Nanorheological Mapping of Rubbers by Atomic Force Microscopy

Feb 22, 2013 - ... 1 to 248 MPa as the frequency was increased from 1 Hz to 20 kHz. ... Master curve obtained by DMA and nanorheological measurement...
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Nanorheological Mapping of Rubbers by Atomic Force Microscopy Takaaki Igarashi,†,‡,§,* So Fujinami,‡ Toshio Nishi,⊥ Naoki Asao,‡,§ and and Ken Nakajima‡ †

Bridgestone Corporation, Tokyo, Japan WPI Advanced Institute for Materials Research, Tohoku University, Sendai, Japan § Department of Chemistry, Graduate School of Science, Tohoku University, Sendai, Japan ⊥ International Division, Tokyo Institute of Technology, Tokyo, Japan ‡

S Supporting Information *

ABSTRACT: A novel atomic force microscopy (AFM) method is used for nanometer-scale mapping of the frequency dependence of the storage modulus, loss modulus, and loss tangent (tan δ) in rubber specimens. Our method includes a modified AFM instrument, which has an additional piezoelectric actuator placed between the specimen and AFM scanner. The specimen and AFM cantilever are oscillated by this actuator with a frequency between 1 Hz and 20 kHz. On the basis of contact mechanics between the probe and the sample, the viscoelastic properties were determined from the amplitude and phase shift of the cantilever oscillation. The values of the storage and loss moduli using our method are similar to those using bulk dynamic mechanical analysis (DMA) measurements. Moreover, the peak frequency of tan δ corresponds to that of bulk DMA measurements.

1. INTRODUCTION

Kajiyama et al. have reported that the glass transition temperature of a polymeric surface can be determined from the frequency and temperature dependence using LFM.5 In LFM, the cantilever moves parallel to the specimen surface, which is disadvantageous in terms of spatial resolution. The spatial mapping with a temperature-dependence capability is somewhat difficult because the temperature sweep is a lengthy procedure. Moreover, the temperature just beneath the AFM probe cannot be measured precisely. FM-AFM is a well-known method used to determine the frequency dependence of viscoelastic properties, where the piezoelectric scanner6,7 or cantilever8 is oscillated perpendicular to the sample surface. When the piezoelectric scanner to be normally used for xyz-movement is oscillated as perturbation, its resonance frequency limits the range of measurable oscillation frequency to a maximum of only about 300 Hz. When the cantilever is oscillated using piezoelectric actuator placed at its base, the frequency is usually fixed at the resonance frequency of the actuator to ensure the enough level of cantilever oscillation amplitude. Consequently, FM operation in this mode is not a frequency sweep method. These two modes of FM-AFM are insufficient to evaluate the frequency dependence of the viscoelasticity of rubber. CR methods have recently been demonstrated for viscoelastic measurements9−12 where the resonance frequency is measured when the cantilever is in contact with the sample and compared to that of the free cantilever. Killgore et al.

Most polymeric materials have inhomogeneous structures on the nanometer scale. In particular, rubber materials have crosslinked network and filler dispersion. Consequently, an evaluation method that can visualize the mechanical properties of inhomogeneous structures with a nanometer-scale resolution is necessary to predict the properties of polymeric materials with complex structures. Atomic force microscopy (AFM)1 is commonly used to observe the structure of soft materials, such as polymers and biomolecules. Additionally, the principle behind AFM in which a tiny probe comes into contact with and deforms the sample allows the physical properties of soft materials to be measured. The spatial resolution of AFM is on the atomic scale, while the force resolution is on the pN order. Thus, the mechanical properties of soft materials can be measured on the nanometer scale. Polymeric materials exhibit viscoelastic phenomena, which influence the materials’ applications. For example, rubber in a tire receives stimuli over a wide frequency and temperature range from a road’s surface. For bulk specimens, the frequency and temperature can be converted mutually based on the time− temperature superposition (TTS) principle.2 However, TTS is an empirical rule. Consequently, an actual measurement method with a wide frequency and temperature range is necessary to precisely predict the properties of practical products. Various conventional methods have been proposed to measure viscoelasticity via AFM such as lateral force microscopy (LFM),3−5 force modulation (FM),6−8 and contact resonance (CR).9−12 © 2013 American Chemical Society

Received: December 22, 2012 Revised: February 1, 2013 Published: February 22, 2013 1916

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experimentally demonstrated that the physical properties obtained by CR-AFM and the bulk properties obtained by TTS are correlated. However, CR-AFM can only be used to measure the viscoelasticity near the resonance frequency of the cantilever (800 kHz).11 Furthermore, this method is not suitable for softer and adhesive materials such as rubber.12 Herein we propose a modified AFM method to measure the viscoelastic properties of polymeric materials, especially rubber, over a wide frequency range. Additionally, we develop a procedure to map the nanoviscoelasticity. Our method can map the storage modulus, loss modulus, and loss tangent with help of contact mechanics analysis. Finally, we demonstrate that this method can be practically applied to rubber examples.

2. EXPERIMENTAL SECTION Figure 2. Frequency response measured on mica.

2.1. Instrumentation and Measurement Method. Figure 1 schematically diagrams our novel measurement system, which is a

scan. We developed an original program (LabVIEW, National Instruments, USA), which was synchronized with the AFM controller, to control the lock-in amplifier and built-in oscillator in it. 2.2. Analysis Method. 2.2.1. Signal Analysis. Figure 3 shows the relationships between the oscillation of the piezoelectric actuator and that of the cantilever on mica (reference) and the polymeric specimen. Ap and ωp = 2πf p are the amplitude and angular frequency of the actuator oscillation, respectively. Because the oscillation of the actuator itself cannot be measured, the amplitude Acm and phase shift ϕcm of the cantilever oscillation were monitored on the mica plate as a reference. Acs and ϕcs are the measured amplitude and phase shift of the cantilever oscillation on the specimen, respectively. Sample deformation Δs is defined as Δs ≡ Δcm − Δcs

Figure 1. Schematic diagram of the nanorheological mapping equipment. The electrically isolated piezoelectric actuator was sandwiched between the sample and the cantilever to obtain oscillatory perturbation.

= Acm cos(ωpt + ϕcm) − Acs cos(ωpt + ϕcs) ≡ A s cos(ωpt + ϕs)

(1)

where As and ϕs are the amplitude and phase shift of the sample deformation oscillation, respectively. As and ϕs can be expressed as

modified commercial AFM (NanoScope V with MultiMode 8, Bruker AXS, USA). To encompass a wide-frequency range, a tiny piezoelectric actuator (PCh150/3 × 3/2, Piezomechanik, Germany), measuring 3 mm × 3 mm × 2 mm, was bonded to a metallic sample holder located on the AFM scanner. The piezoelectric actuator was driven by the built-in oscillator of the lock-in amplifier (7280BFP, SIGNAL RECOVERY, USA), which was electrically isolated from all the AFM circuits. The lock-in amplifier was used to measure the amplitude and phase shift between the photodiode deflection signal and oscillator signal. The spring constant of the cantilever (OMCL-AC240TS-C2, Olympus, Japan), which was determined by the thermal noise method,13 was 1.72 N/m. The cantilever deflection was calibrated on a stiff mica plate. Our method combined the above-mentioned oscillation and force− distance curve measurements. When the cantilever deflection was reached to 1.5 nm in the force distance curve measurement, the piezoelectric actuator started to oscillate, and the cantilever was maintained on the specimen surface while the frequency sweep was completed in 30 (7.2) s for a single point (mapping) measurement using surface delay control. The oscillation amplitude of the actuator was ∼5 nm. For a single point (mapping) measurement, 22 (13) frequencies, ranging from 1 Hz to 20 kHz (10 Hz to 20 kHz), were selected. The oscillator signal was regulated such that the frequency responses of the amplitude and phase shift on mica were flat as shown in Figure 2. The time constants of the lock-in amplifier were selected according to the drive frequencies. The mapping method contained an array of 64 × 64 pixel data set of force−distance curves for the measured specimen area (force-volume mode equipped in NanoScope V). The original AFM controller controlled the AFM scanner movements, including the approach, surface delay, retraction, and

Acm 2 + Acs 2 − 2Acm Acs cos(ϕcs − ϕcm)

As =

tan ϕs =

(2)

Acm sin ϕcm − Acs sin ϕcs Acm cos ϕcm − Acs cos ϕcs

(3)

Note that Acm, Acs, ϕcm and ϕcs were experimentally acquired. As a viscoelastic property, the dynamic stiffness, S′ and S″ are defined as (the derivation of eqs 4 and 5 is given in Supporting Information) S′ = k

Acs cos(ϕcs − ϕs) As

(4)

S″ = k

Acs sin(ϕcs − ϕs) As

(5)

Moreover, the loss tangent (tan δ), which is defined as the ratio between loss and storage contributions, can be expressed as tan δ ≡

S″ = tan(ϕcs − ϕs) S′

(6)

Here, ϕcs − ϕs is defined as δ. 2.2.2. Calculated Storage and Loss Modulus. By considering the contact mechanics between the probe and sample surface, the elastic modulus of the sample can be determined from the sample’s stiffness. Ideally, the contact area should be directly measured or analyzed in situ under dynamic experiment. However, nanometer-scale contact area under AFM probe cannot be visualized at the current state of art. Furthermore, the contact mechanics for viscoelastic material is not sufficiently mature. Therefore, we this time estimated the contact 1917

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Figure 3. Schematic of a nanorheological measurement. The probe tip radius, R, the sample deformartion, d, and the contact length, a, are defined as in this figure. condition using the elastic theory with assuming that the viscoelastic effect on the contact area can be regarded as perturbation. Figure 4

E′ =

(1 − ν 2)S′ 2a1

(7)

E″ =

(1 − ν 2)S″ 2a1

(8)

where ν is Poisson’s ratio which is 0.5 for a typical rubber material and a1 is the contact length at point “1” where d = d1. Because contact length cannot be experimentally measured, it was estimated from the following equation for Hertzian contact using the measurable value d.

a = (Rd)1/2

(9)

where R is the probe tip radius. Since the force−deformation curve shown in Figure 4 was not obviously described by Hertzian contact, it would be anticipated that the calculated moduli might deviate, which will be discussed later. On the other hand, JKR theory20 is more suitable to analyze contact with soft and adhesive materials like rubber. Assuming a JKR contact, the relationship between the dynamic stiffness and the dynamic modulus is expressed as21 (the derivation of eqs 10−13 is given in the Supporting Information)

Figure 4. Force−deformation curve measured on pure IR vulcanizate. Point “1” is the starting point of the retraction process. The apparent force becomes zero at point “0” and the maximum negative force due to adhesive interaction is seen at point “c.” The superimposed solid line is the theoretical JKR curve calculated with the evaluated E and w values.

E′ =

E″ = shows the force− (P−) deformation (d) curve measured on vulcanized isoprene rubber (IR), which was converted from the force−distance curve obtained when the AFM probe was in contact with the specimen surface.14−18 The zero-point determination for the sample deformation was made as the jump-in point in the force−distance curve during approaching process. In viscoelastic specimens, the start of the retraction process does not correspond to the end of the approach process because sample deformation relaxes while the cantilever is maintained on the surface. Herein, it was assumed that the contact condition during an oscillation measurement is the same as the contact condition when the retraction process begins and remains constant throughout the measurement (point “1” in Figure 4). Assuming a Hertzian contact, the relationship between the dynamic stiffness and the dynamic modulus, the storage modulus E′ and the loss modulus E″ is expressed as19 (the derivation of eqs 7 and 8 is given in the Supporting Information)

(1 − ν 2)S′ 1 − 1/6(a0 /a1)3/2 2a1 1 − (a0 /a1)3/2

(10)

(1 − ν 2)S″ 1 − 1/6(a0 /a1)3/2 2a1 1 − (a0 /a1)3/2

(11)

(1 − ν 2)S′ 1 − 1/3(ac /a1)3/2 2a1 1 − (ac /a1)3/2

(12)

(1 − ν 2)S″ 1 − 1/3(ac /a1)3/2 2a1 1 − (ac /a1)3/2

(13)

or

E′ =

E″ =

where a0 is the contact length at the “zero point”, where the apparent force exerted on the cantilever becomes zero (“0” in Figure 4). ac is the contact length at the maximum adhesive point (“c” in Figure 4). As mentioned before, the oscillation measurement was executed at a = a1. Because a0, ac, and a1 were not experimentally measurable values, they were estimated by applying JKR theory to the static force−distance curve. In this paper, we adopted the so-called “two-point method,” 1918

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introduced by Walker et al.22 In the two-point method, the deformation d0, dc, and the force Pc in two special points from the force-deformation curvethe zero point (“0” in Figure 4) and maximum adhesion point (“c” in Figure 4)are used to calculate contact length via Young’s modulus and adhesive energy w algebraically. 2.3. Materials. The freshly cleaved mica was used as the reference sample. Vulcanized styrene−butadiene rubber (SBR), IR, and a SBR/ IR 7/3 blend were selected as model specimens. Table 1 shows their

respectively, although they can be experimentally controllable parameters. In another experiment, the value of E′ or E″ slightly differed depending on the type of cantilever (data not shown). Although this issue requires further investigation, however, the order of the absolute values of E′ and E″ remained constant for all types of cantilevers. Therefore, we present hereafter the data obtained from the same type of cantilever with the aforementioned parameters. As for the difference in E′ and E″ between the Hertz and JKR models, E′JKR/E′Hertz was 0.67 and 0.89 in SBR and IR, respectively. Because the Hertz model does not consider adhesion, the contact length is underestimated, especially in the case of more adhesive SBR. In IR, E′Hertz was almost the same as that for E′JKR due to the relatively small adhesion. As expected, the JKR model is better suited than Hertz model which was also assured by the theoretical JKR curve superimposed in Figure 4 well reproduces the experimental retracting curve. Figure 5 shows E′, E″, and tan δ measured by nanorheological AFM. From the result of SBR homopolymer in Figure 5a, E′ increased from 3 to 410 MPa and E″ increased from 1 to 248 MPa as the frequency was increased from 1 Hz to 20 kHz. The frequency dependence of tan δ had a peak at 300 Hz. These results indicated that SBR encountered the glass-transition phenomena at the measurement temperature of

Table 1. Sample Recipes (phr)

SBR

SBR IR SBR/IR blend

100 70

IR

stearic acid

ZnO

accelerator

sulfur

100 30

2 2 2

2.5 2.5 2.5

4.1 4.1 4.1

1.5 1.5 1.5

recipes. The glass-transition temperatures measured by differential scanning calorimetry (DSC) (Q200, TA Instruments, USA) for SBR and IR were −5 and −65 °C, respectively. The specimens were cut into 500 nm-thick thin films using an ultramicrotome (UC6, Leica Microsystems, Germany) at −100 °C and placed on mica substrate. The sample thickness was controlled by the cutting spacing of ultramicrotome as the setting parameter. The thickness was well thick not to observe any thin-film effects. 2.4. Bulk DMA measurement. The viscoelastic properties for a bulk specimen were obtained by a temperature−(T−) frequency ( f) dispersion measurement (ARES, RDA, TA Instruments, USA). The raw data were obtained by the shear mode under a constant strain amplitude in a frequency range of 0.05 to 50 Hz over a temperature range of −65 to +45 °C . The shear modulus (G′, G″) can be converted into the tensile modulus (E′, E″) using the following equations: G′ = E′/2(1 + ν) and G″ = E″/2(1 + ν). Here, Poisson’s ratio ν is assumed to be 0.5 for rubber materials. The raw data were shifted to obtain master curve, i.e., the relationship between reduced frequency aT f and E′, E″, tan δ using the Williams−Landel−Ferry (WLF) equation. The shift factor (aT) was calculated with

log aT =

C1(T − Tr) (aT → a T) C 2 + T − Tr

(14)

where the reference temperature Tr was set to Tg + 50 °C so as to use the universal constant for C1 (=8.81) and C2 (=101.6).

3. RESULTS AND DISCUSSIONS First of all, we discuss the validity of contact mechanics models in calculating E′ and E″ obtained by our method. The calculation was conducted using the Hertz (eqs 7 and 8) or the JKR (eqs 12 and 13) model. Parameters used for the calculation were obtained by analyzing the force−deformation curve as exemplified in Figure 4 and were summarized in Table 2. The trigger threshold of deflection and oscillation amplitude of the cantilever used in this experiment were set to 1.5 and 5 nm, Table 2. d0, dc, d1, and Pc, Which Are Measurable Values, While w, ac, and a1 Are Calculated SBR d0 dc d1 Pc w ac a1

IR

Hertz

JKR

Hertz

JKR

− − 15.2 nm − − − 17.4 nm

15.2 nm −36.8 nm − −20.3 nN 0.22 J/m2 29.7 nm 45.6 nm

− − 62.6 nm − − − 35.4 nm

54.9 nm −31.7 nm − −8.0 nN 0.09 J/m2 38.4 nm 63.4 nm

Figure 5. Frequency dependence of E′, E″, and tan δ measured by nanorheological AFM. (a) Data at a point of SBR homopolymer (filled symbols) and at a point in the sea region in a SBR/IR blend (open symbols). (b) Data at a point of IR homopolymer (filled symbols) and at a point in the island region in a SBR/IR blend (open symbols). 1919

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Figure 6. Nanorheological mapping of a SBR/IR blend sample. Parts a, b, and c are mapping images of E′, E″ and tan δ, respectively. Here, 1, 2, 3, 4, and 5 indicate 10 Hz, 300 Hz, 1 kHz, 5 kHz, and 20 kHz, respectively.

25 °C. On the other hand, from the result of IR homopolymer in Figure 5b, E′ only increased from 1.6 to 3.4 MPa, while E″ increased from 0.07 to 1.6 MPa as the frequency was increased from 1 Hz to 20 kHz. tan δ did not have a peak in this

frequency range. These results indicated that IR is already in the rubbery plateau region at 25 °C. Next we applied our method to two-dimensional mapping. Figure 6 shows the nanorheological mapping of the SBR/IR 1920

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blend sample at five representative frequencies. In our method, the nanorheological mapping data was taken as 64 pixel × 64 pixel image for 2 μm × 2 μm square region, where each pixel contained the data measured at 13 different oscillation frequencies (0.01, 0.05, 0.1, 0.3, 0.5, 0.7, 1, 2, 3, 5, 7, 10, and 20 kHz). Although approximately 8 h were required to capture one image, the figures in Figure 6 were obtained at the same time and at the same location. The AFM images revealed a seaisland-like structure for the sample because SBR and IR are immiscible. On the basis of the blend ratio, the sea should be SBR and the islands should be IR. In the E′ image acquired at 1 kHz, the smallest IR domain had a diameter of 90 nm. Therefore, this nanorheology mapping method has at least a lateral resolution of 90 nm. In the E′ and E″ images, the sea and the islands were almost indistinguishable at lower frequencies, but the contrast became clearer at higher frequencies. The contrast of the tan δ images was enhanced at 300 Hz, whereas the sea and islands are almost indistinguishable at 20 kHz. E′, E″, and tan δ of each point taken from the sea or the island region were also superimposed in Figure 5, parts a and b, respectively. The almost perfect coincidence between the data on homopolymers and on the sea-island regions of blend sample indicates that at first the blend sample used in this study was really immiscible one and that furthermore our measurement can distinguish the viscoelastic nature of different specimens at the level of nanometer resolution. This statement would be particularly important to investigate more complex systems where the blend is not totally immiscible. Our method may play a very important role in investigating such specimens. Such a study is now under considerarion. Figure 7 shows master curves of E′, E″, and tan δ obtained for bulk specimens by DMA and for a nanometer-scale single point by nanorheological AFM. As mentioned, the reference temperature was set to be Tr = Tg + 50 °C in order to use the universal constants. This means that we this time did not perform a kind of empirical shifting and also means that we assumed thermorheological simplicity for SBR and IR. Although we knew this assumption was too much simplified case, we did so since we wanted to use the same shift factor for nanorheological AFM data which was only taken at a fixed temperature (25 °C). E′, E″, and tan δ of SBR and IR obtained by AFM nicely corresponded to the master curves obtained by DMA. The peaks of tan δ were perfectly in good agreement to each other in the case of SBR. The small deviation of the value of tan δ was mainly attributed to the deviation in E″. Although further elaboration is necessary, we are speculating the reason for this deviation mainly comes from the assumption of JKR contact. Since the viscoelastic nature dominates at the glass transition region, force-deformation curve at such situation always shows a less negligent deviation from JKR theoretical curve.14,16,23 Moreover, it was further confirmed the reason why any peak of tan δ was not observed for IR in measurable frequency range of AFM by comparing it with the bulk master curve. The measurable frequency range was already corresponded to the rubbery plateau for IR. It is worthwhile to note that in higher frequency range (aT f ∼ 10) the onset of the glass transition was seen, which was also observed in the bulk master curve. Therefore, it is concluded that our method can observe the glass transition behavior and can evaluate viscoelasticity of polymers reasonably. In addition, we might be able to conclude that the contrast in nanorheological mapping images shown in Figure 6 had viscoelastic origin. The many of AFM mapping

Figure 7. Master curve obtained by DMA and nanorheological measurement. (a) and (b) for SBR and IR homopolymers, respectively. The reference temperature was (a) +45 °C and (b) −15 °C.

techniques of energy dissipative processes have affected by the existence of adhesive hysteresis as another energy dissipation pathway especially in the case of so-called tapping-mode phase contrast imaging.24 In our case, this contribution was at least partially minimized by adopting JKR contact mechanics which take not only elastic but also adhesive interactions into consideration. The capability to measure the frequency dependence of the viscoelasticity over seven-figure frequency range for a single point measurement or five-figure one for a mapping provides significant advantages. First, measurements over a wide frequency range will improve the accuracy of TTS, which is necessary to precisely predict the properties of polymeric materials and to create a ‘dispersion map’ which is described by axes of temperature and frequency. We this time assumed the universal constants in our analysis in Figure.7. However, these constants should not be necessarily same for surface properties or nanometer-scale objects. Our wide-frequency measurement combined with precise temperature control will be useful to say something on this issue in the near future. However, in our current setup, the piezoelectric actuator must be heated or cooled together with specimens. Therefore, a temperature range is limited by the properties of piezoelectric actuator, such as its Curie temperature. More practically, whereas conventional bulk measurements can only measure the viscoelasticity 1921

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(18) Liu, H.; Chen, N.; Fujinami, S.; Louzguine-Luzgin, D.; Nakajima, K.; Nishi, T. Macromolecules 2012, 45, 8770. (19) Oliver, W. C.; Pharr, G. M. J. Mater. Res. 1992, 7, 1564. (20) Johnson, K. L.; Kendall, K.; Roberts, A. D. Proc. R. Soc. London. Ser. A. 1971, 324, 301. (21) Wahl, K. J.; Asif, S. A. S.; Greenwood, J. A.; Johnson, K. L. J. Colloid Interface Sci. 2006, 296, 178. (22) Sun, Y.; Akhremitchev, B.; Walker, G. C. Langmuir 2004, 20, 5837. (23) Nagai, S.; Fujinami, S.; Nakajima, K.; Nishi, T. Compos. Interf. 2009, 16, 13. (24) Gómez, C. J.; García, R. Ultramicroscopy 2010, 110, 626.

up to 100 Hz at most, our apparatus can measure the viscoelasticity up to 20 kHz. Thus, another advantage of our method is the ability to measure the viscoelasticity at frequencies close to those found in the usage environment without assuming TTS.

■

4. CONCLUSIONS Our nanorheological AFM instrument could measure the viscoelastic properties, including the storage modulus, loss modulus, and tan δ, from 1 Hz to 20 kHz. These quantities obtained by AFM were almost identical to those obtained by macroscopic measurements. Using nanorheological AFM, we were able to observe the different frequency dependencies of tan δ for SBR and IR; the tan δ of SBR had a peak around 300 Hz, whereas that of IR did not. Our mapping method visualized the distribution of the frequency-dependent viscoelastic properties of rubber blend specimen on the nanometer scale. Our future direction would be giving some insight into TTSrelated phenomena using our nanorheological AFM.

■

ASSOCIATED CONTENT

S Supporting Information *

Definition of dynamic stiffness and calculated storage and loss modulus. This material is available free of charge via the Internet at http://pubs.acs.org.

■ ■

AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

REFERENCES

(1) Binnig, G.; Quate, C. F.; Gerber, C. Phys. Rev. Lett. 1986, 56, 930. (2) Williams, M. L.; Landel, R. F.; Ferry, J. D. J. Am. Chem. Soc. 1955, 77, 3701. (3) Overney, R. M.; Meyer, E.; Frommer, J.; Guntherodt, H. J.; Fujihira, M.; Takano, H.; Gotoh, Y. Langmuir 1994, 10, 1281. (4) Overney, R.; Meyer, E.; Frommer, J.; Brodbeck, D.; Howald, L.; Guntherodt, H.; Fujihira, M.; Takano, H.; Gotoh, Y. Nature 1992, 359, 133. (5) Kajiyama, T.; Tanaka, K.; Takahara, A. Macromolecules 1997, 30, 280. (6) Maivald, P.; Butt, H. J.; Gould, S. A. C.; Prater, C. B.; Drake, B.; Gurley, J. A.; Elings, V. B.; Hansma, P. K. Nanotechnology 1991, 2, 103. (7) Radmacher, M.; Tillmann, R. W.; Gaub, E. Biophys. J. 1993, 64, 735. (8) Galuska, A. A.; Poulter, R. R.; McElrath, K. O. Surf. Interface Anal. 1997, 25, 418. (9) Yuya, P. A.; Hurley, D. C.; Turner, J. A. J. Appl. Phys. 2008, 104, 074916. (10) Yuya, P. A.; Hurley, D. C.; Turner, J. A. J. Appl. Phys. 2011, 109, 113528. (11) Killgore, J. P.; Yablon, D. G.; Tsou, A. H.; Gannepalli, A.; Yuya, P. A.; Turner, J. A.; Proksch, R.; Hurley, D. C. Langmuir 2011, 27, 13983. (12) Yablon, D. G.; Gannepalli, A.; Proksch, R.; Killgore, J.; Hurley, D. C.; Grabowski, J.; Tsou, A. H. Macromolecules 2012, 45, 4363. (13) Hutter, J. L.; Bechhoefer, J. Rev. Sci. Instrum. 1993, 64, 1868. (14) Wang, D.; Fujinami, S.; Liu, H.; Nakajima, K.; Nishi, T. Macromolecules 2010, 43, 9049. (15) Liu, H.; Fujinami, S.; Wang, D.; Nakajima, K.; Nishi, T. Macromolecules 2011, 44, 1779. (16) Wang, D.; Liang, X. B.; Liu, Y. H.; Fujinami, S.; Nishi, T.; Nakajima, K. Macromolecules 2011, 44, 8693. (17) Wang, D.; Nakajima, K.; Fujinami, S.; Shibasaki, Y.; Wang, J. Q.; Nishi, T. Polymer 2012, 53, 1960. 1922

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