Langmuir 2006, 22, 1711-1714
1711
Designing for Optimum Liquid Repellency C. W. Extrand* Entegris, Inc., 3500 Lyman BlVd., Chaska, Minnesota 55318 ReceiVed September 16, 2005. In Final Form: December 6, 2005 In the current state-of-the-art, most super repellent surfaces are not sufficiently robust to move out of the laboratory into the commercial realm. With the hope of creating super repellent surfaces that could be employed in a wider variety of commercial applications, means to improve the robustness of ultralyophobic surfaces have been explored theoretically. Suspension pressures and drop retention forces were examined in terms of asperity shape, size, and spacing. The findings from this study suggest a strategy for creating surfaces that maintain their liquid repellency even after exposure to large hydrostatic pressures associated with liquid columns or jets.
Introduction As the name implies, super liquid repellency describes a solid surface with an extraordinary ability to repel liquids. Studies of super repellent surfaces first appeared in the scientific literature in the 1930s.1 Since that time, this subject has received continued attention,2-7 but interest has intensified in recent years8-18 due to the potential use of ultralyophobicity19 in a variety of applications, such as super repellent fabrics, self-cleaning surfaces, microfluidic devices, and drag reduction in fluid flow.20,21 The art of producing super repellent surfaces as well as the scientific understanding of them is advancing at a rapid pace. However, their use will likely be limited to a few niche applications because many surfaces produced today lose their repellency under high hydrostatic pressures. For example, allowing drops to fall from small heights13 or pressing on suspended drops9,22 can push liquid into the inter-asperity spaces, thereby defeating the suspension pressure and destroying repellency. In this report, a recently developed model12,23,24 was used to investigate means of maximizing suspension pressure and minimizing drop retention. Using findings from this investigation, * To whom correspondence
[email protected].
should
be
addressed.
E-mail:
(1) Wenzel, R. N. Ind. Eng. Chem. 1936, 28, 988. (2) Bartell, F. E.; Shepard, J. W. J. Phys. Chem. 1953, 57, 211. (3) Holloway, P. J. Pestic. Sci. 1970, 1, 156. (4) Johnson, R. E., Jr.; Dettre, R. H. In Contact Angle, Wettability, and Adhesion; Gould, R. F., Ed.; American Chemical Society: Washington, DC, 1964; Vol. 43, pp 112-135. (5) Kunugi, Y.; Nonaku, T.; Chong, Y.-B.; Watanabe, N. J. Electroanal. Chem. 1993, 353, 209. (6) Morra, M.; Occhiello, E.; Garbassi, F. Langmuir 1989, 5, 872. (7) Cassie, A. B. D.; Baxter, S. Trans. Faraday Soc. 1944, 40, 546. (8) Barthlott, W.; Neinhuis, C. Planta 1997, 202, 1. (9) Bico, J.; Marzolin, C.; Que´re´, D. Europhys. Lett. 1999, 47, 220. (10) Chen, W.; et al. Langmuir 1999, 15, 3395. (11) Erbil, H. Y.; Demirel, A. L.; Avci, Y.; Mert, O. Science 299, 1377 2003. (12) Extrand, C. W. Langmuir 2002, 18, 7991. (13) He, B.; Patankar, N. A.; Lee, J. Langmuir 2003, 19, 4999. (14) Hozumi, A.; Takai, O. Thin Solid Films 1997, 303, 222. (15) Krupenkin, T. N.; Taylor, J. A.; Schneider, T. M.; Yang, S. Langmuir 2004, 20, 3824. (16) Onda, T.; Shibuichi, S.; Satoh, N.; Tsujii, K. Langmuir 1996, 12, 2125. (17) O ¨ ner, D.; McCarthy, T. J. Langmuir 2000, 16, 7777. (18) Tadanaga, K.; Katata, N.; Minami, T. J. Am. Ceram. Soc. 1997, 80, 1040. (19) Super repellency also is referred to as super or ultra lyophobicity. If the liquid is water, then it is termed super hydrophobicity. (20) Blossey, R. Nat. Mater. 2003, 2, 301. (21) Watanabe, K.; Udagawa, Y. H. J. Fluid Mech. 1999, 381, 225. (22) Lafuma, A.; Que´re´, D. Nat. Mater. 2003, 2, 457. (23) Extrand, C. W. Langmuir 2004, 20, 5013. (24) Extrand, C. W. Langmuir 2005, 21, 10370.
a strategy is presented for creating surfaces with optimal liquid repellency that resist wetting even after exposure to large hydrostatic pressures.
Background What separates a super repellent surface from a “regular” repellent one? Among materials that exist today, natural or synthetic, fluorocarbon compounds, such as Teflon,25 arguably have the greatest intrinsic lyophobicity. These fluorocarbon compounds are comprised primarily of fluoromethylene (-CF2-) groups and may contain other functional groups that terminate with fluoromethyl groups (-CF3). Yet if smooth as depicted in Figure 1, panels a and b, they seldom exhibit contact angles greater than 120-130° 26-28 and thus represent the upper limit of “regular” repellency.29 In contrast, super repellent surfaces combine intrinsic lyophobicity and highly structured topography. The topography may be well defined with regular features or less orderly with random features. Super repellency is arbitrarily defined as a liquid-solid pair that has a θa value in excess of 140-150° with minimal liquid-solid adhesion. In the extreme limits, apparent contact angles can approach 180°.16,17 Figure 1, panels c and d, also shows a small liquid drop on a super repellent surface. In this example, the surface is covered with lyophobic asperities that take the form of square pillars of width x, spacing y, height z, and rise angle ω, Figure 1, panels e and f. The liquid drop is suspended atop the asperities with gas or vapor between them. The apparent contact area between the liquid drop and the solid between is a composite of liquid/vapor and liquid/solid interfaces. The drop exhibits one of the distinctive traits of super repellency, a large apparent advancing contact angle θa.30 (25) Teflon is a registered trademark of DuPont. (26) Mahadevan, L. Nature 2001, 411, 895. (27) Fabretto, M.; Sedev, R.; Ralston, J. In Contact Angle, Wettability and Adhesion; Mittal, K. L., Ed.; VSP: Boston, 2003; Vol. 3, pp 161-173. (28) Nishino, T.; Meguro, M.; Nakamae, K.; Matsushita, M.; Ueda, Y. Langmuir 1999, 15, 4321. (29) The most widely known form of Teflon is poly(tetrafluoroethylene) (PTFE), which is comprised solely of fluoromethylene groups. If smooth, PTFE has a contact angle of approximately 110°. DuPont manufactures a number of PTFE copolymers that are sold under the Teflon trademark, such as fluorinated ethylene propylene (FEP), perfluoroalkoxy (PFA), and an amorphous 2,2-bistrifluoromethyl4,5-difluoro-1,3-dioxole (PDD)/tetrafluoroethylene (TFE) copolymer (Teflon AF). These copolymers all contain comonomers with side chains that are fluoromethyl terminated. Among these, the PDD/TFE copolymer contains the highest number of fluoromethyl groups and consequently can show contact angles as high as 130°. Other fluorocarbon compounds, such as fluorowaxes and fluorosurfactants, also can be used to create smooth layers that show water contact angles in excess of 120°.
10.1021/la052540l CCC: $33.50 © 2006 American Chemical Society Published on Web 01/24/2006
1712 Langmuir, Vol. 22, No. 4, 2006
Extrand
∆θo ) θa,o - θr,o
(3)
θa,o and θr,o are intrinsic advancing and receding contact angles; that is, the contact angles of a liquid advancing or receding on a smooth portion of a solid surface, regardless of the solid orientation relative to the horizon. λp also serves as a measure of the asperity size-to-spacing ratio. Intrinsic lyophobicity and highly structured topography alone are not sufficient to produce super repellency. For surfaces to suspend liquids and show super repellency, the liquid surface tension γ acting around the perimeter of the asperities must create a suspension pressure that is greater than or equal to any downward directed hydrostatic pressures.31 The maximum suspension pressure ∆Ps can be estimated as23
∆Ps ) -[Λ/(1 - Rp)]γ cos(θa,o + ω - 90°)
(4)
where Λ is the contact line density per unit area and Rp is the fraction of liquid-solid contact area within the composite interface.32 For surfaces covered with a regular array of square pillars as described in Figure 1, panels e and f, Λ, Rp, and λp are
Λ ) 4x/y2
(5)
Rp ) (x/y)2
(6)
λp ) x/y
(7)
and Figure 1. Interaction of small liquid drops with smooth and super repellent surfaces. (a) A liquid is slowly injected into a sessile drop residing on a smooth surface. When injection stops, the advancing contact line comes to rest on the smooth surface and the drop exhibits an intrinsic advancing contact angle θa,o. (b) A small amount of liquid is slowly withdrawn from a sessile drop on a smooth surface. After the receding contact line stops, the drop shows an intrinsic receding contact angle θr,o. (c) A liquid is slowly injected into a sessile drop suspended on a super repellent surface. Once movement of the contact line pauses, the drop exhibits an apparent advancing contact angle θa. (d) A liquid is slowly withdrawn from a sessile drop suspended on a super repellent surface. After retreat of the contact line, the drop exhibits an apparent receding contact angle θr. Panels e and f show enlarged views of the interfaces between a liquid drop and a super repellent surface. (e) Side view of square asperities of width, x, spacing, y, height, z, and rise angle, ω. (f) Plan view of the asperity tops.
Most surfaces exhibit two stable contact angles, an advancing angle as well as a receding one, θr. The difference between θa and θr
∆θ ) θa - θr
(1)
is referred to as contact angle hysteresis. ∆θ is an important consideration for the construction of super repellent surfaces, since it plays a key role in drop retention. Contact angles on super repellent surfaces, both advancing and receding values, are greater than those observed on the corresponding smooth surface with the same chemical composition. Assuming that apparent contact angles manifest themselves as simple averages along the contact line, expressions have been derived for estimating ∆θ that include the influence of sharp edges12
∆θ ) λp(∆θo + ω)
(2)
where λp is the linear fraction of contact line on the asperities, ω is the rise angle of the individual asperities, and ∆θo is intrinsic contact angle hysteresis, defined as
After exposure to a liquid column, gravity will easily drain away most of the liquid from a horizontal surface. However, any small, suspended drops left behind will require additional work to remove them.33 The retention force Fr that must be overcome to initiate movement of a drop depends on the difference between the cosines of the advancing and receding contact angles along with the surface tension of the liquid γ.34-36 Fr can be calculated for drops with circular contact lines as37,38
Fr ) (2/π)γD(cos θr - cos θa)
(8)
where D is the contact diameter.39 For small spherical drops that are not appreciably distorted by gravity, D can be estimated from drop volume (V) and θa40
D ) 2(6V/π)1/3{tan(θa/2)[3 + tan2(θa/2)]}-1/3
(9)
Note that, the smaller the value of cos θr - cos θa or D, the more easily a drop can be displaced.
Results and Discussion Figure 2 shows the expected change in ∆θ as a function of λp for super repellent surfaces with varying degrees of intrinsic (30) The apparent advancing contact angle, θa, refers to the perceived angle of the liquid contact relative to the horizon, regardless of the local orientation and/or roughness of the solid surface. If the solid surface is smooth and horizontal, then θa,o ) θa. Otherwise, if a solid surface is rough and/or the contact line resides on a nonhorizontal portion, then θa,o * θa. (31) Thorpe, W. H.; Crisp, D. J. J. Exp. Biol. 1947, 24, 227. (32) Eq 4 is for a flat horizontal sheet of liquid. The suspension pressures required to repel impinging drops will be somewhat larger. (33) Even though drop curvature increases the downward pressure above and beyond that associated with the height of the liquid drop, a suspension pressure that successfully repels a column of liquid will easily repel small residual drops. (34) MacDougall, G.; Ockrent, C. Proc. R. Soc. (London) 1942, 180A, 151. (35) Furmidge, C. G. L. J. Colloid Sci. 1962, 17, 309. (36) Kawasaki, K. J. Colloid Sci. 1960, 15, 402. (37) Extrand, C. W.; Gent, A. N. J. Colloid Interface Sci. 1990, 138, 431. (38) Extrand, C. W.; Kumagai, Y. J. Colloid Interface Sci. 1995, 170, 515.
Optimum Liquid Repellency
Figure 2. Contact angle hysteresis ∆θ of super repellent surfaces covered with a regular array of square pillars as a function of λp for various ∆θo values. Here, λp ) x/y. ∆θ values were estimated from eq 2 assuming ω ) 90°.
Figure 3. Suspension pressure ∆Ps as a function of pillar spacing y for various λp values. ∆Ps values were calculated for water on super repellent surfaces covered with a regular array of square pillars using eqs 4-6 with γ ) 0.072 N/m, ω ) 90°, and θa,o )120°.
hysteresis. Although larger values of intrinsic hysteresis lead to increases in ∆θ, the greatest influence on the observed ∆θ of super repellent surfaces is the relative amount of liquid contacting the asperities. Thus, if one wishes to reduce ∆θ of a super repellent surface, the most effective way is to decrease λp. The data shown in Figure 2 was calculated with ω ) 90°. If ω were increased, ∆θ would increase too. By examining eq 4, it is clear that there are a number of parameters that could be manipulated to increase the ∆Ps of a super repellent surface. If possible, γ could be increased. Perhaps a more practical approach would be to increase θa,o or ω. However, everything else being equal, the biggest gains in ∆Ps would come from increasing Λ by simultaneously shrinking the size and spacing of the lyophobic surface features. Figure 3 shows ∆Ps versus y for water on families of super repellent surfaces covered with regular arrays of square pillars. λp values represent various asperity width-to-spacing ratios, x/y. As y becomes smaller, ∆Ps is expected to increase quite dramatically. Thus, to create super repellent surfaces that can withstand high hydrostatic pressure, the spacing as well as the relative size of the features should be reduced to nanoscopic dimensions. Increasing λp for a given y will further increase ∆Ps, but potentially will have negative consequences in the form of greater drop retention. (39) The early papers on drop retention cited here assume a constant advancing contact angle at the front of the drop and a constant receding value at the rear. Although this may be approximately true for elongated drops, it is not the case for drops with circular contact lines. If drops are not stretched much, which is the case for super repellent surfaces, then their contact line remains circular, and the contact angle varies continuously from front to back. The pre-factor in eq 8 arises from integrating the dot product of the liquid surface tension and the cosine of the contact angle from the advancing value at the front of the drop to the receding value at the rear. (40) Bikerman, J. J. Trans. Faraday Soc. 1940, 36, 412.
Langmuir, Vol. 22, No. 4, 2006 1713
Figure 4. Retention force Fr of small water drops on super repellent surfaces as a function of ∆θ for various θa values. Fr values were determined using eqs 8 and 9 with γ ) 0.072 N/m and V ) 1 µL.
Figure 4 shows Fr values versus ∆θ for water drops. It is assumed that the drops are sufficiently small that gravity does not distort their spherical shape but are much larger than the asperity size and spacing.41 As ∆θ tends toward zero, so does Fr. Note that for a given value of ∆θ, the larger the θa value, the smaller the retention, due to a decrease in the contact diameter of small, spherical drops. To a lesser extent, drop retention can be reduced by lowering γ. An ideal super repellent surface would withstand large hydrostatic pressures and exhibit minimal drop retention. These two characteristics conflict. Maximizing ∆Ps to improve the robustness of repellency generally will lead to increased drop retention. Similarly, increasing ω will increase ∆Ps but will also increase Fr. A general strategy for designing surfaces that can withstand large hydrostatic pressures yet still maintain their liquid repellency is as follows. First, the appropriate magnitude of ∆Ps should be determined for a given application. Next, λp, ω, and ∆θo should be adjusted to achieve the desired balance between ∆Ps and Fr. Finally, the height of the asperities (or the depth of the cavities) should be set to ensure that neither curvature of the liquid interfaces nor transient pressure events force liquid into the spaces between asperities, thereby destroying repellency. Having introduced a general strategy for constructing surfaces with improved repellency, let us look at a few examples. Consider a surface covered with a regular array of microscopic square pillars such that x ) 1 µm, y ) 10 µm, and z ) 20 µm. Assume this surface is hydrophobic with water θa,o and θr,o values of 120° and 100°. With ω ) 90°, such a surface would be expected to exert a ∆Ps of 1.45 kPa, supporting a water column that would be 0.15 m high. Now hold the ratio x/y constant at λp ) 0.1 and reduce both pillar size and spacing, such that x ) 10 nm and y ) 100 nm. Everything else being the same as in the previous example, ∆Ps would increase by 2 orders of magnitude to 145 kPa, enough to support 15 m of water without the loss of super repellency! Since this surface would produce θa of 170°, after draining the water column from this surface, the force to remove a small residual water drop (one µliter) would be around 0.5 µN. Removing the same drop from a corresponding smooth surface with the same chemical constitution would require a much larger force, Fr ) 17 µN. Increasing λp to 0.5 for an otherwise equivalent surface with y ) 100 nm would further increase the suspension pressure (∆Ps ) 960 kPa), but it also would increase the retention force by 10-fold. This type of surface might be ideal for the submerged hull of a ship, where high suspension pressures are needed, but drop retention is of little importance. Alternatively, if λp were (41) If very small drops with diameters equal to or less than asperity spacing fall between asperities, these drops may behave differently. Small drops entering pores have been studied by Marmur, A. J. Colloid Interface Sci. 1988, 122, 209.
1714 Langmuir, Vol. 22, No. 4, 2006
decreased to 0.01 while still maintaining y ) 100 nm, then ∆Ps and Fr would both drop dramatically to 14.4 kPa and 0.035 µN. This surface might be better suited for a rain repellent window, where a lower suspension pressure would suffice and minimal drop retention is a more desirable trait. Asperity size cannot be shrunk indefinitely. The ∆Ps curves shown in Figure 3 were extended to x ) 0.1 nm, which is approximately the molecular limit. In practice, the limit is probably larger, say 2-5 nm, where macroscopic intrinsic properties begin to vary.42-44 As asperity size approaches molecular dimensions, line tension also may influence ∆Ps and Fr.45 Also, a practical super repellent surface must be constructed with asperities that are sufficiently stiff and tough, such that they do not buckle or break under high ∆Ps.31 Even though the discussion has focused primarily on square pillars, the approach described here generally could be applied to protrusions or cavities of any size or shape on surfaces with ordered or random topography. (42) Christenson, H. K. J. Colloid Interface Sci. 1985, 104, 234. (43) Fenelonov, V. B.; Kodenyov, G. G.; Kostrovsky, V. G. J. Phys. Chem. B 2001, 105, 1050. (44) Fisher, L. R.; Israelachvili, J. N. J. Colloid Interface Sci. 1981, 80, 528. (45) Marmur, A. J. Colloid Interface Sci. 1997, 186, 462.
Extrand
Summary In summary, simultaneously shrinking asperity size and spacing is the most effective way of maximizing suspension pressure. However, a conflict exists between suspension pressure and drop retention: maximizing suspension pressure also can lead to greater drop retention. To create surfaces with optimal repellency, first choose asperity size, shape, and spacing to produce a suspension pressure that can withstand the magnitude of the applied external pressure, due to for example, a liquid column or impinging drops. Next, the asperity geometry (λp and ω) and chemical constitution (θa,o and θr,o) should be tweaked to adjust the balance between suspension pressure and drop retention. Finally, it must be verified that the asperities are sufficiently tall such that external pressure does not force liquid to fill the spaces between asperities, thereby destroying repellency. If liquid is forced to the bottom of interstitial spaces between asperities or condenses in them, repellency will be lost. Acknowledgment. I thank Entegris management for supporting this work and allowing publication. LA052540L
