.K.
Donal Sharpe, Julian Eastoe, and Paul Reynolds School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, U.K. Received May 5, 1997. In Final Form: September 11, 1997X Dynamic surface tensions have been measured for hexadecyltrimethylammonium bromide solutions in an overflowing cylinder by three independent methods. The surface tensions are derived by two noninvasive techniques, surface light scattering and ellipsometry, agreed well over the entire concentration range. Surface tensions determined by the classical Wilhelmy plate technique also agreed with the noninvasive measurements provided that the plate was completely wetted by the solution.
Introduction The dynamic surface tension, σdyn, plays an important role in many physical processes including wetting, coating, foaming, and two-phase flow. A range of techniques has been developed for the measurement of σdyn.1-4 Some of these, like the Wilhelmy plate (WP) and du Nou¨y ring, are invasive measurements while others, such as the maximum bubble pressure and oscillating jet, are noninvasive. An important concern with invasive techniques is the extent to which the surface is perturbed by the measurement. In this Letter, we report values of σdyn for solutions of hexadecyltrimethylammonium bromide (CTAB, critical micelle concentration (cmc) ) 0.92 mmol dm-3) in an overflowing cylinder (OFC).5 Historically, measurements of σdyn in an OFC have employed the classical WP technique or related methods.6-12 Here we compare WP results with noninvasive measurements made by two optical methods, surface light scattering (SLS)13 and ellipsometry.14-17 The WP method is one of the oldest and most direct measurements of surface tension, and descriptions may X
Abstract published in Advance ACS Abstracts, October 15, 1997.
(1) Dukhin, S. S.; Kretzschmar, G.; Miller, R. Dynamics of Adsorption at Liquid Interfaces; Elsevier: Amsterdam, 1995. (2) Edwards, D. A.; Brenner, H.; Wasan, D. T. Interface Transport Processes and Rheology; Butterworth-Heinemann: Boston, MA, 1991. (3) For example: Adamson, A. W. Physical Chemistry of Surfaces, 5th ed.; Wiley: New York, 1990. (4) Chang, C.-H.; Franses, E. I. Colloids Surf., A 1995, 100, 1. (5) Manning-Benson, S.; Bain, C. D.; Darton, R. C. J. Colloid Interface Sci. 1997, 189, 109. (6) Padday, J. F. Proc. Int. Cong. Surf. Act. 1957, 1. (7) Piccardi, G.; Ferroni, E. Ann. Chim. (Rome) 1951, 41, 3. (8) Bergink-Martens, D. J. M. Interface Dilation. The Overflowing Cylinder Technique. Ph.D. Thesis, Agricultural University, Wageningen, 1989. (9) Bergink-Martens, D. J. M.; Bos, H. J.; Prins, A.; Schulte, B. C. J. Colloid Interface Sci. 1990, 138, 1. (10) Bergink-Martens, D. J. M.; Bos, H. J.; Prins, A. J. Colloid Interface Sci. 1994, 165, 221. (11) Bergink-Martens, D. J. M.; Bos, H. J.; van Kalsbeek, H. K. A. I.; Prins, A. In Food Colloids and Polymers: Stability and Mechanical Properties; Dickenson, E., Walstra, P., Eds.; Royal Society of Chemistry: Cambridge, U.K., 1993; pp 291, 376. (12) Darton, R. C.; Grunnet-Jepsen, H.; Thomas, P. D.; Whalley, P. B. Paper 132C, AIChE Conference, San Francisco, 1994. (13) Langevin, D. In Light Scattering by Liquid Interfaces and Complementary Techniques; Langevin, D., Ed.; Marcel Dekker: New York, 1992; part 1.
S0743-7463(97)00457-5 CCC: $14.00
be found in many textbooks.3 SLS, by contrast, is a modern technique that has never before been applied to flowing liquid surfaces. In the SLS experiments reported here, we measured light scattered from thermally excited capillary waves with frequencies in the range (2-4) × 104 s-1. From an analysis of the correlation function, both σdyn and the dynamic Gibbs elasticity, dyn, can be determined in a single measurement. Ellipsometry also has a distinguished pedigree but has only recently been applied to dynamic studies of water surfaces.5 In ellipsometry, the polarization of light reflected from the flowing surface is measured. Ellipsometry does not provide surface tensions directly, but it can be calibrated against surface tensiometry from measurements on static solutions at equilibrium. In an OFC, liquid is pumped vertically upward through a cylinder. The surface flows radially from the center toward the rim creating a uniform, steady-state surface expansion with expansion rates in the range 1-10 s-1.18 In contrast to most other geometries used for the measurement of dynamic interfacial properties, the OFC has a large flat surface that is ideally suited for a range of spectroscopic and scattering measurements. Experimental Section CTAB (Fluka, 99%) was used without further purification for measurements on the OFC by SLS and ellipsometry. For measurements on the OFC with the WP method, CTAB was recrystallized once from 1:1 acetone/methanol to reduce contamination of the WP (amines adsorb strongly on platinum).19 For equilibrium measurements CTAB was recrystallized three times (as above). Ultrahigh purity (UHP) water (Elga UHQ) (14) Meunier, J. In Light Scattering by Liquid Interfaces and Complementary Techniques; Langevin, D., Ed.; Marcel Dekker: New York, 1992; Chapter 17. (15) Beaglehole, D. Physica B 1980, 100, 163. (16) Lyklema, J. Fundamentals of Interface and Colloid Science, 2nd ed.; Academic Press: New York, 1993; Vol. 1, Chapter 7. (17) Drude, P. The Theory of Optics; Dover: New York, 1959. (18) The surface expansion rate is defined by d ln A/dt where A is the area of a surface element. The reciprocal of the surface expansion rate is a measure of the surface age. (19) Bigelow, W. C.; Pickett, D. L.; Zisman, W. A. J. Colloid Sci. 1946, 1, 513.
© 1997 American Chemical Society
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was used throughout. All glassware was soaked in an alkaline detergent (Decon 90) and rinsed thoroughly with UHP water. All measurements were carried out at 298 ( 0.5 K. The OFC is a stainless steel cylinder (diameter, 80 mm 140 mm height) containing a resistance plate and a flow straightener to generate a flow profile approximating plug flow well below the surface. The flow rate was 16 cm3 s-1, corresponding to a vertical velocity of 3.2 mm s-1 in the cylinder. The length of the freefalling film on the outside of the cylinder was 120 mm. Both these parameters were above their critical values.5,8-10 The SLS rig20 and analysis procedures have been described previously.21,22 Readings were taken at a radial distance, r ) 15 mm, where the signal to noise (S/N) ratio was highest. The reproducibility of measurements at the cmc was (1.2 mN m-1. Equilibrium surface tension measurements were made by the du Nou¨y ring method according to established procedures.23 Two types of Wilhelmy plates were used for measurements of σdyn, platinum (20.73 mm wide, 0.22 mm thick) and high density filter paper (Nima, ∼10 mm wide).24 The plate was lowered at a rate of ∼5 mm min-1 until it touched the surface and then for a further 60 s. The plate was held stationary for 20 s and then raised at the same rate until it detached completely from the surface. The surface expansion, caused by the slow withdrawal of the plate is negligible compared to the surface expansion rates at the surface of the OFC. The force on the plate was recorded continuously with a force transducer (HBM Ltd.) and converted into surface tension at the point where the bottom of the plate was exactly parallel to the undisturbed surface (where there is no buoyancy correction)25 and prior to detachment (where there is the minimum perturbation to the flow). After the latter measurement was corrected for buoyancy, the differences between the two readings were not significant. The surface tensions recorded when the plate was level with the surface are presented in Figure 1. The filter paper WP was saturated with solution before each measurement. Since the perimeter of the wet filter paper is unknown, the plate was calibrated with UHQ water. In all cases, the plate was suspended in the direction of the radial flow and centered at r ) 15 mm.26 The standard error in σdyn for repeated measurements with the platinum WP on the same sample was 0.3 mN m-1, and the reproducibility for multiple measurements on different samples ranged from (0.5 mN m-1 at the cmc to (1.7 mN m-1 at 0.4 × cmc (errors are the limits in five independent experiments). The large errors at 0.4 × cmc are a consequence of incomplete wetting (see later). A detailed description of ellipsometry measurements on an OFC has been published recently.5 Both SLS and ellipsometry used a HeNe laser at 632.8 nm.
Figure 1. Dynamic surface tension, σdyn, measured with a platinum Wilhelmy plate (crosses), with a filter paper Wilhelmy plate (open circles), and by surface light scattering (closed circles) as a function of the bulk concentration of CTAB. The equilibrium surface tension, σe, measured with a du Nou¨y ring (diamonds), is also shown. The arrow marks the cmc. Error bars for platinum WP data are shown at the two concentrations to indicate the reproducibility of σdyn. For the SLS data, the error bars represent the errors calculated by the program used to fit the correlation functions.
Results and Discussion Figure 1 compares values of σdyn obtained with a platinum WP, a filter paper WP, and by SLS as a function of the concentration of CTAB in the OFC.27 The equilibrium surface tensions are also shown for comparison. There is good agreement between the filter paper WP and the SLS techniques over the entire concentration range. The platinum WP yielded reasonable agreement with the other two techniques at concentrations near the cmc, but (20) Sharpe, D.; Eastoe, J. Langmuir 1996, 12, 2303. (21) Earnshaw, J. C.; McGivern, R. C. J Colloid Interface Sci. 1988, 123, 23. (22) Earnshaw, J. C.; McGivern, R. C.; McLaughlin, A. C.; Winch, P. J. Langmuir 1990, 6, 649. (23) Zuidema, H. H.; Waters, G. W. Ind. Eng. Chem., Anal. Ed. 1941, 5, 312. (24) Gaines, G. L. J. Colloid Interface Sci. 1977, 62, 191. (25) Jordan, D. O.; Lane, J. E. Aust. J. Chem. 1964, 17, 7-15. (26) The WP measures an average value of σdyn. For the platinum WP the average is between r ) 5 and r ) 25 mm, and between r ) 10 mm and r ) 20 mm for the filter paper WP. Since σdyn is a quadratic function of r,8 the plate will overestimate σdyn at r ) 15 mm by a small amount (e0.1 mN m-1). (27) The values of the Gibbs elasticity, e, we obtained from the fits to the SLS data for static solutions are in good agreement with those calculated from the du Nou¨y data in Figure 1 using e ) -dσ/d ln Γ. Values of dyn could also be extracted from the SLS measurements on the OFC. As expected dyn < e since the surface coverage is lower under dynamic conditions, e.g. at [CTAB] ) cmc, e ∼ 60 mN m-1 and dyn ∼ 15 mN m-1.
Figure 2. Dynamic surface tension, σdyn, measured by surface light scattering (closed circles) and calculated from ellipsometric data (open squares), as a function of the concentration of CTAB. The equilibrium surface tension, σe, measured with a du Nou¨y ring (diamonds), is also shown. The standard errors for the ellipsometric data lie within the symbol, except where shown. For the SLS data, the error bars represent the errors calculated by the program used to fit the correlation functions.
at concentrations between 0.2 and 0.6 × cmc the platinum WP measurements fell significantly below the filter paper WP and SLS data. We noted that the meniscus on the Pt plate appeared irregular at these intermediate concentrations and the discrepancy between the Pt and filter paper WP is probably therefore a reflection of incomplete wetting of the Pt.28 Since the measured force is proportional to cos θ (where θ is the contact angle) partial wetting leads to artificially low values of σ if perfect wetting is assumed.
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Figure 2 compares values of σdyn of CTAB solutions obtained by the two noninvasive techniques, ellipsometry and SLS. To convert ellipsometric readings to surface tensions, we used a calibration curve generated from measurements on static solutions.5 This procedure is only valid if the monolayer at the surface of the OFC is in equilibrium with the bulk solution immediately below the surface. Good agreement between the two methods is found over the entire concentration range. This agreement validates both sets of measurements and, in addition, suggests that the expanding surface of the OFC is at, or near, local equilibrium. Conclusions The dynamic surface tension of CTAB solutions has been measured in an OFC by both invasive and noninvasive methods. Despite the fact that a WP disturbs the flow pattern, the surface tensions measured with a filter paper WP agreed with measurements made with the two noninvasive techniques, SLS and ellipsometry, to within experimental error. This agreement helps to validate dynamic surface tension measurements made with Wilhelmy plates. Values of σdyn measured with a Pt plate were significantly lower in the concentration range (0.2(28) It is well-known that CTAB solutions do not wet glass well due to the adsorption of a hydrophobic monolayer of CTAB on the glass surface (Birch, W. R.; Knewtson, M. A.; Garoff, S.; Suter, R. M.; Satija, S. Colloids Surf. 1994, 89, 145). Attempts to measure the surface tension with a roughened glass plate confirmed this problem.
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0.6) × cmc, due to incomplete wetting of the plate. The problem of wetting does not arise with the SLS and ellipsometry. The viability of surface light scattering experiments from flowing surfaces has been demonstrated, and consistent surface tensions were obtained by ellipsometry and SLS. SLS and ellipsometry in combination offer a particularly powerful approach to the analysis of the surface tension of moving surfaces. SLS measurements of σdyn at a reference point on the surface can be used to calibrate the ellipsometric response. Ellipsometry can then be used to explore the entire surface and, since ellipsometry provides an extremely precise, local measurement, to map the variation in σdyn across the surface. Finally, the excellent agreement between measurements of σdyn by SLS and ellipsometry suggests that surfaces of CTAB solutions are at local equilibrium at the expansion rates probed on an OFC. Acknowledgment. This work was supported by the EPSRC (GR/K79611 and GR/K85247), the BBSRC (F10702), and Unilever Research (Port Sunlight Laboratory). We thank Professor J. Earnshaw (Queen’s University of Belfast) for providing the SLS analysis programs and K. Hayward and Dr. J. Varley (Reading University) for allowing us to use their WP tensiometer. LA970457V
