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Contact Angles of Liquid Drops on Super Hydrophobic Surfaces: Understanding the Role of Flattening of Drops by Gravity C. W. Extrand* and Sung In Moon Entegris, Inc., 101 Peavey Road, Chaska, Minnesota 55318, United States Received June 28, 2010. Revised Manuscript Received October 1, 2010 Measurement of contact angles on super hydrophobic surfaces by conventional methods can produce ambiguous results. Experimental difficulties in constructing tangent lines, gravitational distortion or erroneous assumptions regarding the extent of spreading can lead to underestimation of contact angles. Three models were used to estimate drop shape and perceived contact angles on completely nonwetting super hydrophobic surfaces. One of the models employed the classic numerical solutions from Bashforth and Adams. Additionally, two approximate models were derived as part of this work. All three showed significant distortion of microliter-sized drops and similar trends in perceived contact angles. Liquid drops of several microliters are traditionally used in sessile contact angle measurements. Drops of this size are expected to and indeed undergo significant flattening on super hydrophobic surfaces, even if the wetting interactions are minimal. The distortion is more pronounced if the liquid has a lesser surface tension or greater density. For surfaces that are completely nonwetting, underestimation of contact angles can be tens of degrees. Our modeling efforts suggest that accurate contact angle measurements on super hydrophobic surfaces would require very small sessile drops, on the order of hundreds of picoliters.
Introduction Interest in super repellent surfaces has exploded in recent years. Hundreds of papers have been published describing techniques for making them. The criteria for super repellency are often given to be an advancing contact angle of 150° or greater and a minimal inclination angle to initiate movement of a small liquid drop. This definition is somewhat arbitrary and rather qualitative. One of the reasons is that measurement of very large contact angles is challenging. Forty years ago in a classic review of wetting, Johnson and Dettre1 stated that the uncertainty is greater for very large angles “because of the difficulties in locating the point of contact and constructing a tangent to the drop profile”. In addition to these pitfalls, operator bias about the drop shape can also be a problem, incorrectly assuming that a drop is not distorted by gravity and has spherical proportions can lead to systematic measurement error.2 Thus, the accuracy of contact angle measurements made on super repellent surfaces has been questioned.2-8 In the absence of wetting interactions and gravity, drops would form spheres that would contact the underlying surface at a single point. On the other hand, in the absence of gravity, wetting *To whom correspondence should be addressed. Tel: 1-952-556-8619. E-mail:
[email protected]. (1) Johnson, R. E., Jr.; Dettre, R. H. Wettability and Contact Angles. In Surface and Colloid Science; Matijevic, E., Ed. Wiley: New York, 1969; Vol. 2, pp 85-153. (2) Extrand, C. W. Model for Contact Angles and Hysteresis on Rough and Ultraphobic Surfaces. Langmuir 2002, 18(21), 7991–7999. (3) Dorrer, C.; R€uhe, J. Advancing and Receding Motion of Droplets on Ultrahydrophobic Post Surfaces. Langmuir 2006, 22(18), 7652–7657. (4) Gao, L.; McCarthy, T. J. A Perfectly Hydrophobic Surface (θA/θR = 180°/ 180°). J. Am. Chem. Soc. 2006, 128(28), 9052–9053. (5) Gao, L.; McCarthy, T. J. A Commercially Available Perfectly Hydrophobic Material (θa/θr = 180°/180°). Langmuir 2007, 23(18), 9125–9127. (6) Yeh, K.-Y.; Chen, L.-J.; Chang, J.-Y. Contact Angle Hysteresis on Regular Pillar-like Hydrophobic Surfaces. Langmuir 2008, 24(1), 245–251. (7) Extrand, C. W.; Moon, S. I. When Sessile Drops Are No Longer Small: Transitions from Spherical to Fully Flattened. Langmuir 2010, 26(14), 11815– 11822. (8) Patankar, N. A. Hysteresis with Regard to Cassie and Wenzel States on Superhydrophobic Surfaces. Langmuir 2010, 26(10), 7498–7503.
17090 DOI: 10.1021/la102566c
interactions would cause drops to spread and produce a spherical segment. If both are in play, sorting out “flattening” due to wetting interactions versus flattening due to gravitational distortion is not a trivial task. One way of separating the two effects would be to use liquid drops that are sufficiently small such that there is no gravitational distortion. Thus, any flattening of the bottom of drops on super repellent surface could then be attributed to wetting. However, the appropriate volume of drop required to meet this criterion is not straightforward. The transitions are gradual and the mathematics that describes the shape of sessile drops is complicated and generally requires sophisticated iterative numerical methods to solve. General guidelines have been given regarding the appropriate drop size ( > 2=3 #2 = > 2 Fg 3Vs ; :2 Fg 3Vs
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Extrand and Moon
Article
Table 1. Properties of Liquids Commonly used in Contact Angle Measurements: Surface Tension (γ) and Density (G) liquid
γ (mN/m)
F (kg/m3)
water ethylene glycol diiodomethane hexadecane
72 48 51 28
998 1110 3320 773
Table 2. Partial List of x/b and z/b Values for β = 0.125, Taken from Table II of Bashforth and Adams,13 along with Values of (x, z, and z0 Calculated for Water, where b = 0.965 mm dimensionless values
Figure 3. Small drop of water and a super hydrophobic surface: (a) before and (b) after deposition.
Details regarding derivation of the two approximations are given in the Appendix.
Experimental Details To test these various models, we attempted to prepare completely nonwetting surfaces using a tetrafluoroethylene (TFE) powder (Central Glass Company, Japan) kindly provided by McCarthy.5 The TFE powder was dispersed in hexane (Anhydrous, 95%, Sigma-Aldrich) at roughly 10% by weight and then spread on 100 mm silicon wafers. The process was repeated until the surface was uniformly covered and then allowed to dry. The wetting liquids used in the experiments were 18 MOhm cm deionized (DI) water, ethylene glycol (Sigma-Aldrich, anhydrous 99.8%), diiodomethane (Alfa Æsar, 99þ%) and hexadecane (Alfa Æsar, 99%). Sessile drops of volume V were deposited on the TFE surfaces with adjustable volume pipettes (Eppendorf Reference Series 2000, 2-20 μL and 10-100 μL). Table 1 lists the properties of the liquids.19,20 A drop shape analyzer (Kr€ uss DSA10) was used to observe the drops and capture images. Drop heights and base diameters were measured using Image-Pro Plus software. Unless noted otherwise, images and experimental data came from drops with advancing contact lines. All measurements were performed at 25 ( 1 °C. Error of the dispensed liquid volume from the pipet was
