Mimicking lotus leaves for designing superhydrophobic/hydrophilic. super-attractive/repulsive nanostructured hierarchical surfaces

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1 Research Signpost 37/66 (2), ort P.O., Trivandrum , Kerala, India The anomechanics in Italy, 2007: -9 ISB: Editor: icola Maria Pugno Mimicing lotus leaves for designing superhydrophobic/hydrophilic and super-attractive/repulsive nanostructured hierarchical surfaces icola M. Pugno Department of Structural Engineering, Politecnico di Torino, orso Duca degli Abruzzi 24, 029 Torino, Italy Abstract In this hapter we demonstrate the feasibility of super-hydrophobic/hydrophilic and simultaneously super-attractive/repulsive surfaces, mimicing ature thans to hierarchical architectures. Super-hydrophobia is found to tae place for a number of ~2 hierarchical orrespondence/reprint request: Dr. icola M. Pugno, Department of Structural Engineering, Politecnico di Torino, orso Duca degli Abruzzi 24, 029 Torino, Italy. nicola.pugno@polito.it

2 2 icola M. Pugno levels, as observed in several plants, e.g. lotus. Moreover, the strength of the capillary attractive or repulsive interaction is found to be enormously enhanced by the hierarchical architecture. Thus, the analysis suggests the feasibility of innovative self-cleaning and simultaneously super-adhesive hierarchical materials, as observed in gecos.. Introduction Several natural materials exhibit super-hydrophobia, with contact angles between 50 and 65, often a strategy for allowing a safe interaction with water, see the review on non-sticing drops by Quéré []. This is the case for the leaves of about 200 plants, including asphodelus, drosera, eucalyptus, euphorbia, gingo biloba, iris, tulipa and, perhaps the most famous, lotus [2, 3], igure. Similarly, animals can be super-hydrophobic, as for the case of water strider legs, butterfly wings, duc feathers and bugs [4-6]. These surfaces are generally composed of intrinsic hydrophobic material (contact angle larger than 90, often around 20 ) with a two-level hierarchical micro-sized architecture. Super-hydrophobia (contact angle larger than ~50, see []) is extremely important, e.g., in micro/nano-fluidic devices for reducing the friction associated with the fluid flow, but also for selfcleaning: super-hydrophobic materials are often called self-cleaning materials since drops are efficiently removed taing with them the dirty particles which were deposited on them [3, 7]. This effect is extremely important, (e.g., for producing self-cleaning syscraper glass). Researchers [8] have proved that the adhesive setae of gecos become cleaner with repeated use; super-adhesion and self-cleaning are both probably a consequence of the hierarchical nature of the geco foot. On the other hand, hydrophily (contact angle smaller than 90 ) is needed to achieve high wettability, (e.g. for surfaces to be painted). In this letter we demonstrate the feasibility of super-hydrophobic/ hydrophilic and simultaneously super-attractive/repulsive surfaces, mimicing ature thans to hierarchical architectures. 2. Super-hydrophobic/hydrophilic and superattractive/repulsive surfaces The contact angle (igure 2a) between a liquid drop and a solid surface was found by Young [9] according to cos θ ( γ SV γ SL ) γ, where γ γ LV and the subscripts of the surface tensions describe the solid (S), liquid (L) and vapour (V) phases. ote that for ( γ SV γ SL ) γ > the drop tends to spread completely on the surface and θ 0, whereas for ( γ SL γ SV ) γ > the drop is in a pure non-wetting state and θ 80. According to the well-nown

3 Mimicing lotus leaves 3 (a) (b) (c) igure. Super-hydrophobic behaviour in lotus leaves. Liquid drops of small (a), medium (b) or large size (c). Photos taen by the Author. θ θ θ (a) (b) (c) igure 2. ontact angles for a drop on a flat surface (a) or on a rough surface in the enzel (b) or in the air (c) state. enzel s model [0, ] the apparent contact angle θ is a function of the surface roughness w, defined as the ratio of rough to planar surface areas, namely, w (igure 2b). The apparent contact angle varies also with the heterogeneous composition of the solid surface, as shown by assie and Baxter [2]. onsider a heterogeneous surface made up of different materials characterized by their intrinsic contact angles θ i and let ϕ i be the area fraction of each of the species; the individual areas are assumed to be much smaller than the drop size. Accordingly, the apparent contact angle θ B can be derived as cos θ ϕ [2]. B i i i A droplet can sit on a solid surface in two distinct configurations or states (igure 2b,c). It is said to be in enzel state (igure 2b) when it is conformal with the topography. The other state in which a droplet can rest on the surface is called the air state, after Quéré [3], where it is not conformal with the topography and only touches the tops of the protrusions on the surface (igure 2c). The observed state should be the one of smaller contact angle, as can be evinced by energy minimization [4].

4 4 icola M. Pugno Let us consider a hierarchical surface (igure 3). The first level is composed by pillars in fraction ϕ (as in igure 2b,c). Each pillar is itself structured in n sub-pillars in a self-similar (fractal) manner, and so on. Thus, the pillar fraction at the hierarchical level is ϕ, whereas the related number of pillars at the level is n. Applying the assie and Baxter law [2] for the described composite (solid/air) hierarchical surface (the contact angle in air is by definition equal to 80 ) we find for the hierarchical fair state: ( ) ϕ ( + ) () ( ) ote that for 0 0 as it must be, whereas for () ϕ( + ), as already deduced for the case described in igure 2c [5]. Eq. () quantifies the crucial role of hierarchy and suggests that hierarchical surfaces are fundamental to realize super-hydrophobic materials (effective contact angle larger than θ 50 ), since we predict ( ) θ 80. The minimum number of hierarchical levels necessary to achieve super-hydrophobia is thus: ( ) + log + logϕ (2) and the logarithmic dependence suggests that just a few hierarchical levels are practically required. By geometrical argument the roughness w of the introduced hierarchical surface (igure 3) can be calculated in closed form. The roughness at the hierarchical level is given by ( ) ( w + S ) L A in which A is the nominal contact area and ( ) S is the total lateral surface area of the pillars. The pillar at L the level has an equivalent radius r and a length l and the pillar slenderness s, defined as the ratio between its lateral and base areas, is igure 3. A hierarchical surface (with 2 levels).

5 Mimicing lotus leaves 5. The air surface area at the level can be computed as A( ϕ ) s 2l r equivalently as onsequently: A 2 n πr, thus we deduce r ( ) 2 r0 ϕ n, with A or 2 π. A 0 r 0 w ( ) + ϕ ϕ + 2πr l n + s ϕ + s 2 πr ϕ 0 n (3) ote that the result becomes independent from n (and that ( 0 ) ( ) ( w ϕ w ) ( ϕ 0 ) ( ), w + sϕ, whereas ( w ) ( ϕ ) ). Thus we find for the hierarchical enzel state: ( ) ( ) w + ϕ ϕ + s ϕ (4) Eq. (4) suggests that hierarchical surfaces can be interesting also to realize super-hydrophilic materials, since we predict ( ) ( ) w with ( ) ( ) w + sϕ ( ϕ) ; thus if cos θ > 0 θ 0, for s or ϕ. ( ) However note that for cos θ < 0, θ 80 ( s or ϕ ), and thus super-hydrophobia can tae place also in the enzel state, without invoing fair drops. The minimum number of hierarchical levels necessary to render the surface super-hydrophobic/hydrophilic is thus: ( ), phi log + ( ϕ), ϕ s logϕ phi where effective contact angles smaller than θ SHphi define super-hydrophily. omparing ( ) ( ) θ and θ, we find that the air state is activated at each hierarchical level for (we omit here second order problems, related to metastability, contact angle hystheresis and limit of the enzel s approach, for which the reader should refer to the review by Quèrè []): θ > θ, ϕ ϕ (6) w ( ) ( ) ϕ w + ϕ( s ) ote that the result is independent from and θ 90 for s or ϕ, and thus a hydrophobic\hydrophilic material composed by sufficiently (5)

6 6 icola M. Pugno slender or spaced pillars surely will/will not activate fair drops and will become super-hydrophobic\hydrophilic for a large enough number of hierarchical levels. Thus hierarchy can enhance the intrinsic property of a material. The role of hierarchy is summarized in igure 4. or example, for plausibly values of ϕ 0.5 and s0 we find from eq. (6) θ 95.2 o ; thus assuming θ 95 o the air state is not activated and the enzel state prevails (if the air state still prevails it is metastable, see []). ( ) rom eq. (3) ( 2) ( ) w 6, w 8.5, 3 ( 4) w 9.75 and w ; accordingly () from eq. (4) ( 2) ( ) θ 22, θ 38, θ 3 48 and ( 4 θ ) 55, thus 4 hierarchical levels are required for activating super-hydrophobia (from eq. (5) ( ) 3.2 ). On the other hand, assuming θ 00 fair drops are activated and from eq. () ( ) θ 26, ( 2) θ 43 and 3 ( ) θ 54, thus 3 hierarchical levels are sufficient to achieve super-hydrophobia (from eq. (2) ( ) 2.6 ). Superhydrophily Hydrophily Hydrophobia Superhydrophobia /w ( ) Ν Ν0 Ν +ϕ Ν /w ( ) /w (Ν) air state enzel state ( ) * igure 4. Effective contact angle θ θ, as a function of the intrinsic one θ by varying the number of hierarchical levels. Thus, super-hydrophobic/hydrophilic surfaces can be obtained by an opportune design of the hierarchical architecture, according to this phase diagram and reported equations (note that metastable fair drops could be observed also in the enzel region, dotted line, see []).

7 Mimicing lotus leaves 7 The capillary force between a hierarchical surface and a flat plane can also be derived, according to the well-nown Laplace s law [6], as a function of the contact angle. Some insects, such as the beetle Hemisphaerota cyanea, use capillary to stic to their substrate, generating a force close to g (i.e. 60 times its body mass) for more than 2min [7], allowing them to resist attacing ants; toay gecos use the same principle (in addition to van der aals forces) to generate their tremendous adhesion [8], that could probably be scaled-up in order to produce a Spiderman Suit [9] (see also the related ew Scientist story: Geco inspired suit could have you climbing the wall, by J. Palmer, 28 April, 2007). Between a spherical surface (contact angle θ ) of radius r 0 and a flat plate (contact angle θ P ), the capillary attractive or repulsive force is predicted to be 2πr 0 γ ( + P ) [20]. Thus, for a spherical pillar of size r 0 composed by hierarchical levels the force is ( ) ( ) ( ) 2 n 2 πr γ ( + P ) and the nominal strength σ ( πr 0 ) becomes: σ 2 ( ) ( ) ( ) 2 ϕn r 0 γ ( + ), P (7) ote that for 0 such a capillary strength corresponds to the previously discussed law. or the strength scales as n, in agreement with a recent discussion [2]: splitting up the contact into n sub-contacts would result in a stronger interaction (with a cut-off at the theoretical strength): smaller is stronger [22]. This explains the observed miniaturized size of biological contacts. Introducing the previously computed contact angle related to the hierarchical surface allows one to evaluate the hierarchical capillary force, with or without activation of the air state. Super-attraction/repulsion can be ( ) ( 0 achieved due to hierarchy, as emphasized by ) 2 σ σ ( ϕn). 3. onclusions Summarizing, the analysis demonstrates and quantifies that superhydrophobic/hydrophilic and simultaneously super-attractive/repulsive surfaces can be realized, mimicing lotus leaves, thans to hierarchical architectures. or example, assuming ϕ 0. 5, ns0 and θ 20 (as in lotus leaves, igure ), the analysis shows that fair drops are activated and only two hierarchical levels are required to achieve super-hydrophobia ( ) ( θ > θ 95.2,.9 ; ( ) θ 39, ( 2) θ 5 ), in agreement with direct observations on super-hydrophobic plants. Simultaneously, we deduce () ( 0) ( 2) ( 0) ( 3) ( 0) σ 2.2σ, σ 5.0σ and σ.2σ, i.e. just three hierarchical

8 8 icola M. Pugno levels (or even two, if ϕ and n 0 ) are sufficient to enhance the capillary strength by one order of magnitude, generating super-attractive ( ( 0) σ > 0 ) or super-repulsive ( ( 0) σ < 0 ) surfaces. Acnowledgement The author is supported by the Bando Ricerca Scientifica Piemonte BIADS: ovel biomaterials for intraoperative adjustable devices for fine tuning of prostheses shape and performance in surgery. References. Quéré D on-sticing drops Rep. Prog. Phys einhuis. and Barthlott. 997 haracterisation and distribution of waterrepellent, self-cleaning plant surfaces Ann. Bot Barthlott. and einhuis. 997 Purity of scared lotus or escape from contamination in biological surfaces Planta 202 S agner T., einhuis. and Barthlott. 996 ettability and. contaminability of insect wings as a function of their surface sculture Acta Zool Lee., Jin M K., Yoo. and Lee J K anostructuring of a polymeric substrate with well- defined nanometer-scale topography and tailored surface wettability Langmuir Gao X. and Jiang L Biophysics: water-repellent legs of water striders ature Blossey R Self-cleaning surfaces virtual realities ature Mater Hansen.R. and Autumn K Evidence for self-cleaning in geco setae Proc. atl. Acad. Sci. USA Young T. 805 An essay on the cohesion of fluids Phil. Trans. R. Soc. Lond Timosheno SP and Gere JM 96 Theory of elastic stability, McGraw- Hill, ew Yor. 0. enzel R Resistance of solid surfaces to wetting by water Ind. Eng. hem enzel R Surface roughness and contact angle J. Phys. hem assie A.B.D. and Baxter S. 944 ettability of porous surfaces Trans. araday Soc Quéré D air droplets ature Mater Bico J., Thiele U. and Quèrè D etting of textured surfaces olloids Surf. A Bico J., Marzolin. and Quèrè D. 999 Pearl drops Europhys. Lett Laplace P.S. 847 Oeuvres omplètes, Imprimerie Royale Paris. 7. Eisner T. and Aneshansley D. J Defense by foot adhesion in a beetle (Hemisphaerota cyanea) Proc. atl Acad. Sci. USA Huber G., Mantz H., Spolena R., Mece K., Jacobs K., Gorb S. and Arzt E Evidence for capillarity contributions to geco adhesion from single spatula and nanomechanical measurements Proc. atl. Acad. Sci. USA

9 Mimicing lotus leaves 9 9. Pugno Towards a Spiderman suit: large invisible cables and self-cleaning releasable super-adhesive materials J. of Physics ond. Mat. 9, (7pp.). 20. Mcarlane J.S. and Tabor D. 950 Adhesion of solids and the effects of surface films Proc. R. Soc. Lond. Ser. A Arzt E., Gorb S. and Spolena R rom micro to nano contacts in biological attachment devices Proc. atl. Acad. Sci. USA arpinteri A. and Pugno Are the scaling laws on strength of solids related to mechanics or to geometry? ature mat