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Contact Angle Hysteresis near a First-Order Wetting Transition J. Y. Wang, M. Crawley, and B. M. Law* Condensed Matter Laboratory, Department of Physics, Kansas State University, Manhattan, Kansas 66506 Received December 11, 2000. In Final Form: March 7, 2001 We examine the contact angle hysteresis for n-octane droplets on a n-hexadecyltrichlorosilane-coated silicon wafer in the vicinity of a first-order wetting transition with wetting temperature Tw ) 49.5 °C. A pinning transition is observed at Tp ) 46.8 °C for the receding contact angle. Above this temperature, the contact line for receding droplets is pinned; consequently, the receding contact angle θr ) 0°. We use contact angle data to quantify the substrate surface energy difference, ∆σ(T) ) σsv(T) - σsl(T), and the relative surface heterogeneity, h0/σlv, as a function of temperature T where σij is the surface energy between phases i and j.
1. Introduction The study of droplets deposited upon solid surfaces and their solid-liquid-vapor contact lines in the vicinity of a wetting transition, where the contact angle θ∞ approaches 0° as the temperature T approaches Tw (the wetting transition temperature), has received considerable attention in recent years. The contact angle,1 contact angle hysteresis (which represents the contact angle difference between advancing and receding droplets),2-4 contact line roughness,5 and the line tension of droplets6,7 have all been studied in the vicinity of Tw. Many of these studies examined the behavior of liquid He4 2-5 or liquid H2 droplets1,4 on Cs substrates at very low temperatures (Tw j 20 K). These low-temperature studies contributed considerably to our understanding of the behavior of liquids in the vicinity of a wetting transition; however, the high reactivity of the Cs surface and the low temperatures prevented an accurate quantification and correlation of the substrate surface roughness with liquid behavior. In particular, the behavior of the contact angle hysteresis for liquid He4 on Cs2-4 was found to vary widely from substrate to substrate where the origins of this behavior are not understood. It is not known whether this wide variation is due to the (unknown) surface roughness of the substrate or is in some way related to the superfluidity of the liquid helium. Liquid H2 droplets deposited upon similar Cs substrates1 exhibited a much smaller contact angle hysteresis than was observed for liquid He4. Recently, we examined the line tension of n-octane droplets deposited upon n-hexadecyltrichlorosilane-coated silicon wafers in the vicinity of a wetting transition6,7 where Tw ∼ 320 K. Contact mode atomic force microscopy measurements indicated that these silane-coated silicon wafers are molecularly flat with a surface roughness of ∼0.5 nm over a 10 µm × 10 µm area. These coated wafers (1) Ross, D.; Taborek, P.; Rutledge, J. E. Phys. Rev. B 1998, 58, R4274. (2) Klier, J.; Stefanyi, P.; Wyatt, A. F. G. Phys. Rev. Lett. 1995, 75, 3709. (3) Ross, D.; Rutledge, J. E.; Taborek, P. Science 1997, 278, 664. (4) Rutledge, J. E.; Ross, D.; Taborek, P. J. Low Temp. Phys. 1998, 113, 811. (5) Rolley, E.; Guthmann, C.; Gombrowicz, R.; Repain, V. Phys. Rev. Lett. 1998, 80, 2865. (6) Wang, J. Y.; Betelu, S.; Law, B. M. Phys. Rev. Lett. 1999, 83, 3677. (7) Wang, J. Y.; Betelu, S.; Law, B. M. Phys. Rev. E 2001, 63, 31601.
therefore form rather ideal substrates upon which to conduct contact angle measurements. In this paper, we extend our measurements of n-octane droplets on silanecoated Si wafers to a study of the contact angle and contact angle hysteresis and compare these measurements to the earlier low-temperature wetting studies on Cs substrates in order to gain a better generic understanding of droplet behavior in the vicinity of a wetting transition. Our measurements may also be of interest to scientists interested in the behavior of liquids in the vicinity of structured surfaces,8,9 such as the self-assembled silane monolayers that we deposit upon silicon wafers. 2. Theory For a liquid droplet, which is situated upon a molecularly smooth and homogeneous solid surface, the contact angle θ∞ is related to the surface energies σsv, σsl, and σlv between solid (s), liquid (l), and vapor (v) phases by the YoungDupre equation:10
cos θ∞ )
σsv - σsl σlv
)1+
S0 σlv
(1) (2)
where we have introduced the spreading coefficient S0 ≡ σsv - σsl - σlv in the second equality. This equation is strictly valid only for large droplets (with lateral radius r f ∞) which are in mechanical equilibrium with any adsorbed film on the solid surface. For droplets of finite lateral radius r, the line tension τ, corresponding to the energy per unit length associated with the solid-liquidvapor contact line, influences the contact angle θ where11
cos θ ) cos θ∞ -
τ rσlv
(3)
(8) Drelich, J.; Wilbur, J. L.; Miller, J. D.; Whitesides, G. M. Langmuir 1996, 12, 1913. (9) Fery, A.; Pompe, T.; Herminghaus, S. J. Adhes. Sci. Technol. 1999, 13, 1071. Pompe, T.; Herminghaus, S. Phys. Rev. Lett. 2000, 85, 1930. (10) Adamson, A. W. Physical chemistry of surfaces, 4th ed.; Wiley: New York, 1982. (11) Drelich, J. Colloids Surf., A 1996, 116, 43.
10.1021/la0017328 CCC: $20.00 © 2001 American Chemical Society Published on Web 04/19/2001
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In prior work,6,7 we have used eq 3 to determine both τ and θ∞ by examining the variation in the contact angle θ with lateral radius r for droplets in the vicinity of a firstorder wetting transition. According to eq 1, the contact angle θ∞ provides important information about the solid surface energy difference
∆σ(T) ) σsv(T) - σsl(T)
(4)
at temperature T. As T approaches the wetting transition temperature Tw, the contact angle θ∞, or equivalently S0, approaches zero and the quantity ∆σ(Tw) ≡ σc defines a “critical surface tension” whose value is primarily determined by the molecular end-group prevalent upon the solid substrate.12 For example, if the solid substrate is coated with a self-assembled monolayer whose molecular end-group consists of the methyl end-group, -CH3, then σc ≈ 20 erg/cm2 12,13 and liquids with σlv E σc wet the surface whereas liquids with σlv > σc form droplets possessing a finite-contact angle. The quantity ∆σ(T) has rarely been measured in the vicinity of a wetting transition1,2 and is not well understood. Real surfaces are never completely homogeneous or atomically smooth. The chemical heterogeneity and roughness of a surface gives rise to contact angle hysteresis where the advancing contact angle θa differs from the receding contact angle θr for a droplet.14 According to the dilute defect model,14,15 for a weakly chemically heterogeneous surface, where the spreading coefficient S(x, y) varies from point to point about its average value S0, the local heterogeneity
h(x, y) ) S(x, y) - S0
(5)
produces a defect mediated force on the three-phase solidliquid-vapor contact line. If h(x, y) is a random function of position, correlated over a distance d, with
〈h〉 ) 0
(6)
〈h(r) h(r′)〉 ) h02 exp(-|r - r′|2/d2)
(7)
and
then one can show that the contact angle hysteresis14,15
cos θr - cos θa )
h02 σlv|S0|
(8)
in the limit of small contact angles (near a wetting transition). Hence, from eqs 8 and 1, the ratio
h0 ) [(cos θr - cos θa)(1 - cos θ∞)]1/2 σlv
(9)
provides a measure of the strength of the chemical heterogeneity for a surface. In the following, we examine the behavior of θa(T), θr(T), ∆σ(T), and h0/σlv for n-octane droplets on a n-hexadecyltrichlorosilane-coated Si wafer in the vicinity of a wetting transition; these results are compared with prior wetting studies of liquid He4 and liquid H2 droplets on a Cs substrate at very low temperatures. (12) Zisman, W. A. Adv. Chem. Ser. 1964, 43, 1. (13) Brzoska, J. B.; Ben Azouz, I.; Rondelez, F. Langmuir 1994, 10, 4367. (14) Leger, L.; Joanny, J. F. Rep. Prog. Phys. 1992, 55, 431. (15) Robbins, M. O.; Joanny, J. F. Europhys. Lett. 1987, 3, 729.
Figure 1. Measurements of advancing (solid) and receding (open) contact angles θ as a function of lateral radius r at temperatures close to the wetting transition at Tw ) 49.5 °C for n-octane droplets upon a n-hexadecyltrichlorosilane-coated Si wafer. The arrows in the diagram for a temperature of 42.1 °C indicate the direction of increasing time as discussed in the text.
3. Experiment Our experimental setup for accurately quantifying the contact angle of droplets and our technique for preparing self-assembled monolayers on molecularly smooth silicon wafers have been described in detail elsewhere.7 We provide a brief description here. Self-assembled n-hexadecyltrichlorosilane monolayers were formed upon a (100) silicon wafer surface by first cleaning the wafer using the RCA method16 followed by a standard solution chemistry procedure for depositing a self-assembled silane monolayer upon a silicon wafer.13 n-Octane droplets deposited upon this silane-coated silicon wafer possess a small contact angle (
