Atomic Force Microscopy Cantilever-Based Nanoindentation: Mechanical Property Measurements at the Nanoscale in Air and Fluid

Ashton E. Enrriques; Sean Howard; Raju Timsina; Nawal K. Khadka; Amber N. Hoover; Allison E. Ray; Ling Ding; Chioma Onwumelu; Stephan Nordeng; Laxman Mainali; Gunes Uzer; Paul  H. Davis

doi:10.3791/64497

JoVE Journal > Engineering

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Ingénierie

Atomic Force Microscopy Cantilever-Based Nanoindentation: Mechanical Property Measurements at the Nanoscale in Air and Fluid

Published: December 02, 2022

doi:

10.3791/64497

Summary

Quantifying the contact area and force applied by an atomic force microscope (AFM) probe tip to a sample surface enables nanoscale mechanical property determination. Best practices to implement AFM cantilever-based nanoindentation in air or fluid on soft and hard samples to measure elastic modulus or other nanomechanical properties are discussed.

Abstract

An atomic force microscope (AFM) fundamentally measures the interaction between a nanoscale AFM probe tip and the sample surface. If the force applied by the probe tip and its contact area with the sample can be quantified, it is possible to determine the nanoscale mechanical properties (e.g., elastic or Young's modulus) of the surface being probed. A detailed procedure for performing quantitative AFM cantilever-based nanoindentation experiments is provided here, with representative examples of how the technique can be applied to determine the elastic moduli of a wide variety of sample types, ranging from kPa to GPa. These include live mesenchymal stem cells (MSCs) and nuclei in physiological buffer, resin-embedded dehydrated loblolly pine cross-sections, and Bakken shales of varying composition.

Additionally, AFM cantilever-based nanoindentation is used to probe the rupture strength (i.e., breakthrough force) of phospholipid bilayers. Important practical considerations such as method choice and development, probe selection and calibration, region of interest identification, sample heterogeneity, feature size and aspect ratio, tip wear, surface roughness, and data analysis and measurement statistics are discussed to aid proper implementation of the technique. Finally, co-localization of AFM-derived nanomechanical maps with electron microscopy techniques that provide additional information regarding elemental composition is demonstrated.

Introduction

Understanding the mechanical properties of materials is one of the most fundamental and essential tasks in engineering. For the analysis of bulk material properties, there are numerous methods available to characterize the mechanical properties of material systems, including tensile tests¹, compression tests², and three- or four-point bending (flexural) tests³. While these microscale tests can provide invaluable information regarding bulk material properties, they are generally conducted to failure, and are hence destructive. Additionally, they lack the spatial resolution necessary to accurately investigate the micro- and nanoscale properties of many material systems that are of interest today, such as thin films, biological materials, and nanocomposites. To begin addressing some of the problems with large-scale mechanical testing, mainly its destructive nature, microhardness tests were adopted from mineralogy. Hardness is a measure of the resistance of a material to plastic deformation under specific conditions. In general, microhardness tests use a stiff probe, usually made from hardened steel or diamond, to indent into a material. The resulting indentation depth and/or area can then be used to determine the hardness. Several methods have been developed, including Vickers⁴, Knoop⁵, and Brinell⁶ hardness; each provides a measure of microscale material hardness, but under different conditions and definitions, and as such only produces data that can be compared to tests performed under the same conditions.

Instrumented nanoindentation was developed to improve upon the relative values obtained via the various microhardness testing methods, improve the spatial resolution possible for the analysis of mechanical properties, and enable the analysis of thin films. Importantly, by utilizing the method first developed by Oliver and Pharr⁷, the elastic or Young's modulus, E, of a sample material can be determined via instrumented nanoindentation. Furthermore, by employing a Berkovich three-sided pyramidal nanoindenter probe (whose ideal tip area function matches that of the Vickers four-sided pyramidal probe)⁸, direct comparison between nanoscale and more traditional microscale hardness measurements can be made. With the growth in popularity of the AFM, AFM cantilever-based nanoindentation began receiving attention as well, particularly for measuring the mechanical properties of softer materials. As a result, as depicted schematically in Figure 1, the two most commonly employed techniques today to interrogate and quantify nanoscale mechanical properties are instrumented nanoindentation (Figure 1A) and AFM cantilever-based nanoindentation (Figure 1B)⁹, the latter of which is the focus of this work.

Figure 1: Comparison of instrumented and AFM cantilever-based nanoindentation systems. Schematic diagrams depicting typical systems for conducting (A) instrumented nanoindentation and (B) AFM cantilever-based nanoindentation. This figure was modified from Qian et al.⁵¹. Abbreviation: AFM = atomic force microscopy. Please click here to view a larger version of this figure.

Both instrumented and AFM cantilever-based nanoindentation employ a stiff probe to deform a sample surface of interest and monitor the resultant force and displacement as a function of time. Typically, either the desired load (i.e., force) or (Z-piezo) displacement profile is specified by the user via the software interface and directly controlled by the instrument, while the other parameter is measured. The mechanical property most often obtained from nanoindentation experiments is the elastic modulus (E), also referred to as the Young's modulus, which has units of pressure. The elastic modulus of a material is a fundamental property relating to the bond stiffness and is defined as the ratio of tensile or compressive stress (σ, the applied force per unit area) to axial strain (ε, the proportional deformation along the indentation axis) during elastic (i.e., reversible or temporary) deformation prior to the onset of plastic deformation (equation [1]):

(1)

It should be noted that, because many materials (especially biological tissues) are in fact viscoelastic, in reality, the (dynamic or complex) modulus consists of both elastic (storage, in phase) and viscous (loss, out of phase) components. In actual practice, what is measured in a nanoindentation experiment is the reduced modulus, E*, which is related to the true sample modulus of interest, E, as shown in equation (2):

(2)

Where E_tip and ν_tip are the elastic modulus and Poisson's ratio, respectively, of the nanoindenter tip, and ν is the estimated Poisson's ratio of the sample. The Poisson's ratio is the negative ratio of the transverse to axial strain, and hence indicates the degree of transverse elongation of a sample upon being subjected to axial strain (e.g., during nanoindentation loading), as shown in equation (3):

(3)

The conversion from reduced to actual modulus is necessary because a) some of the axial strain imparted by the indenter tip may be converted to transverse strain (i.e., the sample may deform via expansion or contraction perpendicular to the direction of loading), and b) the indenter tip is not infinitely hard, and thus the act of indenting the sample results in some (small) amount of deformation of the tip. Note that in the case where E_tip >> E (i.e., the indenter tip is much harder than the sample, which is often true when using a diamond probe), the relationship between the reduced and actual sample modulus simplifies greatly to E ≈ E*(1 - v²). While instrumented nanoindentation is superior in terms of accurate force characterization and dynamic range, AFM cantilever-based nanoindentation is faster, provides orders of magnitude greater force and displacement sensitivity, enables higher resolution imaging and improved indentation locating, and can simultaneously probe nanoscale magnetic and electrical properties⁹. In particular, AFM cantilever-based nanoindentation is superior for the quantification of mechanical properties at the nanoscale of soft materials (e.g., polymers, gels, lipid bilayers, and cells or other biological materials), extremely thin (sub-µm) films (where substrate effects can come into play depending upon indentation depth)¹⁰^,¹¹, and suspended two-dimensional (2D) materials¹²^,¹³^,¹⁴ such as graphene¹⁵^,¹⁶, mica¹⁷, hexagonal boron nitride (h-BN)¹⁸, or transition metal dichalcogenides (TMDCs; e.g., MoS₂)¹⁹. This is due to its exquisite force (sub-nN) and displacement (sub-nm) sensitivity, which is important for accurately determining the initial point of contact and remaining within the elastic deformation region.

In AFM cantilever-based nanoindentation, displacement of an AFM probe toward the sample surface is actuated by a calibrated piezoelectric element (Figure 1B), with the flexible cantilever eventually bending due to the resistive force experienced upon contact with the sample surface. This bending or deflection of the cantilever is typically monitored by reflecting a laser off the back of the cantilever and into a photodetector (position sensitive detector [PSD]). Coupled with the knowledge of the cantilever stiffness (in nN/nm) and deflection sensitivity (in nm/V), it is possible to convert this measured cantilever deflection (in V) into the force (in nN) applied to the sample. Following contact, the difference between the Z-piezo movement and the cantilever deflection yields the sample indentation depth. Combined with the knowledge of the tip area function, this enables calculation of the tip-sample contact area. The slope of the in-contact portions of the resulting force-distance or force-displacement (F-D) curves can then be fit using an appropriate contact mechanics model (see the Data Analysis section of the discussion) to determine the nanomechanical properties of the sample. While AFM cantilever-based nanoindentation possesses some distinct advantages over instrumented nanoindentation as described above, it also presents several practical implementation challenges, such as calibration, tip wear, and data analysis, which will be discussed here. Another potential downside of AFM cantilever-based nanoindentation is the assumption of linear elasticity, as the contact radius and indentation depths need to be much smaller than the indenter radius, which can be difficult to achieve when working with nanoscale AFM probes and/or samples exhibiting significant surface roughness.

Traditionally, nanoindentation has been limited to individual locations or small grid indentation experiments, wherein a desired location (i.e., region of interest [ROI]) is selected and a single controlled indent, multiple indents in a single location separated by some waiting time, and/or a coarse grid of indents are performed at a rate on the order of Hz. However, recent advances in AFM allow for the simultaneous acquisition of mechanical properties and topography through the utilization of high-speed force curve-based imaging modes (referred to by various tradenames depending on the system manufacturer), wherein force curves are conducted at a kHz rate under load control, with the maximum tip-sample force utilized as the imaging setpoint. Point-and-shoot methods have also been developed, allowing for the acquisition of an AFM topography image followed by subsequent selective nanoindentation at points of interest within the image, affording nanoscale spatial control over nanoindentation location. While not the primary focus of this work, specific selected application examples of both force curve-based imaging and point-and-shoot cantilever-based nanoindentation are presented in the representative results, and can be used in conjunction with the protocol outlined below if available on the particular AFM platform employed. Specifically, this work outlines a generalized protocol for the practical implementation of AFM cantilever-based nanoindentation on any capable AFM system and provides four use case examples (two in air, two in fluid) of the technique, including representative results and an in-depth discussion of the nuances, challenges, and important considerations to successfully employ the technique.

Protocol

NOTE: Due to the wide variety of commercially available AFMs and diversity of sample types and applications that exist for cantilever-based nanoindentation, the protocol that follows is intentionally designed to be relatively general in nature, focusing on the shared steps necessary for all cantilever-based nanoindentation experiments regardless of instrument or manufacturer. Because of this, the authors assume the reader possesses at least basic familiarity with operating the specific instrument chosen for performing ca…

Representative Results

Force-displacement curves Figure 7 shows representative, near-ideal F-D curves obtained from nanoindentation experiments performed in air on resin-embedded loblolly pine samples (Figure 7A) and in fluid (phosphate-buffered saline [PBS]) on mesenchymal stem cell (MSC) nuclei (Figure 7B). The use of any contact mechanics model relies on the accurate and reliable determination of the initial tip-sample contact po…

Discussion

Sample preparation
For nanoindentation in air, common preparation methods include cryosectioning (e.g., tissue samples), grinding and/or polishing followed by ultramicrotoming (e.g., resin-embedded biological samples), ion milling or focused ion beam preparation (e.g., semiconductor, porous, or mixed hardness samples not amenable to polishing), mechanical or electrochemical polishing (e.g., metal alloys), or thin film deposition (e.g., atomic layer or chemical vapor deposition, molecular beam epita…

Divulgations

The authors have nothing to disclose.

Acknowledgements

All AFM experiments were performed in the Boise State University Surface Science Laboratory (SSL). SEM characterization was performed in the Boise State Center for Materials Characterization (BSCMC). Research reported in this publication regarding biofuel feedstocks was supported in part by the US Department of Energy, Office of Energy Efficiency and Renewable Energy, Bioenergy Technologies Office as part of the Feedstock Conversion Interface Consortium (FCIC), and under DOE Idaho Operations Office Contract DE-AC07-051ID14517. Cell mechanics studies were supported by the National Institutes of Health (USA) under grants AG059923, AR075803, and P20GM109095, and by National Science Foundation (USA) grants 1929188 and 2025505. The model lipid bilayer systems work was supported by the National Institutes of Health (USA) under grant R01 EY030067. The authors thank Dr. Elton Graugnard for producing the composite image shown in Figure 11.

Materials

Atomic force microscope	Bruker	Dimension Icon	Uses Nanoscope control software, including PeakForce Quantitative Nanomechanical Mapping (PF-QNM), FastForce Volume (FFV), and Point-and-Shoot Ramping experimental workspaces
AtomicJ	American Institute of Physics	https://doi.org/10.1063/1.4881683	Flexible, powerful, free open source Java-based force curve analysis software package. Supports numerous contact mechanic models, such as Hertz, Sneddon DMT, JKR, Maugis, and cone or pyramid (including blunt and truncated). Also includes a variety of initial contact point estimation methods to choose from. Supports batch processing of data and subsequent statistical analysis (e.g., averages, standard deviations, histograms, goodness of fit, etc.). Literature citation is: P. Hermanowicz, M. Sarna, K. Burda, and H. Gabry, “AtomicJ: An open source software for analysis of force curves” Rev. Sci. Instrum. 85: 063703 (2014), https://doi.org/10.1063/1.4881683
Buffer solution (PBS)	Fisher Chemical (NaCl), Sigma Aldrich (KCl), Fisher BioReagents (Na₂HPO₄ and KH₂PO₄)	S271 (>99% purity NaCl), P9541 (>99% purity KCl), BP332(>99% purity Na₂HPO₄), BP362 (>99% purity KH₂PO₄)	Phosphate buffered saline (PBS) was prepared in the laboratory as an aqueous solution consisting of 137 mM NaCl, 2.7 mM KCl, 10 mM Na₂HPO₄, and 1.8 mM KH₂PO₄ dissolved in ultrapure water. Reagents were measured out using an analytical balance, and glassware was cleaned with soap and water followed by autoclaving immediately prior to use.
Chloroform
Diamond tip AFM probe	Bruker	PDNISP	Pre-mounted factory-calibrated cube corner diamond (E = 1140 GPa) tip AFM probe (nominal R = 40 nm) with a stainless steel cantilever (nominal k = 225 N/m, f₀ = 50 kHz). Spring constant is measured at the factory (k = 256 N/m for the probe, Serial #13435414, used here) and calibration data (including AFM images of indents showing probe geometry) is provided with the probe.
Diamond ultramicrotome blade	Diatome	Ultra 35°	2.1 mm width. Also used a standard glass blade for intial rough cut of sample surface before transitioning to diamond blade for final surface preparation
Epoxy	Gorilla Glue	26853-31-6	Epoxy resin and hardner were mixed in a 1:1 ratio, a small drop was placed on a stainless steel sample puck (Ted Pella), and V1 grade muscovite mica (Ted Pella) was attached to create an atomically flat surface for preparation of phospholipid membranes.
Ethanol
LR white resin, medium grade (catalyzed)	Electron Microscopy Sciences	14381	500 mL bottle, Lot #150629
Mesenchymal stem cells (MSCs)	N/A	N/A	MSCs for nanomechanical studies were primary cells harvested from 8-10 week old male C57BL/6 mice as described in Goelzer, M. et al. "Lamin A/C Is Dispensable to Mechanical Repression of Adipogenesis" Int J Mol Sci 22: 6580 (2021) doi:10.3390/ijms22126580 and Peister, A. et al. "Adult stem cells from bone marrow (MSCs) isolated from different strains of inbred mice vary in surface epitopes, rates of proliferation, and differentiation potential" Blood 103: 1662-1668 (2004), doi:10.1182/blood-2003-09-3070.
Modulus standards	Bruker	PFQNM-SMPKIT-12M	Used HOPG (E = 18 GPa) and PS (E = 2.7 GPa). Also contains 2x PDMS (Tack 0, E = 2.5 MPa; Tack 4, E = 3.5 MPa), PS-LDPE (E = 2.0/0.2 GPa), fused silica (E = 72.9 GPa), sapphire (E – 345 GPa), and tip characterization (titanium roughness) sample. All samples come pre-mounted on a 12 mm diameter steel disc (sample puck).
Muscovite mica	Ted Pella	50-12	12 mm diameter, V1 grade muscovite mica
Nanscope Analysis	Bruker	Version 2.0	Free AFM image processing and analysis software package, but designed for, and proprietary/limited to Bruker AFMs; similar functionality is available from free, platform-independent AFM image processing and analysis software packages such as Gwyddion, WSxM, and others. Has built-in capabilities for force curve analysis, but AtomicJ is more flexible/full featured (e.g., more built-in contact mechanics models to choose from, statistical analysis of force curve fitting results, etc.) for force curve analysis and handles batch processing of force curves.
Phospholipids: POPC, Cholesterol (ovine)	Avanti Polar Lipids	POPC: CAS # 26853-31-6, Cholesterol: CAS # 57-88-5	POPC lipid dissolved in chloroform (25 mg/mL) was obtained from vendor and used without further purification. Cholesterol powder from the same vendor was dissolved in chloroform (20 mg/mL).
Probe holder (fluid, lipid bilayers)	Bruker	MTFML-V2	Specific to the particular AFM used; MTFML-V2 is a glass probe holder for scanning in fluid on a MultiMode AFM.
Probe holder (fluid, MSCs)	Bruker	FastScan Bio Z-scanner	Used with Dimension FastScan head (XY flexure scanners). Serial number MXYPOM5-1B154.
Probe holder (standard, ambient)	Bruker	DAFMCH	Specific to the particular AFM used; DAFMCH is the standard contact and tapping mode probe holder for the Dimension Icon AFM, suitable for nanoindentation (PF-QNM, FFV, and point-and-shoot ramping)
Sample Puck	Ted Pella	16218	Product number is for 15 mm diameter stainless steel sample puck. Also available in 6 mm, 10 mm, 12 mm, and 20 mm diameters at https://www.tedpella.com/AFM_html/AFM.aspx#anchor842459
Sapphire substrate	Bruker	PFQNM-SMPKIT-12M	Extremely hard surface (E = 345 GPa) for measuring deflection sensitivity of probes (want all of the deflection to come from the probe, not the substrate). Part of the PF-QNM/modulus standards kit.
Scanning electron microscope	Hitachi	S-3400N-II	Located at Boise State. Used to perform co-localized SEM/EDS on all samples except additively manufactured (AM) Ti-6Al-4V.
Silicon AFM probes (standard)	NuNano	Scout 350	Standard tapping mode silicon probe with reflective aluminum backside coating; k = 42 N/m (nominal), f₀ = 350 kHz. Nominal R = 5 nm. Also available uncoated or with reflective gold backside coating. Probes with similar specifications are available from other manufacturers (e.g., Bruker TESPA-V2).
Silicon AFM probes (stiff)	Bruker	RTESPA-525, RTESPA-525-30	Rotated tip etched silicon probes with reflective aluminum backside coating; k = 200 N/m (nominal), f₀ = 525 kHz. Nominal R = 8 nm for RTESPA-525, R = 30 nm for RTESPA-525-30. Spring constant of each RTESPA-525-30 is measured individually at the factory via laser Doppler vibrometry and supplied with the probe.
Silicon carbide grit paper (abrasive discs)	Allied	50-10005	120 grit
Silicon nitride AFM probes (soft, large radius hemispherical tip)	Bruker	MLCT-SPH-5UM, MLCT-SPH-5UM-DC	Also MLCT-SPH-1UM-DC. New product line of factory-calibrated (probe radius and spring constants of all cantilevers) large radius (R = 1 or 5 mm) hemispherical tip (at the end of a 23 mm long cylindrical shaft) probes. DC = drift compensation coating. 6 cantilevers/probe (A-F). Nominal spring constants: A, k = 0.07 N/m; B, k = 0.02 N/m; C, k = 0.01 N/m; D, k = 0.03 N/m; E, k = 0.1 N/m; F, k = 0.6 N/m.
Silicon nitride AFM probes (soft, medium sharp tip)	Bruker	DNP	4 cantilevers/probe (A-d). Nominal spring constants: A, k = 0.35 N/m; B, k = 0.12 N/m; C, k = 0.24 N/m; D, k = 0.06 N/m. Nominal radii of curvature, R = 10 nm.
Silicon nitride AFM probes (soft, sharp tip)	Bruker	ScanAsyst-Air	Nominal values: resonance frequency, f₀ = 70 kHz; spring constant, k = 0.4 N/m; radius of curvature, R = 2 nm. Designed for force curve based AFM imaging.
Superglue	Henkel	Loctite 495	Cyanoacrylate based instant adhesive. Lots of roughly equivalent products are readily available.
Syringe pump	New Era Pump Systems	NE1000US	One channel syringe pump system with infusion and withdrawal capacity
Tip characterization standard	Bruker	PFQNM-SMPKIT-12M	Titanium (Ti) roughness standard. Part of the PF-QNM/modulus standards kit.
Ultrahigh purity nitrogen (UHP N₂), 99.999%	Norco	SPG TUHPNI – T	T size compressed gas cylinder of ultrahigh purity (99.999%) nitrogen for drying samples
Ultramicrotome	Leica	EM UC6	Equipped with a glass blade (standard, for intial sample preparation) and a diamond blade (for final preparation)
Ultrapure water	Thermo Fisher	Barnstead Nanopure Model 7146	Model has been discontinued, but equivalent products are available. Produces ≥18.2 MΩ*cm ultrapure water with 1-5 ppb TOC (total organic content), per inline UV monitoring. Includes 0.2 µm particulate filter, ion exchange columns, and UV oxidation chamber.
Variable Speed Grinder	Buehler	EcoMet 3000	Used with silicon carbide grit papers during hand polishing.
Vibration isolation table (active)	Herzan	TS-140	Used with Bruker MultiMode AFM. Sits on a TMC 65-531 vibration isolation table. Bruker Dimension Icon AFM utilizes strictly passive vibration isolation (comes from manufacturer with custom acoustic hood, air table, and granite slab).
Vibration isolation table (passive)	TMC	65-531	35" x 30" vibration isolation table with optional air damping (disabled). Used with Bruker MultiMode AFM. Herzan TS-140 "Table Stable" active vibration control table is located on top.

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Enrriques, A. E., Howard, S., Timsina, R., Khadka, N. K., Hoover, A. N., Ray, A. E., Ding, L., Onwumelu, C., Nordeng, S., Mainali, L., Uzer, G., Davis, P. H. Atomic Force Microscopy Cantilever-Based Nanoindentation: Mechanical Property Measurements at the Nanoscale in Air and Fluid. J. Vis. Exp. (190), e64497, doi:10.3791/64497 (2022).