Nanoscale Mechanical Property Analysis for Diverse Materials Using AFM Tools

Topics Covered

Introduction
Asylum Research’s NanomechPro Toolkit
Force Curves and Force Volume Mapping
Asylum AFMs for Force Curves and Force Mapping
Fast Force Mapping Mode
Instrumented Vertical Nanoindentation
Force Modeling
Phase Imaging
Bimodal Dual AC™ Imaging
Loss Tangent Imaging
AM-FM Viscoelastic Mapping Mode
Contact Resonance Viscoelastic Mapping
Asylum AFMs for Dynamic Nanomechanical Modes
Force Modulation Imaging
Asylum AFM Actuators
Conclusions

Introduction

For many applications, it is very important to consider mechanical properties at the nanoscale. A range of complementary AFM techniques are offered by Asylum Research in the NanomechPro™ Toolkit that allow users to measure everything from cells to ceramics.

An extensive range of nanomechanical behavior including adhesive forces, viscoelastic properties and hardness can be accurately evaluated using the NanomechPro™ Toolkit. The different techniques offer greater flexibility for a range of applications and give deeper insight via the comparison of results.

Asylum Research’s NanomechPro Toolkit

Asylum Research provides a large number of AFM techniques together known as the NanomechPro™ Toolkit, to satisfy an extensive spectrum of nanomechanical characterization needs (Table 1).

Table 1. Comparison of techniques as implemented by Asylum Research in the NanomechPro Toolkit.

Research Modes in the Asylum NanomechPro™ Toolkit Elastic Modulus Range Loss Modulus / Loss Tangent Acquisition time (256x256 image) Advantages Disadvantages
Quasistatic Modes
Force Curves / Force Volume Mapping •••••••oo
1 kPa -1 GPa
No ~3 hr (6 Hz ramp rate) Many indentation models supported, including Hertz/ Sneddon, Derjaguin MUller-Toporov (DMT), Johnson-Kendall-Roberts (JKR), Oliver- Pharr Impractically slow at higher pixel density
Fast Force Mapping Mode o••••••••
10 kPa -100 GPa
No ~9 min (300 Hz ramp rate) Relatively slow
Instrumented Vertical Nanoindentation oooo•••••
10 MPa - 100+ GPa
No Usually single points or very coarse mapping Relatively large/deep indentations. Only single points or very coarse mapping.
Force Modulation Imaging ooo••••oo
1 MPa - 1 GPa
Dissipation, but not directly tan δ ~4 min (1 Hz line rate) Can measure response at fixed frequencies over a wide range Currently only qualitative analysis in Asylum software
Dynamic Modes
Phase Imaging •••••••••
1 kPa - 100 GPa
No ~10s(20 Hz line-10 rate using small cantilevers) Rapid and simple Only qualitative contrast, can be difficult to interpret
Bimodal Dual AC Imaging •••••••••
1 kPa - 100 GPa
No ~10 s (20 Hz line rate using small cantilevers) Rapid and simple. Can provide enhanced contrast and resolution vs. phase imaging. Only qualitative contrast. Can be difficult to interpret.
Loss Tangent Imaging •••••••••
1 kPa - 100 GPa
Yes ~10 s (20 Hz line rate using small cantilevers) Rapid and simple. Quantifies loss tangent, simplifying interpretation of phase data. Quantifies only loss tangent when used without full AM-FM Mode
AM-FM Mode oo•••••••
100 kPa - 100+ GPa
Yes ~10s (20 Hz line rate using small cantilevers) Rapid and simple. Measures both E' and tan δ. Currently only supports Hertzian contact mechanics
Contact Resonance Mode oooooo•••
1 GPa - 100+ GPa
Yes ~4 min (1 Hz line rate) Measures both E' and E" Currently only supports Hertzian contact mechanics

Table 1: Comparison of techniques as implemented by Asylum Research in the NanomechPro Toolkit. The approximate elastic modulus range of applicability is shown for each mode, where the dots represent orders of magnitude in storage modulus E’ from 1 kPa to 100 GPa. Image acquisition times are given for readily achievable scan or ramp rates and assume the use of small cantilevers for techniques based on tapping mode. Actual speeds may differ depending on a variety of factors. Note that AM-FM and Contact Resonance modes are the only techniques listed that can quantitatively measure both the elastic response (E’) and viscous response (loss modulus, E” or loss tangent, tan δ).

A range of mechanical quantities, including elastic properties such as Young’s modulus, contact stiffness, storage modulus E', viscous properties such as contact damping, loss modulus E", loss tangent tan δ, adhesive and van der Waals forces, and hardness can be measured with the techniques in the NanomechPro™ Toolkit.

In this article, a number of important techniques in the NanomechPro™ Toolkit available on Asylum Cypher and MFP-3D family AFMs are discussed. Depending on the cantilever actuation frequency and the characteristic resonant frequency of the cantilever, techniques are considered as either quasistatic (near-DC or low frequency) or dynamic (higher frequency).

Quasistatic data interpretation for material properties is better known. However, latest advancements show exciting progress for high-sensitivity quantitative measurements with dynamic modes.

Force Curves and Force Volume Mapping

Surface forces can be probed using a well-known quasistatic technique, referred to as force curves. They offer quantitative data on hardness, elastic modulus, adhesive and van der Waals forces when used in nanomechanical experiments.

Force curves show maximum sensitivity when the cantilever spring constant roughly matches with the stiffness of the tip-sample contact. They are therefore ideally suited for polymeric and biological materials with elastic modulus up to only a few GPa, if standard commercial cantilevers are used.

To obtain force curves, the AFM cantilever base is lowered until the tip and the sample come into contact with one another. The movement continues and the tip indents or deforms the sample until a trigger threshold, such as a cantilever deflection or base displacement, is reached.

The cantilever is pulled away until the tip loses contact with the sample. The cantilever deflection value against the Z sensor position at the time of this load-unload cycle is converted to a force curve, with measurements of the cantilever sensitivity and spring constant.

Examples of force curves obtained on cortical neurons are shown in Figure 1. One force map can offer several images of a range of properties simultaneously measured such as adhesion, elastic modulus, and height.

Figure 1. Force mapping experiments on chemically unmodified, live cortical neuronal cells to investigate the variation of elasticity with temperature. (top) Example force curve of a cell at 25ºC (left) and 37ºC (right). The inset images show optical micrographs of the cell. (bottom) Histograms of cell elastic modulus were derived from 16µm x 16µm force maps. Noticeable variations in modulus from 25ºC (blue) to 37ºC (red) can be observed. Experiments were carried out in liquid on the MFP-3D AFM with the BioHeater temperature stage.

The number of array points and the size and location of the region of interest can be specified by the user. For individual analysis, each force curve is separately saved. Using conventional force curve methods it is not possible to directly quantify the viscous properties of the sample.

For this purpose, modifications to the basic force curve technique are required. For instance, it is possible to perform stress relaxation and creep compliance measurements by inserting a hold interval of constant force between the load and unload segments. Also adding a low-amplitude AC modulation of approximately 5 to 200Hz at the time of the hold segment allows quantitative measurements of storage and loss modulus.

Asylum AFMs for Force Curves and Force Mapping

Asylum AFMs can be used for force mapping and force curves as detailed below:

  • Only Brownian (thermal) motion limits force measurements on Asylum AFMs. In combination with the ultra-low-noise Z sensors of Asylum, both force curve axes are determined with the highest accuracy and sensitivity
  • All Asylum AFMs feature the GetReal™ software that automatically calibrates the deflection sensitivity and cantilever spring constant with a single click without ever touching the surface of the sample
  • The open architecture of the control software on all Asylum AFMs offers excellent versatility for custom experiments and allows advanced force measurements with powerful capabilities

Fast Force Mapping Mode

Force volume mapping is a great tool for the correlation of functional and structural data, however the process is slow. Asylum’s Fast Force Mapping Mode is capable of obtaining force curves at pixel rates up to 300 Hz on MFP-3D Infinity™ AFMs and at a more rapid rate on Cypher family AFMs.

Fast force mapping mode can capture a complete array of force curve in just a few minutes. A 1024x1024 pixel image captured using the Fast Force Mapping Mode on a polymer blend sample is shown in Figure 2 where features as small as approximately 10nm are resolved.

Figure 2. (top) Elastic modulus overlaid on topography for a polystyrene (PS)-polycaprolactone (PCL) blend. Imaged with Fast Force Mapping Mode on the MFP-3D Infinity AFM. Image size 4µm. The 1024x1024 pixel image would be impractically slow to obtain with conventional force volume techniques.As expected from bulk literature values, PS regions (yellow) have higher modulus (~3 GPa) than PCL regions (purple, ~350MPa). (bottom) Examples of complete force curves acquired during imaging in Fast Force Mapping Mode. The curves on PS have higher slope than those on PCL, indicating higher modulus.

Without any hidden data manipulation, the entire force curve for each image pixel is captured and saved in the Fast Force Mapping Mode. Offline and real time analysis models can be applied for determining adhesion, modulus and other properties.

If desired, models can be fully accessed for user modification or inspection. Depending on the cantilever choice, fast force mapping mode is applicable to samples with modulus from approximately 10kPa to over 100GPa.

Instrumented Vertical Nanoindentation

The elastic modulus and hardness on micro- to nanometer length scales can be determined using instrumented nanoindentation. Though the technique is particularly useful on highly stiff materials (elastic modulus greater than 100GPa) such as ceramics and metals, it can be applied on compliant materials such as polymers too.

AFM force curve techniques use a cantilever that is mounted at an angle with respect to the sample plane. However, instrumented nanoindentation techniques push a very stiff tip, such as diamond or sapphire, vertically into the sample and then retract it.

The resulting sample deformation and the applied force are directly determined during the complete load-unload cycle. Elastic modulus and hardness values are obtained from the force-deformation curves with a model for the tip-sample contact (usually Oliver-Pharr). The pressure applied is sufficiently high to deform the sample, with typical applied forces ranging from µNs to mNs and a tip-sample contact area of ~1 µm2.

The exclusive NanoIndenter™ option from Asylum Research for MFP-3D AFMs combines the AFM with instrumented nanoindentation. Combining the indenter and the AFM offers the additional benefit of quantifying indentation contact areas. AFM determination of the tip area function enables material property analysis with unrivalled accuracy relative to indirect calculation methods. AFM metrology of sample indentations (Figure 3) yields experimental data for enhancing accuracy of analysis theories.

Figure 3. (top) AFM topography image of an indent created in fused silica by the MFP-3D NanoIndenter option with a Berkovich diamond tip. Scan size 1 µm. (bottom) The experimental indentation data agree very well with finite element modeling predictions and yield a Young’s modulus of 70.3GPa for fused silica.

Force Modeling

From AFM and nano-indentation force curves, it is possible to obtain quantitative data on mechanical properties including hardness, elastic modulus and adhesion.

The software offered by Asylum Research contains a range of analysis models for flexibility and convenience. It is possible for an investigator to alter the different parameters in each model from the main software panel as required. Furthermore, the open architecture of Asylum Research software makes all routines accessible for user modification, if desired.

Pre-programmed models in the software include:

  • Hertz / Sneddon: According to this popular model, the tip-sample interaction is linearly elastic. The impact of adhesion or other surface interactions are not included. The software by Asylum Research allows the user to select from a number of tip shapes including hemisphere, cone, and flat punch.
     
  • Johnson-Kendall-Roberts (JKR): In cases where the adhesive contact between the tip and the sample is strong, the JKR model is used. Inside the contact area alone, adhesion effects are included. It is applicable in cases where the tip radius is comparatively larger than the indentation depth.
     
  • Derjaguin-Müller-Toporov (DMT): The DMT model is beneficial for samples with weak but detectable adhesive forces. Outside the contact area only, attractive interactions, such as adhesion, are included. This model is most useful for stiffer samples that have low adhesion, and when the tip radius is comparatively smaller than the sample indentation depth.
     
  • Oliver-Pharr: In cases where permanent plastic deformation to the sample is caused by the indentation process, this model is used. It is used mainly on data from instrumented vertical nanoindentation devices such as the Asylum Research MFP-3D NanoIndenter option.

Figure 4 shows the excellent capabilities for force curve analysis available in Asylum Research software. The software includes an exclusive model selection guide to study a number of parameters including plasticity index, force-to-adhesion ratio, and Tabor coefficient. The selection guide allows users to find out the most suitable mechanical model for their data.

Figure 4. Example of force curve modeling with Asylum Research software. The top window shows a force curve acquired on a silicone elastomer gel. The applied force versus sample indentation is shown for both the extend (red) and retract (blue) segments of the cantilever loading- unloading cycle. The bottom window shows the extensive features of analysis software on all Asylum AFMs. As suggested by the Model Selection Guide (center of panel), a JKR fit was applied. The resulting fitted values are displayed in the bottom right of the analysis panel and are used to generate the black dotted line on the force curve.

Phase Imaging

Since the first time it was demonstrated in the 1990s, tapping mode with phase imaging has become a highly valuable technique as it can provide contrast between different sample components.

The phase response is not only based on the mechanical properties of the sample but also on other operational parameters and dissipative forces. The contrast may even reverse based on operating conditions. Phase imaging is still widely used as it is very easy to measure.

Bimodal Dual AC™ Imaging

The simultaneous excitation of two resonant frequencies of the cantilever is referred to as Bimodal AFM. The lower, or the first, mode operates just like the regular tapping mode in bimodal AFM. In the patented Bimodal Dual AC technique from Asylum, a second, higher-order cantilever resonance is simultaneously driven along with the first mode and its phase response and amplitude are also determined. As seen in Figure 5, phase images and bimodal amplitude can offer improved contrast and spatial detail.

Figure 5. Bimodal Dual AC images of (left) mode 1 phase and (right) mode 2 phase for a tire sample. The sample contained a blend of several rubbers as well as carbon black and silica. The higher-mode mage shows increased contrast and finer detail. Scan size 500 nm; data scale in both images is 43°. Imaged with the Cypher S AFM.

Loss Tangent Imaging

The loss tangent tan δ = E"/E' considers viscous dissipation and elastic energy together instead of treating them separately. It is measured in AFM experiments from the ratio of dissipated energy to stored energy per cycle of the tip’s periodic deformation.

As a ratio the loss tangent alone does not differentiate if contrast is due to loss modulus or storage variations, it can often distinguish sample components in cases where phase or topography cannot. Loss tangent imaging offers useful estimates for assessing viscoelastic materials, as seen in Figure 6.

Figure 6. Image of loss tangent tan δ for a commercial coffee packaging bag in cross-section. Sample features including vapor barriers, “tie” layers, and a metal layer are clearly distinguished. Scan size 15 µm.Imaged with the Cypher S AFM.

AM- FM Viscoelastic Mapping Mode

Asylum Research’s exclusive AM-FM Viscoelastic Mapping Mode was derived from AFM principles for quantitative mapping of viscoelastic properties. It can be applied from hundreds of kPa to over 100GPa in terms of storage modulus, making it a highly versatile technique. The data obtained from the AM-FM mode include storage modulus, contact stiffness, loss tangent, and loss modulus.

Similar to Bimodal Dual AC Imaging, AM-FM Mode uses tapping mode operating concurrently at two different cantilever mode frequencies. As AM-FM and tapping mode work similarly, it has all the benefits of tapping mode including high spatial resolution, fast scanning, and gentle forces, and as a scanning method, it is more rapid than methods based on individual force curves.

It is also observed that the AM-FM mode deforms the sample lesser than force curves or contact methods such as contact resonance and force modulation imaging. Figure 7 shows an example of AM-FM Mode on a metallic solder.

Figure 7. Elastic modulus overlaid on topography of a tin/lead alloy solder. Tin-rich (lighter) and lead-rich (darker) regions can be identified. Scan size 8µm. Acquired in AM-FM Mode on the Cypher S AFM at 1.5Hz line scan rate with blueDrive™ photothermal excitation.

Contact Resonance Viscoelastic Mapping

Contact resonance is another dynamic mode, which allows quantitative imaging at high resolution of both viscous loss modulus and elastic storage modulus. It is suited for materials with moderate to high modulus (approximately 1-200GPa). In this mode, a cantilever vibrational resonance is excited while the tip is in contact with the sample.

Figure 8 shows an instance of Contact Resonance Mode imaging on a patterned thin film on silicon. Similar to other techniques, the contact resonance mode can be operated either with the least calibration for rapid qualitative imaging or can be calibrated with a material of known properties for more quantitative results.

Figure 8. Elastic modulus map overlaid on topography for a patterned titanium film on silicon. Acquired in DART Contact Resonance Mode with blueDrive photothermal excitation on the Cypher AFM. Scan size 25µm. Note the ability of Contrast Resonance Mode to provide strong contrast between two materials with very high modulus.

Asylum AFMs for Dynamic Nanomechanical Modes

Details on Asylum AFMs for dynamic nanomechanical modes are given below:

  • GetStarted™ software automatically sets tapping mode parameters and reduces setup time on MFP-3D Infinity AFMs for phase and loss tangent imaging
     
  • AM-FM Mode provides quantitative nanomechanical property mapping at more rapid speeds when compared to other methods when performed on Cypher family AFMs with small cantilevers
     
  • With Asylum’s exclusive Bimodal Dual AC™ Mode, software controls allow simultaneous excitation at two frequencies with independent drive amplitudes. The detected photodiode signal is processed simultaneously by two lock-in amplifiers to measure the phase and amplitude at both frequencies
     
  • Dual AC™ Resonance Tracking (DART) and Band Excitation (BE) are proprietary Asylum techniques for imaging in Contact Resonance Mode. DART captures both resonance frequency and quality factor while operating at normal imaging rates, or even at fast scanning rates with small cantilevers on the Cypher AFM. BE records the full resonance spectrum, making it a complementary technique to confirm DART results or to apply more complex analysis models
     
  • Using the Asylum’s ModeMaster™ software feature, working with dynamic modes is more rapid and easier.It automatically configures the software and guides you through the experiment. For techniques like AM-FM Mode and Contact Resonance Mode, the software panel assists in both setting up the measurement and performing calibrations with a reference sample of known
    modulus. This lets you start making measurements with well-established methods but without the full complexity
     
  • GetReal software which is free on all Asylum AFMs helps easy and precise calibration of cantilever spring constants. Spring constant values are needed, for example,
    to measure absolute contact stiffness with AM-FM Mode and absolute applied force in Contact Resonance Mode

Force Modulation Imaging

This was one of the earliest AFM techniques formulated for quantitative imaging of nanomechanical properties. It is suited for relatively compliant samples such as biomaterials and polymers.

Figure 9 shows force modulation imaging on a multilayer polymer sample. Asylum Research provides actuators with a high bandwidth and a flatter frequency response than previously available, offering exciting new possibilities for force modulation.

Figure 9. Force modulation amplitude overlaid on topography for a polymer sandwich. The sample contained layers of (left to right) Viton fluoroelastomer, epoxy, and ethylene propylene diene monomer rubber (EPDM). The difference in hardness between Viton® (Shore A 78) and EPDM (Shore A 58) is clearly resolved.

The actuators enable force modulation measurements over a broad frequency range with very high amplitudes. This will not just offer enhanced and often mechanical contrast in a number of applications, but will also allow precise measurements of frequency-dependent mechanical characteristics.

Asylum AFM Actuators

The demands placed by dynamic modes, such as AM-FM Viscoelastic Mapping Mode and Contact Resonance Viscoelastic Mapping Mode, on the excitation source are more stringent than the standard tapping mode. For example, a very even frequency response or very high bandwidth may be required. Asylum Research offers a number of alternatives to the cantilever holder’s piezoelectric actuator.

Asylum’s sample actuators, which can be seen in Figures 10 (a) and 10 (c), provide very high performance for high-frequency force modulation and contact resonance AFM. With oddly shaped or large samples or when using a heating stage, the sample cannot be actuated in contact resonance mode or frequency modulation. In such cases Asylum offers AM-FM Probe holders Figures 10 (b) and 10 (d).

Asylum also offers the blueDrive photothermal excitation option for Cypher family AFMs that enables superior and stable actuation as it deploys a laser in place of a mechanical actuator.

Figure 10. High-frequency actuation options: (a) sample actuator and (b) cantilever holder for MFP-3D family AFMs, (c) sample actuator for Cypher S AFM, and (d) cantilever holder for Cypher S and ES AFMs. (e) Conceptual drawing of blueDrive photothermal excitation for Cypher family AFMs. The focused blue laser excites the cantilever, while the standard red laser is used for imaging feedback and monitoring.

Conclusions

In order to understand the behaviour and performance of a material, it is important to gain insight into its mechanical properties at the nanoscale. The availability of different advanced material systems implies that no single AFM technique can offer precise, comprehensive information for every need.

Asylum Research offers a range of techniques in the NanomechPro™ Toolkit, so that the best approach for a particular application can be selected. The various techniques can be used together on almost any material and a broad range of properties can be measured including loss and storage modulus, elastic stiffness, viscous damping, adhesion, and hardness. With a range of modes, complementary information can be obtained by probing different types of mechanical response.

This information has been sourced, reviewed and adapted from materials provided by Asylum Research - An Oxford Instruments Company.

For more information on this source, please visit Oxford Instruments Asylum Research.

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