January 2008 EPL, 81 (2008) 26006 doi: 10.1209/0295-5075/81/26006 www.epljournal.org Impalement of fakir drops M. Reyssat 1,J.M.Yeomans 2 and D. Quéré 1 1 Physique et Mécanique des Milieux Hétérogènes, UMR 7636 du CNRS, ESPCI - 75005 Paris, France 2 The Rudolf Peierls Centre for Theoretical Physics, University of Oxford - 1 Keble Road, Oxford OX1 3NP, UK received 7 September 2007; accepted in final form 19 November 2007 published online 20 December 2007 PACS PACS 68.08.-p Liquid-solid interfaces 68.08.Bc Wetting Abstract Water drops deposited on hydrophobic materials decorated with dilute micro-posts generally form pearls. Owing to the hydrophobicity of the material, the drop sits on the top of the posts. However, this fakir state is often metastable: if the drop impales inside the texture, its surface energy is lowered. Here we discuss the transition between these two states, considering the drop size as a parameter for inducing this transition: remarkably, it is found that a drop impales when it becomes small, which is interpreted by considering its curvature. This interpretation allows us to propose different recipes for avoiding this detrimental effect. Copyright c EPLA, 2008 As shown by Young two hundred years ago, the contact angle of a drop on an ideal solid is fixed by the nature of the three coexisting phases [1]. On real surfaces (that is, chemically heterogeneous and rough), the contact line can be pinned on the solid defects, leading to multiple contact angles (contact angle hysteresis). On such solids, if the drop size becomes comparable to the size of the solid defects (often micrometric), rearrangements occur, which explain why the contact angle is generally observed to vary as the drop gets smaller than typically one micrometer [2]. Here we consider hydrophobic solids decorated with regular arrays of micropillars. This design was shown to promote both super-hydrophobicity and structural colors, for post density below 10% [3 6]. Two states are possible for a drop on such a solid: either the drop sits on the tops of the pillars (fakir state, first described by Cassie), or it sinks inside the texture (impaled state, known since Wenzel) [6 8]. In the fakir state, the contact angle is high (there is mainly air below the drop), and the contact angle hysteresis is low (owing to a the reduced solid/liquid contact). In the impaled state, the contact angle is close to the one on a flat hydrophobic surface (the pillars are dilute), and the hysteresis may be very large, owing to the strong pinning of the contact line on the pillars. In the limit of dilute microstructures, the fakir state should generally be metastable [6,7]. Irreversible transitions towards the more stable impaled state can be provoked by applying a pressure on the drop [8], or by making it impact the structured material [9,10]. It was also shown that the drop size may also influence its state: on a given substrate, water deposited as a spray was found to be pinned in the texture, while millimetric water drops were found to float [8]. This was made more precise by monitoring the evaporation of a drop: on sufficiently dilute pillars, it is indeed observed that the wetting state changes as the drop becomes smaller than a critical value, and this was interpreted as a transition between the fakir and impaled states [11,12]. Here we discuss this transition, and focus in particular on its origin. Our scenario allows us to propose solutions for avoiding this effect, which is generally detrimental: then drops are sticky, contrasting with what is expected for water-repellent materials. Our samples are made of silicon, and decorated with cylindrical micropillars of micrometric diameter d, height h and mutual distance l. The pillars are obtained by photolithography and deep reactive ion etching, allowing us to vary independently the different geometric parameters of the pattern [13]. The surface is coated with a fluoropolymer which is responsible for the chemical hydrophobicity of the samples: deposited on a flat surface, it provides a contact angle θ for water between 100 and 110, while adding a dilute texture makes the angle jump to a value of about 160. As a signature of the fakir state, the receding contact angle (observed as a millimetric drop evaporates) remains high, around about 140. Figure 1 shows the successive states of a water drop evaporating on a substrate whose posts characteristics are d =3µm, h =4.8 µm andl =17µm, which defines a surface concentration φ S = πd 2 /4(l + d) 2 of 2%. During a first stage (five first snapshots), the contact angle remains constant as the drop evaporates, at a value of 138 ± 3. Such a high receding angle (the advancing one 26006-p1
M. Reyssat et al. Fig. 1: Evaporation of a water drop sitting on a hydrophobic surface decorated with pillars (visible in the photos) of diameter d =3µm, height h =4.8 µm and distance l =17µm. The initial radius is 120 µm, and the time interval between two successive photos is 5 s. As the drop radius reaches 75 µm (fifth snapshot), the state of the drop abruptly changes, from a super-hydrophobic state to a hydrophilic-like one. for this system is 165 ± 2 ) indicates that the drop is in a fakir state, as noted above. However, this state changes when the drop becomes smaller than a critical radius R of 75 µm in the experiment reported in fig. 1. High-speed imaging of the transition (shot at 8000 frames per second) proved that it is very sudden, taking place in about 1 ms. Then, the angle gets much smaller, by about 80 (which implies a sharp increase of the solid/liquid contact), and it keeps on decreasing: the liquid is very efficiently pinned, and the receding angle gradually vanishes, from an initial value of 60 down to zero, despite the hydrophobicity of the material. This behavior can be interpreted as resulting from an impalement of the drop in the texture, this state being characterized by a giant hysteresis of the angle [8]. This interpretation can be confirmed by examining the trace left on the material after evaporation (fig. 2). A circular stain [14] is observed at the bottom stage of the solid, where it follows the pillars on which pinning took place, proving that the drop indeed sank inside the texture. Each drop in fig. 1 is a spherical cap with a liquid/vapor interface whose surface area can be easily determined as a function of time. Similarly, it develops an apparent solid/liquid contact, which can also be measured. The impalement transition is also evidenced by following the evolution of both these surface areas, as shown in fig. 3. It is observed that both surface areas first decrease linearly with time, before being subjected to a discontinuity at the transition: there the (apparent) solid/liquid surface area (squares) abruptly increases, owing to a spreading in the texture; later, it becomes constant, indicating a pinning of the contact line. Simultaneously, the surface area of the spherical cap (circles) decreases sharply at the transition, and then more slowly till it joins the value for the solid/liquid area: in the final stage of evaporation, the drop is flat (zero receding angle). Fig. 2: Trace left after drop evaporation in the experiment of fig. 1. A stain resulting from the evaporation-driven flow of dust present in water is clearly visible at the bottom stage of the textured material. The stain follows the pillars, showing that the drop sank inside the texture, and then got pinned on the microstructures. The bar indicates 50 µm. Fig. 3: Surface areas of the drop evaporating in fig. 1, as a function of time. The circles show the evolution of the surface area of the liquid/vapor spherical cap, while the squares hold for the apparent solid/liquid surface (base of the drop). At the transition, both surface areas vary discontinuously. Error bars are of the order of the symbol sizes. It is sometimes suggested that gravity might play a role in drop impalement. This looks surprising considering the scale of the phenomena (such that surface effects largely dominate gravitational ones), and we checked that gravity is indeed not responsible for the transition. We redid again the experiment described in fig. 1, yet upside down. The drop is first deposited on the sample, which then is flipped (along an horizontal axis), so that the drop eventually hangs from the solid. The flip is made when the drop is small enough, in order to avoid its detachment as it gets hung. However, its radius at this moment still is significantly larger than R, showing that the transition, which occurs much later, is not provoked by the flip itself. 26006-p2
Impalement of fakir drops Fig. 4: Sketch of the liquid/vapor interface below a fakir drop. We denote δ as the distance between the bottom of the interface and the top of the posts, andα as the angle between the vertical and the tangent to the interface at the post edge. The drop keeps on evaporating, and the transition is observed for the very same critical radius as in fig. 1. We now examine why such a transition should take place, and what can be the conditions for provoking it. Let us first stress that on materials with a high dilution of micropillars, the fakir state is generally metastable, owing to the presence of liquid/vapor interfaces (of large surface energy) below the drop. Comparing the surface energies of the fakir and the impaled states suggests that a stable fakir state is only possible if the chemical hydrophobicity is large enough: the fakir state has a lower energy than the impaled one if the cosine of the contact angle θ on the bare surface is smaller than (φ S 1)/(r φ S ), denoting r as the roughness of the substrate [6]. In our case (where we generally have d<h and d<l), this condition can be rewritten, as a function of the pillar density φ S and aspect ratio Λ = h/d: cosθ< 1+4Λφ S. For high dilutions (φ S =0.01), this condition cannot be fulfilled, even for large aspect ratio (Λ = 10), owing to the limitations in chemical hydrophobicity (cos θ cannot be smaller than 0.5). Hence if the bottom interface of a floating drop contacts the ground level of the material, we expect the propagation of a solid/liquid contact, of smaller surface energy. Since the curvature of the drop must be constant everywhere, the liquid/vapor interface below the drop must be bent (fig. 4). Denoting δ as the maximum deformation of the interface below the drop, the curvature of this interface will scale as δ/l 2 (considering δ<l). Equating this curvature with the one of the drop (of radius R) yields: δ l 2 /R. A solid/liquid contact will be nucleated on the bottom of the solid provided that δ>h, which gives: R<R l 2 /h. (1) For small pillars (h l), the radius R can become quite large, as observed for example in fig. 1. For l =17µm and h =4.8 µm, eq. (1) predicts R =60µm, a value indeed comparable to the one determined in fig. 1 (R =75µm). More interestingly, this interpretation suggests routes to build super-hydrophobic materials able to resist a pinning transition, even for small droplets. A first way consists of reducing the size of the microstructures. Having microstructures of the order of 100 nm leads to critical radii of the same order, for which evaporation should be quasi-instantaneous: such drops would never get pinned. This might be an explanation for the existence in nature Fig. 5: Evaporation of a water drop (initial radius of 90 µm) sitting on a hydrophobic surface decorated with pillars of diameter d = 3 µm, height h = 36.5 µm and mutual distance l =17µm. The time interval between two successive photos is 9 s. In the second snapshot, the drop radius is about 75 µm, value at which impalement took place in fig. 1: owing to the use of long pillars, the drop can here reach a much smaller radius without sinking in the texture. of sub-structures at this scale, in particular on plant surfaces or at the surface of some mosquito s eyes, which seem to remain dry even if exposed to sprays or fogs [15]. Equation (1) suggests another way for avoiding drop impalement, which consists of making the structures higher, keeping the distance l between posts large enough to maintain a strong hydrophobicity. We show in fig. 5 the successive states of an evaporating drop deposited on a substrate of same pillar density as in figs. 1 and 2, yet consisting of much higher pillars (36.5 µm instead of 4.8 µm). This can be achieved by alternating in the microfabrication process phases of etching and passivation of the surface (Bosch process), allowing us to reach aspect ratios Λ for the pillars as high as 15 [13]. It is observed that the drop remains at the top of the pillars, even if its size is much smaller than in fig. 1. Note that the fakir state is here directly imaged in fig. 5, since the distance between the bottom of the drop and the top of its reflection is seen to be twice the pillar height h, which is here much larger (by a factor 8) than in fig. 1. However, the end of the sequence in fig. 5 (seventh snapshot) is difficult to interpret directly (even if we clearly see that some distance remains between the drop and its reflection). It is possible to go slightly further by investigating the dust figure left after evaporation. The pattern, shown in fig. 6, is very different from the one in fig. 2. The dust now only concentrates on very few pillars, showing that the drop does not pin (i.e. remains in the fakir state) till the end (or very close to the end) of the process. In addition, the dust cluster is found to be located close to the top of the structures, which emphasizes the ability of the drop to resist impalement. Even if it sank at the very end, the (tiny) drop was volatilized before touching the bottom. This effect might contribute to avoid a pollution inside the microtextures, which are difficult to clean. More generally, we measured the critical radius of impalement R for water drops deposited on substrates of various designs (either changing the pillar height 26006-p3
M. Reyssat et al. Fig. 6: Electron microscope picture of the dust trace left after drop evaporation (corresponding to the experiment of fig. 5). This surface has the same density as in fig. 2, yet much higher pillars (h =36.5 µm instead of 4.8 µm). It is observed that the dust accumulates around a few pillars, on a size of about the inter-pillar distance l (here, 17 µm), showing that the drop did not impale till the end of evaporation. keeping the mutual distance constant, or vice versa). Our results are displayed in fig. 7. The critical radius of impalement is found to be in good agreement with our expectations (eq. (1)): it increases linearly with the geometric parameter l 2 /h, and it is of the order of this parameter. However, deviations are observed at small l 2 /h, and we now discuss possible origins for them. Up to now, we implicitly assumed that the contact lines below the drop remain pinned on the edges of the posts, until the liquid/vapor interface reaches the bottom. As known since Gibbs, edges allow for such a pinning, provided that the angle α (defined in fig. 4) remains between π/2 θ and θ, where θ is the contact angle on the bare surface (typically between 100 and 110 on hydrophobic surfaces). Reasoning, for simplicity, in two dimensions, we notice that α is fixed by the geometry (see fig. 4): we have cos α = l/2r, R being the radius of curvature of the drop and thus of the liquid/vapor interface. Hence, we get that the pinning condition α<θ is satisfied provided that R is larger than l/2 cos θ. Hence small drops will sink because they cannot pin. Conversely, if the threshold radius R l 2 /h is larger than the radius of depinning l/2 cos θ, eq. (1) should hold; the latter condition yields l>h/ cos θ, which is generally satisfied in our experiment. However, the regime at small values l 2 /h (in fig. 7) corresponds to samples with tall pillars (h comparable to l, or even larger). Then, our scaling for the curvature is not valid anymore. In addition, as emphasized above, the drop cannot pin on the pillar edges: for h>l cos θ, we expect an impalement driven by the inability of pinning, with a corresponding critical radius R of the order of l/ cos θ. In the limit of moderate hydrophobicity (θ tends towards 90 ), this distance diverges, which (logically) means that the drop should always sink. In our experiments, we made Fig. 7: Critical radius of impalement for water drops evaporating on hydrophobic substrates covered with micropillars of diameter d, height h and distance l, as a function of the geometric factor l 2 /h ( : l =7µm (h =3.9 µm); : l =11µm (h = 9.2, 9.9 µm); : l =17µm (h =2.3, 2.6, 3.4, 3.6, 4.4, 4.8, 5.5, 8, 11, 18 µm); : l =25µm (h =4.4, 19.6 µm)). The inclined dotted line indicates eq. (1). The thin plateau at small l 2 /h gives the value of l/ cos θ (for which impalement induced by depinning should occur), for l =17µmandθ = 110. Error bars indicate dispersion, corresponding to at least five experiments per substrate. series of data by varying h, keeping l constant: then, the depinning regime should be characterized by a plateau at small l 2 /h (i.e. large h), at a value R l/ cos θ. We draw in fig. 7 such a plateau for the data with l =17µm and for θ = 110 (which yields R =45µm). In this regime where the critical radius of impalement is very small, data are quite scattered and imprecise. However, we indeed observe a tendency for the data to intercept the ordinate axis at a non-zero value, as the abscissa vanishes. We can finally note that there again, a reduction in the size of the microtextures implies a smaller R (the interesting practical limit), in qualitative agreement with the experiments performed by Jiang et al. with spray on mosquito eyes decorated by nanometric posts for which impalement is not observed, in spite of the small height of the textures [15]. Other factors might contribute to induce impalement. For two months, we found impalement radii significantly larger (by a factor sometimes as high as 2) than reported in fig. 7. At that time, work was done in a building close to ours: air was extremely dusty, carrying mineral particles resulting from the destruction of this building. If deposited on our substrates, these hydrophilic particles of size comparable to the microstructures should act as nucleation sites for the transition: menisci forming between water and these particles obviously favor the formation of contacts between the bottom stage of the 26006-p4
Impalement of fakir drops textured material and liquid. The only way to opposing this detrimental effect would consist of using materials for which the fakir state is of lower energy than the impaled Wenzel state (criterion discussed before fig. 4). The drop itself might be contaminated. We looked at drops containing small quantities of surfactants. Then, as the liquid evaporates, the surfactant concentrates in the drop, inducing a lowering of its surface tension. Then, pinning transitions were observed for radii much larger than discussed here (of the order of 500 µm, and depending on the initial concentration of surfactant), showing that wetting properties are affected by the presence of surfactant, which was both able to decrease the liquid surface tension and to adsorb on the material, making it hydrophilic. As a conclusion, we showed in this letter that a pinning transition may take place for drops deposited on super-hydrophobic surfaces consisting of dilute arrays of micro-pillars. This transition is driven by the drop size, but surprisingly it is found that the drops impaling inside the texture are the small ones! This was interpreted geometrically, by considering the curvature of the liquid/vapor pockets below the drop: if the impaled state is of lower energy than the fakir one, once a contact is generated on the bottom surface, it should propagate, and this contact can be initiated by the bending of these interfaces as the drop gets smaller. This transition can thus be avoided provided that the pillars are long enough: such designs can be made by deep etching techniques (as used here), but other examples have been recently proposed in the literature, which realize this condition: forests of nanotubes [16,17], or hairy materials [18]. It would be worth checking if indeed drops keep floating as they evaporate on these materials. The question of the behavior of an evaporating drop on a disordered (or more complex) substrate remains open: we can imagine multiple possible states for the drop as it vanishes, so that the simple transition described here should be replaced by multiple transitions. Our findings might be also useful to understand quantitatively why a pinning transition can be induced by applying a pressure, as observed experimentally [8] and in simulations [19]. Similarly, the condition of a constant pressure in the drop implies deformations of the bottom surface, which is likely to reach the base of the substrate. It would be interesting to understand how the system behaves if the impaled state has a larger energy than the floating one: then, the liquid should resist pinning, even for pressures large enough to induce a contact between the interface and the ground. 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