Here, Force distance (FD) spectroscopy is a straightforward and reliable technique to quantitatively study nanomechanical properties such as Young’s modulus and adhesion force on a variety of samples. Therefore, FD spectroscopy has become a fundamental characterization tool in several fields of research, including polymer science, biochemistry, and biology.
Most commonly, Atomic force microscopy (AFM) is used to image sample topographies. Moreover, AFM is often employed to measure nanomechanical properties of surfaces as well. Here, Force distance (FD) spectroscopy is a straightforward and reliable technique to quantitatively study nanomechanical properties such as Young’s modulus and adhesion force on a variety of samples. Therefore, FD spectroscopy has become a fundamental characterization technique in several fields of research, including polymer science, biochemistry and biology. In FD spectroscopy, the cantilever is used as a force sensor. Nanomechanical properties of the sample are measured by monitoring the tip-sample interaction via the vertical cantilever deflection at a single contact point. The approach and retract curves of the cantilever deflection versus the movement of the Z scanner can be converted into FD curves that contain information on deformation, Young’s modulus and adhesion force of the sample at this point. In Park Systems AFMs, FD spectroscopy is the basis for nanomechanical imaging techniques such as force volume imaging and PinPoint mode.
Table 1: Tip-sample interaction forces acting during FD spectroscopy as a function of the distance.
To measure FD curves, the tip approaches and retracts from the sample surface by ramping of the Z scanner, while keeping the XY position constant as shown in Figure 1 (a). By monitoring the cantilever deflection introduced by the tip-sample interaction, deflection versus Z height data is obtained as shown in Figure 1 (b): The cantilever bends towards the sample surface for attractive tip-sample forces, and away from the surface when tip-sample forces are repulsive. Figure 1 (b) illustrates an exemplary FD spectroscopy measurement including the different interaction regions labelled by the letters A to E. In region A, tip far from the surface, there is no tip-sample interaction. Region B marks the snap-in of tip and sample mainly caused by capillary forces in ambient humid conditions, where a thin water layer is present on tip and sample. The snap-in occurs when the attractive force gradient exceeds the spring constant of the cantilever. As the Z scanner further extends towards the sample surface, the repulsive tip-sample force dominates and continues to increase until the pre-determined force setpoint in region C. Once the contact force between the tip and the sample reaches to this setpoint, the Z scanner retracts the tip from the sample surface. Below a certain force threshold in region D, the cantilever bends towards the sample surface due to attractive adhesive forces. In region E, the pull-off between the tip and the sample occurs as the Z scanner retracts further and the spring constant of the cantilever overcomes tip-sample adhesion force.
Figure 1. (a) Schematic experimental setup for FD spectroscopy, including the Z scanner movements during approach and retract in red and blue, respectively. (b) Exemplary approach and retract curves, in red and blue, respectively. The different interaction regions between the tip and the sample are labeled by the letters A to E and the according cantilever deflection for each region is shown on the right.
How to obtain quantitative nanomechanical data?
The raw data of force (nN) vs. distance (nm) curve is the A-B value (V) of the cantilever deflection measured from photo detector vs. Z scanner position (nm). To obtain the quantitative tip-sample force from the cantilever deflection, the spring constant of the cantilever needs to be calibrated. The thermal tune and Sader are commonly used methods for spring constant calibration. In the thermal tune method, the equipartition theorem relates the cantilever’s Brownian motion to its spring constant. The Sader method, on the other hand, derives the spring constant from an analytical equation that uses the cantilever’s free resonance frequency, dimensions and the quality factor. A practical rule of thumb is, for cantilevers with a resonance frequency < 100kHz, thermal tune method is adopted and for > 100 kHz, Sader method is adopted for reliable spring constant calibration.
Besides the spring constant calibration, the approach and retract curves should be converted into FD or force vs. separation curves for quantitative modulus measurements (Figure 2). This is necessary, because the measured signal from cantilever is a combination of sample deformation (indentation) and cantilever deflection. Separation is defined as:
Here, Height refers to the position of the Z scanner during the FD measurement, and ΔSeparation is the tip position with respect to the sample surface, i.e., the true tip-sample distance. Therefore, the separation or distance corrects the recorded data for the cantilever deflection. The correction for the cantilever deflection is particularly important for quantitative elasticity measurements, which are based on the indentation of the tip on the sample surface. This requires an accurate separation of deflection and indentation and, therefore, the conversion of height to separation between the tip and the sample.
(a) Approach and retract curves of force vs. height showing the superposition of indentation and cantilever deflection and (b) approach and retract curves of force vs. separation with the indentation contribution only.
Various mechanical properties of sample surface can be obtained from the force-separation curves, as shown in Figure 3. The stiffness of the sample can be determined from the slope of the force-separation curve in the contact region. In order to convert stiffness, extrinsic sample property, to quantitative Young’s modulus, intrinsic material property, the geometry of the tip-sample contact has to be taken into account. This is achieved by using at least one of the contact mechanics models (e.g., Hertz, DMT, JKR, and Oliver-Pharr models) depending primarily on the tip geometry and types of forces which dominate the contact. In addition to stiffness and Young’s modulus, the adhesion force (the force required to separate two surfaces in contact) can be measured as the maximum negative force in the retract curve. The adhesion energy is given as the area between the retract curve and the base line. Finally, the energy dissipation (which represents the energy loss caused by an irreversible process) is determined by the hysteresis between approach and retract (the yellow shaded area in the force-separation curve in Figure 3).
Figure 3. Measurable mechanical properties in the force-separation curve: Young’s modulus and stiffness are determined from the sample indentation, the adhesion force and energy can be calculated from the retract curve and the energy dissipation is given by the hysteresis between approach and retract.
The shape of the force-separation curve strongly depends on the nature of tip, sample and tip-sample interaction. Figure 4 shows various force-separation curves for materials with different properties. Comparing a hard and a soft sample in figures 4 (a) and (b) shows that the harder the sample surface, the larger the slope of the curve in the contact regime between the tip and sample surface. The large slope is due to the fact that hard samples cannot be indented easily and repulsive tip-sample interactions rapidly increase. Comparing samples with low and high adhesion in figures 4 (c) and (d) the retract curve of the adhesive sample features a pronounced rise in the magnitude of negative force, as a higher restoring force is required to separate tip and sample. Depending on the properties of cantilever and sample, the tip can cause elastic (reversible) of plastic (irreversible) deformations of the sample. For purely elastic deformations, the slope of the approach and retract curve overlap, as shown in Figure 4 (e), and the energy dissipation is limited to the sample adhesion. However, if the sample is compressed excessively by a hard cantilever, the sample surface will deform irreversibly. For this plastic deformation, the slope of the approach and retract curve differ as shown in Figure 4 (f), thereby contributing to the energy dissipation.
Figure 4. Trends in force-separation curves depending on different sample properties, including elasticity (a) and (b), adhesion (c) and (d), and energy dissipation (e) and (f).
Examples of FD spectroscopy
Biology
On biological samples, often the topography of a cell surface is imaged through non-invasive True Non-Contact mode™ AFM and subsequently the mechanical properties of an area of interest are obtained through FD spectroscopy. This approach preserves the sensitive biological samples from tip-induced damage. Figure 5 shows the True Non-Contact topography of a fixed embryonic stem cell and subsequent protein unfolding by the tip during a single FD measurement. During approach a microvilli protein binds to the tip. The retract curve (blue) in figure 5 (b) shows two distinct step-features in the adhesion force in the range of 300 pN. The steps originate from changes in the measured adhesion force as the microvilli attached to the tip detaches during retracting.
Figure 5. Topography of fixed embryonic stem cell in liquid in True Non-Contact mode™ (a). Force-distance curve (b) obtained subsequently at the marked point in (a). The red line is approach curve, and the blue is the retract curve in (b).
Single-molecule spectroscopy
In order to measure the mechanical properties of molecules such as DNA, both the tip and the sample can be functionalized, as shown in Figure 6 (a). In the first step of tip and sample functionalization, dendron molecules are chemically bonded to the tip and a substrate. Subsequently the DNA oligonucleotides physically bind to the dendron molecules. With the oligonucleotide sequences immobilized on the dendron-modified the tip and surface, the single FD curves now show the association and dissociation of the DNA duplex bonds in the retract curves in figure 6 (b). In this case, FD spectroscopy was repeated about 200 times at one point to obtain the unbinding force statistics in the FD retract curves. In figure 6 (c), the mean value of the unbinding force about 64 pN with a narrow distribution shows that AFM can be a useful tool to study the interactions of a single DNA molecules with RNA molecules, proteins or other single DNA molecules.
Figure 6. FD curve using functionalized tip and sample surface. (a) The chemical attachment process of 50-mer DNA oligonucleotides involves self-assembled monolayers (SAMs) of DNA-functionalized dendrons. (b) A typical FD curve of the interaction between a DNA probe and the complementary 50-mer DNA. (c) The histogram of unbinding forces acquired from the 200 FD curves.
Polymer composite
In FD spectroscopy, it is possible to measure not only a single FD curve, but also a force volume (FV) image based on FD curve mapping. FV imaging provides a detailed map of sample’s mechanical properties by plotting parameters such as stiffness, snap-in, and adhesion. Parameters extracted from FD curves are acquired in matrix area, where point number and size of matrix can be controlled, which allows researchers to gain insights about samples’ nanomechanical properties as shown in figure 7 (a). In figure 7 (c), the FD curve on polymer shows lower slope and bigger adhesion comparing to glass substrate. And the obvious differences between polymer and glass on mechanical properties such as stiffness and adhesion force were observed in FV imaging, as shown in figures 7 (d) and (e).
Figure 7. SmartScan user interface of FV imaging function (a). Mechanical properties measurement of a polymer embedded in a glass substrate. Topography (b), FD curves on polymer and glass (c), and force volume image by stiffness (d) and adhesion force (e).