DC conductivity percolation on drying moistened mesoporous silica SBA-15

Microporous and Mesoporous Materials 206 (2015) 202–206

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DC conductivity percolation on drying moistened mesoporous silica SBA-15 J. Nowak a, D. Dziob a, M. Rutkowska b, L. Chmielarz b, U. Gorska a,1, D. Sokolowska a,⇑, J.K. Moscicki a a b

Smoluchowski Institute of Physics, Jagiellonian University, Lojasiewicza 11, 30-348, Krakow, Poland Faculty of Chemistry, Jagiellonian University, Ingardena 3, 30-060 Krakow, Poland

a r t i c l e

i n f o

Article history: Received 20 May 2014 Received in revised form 26 November 2014 Accepted 29 November 2014 Available online 6 December 2014 Keywords: SBA-15 Conductivity percolation Structured interface

a b s t r a c t DC conductivity percolation on drying to air in water-moistened SBA-15 was characterized. The percolation exponent value, lh  1, is typical for hydrophilic fumed silica and biological porous materials. Somewhat surprisingly, we found that the percolation water content threshold depends linearly of the initial hydration of dry SBA-15 material. The finding is rationalized within the concept of morphological wetting transition at hydrophilic/phobic structured interface of moistened SBA-15. Ó 2014 Elsevier Inc. All rights reserved.

1. Introduction The importance of understanding the fast proton transport at interfaces of biological, on one hand, and technological (e.g., ion/ fuel membranes [1]) materials is well recognized. In many aspects a mechanical and chemical landscape of common interfaces of biological and manmade origin water interacts with is alike. At the molecular scale of the water molecule, the interfaces are mechanically rough and chemically inhomogeneous lending them hydrophilic/phobic heterogeneity, leading to formation of closely bound water clusters domains on one hand, and linear chains of waters along polar domains or hydrophobic clefts, on the other. This, in turn, in many aspects grants compatibility between biological systems and the latter, and stimulates the use of silica-based materials in medical applications [2,3]. However, knowledge of mechanisms and pathways of proton lateral migration in this residual, interfacial water layer is still an open question [4–6]. Quite recently we reported on DC conductivity percolation in drying moistened samples of hydrophilic fumed silica powders (AerosilÒ) of different grain diameters and specific surface [7]. Careri with colleagues were first to observe long before similar conductivity percolation in biological systems [8], so the initial choice of fumed silica for the conductivity study was not accidental, suggested by apparent geometrical similarities between yeast cells and AerosilÒ beads, yeast colonies and AerosilÒ in bulk, ⇑ Corresponding author. Tel.: +48 12 664 4690. E-mail address: [email protected] (D. Sokolowska). Present address: Institute of Psychology, Department of Phychophysiology, Jagiellonian University, Mickiewicza 3, 31-120 Krakow, Poland. 1

http://dx.doi.org/10.1016/j.micromeso.2014.11.032 1387-1811/Ó 2014 Elsevier Inc. All rights reserved.

response of moistened materials to electric field, and behaviour on dehydration. Many additional studies followed Careri work, and it is well established now that DC conductivity in hydrophilic granular materials undergoes percolation transition on drying, and it is believed to be due to proton transport [9,10]. In bulk moistened AerosilÒ powder we found that the percolation transition happens when water reaches the state of a residual film at the bead surface. At this stage of bulk AerosilÒ hydration, silica surfaces are covered with a residual film of water which, in turn, is connected to other, ‘‘internal’’, reservoirs of water deposited in the form of pendular rings around points of contact between the beads. On water evaporation from the water–air interface, the surfacial water is replenished from these internal reservoirs as long as aqueducts are intact. We found that the percolation threshold and percolation exponent are independent of the bead diameter, and the transition shows up when the residual aqueous layer is no more than triple monolayer thick, i.e., the percolation transition is quasi two-dimensional in nature. The surface and porosity geometry of template-based mesoporous silica as SBAs, MCMs and alike, is quite different in comparison with bulk of poreless molten AerosilÒ grains. SBA-15 chosen for the next conducto-gravimetric studies is a complex, micro–mesoporous material with highly parallel-ordered cylindrical mesopores obtained via chemical reaction of tetraethyl orthosilicate with the use of an appropriate micellar template [11,12]. Particular final form and geometry of mesoporous materials highly depends on the synthesis procedure [13–15]. While AerosilÒ forms a randomly porous material with the pore surface being convex in curvature, SBA-15’s cylindrical pores feature, in turn, the concave free surfaces. Therefore, the internal water reservoirs and their

J. Nowak et al. / Microporous and Mesoporous Materials 206 (2015) 202–206

connectivity to the water–air interface should be quite different, and influence the dehydration process. Conducto-gravimetric studies are well positioned to reveal such differences. 2. Experimental (methods, techniques and materials studied) 2.1. SBA-15 synthesis and characterization SBA-15 was prepared according to the procedures outlined by Meynen and others [12]. 4 g of Pluronic P123 triblock copolymer surfactant (EO20-PO70-EO20, MW 5800) was dissolved in solution of 130 ml of water with 20 ml of concentrated HCl. Subsequently, a suitable amount of tetraethyl orthosilicate (TEOS) was added and the mixture stirred at 45 °C for 7 h, and then aged at 80 °C for 15 h. The solid product was separated by filtration, washed with distilled water and dried at room temperature. Finally, the sample was calcined over the isothermal period of 6 h, in an air atmosphere at 550 °C, with the heating rate of 1 °C/min. Textural properties of mesopores silica were determined using TEM (cf. Fig. 1) and ASAP 2010 Micromeritics instruments. Prior to measurement, the sample was outgassed at 200 °C for 16 h. The surface area was calculated using BET (Brunauer–Emmett– Teller) model, the micropore volume determined from t-plot analysis and the pore size distribution was estimated using BJH method. The total pore volume was determined at P/P0 of 0.99. Fig. 2a shows the nitrogen adsorption–desorption isotherm obtained for SBA-15 batch prepared in this work. The isotherm is type IV in the IUPAC classification, and typical of mesoporous materials. The hysteresis loop is H1-type, characteristic for both side open cylindrical mesopores. The SBA-15 batch is characterized by a relatively high surface area and total pore volume of 654 m2/g and 0.728 cm3/g, respectively. The micropore volume, related to the presence of narrow pores connecting mesoporous parallel channels in SBA-15, was equal to 0.119 cm3/g. The sample is characterized by the uniform pore size distribution with the most possible diameter of 6.7 ± 0.5 nm determined respectively from adsorption branch of the isotherm, cf. Fig. 2b.

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7131 ultrasonic humidifier for a period of a few hours, at temperatures just below 40 °C. The moistening kinetics was quite similar to what we observed with Aerosil samples [7]. Initial water intake by a sample was very slow, e.g., about 0.03 g in total, but after 4–5 h the process picked-up the speed and the sample gained 0.3 g just in the next 30–45 min. The hydration procedure was kept long enough to moisten the nanoparticles surfaces, but sufficiently short to avoid sample’s gelation. This way, we repetitively got samples without gelation with the initial hydration ½mgH2 O =m2 , q0, in the range, 1 < q0 < 7.

2.3. Conducto-gravimetric measurements The measurements were performed with the use of experimental setup and procedure described in detail by Sokolowska et al. ([7] and references therein). The wet material was placed in a custom made parallel plate, gold-plated cupper disc capacitor, with the empty cell capacitance of C0 = 8.57 ± 0.12 pF. The perforated upper electrode contains 56 circular holes 2 mm in dia., ensuring sufficient gas exchange between the sample and the ambient still atmosphere. The weight of sample-loaded capacitor was monitored continuously to within 20 lg accuracy by a laboratory balance (Radwag WAA 160/C/2). Sample dried at a natural evaporation rate, 0.05–0.15 g h1, and at the balance chamber air temperature of T = 23–25 °C, and RH of 35–40%. Either Novocontrol Alpha-A or Agilent E4980A were used to collect complex dielectric permittivity spectra, e⁄ = e0 (f)  ie00 (f), in the frequency range 100 Hz 6 f 6 20 MHz, cf. Fig. 3, with voltage amplitude 0.1 V. The spectrum and the cell weight were automatically recorded every 300 s during the whole drying process.

2.2. Sample hydration A sufficient amount of the dry SBA-15 batch for filling the dielectric cell was exposed to tap water mist produced by BOVECO

Fig. 1. Typical TEM image of the studied SBA-15 batch.

Fig. 2. (a) N2 adsorption–desorption isotherms and (b) the pore diameter distribution of the SBA-15 batch prepared for conductivity studies, determined by the BJH method. Error (std) bars are smaller than the size of the symbol.

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solutions [17], and are indicative of a very pronounced electrode polarization contribution to the spectra [18,19]. Fortunately, this phenomenon – still intriguing on its own – does not obscure quantitative estimation of DC conductivity values [17]. Main features of spectra in Fig. 3 are pretty similar to those observed earlier in conductivity studies of dehydrating, e.g., yeast, algae, and Aerosil silica, and in agreement with protonic nature of conductivity ([7], and references therein). In particular, in the kHz frequency range, f 6 100 kHz, the dielectric loss spectra are overwhelmingly dominated by contribution from DC conductivity, rDC: e00 (f) ffi rDC/(2pe0f), e0 being the permittivity of the vacuum. This observation, substantially simplifies and facilitates conductivity percolation analysis. The variation of monochromatic dielectric loss factor, e00 |f, at any fixed frequency from this range can be used explicitly in the vicinity of the percolation threshold, h P h⁄, to find the conductivity percolation threshold, h⁄ and the percolation exponent, lh [20]: lh

ðe00 jf  e00 jf Þ / ðh  h Þ

() log e00 jf  e00 jf

¼ lh log jh  h j þ const:

ð1Þ

where asterisks denote values at the threshold, cf. Fig. 4. Results of the linear regression analysis of the percolation scaling are summarized in Table 1. Fig. 3. Pre moistened hydrophilic SBA-15 powders freely drying to ambient air. Typical (a) dielectric permittivity, e0 (f), and (b) dielectric loss factor, e00 (f), spectra shown for three different hydrations levels: (j) h = 3.482, (s) h = 0.433, and (N) h ¼ 0:215 ½mg½H2 O =g½silica . Initial hydration, h0 ¼ 3:57 ½mg½H2 O =g½silica . Error (std) bars are smaller than the size of the symbol.

4. Discussion From Table 1 it is clear that percolating aqueous medium in SBA-15 has similar proton conducting properties to those observed in AerosilÒ and, for example, yeasts, cf. ([7] and references therein), manifested in the critical exponent value close to one, lh  1. It was shown long ago that such value of the exponent for percolation in 2D could indicate failure of a continuous film via randomly rupturing holes in it [21,22], or limitations in the size of percolating discrete network [23], or the discrete network resistance bistability – switching the bond resistance from low to high on percolation transition [24]. In the case of AerosilÒ, conceptually

3. Results Representative behaviour on drying of the real, e0 , and imaginary, e00 parts of the low-frequency complex dielectric spectrum of the SBA-15 sample is shown in Fig. 3. Noticeable at the first glance are very high values of dielectric permittivity, e0 , albeit this is not very surprising; similarly high values were observed before for tap, filtered or distilled water [16], and, e.g., in NaCl aqueous

Fig. 4. Pre moistened hydrophilic SBA-15 powders freely drying to ambient air. Double-logarithmic plots of the monochromatic (f = 10 kHz) loss factor, e00 |f vs. hydration level, h½mg½H2 O =g½silica , across the whole dehydration range studied. Typical e00 |f evolution for three different initial moisture contents: (a) h0 = 3.57, (b) h0 = 4.88, and (c) h0 ¼ 6:82 ½mg½H2 O =g½silica . To emphasize presence of the transition, the quantities are plotted relative to values at the percolation threshold (denoted by asterisks). Straight solid lines are the linear regression fits of Eq. (1) to data, cf. Table 1. Error bars indicate typical variation of std across the hydration range.

Table 1 Samples characteristics and critical parameters. S½m2silica =gsilica  – specific surface, D[Å] – pore mean size (cavity for A380), h0 ½g H2 O =gsilica  – initial hydration, h ½g H2 O =gsilica  – percolation threshold, lh – critical exponent, and q ½gH2 O =m2silica  – threshold water surface density. The last column gives silica mean surface area (Å2) available to a single water molecule at the percolation threshold. For comparison, the same data for AerosilÒ A380 are shown in the bottom row. Sample

S

D

h0

h⁄

lh

q⁄ = h⁄/S

SBA-15 (a) SBA-15 (b) SBA-15 (c) AerosilÒ A380 [5]

654 654 654 380

67 ± 5 67 ± 5 67 ± 5 70 ± 20

3.57 4.88 6.82 3.44

0.159 ± 0.002 0.417 ± 0.009 0.828 ± 0.007 0.244 ± 0.003

0.964 ± 0.002 0.979 ± 0.005 1.032 ± 0.004 1.01 ± 0.01

2.43 ± 0.28  10-4 6.38 ± 0.56  10-4 12.7 ± 1.1  10-4 6.42 ± 0.06  10-4

12.35 4.70 2.37 4.67

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Fig. 5. Correlation between the water surface density percolation threshold, q⁄, and the water surface density at the initial sample hydration, q0, for Aerosil (closed symbols) and SBA-15 (open symbols) powders freely drying to ambient air. Error bars indicate std.

all three models were acceptable for explanation of the percolation exponent [7]. What is new in SBA-15 results is a surprising correlation between the water surface density at the percolation threshold, q⁄ = h⁄/S, S being the specific surface area, and that at the initial hydration level, q0 = h0/S, cf. Fig. 5. In AerosilÒ samples, regardless their specific surface area, initial hydration had no effect on the percolation threshold, q⁄, showing up more or less at the same water surface density [7]. In SBA-15, the hydration level at the percolation threshold is linearly coupled to the amount of water accumulated in the sample at the beginning. This linearity suggests strong coupling of the phenomenon to the honeycomb geometry of SBA-15 pore structure, cf. Fig. 1. SBA-15, depending on the synthesis protocol can have a variety of final forms [15], although no matter how thin or thick flake structures are, the characteristic underlying honeycomb scaffold of mesopores is preserved. Since the interior of native silica mesopores is hydrophilic, on hydration water prewetting of the pore’s walls is instantly favoured [25]. If pores are, as in the present case, rather narrow, as soon as water reaches them, they became filled completely by capillary effect. Hydrophilic/phobic situation could be different at the pore openings, since the silica free interface curvature rapidly changes there from that concave pore interior to being short radius convex at the openings edge, influencing the local density of silanol groups responsible for hydrogen-bonding water molecules [26–28]. The hydrogen-bonding between components of a spanning water network occurs across short distances and a change in the distance between a given hydrogen-bond donor and acceptor pair at the silica surface should rapidly result in the network quality at this point [29]. As a result, water is less willing to wetting the pore edges. Thus, surface of the waterloaded flake becomes hydrophilically/phobically structured, with a regular honeycomb pattern of disconnected hydrophilic domains (pore inlets) separated by (weakly) hydrophobic matrix of the pore edges [30,31]. On further hydration, water, in order to minimize its interfacial area, will spread all over many pore openings, edges, to eventually completely cover the flakes. On consecutive, reverse slow, natural dehydration to ambient air, the hydration level decreases until amount of water in the sample reaches values typical for morphological wetting transition of the order of 1=4 ND3, where N and D are the number of hydrated

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pores and the pore opening diameter, respectively [30]. Below this level of hydration, wetting becomes unstable. As the water volume further decreases, water bulk will tend to break down to form one by one convex-curved cups over of the pore openings. This is specifically facilitated by, e.g., faster evaporation from hydrophobic than from hydrophilic substrates [32,33], and amplification of thermal fluctuations (spinodal decomposition) [34,35]. As a result, the wetting film continuity begins to break down over the hydrophobic parts of the substrate leading to the observed conductivity percolation. There are two natural consequences of accepting such scenario. First, that the proton transfer is realized via hydrogen-bonded water molecules residing over hydrophobic parts of the substrate. Independent in silico studies suggesting that water network at hydrophobic interfaces should provide faster pathways for lateral proton transport than over hydrophilic ones, and that the transport is realized not in the first interfacial water layer but in the next [36], as well as the ability of protons to provoke spontaneous creation of water-based proton-wire pathways (Grotthus mechanism) in hydrophobic environments [6], enhance substantially such envision. Second, that there is plenty of water left in the system at the percolation threshold. Although water invades hydrophilic nonporous quickly [37], its evacuation to air from there would take substantially more time due to strong water molecules interaction with the substrate [33]. More entirely and in detail hydrated SBA-15 sample is, more water-filled mesopores and more water present at the percolation threshold, as witnessed in linear q⁄ vs. q0 dependence, cf. Fig. 5. 5. Conclusions DC conductivity behaviour of moistened SBA-15 shows on dehydration that at some hydration level the water film covering the chemically structured substrate formed by soaked with water honeycomb SBA-15 flakes, undergoes percolative failure. The film failure is driven by the substrate morphology. Conductivity percolation critical exponent is close to 1, independent of the initial SBA-15 hydration, and similar to that observed in moistened hydrophilic AerosilÒ powders. The percolation hydration threshold reflects the initial hydration level, varying in value linearly with the latter. Acknowledgements Authors appreciate the possibility of measuring of the textural properties of the SBA-15 sample at the laboratory of Prof. Pegie Cool (University of Antwerp). Fig. 1, was generously taken and provided by Dr. Vladimir Girman (Pavol Jozef Safarik University of Kosice) and Dr. Eng. Magdalena Jablonska (Jagiellonian University) in the framework of the NANOCEXMAT2 ITMS:26220120035 project. We acknowledge the Polish Ministry of Science and Higher Education financial support under Grant NN202 105836. Experiments were carried out in part with the equipment purchased thanks to the financial support of the European Regional Development Fund in the framework of the Polish Innovation Economy Operational Program (contract no. POIG.02.01.00-12-023/08). Notification of author contributions: J.N., L.C., D.D., and J.K.M. designed research; J.N., D.D., U.G. and M.R. performed experiments; D.D., U.G. and D.S. analyzed data, J.N., M.R., and L.C. contributed new reagents/analytic tools; J.K.M. and L.C. wrote the paper. References [1] R. Jorn, J. Savage, G.A. Voth, Acc. Chem. Res. 45 (2012) 2002–2010, http:// dx.doi.org/10.1021/ar200323q. [2] F. Tang, L. Li, D. Chen, Adv. Mater. 24 (2012) 1504–1534, http://dx.doi.org/ 10.1002/adma.201104763.

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[3] V. Mamaeva, C. Sahlgren, M. Lindén, Adv. Drug Delivery Rev. 65 (2013) 689– 702, http://dx.doi.org/10.1016/j.addr.2012.07.018. [4] Special issue on proton transfer in biological systems, Biochem. Biophys. Acta 1757 (2006) 8. ISSN: 0005-2728. [5] Y. Tanaka, Int. J. Chem. Eng. 2012 (2012) 906952, http://dx.doi.org/10.1155/ 2012/906952. [6] Y. Peng, J.M.J. Swanson, S. Kang, R. Zhou, G. A. Voth, J. Phys. Chem. B (Web: November 4, 2014). http://dx.doi.org/10.1021/jp5095118. [7] D. Sokolowska, D. Dziob, U. Gorska, B. Kieltyka, J.K. Moscicki, Phys. Rev. E 87 (2013) 062404, http://dx.doi.org/10.1103/PhysRevE.87.062404. [8] G. Careri, M. Geraci, A. Giansanti, J.A. Rupley, PNAS 82 (1985) 5342–5346, http://dx.doi.org/10.1073/pnas.82.16.5342. [9] M. Nogami, J. Sol-Gel Sci. Technol. 31 (2004) 359–364, http://dx.doi.org/ 10.1023/B:JSST.0000048017.99331.79. [10] V.V. Turov, V.M. Gun’ko, V.M. Bogatyrev, V.I. Zarko, S.P. Gorbik, E.M. Pakhlov, R. Leboda, O.V. Shulga, A.A. Chuiko, J. Colloid Interface Sci. 283 (2005) 329–343, http://dx.doi.org/10.1016/j.jcis.2004.09.046. [11] V. Meynen, P. Cool, E.F. Vansant, Microporous Mesoporous Mater. 104 (2007) 26–38, http://dx.doi.org/10.1016/j.micromeso.2006.12.003. [12] V. Meynen, P. Cool, E.F. Vansant, Microporous Mesoporous Mater. 125 (2009) 170–223, http://dx.doi.org/10.1016/j.micromeso.2009.03.046. [13] T. Benamor, L. Vidal, B. Lebeau, C. Marichal, Microporous Mesoporous Mater. 153 (2012) 100–114, http://dx.doi.org/10.1016/j.micromeso.2011.12.016. [14] M. Shakeri, R.J.M. Klein Gebbink, P.E. de Jongh, K.P. de Jong, Microporous Mesoporous Mater. 170 (2013) 340–345, http://dx.doi.org/10.1016/ j.micromeso.2012.12.018. [15] Y. Zhu, H. Li, J. Xu, H. Yuan, J. Wang, X. Li, Cryst. Eng. Comm. 13 (2011) 402– 405, http://dx.doi.org/10.1039/C0CE00570C. [16] A. Angulo-Sherman, H. Mercado-Uribe, Chem. Phys. Lett. 503 (2011) 327–330, http://dx.doi.org/10.1016/j.cplett.2011.01.027. [17] A. Serghei, M. Tress, J.R. Sangoro, F. Kremer, Phys. Rev. B 80 (2009) 184301, http://dx.doi.org/10.1103/PhysRevB.80.184301. [18] S. Emmert, M. Wolf, R. Gulich, S. Krohns, S. Kastner, P. Lunkenheimer, A. Loidl, Eur. Phys. J. B 83 (2011) 157–165, http://dx.doi.org/10.1140/epjb/e2011-20439-8. [19] P.B. Ishai, M.S. Talary, A. Caduff, E. Levy, Y. Feldman, Meas. Sci. Technol. 24 (2013) 102001, http://dx.doi.org/10.1088/0957-0233/24/10/102001. [20] J.K. Moscicki, D. Sokolowska, L. Kwiatkowski, D. Dziob, J. Nowak, Rev. Sci. Instrum. 85 (2014) 026102, http://dx.doi.org/10.1063/1.4863321.

[21] B.I. Halperin, S. Feng, P.N. Sen, Phys. Rev. Lett. 54 (1985) 2391–2394, http:// dx.doi.org/10.1103/PhysRevLett.54.2391. [22] L. Benguigui, Phys. Rev. B 34 (1986) 8176–8178, http://dx.doi.org/10.1103/ PhysRevB.34.8176. [23] B. Berkowitz, R. Knight, J. Stat. Phys. 80 (1995) 1415–1423, http://dx.doi.org/ 10.1007/BF02179877. [24] J.P. Straley, Phys. Rev. B 15 (1977) 5733–5737, http://dx.doi.org/10.1103/ PhysRevB.15.5733. [25] H. Ghiradella, W. Radigan, H.L. Frisch, J. Colloid Interface Sci. 51 (1975) 522– 526, http://dx.doi.org/10.1016/0021-9797(75)90149-6. [26] I.-S. Chuang, G.E. Maciel, J. Phys. Chem. B 101 (1997) 3052–3064, http:// dx.doi.org/10.1021/jp9629046. [27] A. Oleinikova, I. Brovchenko, N. Smolin, A. Krukau, A. Geiger, R. Winter, Phys. Rev. Lett. 95 (2005) 247802, http://dx.doi.org/10.1103/PhysRevLett.95. 247802. [28] M. Dürr, U. Höfer, Prog. Surf. Sci. 88 (2013) 61–101, http://dx.doi.org/10.1016/ j.progsurf.2013.01.001. [29] M. Gutman, E. Nachliel, Biochem. Biophys. Acta 1015 (1990) 391–414, http:// dx.doi.org/10.1016/0005-2728(90)90073-D. [30] R. Lipowsky, Curr. Opin. Colloid Interface Sci. 6 (2001) 40–49, http:// dx.doi.org/10.1016/S1359-0294(00)00086-8. [31] J. Bico, U. Thiele, D. Quere, Colloids Surf. A 206 (2002) 41–46, http://dx.doi.org/ 10.1016/S0927-7757(02)00061-4. [32] A. Sharma, R. Verma, Langmuir 20 (2004) 10337–10345, http://dx.doi.org/ 10.1021/la048669x. [33] D.S. Golovko, H.-J. Butt, E. Bonaccurso, Langmuir 25 (2009) 75–78, http:// dx.doi.org/10.1021/la803474x. [34] F. Brochard Wyart, J. Daillant, Can. J. Phys. 68 (1990) 1084–1088, http:// dx.doi.org/10.1139/p90-151. [35] F. Brochard Wyart, P. Martin, C. Redon, Langmuir 9 (1993) 3682–3690, http:// dx.doi.org/10.1021/la00036a053. [36] C. Zhang, D.G. Knyazev, Y.A. Vereshaga, E. Ippoliti, T.H. Nguyen, P. Carloni, P. Pohl, PNAS 109 (2012) 9744–9749, http://dx.doi.org/10.1073/pnas.1121 227109. [37] M. Lee, D. Lee, N. Jung, M. Yun, C. Yim, S. Jeon, Appl. Phys. Lett. 98 (2011) 013107, http://dx.doi.org/10.1063/1.3541958.