Quantitative Nanomechanical Measurement of Elastic and Viscoelastic Properties with FASTForce Volume CR

Quantitative characterization of nanomechanical properties has invariably been a holy grail for atomic force microscopy. This article explains some of the industry’s earlier attempts made at quantitative nanomechanical measurement, and describes a unique method of conducting contact resonance that resolves most of the earlier problems faced with the technique.

The article also discusses the implementation, operation and application examples of FASTForce Volume contact resonance (CR), demonstrating that the method provides a quick, accessible and easy-to-use method for quantitative characterization of viscoelastic and elastic properties.

In view of the intrinsically mechanical interaction between a sample and an AFM tip, it is no surprise that several methods have evolved that take advantage of this mechanical interaction to determine material properties. Tapping mode has been around for more than 25 years and is known to be the most standard AFM imaging technique.

It includes an equally well-known phase channel that creates qualitative contrast from material properties, but accurate quantitative nanomechanical measurements have been shown to be much more challenging for tapping mode. For the quantitative measurement of mechanical properties, several other methods have been developed over the years. Force Volume and PeakForce QNM are some of the methods that have evolved to effectively measure modulus and other mechanical properties.

Contact resonance, a resonant dynamic contact-based method, is another major nanomechanical AFM capability. In this technique, the cantilever vibrates while remaining in contact with the surface where mechanical excitation takes place either through the tip¹ (ultrasonic AFM) or via the sample (atomic force acoustic microscopy).² Originally developed to quantify the elastic properties of stiff materials with enhanced sensitivity^{1, 2}, contact resonance has emerged to include capabilities to determine viscoelastic properties of loss moduli and storage (E', E", tan δ).^3–7

The FASTForce Volume CR from Bruker brings improved contact resonance capability to Dimension^® platform AFMs, allowing a faster, more accessible, robust and easily implemented way for quantitative measurement of nanomechanical properties. In Bruker’s FASTForce Volume CR, the system scans a region on the sample surface, ceasing to touch the surface at each pixel, and then sweeps the frequency of mechanical excitation, as shown in Figure 1a.

The resonant frequency as well as the shape of the contact resonance peak changes in response to the changes in the tip-sample properties, such as dissipation and stiffness (Figure 1b). It is observed that higher contact resonance frequencies relate to stiffer materials, whereas contact resonance peaks with a higher quality factor relate to less damping or dissipation.

In Figure 1b, this translates to material 2 having a lower dissipation and higher stiffness when compared to material 1. Although first developed to probe stiffness and other similar elastic properties, the theory to interpret the dissipation through the peak shape (its quality factor) was developed over the past 10 years⁴ rendering contact resonance as the ideal method for complete analysis of the materials’ viscoelastic properties. So far, the implementation of contact resonance has been limited by its complex analysis, slow imaging speed and specialized hardware for full-spectrum acquisition. By contrast, FASTForce Volume CR has removed these obstacles through flexible and user-friendly software based on highly productive and extensively-adopted FASTForce Volume.

Figure 1. (a) Operating principle of FASTForce Volume CR; (b) The effect of material properties on contact resonance frequency and quality factor, showing material 2 has higher stiffness and lower dissipation than material 1.

Implementation of FASTForce Volume CR

In Bruker’s FASTForce Volume CR, the cantilever comes closer to the surface at each point in the image and then holds on the surface while the frequency is swept to collect the contact resonance tune, and finally the cantilever is retracted.

An example of the approach (blue), hold (green) and red (retract) is shown in Figure 2, where the top panel is force vs. time, the middle panel is Z height vs. time and the bottom panel represents a contact resonance tune.

This contact resonance tune in real-time reveals three contact resonance eigenmodes at 1.5 MHz, 310 kHz and 685 kHz on polypropylene. Flat baseline and excellent signal to noise were noted on the peaks, indicating a highly damped actuator with a well-coupled sample. The first and most important step of contact resonance experiments is to acquire clean and background free contact resonance tunes with a linear response to the drive; it is the key to an effective, quantitative measurement.

Figure 2. Schematic of implementation of FASTForce Volume CR. The blue panel shows the approach of the cantilever toward the surface, then a hold segment in green, and then retraction from the surface in the red panel. The bottom panel shows a sample contact resonance tune during the hold segment.

This implementation provides numerous advantages. It first sweeps the whole frequency range up to 5 MHz, allowing immediate observation and tracking of multiple eigenmodes and also the detection of artifact peaks that should be ignored. The measurement is optimized by the ability to survey all the three modes at the same time. This is because each mode can be analyzed subsequently to choose the one with the best sensitivity and discrimination. Based on the cantilever and material, it is likely that only a single resonance eigenmode would be present in this frequency range. In which case, analysis would focus on that single mode.

This measurement, by integrating the contact resonance with force volume, also provides more data than that allowed by contact resonance alone. Adhesion as well as force-volume modulus measurement can be measured at each point along with the viscoelastic moduli afforded by contact resonance, thus providing a more detailed insight into the material properties at each point.

When compared to other imaging-based contact resonance techniques that are essentially contact mode, the force-volume-based method employed in FASTForce Volume CR also halts the XY scan during the sample-tip contact. As a result, lateral forces on the tip are minimized considerably reducing tip wear and sample damage.

The combined force volume and contact resonance measurement offers large amounts of information, reflected in the huge file sizes. For instance, a “typical” image with 128 x 128 points is approximately 200 MB, based on the length of time for each segment (approach/retract/hold) in the measurement. The software provides easy access to all the channels during real-time acquisition and is particularly developed to manage such large data files. This is combined with integrated averaging and statistics in a streamlined GUI for later analysis.

FASTForce Volume CR Operation

Contact resonance provides streamlined operation, along with ease of use, flexibility and easy visualization and analysis of large data sets. The measurement is then run through mechanical actuation of the sample in a technique called atomic force acoustic microscopy (AFAM), and two sample transducers are provided to hold a sample and a reference in order to facilitate toggling between the two.

Further, the operation of FASTForce Volume CR needs a number of critical additional parameters to a standard force ramp measurement, which are the modulation amplitude (similar to a drive amplitude), the hold time on the surface, and the start and end frequencies for the sweep. Usually, the hold time for the sweep has been the limiting step for contact resonance measurements, rendering them extremely slow.

However, in FASTForce Volume CR, the typical hold time for an entire frequency sweep can be as low as 10 ms. Together with the force-volume measurement, each pixel would therefore take approximately 20 ms to obtain. Narrowing the frequency bandwidth to a sweep of a single mode can speed up acquisition considerably, leading to the collection of a 256 x 256 image within 30 minutes. Only minimal calibrations are needed and involve locating the quality factor and resonant frequency of the cantilever’s free air oscillation modes, which are easily populated into the image file for subsequent or real-time analysis.

These calibrations are in addition to the standard spring constant and deflection sensitivity calibrations for all force volume measurements. All the required calibrations are accomplished through dedicated, step-by-step GUIs.

In addition to the conventional acquisition of the quality factor and contact resonance frequency, it is now possible to perform real-time acquisition of the stiffness, amplitude and viscoelastic parameters of loss modulus, storage modulus and loss tangent. These viscoelastic parameters are either measured in real-time or can be measured subsequently from the saved data. These channels are in addition to the parameters obtained from the force-ramp, such as the force volume modulus and adhesion.

Shown in Figure 3 are contact resonance tunes on the different components of a three-polymer blend of polypropylene (PP), polystyrene (PS) and polyethylene (PE). Initially, a sweep of all the contact resonance peaks was done, showing the three eigenmodes at 1.26 MHz, 296 kHz and 567 kHz (top panel). As shown in the bottom panel, frequency sweeps on the three materials easily distinguish between the three materials in the second model. The highest frequency (i.e. the stiffest material) was shown by the PS and the lowest frequency (i.e. the softest material) was shown by the PE.

Figure 3. A sample contact resonance tune in the top panel revealing three contact resonance eigenmodes with a clean baseline. The contact resonance mode 2 is fitted to a Lorentzian to extract the appropriate frequency and quality factor parameters for further analysis. The bottom panel shows the second contact resonance mode on three different materials, easily revealing the difference in frequency and even the quality factor of the peak on these materials.

Shown in Figure 4 are the images of frequency, topography, amplitude and quality factor from real-time analysis of the second contact resonance mode. By merely re-positioning the red cursors around the required mode, any mode can be effortlessly chosen for these real-time calculations. This data is then applied with the Bernoulli beam model with tilt and modified with the Kelvin-Voigt model⁸.

A reference sample with known mechanical properties is required to create calibration factors to study unknown samples, which in this case was the internal reference of polypropylene. If the sample lacks known components, a second actuator is available to enable calibration using a suitable reference sample. As soon as the system is calibrated, the software performs the calculations automatically and outputs quantitative maps of viscoelastic properties, including loss modulus (E") and storage modulus (E'), which are shown in Figure 4c and 4d.

From Polymers to Metals

Contact resonance is capable of measuring many different materials ranging from polymers to metals. The following sections show a few examples of contact resonance measuring viscoelastic properties of various polymers with moduli in the range of a few GPa. Examples are also provided on contact resonance probing the elastic properties of considerably stiffer materials, such as metals, semiconductors and complex inorganic films with moduli greater than 100 GPa.

With application to such a broad range of moduli and the ability to probe both viscoelastic and elastic properties, contact resonance serves as a robust tool for truly quantitative nanomechanical measurements.

Probing Viscoelastic Properties: E' and E"

As discussed before, the viscoelastic properties of three polymers such as PP, PE and PS are mapped in Figure 4. These maps show how the three materials are separated by contrast, with the contact resonance amplitude demonstrating the strongest differentiation among the components. With the storage modulus map, the PE is easily identified from the PS ad PP and the loss modulus map makes it easy to distinguish between PP and PS or PE. To calculate the loss modulus, a range of models are provided, including ones that require a reference loss modulus^9,10 and a model that does not.⁸

Figure 4. Various channels from the FASTForce Volume CR experiment: a) contact resonance frequency (dark-to-bright Z scale is 519.5 – 653.3 kHz); b) contact resonance quality factor (dark-to-bright Z scale is 1.572 to 23.3); c) storage modulus E' (dark-to-bright Z scale is 270.8 MPa to 4 GPa); d) loss modulus E" (dark-to-bright Z scale is -16.8 MPa to 374.2 MPa); e) contact resonance amplitude (dark-to-bright Z scale is -6.2 to 62.4 mV); and f) 3D rendering of topography with skin based on CR amplitude.

Shown in Table 1 is a comparison between the viscoelastic moduli obtained from the bulk measurement by dynamic mechanical analysis (DMA) against those measured by contact resonance for the maps in Figure 4. It must be noted that DMA measurements have been time-temperature superposed to the frequency of the contact resonance measurement for correct comparison.

Since the PP also serves as an internal reference in this sample, the ratio of the various moduli with regard to PP are too presented in the final two columns. For storage modulus (E') the trend of PS>PP>PE is noted to be the same with excellent agreement between the absolute storage modulus values. Two different models described above, PKAS⁸ and YHT⁹, calculate the loss modulus.

For the loss modulus (E"), the trends are again observed to be the same between the two methods of PP>PE>PS, yet the absolute values are seen to vary considerably. Loss modulus measurements rely on an exact measurement of the peak shape and quality factor calculation, and are usually less accurate when compared to storage modulus measurements that mainly depend on the frequency peak position.⁵

Table 1. Comparison between the viscoelastic moduli from the bulk measurement by DMA with those measured by contact resonance for the maps in Figure 4.

Another example of contact resonance imaging of a polymer blend of polystyrene and polycaprolactone (PCL) is shown in Figure 5. In addition, clean frequency sweeps on the sample reveal the three contact resonance modes for additional analysis. In the top set of data, the second eigenmode is selected for calculating the storage and loss moduli, showing strong differentiation between the PS and PCL materials in both channels.

On the bottom set of data, the third mode can be selected by simply repositioning the red cursors for analysis to create E' and E" maps. Since this third mode is less sensitive to the material properties, it shows less contrast between the materials in storage as well as loss modulus maps. The blue-filled points are those where the model did not fit the data and hence those points are not considered in the analysis. It must be noted that FASTForce Volume CR imaging does not degrade these soft polymers.

Figure 5. Contact resonance tunes and resulting E' and E" maps of a blend of PS-PCL: a) analysis of second eigenmode with corresponding E' map (dark-to-bright Z scale is -4.8 GPa to 4.8 GPa) and E" map (dark-to-bright Z scale is -200 MPa to 200 MPa); b) analysis of same image area but with the third contact resonance eigenmode and corresponding E' and E" maps, revealing poorer discrimination than second mode. Data acquired in collaboration with Prof. Philippe Leclére, U. Mons, Belgium.

Probing Elastic Properties of Stiff Materials

Contact resonance can also be applied to stiffer material with higher moduli; in fact the technique was first developed to study the mechanical properties of these materials with relatively soft AFM cantilevers. However, tip wear is traditionally associated with this class of measurements, directly affecting the sample-tip contact area and hence the contact resonance frequency, which is a critical parameter.

Here, this issue is prevented by using diamond-coated probes. Figure 6 shows a storage modulus map of a sample layered with chromium, aluminum and silicon. This sample covers a modulus range of tens of GPa to a couple of hundred GPa. Shown in the figure is a set of modulus maps that were collected at different loads applied on the surface from 200 nN on the left to 1000 nN on the right. The silicon component acted as the internal reference for this sample.

Figure 6. FASTForce Volume CR conducted on a sample composed of 50 nm films of aluminum and chromium on silicon at different loads. On the left is the storage modulus map imaged at 200 nN load (dark-to-bright Z scale of all images is 32.5 GPa to 320.5 GPa). In the middle is the E' map at 500 nN load and on the right is the E' map at 1000 nN load.

It was observed that the modulus measurements of all the three materials at various loads are identical (within error), as demonstrated in the bar graph comparing the measurements at varying loads (Figure 6). The error bars on the contact resonance measurements indicate the standard deviation for the particular component within the image. Also included in the chart are comparison nanoindentation measurements on all the three components. The chromium modulus determined by contact resonance, about 200 GPa, corresponds well with a modulus of 214 GPa from nanoindentation. The modulus of the auminium, 85–103 GPa depending on the load, corresponds well with the 82 GPa measured by nanoindentation.

Shown in Figure 7 is the same sample at the start (left) and end (right) of a set of 80 images (327,680 contact resonance spectra) gathered on the identical area, demonstrating no sign of degradation in either topography or the quantified modulus of the materials. Although earlier implementations of contact resonance imaging suffered from tip wear caused by contact mode imaging, the combination of FASTForce Volume CR and diamond-coated probes considerably reduces tip wear, thus allowing for repeatable and reliable measurements even on very stiff materials.

Figure 7. FASTForce Volume CR on a blend of aluminum, silicon and chromium showing initial image (left) and the same area imaged 80 frames later (right) revealing no degradation in image quality or measurement stability.

Conclusion

This article has shown how Bruker’s FASTForce Volume CR eliminated most of the challenges associated with contact resonance by combining the productivity of FASTForce Volume CR with flexible software. With easy-to-use GUIs, large data volumes are handled for simple analysis and interpretation.

It quantitatively determines the modulus (through force-volume) as well as the viscoelastic properties of viscoelastic storage modulus (E'), loss tangent and loss modulus (E"). By performing the measurement through FastForce Volume CR, acquisition speed is increased while sample damage and tip wear are reduced. Thus, FastForce Volume CR provides a quick, accessible and easy-to-use implementation of contact resonance for quantitative measurements of both elastic and viscoelastic properties relevant to many different materials, ranging from polymers to metals.

References

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This information has been sourced, reviewed and adapted from materials provided by Bruker Nano Surfaces.

For more information on this source, please visit Bruker Nano Surfaces.