J. Phys. Chem. C 2010, 114, 15029–15035
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Interaction Stress Measurement Using Atomic Force Microscopy: A Stepwise Discretization Method Meysam Rahmat and Pascal Hubert* Department of Mechanical Engineering, McGill UniVersity, 817 Sherbrooke St. West, Montreal, Quebec, Canada H3A 2K6 ReceiVed: May 31, 2010; ReVised Manuscript ReceiVed: July 21, 2010
Atomic force microscopy (AFM) is one of the most common techniques for interaction measurements. However, there are severe problems in attaining and interpreting the current interaction measurements obtained from AFM experiments. The existing procedures do not provide a clear understanding of the interaction mechanism and use misleading and ineffective evaluating criteria. Furthermore, ineffective experimental procedures neglect to use the full range of the AFM force curves for interaction measurement. To overcome the drawbacks of the currently used methods, the current work proposes a new interaction measurement parameter, called interaction stress. From the interaction stress, all other interaction properties, such as interaction force, interaction energy, and internal stress, can be calculated. In order to obtain the interaction stress from the AFM measurements, the details of a new method, a stepwise discretization method, are explained. Finally, a set of AFM experiments are designed and performed, and the results are presented in terms of interaction stress. The validity of the captured results is examined by using well established Hamaker constants. The good agreement between the results of the current work and the literature demonstrates the ability of the stepwise discretization method in capturing the interaction stress properly. Introduction Nonbonded interactions play a critical role in different fields of science, including chemistry,1 material science,2 biology,3 and nanoscience.4 For instance, structural nanocomposites with nonfunctionalized carbon nanotubes rely entirely on van der Waals (vdW) interactions to transfer loads between the reinforcement and the matrix materials.5,6 Various techniques, such as dynamic mechanical analysis,7 Raman spectroscopy,8 and atomic force microscopy9 (AFM), have been employed to characterize interactions. AFM is the most promising technique due to its high level of precision10 and flexibility in manipulating nanoscale objects.11,12 However, three major drawbacks have been identified with AFM interaction measurements: (1) measuring values without a clear understanding of the interaction mechanism; (2) reporting geometry dependent results, which make the comparison difficult; and (3) limiting the experiments by using ineffective procedures. The following paragraphs explain each of these drawbacks in detail. The interaction forces measured with the AFM pull-out technique are often inaccurate due to the lack of understanding of the interaction mechanism involved.13,14 A classical example is the measurement of the interfacial characteristics (e.g., energy, force, and strength) between carbon nanotubes and polymers. Molecular dynamics5,15-18 simulations of the pull-out test show that covalent bonds between less than 1% of the nanotube carbon atoms and the surrounding polymer can increase the shear strength between the nanotube and the polymer by an order of magnitude.19 On the other hand, experimental measurements of the interfacial strength range from 15 to 376 MPa.13,14,20 These values are sometimes higher than the typical polymer strength * Corresponding author. Address: Macdonald Engineering Building, Room 367, 817 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6. Phone: (514) 398-6303. Fax: (514) 398-7365. E-mail: pascal.hubert@ mcgill.ca.
(i.e., 30-130 MPa),21 while, in all the experimental investigations, no trace of broken polymer was observed on the nanotubes’ surface. Thus, local changes in the polymer properties and the existence of strengthening mechanisms were proposed.13,14,20 The proposed strengthening mechanisms include covalent bonding between the nanotube and the polymer19 and also wrapping of polymer chains around the nanotube.16,22 The absence of effective criteria for the interaction measurements makes the results reported in the literature difficult to compare and interpret. Several groups9,23-26 used chemical force microscopy to measure the interaction between substrates and AFM tips made of various materials27 or coated with different terminal functional groups.28 The adhesion forces29 or the adhesion forces normalized by the AFM tip radius28 are reported. However, the adhesion force measured by the AFM is a resultant of a distant-dependent force gradient to the entire AFM tip. Each infinitesimal section of the AFM tip experiences a force based on its distance from the substrate, and the AFM registers the summation of all these forces as the adhesion force. As a result, the adhesion force depends on the tip and substrate geometry and surface roughness.9 Hence, uncertainties arise when comparing the results of the different groups. Finally, most of the studies in the literature28 do not benefit from the capacity of AFM to measure force and distance continuously during the experiment. The results of pull-out experiments15,17 or adhesion force measurements29 are limited to one single value and do not cover the entire domain of interfacial force or energy versus distance between the tip and the substrate. A simple and practical representation (i.e., through mathematical formulas or graphs) of the interaction parameters (e.g., interaction energy and strength) for the entire range of tip-substrate distance is of great interest. It leads to a better understanding of the complicated mechanism at the nanoscale and the prediction of the system’s behavior with more accuracy. For example, Girifalco et al.30 employed the Lennard-Jones potential between carbon atoms
10.1021/jp104993f 2010 American Chemical Society Published on Web 08/18/2010
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and calculated the equilibrium spacing and the cohesive energy for different carbon nanotubes, buckyballs, and ropes with different geometric parameters, such as radius. This work was limited to carbon atoms and the system behavior at the equilibrium state. However, the results of this work were used by Strus et al.31,32 to clearly understand the mechanism and predict the physics of nanoscale peel tests with high accuracy. In the current study, a simple and practical method is presented to use AFM for interaction measurements. First, a force curve, covering the entire range of tip-substrate distance, is presented. Then, a new interaction parameter, the interaction stress, is defined and used in a novel method for the interaction measurement based on the stepwise discretization of the force curve data. Finally, the results of a set of experiments are presented to demonstrate the strength and the flexibility of the proposed method. The accuracy of the presented results was examined by employing the well established Hamaker constant33 and comparing it to the values in the literature. Theory The atomic force microscope can measure the force applied to the AFM tip while the AFM piezo holds the cantilever at a given distance from the substrate. The force versus piezo position graph is usually referred to as the force curve, Figure 1. For tip-substrate distances that are larger than 10 nm, the tip senses no force (between points A and B). During the approach phase, the AFM piezo brings the tip down until the tip starts to sense an interaction force (point B). The tip-substrate distance at this point is called the cutoff distance. After this point, when the gradient of the attractive force exceeds the cantilever spring constant, the AFM cantilever suddenly jumps to the substrate (point C). The AFM piezo brings the cantilever further down until the tip starts to push against the substrate (between C and D). The stiffness of both the tip and substrate with the cantilever spring constant determines the response of the system. During the retraction phase, the piezo brings the cantilever up and the substrate is unloaded (between points D and E). As a result of the sticktion force between the tip and the substrate, the tip stays in contact with the substrate (point E) while the piezo brings the cantilever’s root up. Finally, when the spring force of the cantilever goes beyond the sticktion force, the cantilever is released from the substrate, and by bringing the tip further up (to point F), the AFM no longer senses an interaction force. During the approach phase, the AFM is in a noncontact interaction mode from point B to C, shown in Figure 1 (between the cutoff point and the contact point). The shape of the force curve during this phase depends on the tip geometry, cantilever spring constant, and attractive force gradient. There are two regimes in the force curve between B and C (Figure 1b). In the first regime (the blue section in Figure 1b), the piezo brings the cantilever down while the cantilever experiences small changes in the sensed force. As a consequence, the changes in the cantilever deflection are small. In this regime, the tip-substrate distance is changed dominantly when the piezo z-position varies. However, in the second regime (the red section in Figure 1b) when the cantilever suddenly jumps to the substrate, the piezo z-position does not change significantly. In the second regime, the tip-substrate distance is mainly influenced by the cantilever deflection. Thus, at any point in the noncontact interaction phase, the tip-substrate distance (D) is affected by changes in the piezo z-position and the cantilever deflection as
D ) Dcutoff - (∆Zpiezo + ∆Zdeflect)
(1)
Figure 1. (a) A typical AFM force curve with schematics of AFM probe and substrate at every step. The small gauges on the schematics indicate the piezo z-position with the positive direction downward. (b) Two regimes in a noncontact interaction: regime 1, piezo z-position dominant; regime 2, cantilever deflection dominant.
where Dcutoff is the cutoff distance above which no interaction force is sensed, ∆zpiezo is the change in the tip-substrate distance as a result of the piezo movement, and ∆zdeflect is the tip-substrate distance change due to the cantilever deflection. The tip-substrate interaction force (F) can be extracted from the AFM measured force obtained from the product of the cantilever deflection and spring constant. However, when the cantilever accelerates in a fluid environment (e.g., water), the inertia and hydrodynamic drag forces should also be considered. Hence,
F ) (meff + mhydro)a + Fdrag + k∆Zdeflect
(2)
where meff is the cantilever effective mass, mhydro is the additional mass due to hydrodynamic effects, a is the tip acceleration, Fdrag is the drag force applied to the cantilever, and k is the cantilever spring constant. For a simple cantilever beam with concentrated mass at its end (mend), the effective mass can be found from34
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3 meff ) mbeam + mend 8
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(3)
where mbeam is the mass of the beam. The beam and the concentrated mass can be calculated by knowing the AFM probe dimensions and the material density. The hydrodynamic additional mass can be obtained from35
madd ) (0.6Ff L1/2b3/2)Vcant
(4)
where Ff is the surrounding fluid density, L and b are the cantilever length and width, respectively, and Vcant is the cantilever volume. The drag force that the cantilever experiences can be approximated by36
1 Fdrag ) CDFf V2A 2
(5)
where CD is the drag coefficient, V is the velocity, and A is the cantilever top-view surface area, obtained by multiplying the cantilever width and length. For a three-dimensional flow perpendicular to a rectangular plate, the drag coefficient is 1.28 (ref 36), and the velocity can be approximated by the average velocity of the root and the tip of the cantilever. According to eqs 1-5, the tip-substrate distance and force can be determined at any time during the force curve measurement. The stepwise discretization method starts with introducing a new parameter called the interaction stress. The interaction stress is the state of stress (i.e., a tensor) at any given point of an object as a result of its vicinity to a secondary object. Therefore, if the secondary object is an infinite plane, all components of the interaction stress, except the normal stress in the direction perpendicular to the plane, are zero. The value of this nonzero stress component can be determined on the basis of the interaction force per unit area that is applied from the infinite plane to a flat cross section of the object at a given distance. Unlike the Lennard-Jones potential, it is not restricted to two particles, and dissimilar to the Hamaker theory, it is not limited to particular geometries. The interaction stress is a function of the substrate and object materials, and varies with the object-substrate distance. Therefore, parallel sections within an arbitrary-shaped object experience different interaction stresses based on their distances from the substrate. Knowing the interaction stress versus distance for an object-substrate system, one can predict the amount of force that is applied from the substrate to any parallel section of the object. Furthermore, the interaction stress data for a pair of materials can provide more information such as interaction energy, internal stress, interaction strength, and adhesion force. However, in order to obtain the interaction stress for a pair of materials, a stepwise discretization method, illustrated in Figure 2a, should be applied to an AFM force curve. For distances larger than the cutoff distance (step 0), the substrate applies negligible forces to the tip, leading to zero interaction stress. After a tip displacement ∆D1 (step 1), a fraction of the tip is within the cutoff distance and an interaction force F1 is measured. The AFM cross section area A11, located at an average distance D1, is used to compute the interaction stress σ1 as σ1 ) F1/A11. As the tip moves down by a displacement ∆D2 (step 2), a larger portion of the tip is exposed to the interaction force. Figure 2b shows a three-dimensional schematic of this step. This portion
can be divided into two sections: section 1 has an area A12 at an average distance D1, and section 2 has an area A22 at an average distance D2. The interaction force F2 is the resultant of the forces applied to both sections:
F2 ) σ1A12 + σ2A22
(6)
where σ1 and σ2 are the interaction stresses at the distance D1 and D2 from the substrate, respectively. The stress level at D1 was calculated in step 1; hence, the interaction stress at the distance D2 can be obtained in this step (step 2). Thus, the aforementioned procedure generated two points of the stress versus distance curve shown in Figure 2a. Similarly, for step 3, the interaction force can be expressed as
F3 ) σ1A13 + σ2A23 + σ3A33
(7)
and the stress σ3 at the average distance D3 from the substrate can be calculated. A general expression for the nth step can be derived, and the interaction stress σn applied to a surface at a distance of Dn is n-1
Fn σn )
∑ σiAin i)1
(8)
Ann
The cross section area is a function of the tip geometry. For spherical AFM tips, while the maximum distance of the tip from the cutoff plate is less than the tip radius (i.e., all the cross sections are within the spherical part), the cross section area can be expressed as
{[(
Amn ) π r cos sin-1
r-
(
1 ∆Dm + 2 r
n
∑
i)m+1
))]}
2
∆Di
for m e n (9)
where r is the AFM tip radius, index n defines the step number, and index m specifies the distance of the cross section from the substrate. For instance, A46 represents the cross section area located at distance D4 in step 6. It should be mentioned that, in the above formula, the summation is only valid when the lower index is smaller or equal to the higher index. The stepwise discretization method determines the interaction stress as a function of tip-substrate distance, while the AFM tip moves toward the substrate. However, since the tip-substrate distance is varied in discrete steps, the interaction stress is a discontinuous function. A higher resolution of data acquisition (i.e., smaller displacements at each step) leads to more data points in the interaction stress versus separation distance graph. The interaction stress only depends on the pair of materials and is independent of the geometry. Therefore, once it is calculated for a pair of materials in an environment (e.g., water or air), it can be employed as raw data to obtain various interaction parameters. For instance, the interaction energy is the area under the interaction stress versus separation distance graph. Furthermore, the internal stress in an object as a result of interaction with a flat surface can be determined by subtracting the interaction stresses at various sections parallel to the surface. The interaction force between an object and a
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Figure 2. (a) The stepwise discretization method: two-dimensional schematic of different steps, along with the stress level at different distances. (b) The stepwise discretization method: three-dimensional schematic of step 2 (as an example) with defined cross section areas, tip displacements, and average distances.
Figure 3. (a) Three-dimensional AFM image of the silicon substrate obtained by DNP-10 probes. (b) Surface topology of the silicon substrate along a random line.
flat surface can be calculated by dividing the objects into slices parallel to the surface, and adding up the interaction force applied to each of these sections. The internal stress or interaction force between two objects with arbitrary geometries can also be obtained by repeating the above-mentioned calculations for various sections of the second object, and adding up the results. Experimental Section In order to validate the proposed method, a set of AFM experiments was performed. A flat substrate and a spherical AFM tip were selected, in order to use the Hamaker constant for validation. A Veeco NanoScope V Atomic Force Microscope was used to perform the experiments in distilled water in order to eliminate the effect of capillary forces due to the humidity level in the air. A silicon wafer was selected as the substrate to provide atomic level flatness and eliminate the effect of substrate topology on the results.9,28,37 It was shown that an amorphous layer of native oxide grows on the surface of the silicon wafer,38 and the thickness of this layer varies between 2 and 10 Å, depending on the environment and the exposure time.39 Figure 3 shows an AFM image of the substrate surface, along with the surface topography on a random line. The surface fluctua-
tions are below 1 Å on a 400 nm line, which guaranteed a flat and smooth surface at the atomic level. The AFM probe selection has a direct effect on the sensitivity of the force measurements and the quality of the AFM images. Three types of cantilevers were tested to investigate the effect of cantilever selection on the quality and precision of the force curves: The small and large cantilevers on the Veeco DNP-10 probe and the Veeco RTESP probe. The RTESP has a smaller tip radius, while the DNP-10 cantilevers are more compliant. According to the manufacturer, the RTESP probes are made of 1-10 Ω-cm phosphorus (n) doped silicon. They have a nominal tip radius of 8 nm and a cantilever spring constant in the range 20-80 N/m. The DNP-10 probes are made of silicon nitride and have four cantilevers with a nominal tip radius of 20 nm. The spring constant is in the range 0.06-0.12 N/m for the longer cantilevers and 0.32-0.58 N/m for the shorter ones. During the preliminary tests, the spring constants for the RTESP cantilevers were calculated,40 but the obtained force curves demonstrated that these cantilevers were too stiff and could not sense the range of small forces between the tip and the silicon wafer substrate properly. On the other hand, the long DNP-10 cantilevers had a small spring constant41 and jumped to the surface at low interaction forces. Furthermore, during the retrace, they stuck to the surface for a larger upward deflection (because of their lower spring constant) and therefore called for a larger range of piezo z-position. A larger range of piezo z-position reduced the data resolution (fixed number of data points over a larger range). The data resolution defines the size of infinitesimal displacements at each step and determines the number of data points in the interaction stress versus separation distance graph. However, the short DNP-10 cantilevers provided a trade-off between the level of precision and data resolution. Figure 4 shows scanning electron microscopy (SEM) images of the DNP10 probes. According to the manufacturer, the nominal radius of these tips varies from a nominal value of 20 nm to a maximum value of 60 nm. However, similar to most interaction measurement techniques,24 the stepwise discretization method requires the tip radius precisely. Therefore, high magnification (110 kx) images were captured and the radius was estimated as 30 nm. Among various techniques of spring constant measurement,40-42 the thermal tuning technique41 was used and a value of 0.23 N/m was measured. The AFM force curve measurements were performed at room temperature. The cantilever natural frequency was measured as 48.9030 kHz, and the quality factor was obtained to be 68 in air. The hard surface of the silicon wafer was used to measure the deflection sensitivity of the cantilever as 41.64 nm/V. The force curves were obtained under distilled water, and a ramp frequency of 1 Hz was selected. Lower ramp frequencies may lead to cantilever drift, and higher frequencies provide lower data resolution. A ramp size of 30 nm was chosen in order to provide high data resolution and prevent the tip damage due to
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Figure 4. Scanning electron microscopy (SEM) images of the Veeco DNP-10 probe. The scale bar is (a) 10 µm, (b) 2 µm, and (c) 100 nm.
Figure 5. Raw force curve obtained from the AFM with DNP-10 probes and silicon wafer substrate under water. The letters correspond to the typical force curve shown in Figure 1.
Figure 6. Statistical distribution of the measured sticktion force for 500 force curves for the Si3N4/H2O/SiO2 system.
high contact forces in the contact regime.43 Therefore, the tip had a forward and reverse velocity of 60 nm/s, which according to Meurk et al.24 should lead to negligible hydrodynamic effects. In order to simulate the realistic geometry of the AFM tip, it was assumed that the spherical tip was flattened 2 nm from the bottom. Results and Discussion Figure 5 illustrates a sample of the force curves obtained with the above settings. The blue curve indicates the approach section, while the magenta curve illustrates the retract section of the force ramp. The approach section showed two sudden increases in the force signal. The first event at a piezo z-position of 16 nm occurred before the tip entered a semicontact regime. The tip stayed in this regime until the second event at a piezo z-position of 24 nm where the tip came into contact with the substrate. The slope after this point (point C) demonstrated the cantilever’s spring constant. However, since a small ramp size was selected, the ramp stopped before the tip-substrate force went to positive values, and hence the tip damage was prevented. During the retrace, the tip stayed in contact with the substrate for a longer time (until point E). The amount of force at point E corresponds to the sticktion force. Two sudden changes in the force signals were observed at a piezo z-position of 1 and 2.5 nm before it eventually went back to zero at point F. The consistency of the results and the repeatability of the force curve measurements were evaluated by performing 500 force curves within a 400 nm × 400 nm area. These force curves were carried out on points that were separated in rows and columns with a spacing of 12.9 nm. Figure 6 shows the distribution of the measured sticktion forces (the force at point E in Figure 5). The measured values have an average of 4.243 nN, with a standard deviation of 0.260 nN and a standard deviation of mean value of 0.012 nN. On the basis of these
Figure 7. Interaction stress as a function of separation distance for the Si3N4/H2O/SiO2 system for four tests.
parameters, a Gaussian distribution function was also fit to the data. According to Figure 6, the results showed a fairly sharp peak indicating a high level of consistency and repeatability. The consistency and repeatability in the results demonstrates that a few repetitions of the experiment can represent the results properly. The raw noncontact portion of the force curve data for the DNP-10 tip and silicon wafer substrate under water were processed using the stepwise method presented previously. Figure 7 shows the interaction stress versus separation distance for four different experiments. The negative values demonstrate an attractive stress. According to this figure, the interaction stress is negligible when the objects are farther than 3 nm from each other. However, there is a sudden decrease in the interaction stress followed by a minimum at a separation distance of 1 nm. The interaction stress then increases until the AFM tip enters the semicontact regime, where analysis stops. The minimum point in Figure 7 indicates the maximum value of the attractive stress (attractive stress is negative). The combination of Si3N4/
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H2O/SiO2 had a highest attractive stress of 31.04 kPa, with a standard deviation of 0.91 kPa, and a standard deviation of mean of 0.53 kPa. This is a fairly low value compared to the strength of the involved materials (hundreds of MPa). However, under water, the velocity of the electromagnetic waves is lower compared to the vacuum and the dipole-dipole interaction, and consequently the van der Waals forces are smaller.9 According to Goodman and Garcia,23 there is a great increase (by factors of up to 10 and more) in the van der Waals forces, when the medium is air or vacuum, as opposed to water or other liquids. Therefore, a corresponding increase in the magnitude of the interaction stress is expected when considering the interaction under vacuum or air. In order to validate the obtained results, the Hamaker constant33 was employed. During the short separation interaction, where the tip radius r is much smaller than the separation distance D, the van der Waals forces between a sphere and a flat surface can be estimated by Derjaguin fitting as
FvdW(D) ) -
Aabcr 6D2
(10)
where Aabc is the Hamaker constant for the combination of the material pair a and c and the environment b. The Hamaker constant is the vdW force scaling constant and is calculated by various techniques.25 The Hamaker constant can be calculated from eq 10, provided the interaction force, tip radius, and separation distance are known. Therefore, for each data point shown in Figure 7 (any pair of force/distance or stress/distance), a Hamaker constant was calculated. They were in the range (0.4-13.9) × 10-20 J, with a mean value of 5.4 × 10-20 J. The standard deviation of the values was 4.3 × 10-20 J, and the standard deviation of mean of the data was obtained to be 0.9 × 10-20 J. The range of the determined Hamaker constants in the literature also shows a wide range of variations.25 Jaiswal et al.9 calculated the Hamaker constant for Si3N4/H2O/SiO2 using the combination relation and obtained a value of 0.4 × 10-20 J, while in the literature a range of (1.0-2.8) × 10-20 J was reported. However, their AFM experiments resulted in a Hamaker constant of 6 × 10-20 J. Jaiswal et al.9 calculated their Hamaker constant before the tip jumped to the substrate, and mentioned that the behavior of the system during the jump was not well described by equilibrium. In this work, the Hamaker constants were calculated throughout the entire range of noncontact force curve. The average value of 5.4 × 10-20 J, calculated in this work, agrees well with the value 6 × 10-20 J, obtained by Jaiswal et al.9 Conclusion In this work, the existing drawbacks of using AFM for interaction measurements in the literature were recognized as (1) lack of a clear understanding of the interaction mechanism, (2) reporting noncomparable results, and (3) using ineffective procedures. Therefore, a new interaction measurement parameter, called interaction stress, was introduced to overcome these shortcomings. The interaction stress is independent of geometry and only depends on the material pair and the environment. It can be used to calculate several interaction parameters, such as interaction force, interaction energy, and internal stress in the interactive bodies. In order to find the interaction stress for a combination of materials, a stepwise discretization method was developed. This method is a novel technique to extract interaction data from AFM force curves. The concept was demonstrated
by performing a set of AFM experiments for a silicon nitride AFM tip and a silicon wafer substrate under water. The interaction stress as a function of separation distance was presented for this system, and the validity of the experiment was examined by using the Hamaker constant. The results showed good agreement with the literature and proved the validity of the stepwise discretization method in capturing the correct interaction parameters. Acknowledgment. This work was funded by McGill University through McGill Engineering Doctoral Award and the Chemical, Biological, Radiological and Nuclear (CBRN) Research and Technology Initiative (CRTI), project CRTI07121RD. Furthermore, the authors thank Dr. Hossein Ghiasi and Erin Quinlan for their assistance. References and Notes (1) Chandler, D. Nature 2005, 437, 640. (2) Atwood, J. L.; Barbour, L. J.; Jerga, A.; Schottel, B. L. Science 2002, 298, 1000–1002. (3) Pennisi, E. Science 2002, 296, 250–251. (4) Min, Y.; Akbulut, M.; Kristiansen, K.; Golan, Y.; Israelachvili, J. Nat. Mater. 2008, 7, 527. (5) in het Panhuis, M.; Maiti, A.; Dalton, A. B.; van den Noort, A.; Coleman, J. N.; McCarthy, B.; Blau, W. J. J. Phys. Chem. B 2003, 107, 478. (6) Gates, T. S.; Odegard, G. M.; Frankland, S. J. V.; Clancy, T. C. Compos. Sci. Technol. 2005, 65, 2416. (7) Lopez-Manchado, M. A.; Biagiotti, J.; Valentini, L.; Kenny, J. M. J. Appl. Polym. Sci. 2004, 92, 3394. (8) Bassil, A.; Puech, P.; Landa, G.; Bacsa, W.; Barrau, S.; Demont, P.; Lacabanne, C.; Perez, E.; Bacsa, R.; Flahaut, E.; Peigney, A.; Laurent, C. J. Appl. Phys. 2005, 97, 34303. (9) Jaiswal, R. P.; Kumar, G.; Kilroy, C. M.; Beaudoin, S. P. Langmuir 2009, 25, 10612. (10) Friddle, R. W.; Lemieux, M. C.; Cicero, G.; Artyukhin, A. B.; Tsukruk, V. V.; Grossman, J. C.; Galli, G.; Noy, A. Nat. Nanotechnol. 2007, 2, 692. (11) Fukuda, T.; Arai, F.; Dong, L. Proc. IEEE 2003, 91, 1803. (12) Barber, A. H.; Cohen, S. R.; Wagner, H. D. Nano Lett. 2004, 4, 1439. (13) Barber, A. H.; Cohen, S. R.; Kenig, S.; Wagner, H. D. Compos. Sci. Technol. 2004, 64, 2283. (14) Barber, A. H.; Cohen, S. R.; Wagner, H. D. Appl. Phys. Lett. 2003, 82, 4140. (15) Gou, J.; Liang, Z.; Zhang, C.; Wang, B. Composites, Part B 2005, 36, 524. (16) Zhiyong, L.; Gou, J.; Chuck, Z.; Wang, B.; Kramer, L. Mater. Sci. Eng., A 2004, 365, 228. (17) Frankland, S. J. V.; Harik, V. M. Surf. Sci. 2003, 525, 103–108. (18) Werder, T.; Walther, J. H.; Jaffe, R. L.; Halicioglu, T.; Koumoutsakos, P. J. Phys. Chem. B 2003, 107, 1345. (19) Frankland, S. J. V.; Caglar, A.; Brenner, D. W.; Griebel, M. J. Phys. Chem. B 2002, 106, 3046. (20) Cooper, C. A.; Cohen, S. R.; Barber, A. H.; Wagner, H. D. Appl. Phys. Lett. 2002, 81, 3873. (21) Mallick, P. K. Fiber-reinforced composites: materials, manufacturing, and design, 2nd ed.; Marcel Dekker, Inc.: New York, 1993. (22) Nish, A.; Hwang, J.-Y.; Doig, J.; Nicholas, R. J. Nat. Nanotechnol. 2007, 2, 640. (23) Goodman, F. O.; Garcia, N. Phys. ReV. B: Condens. Matter Mater. Phys. 1991, 43, 4728. (24) Meurk, A.; Luckham, P. F.; Bergstrom, L. Langmuir 1997, 13, 3896. (25) Eichenlaub, S.; Chan, C.; Beaudoin, S. P. J. Colloid Interface Sci. 2002, 248, 389. (26) Hutter, J. L.; Bechhoefer, J. J. Vac. Sci. Technol. B 1994, 12, 2251. (27) Biggs, S.; Mulvaney, P. J. Chem. Phys. 1994, 100, 8501. (28) Poggi, M. A.; Bottomley, L. A.; Lillehei, P. T. Nano Lett. 2004, 4, 61. (29) Xiaojun, L.; Wei, C.; Qiwen, Z.; Liming, D.; Sowards, L.; Pender, M.; Naik, R. R. J. Phys. Chem. B 2006, 110, 12621. (30) Girifalco, L. A.; Hodak, M.; Lee, R. S. Phys. ReV. B: Condens. Matter Mater. Phys. 2000, 62, 13104. (31) Strus, M. C.; Cano, C. I.; Byron Pipes, R.; Nguyen, C. V.; Raman, A. Compos. Sci. Technol. 2009, 69, 1580. (32) Strus, M. C.; Zalamea, L.; Raman, A.; Pipes, R. B.; Nguyen, C. V.; Stach, E. A. Nano Lett. 2008, 8, 544. (33) Hamaker, H. C. Physica 1937, 4, 1058.
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