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Remodeling of Super-hydrophobic Surfaces C. W. Extrand* CPC, 1001 Westgate Drive, St. Paul, Minnesota 55114, United States ABSTRACT: An experimental study on the underlying mechanisms of structured super-hydrophobic surfaces was recently published [Butt, H.-J.; et al. How Water Advances on Superhydrophobic Surfaces. Phys. Rev. Lett. 2016, 116, 096101. DOI: 10.1103/PhysRevLett.116.096101]. After depositing small drops of water, Butt’s group inclined their surfaces to initiate movement. They examined the contact between the water and structured surfaces with confocal microscopy. They observed that drops were suspended atop the protruding features and movement of water was different at the advancing and receding edges. At the advancing edge, the water interface descended downward and draped itself across the features. At the receding edge, water jumped from one feature to the next. As Butt and co-workers did not test their data against any existing model, that is done in this paper. Here, a previously proposed model that employs linear averaging at the contact line was adapted to their surfaces in an attempt to estimate their contact and sliding angles. Predictions from the model generally agreed with their experimental measurements.
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INTRODUCTION Super-repellent surfaces that combine structure and inherent hydrophobicity continue to attract much attention from the scientific community. These types of surfaces, which can be used dry or after being impregnated with a liquid, are generally referred to as being super-hydrophobic. If a water drop is deposited and allowed to advance across a dry structured surface that exhibits super-hydrophobicity, the apparent contact angle between the water drop and solid surface will be quite large, as depicted in Figure 1. Super-hydrophobic surfaces have
validity of many of the reported contact angles from superhydrophobic surfaces. This discrepancy has persisted, in part, due to lack of experimental evidence of how water interacts with microscopic or nanoscopic features that cover these surfaces. In the past few years, investigators have used scanning electron microscopy or confocal microscopy to observe local interactions.11−16 Recent observations and measurements by Hans-Jürgen Butt and co-workers that demonstrate how water moves across super-hydrophobic surfaces covered with microscopic pillars16 are reviewed in this paper, and then a model that employs linear averaging at the contact line is used to estimate contact and sliding angles for their surfaces. Finally the estimates are compared to their experimental findings.
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Butt and co-workers created super-hydrophobic surfaces from epoxy-based SU-8 photoresist using photolithography. Their surfaces were covered with cylindrical pillars, as depicted in Figure 2. The pillars had flat tops and vertical side walls (ω = 90°). They were arranged on a square lattice, where the pillar diameter (D) ranged from 5 to 25 μm and the center-to-center spacing (y) from 20 to 100 μm. The aspect ratios of the three surfaces were all D/y = 0.25. They were treated with a fluorosilane to render them hydrophobic. Chemically equivalent, flat SU-8 surfaces produced intrinsic advancing and receding contact angles of θa = 124 ± 2° and θr = 85 ± 5°.
Figure 1. Depiction of a small liquid drop on a super-hydrophobic surface that exhibits an apparent advancing contact angle of θapa. The drop has a surface tension of γ, a density of ρ, a volume of V, a height of h, a contact diameter of 2a, and an apex radius of curvature of b.
been arbitrarily classified as having an apparent advancing contact angle (θapa) greater than 150° and a roll-off angle (α) less than 10°. Unfortunately, large contact angles are notoriously difficult to measure accurately, due to a variety of experimental challenges.1−10 Even though these pitfalls have been discussed frequently in the past few years, there is not widespread agreement on the © XXXX American Chemical Society
EXPERIMENTAL OBSERVATIONS
Received: June 20, 2016 Revised: July 25, 2016
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DOI: 10.1021/acs.langmuir.6b02292 Langmuir XXXX, XXX, XXX−XXX
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angle sometimes exceeded 180° due to curvature of the air− water interface at the pillars, reaching values as high as 188°.16 (As an aside, Butt and co-workers’ measurements with a goniometer equipped with a camera and drop shape analysis software gave a “low” value of θapa = 165 ± 3°.) In contrast, at the back edge of drops, water receded by jumping from one pillar to the next. Water on top of the last row of pillars exhibited high curvature. As water lurched along, the apparent receding contact angle (θapr) varied by as much as 15° with a minimum value of θapr = 140 ± 3°. (Measurements from their goniometer gave θapr = 142 ± 5°.) Their measured values of apparent contact angles and sliding angles, summarized in Table 1, were independent of pillar size and spacing.
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MODEL
In this section, a previously proposed model2,10,22−24 that employs linear averaging at the contact line is used to derive predictive equations for pressures, contact angles, and sliding angles for Butt’s surfaces. Suspension? Consider the side view of the sessile water drop shown in Figure 1. The drop has a surface tension of γ, a density of ρ, a volume of V, a height of h, a contact diameter of 2a, and an apex radius of curvature of b. The drop is suspended on cylindrical pillars. This suspension is often referred to as the Cassie state.25 For structured surfaces to impede intrusion, capillary forces acting around the features must be directed upward and of greater magnitude than any downward forces from gravity or Laplace curvature. With modest pressure, the water generally will remain on top of the pillars.2,4,12−15,26−30 Otherwise, if pressure were to increase beyond some critical value, water would be driven into the structure, completely wetting it, creating the so-called Wenzel state.31 In the absence of trapped or compressed gas, the ability of a structured surface to resist intrusion of water can be cast as a competition between the maximum capillary pressure (Δpc) arising from interactions at the contact line versus the hydrostatic pressure (Δph) and Laplace pressure (ΔpL) of the drop,
Figure 2. Side and plan views of a structured surface covered with a square array of cylindrical pillars. The diameter of the pillars is D, and their center-to-center spacing is y. The pillars have flat tops and vertical side walls, ω = 90°. The plan view includes a depiction of a water suspended on the pillars. The black lines and circles represent the dry pillars, and the light blue circles show the interior contact lines of the suspended water. The perimeter contact line at the outer edge of the drop is depicted as dark blue line segments connected by dark blue semicircles.
To assess repellency, a water drop with a volume (V) of 5 ± 1 μL was deposited on one of the surfaces. While observing with confocal microscopy, the surface was gradually tilted along one of the axes of the pillars to a critical angle of α = 9 ± 1°. The drops distorted. After an induction period, they rolled off. Confocal microscopy confirmed that drops were suspended atop the pillars. At the advancing edge, the water interface descended downward and flattened across the pillars, effectively producing an apparent advancing contact angle (θapa) of 180°, as previously anticipated.2,17−21 Locally the advancing contact
Δpc > Δph + ΔpL
(1)
The maximum capillary pressure (Δpc) can be estimated from vertical component of the liquid surface tension (γ) acting on the contact line around the interior pillars,2
Δpc = −Λγ cos(θa + ω − 90°)
(2)
Table 1. Experimentally Measured Intrinsic Contact Angles (θa and θr) from Smooth, Flat Surfaces as Well as Apparent Contact Angles (θapa and θapr) and Sliding Angles (α) for 5 μL Water Drops on the Hydrophobic Square Arrays of Cylindrical Pillars from Butt and Co-workers, along with Estimated Values of Capillary Pressure (Δpc), Sum of the Hydrostatic and Laplace Pressures (Δph + ΔpL), Linear Fraction of the Perimeter Contact Line Touching Pillars (λp), Apparent Contact Angles (θapa and θapr), and Sliding Angles (α) for the Same Surfacesa Measured Values D (μm)
y (μm)
θa (deg)
θr (deg)
θapa (deg)
θapr (deg)
α (deg)
5 10 25
20 40 100
124 ± 2
85 ± 5
180
140 ± 3
9±1
Estimated Values D (μm)
y (μm)
Λ (mm/mm2)
Δpc (kPa)
Δph + ΔpL (kPa)
λp
θapa (deg)
θapr (deg)
α (deg)
5 10 25
20 40 100
39 20 7.9
1580 790 320
150 150 150
0.34 0.34 0.34
180 180 180
147 147 147
7 7 7
a D is the pillar diameter, and y is center-to-center pillar spacing. Λ is the contact line density from eq 3. Δpc, Δph, and ΔpL were estimated with eqs 5−7. Values of λp, θapa, θapr, and α were computed with eqs 10, 15, 17, and 18.
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DOI: 10.1021/acs.langmuir.6b02292 Langmuir XXXX, XXX, XXX−XXX
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πD y2
(3)
ω = 90°
(4)
Λ= and
Combining eqs 2−4 yields
Δpc = −
πD γ cos θa y2
(5)
The hydrostatic pressure (Δph) of the drop depends on its height (h),
Δph = ρgh
(6)
where ρ is the density of water and g is the acceleration due to gravity. On the other hand, the Laplace pressure (ΔpL) depends on surface tension (γ) of water and apex radius of curvature (b) of the drop,32,33
ΔpL =
2γ b
(7)
Pillar Contact and Apparent Contact Angles. In reality, the shape of contact line around the periphery of a suspended drop is quite complex. The free surface of the liquid probably has extensive curvature; local contact angles likely have a strong positional variation. Nevertheless, to simply estimate apparent contact angles, it is assumed that the shape of the contact line at the outer edge of drops can be approximated as a series of semicircles and straight segments,2 as depicted in Figure 2. Semicircles represent the portion of the perimeter contact line on the edge of the pillars and the straight segments, the portion suspended between them. The length of the perimeter contact line on each pillar (lp) is lp = πD/2
Figure 3. Movement of the contact line at the advancing and receding edge of drops. The drop is suspended atop of the pillars. At the advancing edge, the water interface descends downward and drapes itself across the pillars. At the receding edge, the contact line remains pinned until the intrinsic receding contact angle (θr) is established atop the last row of pillars. With further retraction, the contact line jumps to the next row, and the process starts again. Combining eqs 11−14 produces an expression for the apparent contact angle,
θapa = λp(θa + 90°) + (1 − λp) × 180° = λp(θa − 90°) + 180°
(8)
(15) The receding edge of a drop behaves differently than the advancing edge. As the drop retreats, the apparent contact angle decreases. The receding contact line remains pinned until the intrinsic receding contact angle (θr) is established atop the back edge of the last row of pillars,
and the length between them (lb) is
lb = y − D
(9)
The linear fraction (λp) of the contact line that resides on the pillars is λp =
lp lp + lb
=
1 1 + (2/π )(y/D − 1)
θp,r = θr (10)
With further retraction, the contact line jumps to the next row of pillars, and the process starts again. Combining eqs 11−13 and 16 produces an equation for estimating the apparent receding angle (θapr),
and the linear fraction between them (λb),
λb = 1 − λ p
(11)
θapr = λpθr + (1 − λp) × 180° = λp(θr − 180°) + 180°
Apparent contact angles fall between the intrinsic contact angles of the solid pillars and the surrounding air. If we estimate these apparent contact angles as simple linear averages, then the working equation takes the general form,2 θi = λpθp, i + λbθ b
(12)
sin α =
48 γa (cos θapr − cos θapa) π 3 ρgV
(18)
Uncertainty in Model Estimates. The uncertainty in the apparent contact angles and sliding angle was estimated with standard error propagation techniques involving partial derivatives.40 Using the reported experimental error for θa, θr, and V, and assuming the uncertainty in λp is 10%, the uncertainties in predictions of the apparent contact angles and sliding angle are expected to be ±4° and ±2°, respectively. In practice, the uncertainty in the apparent contact angles may be larger than ±4°, especially at the advancing edge. Difficulties in locating the precise point of contact between the liquid and solid, positioning of the baseline, construction of tangent lines, gravitation distortion, and erroneous assumptions about the extent of spreading can all further exacerbate the uncertainty in the measure-
(13)
Figure 3 shows a microscopic depiction of the advancing and receding edges of the water drop. Drops are suspended atop the pillars. At the advancing edge, the water interface descends downward and drapes itself across the pillars. The apparent advancing contact angle (θapa) depends on the intrinsic advancing contact angle (θa) and the reorientation of the air−water interface due to pinning at the pillar edge (ω = 90°),
θp,a = θa + ω = θa + 90°
(17)
Sliding Angle. To estimate sliding angles (α), the global capillary force acting around the perimeter contact line is equated to the body force acting on the mass of the drop.34 The working equation for α takes the following form,35−39
where θp,i is the local contact angle on the outer edge of the pillars, θb is the local contact angle with the air between them, and i = either a or r for advancing or receding contact lines. In all cases, it is assumed that θ b = 180°
(16)
(14) C
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angle of 180°. By adapting an existing model that assumes linear averaging along the contact line, it was possible to accurately estimate apparent contact angles and sliding angles for their surfaces.
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COMPARISON OF EXPERIMENTAL OBSERVATIONS AND MODEL To estimate pressures, contact angles, and sliding angles with the working equations derived here, several additional parameters are needed: the height (h), contact diameter (2a), and apex radius of curvature (b). Butt and co-workers did not report these, but using their values of drop volume (V) and apparent advancing contact angle (θapa), these dimensions can be estimated by plotting Bashforth and Adams’s values7,41 of h, 2a, and b versus V and interpolating. For a 5 μL water drop on a super-hydrophobic surface, drop dimensions are estimated to be h = 1.91 mm, 2a = 0.639 mm, and b = 1.11 mm. Table 1 also lists estimates of pressures, contact angles, and sliding angles for the pillared surfaces produced by Butt and coworkers. Because one size of water drop was used, the hydrostatic and Laplace pressures are expected to be constant for all three surfaces. Most of the downward pressure generated by the drops came from surface tension and curvature, ΔpL = 130 Pa. The sum of hydrostatic and Laplace pressures (Δph + ΔpL) was 150 kPa. On the other hand, the maximum capillary pressure (Δpc) varied with pillar size and spacing, from 1580 Pa for the surface with the greatest contact line density (Λ = 39 mm/mm2) to 320 Pa for surface with the sparsest coverage of pillars (Λ = 7.9 mm/mm2). For all three surfaces, Δpc > Δph + ΔpL. Thus, the model correctly predicts that these surfaces should suspend water. The fractional contact (λp) of water with the pillars around contact line perimeter was estimated with eq 10. In the design of Butt’s pillared surfaces, the aspect ratio D/y was held constant. Therefore, the relative contact around the perimeter of the water drops should be the same for all three surfaces, approximately λp = 0.34, with the remaining “contact line” suspended between pillars. Using this value of λp along with measured values of θa and θr, eqs 15 and 17 predict single values of the apparent advancing contact angle, θapa = 180°, and the apparent receding angle, θapr = 147°. These estimates agree well with the experimental observations, both in their magnitude and their independence of pillar size and spacing. (Equation 15 predicts a maximum local apparent angle of 192°, but from a global macroscopic perspective, θapa effectively will be 180°.) Finally, using eq 18 along with predicted values of θapa and θapr, the sliding angle for 5 μL water drops was estimated to be α = 7° on all three surfaces. On the other hand, if the experimentally reported values of θapa and θapr were used, then α = 10°. Butt and co-workers echoed concerns raised previously. Goniometers tend to underestimate large θapa.1,7,8 Surfaces that are super-hydrophobic generally produce θapa = 180°.2−8,10 Both advancing and receding angles are required to understand repellency.20,28,42 The Cassie−Baxter equation, frequently used to estimate apparent contact angles, does not reflect the underlying physical process43,44 nor does it produce accurate estimates.2,17−19,28,43,44
AUTHOR INFORMATION
Corresponding Author
*Tel.: +1-651-999-1859. E-mail: chuck.extrand@cpcworldwide. com. Notes
The author declares no competing financial interest.
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ACKNOWLEDGMENTS Thanks to M. Acevedo, T. Adamson, L. Castillo, D. Downs, J. Doyon, R. Komma, K. Long, D. Meyer, K. Sekeroglu, K. Vangsgard, G. Wilhelm, and G. Zeien for their support and their suggestions on the technical content and text.
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CONCLUSIONS Videos captured with confocal microscopy by Butt and coworkers confirm earlier claims that water advances across pillared super-hydrophobic surfaces with an apparent contact D
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