Anisotropy in the hydrophobic and oleophilic characteristics of patterned surfaces

A significant difference in the wetting angles of water and oil was observed on patterned substrates, combining interstitial spaces along with hydrophobic solid surfaces, as a function of the orientation. The difference was ascribed to a modification of the liquid–interstice interfacial surface energy due to different degrees of penetration of the liquid. A roughness metric related to the extent to which the liquid infiltrates the interstice normalized by the geometrically determined area is proposed. This study has implications in modulating surface slip behavior and would be of importance in guiding liquid droplets.

The extent of wettability of a surface is dependent on the underlying substrate surface energies (γ). Considering the substrate-wetting liquid energy (γ_SL), the substrate-ambient energy (γ_SA), and the liquid—ambient (e.g., air) energy (γ_LA), two related well-known parametric measures¹ are the spreading parameter, S, and the contact/wetting angle, θ, which are determined through the Young relation as follows:

The extension to predict the wetting behavior of rough or patterned surfaces has been done through the Cassie-Baxter/fakir model: Fig. 1(a) or the Wenzel (W) model and Fig. 1(b), which broadly deal with two extremes related to complete exclusion (/inclusion) of the interstices in the solid substrate by the liquid, respectively. In this letter, we investigate the plausible intermediate regime [Fig. 1(c)], where there would be partial liquid penetration into patterned substrates [Fig. 1(d)]. The parameters of relevance in the Cassie-Baxter and Wenzel models are the respective area fractions of the interstice surface area (ϕ_I) and the solid surface area (ϕ_s), where ϕ_I + ϕ_s = 1, and a somewhat arbitrarily defined roughness parameter (r) which is the ratio of the total surface area to the projected/apparent surface area, which would of course depend on the measurement scale. For instance, the Cassie-Baxter model relates the overall wetting angle (θ_net) to the wetting angle on the air in the interstice (i.e., θ_int) and that in the constituent solid (i.e., θ_sol) as Alternately, the Wenzel model indicates a roughness (r) related θ^W_net through

Per recommendations² on the proper use of Eq. (2), we did not assume that the liquid-vapor interface was smooth and consider liquid penetration into the troughs of the rough surface.³ An effective medium approach (EMA)^4,5 was implicitly assumed to average the water penetration, whereby the extent of the wetting liquid is much larger compared to the underlying texture, and the perturbations to the liquid drop in the interstice could be considered small.

However, a major issue is that these models do not explicitly consider the anisotropy of the underlying substrate texture. The wetting angle related to the placement of a liquid drop (say, of the radius, R ∼ 0.3 cm) on a patterned surface (e.g., with 20 μm (=w) ridges, with ϕ_I = 0.5) would not be expected through the use of the fakir and the Wenzel models to be a function of the orientation of the ridges. However, experimentally, we did notice a change with a larger contact angle when the drop would be translated perpendicular to the ridges compared to an orientation parallel to the ridges (Fig. 2). The two contact angles imply differing radii of curvature for the impregnated liquid parallel and perpendicular to the ridges.¹ 

Much previous work on the anisotropy of wetting on textured surfaces⁶ has not quantitatively estimated the penetration of liquid into interstices.⁷ Measurements on sub-micron scale triangular grooves indicated⁸ a state where the water completely penetrates the grooves. It was also discussed⁹ that a water droplet may be suspended on patterns (modified with hydrophobic coatings¹⁰) and does not directly contact the substrate. Along with contact angle hysteresis,¹¹ a proposal that the contact angle decreases as penetration progresses was posited.² A related aspect of interest concerns the wetting dynamics, e.g., in low Reynolds number (Re) flow. The fakir and the Wenzel models are often implicitly assumed in fluid flow¹² for understanding the efficacy of hydrophobic/super-hydrophobic surfaces in reducing fluid drag and inducing slip,¹³ through reduced shear stress at the moving liquid-air interface. It is the aim of this paper to examine the influence of anisotropy related to the substrate¹⁴ on the wetting characteristics in static and quasi-static scenarios and lay out the physical rationale behind liquid penetration into the grooves.

The tested Parylene-C coated patterned surfaces (on Si substrates) were patterned through standard photolithography. Briefly, coated photoresist on a Si wafer (n-type, ⟨110⟩, and a thickness of 500 μm) was patterned, developed, and subject to reactive ion etching (RIE) to a trench depth of about 95 μm. The photoresist was then removed, and the surface was coated with 1 μm thick Parylene-C. The ridged pattern surface morphology is shown in Fig. 1(d). The average width (w) and height (h) were ∼18 μm and ∼95 μm, respectively, at a distance (d) of 18 μm. We define an interstice fraction (ϕ_I) as the ratio [=d/(d + w)], with distances measured through scanning electron microscopy. Two different substrate patterns, lithographically designed for ϕ_I = 0.5 and ϕ_I = 0.75, were used. To probe the related anisotropic wetting characteristics, a liquid drop (i.e., 10 $μL$ water, with a γ_LA value of 72.8 mJ/m², and 3 $μL$ oil: Krytox^® GPL104,¹⁵ with a γ_LA value of 18 mJ/m²) was placed on the Parylene-C coated patterned substrates (using a reported¹⁶ γ_SV value of 46.2 mJ/m²), and the contact angles were observed in two orthogonal orientations at 20 °$C$ using a Ramé-Hart Model 190 Contact Angle Goniometer. For comparison, the contact angle of water drops on the Parylene-C coated substrate (flat and unpatterned) was ∼94.6°, with a corresponding γ_SL value of 51 mJ/m² estimated through Eq. (1b). Detailed contact angle measurements as a function of the orientation are indicated in Fig. 2 and listed in Table I.

We denote the S-L energies on the patterned surfaces as γ_SL, _mod, as modified from the values obtained from those on unpatterned Parylene-C coated surfaces. The shapes of the droplets were elliptical, with the major axis along the ridge/groove, indicative of macroscopic preferential wetting in such a direction. In all cases, the underlying pattern texture enhanced the degree of hydrophobicity, compared to the planar substrate, as indicated by an increase in the wetting angle to greater than 94.6°. It was noted that the contact angles on the patterned surfaces differ significantly, e.g., by ∼36° (the difference between 147° in the perpendicular orientation and 111° in the parallel direction) and correlate with the variation in the estimated γ_SL (=γ_{SL, mod}) from ∼107 mJ/m² to ∼72 mJ/m².

Generally, when a liquid drop is placed on a patterned surface, a small deflection/bowing (δ) of the liquid into the interstices (I) is expected based on gravitational considerations¹ [Fig. 1(c)]. We consider the surface energy related to the liquid over the interstices as γ_LI, e.g., γ_LI = γ_LA, if the interstice is mostly air (A). Here, for a liquid drop of radius R and an interstitial length of d, from elementary geometrical considerations, δ ∼ d²/8R. Such deflection is also favored on energetic considerations,¹⁷ when γ_LI is smaller/comparable to γ_SL. However, considering gravitational forces in addition to surface tension, δ would be proportional to R³/l_c², and the lateral spread (l_spread) on the substrate would be proportional to R²/l_c, where l_c (=$γ/ρg$⁠) is the capillary length, with ρ as the liquid density and g the acceleration due to gravity. Consequently, a larger δ or l_spread would be favored by a larger/heavier drop and a smaller γ. Then, for a given drop size, the drop infiltrates into the interstice or spreads to lower the net γ. For a large liquid drop on top of a patterned surface, where R ≫ w and d, the net γ could be formulated through

Here, $ϕI′$ is related to the extent to which the liquid penetrates the interstice and may not necessarily be equal to the geometrically patterned ϕ_I. While we designed our patterns [see Fig. 1(d), with ϕ_I (= ϕ_s) = 0.5], a smaller γ_LI (/ γ_LA) would implicate a larger $ϕI′$ when other parameters in Eq. (3) are fixed. The computed γ_SL,mod would then be a better metric to estimate the spreading (S) instead of γ_SL.

A measure of drop spreading¹⁸ could occur due to a very small pressure gradient, additional to l_spread. When a liquid drop is moved parallel to the direction of the ridges, a given unit of the drop is constantly in contact with the underlying solid or the interstitial region, during the entire trajectory of the motion. However, when the liquid drop is moved perpendicular to the direction of the ridges, the drop unit alternates contact between the underlying solid and the interstitial region. Consequently, in the latter case, the moving liquid drop does not benefit from penetrating further into the interstice, as in the former situation. It would also be expected that a larger air fraction would increase the penetration and further decrease the extent of wetting on top of the patterned surface, manifesting a larger contact angle [Table I]. It is pertinent to note that that such impregnation of the liquid into the interstices yields an overall lower macroscopic wetting of the surface of the patterned substrate.¹⁹ 

Using Eq. (3), with a computed γ_SL,mod of ∼72 mJ/m² (from Table I), ϕ_s = 0.5, γ_SL = 51 mJ/m², and γ_LI ∼ 72.8 mJ/m², we obtain a $ϕI′$ value of 0.64 [Table II (a)]. Alternately, with a γ_{SL. mod} value of ∼107 mJ/m² and ϕ_s = 0.5, we obtain $ϕI′$ = 1.12 [Table II (a)]. It is to be noted that as $γLI>γSL$⁠, the liquid would be in intimate contact with the solid surface. Then, ϕ_s and the related $γSL$ would not change and be equal to the geometrical/patterned value. The solid-liquid interfacial area could then be essentially considered flat. In both cases, the obtained $ϕI′$ is greater than the patterned ϕ_I of ∼0.5. The corresponding $ϕI′$ values, with a ϕ_s value (or a ϕ_I value of ∼0.75) of ∼0.25, were 1.02 and 1.31—see Table II(a), for the parallel and perpendicular orientations, respectively. Generally, spread of liquid into the groove would be expected since γ_SL (∼51 mJ/m²) is less than γ_LI (∼73 mJ/m²); this would be in addition to the gravity induced penetration into the interstice.

Correlating the contact angle measurements in Table I and the corresponding $ϕI′$ in Table II (a), we can find that larger water penetration will result in larger $ϕI′$ and contact angle, and the anisotropy of wetting angles can be attributed to the different degrees of water penetration in different directions. We also directly observe water penetration via confocal microscopy (using a Photron FASTCAM camera) [Fig. 3 and inset]. The side-view images, on the bottom left and right of Fig. 3(b), indicate both non-uniform and partial penetration of the liquid (red dotted lines) and full penetration into the interstices, respectively. Our studies preclude evaporation related considerations.²⁰ 

The obtained γ_{SL. mod} values, together with the degree of penetration of the liquid into the interstices, are intermediate to the solid substrate surface energies (∼46.2 mJ/m²) and the summation of the surface energies of the solid substrate and the liquid of ∼119 mJ/m² (=72.8 mJ/m² + 46.2 mJ/m²), where water was completely penetrating the interstices and tending to avoid the top solid substrate. The anisotropic tendencies in the underlying substrate modulate the extent of wetting/hydrophobic character.

We additionally tested the influence of anisotropy through the placement of Krytox^® GPL104 oil on the patterned substrates, with a patterned ϕ_s of 0.5. It was noted that the contact angles parallel and perpendicular to the ridges was ∼21.0° and ∼30.1°, respectively. For reference, the contact angle of the oil drop on the unpatterned Parylene-C coated surface was ∼24.1°, implying a γ_SL value of 29.6 mJ/m², from Eq. (1b). While the smaller angles indicate a greater oleophilic character for the patterned surfaces, we estimate from Eq. (3), correspondingly higher $ϕI′$ of ∼0.8 and ∼0.9, respectively, as in Table II(b)—indicating again an area enhancement of the oil in the interstice. Contrasting the time-dependent behavior of the water and the oil on the patterned surface (Fig. 4), while the shape of water did not change much with time with little spreading, the oil drop spreads along and into the grooves quickly. A film propagates in advance of the oil drop, indicating the enhanced oleophilic character due to the ridges.

Based on the results of our measurements and analyses, it is concluded that the anisotropy of wetting is related to the liquid penetration, where a larger effective air fraction implies larger penetration, yielding a larger contact angle. In most studies²¹ related to the influence of patterned surfaces on inducing hydrophobic behavior, the degree of liquid penetration into the interstices has not been much considered.²² The ratio of the estimated $ϕI′$ to ϕ_I (which may be larger or smaller than unity) would enable the definition of a roughness metric, in contrast to the traditional¹ definition [Eq. (2b)]. We have indicated that a larger penetration, with a larger interfacial area/contact angle and lower shear, would be of significance in modulating hydrophobic and surface slip behavior. The concomitant traversal direction dependent penetration of the liquid into the interstices may also be related to the system size and a shear-dependent effective slip length.²³ 

Related considerations would also be of importance in guiding liquid droplets, e.g., in electrophoretic applications²⁴ and the design of drag-reducing super-hydrophobic surfaces.^13,22 Future work would focus on the study of liquid flow dynamics as a function of the degree of anisotropy of the underlying patterned surfaces.

The authors are grateful for support from the National Science Foundation (NSF: CMMI 1246800 and CBET 1606192). The discussions with A. Bhattacharya are appreciated. We also appreciate the assistance of Professor James Friend, Shuai Zhang, and Dr. Jonathan Yu for help with imaging and confocal microscopy.