pubs.acs.org/Langmuir © 2009 American Chemical Society
Comment on Water Wetting Transition Parameters of Perfluorinated Substrates with Periodically Distributed Flat-Top Microscale Obstacles
Wetting transitions occurring on rough surfaces were subjected to intensive experimental and theoretical research recently.1-18 These transitions accompanied by the change in apparent contact angles could be promoted by vibration drops, applying hydrostatic pressure, or bouncing drops on rough surfaces.1-16 Barbieri et al. recently calculated the energy barrier to be surmounted for the Cassie-Wenzel transition.6 It was assumed that this energy barrier corresponds to the surface energy variation between the Cassie state (depicted in Figure 1A) and the hypothetical composite state with the almost complete filling of surface asperities by water, keeping the liquid-air interface under the droplet and the contact angle constant, as shown in Figure 1B.5,6 The calculation performed by Barbieri and coauthors implied the 2D character of the wetting transition (in which all pores underneath the drop must be filled with water). We demonstrate that the methodology proposed in ref 5 can also justify 1D character of the Cassie-Wenzel transition (in which only the pores in the vicinity of the three-phase line are filled). It should be stressed that the apparent contact angle is dictated by the wetted area adjacent to the three-phase (triple) line.19 Let us revisit the experimental data reported in our previous papers when wetting transitions were promoted by the vibration of water drops deposited on the rough, low-density polyethylene (LDPE) surfaces9 shown in Figure 2A. LDPE is a hydrophobic polymer, as in ref 6, with a contact angle as high as 105°. The LDPE relief shown in Figure 2A, B is characterized by “channels” of height h and length l with a distance p between them (see also Figure 1A). According to Barbieri et al.,6 the mentioned energy barrier is considered to be connected to wetting the side surfaces. The side surface of one channel is 2lh, and there are l/p channels in the l l square of the relief in Figure 2B. Thus, the side channels’ surface per unit surface of the horizontal plane is 2h/p. To wet this side surface under a droplet with contact radius R, the additional energy Etrans ¼ 2πR2 hðγSL -γSA Þ=p ¼ -2πR2 hγcos θ=p
ð1Þ
(1) Reyssat, M.; Yeomans, J. M.; Quere, D. Europhys. Lett. 2008, 81, 26006. (2) Lafuma, A.; Quere, D. Nat. Mater. 2003, 2, 457–460. (3) Liu, B.; Lange, F. F. J. Colloid Interface Sci. 2006, 298, 899–909. (4) Ishino, C.; Okumura, K. Europhys. Lett. 2006, 76, 464–470. (5) Patankar, N. A. Langmuir 2004, 20, 7097–7102. (6) Barbieri, L.; Wagner, E.; Hoffmann, P. Langmuir 2007, 23, 1723–1734. (7) Zheng, Q.-S.; Yu, Y.; Zhao, Z.-H. Langmuir 2005, 21, 12207–12212. (8) Wang, J.; Chen, D. Langmuir 2008, 24, 10174–10180. (9) Bormashenko, E.; Pogreb, R.; Stein, T.; Whyman, G.; Erlich, M.; Musin, A.; Machavariani, V.; Aurbach, D. Phys. Chem. Chem. Phys. 2008, 27, 4056–4061. (10) Bormashenko, E.; Pogreb, R.; Whyman, G.; Bormashenko, Ye.; Erlich, M. Langmuir 2007, 23, 6501–6503. (11) Bormashenko, E.; Pogreb, R.; Whyman, G.; Erlich, M. Langmuir 2007, 23, 12217–12221. (12) Park, Ch. I.; Jeong, H. E.; Lee, S. H.; Cho, H. S.; Suh, K. Y. J. Colloid Interface Sci. 2009, 336, 298–303. (13) Jung, Y. Ch.; Bhushan, Bh. Scr. Mater. 2007, 57, 1057–1060. (14) Bartolo, D.; Bouamrirene, F.; Verneuil, E.; Buguin, A.; Silberzan, P.; Moulinet, S. Europhys. Lett. 2006, 74, 299–305. (15) Jung, Y. Ch.; Bhushan, Bh. Langmuir 2008, 24, 6262–6269. (16) Jung, Y. Ch.; Bhushan, Bh. Langmuir 2009, 25, 9208–9218. (17) Sbragaglia, M.; Peters, A. M.; Pirat, Ch.; Borkent, B. M.; Lammertink, R. G.H.; Wessling, M.; Lohse, D. Phys. Rev. Lett. 2007, 99, 156001. (18) Peters, A. M.; Pirat, C.; Sbragaglia, M.; Borkent, B.M.; Wessling, M.; Lohse, D.; Lammertink, R. G. H. Eur. Phys. J. E. 2009, 29, 391–397. (19) Bormashenko, E. Langmuir 2009, 25, 10451–10454.
13694 DOI: 10.1021/la9020959
Figure 1. (A) Cassie wetting state. (Geometrical parameters are depicted.) (B) Composite wetting state.
Figure 2. (A) Rough, low-density polyethylene substrate studied with vertical drop vibrations. The scale bar is 1 mm. (B) Geometric parameters of the LDPE relief.
is needed where γSL, γSA, and γ are the surface tensions on the solid-liquid, solid-air, and liquid-air interfaces, respectively, and the Young formula for the local contract angle θ is taken into account. The change in the droplet volume is negligible for the present values of the geometrical parameters, and according to ref 6, the droplet apparent contact angle does not change in the transition state. This means that the liquid-air interface and the contact radius of the droplet are conserved in the process of filling the channels. After water reaches the bottom of the channel, the energy of the system decreases because of the disappearance of the high-energy water-air interface over the channels and the optimization of the apparent contact angle. As a result, the system is stabilized in the Wenzel state shown in Figure 3A.6 It has to be stressed that according to eq 1 the energy barrier scales as Etrans ≈ R2.
Published on Web 11/06/2009
Langmuir 2009, 25(23), 13694–13695
Comment
Figure 3. (A) Wenzel wetting state. The 2D scenario of the transition is depicted; all pores underneath the droplet are filled with water. (B) Wenzel wetting state. The 1D scenario of the transition is depicted; only pores in the vicinity of the three-phase line are filled.
However, it is experimentally established that the wetting transition under droplet vibration takes place when the critical value of the force Fcr acting on the unit length of the triple line is surpassed.9-11 The energy barrier δE to be surmounted for the elementary displacement of the triple line δr could be estimated to be δE≈2πRFcr δr
ð2Þ
which scales as R. This obviously contradicts the given above scaling law. To eliminate the discrepancy, we assume that the discussed wetting transition is conditioned by filling channels only in the vicinity of the triple line of the droplet as shown in Figure 3B. The area of this ring is 2πRp, and the side channels’ surface per unit of horizontal surface is 2h/p as mentioned above, which leads to Etrans ¼ -4πRhγ cos θ
ð3Þ
and it could be seen that the scaling discrepancy is avoided. Now let us make numerical estimations. The critical value of the depinning force Fcr for LDPE surfaces has been established experimentally in ref 9 as Fcr ≈ 350 mN m-1. The potential barrier (20) Bormashenko, E. Colloids Surf., A 2008, 324, 47–50. (21) Sun, M. H.; Luo, C. X.; Xu, L. P.; Ji, H.; Qi, O. Y.; Yu, D. P.; Chen, Y. Langmuir 2005, 21, 8978–8981. (22) Nosonovsky, M. Langmuir 2007, 23, 3157–3161.
Langmuir 2009, 25(23), 13694–13695
δE calculated for a drop with a radius of R ≈ 1 mm and the elementary displacement δr ≈ p/2=10-5 m equals according to eq 2 δE ≈ 20 nJ. The numerical estimation of the energy barrier according to eq 3 with the parameters h = 20 μm, R = 1 mm, θ =105°, and γ = 72 mJ m-2 gives a value of Etrans = 5 nJ that is less than that calculated according to eq 2 but of the same order of magnitude. The energy barrier calculated according to eq 2 comprises not only filling pores but also depinning of the triple line due to the long-range interaction with the substrate, nanoroughness, and so forth. Thus, its value is naturally larger than that predicted by eq 3, which takes into account the wetting of pores only. At the same time, eq 1 with p ≈ h ≈ 20 μm gives a value of 120 nJ that is 1 order of magnitude larger. We conclude that the corrected version of the methodology proposed in ref 6 predicts realistic values of energy barriers separating wetting states when suited for the 1D scenario of the transition with pores filled only in the vicinity of the triple line. The model proposed in our comment contradicts the results reported by other groups, which assumed that the Cassie-Wenzel transition proceeds from the center of the wetted area to its periphery.4,17,18 The natural explanation of this discrepancy arises from the fact that in our investigations the drop was deposited onto a porous substrate, whereas the authors of refs 17 and 18 dealt with drops on posts. Generally, the topography of a rough surface is represented by two main types, which are pores formed in the matrix (bulk) and posts looming above the interface.5,9-11,17,18 A formal application of the Cassie-Baxter equation yields the same apparent contact angles in these cases when relative fractions of the phases underneath the drop are the same.20 It is noteworthy that the calculation of the energy barrier to be surpassed for the Cassie-Wenzel transition could be applied for the both kinds of roughness (i.e., for both pores and posts). However, wetting behavior and the scenario for a wetting transition (1D for pores or 2D for posts) could be quite different.21,22 We plan to perform a direct experimental study of the process of filling pores under a wetting transition, which will clarify the situation. Acknowledgment. We are indebted to an anonymous referee for fruitful refereing the manuscript. Edward Bormashenko,* Roman Pogreb, and Gene Whyman Ariel University Center of Samaria, The Research Institute, Applied Physics Faculty, Department of Chemistry and Biotechnology Engineering, 40700 Ariel, Israel Received June 11, 2009
DOI: 10.1021/la9020959
13695
