ARTICLE pubs.acs.org/Langmuir
Controlling Adhesion Force by Means of Nanoscale Surface Roughness Shivaprakash N. Ramakrishna, Lucy Y. Clasohm, Akshata Rao, and Nicholas D. Spencer* Laboratory for Surface Science and Technology, Department of Materials, ETH Zurich, Wolfgang-Pauli-Strasse 10, 8093 Zurich, Switzerland ABSTRACT: Control of adhesion is a crucial aspect in the design of microelectromechanical and nanoelectromechanical devices. To understand the dependence of adhesion on nanometer-scale surface roughness, a roughness gradient has been employed. Monomodal roughness gradients were fabricated by means of silica nanoparticles (diameter ∼12 nm) to produce substrates with varying nanoparticle density. Pull-off force measurements on the gradients were performed using (polyethylene) colloidalprobe microscopy under perfluorodecalin, in order to restrict interactions to van der Waals forces. The influence of normal load on pull-off forces was studied and the measured forces compared with existing Hamakerapproximation-based models. We observe that adhesion force reaches a minimum value at an optimum particle density on the gradient sample, where the mean particle spacing becomes comparable with the diameter of the contact area with the polyethylene sphere. We also observe that the effect on adhesion of increasing the normal load depends on the roughness of the surface.
1. INTRODUCTION Even when two polished surfaces come into contact, they have a low contact area due to the micro/nanoscale roughness on the surface. Fabricating a surface with zero roughness is essentially impossible. Roughness exists on all length scales and is known to greatly influence the tribological performance between any two moving parts. The effect of the nanoscale surface roughness on adhesion force becomes very significant in the areas of microelectromechanical and nanoelectromechanical devices (MEMS/ NEMS)13 and in micro/nanorobotics.4 The consequences of adhesion and friction on the nanoscale can differ from what is observed at the macroscale due to an increase in the surface-tovolume ratio, and can lead to undesirable effects, such as static friction of mechanical parts in microdevices. As the sizes of mechanical components continue to decrease, accurate determination of the adhesive forces on the nanoscale are becoming crucial for device design, materials selection, and performance. Also, tuning the roughness on surfaces becomes a potential tool for tailoring the adhesion. Several studies have dealt with the effect of micrometer/ submicrometer-scale roughness on adhesion force,515 particularly after the colloidal-probe atomic force microscopy (AFM) technique was introduced by Ducker et al.16 Most of these studies reveal that roughness decreases the adhesion force, due to the reduction in real contact area between the probe and the substrate. In this study, we have systematically investigated the effect of nanoscale surface roughness on adhesion force by measuring the pull-off force between a polyethylene microsphere mounted on r 2011 American Chemical Society
an AFM cantilever and a silica-nanoparticle-based roughness gradient. We have also discussed the influence of normal load on the pull-off forces measured on gradient sample. We have compared our experimental results with existing models that are based on the Hamaker approximation. We also monitored the force curves taken between the rough and smooth ends of the gradient and investigated the transition from multiasperity detachment to the single snapping off of the probe during the retraction.
2. THEORY The pull-off force necessary to separate two elastically smooth surfaces in adhesive contact can be analyzed with contact mechanics. Theories such as those of Johnson, Kendall, and Roberts (JKR)17 or Derjaguin, M€uller, and Toporov (DMT)18 estimate the adhesion between two contacting surfaces by surface-energy approximations, but the models neglect any roughness effect, which causes a nonuniform pressure distribution across the real contact area. The interpretation of adhesion force by means of Hamaker’s approximation has also been reported, and assumes that only van der Waals forces are acting between the interacting surfaces. A Hamaker-based approach for calculating the van der Waals force on nanoscale rough surfaces was described by Rumpf19 for hemispherical asperities on surfaces (eq 1) and later modified by Received: May 9, 2011 Revised: June 30, 2011 Published: July 02, 2011 9972
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asperities. Fadh
" # AH R 1 1 þ ¼ 6H02 1 þ R=ð1:48rmsÞ ð1 þ 1:48rms=H0 Þ2 ð2Þ
Figure 1. Cartoon picture of a gradient sample, showing designations of high- and low-particle-density ends and scale.
Further, Rabinovich extended the modified Rumpf model (Rabinovich model), to include both the rms roughness of the surface and also the distance between the asperities (eq 3). 3 2 Fadh ¼
AH R 6 6 6 6H02 4
7 1 1 7 þ 2 7 32Rk1 rms k1 rms 5 1 þ 1 þ 2 λ H0 ð3Þ
where rms is root-mean-square roughness, k1 is a coefficient related to ymax and rms, and λ is the peak-to-peak distance of the surface aperities. The Katainen model (eq 4) is also an extension of the Rumpf model in which the interaction is considered between a large, blunt sphere and hemispherical asperities on the surface. This model assumes multiple contacts underneath the sphere and the average number of asperities that come into contact is the product of the contact area with the number density of the asperities. " # AH A 1 Fr þ ð4Þ Fadh ¼ 6H02 πH0 ð1 þ ymax =H0 Þ3
Figure 2. SEM images of the 12-nm-diameter particles along the gradient sample. From top 0.8 cm, 0.6 cm, 0.4 cm, 0.2 cm, and 0 cm, of the gradient sample. The corresponding particle densities are 25/μm2, 67/μm2, 175/μm2, 320/μm2, 396/μm2.
Rabinovich et al20 (eqs 2 and 3) by considering the rms roughness of the substrate. The recent model (eq 4) by Katainen8 et al. modifies the Rumpf model by assuming a blunt particle to be in contact with many asperities on the substrate. All these models take two components of the interaction into account, the first part being due to contact between sphere and the asperities and the second part resulting from the noncontact interaction between the sphere and the substrate below the asperities. The Rumpf model assumes that the sphere is interacting with hemispherical asperities on a smooth surface and the adhesion force is calculated as " # AH R r 1 þ ð1Þ Fadh ¼ 6H02 r þ R ð1 þ r=H0 Þ2 where Fadh represents the total van der Waals force, AH is the Hamaker constant, R is the radius of the colloidal sphere, r is the radius of the asperities whose maximum height is given by ymax, and H0 is the distance of closest approach between the two surfaces. Later, Rabinovich et al. modified this model, which is known as the modified Rumpf model (eq 2), by introducing a rms roughness parameter and assuming close packing of the
where A is the contact area and F is the number density of the asperities. From Israelachvili’s simplification21 of the Lifshitz continuum theory,22 the Hamaker constant AH, which includes both zerofrequency term and nonretarded dispersion term, can be expressed as 3 ε1 ε3 ε2 ε3 3hγ þ pffiffieffi AH ¼ Aγ ¼ 0 þ Aγ > 0 ≈ kT 4 ε1 þ ε3 ε2 þ ε3 8 2
ðn21 n23 Þðn22 n23 Þ n o 1=2 ðn21 þ n23 Þ ðn22 n23 Þ1=2 ðn21 þ n23 Þ1=2 þ ðn22 þ n23 Þ1=2
ð5Þ where ε1, ε2, ε3, and n1, n2, n3 represent the dielectric constants and refractive indices, respectively, of the two interacting phases 1 and 2 and the medium 3. The absorption frequency γe is assumed to be same for all three components of the van der Waals interaction (dipoledipole, dipoleinduced-dipole, and the dispersion (London) contributions). T is the temperature, k is Boltzmann’s constant, and h is Planck’s constant.
3. EXPERIMENTAL SECTION 3.1. Materials and Experimental Procedures. In this study, an atomic force microscope (MFP3D, Asylum Research, Santa Barbara, USA) was used for measuring pull-off forces from a silica-nanoparticle roughness gradient. To eliminate the capillary forces, all measurements were performed in a liquid medium. To further screen the influences of different surface interactions and amplify the van der Waals forces, perfluorodecalin (Aldrich chemicals, purity 95%) was used as a medium for the experiments. Perfluorodecalin (C10F18) is a nonpolar liquid, which has a low refractive index (1.313) and dielectric constant (1.8). According 9973
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Figure 3. AFM contact-mode image and the line profile of a polyethylene sphere as used in the colloidal-probe measurements. A polyethylene sphere was glued to the end of a soft cantilever (k = 0.1 N/m) and scanned across a TGT 01 silicon tip array. to the Israelachvili simplification of the Lifshitz continuum theory (eq 5), the Hamaker constant for two macroscopic phases 1 and 2 interacting across medium 3 can be tuned by choosing an appropriate medium for the measurement. Thus, the van der Waals force can be amplified by choosing a low-refractive-index liquid as medium.23 3.2. Preparation of Nanoparticle Roughness Gradient. The technique used for preparing a gradient samples has been previously described.24 The method relies upon the simple electrostatic attraction of negatively charged silica nanoparticles onto an oxidized silicon surface, which has been rendered positively charged by coating with poly(ethylene imine) (PEI). The PEI-modified silicon wafer was mounted on a linearmotion drive and gradually immersed into an aqueous silica-nanoparticle suspension (ϕ ≈ 12.1 nm, coefficient of varience (CV) < 15%, purchased from Microspheres-Nanospheres, Cold Spring, NY). The kinetics of adsorption therefore result in a variation of particle density along the sample. The sample was finally dried with nitrogen and sintered at 1080 °C for 2 h to remove any excess polymer on the surface and to partially sinter the nanoparticles into the surface. The prepared gradient was then characterized with scanning electron microscopy (SEM) and atomic force microscopy (AFM). A nanoparticle-density-gradient sample was prepared, the particle density being varied from 416/μm2 (rough end) to 0/μm2 (smooth end). The particles were fused into the surface, protruding 6 ( 2 nm. The use of such a gradient sample is advantageous as it allows a well-defined roughness to be gradually varied along the substrate in a controlled manner. This enables the investigation of the roughness effects on adhesion force, while keeping all other experimental conditions identical. 3.3. Characterization. A gradient sample of typical length 1 cm was prepared and marked as shown in Figure 1. Figure 2 shows scanning electron microscope (FEI Quanta 200 FEG) images of a gradient sample prepared by the procedure described in the Experimental section. The particle densites were calculated from these images by taking the average over 3 different spots at various positions along the gradient. Tapping-mode AFM imaging was conducted with silicon nitride cantilevers (OMCL-AC160TS -Olympus microcantilevers, Japan) having a spring constant ∼26 N/m and resonant frequency ∼300 kHz in air under ambient conditions. The average height of the particles was measured to be 6 ( 2 nm.
3.4. Pull-off Force Measurement by Colloidal-Probe AFM. Polyethylene microspheres (Type CL-2080, Kobo Products, Inc. South Plainfield, NJ) were glued to a tipless cantilever (Mikromasch, Tallinn, Estonia) with Araldite epoxy glue using a home-built micromanipulator. The Young’s modulus, Poisson’s ratio, and yield strength of the
Figure 4. Example of adhesion mapping and the obtained histogram taken at the rough end of the gradient sample. 200 pull-off-force measurements were taken over a 20 μm 20 μm area. The mean and standard deviation were calculated by fitting the histogram to a Gaussian distribution. polyethylene sphere were determined from the manufacturer’s density data (0.918 g cm3), using the correlation by Crist et al.25 to be 0.2 GPa and 7 MPa, respectively. The Poisson’s ratio was assumed to be 0.4. The diameter of the sphere used in this study was 18 μm and 20 μm for lowand high-load experiments, respectively. Figure 3 shows an AFM image (Veeco, Dimension 3000) and line profile of a typical polyethylene sphere that was obtained by means of a reverse-imaging technique. The sphere was glued to a soft cantilever and scanned across an array of ultrasharp tips (TGT01, Mikromasch) using contact mode imaging to obtain the image of the sphere. The normal calibration of the cantilevers was carried out by the thermal noise method26 before attachment of the colloidal sphere. Two different cantilevers were used, referred to below as “soft” and “stiff”, with spring constants k = 0.066 N/m and 9.59 N/m, respectively. To characterize the adhesion force, 200 force curves were obtained in perfluorodecalin over an area 20 μm by 20 μm between a polyethylene microsphere at each point of interest along the silica-particle-gradient substrate. An adhesion histogram was generated from the results. By fitting a Gaussian distribution to the histogram, the mean and standard deviation of the pull-off force were calculated, as shown in Figure 4.
4. RESULTS AND DISCUSSION Adhesion measurements by AFM on a roughness gradient using a soft cantilever (low load) and a stiff cantilever (high load) are presented below (section 4.1 and section 4.2). The variation in the adhesion forces as a function of particle density, normal load, and number of particles in contact is also discussed. 9974
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Figure 5. Pull-off force vs particle density along the gradient sample. Cantilever used with spring constant, k = 0.066 N/m, PE colloidal sphere radius R = 9 μm, load applied = 5 nN. Insets represent the type of contact obtained between the sphere and the gradient sample.
Figure 6. Histogram of the pull-off forces measured at four locations along the gradient substrate for the applied load of 5 nN. High adhesion and low standard deviation are observed at the smooth end of the gradient. Low adhesion and greater spread in the data are observed at the rough end. A minimum in adhesion is observed at the lowest particle density sufficient to prevent direct contact of colloidal probe and silicon substrate (145/μm2).
4.1. Adhesion Force at Low Applied Loads. Pull-off-force measurements were performed at a low applied load (5 nN) by means of soft cantilevers. Figure 5 shows the plot of pull-off forces measured vs particle density along the gradient surface. At the rough end of the gradient surface (particle density 416/μm2), the contact between the tip and the substrate would be mainly between the asperity of PE sphere and the nanoparticles, which lowers the real area of contact significantly. Accordingly, the measured pull-off force was less than that obtained for the smooth end (particle density 0/μm2); however, a high standard deviation for the pull-off forces was observed. Moving along the gradient toward the smooth end, a slight decrease in the mean pull-off force value was observed as the particle density (396/μm2 to 175/μm2) decreased. The lowest force was observed at a position on the gradient (at particle density 145/μm2) when the PE sphere is supported by minimum number of nanoparticles. Here, the mean particle spacing becomes comparable with the diameter of the contact area with the PE sphere. When the particle density is further decreased (38/μm2), the colloidal sphere starts to touch the lower Si substrate in between the particles. This increases the pull-off force, which is due to the combined effect of sphereparticle and spheresubstrate interactions. At the smooth end of the gradient (particle density 0/μm2), the calculated van der Waals adhesion force via the Lifshitz theory (eq 5) is about 1420 nN. However, a pull-off force of only 25 nN was observed, which is likely to be due to the presence of submicrometer-sized asperities on the polyethylene sphere,27
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which at the low loads are negligibly compressed, leading to a low contact area. The stochastic nature of the particle spacing affects the standard deviation observed for the measured pull-off forces on a rough surface. Figure 6 represents the spread of the pull-off forces observed at four different particle densities. At the smooth end (red bars), high adhesion with low standard deviation was observed for the measured 200 force curves. At the rough end (yellow bars), low adhesion values with a large spread in the data were observed due to variation in the number of particles that come into contact with each measurement. At the optimum particle density (green bars), the spread in the data was minimized, as we achieve a minimum number of particles in contact between the sphere and the substrate. Moving toward the smooth end of the gradient, the contact between the sphere and the Si substrate beneath increases (blue bars). The measured pull-off forces show two different peaks in the histogram, which represent the values obtained when the sphere is in contact with the substrate or when it is only in contact with the nanoparticles, the average of these leading to a large standard deviation. Figure 7 represents force curves obtained at the rough (a) and the smooth (b) ends of the gradient. At the rough end of the gradient, a gradual retraction of the sphere from the surface was observed due to the multiple detachment points of the contact. At the smooth end, the force curve shows an abrupt snap-off of the cantilever from the surface. In Figure 7, we also observe a slight attractive force when approaching the rough end of the gradient. Similarly, a weak repulsive force was observed at the smooth end of the gradient. These small forces, whose magnitudes varied from experiment to experiment, could be due to traces of water present at the interface28 of the silicon surface, leading to a development of charge and thus a Coulombic force— possibly a non-DLVO force29—which is dependent on an illdefined local pH value. However, close to the surface, where the adhesion is occurring, such forces are weak in comparison to the van der Waals forces, and we have therefore neglected these effects in our study. 4.2. Adhesion Force at High Applied Loads. To study the effect of normal load on pull-off forces on the gradient substrate, the stiff cantilever was chosen for the measurements. Figure 8 shows the pull-off force as a function of normal load applied and number of particles in contact for all particle densities on the gradient. The actual number of particles in contact with the colloid probe is shown with the color code. The total contact area of a PE sphere interacting with a flat, oxidized silicon substrate in perfluorodecalin was estimated by means of the classical Hertz equation30 at different applied loads. The number of particles in contact can be estimated by multiplying the calculated contact area (on a flat surface) by the particle density. In the high-density region of the gradient (particle density 416/μm2, 396/μm2, 360/μm2, 320/μm2) increasing load led to a slight increase in the pull-off force due to the linear increase in the number of particles in contact with the colloidal probe (Figure 8). In this case, the shape of the pull-off curve again corresponds to multiasperity detachment. Under high loads at the rough end, hysteresis between the loading and unloading portions of the curve is observed (Figure 9a). The adhesion hysteresis is caused by the mechanical instability arising from the spontaneous jumping in and out of contact of the cantilever. The adhesion energy needed to separate the surfaces from contact is therefore greater than that upon approach.31 Upon contact, the adhesion hysteresis could be due to the viscoelastic behavior of the 9975
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Figure 7. Forcedistance curve taken at smooth end (a) and rough end (b) of the gradient with soft cantilever (load applied = 5 nN). At the smooth end, snapping off and at rough end multiple detachments were observed during retraction of the colloid probe.
Figure 8. Pull-off force as a function of load and particle density on the gradient. The actual number of particles in contact with the colloid probe (calculated from the Hertz model) is shown with the color bar, and the standard deviations are shown with the pins. For the sake of visual clarity, the data at 175/μm2 have been removed, due to their abnormally high standard deviations. A minimum in adhesion occurs (indicated by red arrow) at a combination of particle density and load that lead a minimum number of particles under the sphere that still prevent contact with the flat silicon substrate below.
Figure 9. Forcedistance curve taken at the rough end (a) and smooth end (b) of the gradient with the stiff cantilever (load applied = 1.4 μN). During retraction of the colloid probe, snapping off was observed at the smooth end, while at rough end, multiple detachment with hysteresis was found.
material or plastic deformation of the contacting materials. The effect of the surface roughness could be the cause of the adhesion hysteresis we observed at high loads at the rough end of the gradient surface and was recently studied by Wei et al.32 The minimum adhesion force was obtained for loads below 400 nN and for a particle density of around 67/μm2 (which is shown by the red arrow in Figure 8), where the combination of
particle density and load leads to a minimum number of particles in contact under the sphere, while still preventing contact of the sphere with the flat silicon substrate. At the highest applied loads, below the particle density of 320/μm2 a steady increase in the measured pull-off forces was observed. The increase in the applied loads causes the PE sphere to touch the substrate beneath (at load 1.3 μN, the calculated 9976
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Table 1. Input Values for the Katainen Model (eq 4), which Assumes a Large Blunt Sphere in Contact with Hemispherical Asperities on the Surface Hamaker constant AH (calculated from eq 5)
7.552 1020 J ε1 = 2.3, ε2 = 11.7, ε3 = 1.8 n1 = 1.51, n2 = 3.02, n3 = 1.313, γe = 3 10 15 Hz
Hertzian contact area A A = ((3/4)(PR)/(E*))1/3
load, P varied from 135 nN
P normal applied load, R
for the maximum load,
to 1.61 μN. effective radius of curvature R = (R1R2)/(R1 + R2) (1)/(E*) = (1 ν21)/(E1)
P = 1.61 μN, A = 0.431 1012 m2 R = 10 μm, E1 = 0.2 GPa,
+ (1 ν22)/(E2) effective modulus
E2 = 130 GPa
at the contact, where E1, E2 and ν1, ν2 are the Young’s moduli and
ν1 = 0.4, ν2 = 0.28
Poisson’s ratios of the contacting materials. equilibrium separation, H0
0.3 nm
maximum asperity height, Ymax
6 nm
number of particles in contact is around 70). After this particle density (from 175/μm2 to 0/μm2), in spite of decreased number of particles in contact the sphere begins to touch the substrate leading to large pull-off force at higher loads. The total adhesion force between the sphere and the substrate is assumed to include the contact between the sphere and the nanoparticles, as well as the contact between the sphere and the silica substrate. The latter dominates the total adhesion force, and hence, a significant increase in pull-off force was observed with load. The combined effects of sphereparticle and spheresubstrate interactions increase the standard deviation of the measured values (represented by the pins in Figure 8). When the applied load was sufficiently high to compress all the submicrometer asperities of the PE colloidal sphere,27 the measured pull-off force values at the smooth end (at particle density 0/μm2) of the gradient were found to be 1950 nN which is in close agreement to those calculated from the van der Waals force via Lifshitz theory. This was the highest pull-off force with low standard deviation of the measured forces. At the smooth end, again the force curves show a single snap-off of the cantilever from the surface during the retraction (Figure 9b). It would be of interest to know whether the indentation of the nanoparticles into the polyethylene sphere exceeds the plastic limit. Unfortunately, the use of Hertzian theory to determine details of the contact is not appropriate, since the nanostructure of the polyethylene is on a similar scale to that of the nanoparticles, and Hertzian analysis makes the assumption of a continuum. Empirically, however, the PE spheres were used for up to several thousand pull-off measurements without any noticeable change in pull-off force in any given area of the gradient. Whether or not a slight degree of plastic deformation might be occurring on the local level, it does not seem to interfere with the conclusions of the study. 4.3. Comparing Pull-off Force Measurement with Existing Models (Hamaker Approximation). In this section, the measured
Figure 10. Dotted lines with marker shows the experimental pull-off force obtained from Figure 8, in the region where direct contact to the silicon substrate is not occurring, and the solid lines show the fit by the model of Katainen et al.
pull-off forces across the gradient sample were compared with the models discussed in the Theory section. Modified Rumpf and Rabinovich Model. The modified Rumpf model and the extended model by Rabinovich et al. were conceived for stochastically rough surfaces and consider the rms roughness of the substrate in order to estimate the van der Waals forces. The model did not fit our experimental results and led to a substantial underestimation of the experimental pull-off forces. In no case does either model predict a pull-off force in excess of 10 nN, even at the rough end of the sample. This is because in both models the deformation of the sphere is neglected. As the polyethylene sphere deforms considerably upon contact, this would underestimate the results obtained. Katainen Model. The model proposed by Katainen et al.8 assumes a blunt sphere to be in contact with the hemispherical asperities on the surface. Considering the measurements for the four highest-density positions along the gradient (at particle density 416/μm2, 396/μm2, 360/μm2, 320/μm2), the pull-off force is a combination of two forces (eq 4), the first part being due to contact between sphere and the particles and the second part resulting from the noncontact interaction between the sphere and the substrate. The Hamaker constant AH is calculated from the macroscopic Lifshitz equation which was discussed in section 2. Table 1 shows the input values for the Katainen model. Figure 10 shows the measured and the fitted (Katainen model) pull-off forces plotted against the calculated number of particles that comes into contact at a given load for particle densities 416/μm2 to 320/μm2. This model is in close agreement with our results. The model makes a better estimate of contact area by including deformation. In addition, the particle density, rather than the rms roughness, is used in the calculation, which is more appropriate in our case.
5. CONCLUSION In our study, a nanoparticle-based morphology gradient was successfully used for studying the effect of nanoscale surface roughness on adhesion force, in the absence of all forces except van der Waals interactions. The measured pull-off force by AFM depends on the stiffness of the cantilever, to which a polyethylene colloidal sphere is attached. The adhesion force is due to a 9977
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Langmuir combination of asperityasperity contact between the probe and a noncontact interaction with the substrate. The roughness on the substrate decreases the pull-off force, compared to the flat substrate, and increases the standard deviation value. Our results show that a minimum adhesion force can be achieved at an optimum particle density at which the separation of the particles is comparable with the size of the total contact region. The normal load affects the adhesion force slightly at the rough end of the gradient. The increase in normal load affects the adhesion force more when the particle density is low enough for the colloidal probe to contact the substrate below. We compared our experimental results to existing models, which are based on Hamaker constant calculations. The model by Katainen et al. provides a reasonable fit to the data. The measured force distance curves at the rough end of the gradient are direct evidence of multiasperity detachment of the probe during pull-off force measurements.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT The authors gratefully acknowledge partial funding by the ETH Research Commission (CHIRP1 Program). Effort also partially sponsored by the Air Force Office of Scientific Research, Air Force Material Command, USAF, under grant number FA8655-09-C-4005. The U.S. Government is authorized to reproduce and distribute reprints for Government purpose notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the U.S. Government. The authors acknowledge the Electron Microscopy Center of the ETH Zurich (EMEZ) and Dr. Kunze Karsten for taking the SEM images for the gradient samples, and would also like to thank Prof. Theo Tervoort, Prof. Mark Robbins, Dr. Kathy Wahl, and Prof. Robert Carpick for useful discussions.
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(12) Schaefer, D. M.; Carpenter, M.; Gady, B.; Reifenberger, R.; Demejo, L. P.; Rimai, D. S. J. Adhes. Sci. Technol. 1995, 9, 1049–1062. (13) Tormoen, G. W.; Drelich, J.; Nalaskowski, J. J. Adhes. Sci. Technol. 2005, 19, 215–234. (14) Yang, S.; Zhang, H.; Hsu, S. M. Langmuir 2007, 23, 1195–1202. (15) Liu, D. L.; Martin, J.; Burnham, N. A. Appl. Phys. Lett. 2007, 91, 043107. (16) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Nature 1991, 353, 239–241. (17) Johnson, K. L.; Kendall, K.; Roberts, A. D. Proc. R. Soc. London, Ser. A 1971, 324, 301–313. (18) Derjaguin, B. V.; Muller, V. M.; Toporov, Y. P. J. Colloid Interface Sci. 1975, 53, 314–326. (19) Rumpf, H. Particle Technology; Chapman & Hall: London/ New York, 1990. (20) Rabinovich, Y. I.; Adler, J. J.; Ata, A.; Singh, R. K; Moudgil, B. M. I. J. Colloid Interface Sci. 2000, 232, 10–16. (21) Israelachvili, J. Intermolecular and Surface Forces; Academic Press: London, 1992; Chapter 11. (22) Lifshitz, E. M. Sov. Phys. Jetp: USSR 1956, 2, 73–83. (23) Feldman, K.; Tervoort, T.; Smith, P.; Spencer, N. D. Langmuir 1998, 14, 372378 (1998). (24) Huwiler, C.; Kunzler, T. P.; Textor, M.; Voros, J.; Spencer, N. D. Langmuir 2007, 23, 5929–5935. (25) Crist, B.; Fisher, C. J.; Howard, P. R. Macromolecules 1989, 22, 1709–1718. (26) Butt, H. J.; Jaschke, M. Nanotechnology 1995, 6, 1–7. (27) Tormoen, G. W.; Drelich, J. J. Adhes. Sci. Technol. 2005, 19, 181–198. (28) Briscoe, W. H.; Horn, R. G. Langmuir 2002, 18, 3945–3956. (29) Clasohm, L. Y.; Vakarelski, I. U.; Dagastine, R. R.; Chan, D. Y. C.; Stevens, G. W.; Grieser, F. Langmuir 2007, 23, 9335–9340. (30) Hertz, H., J. Reine Angew. Math. 1881, 92, 156. (31) Chen, Y. L.; Helm, C. A.; Israelachvili, J. N. J. Phys. Chem. 1991, 95, 10736–10747. (32) Wei, Z.; He, M. F.; Zhao, Y. P. J. Adhes. Sci. Technol. 2010, 24, 1045–1054.
’ REFERENCES (1) Burton, Z.; Bhushan, B. Nano Lett. 2005, 5, 1607–1613. (2) Delrio, F. W.; De Boer, M. P.; Knapp, J. A.; Reedy, E. D.; Clews, P. J.; Dunn, M. L. Nat. Mater. 2005, 4, 629–634. (3) Komvopoulos, K. J. Adhes. Sci. Technol. 2003, 17, 477–517. (4) Murphy, M. P.; Kute, C.; Meng€u)c , Y.; Sitti, M. Int. J. Robotics Res. 2010, 30, 118–121. (5) Ando, Y.; Ino, J. Sens. Actuators, A 1996, 57, 83–89. (6) Beach, E. R.; Tormoen, G. W.; Drelich, J.; Han, R. J. Colloid Interface Sci. 2002, 247, 84–99. (7) Esayanur, M. S.; Yeruva, S. B.; Rabinovich, Y. I.; Moudgil, B. M. J. Adhes. Sci. Technol. 2005, 19, 611–626. (8) Katainen, J.; Paajanen, M.; Ahtola, E.; Pore, V.; Lahtinen, J. J. Colloid Interface Sci. 2006, 304, 524–529. (9) Meine, K.; Kloss, K.; Schneider, T.; Spaltmann, D. Surf. Interface Anal. 2004, 36, 694–697. (10) Mendez-Vilas, A.; Gonzalez-Martin, M. L.; Labajos-Broncano, L.; Nuevo, M. J. J. Adhes. Sci. Technol. 2002, 16, 1737–1747. (11) Rabinovich, Y. I.; Adler, J. J.; Ata, A.; Singh, R. K.; Moudgil, B. M. J. Colloid Interface Sci. 2000, 232, 17–24. 9978
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