Using Lorentz Contact Resonance to Determine the Viscoelastic Behaviour of Blended Polymers

The potential to measure mechanical properties through scanning probe microscopy (SPM) has been a huge goal as the field has advanced over the past two decades. Different measurement methods have been introduced, but the potential to reliably provide unambiguous mechanical property contrasts, particularly for soft matter such as polymer containing materials or polymers, remains elusive.

Phase imaging, in which the difference in the phase between the response and the cantilever drive is monitored, is perhaps the most common SPM method to provide contrast due to mechanical properties. Phase imaging, however, is plagued by well-known artifacts including phase shift and contrast inversion due to multiple mechanical property intricacies, such as adhesion, stiffness and dissipation.

Contact resonance (CR) has developed as a robust method to measure surface mechanical properties and was recently extended to probe viscoelastic materials¹. In contact resonance, the AFM cantilever is in contact with the sample and oscillated with small amplitudes in a direction normal to the substrate. The tip-sample contact can either be actuated through the sample or the tip.

The sensitivity of contrast to surface mechanical properties is based on the principle that the CR frequency and quality factor (Q) will change in response to changes in tip-sample stiffness and damping, as illustrated in Figure 1. Thus, if the frequency (blue) and quality factor (red) of the contact resonance peak is monitored over varied materials, both damping (dissipation) and stiffness of the material can be monitored.

Figure 1. A sample contact resonance tune showing the relevant parameters of CR frequency and quality factor to differentiate viscoelastic properties.

As a result of these developments, Anasys Instruments introduced Lorentz Contact Resonance (LCR), whereby the tip-sample contact is actuated by a magnetic field at the end of the probe.

The Lorentz force, the electromagnetic force experienced by a point charge due to an external electric field and magnetic field, is at the heart of this technology, and provides a number of key advantages over standard contact resonance methods that use piezoelectric actuation in order to actuate the tip-sample contact. Advantages of LCR include:

1. Clean contact resonance spectra. Figure 2 compares a piezo driven CR spectrum (a) with a LCR spectrum (b), where the Lorentz driven tune shows a clean spectrum with enhanced signal to noise ratio.

2. Quick broad range sweeps. Frequency sweeps of multiple cantilever flexural and torsional modes at once can now be collected (Figure 2b), which are fast and easy to measure; a typical 2 MHz sweep of a cantilever takes only 20 seconds.

3. Access to a variety of cantilever motions. The use of Thermalever™ probes with a two-arm cantilever design allows for other cantilever motions that are accessible in addition to the standard flexural modes, including asymmetric flexural and torsional modes, which provide new channels of interaction with surfaces that provide differentiation and contrast.

Figure 2. A piezo driven contact resonance tune (a) and Lorentz driven tune (b) showing a clean spectrum with improved signal to noise ratio in the Lorentz tune.

The first free air and second flexural modes of a ThermaLever probe are similar to those in a conventional single beam-like cantilever (Figure 3).

Asymmetric flexural modes result when the right and left arms of the cantilever experience uncoupled motion (bottom diagram). Torsional modes are considered to be more measurable co-ordinated techniques that combine asymmetric bending of the arms with the rocking of the cantilever end.

Figure 3. A Thermalever beam in which the two arms can exhibit a variety of motions, resulting in multiple vibrational modes. The different motions of the two arms are shown.

This article describes the application of LCR to successfully rank polymer materials based on their damping (viscous) and stiffness (elastic) properties, and its ability to quickly and cleanly sweep through multiple cantilever modes in order to choose the most sensitive modes.

In each example, the quality factor and frequency peak position are examined to provide a ranking of stiffness and dissipation for each material and then compared with bulk macroscopic storage and loss moduli (E’ and E” respectively) measured by DMA*.

Thermoplastics

LCR was applied to a tri-polymer blend comprising of polypropylene, polyethethylene and polystyrene (60%/20%/20% by weight, respectively), with an AN 200 Thermalever probe (spring constant ~0.5-3 N/m). An AFM image of the blend, shown in Figure 4b, demonstrates the possibility of differentiating the three materials through their morphology, where PE appears as bright yellow domains, PP as the matrix material and PS in the large round domain to the left. Figure 4a shows an LCR spectrum collected on all three materials, with the PP domain in blue, PE domain in red and PS domain in green.

The LCR spectra show four characteristic peaks, where the first (F1) and fourth (F4) peaks at approximately 380 kHz and 1600-1900 kHZ are identified as the first and second flexural mode. The second peak (F2) at 420 kHz is identified as the asymmetric flexural mode, while the third mode (F3) at 800-1050 kHz the torsional mode.

Differentiation among the 3 polymer materials is effortlessly observed in the first and second flexural modes (F1 and F4). The asymmetric flexuralmode (F2) shows no differentiation, while the key peak of the torsional mode (F3) at 950 kHz also shows little differentiation.

The frequency peak position normalized against the first flexural mode (F1) is plotted with the polymer storage modulus in Figure 5 and shows exceptional differentiation between the three materials in the first and second flexural modes (light blue and dark blue circles).

The LCR spectra are compared to the contact resonance spectra with conventional piezo actuation² that was collected either in a 2-point method³ marked by red triangles or in a method that collects the whole tune⁴ , marked by orange triangles. Note that the differentiation of polymer materials through LCR shows a marked development over contact resonance collected with either of the piezo actuated methods.

Figure 4. LCR spectra (a) and AFM height image (b) showing spectra of individual points on the PP matrix in blue, PE in red and PS in green.

Additionally, the other two cantilever modes of torsional (yellow) and asymmetric flexural modes (green) show less sensitivity.

The asymmetric flexural mode frequently does not involve any tip motion, thus typically minimally sensitive to either vertical, longitudinal or transverse stiffness. The torsional mode does normally exhibit sensitivity to transverse stiffness, in this case demonstrating no considerable differentiation among the three materials with this behavior.

Figure 5. Normalized frequency peak positions of the various modes comparing sensitivity to storage modulus of PE, PP, PS. The first and second flexural modes collected by LCR provide the best differentiation of the materials.

Figure 6. Quality factor of all modes comparing sensitivity to PP, PE, and PS.

Next, the tip-sample damping was examined to explore the effects of mode sensitivity on the loss modulus of the polymers, which are inversely proportional to each other.

The contact resonance curves were then fit with a damped single harmonic oscillator model in order to extract the quality factor of each individual mode. Since the calculation of the loss modulus from contact resonance data involves both the quality factor data and frequency, a direct comparison with loss modulus is not possible.

Therefore, plotted in figure 6 is quality factor against loss modulus, in order to compare the different mode sensitivities.

In Figure 6, the quality factor of the varied modes is compared with the material loss modulus, including the quality factor as measured by the conventional piezo-actuated contact resonance data. Poor sensitivity is exhibited by the asymmetric flexural (green circle), while the other LCR modes of the first (light blue circle), second flexural (dark blue circle) and the torsional modes (yellow circle) exhibit strong discrimination between the PS and PE.

The PP discrimination shows mixed results, in that it has a lower quality factor than the PE in the first flexural mode, but similar quality factor to PE in the second flexural and torsional modes. Similar sensitivity with the quality factors measured in the piezo actuated contact resonance measurements (red and orange triangles) are showed in the LCR results.

Elastomer Blend

LCR measurements on a blend of polypropylene with a brominated poly(isobutyleneco-p-methylstyrene) [BIMS] elastomer were conducted with a AN200 Thermalever probe, with results displayed in Figure 7.

The AFM image of the topography of the blend is shown revealing small <1 µm size domains of elastomer in the PP matrix, as shown in Figure 7b. Collected LCR spectra (Figure 7a) with measurements on PP (blue points) and elastomer (red points) reveal a wide range of spectra features. The peak at 280-400 kHz is identified as the first flexural mode (f1), the sharp peak at 440 kHz (f2) the asymmetric flexural mode, the sharp peak at ~1000 kHz (f3) the torsional mode and the peak at 1600-1800 kHz (f4) the second flexural mode.

Figure 7. LCR spectra (a) and AFM height image (b) showing spectra of individual points on the PP matrix in blue and elastomer domains in red.

A number of significant differences are rapidly observed in the LCR spectra between the Elastomer and PP. The peaks in the elastomer occur at significantly lower frequencies than their corresponding peaks for the PP, reflecting a considerably lower storage modulus of the elastomer than the PP.

Two arrows identifying the peaks of PP (blue spectra) and the elastomer (red spectra) in each of the first flexural (f1) and second flexural (f4) are pointed out for clarity. Moreover, the elastomer, being a severely damped material with an extremely high loss modulus, shows low quality factors in individual peaks with respect to their counterpart peaks in PP.

Table 1. (A) Ratios of PP frequency: elastomer frequency for various mordes; (B) Ratios of PP quality factor: elastomer quality factor for the various modes.

Table 1A (available in the full white paper) displays a comparison in the various modes of the ratio of polypropylene frequency to the elastomer frequency. Similar to the case of the tripolymer blend, the second flexural (f4) and first flexural (f1) modes displayed the most sensitivity between the two materials, whereas the torsional and asymmetric flexural modes show little sensitivity.

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Table 1 lists the ratio of PP quality factor to elastomer quality factor for the different modes. This data is related to the damping of the material (loss modulus) and shows exceptional sensitivity between the two materials in the asymmetric flexural mode and first flexural mode. Weak sensitivity is showed by the second flexural mode.

Conclusions

In this article, LCR was applied to effectively discriminate in both the damping and stiffness of an elastomer containing blend and a thermoplastics blend.

LCR provides a powerful method to reliably compare a variety of viscoelastic material properties with nanoscale spatial resolution, and correlate these properties with topographic and structural features. The quality factors and frequencies of individual LCR spectral peaks can be further examined to provide relevant information on the damping and stiffness of the material. Using magnetic actuation provided by LCR, the ability to cleanly and quickly tune through a wide rage of cantilever vibrational modes enables instant access to multiple avenues for discrimination.

These study results highlight the promise of LCR as a nanoscale characterization method for true differentiation of a wide range of material properties.

References

1. Yuya, P. A.; D.C.Hurley; Turner,J. A., Contact resonance atomic force microscopy for viscoelasticity. Journal of Applied Physics piezo actuation² 2008, 104 (7).

2. Yablon, D. G.; Grabowski, J.; Killgore, J. P.; Hurley, D. C.; Proksch, R.; Tsou, A. H., Quantitative mapping of viscoelasticpropertiesofpolyolefinblends withcontact resonance atomic force microscopy. Macromolecules 2012, 45 (10), 4363-4370.

3. Gannepalli, A.; Yablon, D. G.; Tsou, A. H.; Proksch, R., Contact Resonance Imaging of Nanoscale Elasticity and Dissipation. Nanotechnology 2011, 22, 355705. 4. Jesse, S.; Kalinin, S. V.; Proksch, R.; Baddorf, A. P.; Rodriguez, B. J., The band excitation method in scanning probe microscopy for rapid mapping of energy dissipation on the nanoscale. Nanotechnology 2007, 18, 435503.

4. Jesse, S.; Kalinin, S. V.; Proksch, R.; Baddorf, A. P.; Rodriguez, B. J., The band excitation method in scanning probe microscopy for rapid mapping of energy dissipation on the nanoscale. Nanotechnology 2007, 18, 435503.

*Note the comparison is conducted with time-temperature superposed values of E’ and E”. The time temperature superposition adjustment is important since bulk macroscopic DMA measurements are typically made at low frequency (e.g. 1-10Hz), while the contact resonance measurements are made at very high frequencies that are 6-9 orders of magnitude higher (kHz).

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.