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Mapping of the Surface’s Mechanical Properties Through Analysis of Torsional Cantilever Bending in Dynamic Force Microscopy

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Abstract

In atomic force microscopy, the cantilever probes provide sensing of the tip-sample forces, therefore are used for the surface’s topography imaging as well as the mechanical properties mapping at nanoscale. As in most techniques developed for local stiffness imaging based on so-called contact mode, the force applied to the surface exceeds acceptable level often causing damage to the sample. On the other hand, the most popular measurement technique based on the intermittent contact mode, where dynamic tip-sample interaction is measured and processed in order to provide surface’s shape tracking as well as imaging of energy dissipation, allows to perform the measurements with much less force and can be applied to a wide range of samples. This method, however, is insufficient in many cases, as it cannot provide detailed information about certain mechanical properties of the sample. Therefore, a new approach has been lately developed and successfully utilized in a number of applications. By the analysis of higher harmonics of the cantilever’s oscillation, one can obtain more specific information about the tip-sample interaction than in the case of phase imaging. Moreover, the time-resolved tapping mode, where advanced high-bandwidth signal processing is implemented, allows performing fast imaging of the stiffness, adhesion, peak force, and energy dissipation. As this technique provides gentle interaction with the surface, it can be used in imaging of fragile objects, such as biological samples. Due to the mechanical properties of the cantilever causing significant deformations of the detection bandwidth, the torsional bending of the cantilever is utilized in order to obtain the desired signal. In this chapter we discuss the principles of the implementation of this method and its application issues.

Keywords

Torsional Oscillation Force Spectroscopy Friction Force Microscopy Intermittent Contact Mode Hydrogenate Nitrile Butadiene Rubber 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

11.1 Introduction

Atomic force microscopy as one of the very few methods allowing subnanometer imaging of the surface [1, 2, 3], offers also the possibility of measuring the forces acting between the scanning tip and the sample. Its role as a diagnostic tool in various fields of science and technology has undoubtedly been appreciated and widely used for over two decades [4, 5]. Among the wide range of the measurement modes allowing observation of the distribution of morphological, electrical, magnetic, thermal, and optical properties of the surface, information about certain mechanical properties can also be obtained. The Force Modulation Microscopy mode, for example, provides a mapping of the local stiffness. It may, however, relatively easily cause modifications of the surface due to large forces applied to the sample [6]. Although the Force Volume Microscopy method utilizing contact mode and force spectroscopy acquisition [7, 8] was successfully utilized in investigations of biological or chemical samples, it is, nevertheless, time-consuming and provides the force mapping resolution significantly lower than the topography imaging (e.g. \(32 \times 32\)). Jumping mode scanning force microscopy [9, 10] and digital pulse force mode [11, 12] were also proposed as techniques allowing to investigate the mechanical properties of the surface; however, the mapping speed was still insufficient. To compensate the drawbacks mentioned before, another approach, described in this chapter, was required in order to provide high-speed mapping of the mechanical properties of the sample.

In dynamic detection methods of the tip-sample interaction known as intermittent contact mode (semicontact mode, tapping mode) the tip acts on the sample with significantly smaller force than in contact mode, allowing one to investigate fragile objects [13]. Also the wear of the tip, as well as the risk of its contamination is significantly lower than in contact related modes [14, 15]. In this technique the tip oscillates with a frequency near to its resonant frequency, perpendicularly to the surface [16, 17]. During every oscillation cycle, the tip presses the sample for a certain time period. When the tip experiences attractive and repulsing forces, the oscillation amplitude of the cantilever is damped, which is used to control the tip-sample distance while the surface imaging is being performed [18]. Also the phase shift between the excitation signal and the cantilever’s response is present and can be utilized to create a map of the energy dissipation which is related to the viscous and elastic forces [19, 20, 21, 22, 23]. This feature is very helpful when the non-homogeneities of the material should be investigated. An example of such a result obtained on the polymer film containing nanofillers is presented in Fig. 11.1a. This imaging mode can also be used as a source of information about the molecular structure of the material, such as C\(_{60}\)H\(_{122 }\) alcane, when the topography data does not provide sufficient contrast (Fig. 11.1b).
Fig. 11.1

Examples of phase imaging maps revealing certain details invisible in topography images. Complex polymer film containing various compounds mixed up (a), molecular chains of the C\(_{60}\)H\(_{122 }\) alcane deposited on mica substrate (b)

It should be emphasized, however, that it is very difficult to distinguish the origin of the interaction responsible for the observed phase shift. Moreover, determining of the relation between the change of the specific property and signal’s variations requires certain procedures and varies depending on some settings of the instrument. Therefore, the interpretation of the obtained results is challenging. Additionally, the complexity of the tip-sample interaction phenomena can also be a source of misinterpretation resulting in imaging artifacts [17]. The best-known issue is the nonlinear dynamics effect causing the appearance of artifacts in the topography as well as in the phase image [24]. Although one can perform comparison procedures in order to establish some relation between the change of the properties and the system response, it cannot be used as an infallible approach in data analysis. Moreover, the response of the setup depends on settings of the detection system (e.g. tip oscillation amplitude, set-point,...). Therefore, performing all the measurements in precisely the same conditions in order to avoid any misinterpretation would be necessary. An example of unwanted features (artifacts) in phase imaging data is shown in Fig. 11.2, where the nonlinear dynamics effect introduced both: the instability in keeping the tip-sample distance constant as well as rapid phase shift changes. Consequently, one needs to analyze carefully the behavior of the measurement setup and the obtained results in order to avoid such situations. Concerning the number of above-mentioned drawbacks of the phase imaging feature, another approach basing on intermittent contact mode is needed. The alternative solution can be implemented using the detection of higher harmonic of the cantilever’s oscillation.
Fig. 11.2

Examples of phase imaging artifacts presented as color palette on a 3D view of the topography. Transitions of the bistable tip-sample interactions (attractive and repulsive) cause the presence of jumps over several degrees as well as topography artifacts (a). Switching of the detection phase reverses the indication of the energy dissipation (b)

In the remaining sections of this chapter we describe methods that enable acquisition and processing of the time-varying tip-sample force waveforms in intermittent contact AFM. The simple model to calculate the time-varying tip-sample force waveforms and the relation between those forces and the sample properties is presented. We also describe the way the reconstruction of the tip-sample force curve known also as the force spectroscopy curve is performed. The technical issues of the real-time signals processing in developed measurement system are also presented. Then an alternative method of utilization of the high-harmonics analysis as surface’s stiffness mapping is described. Finally we present examples of the utilization of this method in mapping of mechanical properties of the surface.

11.2 Time-Resolved Tapping Mode in Mapping of the Mechanical Properties of the Surface

Intermittent contact mode is one of the most popular AFM imaging techniques. Therefore, a number of theoretical and experimental studies of this method have been carried out and published [4, 5, 16, 17, 18, 19, 20, 21, 22, 23, 24]. Nevertheless, some specific phenomena and measurement solutions are in the field of interest of various research groups, including newly developed time-resolved tapping mode technique, which enabled high-resolution and high-speed mapping of the mechanical properties of the surface. As the principles of the tip-sample interactions in intermittent contact method are well-documented, in following subsections we focus on particular issues referring to the high-bandwidth tip-sample interactions detection and processing. In order to provide the impression of the differences between the typical tapping mode and the new approach, we present also the practical aspects of its implementation on commercially available AFM system, with typical cantilever’s deflection detection feature [25]. Implemented solution allowed to acquire some experimental data which are presented here in order to illustrate certain issues of the system’s development.

11.2.1 Modeling of Tip–Sample Interaction Forces in Intermittent Contact AFM

As during the scanning process the tip repeatedly presses the sample and retracts, a dynamically changing signal can provide much more information than the amplitude and the phase shift as deduced from typical intermittent contact mode. Figure 11.3 illustrates the relation between the distance-force curve and two dynamic phenomena: the cantilever’s oscillation and the tip-sample interaction forces curve. It can be noted that as the cantilever repetitively moves toward the sample and retracts, the tip senses the attractive and repulsive forces every cycle of the oscillation. As in the intermittent contact mode, the lock-in amplifier-based detection system allowed to detect only the amplitude and phase shift of the cantilever’s oscillation, the complex tip-sample interaction forces waveform was not accessible and remained unused. A specific approach was developed in order to obtain the access to this information and utilize it in terms of determining local mechanical properties of the surface.
Fig. 11.3

The tip-sample forces graph with correlated path of the cantilever’s oscillation and the tip-sample interaction forces caused by tapping of the tip against the surface. Some of the proportions have been disturbed in order to provide good readability of the curves

Since most of the tip-sample interactions can be described with the Derjaguin–Muller–Toporov (DMT) model [26], one can see that dynamics of the force change along one tap cycle varies depending on the stiffness of the sample (Fig. 11.4). In order to verify the relation between the mechanical properties of the surface and the shape of the tip-sample interaction force curve, the modeling was performed.
Fig. 11.4

The results of the simulation of the tip-sample interaction during the tip oscillation, basing on the DMT model (a, c, e). The FFT transformation of the simulated graphs (b, d, f). The Young moduli of the surface used in the simulation are: 10 GPa (a, b), 5 GPa (c, d) and 1 GPa (e, f)

Equations 11.1 and 11.2 were used to calculate time-resolved waveforms [27, 28].
$$\begin{aligned} F_\mathrm{ts}&= {\left\{ \begin{array}{ll} \displaystyle -\frac{HR}{6d^2},&d>a_0\\ [3mm]\displaystyle -\frac{HR}{6a_0^2}+\frac{4}{3} E^*\sqrt{R(a_0-d)^{3/2}}+\left(-\frac{4\pi \gamma _{\mathrm{H}_2\mathrm{O}} R}{1+d/h}\right),&d\le a_0 \end{array}\right.} \end{aligned}$$
(11.1)
$$\begin{aligned} {} E^*&= \left[\frac{1-\vartheta _\mathrm{tip}^{2}}{E_\mathrm{tip}}+ \frac{1-\vartheta _\mathrm{sample}^{2}}{E_\mathrm{sample}}\right]^{-1} \end{aligned}$$
(11.2)
where:

\(\gamma _{\mathrm{H}_2\mathrm{O}}\) is the liquid–vapor interfacial energy of water, \(E^*\) is the effective elastic modulus between the tip and the sample system, d is the tip-sample gap, \(a_{0}\) is the intermolecular distance and h is thickness of the water film.

Also the variables were used: the driving frequency, which is chosen close to the fundamental frequency of the cantilever \(f_{0}=50\) kHz, Young modulus of the tip \(E_{t}=130\) GPa, Young modulus of the surface \(E_{s}=1\), 5 and 10 GPa, respectively, radius of the tip \(R=20\) nm, Poisson’s ratio respectively tip and sample \(\vartheta _t=\vartheta _s=0.3\), spring constant of the cantilever \(k_{c}=40\) N/m, quality of the cantilever’s resonance \(Q=400\), Hamaker constant \(H=7\times 10^{-12}\) J.

Figure 11.4 presents the time-force graphs calculated using the formula (11.1). It can be noted that, as the stiffness of the sample \(E_{s}\) increases, the slope of the tip-sample interaction force increase becomes steeper.

As the intermittent contact mode bases on periodic oscillations of the cantilever, its movement influenced by the tip-sample interaction can be represented using frequency-domain methods. These methods will be mostly important for the signal analysis described in the next sections.

The tip-sample force \(F_\mathrm{ts}\), can be represented as a Fourier series:
$$\begin{aligned} F_\mathrm{ts}(t)=\sum _{n=0}^{\infty }a_n\cos (n\omega t)+b_n\sin (n\omega t) \quad n=0,1,2,\ldots \end{aligned}$$
(11.3)
where \(\omega \) is the driving frequency, as previously mentioned, near to the resonant frequency of the cantilever. The coefficients can be expressed:
$$\begin{aligned} a_n&=\frac{\omega }{\pi }\int \limits _{0}^{\frac{2\pi }{\omega }}F_\mathrm{ts}\cos (n\omega t)\mathrm{d}t\end{aligned}$$
(11.4)
$$\begin{aligned} b_n&=\frac{\omega }{\pi }\int \limits _{0}^{\frac{2\pi }{\omega }}F_\mathrm{ts}\sin (n\omega t)\mathrm{d}t \end{aligned}$$
(11.5)
Therefore the nth harmonic of the signal can be described as follows:
$$\begin{aligned} F_{\mathrm{ts}_n}\cos (n\omega t+\theta _n)=a_n\cos (n\omega t)+b_n\sin (n\omega t) \end{aligned}$$
(11.6)
where \(F_{\mathrm{ts}_n}=\sqrt{a_n^2+b_n^2}\) and \(\theta _{n}\) are magnitude and phase of the nth harmonic force. Therefore, the movement of the tip can be analyzed as a superposition of harmonic forces and the utilization of harmonics measurement can be a source of information about the stiffness of the sample [29].
In order to provide one equation describing the steady state dynamics of the tapping cantilever in terms of analysis of the balance of the total harmonic force (driving force plus the first harmonic of the tip-sample force), the vibration amplitude, and phase, Sahin et al. developed formula, showing that these resonant harmonics are sensitive to variations of the mechanical properties of the material [30]. Moreover, by performing a series of measurements, Sahin et al. showed [31], that independently measured time-varying tip-sample forces quantitatively satisfy the steady state equations for the cantilever dynamics described by Eq. (11.7).
$$\begin{aligned} F_T e^{i[\omega t+\beta (\omega )]}=F_D e^{i[\omega t+\phi ]}+F_{ts1}e^{i[\omega t+\theta ]} \end{aligned}$$
(11.7)
which can be described as follows:
$$\begin{aligned} K_1A_ST(\omega )e^{i\beta (\omega )}=K_1A_0T(\omega )e^{i\phi }+F_{\mathrm{ts}1}e^{i\theta } \end{aligned}$$
(11.8)
where:
$$\begin{aligned}&\tan [\beta (\omega )]=\frac{\frac{\omega \omega _0}{Q}}{\omega ^2-\omega _0^2}, \quad \beta \in \{0,\pi \} \end{aligned}$$
(11.9)
$$\begin{aligned}&T(\omega )=\left\{ 1-\left(2-\frac{1}{Q^2}\right)\left(\frac{\omega }{\omega _0}\right)^2 +\left(\frac{\omega }{\omega _0}\right)^4\right\} \end{aligned}$$
(11.10)
$$\begin{aligned}&F_{\mathrm{ts}1}e^{i\theta }=\frac{\omega }{2\pi }\int \limits _{\frac{2\pi }{\omega }}f_\mathrm{ts}(t)e^{-i\omega t}\mathrm{d}t \end{aligned}$$
(11.11)
and \(F_{T}\), \(F_{D}\), and \(F_\mathrm{ts1}\) are the magnitudes of the total harmonic force, driving force, and the first harmonic of the tip-sample force, respectively, \(\omega \) is the drive frequency, \(\omega _{0}\) is the resonance frequency, Q is the quality factor of fundamental resonance, \(K_{1}\) is the effective spring constant of the fundamental flexural mode, \(A_{0}\) is the free vibration amplitude, \(A_{s}\) is the vibration (set point) amplitude, \(\phi \) is the phase difference between the driving force and the cantilever motion (reference), \(\theta \) is the phase difference between the driving force and the first harmonics.

11.2.2 Extraction of the High Bandwidth Oscillation of the Cantilever

In order to provide appropriate conditions for the measurement of the high bandwidth phenomena, the detection system should respond linearly, without major distortions. Otherwise, the acquired signal is useless, as every frequency is attenuated or amplified in a different way. Figure 11.5 shows two responses of the HMX cantilever from Bruker AXS Inc. (Madison, WI, USA): (a) flexural and (b) torsional response (Fig. 11.5a, b, respectively). As the torsional response allows one to obtain only slightly distorted signal with nicely visible harmonic frequencies, it proves its usability in detecting the tip-sample interactions during every cycle of the oscillation. The flexural response, however, allows to detect only the base frequency along with very few higher harmonics of the signal. Therefore, it is useful only in an intermittent contact mode setup, where the base frequency response is utilized. The visible bending of the detected signal spectrum is connected to the properties of the electronic detection setup (3 dB cutoff frequency) and to some extent can be compensated relatively easy. Some measurement systems have relatively wide plateaus of the detection bandwidth, therefore further signal processing does not require any compensation of the band reduction [29].
Fig. 11.5

Vibration spectra of a HMX cantilever measured in an intermittent contact mode AFM. The excitation signal is equal to the fundamental resonance frequency. The flexural response (a) contains only few frequencies due to the specific behavior of the cantilever, while the torsional response (b) shows a wide spectra of frequencies

The mechanical response of cantilevers with rectangular cross-section shapes can be calculated using the Euler–Bernoulli equation [24]. The first resonance frequency in torsional direction is about 20 times the flexural base frequency (Fig. 11.6). Therefore, the above-mentioned condition of the linear response of the cantilever can be achieved that way. This approach was proposed by Sahin et al. [29, 30, 32]. As a consequence of this solution one must assume that in the case of a typical cantilever, when the tip is placed on the symmetry axis of the cantilever, the bending momentum is too small to cause sufficient torsional bending of the cantilever in order to provide reasonable signal detection. Therefore, Sahin et al. designed a series of cantilevers applicable for torsional bending [33, 34, 35] (Fig. 11.7). Recently the T-shaped cantilevers have become a commercially available product (Table 11.1). Another method of the longitudinal resonance frequency increase was proposed by Sarioglu et al. [36, 37]. The developed finger-like micromachined cantilever and differential interferometric measurement of the oscillation allowed one to obtain very high sensitivity of the force detection. It requires, however, utilization of a specific signal detection setup. Moreover, as the design of the probe is relatively complex, one can expect that the price would also be considerably higher than in the case of T-shaped cantilevers.
Fig. 11.6

The flexural (a) and torsional (b) oscillation modes of a rectangular cantilever. Frequency responses calculated using Euler–Bernoulli equation [10] for both oscillation modes, respectively

Fig. 11.7

A typical setup for the optical detection of the cantilever’s bending (a). The \((\mathrm{TL}+\mathrm{BL})-(\mathrm{TR}+\mathrm{BR})\) signal is used for the detection of the flexural bending, \((\mathrm{TL}+\mathrm{TR})-(\mathrm{BL}+\mathrm{BR})\) signal is used for torsional bending detection. The optical microscope view of the HMX cantilever (b). The arrow points at the location of the hammer-shaped end of the cantilever with the asymmetrically placed tip

In order to detect the torsional signal in the case of the T-shaped cantilevers, typically quadrant photodiodes are used. As for the detection of the flexural oscillations the top–bottom pairs of sections are used, the torsional oscillations can be detected using the left–right pairs of the detector (Figs. 11.7 and 11.8). A similar approach is applied in case of friction force microscopy (FFM) [38] known also as lateral force microscopy (LFM). One should, however, take into account that due to the specific application of that detection channel, its bandwidth can be significantly reduced in order to provide a low noise level when FFM is active. Therefore, this issue should be verified if one is intend to implement the described solution in a commercially available AFM system.
Fig. 11.8

The principles of the detection system and the acquired signals. Signals: S1, excitation; S2, flexural response; S3, torsional response. The amplitude A is used for keeping the tip-sample distance constant, while the phase shift \(\phi \) is used for energy dissipation imaging

Table 11.1

The list of commercially available T-shaped cantilevers and their specifications

Manufacturer

Name

\(f_{0}\) (kHz)

\(f_\mathrm{tr}/f_\mathrm{fl}\)

\(k^{*}\) (N/m)

Length (\(\upmu \)m)

Width (\(\upmu \)m)

Thickness (\(\upmu \)m)

Bruker

HMX

60

17

4,0

300

25

4

Bruker

HMX-S

40

17

1,0

300

25

3

MicroMasch

TL01

90

10

2,0

180

20

2

MicroMasch

TL02

60

17

3,0

300

20

5

11.2.3 Recovering the Time-Varying Interaction Signal of the Tip–Sample Forces

Although the torsional bending of the T-shaped cantilever enables convenient detection of the high-bandwidth waveform of the tip-sample interaction, it should be underlined, that signal processing is necessary as one expects to recover the shape allowing to perform further interpretation. Figure 11.9a represents both: vertical and torsional signals acquired at the four-quadrant photodiode [5]. As explained before, the vertical signal contains very few harmonics, with major fraction of the base resonant frequency of the cantilever. Therefore, this waveform cannot be used in extracting of the tip-sample interaction curve. The torsional signal, however, is more complex, and after some filtering steps it can enable access to desired information. It should be noted, that even though the special T-shaped cantilever is utilized, the torsional signal is still much smaller than the vertical one, therefore the detection (ADC conversion) feature must provide appropriate sensitivity and resolution. Additionally, special effort must be taken in order to obtain the signal–noise ratio high enough to provide the acquisition of legible waveforms that could be interpreted.
Fig. 11.9

Vibration signals from flexural and torsional motions, and tip-sample forces. a The signals at the four-quadrant photodetector for vertical and torsional displacement. The solid curve is the torsional signal. The torsional signal was multiplied by a factor of 10 to provide clear view of both curves in one graph. b The torsional vibration signal after being divided by the torsional frequency response. Except for the pulse located between the 300 and 400th time steps, the tip-sample forces should have been close to zero, because the tip is far away from the surface at those times. The measured signals when not in contact come from crosstalk from the flexural deflection signal. The dashed curve estimates the error introduced by these curves. When it is subtracted from the solid curve one gets the time-varying forces plotted in c [5]

Once the torsional signal is divided by the torsional signal response (Fig. 11.9b), one can observe the shape containing the tip-sample interaction feature that was obtained during the simulation. The rest of the waveform does not contain any useful data as the tip is away from the surface and the interaction force is nearly zero. One can, however, notice presence of waviness of the curve, which is caused by the crosstalk signal (the harmonic of the flexural base frequency of the cantilever), which has to be removed. Also the base frequency of the torsional oscillations of the cantilever is undesired feature. Those frequencies can be filtered out relatively easily by applying the FFT filtering (Fig. 11.10). Finally, the time-varying tip-sample interaction waveform is obtained (Fig. 11.9c). Various signal processing approaches were described in detail by Sahin et al. [29, 30, 33, 34] and Stark et al. [39].

It should be emphasized, that the stage of the signal processing is the most complex task in development of the technique, as the filtering should provide extraction of certain signals without losing any relevant information. Therefore, advanced tools are utilized in order to obtain the optimal results in terms of filtering quality and the process efficiency. The most popular way is the implementation of the procedure including conversion of the waveform into the frequency domain (FFT), and then elimination of unwanted frequencies (Fig. 11.10) and obtained data converting back into the time domain (Inverted FFT). Legleiter et al. presented solution, where the cross talk and high background noise was removed with advanced software tools like comb filter and spectral filtering [40]. Sahin applied the least square-fitted waveform filtering in order to remove the unwanted components of the signal [32]. Quite different approach based on direct observation and interpretation of the oscillation signal was presented by Sarioglu and Solgaard [36]. It was however, possible as their setup introduced much less distortion than in case of T-shaped based solution.
Fig. 11.10

The spectrum of the torsional oscillation of the cantilever after primary deconvolution process. The harmonics marked with H1 and H2 should be removed, the marked group of the harmonics are useful for the interaction signal recovery

Once the tip-sample interaction curve is acquired, it is processed in order to obtain a reconstruction of the force-distance curve. In order to obtain that, the dividing of the waveform must be performed, as each peak has to be in separated dataset. Eventually, on each dataset, the stitching like operation must be done, as the spectroscopy curve contains two lines related to the decrease and increase the tip-sample distance. In order to provide the best possible result of the curve reconstruction, the DMT model fitting can be implemented as one of the last steps.

As the developed NanoSwing setup [25] allowed to extract certain data during following signal processing steps, the selected stages are illustrated in Fig. 11.11. The direct signal from the photodiode (Fig. 11.11a) is acquired, and the FFT as well as the comb filtering is performed to remove unwanted components of the signal (Fig. 11.11b). Eventually as the tip-sample force interaction waveform is available, the algorithm performs dividing the signal into sections (dividing lines—“d”) and the stitching operation is carried out (Fig. 11.11c). The stitching points “s” are related to the highest values of the tip-sample interaction force. Finally, the reconstructed force spectroscopy curve is available, containing approach and retract parts (Fig. 11.11d). It should be underlined, that unlike in typical force spectroscopy measurement, in time-resolved tapping mode the cantilever’s movement is driven with the sinusoidal waveform. Therefore, additionally, the linearization of acquired response is necessary in order to avoid the distortions of reconstructed curve. As the tip-sample contact event occurs with the frequency typical for certain cantilever (Table 11.1), which is in range of 50–90 kHz, the averaging of obtained curve is possible. Typically one can define the number of averaged curves in range of few to few hundreds. One must be aware that the reconstructed force-distance curve obtained with the time-resolved tapping mode and the typical force spectroscopy measurement procedure can differ due to imperfections of the processing algorithms as well as differences in dynamics of various phenomena as for instance the adhesion [41, 42, 43]. It should be mentioned, that there are AFM systems with such functionality commercially available [44].
Fig. 11.11

Following steps of the force curve reconstruction: raw signal (a), FFT spectrum of the signal after removing the harmonics related to flexural and torsional base frequencies of the cantilever (b), time-domain interaction signal with marked dividing lines “d” and central points for stitching operation “s” (c), distance domain force spectroscopy curve with marked dividing ends “d”, and central point for stitching operation “s” (d)

It should be mentioned, that during preparation of the AFM system for the measurement procedure, certain factors should be taken into account. Because the quality of the force spectroscopy curve reconstruction is essential, the tip-sample interaction signals must be at an appropriate level. Therefore, one should be able to verify key steps of the reconstruction process. As the number of analyzed harmonic frequencies has a direct impact on the amount of processed data, one should be able to observe the real-time behavior of the signal’s spectra. Due to varying properties of the probes, it is also important to adjust the detection frequency range that is considered to be useful in a certain case. By displaying the time-resolved tip-sample interaction signal one can verify, if the filtering feature is adjusted properly and the shape of the curve meets the expectation of the operator. Finally, the real-time view of the reconstructed force-distance curve allows one to verify if the tip-sample interaction is stable and allows one to perform the measurement. As the amount of the oscillations is relatively high, the averaging feature allows reducing the noise. The number of the averaged periods of the cantilever’s oscillation should also be adjusted carefully.

Appropriate mapping of the mechanical properties of the surface is much more challenging than usual topography measurement in intermittent contact mode. The major settings: the free oscillation amplitude of the cantilever and the setpoint must be chosen very carefully. Figure 11.12 presents three cases, where, by changing the setpoint, we were able to adjust the tip-sample interaction in order to modify the response of the cantilever and, eventually, to observe changes in the reconstruction result. As the setpoint is too high (93 % of free oscillation amplitude), the interaction is too weak and one can see very few harmonics or too low level of the signal. The reconstruction in such case is possible, however, due to insufficient tip-sample interaction in the repulsive forces area, the stability of interactions is not satisfying and the stiffness of the surface cannot be estimated correctly. The appropriate value of the setpoint (70 %) allows one to perform the scanning process with desired quality of the obtained maps. It can be noted that apparently insignificant differences of the signal spectra in the first two cases, have a severe impact on the final result. On the other hand, a too small value of the setpoint (40 %) causes permanent damping of the torsional oscillations of the cantilever and precludes the reconstruction of the force-distance spectrum. Such behavior is not observed in the intermittent contact mode, as the scanning process can be successfully performed in a much wider range of setpoint values. Although one must be aware of possible consequences, such as surface modification or tip contamination, it is possible to obtain still a correct topography image. Therefore, utilization of the time-resolved intermittent contact mode requires much more attention and expertise.
Fig. 11.12

Examples of the force spectroscopy reconstruction quality for various setpoint values (b, d, f) and the correlation to the FFT spectra used as an indicator of the tip-sample interaction (a, c, e). The setpoint values were as follows: 0.93 (a, b), 0.7 (c, d), and 0.4 (e, f) with a free oscillation amplitude \(A_{0}=18\) nm

In order to estimate the range of the setpoint values that can be applied to obtain a correct force spectroscopy reconstruction, its impact on the Young modulus estimation was investigated. As this method was designed to visualize the non-homogenous materials, the relation was verified for two materials present on the test sample used in the previous section. The obtained results are presented in Fig. 11.13. Fixing the setpoint within the range 0.58–0.81 allowed us to acquire stable readouts for both materials. As presented above, too high or too small values of the setpoint can lead to incorrect determinations of the properties of the surface. Therefore, one should verify the response of the measurement system, if the applied scanning factors provide reliable signal processing.
Fig. 11.13

Comparison of the Young moduli as a function of the setpoint value. Free oscillation amplitude \(A_{0}=18\) nm

The oscillation amplitude of the cantilever also determines the way the reconstruction is performed. When too small amplitudes are applied, the tip is not retracted far enough from the surface to acquire a full force-distance curve. On the other hand, too large amplitudes can cause tip and surface wear as well as an introduction of significant errors of the reconstruction due to utilization of a wrong interaction model as the tip would indent the surface much deeper than previously assumed. As the use of torsional harmonic cantilevers in the tip-sample interactions detection is a very complex problem, it was analyzed both theoretically and experimentally [45, 46, 47, 48].

The additional advantage of the force spectroscopy reconstruction observation is the ability of tip contamination detection. While in intermittent contact mode one can perform the measurements with a contaminated tip, it is very difficult to obtain the force spectroscopy curve in such a situation. Therefore, the probability of the presence of topography artifacts can be significantly reduced.

11.2.4 Mapping of the Mechanical Properties Basing on Advanced Signal Processing

After the force spectroscopy curve is reconstructed, it can be analyzed by software in order to determine following mechanical properties: stiffness, peak force, adhesion, energy dissipation for deformation, and energy dissipation for tip-sample separation. The relation between the listed properties and the shape of the reconstructed force spectroscopy curve is shown in Fig. 11.14.

As the tip approaches the surface (A1), it can experience attractive forces, the snap-in event (A2), and then repulsive forces (A3). During retraction (R1) the repulsive forces decrease and again the attractive forces are present up to the snap-off moment (R2). During such cycle one can observe changes of all presented sections of the curve. Therefore, their determination and mapping is essential. Two reconstructed force spectroscopy curves are presented in order to show the differences of various details. By continuous signal acquiring, filtering, processing, and analyzing, one can perform the mapping of the mechanical properties of the sample. The example of the obtained maps is presented in Fig. 11.15. Additionally, the topography as well as the phase imaging map are shown in order to correlate all available data. The measurement was performed in ambient conditions (\(T=26\,^{\circ }\)C, RH\({}=32\) %) at a scanning speed of 0.3 Hz.
Fig. 11.14

Typical force spectroscopy curve and the related mechanical properties of the surface (a). The parameters are: F1, snap-in force; F2, peak force; F3, adhesion. R1 (slope), elasticity; E1, energy dissipation for deformation; E2, energy dissipation for tip-sample separation. Two reconstructed force spectroscopy curves measured in different areas of the test sample (b)

In order to observe the efficiency of the imaging mode, a commercially available test sample [25] was used: a blend of polystyrene (PS) and polyolefin elastomer (ethylene-octene copolymer) deposited on a silicon substrate with a spin-cast method. The PS regions of the sample have elastic modulus value approximately 2 GPa, while the copolymer regions have elastic modulus value approximately 0.1 GPa. Such a range of stiffness values on the same surface allowed to clearly show the difference of the system’s response for various values of the Young modulus.
Fig. 11.15

The results of scanning of the test structure: topography (a), phase imaging (b), adhesion (c), stiffness (d), peak force (e), energy dissipation for tip-sample separation (f), and energy dissipation for deformation of the surface (g)

The interpretation of the results is intuitive, as the brightness of the map represents higher values of certain parameters. Although one may guess that all maps are qualitatively identical, but the distribution histograms presented in Fig. 11.16 show significant differences between most of the properties.
Fig. 11.16

The comparison of spectrum histograms from Fig. 11.20

The presented data are no absolute values, it is, however, possible to calibrate the system in order to provide specific information about the values of the forces, the stiffnesses, or the energies.

As one expects to obtain quantitative information, the relation between the real tip-sample force and its electrical representation in the measurement system must be established. The formula correlating the corrected voltage waveform \(V_\mathrm{TC}\) acquired at the photodiode and the tip-sample forces can be written as follows [49]:
$$\begin{aligned} V_\mathrm{TC}(\omega )=\frac{\omega _T^2-\omega ^2+\frac{i\omega \omega _T}{Q_T} }{\omega _T^2}V_T(\omega )=c_\mathrm{optical}\frac{d}{k_T}F_\mathrm{TS}(\omega ) \end{aligned}$$
(11.12)
where the \(\omega _{T}\) and \(Q_{T}\) are torsional resonance frequency and quality factor are denoted, respectively, \(k_{T}\) is a torsion constant of the first torsional mode, defined as the angular deflection for a unit torque around the long axis of the lever, d is an offset distance from the longitudinal axis of the lever, \(c_\mathrm{optical}\) is the detector signal for a unit torsional deflection angle, \(V_\mathrm{T(w)}\) is the Fourier transform of the detector signal \(\upsilon _{T}\)(t). The frequency response of the detector can be neglected if is properly compensated, or the cutoff frequency is well above the harmonic frequencies. As one can note, in time domain both waveforms \(V_\mathrm{TC}\) and \(F_\mathrm{TS}\) has the same shape within scalar factor. \(V_\mathrm{TC}\), however, still remains in electrical unit. Therefore, it has to determined.

Typical routine based on determining the cantilever’s deflection detection sensitivity and the cantilever’s spring constant [44] is similar to the procedure performed in typical force spectroscopy measurements, when contact cantilevers must be evaluated (thermal tuning feature implemented in AFM software). Additionally, the tip radius must be determined in order to calculate properly the Young modulus. In order to obtain such data, one can use high resolution electron microscopy or perform the blind reconstruction of the tip’s shape [50, 51]. However, this solution is time-consuming, it was successfully utilized by Ihalainen et al. [52] in determination of mechanical properties of pigment-latex coated paper samples.

An alternative method, is utilization of the reference sample, where at least two well-defined components can be measured [44]. Lanniel et al. used reference surface of polystyrene and low density polyethylene thin film, knowing that the stiffness of the polystyrene sample is 1.6 GPa [53]. As the response of the system is linear [54], one can extrapolate the response of the measurement system within the range of the Young modulus values related to the spring constant of the cantilever. For instance, the HMXS and HMX cantilevers can properly measure the values from 0.5 MPa to 1 GPa and from 10 MPa to 10 GPa, respectively. Below and beyond this range, one can perform successfully imaging of the mechanical properties, however, the estimation of the certain values can suffer very low accuracy. The reference sample-based approach is less effort-consumable, however, one must be aware, that the mechanical properties of the sample can vary with time as well as the environmental conditions. Therefore, it should be verified periodically, as every standard or reference sample. In order to do that, one can perform typical force spectroscopy measurement, or to calibrate time-resolved tapping mode system as described above and then to scan the sample in order to compare expected and measured values.

11.2.5 The Principles of the Measurement Setup

Although only few commercial AFM systems were designed to utilize the T-shaped cantilevers [44], the detection of the torsional bending of the cantilever can be performed in a number of commercially available and homemade setups. As mentioned above, the only condition is an access to the raw left–right signal of the quadrant photodiode detection module. Due to requirement of a high-bandwidth, the minimum amount of filters and other signal processing/adapting modules are recommended before signal acquisition, as every such an object can introduce distortions.

In order to develop the time-resolved tapping mode with detection of the torsional bending of the T-shaped cantilever, commercially available AFM system working in typical tapping mode was used [25]. Therefore, some modifications were necessary in order to perform experiments described in following sections. The access to the high-bandwidth \((\mathrm{TL}+\mathrm{TR})-(\mathrm{BL}+\mathrm{BR})\) signal was obtained by changing a few internal connections in the scanning head. Additionally, the synchronizing signal from the AFM controller was used to connect an auxiliary computational unit providing A/D signal conversion, data acquisition, processing, and storage (Fig. 11.17). The role and importance of the synchronization of the modules involved in the measurement process will be explained in the last section of this chapter. As the performance of the signal processing is essential, commercially available real-time signal acquisition and data processing unit was utilized. The data processing algorithms were developed using commercially available graphical programming environment. This solution provided useful tools and processing modules in order to develop the software quickly and flexibly. The correctness of the scanning head’s modifications could be verified with an oscilloscope (Fig. 11.18) when the torsional signal was observed. One can see the complex waveform of the signal as well as its Fast Fourier Transform revealing presence of the expected high-order harmonic frequencies. It is distinctive that only odd multiple values of the driving frequency are present in the spectrum.
Fig. 11.17

Simplified diagram illustrating the hardware configuration of the detection setup to measure the torsional bending of the cantilever

Fig. 11.18

The torsional response signal in time and frequency domain as acquired directly from the optical detection system. The complexity of the signal as well as the high-order harmonics are clearly visible

One should be aware that processing of wide-bandwidth signals requires utilization of a high-speed analog–digital converting unit. As typically one can observe the presence of the relevant harmonic frequencies up to 1 MHz, the converter should provide at least 2 Ms/s sampling ratio according to Nyquist-Shannon-Kotelnikov criteria. Practically, however, the signal processing provides better accuracy when 4 or even 10 Ms/s sampling ratio is utilized [25]. Also the resolution and the input voltage range of the converter are crucial, as the signal rarely exceeds 400 mV peak-peak value.

11.2.6 Signal Acquisition and Processing Issues in Terms of the Algorithm’s Efficiency Demands

As the data acquisition and processing unit should work simultaneously with the AFM controller, it is essential that every cycle of the signal processing is performed within certain time limits. When the development of the AFM system is planned, one of the most important issues is the synchronization of the central unit and the auxiliary computational device. The problems with fulfilling those conditions can lead to improper image creation and the presence of the artifacts [40].

In the case of utilized commercial system [25], the synchronizing signal is available, which delivers the electrical pulse at every single acquired pixel (Fig. 11.19). Therefore, it is possible to provide precisely the same data acquisition timing for the external software as for the original one. Thanks to this, the data gathered by the two devices is fully coherent. As one can see from the time between two pixels, the time period available for single pixel calculation is smaller than 4 ms. According to our tests, even 10 ms can be insufficient, when complex NanoSwing operations are to be performed on a Windows–based platform. Therefore, a real-time solution was implemented in order to provide necessary stability and repeatability of the computational tasks. Figure 11.20 shows the difference between the real-time system and often utilized software solution. Every signal processing task has to be finished within a certain time. If it takes longer, the information can be lost and a void pixel is acquired. Moreover, such situation can also induce a permanent delay in data processing and eventually cause a major data corruption. On the other hand, the real-time solution provides very stable computation conditions. In this case, the software procedure is performed with a very small standard deviation of the processing time.
Fig. 11.19

View of the signals present in the AFM system. The fast scanning signal (X axis) and the pulse synchronization signal are necessary to simultaneously work with the AFM controller and the auxiliary computational unit. The signals were obtained during scanning with 0.6 Hz scanning speed and \(512 \times 512\) resolution

Fig. 11.20

Time diagram showing the difference between real-time (lower part) and non real-time (upper part) signal processing in advanced signal processing during surface scanning with the AFM

As the AFM acquires more than 65,000 pixels during a single measurement procedure, it is important to avoid any delays or glitches in signal processing. In order to verify the efficiency of the real-time solution implemented in the described setup, a test procedure was performed. The data processing loop was performed 5,000 times and every execution time was measured and saved in the statistical data set. The tests were carried out also for the Windows-based solution in order to illustrate the impact of the specific behavior of such a system. Additionally, three levels of the algorithm optimization were evaluated, as one of the aim was to maximize the efficiency of the software. The first level of optimization was the code rearrangement, the second—enabling the pipeline processing, and the third one—enabling multithreading. The improvement of the efficiency is significant. The distribution of the measured processing time is shown in Fig. 11.21. It should be underlined, that the average time of the processing in such an application should not be taken into account, as the worst result determines the real performance of the system. Therefore, Table 11.2 summarizes the standard deviation as well as the maximum duration of the single loop execution.
Fig. 11.21

The distribution of the time periods for performing a single signal processing cycle for a single pixel, for two solutions: non real-time—“WIN” (Windows 7 based) and real-time—“RT” and various levels of the algorithm performance (1-raw algorithm, 2-optimized algorithm, 3-pipeline processing, 4-multithreading) are also presented

As one can see, the Windows-based solution cannot be applied in such systems, as it is not possible to control or predict the maximum time of the signal processing. Considering the amount of data that is calculated during every measurement, it is very likely that practically every set of results would contain artifacts.
Table 11.2

Comparison of the standard deviation and average time of the data processing duration for a single pixel

Time (\(\upmu \)s)

Performance 1

Performance 2

Performance 3

Performance 4

 

Std. dev./average

Std. dev./average

Std. dev./average

Std. dev./average

Real-time

26/4325

28/3848

15/2366

20/2077

Windows7

180/6756

125/6949

90/3959

69/3787

Windows7\(^\mathrm{a}\)

2493/59157

   

\(^\mathrm{a}\)Measured during induced activity of other applications

11.2.7 Utilization of High-Order Harmonics of the Cantilever’s Oscillations for the Surface’s Stiffness Mapping

As the bandwidth of the cantilever’s response signal is related to the stiffness of the sample (Fig. 11.3), it can be used for the mapping of this particular property [29, 35, 55, 56]. By measuring the power of certain high-order harmonic frequencies, one can relatively easily perform the imaging processing. Therefore, a lock-in amplifier should be used in order to provide necessary selectivity and sensitivity. Such approach cannot deliver quantitative information about mechanical properties of the surface, nevertheless it is useful in terms of interpretation of the results. It also simpler to implement than the time-resolved tapping mode technique.

In order to verify the usability of certain frequencies in the mapping process, we have developed a software-based eight-channel lock-in amplifier [57]. The structure of the hard-/software setup is shown in Fig. 11.22. The user can select the value of the multiplier for every channel independently, therefore the flexibility of detection is provided. The number of channels allows, however, to cover almost all useful harmonic frequencies of the torsional oscillation signal. It should be underlined, that such an approach permits to perform the experiment within a reasonable time period, without acquiring additional expensive hardware. Additionally, all the obtained data refer to the same area, therefore the comparison of data from different frequency ranges is easy and reliable.
Fig. 11.22

The diagram showing the concept of the implementation of the eight-channel software-based lock-in amplifier with the signal imaging feature

In order to verify the stiffness imaging ability of developed system, the test sample described in previous subsection was used. Figure 11.23 shows the topography scan and the Fourier transform spectra related to the spots where they were obtained. One can see that at some specific frequencies of the signal the differences are significant. Therefore, mapping of appropriate harmonics can deliver the desired kind of information. As we can verify from the spectra of the signal, the coverage of the bandwidth with eight-channel setup was satisfying, while further frequencies were very close to the torsional resonance of the cantilever. As previously mentioned and confirmed with the spectra graphs, only odd multiplications of the base frequency should be considered as the source of useful information. Therefore, the software was configured in order to perform the mapping of the following harmonic frequencies: 1, 3, 5, 7, 9, 11, 13, 15. As the base frequency of the HMX-S cantilever used was approximately 49.24 kHz, the values were analyzed in the range: 98.48–787.84 kHz. The measurement was performed in ambient conditions (\(T=25\,^{\circ }\)C, RH\({}=34\) %) at a scanning speed of 0.2 Hz.
Fig. 11.23

The results of the comparison of two spectra obtained on the test sample containing materials of different stiffness: 2 GPa (surrounding) and 0.1 GPa (round object)

Obtained results are presented in Fig. 11.24. Also the topography and phase imaging maps are shown in order to allow correlating all available data. It can be noted that the first harmonic does not provide sufficient contrast, however, the maps of higher harmonics show very clearly a good relation between theoretical consideration and the obtained data. The softer area is presented by darker colors, as the values of certain harmonics are lower in a such case. It should be underlined, that higher frequencies (13, 15) are not as distinct as the lower ones, as they would reach higher values in case of mapping stiffer surfaces. In order to compare the effectiveness of the stiffness imaging, the distributions of acquired maps are presented in Fig. 11.25. The height of the peaks as well as the distance between them indicates how legible a certain map is. Therefore, it can be considered as an estimation of the detection sensitivity. The comparison of the distances between peaks is additionally shown in Fig. 11.26. It shows clearly that the largest values were obtained in the case of the 5, 7 and 9th harmonics. Concerning the height of the peaks, the 5 and 9th harmonics provided the higher values. This factor plays very important role as a derivative of the steepness of the tip-sample force curve. Therefore, it can be considered as the indicator of the stiffness detection resolution.

It should be emphasized that in the presented solution, the flatness of the system’s detection bandwidth is not essential, as every harmonic is monitored and mapped independently. Therefore, the mutual relations of certain signals is not as relevant as in case of the force spectroscopy curve reconstruction process described in the following section. Moreover, in the case of a single harmonic with one lock-in amplifier, the simplicity of the presented approach makes it very attractive for a wide range of applications and can be implemented easily in many AFM systems.
Fig. 11.24

The scanning results of the test structure. From left to right: topography (a), phase imaging (b), and following harmonics: 1, 3, 5, 7, 9, 11, 13, 15 (cj, respectively) for the base frequency 49, 24 kHz

Fig. 11.25

The comparison of the distributions of the harmonics acquired with the 8-channel lock-in amplifier

Fig. 11.26

The comparison of the peak–peak distances for acquired histograms of the harmonic changes distribution

It should be noted, that also flexural high-order oscillations were analyzed in terms of mapping of the mechanical properties of the surface.

In numerical analysis based on equivalent electrical circuits to model and simulate the higher harmonics generation in tapping mode, Sahin et al. concluded, that third harmonics is highly sensitive to the tip-sample interaction [58]. Experimental work showing the mapping of mechanical properties of the etched silicon wafer using 13th harmonic was presented by Hillenbrand et al. [59]. The utilization of such solution was more effective than phase imaging technique. In this work, the idea of reconstruction of the tip-sample interaction curve was also proposed. Also Sahin et al. used 10th harmonic to generate maps of the local stiffness changes while the temperature of PS-PMMA polymer film increased [29].

11.3 Application Examples

The utilization of time-resolved tapping mode technique in various fields of science allows to obtain more information about the properties of the sample. Therefore, much more complex materials and phenomena can be observed and interpreted. As one can analyze separate maps of various properties of the surface (stiffness, adhesion) as well as the tip-sample interaction (peak force, energy dissipation), significantly deeper insight into the nanoscaleworld can be enabled. It should be emphasized, that due to the complexity of the measurement technique, mostly commercially available systems are utilized. Additionally, as we have presented in Sect. 11.2.3, optimizing the scanning parameters in terms of appropriate force-distance curve reconstruction and effective mapping of the mechanical properties requires much more expertise and effort than in case of contact or intermittent contact mode. Therefore, this imaging technique can be underestimated. In this subsection, we present few examples of research that gained from utilization of time resolved tapping mode.
Fig. 11.27

Changes in the mechanical properties of a polymer blend near the glass transition. Topography, phase, and tenth-harmonic images of a thin polymer film composed of PS and PMMA recorded at different temperatures. The circular features are PMMA, and the matrix is PS. Brighter color represents larger height, phase, or harmonic amplitude. The scan area is \(2.5 \times 5\) \(\upmu \)m. The color bar represents different height and phase ranges at each temperature (the range is given in the top left corner of each panel). For the harmonic images, the color bar represents a 10 V lock-in output signal at all temperatures. Note that height and phase contrast increases with temperature, whereas the harmonic contrast is first increasing and then decreasing [29]

Observation of dynamically changing properties of the material due to temperature increase was presented by Sahin et al. [29]. In this case, however, the mapping was performed using the 10th harmonic of the flexural cantilever’s base signal instead of recovering the force-distance curve. With this method, the behavior of the polymer film composed of the PS and PMMA near the glass transition was imaged (Fig. 11.27). It was possible to observe that near the 190 \(^{\circ }\)C, the grain boundaries become unclear and the material gained mobility, starting rearrangements of the formerly stable forms.

The mapping of the mechanical properties of pigment-latex coated paper samples was performed by Ihalainen et al. [52]. It was noted, that although being the minor component in the coating color formulation, the latex was appeared to be one of the major components on the surface. Additionally, the tip-sample thermodynamic work of adhesion of the composite materials on the coated surface correlated with the surface energy values obtained by contact angle measurements, showing a higher tip-sample work of adhesion as a function of a higher surface energy.

Lanniel et al. [53] observed the increase of the Young modulus of the hydrogen silsesquioxane, as it was exposed to the electron beam. As the map of the stiffness was acquired, its uniform distribution was observed. Since the Young modulus was determined with nanoindentation method, one could confirm, that locally measured properties were representative.

The mapping of surface elastic moduli in silica-reinforced rubbers and rubber blends was presented by Schön et al. [60]. Styrene–butadiene rubbers (SBR) and ethylene–propylene–diene rubbers (EPDM) and SBR/EPDM rubber blends with varying concentrations of silica nanoparticles were investigated (Fig. 11.28). The results allowed to reveal an increase of the areal fraction of silica particles with rising concentration in the compound preparation mixture. Additionally, measurements revealed the formation of larger silica aggregates in EPDM in contrast to SBR where isolated silica particles can be observed.
Fig. 11.28

DMT modulus images of SBR/EPDM blends filled with 20 phr Ultrasil VN3; a 30/70 SBR/EPDM; b 50/50 SBR/EPDM [59]

Another experiment focused on quantitative mapping of elastic moduli at the nanoscale in phase separated polyurethanes was also performed by Schön et al. [61]. As observed morphology as well as elastic modulus strongly depends on stoichiometric ratio, it was possible to identify the sample. Additionally, the comparison of two commercially available mechanical mapping techniques was performed: torsional oscillations-based time-resolved tapping mode, and based on peak-force detection and feedback next generation imaging technique.

Qu et al. by mapping of the elastic modulus obtained confirmation of presence of the interphase of rubber-particle nanocomposites in hydrogenated nitrile butadiene rubber (HNBR)–carbon black composites [62]. As the bound rubber exhibits mechanical properties distinct from rubber matrix and the particles, it was possible to determine the thickness of the interphase to be below 20 nm.
Fig. 11.29

The results of scanning of the exfoliated graphene: topography (a), phase imaging (b), adhesion (c), stiffness (d), and peak force (e)

Also newly developed materials can be investigated in order to determine their properties. I particular, very promising nanomaterial as the graphene, still requires a number of investigations, as its values can enable new technologies and applications. In present example the exfoliated graphene flakes were placed on silicon wafer covered with 300 nm thick silicon dioxide layer [63]. As we expected, the stiffness of graphene is higher than the stiffness of the silicon dioxide (Fig. 11.29). Moreover, we could observe that the change of the thickness: monolayer and multilayers (from 4 up to over 40) does not affect the stiffness significantly. Additionally, we could observe slightly smaller adhesion on the graphene surface in relation to the substrate. Moreover, the peak force map revealed almost homogenous value, except the right side of the image, which can be related to very thick layer as well as the graphene detaching. One can note, that the phase image could not provide such valuable information. It should be emphasized, that the quantitative measurement in such case would not provide accurate data, as the Young modulus of graphene is far beyond the range of linear response of the system. Nevertheless obtained information can be useful in terms of technology of development of particular devices.

The utilization of time-resolved tapping mode in biological and medical sciences was also significant. Dague et al. observed interaction forces between the pig gastric mucin (PGM) and Lactococcus lactis as the model for lactic acid bacteria [64]. As the L. lactis cells were immobilized on the AFM tip, it was possible to observe the interaction forces between bacteria (lacto probe) and PGM-coated polystyrene.

Cross-correlational research comparing time-resolved tapping mode and conventional nanoindentation technique was performed, concerning investigation of the elasticity of bacterial nanowires from Shewanella oneidensis MR-1 cultured under electron-acceptor limiting [65]. Leung et al. demonstrated good consistency of the results obtained with both methods. Mapping of the elasticity of the bacteria wires did not reveal significant variations, therefore its mechanical homogeneity was verified.

Husale et al. presented utilization of time-varying tip-sample forces analysis in determination of the unique mechanical signatures of the DNA and RNA molecules [66]. Presented solution enabled direct quantification and counting hybridized molecules attached to the surface. The advantage of the method is relatively low cost, high speed, and attomolar-level detection sensitivity while it eliminates the biochemical processes.

11.4 Outlook and Conclusions

In this chapter we have presented the principles, specific issues of the implementation, and example results of the time-resolved intermittent contact technique based on the detection of the torsional cantilever oscillation. In particular, we showed a successful implementation of the NanoSwing solution based on this method. As this technique allows to perform high-speed and high-resolution mapping of the mechanical properties of the surface in intermittent contact mode regime, its range of application is very wide. The obtained maps of: topography, stiffness, adhesion, peak force, and energy dissipation enables the study of the structure of non-homogenous materials, where ingredients can be identified. Although the use of such a technique is much more complex than typical intermittent contact mode and the experience of the operator in setting the scanning parameters determines the effectiveness of its utilization, the advantages of the achieved measurement results are unquestionable as they provide much more detailed insight into the structure and properties of the investigated object.

We have also presented the possible methods of implementation of two measurement techniques utilizing the torsional bending of the cantilever. The presented solutions can be implemented on many AFM systems, where one is able to obtain access to the high-bandwidth unprocessed signals of all sections of the quadrant photodetector.

It should be underlined, that by enabling an access to information about certain tip-sample interaction phenomena, the experiments are performed in order to utilize available information to improve the topography imaging process, as the scanning tip can cause significant deformation of the surface. Such drawback can be reduced by developing new idea of the Z-axis feedback solution [67, 68].

Notes

Acknowledgments

The authors would like to thank Roman Szeloch (Wrocław University of Technology, Wrocław, Poland), Hans-Ulrich Danzebrink, Miriam Friedemann and Mirosław Woszczyna (Physikalisch-Technische Bundesanstalt, Braunschweig, Germany) and other colleagues and coworkers for support and collaboration. This work was supported financially by the Polish Ministry of Science and Higher Education (MNiSW) within the framework of the research project no. N N505 466338.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Division of Electrotechnology and Materials ScienceElectrotechnical InstituteWroclawPOLAND

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