Quantitative Characterization of Nanoadhesion by Dynamic Force

Dec 3, 2008 - Adhesion force-versus-loading rate curves could be fitted with two logarithmic ..... equation (the blue curve in Figure 6) and with the ...
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Langmuir 2009, 25, 256-261

Quantitative Characterization of Nanoadhesion by Dynamic Force Spectroscopy Arkadiusz Ptak,*,† Michael Kappl,‡ Susana Moreno-Flores,§ Hubert Gojzewski,†,‡ and Hans-Ju¨rgen Butt‡ Institute of Physics, Poznan UniVersity of Technology, Nieszawska 13A, PL-60965 Poznan, Poland, Max-Planck-Institute for Polymer Research, Ackermannweg 10, D-55128 Mainz, Germany, and CIC Biomagune, Paseo Miramon 182, 20009 San Sebastian, Spain ReceiVed September 2, 2008. ReVised Manuscript ReceiVed October 14, 2008 We present a method for the characterization of adhesive bonds formed in nanocontacts. Using a modified atomic force microscope, the nanoadhesion between a silicon nitride tip and a self-assembled monolayer of 1-nonanethiol on gold(111) was measured at different loading rates. Adhesion force-versus-loading rate curves could be fitted with two logarithmic terms, indicating a two step (two energy barrier) process. The application of the Bell-Evans model and classical contact mechanics allows the extraction of quantitative information about the effective adhesion potential and characterization of the different components contributing to nanoadhesion.

Introduction Adhesion of nanometer-sized contacts - nanoadhesion - is of interest in various scientific disciplines. Engineers are interested in practical aspects of nanocontacts for construction of microand nanodevices (e.g., MEMS or NEMS),2 biologists investigate cell and protein adhesion,3 and physicists and chemists are interested in describing molecular mechanisms of adhesion in general.4 Adhesion of macroscopic contacts has been widely studied for decades. As a result, there are a number of adhesive theories contributing to the overall study of adhesion: the mechanical interlock theory, the adsorption theory, the chemisorption theory, the electrostatic theory, the diffusion theory, and the weak boundary layer concept.4 However, one of the most important questions, that is how to recognize adhesive interactions (bonds) contributing to resultant adhesion, is difficult to be solved in general. The field of nanoadhesion bridges macroscopic adhesion and single adhesive bonds. Therefore, the study of nanoadhesion can help to unravel the complexity of the phenomenon of adhesion. The aim of this article is to present a method for the characterization of adhesive bonds formed in nanocontacts. The atomic force microscope (AFM)5 is a tool able to probe various mechanical properties of materials at the nanoscale. To study adhesion, the so-called force spectroscopy mode is used, where the interaction of an AFM tip at the end of a microfabricated cantilever with a sample surface is probed. The sample is mounted on a piezo translator and moved up and down while recording the deflection of the AFM cantilever due to the surface forces, resulting in a so-called force-displacement curve. In general, however, atomic force spectroscopy does not provide complete information about the effective interaction potential.6 If the 1

* To whom correspondence should be addressed. E-mail: arkadiusz.ptak@ put.poznan.pl. Tel.:+48 61 6653233. Fax: +48 61 6653178. † Poznan University of Technology. ‡ Max-Planck-Institute for Polymer Research. § CIC Biomagune.

(1) Persson, B. N. J. Wear 2003, 254, 832. (2) Liu, H.; Bhushan, B. J. Vac. Sci. Technol., A 2003, 21, 1528. (3) Lekka, M.; Laidler, P.; Dulinska, J.; Labedz, M.; Pyka, G. Eur. Biophys. J. 2004, 33, 644. (4) Allen, K. W. Int. J. Adhes. Adhes. 2003, 23, 87. (5) Binning, G.; Quate, C. F.; Gerber, C. Phys. ReV. Lett. 1986, 56, 930. (6) Butt, H.-J.; Cappella, B.; Kappl, M. Surf. Sci. Rep. 2005, 59, 1.

tip-sample interaction force is attractive (usually because of van der Waals interactions) and the gradient of the force is bigger than the spring constant of the cantilever, an instability occurs and the tip jumps into contact with the sample. A similar instability occurs during retracting the cantilever from the sample. At some point of the retraction trajectory, the restoring force of the cantilever becomes larger than the adhesion force and the tip jumps out of contact with the sample. Therefore, an activation barrier (or several barriers) of the adhesion forces is not sampled. For this reason, we applied the so-called dynamic force spectroscopy (DFS), that is the measurement of adhesion force versus the force loading rate (i.e., the change in pulling force per time). It is commonly observed that the adhesion force increases with the loading rate. This has been noticed independently in several disciplines with various explanations.7-11 For instance, in macroscopic adhesion it has been ascribed in most cases to energy dissipation within the bulk of the sample.7,9 The most commonly used models to describe mechanical-adhesive interactions between spherical objects are the JohnsonKendall-Roberts (JKR) model,12 the Derjaguin-Muller-Toporov model,13 and the more general Maugis theory.14 All of these models are based on a balance between potential energy, surface energy, and elastic deformation within the solid bodies. Unfortunately, kinetic effects are ignored in this line of analysis. Therefore, we applied the Bell-Evans15,16 model to the adhesion of nanocontacts. In this case, tip-sample interactions were treated as an effective bond although of complex nature. To get reliable quantitative results regarding the interaction potential of nanoadhesion, a large range of loading rates is desirable. Unfortunately, the maximal frequency of z piezoramp (7) Gent, A.; Schultz, J. J. Adhes. 1972, 3, 281. (8) Rief, M.; Gautel, M.; Osterhelt, F.; Fernandez, J. M.; Gaub, H. E. Science 1997, 276, 1109. (9) Ruths, M.; Granick, S. Langmuir 1998, 14, 1804. (10) Zepeda, S.; Yeh, Y.; Noy, A. Langmuir 2003, 19, 1457. (11) Maki, T.; Kidoaki, S.; Usui, K.; Suzuki, H.; Ito, M.; Ito, F.; Hayashizaki, Y.; Matsuda, T. Langmuir 2007, 23, 2668. (12) Johnson, K. L.; Kendall, K.; Roberts, A. D. Proc. R. Soc. London, Ser. A 1971, 324, 301. (13) Derjaguin, B. V.; Muller, V. M.; Toporov, Y. P. J. Colloid Interface Sci. 1975, 53, 314. (14) Maugis, D. J. Colloid Interface Sci. 1992, 150, 243. (15) Bell, G. I. Science 1978, 200, 618. (16) Evans, E.; Ritchie, K. Biophys. J. 1997, 72, 1541.

10.1021/la8028676 CCC: $40.75  2009 American Chemical Society Published on Web 12/03/2008

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Figure 2. Schematic of the sample.

Figure 1. Conceptual interaction potential of a bond confined by an activation barrier. The external force F tilts the potential and lowers the barrier E0.

cycles for commercial AFMs is in the range of 10-100 Hz, resulting in maximal tip-sample separation rates of 100 µm s-1, which significantly limits the range of loading rates. To overcome this limitation, we used a custom-made modified AFM capable of exerting loading rates of up to three orders of magnitude.17 We studied the adhesion between a silicon nitride tip and a self-assembled monolayer (SAM) of alkanethiols. SAMs in general have several applications in science and industry, for example, as biosensors,18 as substrates for cell culture,19 and in nanoscale fabrication of electronics.20 A layer of alkanethiols on gold is a common example of a SAM. Alkanes with a thiol headgroup stick to the gold surface and form an ordered monolayer. The length of the alkyl chain and the chemical nature of the end group determine the surface properties of the resulting monolayer, such as friction,21 adhesion,22 and reactivity.23 We have chosen alkanethiols with a methyl end group because of its hydrophobicity and weak chemical reactivity in air. However, hydrocarbon groups still exhibit adhesion to various materials including metals and semiconductors.

Theory Gent-Schultz Equation. Gent and Schultz found for rubbery adhesives that the work of detachment per unit area W depended strongly on the rate of the separation of adhering interfaces r, and they described the dependence by the empirical relationship:7

W ) arβ + C

(1)

where β ) 0.42 and C is a constant lying between 0.05-0.5 J m-2. The dependence has been later observed in many polymer systems and fitted as a power law with the separation rate to the power of 0.5-0.6.24,25 The separation rate can be easily recalculated into the force loading rate. For the samples stiffer than the AFM cantilever, which is the usual case, the piezo vertical velocity multiplied by the spring constant of the cantilever gives the force loading rate. (17) Ptak, A.; Kappl, M.; Butt, H.-J. Appl. Phys. Lett. 2006, 88, 263109. (18) Tlili, A.; Abdelghani, A.; Hleli, S.; Maaref, M. A. Sensors 2004, 4, 105. (19) Faucheux, N.; Schweiss, R.; Lu¨tzow, K.; Werner, C.; Groth, T. Biomaterials 2004, 25, 2721. (20) Koo, J.-R.; Pyo, S.-W.; Kim, J.-H.; Lee, H.-K.; Kim, Y. K. Jpn. J. Appl. Phys. 2005, 44, 566. (21) Leggett, G. J.; Brewer, N. J.; Chong, K. S. L. Phys. Chem. Chem. Phys. 2005, 7, 1107. (22) Van der Vegte, E. W.; Hadziioannou, G. Langmuir 1997, 13, 4357. (23) Sullivan, T. P.; Huck, W. T. S. Eur. J. Org. Chem. 2003, 1, 17. (24) Maugis, D.; Barquins, M. J. Phys. D: Appl. Phys. 1978, 11, 1989. (25) Greenwood, J. A.; Johnson, K. L. Philos. Mag. 1981, 43, 697.

Bell-Evans Model. A theoretical explanation of the separation rate dependence for a single chemical bond was introduced by Evans and Ritchie16 based on the transition-state theory. Their model treats the unbinding process as a kinetic problem of the escape from a potential well under the influence of the external loading force. This external load tilts the interaction potential and facilitates thermally activated escape from the bound state (Figure 1). Evans and Ritchie describe the rate of escape from the bound state dP/dt under applied load F(t) as a first-order kinetic process:

dP(t) ) -koff(F)P(t) dt

(2)

where koff(F) is the rate constant of dissociation in the presence of loading force F (kinetic off-rate) and P(t) is the probability of being in the bound state at the time t, that is the probability of bond survival.16 The dissociation rate constant contains a term introduced by Bell15 that describes the reduction of the activation barrier due to applied loading force F(t):

koff )

(

E0 - F(t)xβ 1 exp τD kBT

)

(3)

Here, E0 is the height of the activation energy barrier, xβ is the distance between the bound state and the transition state along the direction of the external pulling force, τD is the characteristic diffusion time of motion in the system, kB is the Boltzmann constant, and T is the temperature. The loading force can be ramped in time:

F(t) ) rFt

(4)

where rF is the force loading rate. The solution of eq 2 for the constant loading rate (a condition that applies for our AFM experiments because the retraction velocity is constant and the cantilever spring constant, which is much lower than the stiffness of the adhesive bonds, determines the effective spring constant of the entire system) gives the following expression for the most probable unbinding force:

( )

Fad ) Fβ ln

rF

Fβk0off

(5)

where Fβ ) kBT/xβ is the so-called thermal fluctuation force.16 Thus, Fad increases linearly with ln(rF) and eq 5 provides a way to extract the value of xβ and the thermal dissociation constant k0off (force-free kinetic off-rate) respectively from the slope and intercept of the Fad versus ln(rF) curve fitted to experimental data. The most probable unbinding (adhesion) force equals a mean adhesion force for symmetrical distributions of adhesion force, which is the case of our measurements, as shown in Figure 2.

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The model has been widely applied by several research groups to study intermolecular interactions between or within biomolecules.11,26,27 DFS measurements performed for such samples usually show a logarithmic dependence of adhesion force on force loading rate, whereas DFS measurements for macroscopic adhesion contacts exhibit rather a power dependence or no dependence at all.7,9

Materials and Methods Self-Assembled Monlayers. SAMs of 1-nonanethiol (CH3(CH2)8SH) (95%, Aldrich) were assembled on Au(111) surfaces by immersion in 1 mM ethanol solutions for 12-24 h.28 Au(111) surfaces were prepared by thermal evaporation onto freshly cleaved mica. The mica was preheated at 650 °C for 3 min under a nitrogen stream to prevent contamination just prior to the gold evaporation. Layers of gold 60-70 nm thick were deposited at a pressure of 1 × 10-6 to 2 × 10-6 mbar. Subsequently, the surfaces were annealed at 650 °C for 1 min under nitrogen gas. This method produces flat gold terraces of around 100-200 nm lateral dimension (part a of Figure 3). The self-assembly was performed immediately after the preparation of the gold substrates. After the incubation, the samples were rinsed with pure ethanol, dried under a nitrogen flow, and directly used for experiments. All experiments were performed in air. We applied scanning tunneling microscope (STM) (Multimode, Veeco Instruments Inc., USA) to check the structure of the alkanethiol SAMs. The STM images confirmed that a (3 × 3) R30° lattice structure dominated our samples (part b of Figure 3). Modified AFM. Two components were added to a commercial AFM (Dimension 3100, Veeco Instruments Inc., USA) to extend the range of accessible loading rates by up to three orders of magnitude: 1) an additional z-piezo actuator driven by high voltage (up to 80 V) and a high-frequency (up to 50 kHz) signal; 2) a data-processing and acquisition system, that is a digital oscilloscope and computer with a data acquisition card (Figure S1 in the Supporting Information).17 With these added two components, the frequency of ramping the piezo up and down is limited by the mechanical properties of available AFM cantilevers. The best suited cantilevers for our measurements were silicon nitride cantilevers MLCT-F (Veeco Instruments Inc.) with a nominal spring constant of 0.5 N m-1 and a high resonance frequency of 120 kHz. With these cantilevers, loading rates up to 107 nN s-1 were achieved, which is over four orders of magnitude higher than in previous DFS experiments.10,11 To control the contact time independently of the loading rate, a trapezoidal signal from a programmable waveform generator was applied to drive the piezo actuator (part a of Figure 4). By proper shaping of the signal, we could keep the contact time constant while varying the speed of the retracting movement. This allowed us to distinguish the influences of contact time and loading rate on the adhesion force. Dynamic Force Spectroscopy. We measured adhesion forces by recording the cantilever deflection in the force curve cycle. The average of the pull-off jumps in the retraction part of the force curves provided the measure of the adhesion force. To measure adhesion force as a function of loading rate, we kept the maximal load constant at 10 nN and we varied the retraction rate. The contact time between approaching and retraction phases was controlled and kept constant at 3 ms, but the total contact (26) Merkel, R.; Nassoy, P.; Leung, A.; Ritchie, K.; Evans, E. Nature 1999, 397, 50. (27) Strunz, T.; Oroszlan, K.; Shafer, R.; Guntherodt, H.-J. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 11277. (28) Moreno-Flores, S.; Shaporenko, A.; Vavilala, Ch.; Butt, H.-J.; Schmittel, M.; Zharnikov, M.; Berger, R. Surf. Sci. 2006, 600, 2847.

Figure 3. STM topography images of the sample: a) gold terraces, b) (3 × 3) R30° lattice structure of an alkanethiol SAM.

time (part b of Figure 4) depended also on the loading rate (the slower the loading rate, the longer the total contact time). However, we did not observe any dependence of adhesion force on contact time in the measured range from 3 ms to 100 s. AFM typically requires knowledge of the cantilever spring constant (k) and optical lever sensitivity (w) to determine the force from the cantilever deflection (d):

nN [ nmV ]k[ nm ]

F[nN] ) d[V]w

(6)

The total experimental error of the measured force is the result of three contributions: the random error of the cantilever deflection during tip-sample separation (∆d), the uncertainty of the optical lever sensitivity (∆w), and the uncertainty of the spring-constant calibration (∆k):

∆F ∆d ∆w ∆k ) + + F d w k

(7)

Spring constants were determined using a reference cantilever method.29 We estimate the absolute uncertainty of the spring-

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Figure 5. SEM image of one of the AFM tips used for the experiments. The tip curvature radius is calculated from the circle. R ) 28 nm.

Figure 4. a) Trapezoidal signal supplied to the additional piezo. b) Deflection of the cantilever (recalculated into force) during approach and retraction of a sample to the AFM tip.

constant calibration (∆k/k) to be 20%, and this is the most significant error component. The optical lever sensitivity was measured at the contact of the tip with a hard substrate, and its absolute uncertainty (∆w/w) was about 5%. In our experiments, thermal cantilever noise was negligible as compared to ∆w/w and ∆k/k. To quantify the fluctuations of pull-off deflection (pulloff force) caused by the variations in the tip-sample contact area, we recorded 10 to 1000 individual pull-off forces for every loading rate in each of seven measurement series. The measurements were taken for three different samples and various spots for each of them. To avoid introducing a systematic error in the data associated with sample and tip wear, we varied the loading rates in a random order. Each adhesion force value is the average of the values obtained from different experiments with similar loading rates. It was not possible to use exactly the same values of loading rates because each of the series was measured with a new cantilever having a slightly different spring constant. Because the precise values of the spring constants were measured after experiments to avoid contamination of AFM tips, these variations could be taken into account only after the experiments. The range of variations for each loading rate was lower than 20%, and thus bars indicating the statistical error would be smaller than the symbols used. Measurement of the Radius of AFM Tips. After each experiment, the shape of the AFM tip was imaged by a scanning electron microscope (SEM) using low voltage (LEO 1530 Gemini, Carl Zeiss NTS, Oberkochen, Germany). From the SEM pictures, the curvature radii of used AFM tips were determined by calculating the radius of the circle that coincides with the tip profile (Figure 5). We estimate the uncertainty of such measurements to be 10%.

Results Adhesion forces increased with increasing loading rate (Figure 6). Experimental results could be fitted with the Gent-Schultz equation (the blue curve in Figure 6) and with the Bell-Evans model (the red curves in Figure 6). The fitting with the Bell-Evans model was performed for two loading rate regimes: rF from 4 nN s-1 and rF from 2 × 105 to 2 × 106 nN s-1. The fitting for more than two loading-rate regimes does not improve significantly the fitting accuracy. The values of the errors of calculated parameters and of χ2 are relatively small (Table 1). On the one hand, the good fitting with

Figure 6. Adhesion force vs loading rate curve for nanoadhesion between a silicon nitride tip and a SAM of alkanethiols. The error bars were calculated as a standard deviation of the mean. The blue curve is the fit with the Gent-Schultz empirical equation and the red curves are the fits with the Bell-Evans model for two fitting regimes: 1) loading rates from 4 nN s-1 and 2) loading rates from 2 × 105 to 2 × 106 nN s-1.

the Gent-Schultz equation suggests that the adhesion at the nanoscale resembles that at the macroscale, although we cannot obtain any quantitative data from this line of analysis (the Gent-Schultz equation is empirical). On the other hand, the good fitting with the Bell-Evans model suggests that this singlebond theoretical model can be applied to nanoadhesion. This implies that the adhesive bonds within a nanocontact are not considered individually but rather lumped into one effective tip-sample interaction potential. The bilogarithmic character of the adhesion force versus loading rate dependence can be interpreted by assuming that the effective interaction potential consists of two activation barriers (Figure 7). We cannot exclude the existence of more than two barriers, but these two are dominant and they govern the nanoadhesion phenomenon. Barrier 1 and barrier 2 determine the detachment at low loading rates and at high loading rates, respectively. We would like to emphasize that barrier 2, which is an inner barrier, could not be detected using a commercial AFM system because of the limited range of accessible loading rates (usually up to 104 nN s-1). Each of the barriers characterizes a different kind of adhesive interactions contributing to the effective tip-sample adhesion. We calculated kinetics and barrier parameters for both contributions (Table 2). The distance between the bound state and the transition state (i.e., the elongation needed to rupture the bond), xβ, was calculated

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Table 1. Fitting Parameters According to the Gent-Schultz Empirical Equation (r, β, γ) and the Bell-Evans Model (a, b)a Gent-Schultz Equation

Bell-Evans Model

Fad ) Rrf + γ

Fad ) a ln(rf) - b

β

rf ∈ (4; 2 × 106) (full measured range) R ) 0.24 ( 0.08 [nN] β ) 0.32 ( 0.03 [nN] γ ) 23.0 ( 0.5 [nN] χ2 ) 0.62 a

rf ∈ (4; 2 × 104) (fitting regime 1) a ) 0.8 ( 0.1 [nN] b ) -20.5 ( 0.5 [nN]

rf ∈ (2 × 105; 2 × 106) (fitting regime 2) a ) 6.8 ( 0.3 [nN] b ) 50 ( 4 [nN]

χ2 ) 0.42

χ2 ) 0.25 -1

-1

Fad, the adhesion force [nN]; rf, the dimensionless loading rate [(nN s )/nN s )].

The detailed answer to both questions can be obtained from the analysis of the cooperativity of individual bonds during rupture. In the case of cooperative bonds configured in parallel, the total energy barrier is a sum of individual barrier energies.30 The bonds act as a macro-single bond. Then, the equation for the adhesion force - loading rate dependence can be written as:

( )

Ftot ) Fβ ln N

Figure 7. Conceptual interaction potential of the effective tip-sample bond with two energy barriers. The values of χβ are in Table 2; ∆E0 ) 31kBT. Table 2. Kinetics and Interaction Potential Parameters for the Tip-Sample Interactions Treated as an Effective Bond Calculated Parameters barrier 1 2

a

xβ [nm]

-3

5.1 × 10 6.0 × 10-4

rF [nN s-1]

k0off [s-1]

0

-12

7.0 × 10 1.6 × 103

-12

8.8 × 10 240

t0off [s] 1.1 × 1011 4.2 × 10-3

a xβ, the distance between the bound state and the transition state; rF0, the thermal loading rate; k0off, the thermal dissociation constant; t0off, the bond lifetime.

from the slope (a ) kBT/xβ) of the dependence Fad ) a ln(rf) b, and the dissociation constant, k0off from the intercept (b ) a ln(a k0off)). The slope of the force-rate dependence for rates lower than 2 × 104 nN s-1 corresponds to xβ ) 0.05 Å, whereas the slope at higher rates corresponds to xβ ) 0.006 Å. A very big difference occurs between the bond (force-free) lifetimes corresponding to the two activation barriers. The lifetime for barrier 1 (the outer) exceeds 3000 years, whereas for barrier 2 (the inner) it equals 4 ms. Also, the energy difference between the barriers is significant and equals 1.25 × 10-19 J, which is 31 times kBT, where T is the room temperature. In this way, we obtained a quantitative characteristic for each of the two contributions (kinds of interactions) to the effective tip-sample adhesion.

Discussion We will try to answer the two following questions: 1) What interactions are responsible for the nanoadhesion? 2) Why do they manifest in such a different way? Analyzing the extremely small values of the distance between the bound state and the transition state (0.05 and 0.006 Å), which are unrealistic for single bonds, we can exclude the situation that the measured adhesion is due to single covalent bonds. Performing static (at one loading rate) force spectroscopy experiments, we could not conclude this. Capillary forces caused by condensing water are negligible because the methyl-terminated alkanethiols form a hydrophobic monolayer (the measured contact angle was 98 ( 2°) and the relative humidity was about 30%. Therefore, we can assume that both interaction types refer rather to weak, noncovalent bonds like van der Waals interactions.

rF

Fβk0off

+

(N - 1)E0 xβ

(8)

where N is the number of bonds. There is a big rate-independent component that determines the force-rate relation and could explain the long durability of the adhesion contribution governed by barrier 1. However, a full cooperativity for the individual bonds can be excluded from our interpretation because the value of 0.05 Å for the distance between the bound state and the transition state is too low for a bond. We will discuss this in more detail later. In the case of an uncooperative breakage of N bonds in parallel, that is when the bonds behave completely independently, the equation for force-rate dependence can be simplified as follows:

( )

Ftot ) NFβ ln

rF

Fβk0off

) NFs

(9)

where Fs is the force distributed per one molecule.30 It can explain the strong force-rate dependence for the rates higher than 2 × 105 nN s-1. To calculate the distance between the bound state and the transition state for an individual bond, it is necessary to know the number of individual bonds in the tip-sample contact. We have attempted to estimate the number of thiol molecules in the contact region with the tip. On the basis of our STM measurements and literature data,31 we could assume the average area per thiol molecule as 0.22 nm2. The contact area has been calculated using the JKR model,32 which applies to soft, adhesive systems with relatively high surface energy. The calculation has been performed in a similar way as it was done by Sinniah32 and Moreno-Flores.28 The contact area under adhesion is given as

ac )

(

3πR2W 2K

)

1⁄ 3

(10)

where R is the radius of tip curvature, W is the work of adhesion (per unit area), and K is the elastic modulus of the monolayercoated substrate.33 The work of adhesion relates to the tip radius and the adhesion force as (29) Torii, A.; Sasaki, M.; Hane, K.; Okuma, S. Meas. Sci. Technol. 1996, 7, 179. (30) Evans, E. Annu. ReV. Biophys. Biomol. Struct. 2001, 30, 105. (31) Schreiber, F. Prog. Surf. Sci. 2000, 65, 151. (32) Sinniah, S. K.; Steel, A. B.; Miller, C. J.; Reutt-Robey, J. E. J. Am. Chem. Soc. 1996, 118, 8925. (33) Israelachvili, J. Intermolecular and Surface Forces, 2nd ed.; Academic Press Limited: San Diego, 1994.

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W)

2Fad 3πR

Langmuir, Vol. 25, No. 1, 2009 261

(11)

The curvature radii of used AFM tips determined from the SEM pictures (Figure 5) were in a range of 25-30 nm. The adhesion force measured at the lowest loading rates equaled 22 nN and the calculated work of adhesion equaled 190 mN m-1, which is in good agreement with the literature data for methylterminated surfaces in contact.28,32 In the case of gold substrate, K ) 64 GPa.32 The contact area was calculated to be around 13 nm2, which results in 60 ( 12 contacting molecules. Although it is a rough estimation, it gives information about an average force applied to an individual molecule during a pull-off experiment. The value of the force approximates a few hundred piconewtons. It is a characteristic value for van der Waals bonds and for hydrogen bonds. If we assume that uncooperative bonds are responsible for the existence of barrier 2, then the elongation needed to rupture all single bonds will equal ∼0.4 Å () 0.006 Å × 60). This is a characteristic value for hydrogen bonds. On the basis of presented calculations, we can conclude that C-H-N hydrogen bonds34 can be the uncooperative weak bonds responsible for barrier 2. The behavior of the bonds responsible for barrier 1 is more complicated. On the one hand they should exhibit some cooperativity to form such a durable effective bond; however, on the other hand we have to assume that they are to some degree uncooperative because otherwise the value of the width of the interaction potential well calculated from the pure cooperative model would be unrealistic, that is much too short (∼0.1 Å). The most probable uncooperative interactions between a methylterminated SAM and the silicon nitride surface of the AFM tip are London dispersion forces. They are localized on a discrete number of methyl groups, and from this point of view they seem to be quite independent of the neighbor bonds (uncooperative), (34) Del Bene, J. E.; Perera, S. A.; Bartlett, R. J.; Yanez, M.; Mo, O.; Elguero, J.; Alkorta, I. J. Phys. Chem. A 2003, 107, 3222.

but still we can expect a strong correlation between the interactions originating from the neighboring surface atoms of the silicon nitride tip (cooperative). Unfortunately, there is no mathematical model describing such a mixed behavior of a group of bonds. Therefore, we cannot obtain quantitative results like the width of the interaction potential well or the dissociation constant for the single van der Waals bonds. On the margin of the discussion, we should state that the influence of the van der Waals forces originating from the underlying gold substrate on the adhesion for such a relatively thick SAM (nine carbon atoms) is negligible.

Summary We demonstrate the advantages of adhesion versus loading rate measurements, which provide more detailed information about the adhesion interactions between two interfaces than the classical (static) AFM force spectroscopy. The extension of the capabilities of experimental techniques toward higher loading rates is of particular significance. Measuring forces only over two to three orders of magnitude at low loading rates as is done in standard AFM experiments can miss important features of complex adhesion interactions. The application of the BellEvans model and classical contact mechanics allows us to characterize quantitatively the components contributing to nanoadhesion by calculating kinetics and interaction potential parameters and make conclusions about the kinds of interactions responsible for the contributions. In some cases, quantitative characterization of single adhesive bonds, for example hydrogen bonds, is also possible. Acknowledgment. A.P. thanks the Alexander von Humboldt Foundation for a return fellowship and the Polish Ministry of Science and Higher Education for research grant No. 2859/B/ H03/2008/34. Supporting Information Available: Schematic and details of the modified AFM (pdf file). This material is available free of charge via the Internet at http://pubs.acs.org. LA8028676