Origins of liquid-repellency on structured, flat, and lubricated surfaces
Dan Daniel, Jaakko V. I. Timonen, Ruoping Li, Seneca J. Velling, Michael J. Kreder, Adam Tetreault, Joanna Aizenberg
OOrigins of liquid-repellency on structured, flat, and lubricated surfaces
Dan Daniel, ∗ Jaakko V. I. Timonen, Ruoping Li, Seneca J. Velling,Michael J. Kreder, Adam Tetreault, and Joanna Aizenberg † John A. Paulson School of Engineering and Applied Sciences,Harvard University, Cambridge, MA 02138, USA
There are currently three main classes of high-performance liquid-repellent surfaces: micro-/nano-structured lotus-effect superhydrophobic surfaces, flat surfaces grafted with ‘liquid-like’ polymerbrushes, and various lubricated surfaces. Despite recent progress, the mechanistic understandingof the differences in droplet behavior on such surfaces is still under debate. We measured thedissipative force acting on a droplet moving on representatives of these classes at different velocities U = 0.01–1 mm/s using a cantilever force sensor with sub- µ N accuracy, and correlated it to thecontact line dynamics observed using optical interferometry at high spatial (micron) and temporal( < noTPCL lo s l s liquid-solid-airTPCL liquid-solid-airTPCL s l a b c SOCAL super-hydrophobic lubricated polymer brushes (nm) droplet
FIG. 1. Schematics of liquid-repellent surfaces. a, Structuredlotus-effect superhydrophobic (SH) surfaces. b, Flat surfacesgrafted with polymer brushes, dubbed Slippery OmniphobicCovalently Attached Liquid (SOCAL) surfaces. c, Structured(left) or flat (right) lubricated surfaces. The droplet is shownwith a lubricant cloaking layer, which is usually the case forlow-surface-tension lubricants (see Supplementary Fig. S1).
In Nature, the ability to repel water is often a mat-ter of life and death. For example, insects must avoidgetting trapped by falling raindrops and plants need tokeep their leaves dry for efficient gas exchange throughthe stomata [1, 2]. Similarly, the tendency of water andcomplex fluids, such as blood and oil, to stick to sur-faces pose many problems in industries, ranging fromfuel transport, biomedical devices to hydrodynamic dragin ships [3, 4]. Hence, there is a huge interest in devel-oping liquid-repellent materials. To achieve this, thereare three main approaches. Firstly, hydrophobic micro-/nano-structures can be designed on the surface to main-tain a stable air layer, minimizing contact between theapplied liquid and the solid, i.e. lotus-effect superhy-drophobic (SH) surfaces (Fig. 1a) [3, 5]. Secondly, a ∗ [email protected] † [email protected] flat surface can be grafted with nanometer-thick ‘liquid-like’ polymer brushes (Fig. 1b); the resulting surface,known as Slippery Omniphobic Covalently Attached Liq-uid (SOCAL), is able to repel a wide variety of liquids, in-cluding low-surface-tension alkanes [6–8]. Finally, a suit-able lubricant oil can be added to the surface, which canbe structured as is the case for Slippery Liquid-InfusedPorous Surfaces (SLIPS) [9, 10] or flat as is the case oflubricant-infused organogels [11, 12] (Fig. 1c); any liquidcan then easily be removed, as long as there is a stableintercalated lubricant layer [13–16].While the behaviors of liquids on each of these threesurface types have been studied separately, there havebeen few attempts to compare their relative performanceor explain their unique characteristics. In this letter, wewill elucidate the origin of liquid repellencies for the threesurface classes and how the details of the liquid-solid-airthree phase contact line (TPCL) at the droplet’s base—orthe absence of TPCL in the case of lubricated surfaces—cause qualitatively different behaviors.To quantify and compare the liquid repellencies ofthese surfaces, previous work generally reports the staticapparent contact angle θ app and the contact angle hys-teresis ∆ θ = θ adv − θ rec , where θ adv, rec are the advancingand receding contact angles measured optically from theside (See Table I and Supplementary Tables S1 and S2for typical values) [17]. The dissipative force acting onthe moving droplet F d is related to the contact anglehysteresis ∆ cos θ = cos θ rec − cos θ adv by the Furmidge’srelation: F d = 2 aγ ∆ cos θ , (1) TABLE I. Typical contact angle values for a water dropletSurface θ app ∆ θ ∆ cos θ SOCAL 90–110 ◦ ◦ > ◦ ◦ ◦ ◦ a r X i v : . [ phy s i c s . f l u - dyn ] J a n where a and γ are the base radius and the surface ten-sion, respectively [17, 18]. For the three surface classes, awater droplet is reported to have similar hysteresis valueof ∆ θ < ◦ ; however, for these studies, the exact exper-imental conditions—in particular, the speed of the con-tact line—are often not controlled, which is importantbecause F d (and therefore ∆ θ and ∆ cos θ ) can dependon the droplet’s speed U [19, 20]. Moreover, there aretechnical challenges to contact angle measurements: θ is difficult to determine accurately when its value is toohigh > ◦ (SH surfaces) or when obscured by a wettingridge (lubricated surfaces) [16, 21, 22].To better characterize the differences between thethree surfaces, we measured F d directly using a cantileverforce sensor, as described in our previous work (Fig. 2)[14, 23, 24]. The force acting F t ( t ) acting on the dropletmoving at a controlled speed U was inferred from thedeflection ∆ x ( t ) of the capillary tube attached to thedroplet: F = k ∆ x , where k = 5–25 mN/m for tube-lengths L = 6–9 cm.Fig. 2a shows the characteristic force curves for thethree surface classes. F d was taken to be the long-timeaverage of F t once it had reached a steady state. For alotus-effect surface decorated with micropillars (hexago-nal array, diameter d = 16 µ m, pitch p = 50 µ m, andheight h p = 30 µ m), the force required to jumpstart themotion F peak = 6.6 µ N is larger than the force to main-tain the motion F d = 5 . ± . µ N, reminiscent of thestatic and kinetic friction forces between two solid sur-faces [24]. In contrast, for lubricated and SOCAL sur-faces (see Supplementary section S2 for details on samplepreparation), there is no distinct F peak . At time t ≈ x = 0) and F t →
0; in contrast, for SOCAL and lotus-effect surfaces, F t did not return to zero, but reached afinite value F min ( F t → F min > F min and decay times.As U was varied in the range of 0.01–1 mm/s, we foundthat F d ( U ) acting on a 1 µ l water droplet exhibits dif-ferent functional forms for the different surface types,suggesting different mechanistic origins for the liquid-repellency (Fig. 2b). Firstly, there is a minimum forcerequired to move the water droplet on SH and SOCALsurfaces, F min = 4 and 5 µ N, respectively; in contrast, F d → U → F min = 0. Secondly, F d is inde-pendent of U for SH surfaces (dash-dot line, Fig. 2b), buthas a non-linear dependence on U for SOCAL and lubri-cated surfaces (dashed and solid lines, respectively). Tovalidate the measurements using the cantilever force sen-sor, velocity data (open squares) of water droplets slidingdown the same SOCAL surface at different θ tilt has beensuperimposed on the same plot.These observations account for the qualitatively differ-ent droplet motion on a tilted surface. A 10 µ l waterdroplet was pinned on SH and SOCAL surfaces, when θ tilt is below a critical angle θ crit ≈ ◦ ; above θ crit , at FIG. 2. a, Characteristic force curves for a water droplet mov-ing on the three surface classes measured using a cantileverforce sensor. The motor (to move the substrate) was startedat time t = 0 s and stopped at t ≈
50 s. b, F d for 1 µ lwater droplets moving at speeds U = 0.01–1 mm/s on SH,SOCAL, and lubricated surfaces (filled circles, filled squares,and empty circles, respectively). U of droplets tilted at dif-ferent θ tilt = 25–90 ◦ on the same SOCAL surface and hencesubjected to different F d = W sin θ tilt are shown on the sameplot (empty squares). Each data point has three repeats with∆ F d < µ N, unless otherwise indicated by error bars. θ tilt = 15 ◦ , the water droplet accelerated at a = 0.4 m/s on the SH surface, but moved at constant velocity U const = 8 mm/s on the SOCAL surface (Fig. 3a, b). Even-tually, the accelerating droplet on the SH surface willreach a terminal velocity—likely due air drag—but at amuch larger U const ∼ m/s [5]. In contrast, for lubricatedsurfaces, the droplet was never pinned and moved at in-creasing U with increasing θ tilt (Fig. 3c).To understand the origin and hence the functional formof F d , we analyzed the base of moving droplets on dif-ferent surfaces using reflection interference contrast mi-croscopy (RICM) (Fig. 4) [25]. We used a similar set-up previously to study the lubricant dynamics of lubri-cated surfaces (See supplementary section S2) [14]. UsingRICM, we were able to confirm the presence of a stablemicron-thick air film beneath the droplet on a SH sur-face (Cassie-Baxter state) and to visualize the details ofthe contact line with much improved temporal and spa-tial resolutions compared to other techniques. For ex- FIG. 3. Droplet motion on tilted substrates with θ tilt = 5 ◦ and 15 ◦ for the different surface classes. Depending on whether adroplet is moving with a constant speed U or constant acceleration a , the displacement x varies linearly or quadratically with t , respectively. ample, previous studies using confocal fluorescence mi-croscopy usually require a dye to be added to the wa-ter droplet—which can affect its wetting properties—and can only achieve a temporal resolution of ∆ t of sev-eral seconds [26]. Environmental Scanning Electron Mi-croscopy (SEM) can achieve sub-micron spatial resolu-tion, but again with poor ∆ t of about 1s [27]. Moreover,the high-vacuum and low-temperature conditions of SEMmay introduce artefacts and change the viscosity of theliquid(s), which in turn affects droplet behavior [14, 28].Here, using RICM, we visualized the base of a droplet(without dye) moving on a transparent micropillar sur-faces with a much improved ∆ t < F d by assuming that the force due toeach pillar ∼ γd and the number of pillars in contact atthe receding front ∼ a/d : F d ∼ (2 a/p ) γd ≈ aγφ / , (2)where φ is the solid surface fraction. We confirmed thisscaling law experimentally for water droplets of volumes V = 0.5–8 µ l moving at U = 0.2–0.5 mm/s on differ-ent micropillar surfaces with different solid fractions φ =0.05–0.23 ( d = 2–25 µ m, p = 5–50 µ m, and h p = 5–30 µ m). The prefactor in equation (2) depends on the de-tails of contact line distortion, which in turn depends onthe surface functionalization; this explains the two differ-ent slopes observed in Fig. 4a. The model described here,while simple, is able to account for the pinning force onSH surfaces, at least as well as other models previously proposed in the literature (see Supplementary Figs S4and S5) [29, 31–33].Using RICM, we were also able to visualize the uniquefeatures of the contact line of a water droplet movingon a SOCAL surface at U = 0.2 mm/s (Fig. 4b). Aswas the case with SH surface, the shape of the contactline was elongated in the direction of the droplet mo-tion, but unlike SH surface, the contact line at the reced-ing front is smooth without any visibly discrete pinningpoints (Fig. 4b-1,2, cf. Fig. 4a-1,2). The functional formof F d for water and 30 wt% aqueous sucrose solutiondroplets of volumes V = 1–5 µ l moving at speeds U =0.1–1 mm/s is consistent with Molecular-Kinetic Theory(MKT): F d = 2 aγ ∆ cos θ MKT = 2 aγ [∆ cos θ o + 4 K B T /γξ arcsinh( U/ K o ξ )]. (3)In MKT, the movement of the contact line is modeledas an absorption-desorption process, with a series ofsmall jumps of size ξ and frequency K o , while ∆ cos θ o is∆ cos θ in the limit of U → F d is indistinguishable between water and 30 wt% sucrosedroplets, despite their different viscosities, η = 1 and 4cP, respectively. Dashed line on Fig. 4b shows the best-fit curve, with ∆ cos θ o , ξ and K o as fitting parameters.The values obtained for ξ = 3 nm and K o = 7500 s − are close to what were reported in the literature for otherflat surfaces (see Supplementary Table S3) [34, 35]. Thevalue for ∆ cos θ o = 0 .
07, on the other hand, is muchlower than typically encountered. For example, a flatglass or silicon surface rendered hydrophobic by fluorosi-lanization typically has θ app = 110 ◦ and ∆ θ = 15–30 ◦ , orequivalently ∆ cos θ o = 0.3–0.5 [36]. The origin of the low∆ cos θ o on SOCAL surfaces was hypothesized to origi-nate from ‘liquid-like’ polymer brushes that freely rotateat the moving contact line.Interestingly, a combination of a SH and SOCAL sur-faces, i.e. a micropillar surface coated with the same SO-CAL polymer brush (filled circles, Fig. 4a), behaves ina qualitatively different way from its flat SOCAL coun-terpart: F d no longer depends on U , and scales with FIG. 4. Reflection interference contrast microscopy is usedto visualize a) the intercalated air film on SH surface, b) thecontact line on SOCAL surface, and c) the intercalated lu-bricant film on lubricated surfaces. Scale bars are 70 µ m fora-1 and c-1, 20 µ m for a-2,3 and c-2, 100 µ m for b-1, and 30 µ m for b-2. The dissipative forces F d are well-described byequations (2)–(4). ∆ F d is 1 µ N for a,b and 0.2 µ N for c. equation (2) rather than equation (3). Once again, thisconfirms that the pinning-depinning process at the micro-structured surface is fundamentally different from itschemically analogous flat surface.For lubricated surfaces with a stable, intercalated lu-bricant film, there is no contact line pinning and hencethe droplet base is circular in shape and not elongated(Fig. 4c-1,2, cf. Fig. 4a-1,2 and Fig. 4b-1,2). The entrain-ment of lubricant generates a hydrodynamic lift force,and the droplet levitates over the surface with a film-thickness given by the Landau-Levich-Derjaguin law, i.e. h ∼ RCa / , where Ca = η o U/γ lo is the capillary num-ber, η o is the viscosity of the lubricant oil, and γ lo is theliquid droplet-lubricant-oil interfacial tension [14, 37]. F d is dominated by the viscous dissipation at the rim of the droplet’s base of size l ∼ RCa / , and is therefore givenby: F d ∼ ( ηU/h )2 al ≈ aγ lo Ca / . (4)This was recently experimentally verified (reproducedhere in Fig. 4c for completeness) for droplets of V =1–5 µ l moving at U = 0 . η = 5–20 cP as lubricants [14]. Note that this discus-sion is true only in the absence of solid-droplet contact;if for some reason, the lubricant film becomes unstable, F d becomes dominated by contact line pinning and is in-dependent of U , reminiscent of the contact line pinningobserved in SH surfaces (see Supplementary Fig. S6). TABLE II. Nature of contact angle hysteresisSurface ∆ cos θ Commentssuperhydrophobic ∼ φ / no dependence on U SOCAL ∆ cos θ o + 4 K B T /γξ ∆ cos θ → ∆ cos θ o ,arcsinh( U/ Kξ ) U → ∼ Ca / ∆ cos θ → U → Comparing equations (2)–(4) with equation (1), wecan now get an expression for ∆ cos θ for the differ-ent liquid-repellent surfaces, as summarized in Table II:∆ cos θ ∼ φ / for SH surfaces, ∆ cos θ = ∆ cos θ o +4 K B T /γξ arcsinh( U/ Kξ ) for SOCAL surfaces, and∆ cos θ ∼ ( γ lo /γ ) Ca / ≈ Ca / for lubricated sur-faces. Note that for SOCAL and SH surfaces whichhave TPCL, ∆ cos θ > U →
0; in contrast, forlubricated surfaces with no TPCL, ∆ cos θ → U →
0. Recently, there has been some debate on thecorrect physical interpretation of contact angle hystere-sis for lubricated surfaces [14, 16, 38]. We will addressthis more fully in a future publication, but in general∆ cos θ ∼ Ca / corresponds to optical measurements ofmacroscopic cos θ rec − cos θ adv , and Furmidge’s relationin equation (1) can be applied to lubricated surfaces withsome modifications (see Supplementary Fig. S7).In summary, we have clarified the physics behind thethree classes of liquid-repellent surfaces, in particularhighlighting their distinct and unique properties, whichare not captured by conventional contact angle mea-surements. We measured the dissipation force F d withsub- µ N accuracy, and explicitly showed how the differ-ent functional forms of F d (and hence the correspondingcontact angle hysteresis) arise from details of the contactline. While we have confined our discussion to liquid-repellency, many of the ideas and techniques outlinedhere are relevant to various other problems, ranging fromice-repellency to the rational design of non-fouling mate-rials. Acknowledgements . The work was supported by theOffice of Naval Research, U.S. Department of Defense,under MURI Award No. N00014-12-1-0875. [1] W. K. Smith and T. M. McClean, Am. J. Bot. , 465(1989).[2] T. Darmanin and F. Guittard, Mater. Today , 273(2015).[3] D. Qu´er´e, Annu. Rev. Mater. Res. , 71 (2008).[4] L. Bocquet and E. Lauga, Nat. Mat. , 334 (2011).[5] M. Reyssat, D. Richard, C. Clanet, and D. Qu´er´e, Fara-day discuss. , 19 (2010).[6] J. W. Krumpfer and T. J. McCarthy, Faraday Discuss. , 103 (2010).[7] D. F. Cheng, C. Urata, M. Yagihashi, and A. Hozumi,Angew. Chem. , 2956 (2012).[8] L. Wang and T. J. McCarthy, Angew. Chem. , 252(2016).[9] A. Lafuma and D. Qu´er´e, Euro. Phys. Lett. , 56001(2011).[10] T.-S. Wong, S. H. Kang, S. K. Tang, E. J. Smythe, B. D.Hatton, A. Grinthal, and J. Aizenberg, Nature , 443(2011).[11] C. Urata, G. J. Dunderdale, M. W. England, andA. Hozumi, J. Mater. Chem. A , 12626 (2015).[12] J. Cui, D. Daniel, A. Grinthal, K. Lin, and J. Aizenberg,Nat. Mater. , 790 (2015).[13] J. D. Smith, R. Dhiman, S. Anand, E. Reza-Garduno,R. E. Cohen, G. H. McKinley, and K. K. Varanasi, SoftMatter , 1772 (2013).[14] D. Daniel, J. V. I. Timonen, R. Li, S. J. Velling, andJ. Aizenberg, Nat. Phys (2017).[15] A. Keiser, L. Keiser, C. Clanet, and D. Qu´er´e, Soft Mat-ter , 6981 (2017).[16] F. Schellenberger, J. Xie, N. Encinas, A. Hardy, M. Klap-per, P. Papadopoulos, H.-J. Butt, and D. Vollmer, SoftMatter , 7617 (2015).[17] P.-G. De Gennes, F. Brochard-Wyart, and D. Qu´er´e, Capillarity and wetting phenomena: drops, bubbles,pearls, waves (Springer Science & Business Media, 2013).[18] C. Furmidge, J. Colloid Sci. , 309 (1962). [19] J. H. Snoeijer and B. Andreotti, Annu. Rev. Fluid Mech , 269 (2013).[20] T. D. Blake, J. Colloid Interface Sci. , 1 (2006).[21] S. Srinivasan, G. H. McKinley, and R. E. Cohen, Lang-muir , 13582 (2011).[22] J. T. Korhonen, T. Huhtamki, O. Ikkala, and R. H. Ras,Langmuir , 3858 (2013).[23] D. Pilat, P. Papadopoulos, D. Schaffel, D. Vollmer,R. Berger, and H.-J. Butt, Langmuir , 16812 (2012).[24] N. Gao, F. Geyer, D. W. Pilat, S. Wooh, D. Vollmer, H.-J. Butt, and R. Berger, Nat. Phys. , nphys4305 (2017).[25] J. de Ruiter, F. Mugele, and D. van den Ende, Phys.Fluids , 012104 (2015).[26] F. Schellenberger, N. Encinas, D. Vollmer, and H.-J.Butt, Phys. Rev. Lett. , 096101 (2016).[27] K. Smyth, A. Paxson, H.-M. Kwon, and K. Varanasi,Surf. Innovations , 84 (2013).[28] D. Richard and D. Qu´er´e, Europhys. Lett. , 286 (1999).[29] M. Reyssat and D. Qu´er´e, J. Phys. Chem. B , 3906(2009).[30] L. Gao and T. J. McCarthy, Langmuir , 6234 (2006).[31] C. W. Extrand, Langmuir , 7991 (2002).[32] J. Joanny and P.-G. De Gennes, J. chem. Phys. , 552(1984).[33] H.-J. Butt, N. Gao, P. Papadopoulos, W. Steffen,M. Kappl, and R. Berger, Langmuir (2016).[34] S. R. Ranabothu, C. Karnezis, and L. L. Dai, J. ColloidInterface Sci. , 213 (2005).[35] R. A. Hayes and J. Ralston, Langmuir , 340 (1994).[36] D. Qu´er´e, M.-J. Azzopardi, and L. Delattre, Langmuir , 2213 (1998).[37] L. Landau and V. Levich, Acta Physicochim. USSR ,42 (1942).[38] C. Semprebon, G. McHale, and H. Kusumaatmaja, Softmatter13