pubs.acs.org/Langmuir © 2009 American Chemical Society
Boundary Slip Study on Hydrophilic, Hydrophobic, and Superhydrophobic Surfaces with Dynamic Atomic Force Microscopy Bharat Bhushan,*,† Yuliang Wang,†,‡ and Abdelhamid Maali§ †
Nanoprobe Laboratory for Bio- & Nanotechnology and Biomimetics (NLB2), The Ohio State University, 201 West 19th Avenue, Columbus, Ohio 43210-1142, ‡Mechanical Engineering, Harbin Institute of Technology, Harbin 150001, P.R. China, and §Centre de Physique Moleculaire Optique et Hertzienne, University Bordeaux I 351 cours de la Liberation, F-33405 Talence, France Received February 18, 2009. Revised Manuscript Received March 23, 2009 Slip length has been measured using the dynamic atomic force microscopy (AFM) method. Unlike the contact AFM method, the sample surface approaches an oscillating sphere with a very low velocity in the dynamic AFM method. During this process, the amplitude and phase shift data are recorded to calculate the hydrodynamic damping coefficient, which is then used to obtain slip length. In this study, a glass sphere with a large radius was glued to the end of an AFM cantilever to measure the slip length on rough surfaces. Experimental results for hydrophilic, hydrophobic, and superhydrophobic surfaces show that the hydrodynamic damping coefficient decreases from the hydrophilic surface to the hydrophobic surface and from the hydrophobic one to the superhydrophobic one. The slip lengths obtained on the hydrophobic and superhydrophobic surfaces are 43 and 236 nm, respectively, which indicates increasing boundary slip from the hydrophobic surface to the superhydrophobic one.
1. Introduction Boundary slip at the solid-liquid interface reduces drag in fluid flow, which is particularly meaningful on the micro/nanoscale, where the surface to volume ratio increases inversely with the characteristic length scale. Early experimental results show that Newtonian liquids may undergo slip when flowing over nonwettable surfaces.1,2 In further experiments with surface force apparatus,3-6 AFM (atomic force microscopy),7,8 and PIV (particle image velocimetry)9 techniques, slip length has been measured on hydrophobic surfaces with relatively high resolution. The above experimental results are consistent with the molecular dynamic simulation results performed by Barrat and Bocquet,10 who obtained a 30 molecular diameter slip length on a surface of contact angle 140°, while no slip was observed on hydrophilic surfaces. Current AFM measurements of slip length are carried out in the contact mode.7,11-13 In contact AFM experiments, the AFM cantilever deflection signal induced by the hydrodynamic force and corresponding piezotube displacement are recorded as the tip approaches sample surfaces at high velocity. In such experiments, one has to extrapolate the linear part of cantilever deflection to *Corresponding author. E-mail:
[email protected]. (1) Schnell, E. J. Appl. Phys. 1956, 27, 1149–1152. (2) Churaev, N. V.; Sobolev, V. D.; Somov, A. N. J. Colloid Interface Sci. 1984, 97, 574–581. (3) Baudry, J.; Charlaix, E.; Tonck, A.; Mazuyer, D. Langmuir 2001, 17, 5232– 5236. (4) Zhu, Y. X.; Granick, S. Phys. Rev. Lett. 2001, 87, 096105. (5) Cottin-Bizonne, C.; Jurine, S.; Baudry, J.; Crassous, J.; Restagno, F.; Charlaix, E. Eur. Phys. J. E 2002, 9, 47–53. (6) Cottin-Bizonne, C.; Cross, B.; Steinberger, A.; Charlaix, E. Phys. Rev. Lett. 2005, 94, 056102. (7) Vinogradova, O. I.; Yakubov, G. E. Langmuir 2003, 19, 1227–1234. (8) Honig, C. D. F.; Ducker, W. A. Phys. Rev. Lett. 2007, 98, 028305. (9) Tretheway, D. C.; Meinhart, C. D. Phys. Fluids 2002, 14, L9–L12. (10) Barrat, J. L.; Bocquet, L. Phys. Rev. Lett. 1999, 82, 4671–4674. (11) Craig, V. S. J.; Neto, C.; Williams, D. R. M. Phys. Rev. Lett. 2001, 87, 054504. (12) Bonaccurso, E.; Kappl, M.; Butt, H. J. Phys. Rev. Lett. 2002, 88, 076103. (13) Bonaccurso, E.; Butt, H. J.; Craig, V. S. J. Phys. Rev. Lett. 2003, 90, 144501.
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zero to get the actual contact position. Moreover, the impact of cantilever deflection to the determination of separation distance and squeezing velocity should also be considered. Improper treatment of experimental data may lead to errors in the determination of slip length. Recently, a dynamic AFM method was proposed to study boundary slip.14 In the dynamic AFM method, the amplitude and phase shift data of an oscillating sphere are recorded during approach to sample surfaces at very low velocities. These data are then used to get the hydrodynamic damping coefficient exerted on the sphere. Unlike in the contact AFM method, since the approach velocity in dynamic AFM method is low, the average force exerted on the cantilever is zero, and thus the deflection signal of the cantilevers is zero until the sphere comes into contact with the surface and the cantilever deflection signal increases linearly. Therefore, the actual contact position and separation distance can be determined from the deflection signal of the cantilever with an accuracy better than 1 nm. Although the dynamic AFM method has been used to study boundary slip on hydrophilic and hydrophobic surfaces, the technique has not been used for measurements on superhydrophobic surfaces. Superhydrophobic surfaces are inherently expected to have a high value of roughness on the microscopic scale. Therefore, the liquid between asperities when using superhydrophobic surfaces with an AFM will have an impact on the measured slip length because liquid below the asperities contributes to the flow and reduces the measured hydrodynamic force.13 Furthermore, the contact would occur at some high asperities. The separation distance between the approaching tip and the rough surface would have to be corrected with respect to some virtual flat surface. In this paper, boundary slip studies are carried out on hydrophilic, hydrophobic, and superhydrophobic surfaces with the dynamic AFM method. To minimize the impact of surface (14) Maali, A.; Cohen-Bouhacina, T.; Kellay, H. Appl. Phys. Lett. 2008, 92, 053101.
Published on Web 04/29/2009
DOI: 10.1021/la900612s
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roughness of the sample surfaces, in particular superhydrophobic surfaces, on the measured hydrodynamic damping coefficient, a large contact area is needed and a sphere with a large diameter is used by gluing it to an AFM cantilever. To correct the separation distances between the sphere and the rough hydrophobic and superhydrophobic surfaces, offset distances are calculated and are added to the measured separation distances.
2. Experimental Section In this section, the methodology for the determination of slip length is introduced first, followed by the measurement technique. The fabrication procedure for hydrophobic and superhydrophobic surfaces used for boundary slip studies is presented next. 2.1. Approach. As shown in Figure 1, when a sphere with diameter R approaches a surface, assuming there is slip length b at the solid-liquid interface while there is no boundary slip at sphere-liquid interface, the hydrodynamic force FH exerted on the sphere can be given as15 FH ¼ -f
6πR2 η dD dD ¼ -γH D dt dt
ð1Þ
where 8 9 " #= < 1 6D D 4b 1þ 1þ ln 1 þ -1 f ¼ ; 4: 4b 4b D
ð2Þ
where D is the closest separation distance between the sphere and the solid surface, dD/dt is the velocity of the sphere approaching the surface, η is the viscosity of the liquid, and γH is the hydrodynamic damping coefficient. For a sphere oscillating in liquid excited by an external force while approaching a surface, the total damping coefficient γtot can be given as γtot ¼ γH þ γ0
ð3Þ
where γ0 is the bulk viscous damping coefficient. When excited at its resonance frequency, the relationship between the total damping coefficient γtot and the bulk viscous damping coefficient γ0 can be given using the equation of tip motion16 γtot A0 Q0 sinðjÞ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ γ0 A 1 þ Q0 2 þ 2 AA0 cosðjÞ þ
2
A2
0 pAffiffiffiffiffiffiffiffiffiffi ffi 2
ð4Þ
1 þQ0
where A0 is the free oscillation amplitude of the cantilever far from the surface, while A is the amplitude of the cantilever at a given position, Q0 is quality factor of the cantilever far from the surface, and j is the phase shift at a given position. When the cantilever is far from the surface and excited by a piezoactuator with a constant amplitude Ad, the cantilever oscillation amplitude Aω as a function of excitation frequency ω can be given as16 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ad ω ω2 þ ðω0 =Q0 Þ2 Aω ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðω0 2 -ω2 Þ2 þ ðωω0 =Q0 Þ2
ð5Þ
where ω0 is the resonance frequency of the cantilever. With eq 5, the resonance frequency and quality factor of the cantilever can be obtained by fitting the spectra of the excited cantilever as a function of excitation frequency.
(15) Vinogradova, O. I. Langmuir 1995, 11, 2213–2220. (16) Jai, C.; Cohen-Bouhacina, T.; Maali, A. Appl. Phys. Lett. 2007, 90, 113512.
8118 DOI: 10.1021/la900612s
By using eqs 3 and 4, the hydrodynamic damping coefficient as a function of separation distance is calculated from the measured amplitude and phase shift data. Then eqs 1 and 2 are used to fit the hydrodynamic damping coefficient data to get the slip length. Therefore, in order to obtain the hydrodynamic damping coefficient, the quality factor Q0, oscillation amplitude A, and phase shift data versus the separation distance are needed. The value of viscosity for water used in this study is η = 851.5 μPa s at 300 K.17 In the following section, we will describe how to obtain the above parameters.
2.2. Measurement of Oscillation Amplitude and Phase Shift. To obtain oscillation amplitude and phase shift, the dynamic AFM experiments were performed using a Multimode III atomic force microscope (Veeco) with a probe with a sphere of large radius attached to it.18 A soda lime glass sphere (9040, Duke Sci. Corp., Palo Alto, CA) with a diameter of 42.4 ( 0.8 μm was glued to the end of a silicon nitride rectangular cantilever (ORC8, Veeco) using epoxy (Araldite, Bostik, Coubert, France). The stiffness of the cantilever was calibrated as 1.5 ( 0.1 N/m via the thermal noise method.19 The thermal power spectra of the cantilever used in the stiffness calibration was obtained using a lock-in amplifier (model 7280, AMETEK Inc. Oak Ridge, TN). A large sphere was glued at the end of the commercial AFM cantilever to minimize the impact of roughness. There are several advantages of using large spheres. First, on rough surfaces, the hard contact positions between the spheres and sample surface are geometrically determined by the relationship between the distribution of asperities on the sample surface and the curvature of the sphere. Comparing with small spheres, large spheres have relatively flat curvature and can therefore cover a larger area when in contact with the sample surface and the interaction occurs over a large area. Therefore, large spheres allow averaging of the hydrodynamic interaction on rough surfaces; otherwise, one should make a statistical measurement on different positions on the sample. Spheres with radii from 10 to 12 μm have been used to measure slip length with AFM.11-13 However, in these experiments, the roughness values were relatively low, less than about 12 nm rms (root-mean-square). When it comes to superhydrophobic surfaces, there is inherently high roughness and spheres with larger radii are desirable. Second, from eq 1, one can see that the force exerted on the sphere increases with the square of the radius of a sphere as R2. Therefore, larger spheres are expected to increase the useful signal during experiments and improve the signal-to-noise. Finally, the use of a large sphere minimizes the influence of liquid squeezing by the body of the cantilever beam by increasing its distance from the sample surfaces, a problem that has been reported by Vinogradova and Yakubov.7 A modified tip holder was used to perform all the liquid experiments in this study.20 In this design, the cantilever is excited directly by the piezo. During experiments, the cantilever was excited at its resonance frequency. To obtain the resonance frequency and the quality factor, the cantilever was excited within the frequency range of 6 and 14 kHz when it was far from the surface (about 40 μm). The excitation amplitude as a function of drive frequency is shown in Figure 2. By fitting the cantilever excitation spectra using eq 5, we obtained the quality factor and the cantilever resonance frequency, which are 5.2 ( 0.2 and 11.7 ( 0.1 kHz, respectively. The free oscillation amplitude A0 and reference phase shift data can then be obtained by exciting the cantilever at the resonance frequency when the cantilever was far away from sample surfaces. To minimize the hydrodynamic force, the sample surface was driven at a low approach velocity of (17) Lide, D. R. CRC Handbook of Chemistry and Physics, 88th ed.; CRC Press Inc.: Boca Raton, FL, 2007. (18) Bhushan, B. Nanotribology and Nanomechanics: An Introduction, 2nd ed.; Springer: Heidelberg, Germany, 2008. (19) Matei, G. A.; Thoreson, E. J.; Pratt, J. R.; Newell, D. B.; Burnham, N. A. Rev. Sci. Instrum. 2006, 77, 083703. (20) Maali, A.; Hurth, C.; Cohen-Bouhacina, T.; Couturier, G.; Aime, J. P. Appl. Phys. Lett. 2006, 88, 163504.
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Figure 1. Schematic of an oscillating sphere approaches a surface with a very low velocity and amplitude of velocity profile of fluid flow with and without boundary slip in the dynamic AFM method. The slip length b characterizes the degree of boundary slip at the solid-liquid interface. During the approach process, the amplitude and phase shift data are recorded to measure slip length.
Figure 2. Excitation spectra and corresponding fitting of AFM cantilever oscillation as a function of excitation frequency in water. By fitting, a quality factor of 5.2 and resonance frequency of 11.7 kHz are obtained. 0.16 μm/s. During the cantilever approach to the sample surfaces, the amplitude and phase shift data are recorded with the lock-in amplifier. 2.3. Sample Surfaces. One hydrophilic surface, one hydrophobic surface, and one superhydrophobic surface are used in this study. Mica was taken as the hydrophilic surface. In order to prepare the hydrophobic and superhydrophobic surfaces, smooth epoxy substrates were first prepared using a liquid epoxy resin (Epoxydharz L, no. 236349, Conrad Electronics, Hirschau, Germany) and hardener (Harter S, Nr 236365, Conrad Electronics, Hirschau, Germany) by a conventional molding method. The hydrophobic and superhydrophobic surfaces were then created on the epoxy substrates by self-assembly of alkane nhexatriacontane (CH3(CH2)34CH3) (purity of g99.5%, SigmaAldrich) and Lotus wax (nonacosane-10,15-diol and nonocosan10-ol) deposited by thermal evaporation. The detailed processes of the fabrication of the hydrophobic and superhydrophobic surfaces are described by Bhushan et al.21 and Koch et al.22 Here, we briefly describe them. (21) Bhushan, B.; Koch, K.; Jung, Y. C. Soft Matter 2008, 4, 1799–1804. (22) Koch, K.; Bhushan, B.; Jung, Y. C.; Barthlott, W. Soft Matter 2009, 5, 1386–1393.
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Article The smooth epoxy substrates were placed in a vacuum chamber at 30 mTorr (4 kPa pressure), 2 cm above a heating plate loaded with 500 μg of n-hexatriacontane and 2000 μg of Lotus wax. The n-hexatriacontane and Lotus wax were evaporated by heating them up to 120 °C. After coating, the specimens with n-hexatriacontane were placed in a desiccator at room temperature for 3 days for crystallization of the alkanes to generate the platelet nanostructure.21 After that, the specimen was heated in an oven (85 °C, 3 min) and then immediately cooled down (5 °C) to interrupt the recrystallization process to generate the hydrophobic surface. The specimens with Lotus wax were stored for seven days at 50 °C in a crystallization chamber and exposed to a solvent (20 mL of ethanol) in vapor phase to fabricate the superhydrophobic surface. A tubule nanostructure was produced on the specimen surface.22 After fabrication, the hydrophilic, hydrophobic, and superhydrophobic surfaces were imaged in air with TMAFM. A silicon cantilever rotated force-modulation etched silicon probe (RFESP, Digital Instruments) with a tip radius of
