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

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 point. Thus, the relatively flat, low-noise baseline preceding the initial contact point and the smooth slope of the contact portion of the F-D curves shown in Figure 7 makes them ideal for analysis to extract mechanical properties, as evidenced by the excellent agreement between the approach curves (blue traces) and corresponding fits (green traces) in the insets.

Conversely, there are several common issues that a user may encounter while performing cantilever-based nanoindentation that will lead to nonideal F-D curves. One of the most common issues, particularly immediately after engaging, is the probe tip already being in contact with the sample prior to initiation of a ramp (Figure 5A), which prevents the acquisition of the necessary out-of-contact baseline for determining the initial contact point. This can also lead to excessively large forces in the case of untriggered (i.e., controlled displacement) ramps. This is of particular concern when performing a large ramp with a stiff cantilever, as the resulting forces may break the cantilever and/or damage the sample or tip. To avoid this, monitor the vertical deflection voltage during and after the initial engage. If the measured vertical deflection voltage is positive (assuming proper initial alignment) as shown in Figure 2B, then the cantilever is being deflected and the tip is in contact with the sample. Larger positive voltages correspond to larger cantilever deflections, but regardless of the magnitude of the deflection, the user should manually raise the AFM head (e.g., by employing a stepper motor) away from the sample. The vertical deflection voltage should slowly decrease and may even temporarily dip below zero in the case of strong tip-sample adhesive forces, but will eventually reach 0 V (or close to 0 V) once the tip is no longer in contact with the sample (Figure 2A). From this point, the user can resume optimizing the ramp parameters and performing indents.

Another common problem (particularly for untriggered ramps) is for the entire F-D curve to appear nearly flat, with no obvious sign of tip-sample interaction, as shown previously in Figure 5B. If available on the instrument, the solution to this is to manually lower the SPM head by ~10% less than the ramp size (to avoid crashing the probe tip) and ramp again, repeating until an obvious increase in force is observed due to tip-sample interaction (Figure 5C,D) before proceeding to optimize other ramp parameters.

Tip wear
Figure 8 presents an example of tip wear in an experimental setting. A single, stiff, silicon tapping mode AFM probe (see Table of Materials) was used to image several large areas of a Bakken shale sample (see corresponding application example for more details) using a rapid (kHz rate) force curve-based imaging method, and the BTR method was used to model the tip geometry and estimate the tip end radius before and after each of three consecutive images. The shale samples under investigation consisted of a matrix of clay and organic material (E ~5 GPa) with much harder inorganic mineral inclusions dispersed throughout (E > 30 GPa). Because the sample contained significant variations in surface topography (±2 µm) across the large scan areas (85 µm x 85 µm) imaged, the scan rate was set to the minimum allowable on the instrument used, 0.1 Hz. With a force curve acquisition rate of 2 kHz and a scan rate of 0.1 Hz, over the course of a single 1024 x 1024 pixel image there were over 20 million tip-sample interactions. As a result, the probe tip experienced significant wear relative to its pristine state (Figure 8A) over the course of imaging the sample, increasing by over an order of magnitude from an effective end radius of ~11 nm as received to ~129 nm at the conclusion of the three images (Figure 8D). During the first image the tip appears to have been broken, resulting in the large morphological change seen in Figure 8B. In each subsequent image, the tip becomes progressively more rounded, an excellent example of the more common phenomenon of gradual wear (see discussion). The estimated tip radii from the BTR models are included in Figure 8.

In contrast, Figure 8E,F presents BTR models of a diamond tip probe (see Table of Materials) acquired 6 months apart, with thousands of nanoindents and hundreds of millions of force curve imaging based tip-sample interactions occurring in between. As can be seen from the estimated tip radii of 29 nm (Figure 8E) and 28 nm (Figure 8F), the probe tip radius did not change within the limits of the BTR method, highlighting the extreme wear resistance of diamond. It should be noted, however, that diamond tip probes (like all AFM probes) are susceptible to contamination from loosely adhered debris that can impact the tip area function and effective hardness. Accordingly, sample cleanliness remains vital for tip preservation and accurate nanomechanical measurements.

Application examples
Through the judicious choice of probe material composition, cantilever spring constant, and tip geometry and radius, cantilever-based nanoindentation can be used to quantify the nanoscale mechanical properties of materials with elastic moduli ranging from kPa to GPa, both in fluid and under ambient conditions. Selected application examples follow to highlight a few of the wide range of use cases possible for cantilever-based nanoindentation.

Investigation of loblolly pine mechanical properties for biofuel applications
Loblolly pine trees (Pinus taeda) are a fast-growing softwood species that are highly abundant in the southern United States, occupying over 13 million hectares³¹. Because of their abundance, loblolly pine trees are a critical commercial crop in the southern US, commonly used for both timber and pulp wood. Additionally, they are an important resource for second-generation cellulosic biofuels production³². Importantly, demand has been growing for cellulosic biofuel feedstock due to the Energy Independence and Security Act (EISA) of 2007, which mandates that by 2022, total renewable fuel usage in the US transportation industry should be 36 billion gallons, with 16 billion gallons being derived from cellulosic biomass. Accordingly, due to loblolly pine's fast growth rate and amenability to agroforestry projects, it has become a biofuel feedstock of great interest in recent years³³. Knowledge of the mechanical properties of loblolly pine, including variability across individual trees, anatomical fractions (e.g., whitewood, bark, needles), and cell areas (e.g., cell wall versus interior), may allow for the targeted separation of biomass streams to optimize mechanical processing and thermochemical conversion³⁴.

Figure 9 presents a representative AFM topography (height sensor) image (Figure 9A) and corresponding elastic modulus map (Figure 9B) of a cross-section sample of whitewood obtained from a branch on a 23-year-old loblolly pine with a ~30 nm radius of curvature diamond tip probe mounted on a stainless steel cantilever (k = 256 N/m). The topography and modulus maps were generated simultaneously using rapid kHz rate force curve-based AFM imaging, with the modulus map presenting semi-quantitative results based on nominal values for the probe calibration constants (i.e., spring constant, deflection sensitivity, and tip radius) and fitting the force curves in real time to the DMT (Derjaguin, Muller, and Toporov) contact mechanics model³⁵. Cross-sectioned samples trimmed to be <3 mm in all three dimensions (length x width x height) were prepared for imaging by serial dehydration using increasing concentrations of ethanol (33%, 55%, 70%, 90%, and 100%)³⁶, before infiltrating with resin (see Table of Materials) and polymerizing at 60 °C overnight. Fully cured resin-embedded samples were first ground, then ultramicrotomed with a diamond blade operating at a cutting speed of ~1 mm/s with a feed thickness decreasing from 1 µm down to 50-70 nm per slice to produce a flat surface amenable to AFM imaging. However, as can be seen by the color scale bar in Figure 9A, the resultant surface in this case is still relatively rough, perhaps due to the presence of residual debris on the sample surface and/or ultramicrotome blade, leading to blade "chatter" during sectioning, whereas other samples exhibited much smoother surface topography.

Figure 9C reproduces the AFM topography image from Figure 9A, but with white crosshairs indicating the locations for eight arrays of 50 nanoindents apiece to be performed along selected cell walls within the ROI, as the goal of the project in question was to understand how the nanomechanical properties of loblolly pine differ across various tissue types and tree age. A trigger threshold of 1 µN was typically employed for the ramps (60 nm nominal ramp size conducted at a 1 Hz ramp rate), leading to an indentation depth of ~10 nm along the cell walls (8 ± 2 nm across all samples studied) or slightly deeper (14 ± 4 nm) in the cell interiors, which are somewhat softer than the cell walls. Indents within each line were spaced ≥100 nm apart to ensure they were well separated, and 1,024 data points were collected per ramp to produce well characterized approach and retract curves. By combining rapid force curve-based imaging with point-and-shoot cantilever-based nanoindentation, it was possible to generate statistics and determine differences in moduli across cell structures. For example, as shown in Table 1, it was found that the average elastic modulus of the cell interior was about half that of the cell wall across whitewood samples derived from multiple branches of trees of varying ages.

Table 1: Loblolly pine elastic modulus statistics: cell walls versus cell interior. Measured elastic moduli of the cell walls versus cell interiors for five loblolly pine whitewood branch samples collected from two trees of differing ages. All modulus values were calculated by fitting the approach portion of the force displacement curve to the DMT model and assuming a Poisson's ratio of 0.3 for the sample. Moduli are reported as average ± standard deviation for each sample location, with the number of force curves (count, n) analyzed to produce the reported result indicated. Measured reduced moduli (E*) were converted to actual sample moduli (E), assuming a Young's modulus of 1,140 GPa and Poisson's ratio of 0.07 for the diamond tip indenter employed. Also shown is the average sample deformation for the applied load of 1 µN.

Correlated nanomechanics and electron microspectroscopy on Bakken shales
Bakken shale deposits are found within the Williston Basin in Montana and North Dakota in the United States and parts of Saskatchewan in Canada. They are the second largest hydrocarbon reservoir in the United States, but study of the deposits is still in its infancy³⁷. An investigation of the nanomechanical properties of Bakken shale as a function of composition and thermal maturity was conducted by co-localizing AFM cantilever-based nanoindentation with scanning electron microscope (SEM) imaging and energy dispersive spectroscopy (EDS) elemental composition characterization, as shown in Figure 10. Specifically, SEM-EDS mapping was used to characterize the elemental distribution (Figure 10C), thereby determining the presence and location of various mineral inclusions within the shale matrix. Rapid (kHz rate) force curve-based AFM imaging (Figure 10B) was co-localized with the SEM-EDS maps by defining an optically identifiable origin in the secondary electron (SE) SEM image (Figure 10A) and tracking the stage movement of both the AFM and SEM³⁸. By again utilizing a diamond tip probe mounted on a stiff stainless steel cantilever, mapping of variations in the elastic modulus was possible for large regions (85 µm x 85 µm) containing inclusions of interest (Figure 10D). Note that the modulus map presented in Figure 10D is qualitative rather than quantitative in nature, as the proper probe calibration constants were not entered into the software prior to imaging and data acquisition.

The AFM images in Figure 10B and Figure 10D also highlight one of the drawbacks of the diamond tip probe employed, namely its inability to accurately track high aspect ratio features (see the black oval region in Figure 10B) due to its cube corner tip geometry. The reduced resolution and inability to accurately track steep features can be more clearly seen in Figure 11, where the same general area of a Bakken shale sample has been imaged by the cube corner diamond tip (Figure 11A) and a significantly sharper, higher aspect ratio stiff tapping mode silicon AFM probe (Figure 11B). More specifically, the image shown in Figure 11B was acquired with the probe characterized in Figure 8A–D, between the BTR models in Figure 8A (R = 11 nm) and Figure 8B (R = 43 nm). For direct comparison, image pairs Figure 11C,D, along with Figure 11E,F, present zoomed-in images of the same sample surface features obtained with the diamond tip and silicon probe, respectively, showing the effect of tip geometry and radius on image resolution and fidelity. Figure 11G presents a composite 3D image combining the surface topography acquired with the sharp, high aspect silicon probe (Figure 8A,B) and the modulus values acquired with the diamond tip probe (Figure 8E,F) encoded as the overlaid colored skin.

In addition to the large images shown in Figure 10 and Figure 11, smaller (10 µm x 10 µm) rapid force curve-based images were acquired using the fully calibrated diamond tip probe. These images focused on areas with no optically visible inorganic mineral inclusions to investigate the properties of the surrounding organic matrix in more detail. By employing a pixel resolution of 512 x 512 (i.e., ~20 nm x 20 nm sampling pixels), >262,000 individual F-D curves were captured and saved with each 10 µm x 10 µm image, enabling excellent statistics. The F-D data was batch processed and analyzed using the AtomicJ software package²³ to implement the Derjaguin-Muller-Toporov (DMT)³⁵ contact mechanics model. Following fitting, the data were cleaned to remove curves that resulted in a calculated elastic modulus <0 (non-physical) or >30 GPa (since the study was focused on the non-mineral portion of the shale, E << 30 GPa) similar to other studies^39,40, as well as data with a model fit R² < 0.7. While the R² cutoff is somewhat arbitrary, it was chosen to only remove data the model obviously could not accurately fit. With the exception of one outlier that included a large mineral inclusion in the imaging area, the curves removed accounted for less than 0.5% of the total data for each image. A summary of the statistical results can be found in Table 2. The calculated elastic moduli vary from 3.5 to 6.1 GPa, within the range of what similar studies have also found^39,40.

Table 2: Bakken shales' elastic modulus statistics. Measured elastic moduli of the organic matrices in three Bakken shale samples of different composition and thermal maturity. Sample 1 is a control, while samples 2 and 3 were annealed for 12 h and 48 h, respectively, to artificially simulate thermal maturation. Elastic moduli are reported as average ± standard deviation for each sample location, with the number of force curves (count, n) included in the analysis after employing the data cleaning procedure described in the text indicated. The calculated average moduli (3.5-6.1 GPa) fall within the range reported in other similar studies such as that of Li et al.⁴⁰, which found a modulus range of 2.9-11.8 GPa.

Mesenchymal stem cell nuclear stiffness changes due to external stimuli
Mesenchymal stem cells (MSCs) are progenitor cells that can become chondrocytes, adipocytes, osteoblasts, and myocytes⁴¹. MSC differentiation into these various tissue types is affected by external mechanical stimuli on the cell via the Linker of the Cytoskeleton and Nucleoskeleton (LINC) complex, which physically links the outer cell membrane to the nuclear membrane⁴¹. The LINC complex is composed of SUN and Nesprin proteins that interact with the cell cytoskeleton to detect physical forces on the cell and facilitate nuclear import of the mechanosensitive factors β-catenin and YAP to initiate the differentiation process^42,43,44. Along with the nuclear import of β-catenin and YAP after the mechanostimulation of cells, the cytoskeleton also undergoes rearrangement, including the formation of F-actin filaments around the nucleus as well as the nuclear translocation of actin^44,45,46. Because mechanostimulation initiates changes to the cell cytoskeleton and nuclear entry of actin, the overall stiffness (modulus) of cells and nuclei is affected and can be measured by AFM cantilever-based nanoindentation. Previous studies have confirmed this by detecting a decrease in cell and nuclear modulus after disruption of the LINC complex, and inversely an increase in cell and nuclear modulus after the mechanostimulation of MSCs⁴⁷. Current research is still investigating the mechanisms for actin import to the nucleus and how actin polymerization affects cell and nuclear modulus after mechanostimulation.

To investigate the mechanical properties of live cells, the experiments must be conducted in a buffer solution, typically PBS. Conducting cantilever-based nanoindentation in fluid poses unique problems, specifically for the measurement of very soft samples such as MSCs (E≈ 2 kPa). In particular, the low elastic moduli of living cells necessitates the use of a large probe radius to reduce the stress imparted on the cell structure and avoid puncture of the membrane. Additionally, very low spring constant cantilevers (k = 0.04 N/m) are necessary to measure such low elastic moduli, but this increases the probability of false engaging due to the viscous drag of the fluid, leading to deflection of the soft cantilever during the initial fast lowering step of the AFM engage process. To counteract the higher propensity for false engages, it may be necessary to utilize a larger engage setpoint (i.e., deflection voltage trigger threshold to end the engage process). Since softer cantilevers can generally be elastically deformed to a greater extent than stiff cantilevers, the greater bending experienced with a higher engage setpoint in fluid is generally not detrimental to such soft probes. In addition, it is imperative that the solutions used in a fluid environment are free of debris and bubbles, as floating debris or bubbles can transiently interfere with transmission of the laser through the fluid to the PSD or adhere to the cantilever and block the laser. Interference with the laser beam will negatively impact the resultant F-D curves and often results in false crash detection or false engaging. Finally, nanoindentation on live cells also requires more user input than on harder, inanimate materials. In particular, because the cells and their fluid environment are much more dynamic, it may be necessary to actively adjust the height of the probe for each ramp to ensure a good F-D curve is obtained.

In live cell nanoindentation, much larger sample deformation is often needed to result in the same cantilever deflection relative to stiffer samples. This larger deformation can result in experimental results deviating from the Hertz model's assumption of linear elasticity, and hence a correction factor may need to be applied to account for the hyperelastic behavior for accurate F-D analysis⁴⁸. It has been found that the geometric size ratio , where R₂ is the radius of the indenter and R₁ is the radius of the cell (see Figure 12A), can be used to predict the resulting data's adherence to Hertzian mechanics. The ideal geometric size ratio has been found to be β = 0.3, with β values <0.3 leading to underestimating the elastic modulus and β values > 0.3 leading to overestimating the elastic modulus when analyzed with Hertz contact theory⁴⁸. One common way to avoid nonlinear effects is to keep deformations small. In this study, the indentation depth was limited to 500 nm-1 µm.

A representative data set showing results of a single set of nanoindentation experiments on MSCs and isolated nuclei is shown in Figure 12B. In the data presented in Figure 12B, precalibrated (spring constant via LDV and tip radius via SEM), 5 µm radius hemispherical probes with a nominal spring constant of k = 0.04 N/m were used to investigate differences in modulus between intact live MSCs and isolated MSC nuclei, which served as controls to test the effects of static and dynamic strains on cell and nuclear mechanical properties⁴⁶. Due to differences between and challenges in engaging on the cells and nuclei, the extracted modulus data tends to exhibit a large variation (i.e., distribution of values). Accordingly, the dataset in Figure 12B presents a 75^th percentile of the data collected. Due to this innate variability among live cells and resultant measurement spread, it is recommended to conduct replicate nanoindentation experiments on large numbers of samples with at least three biological replicates in order to generate robust statistics for data analysis and interpretation³⁰.

Mechanical properties of cholesterol-containing lipid bilayers
Supported lipid membranes with very high (>50 mol%) cholesterol (Chol) content, typical of the composition found in eye lens membranes, were prepared and incubated on freshly cleaved muscovite mica⁴⁹. A representative AFM topography image of such a supported lipid membrane (SLM) prepared at a Chol/POPC (POPC = 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine) mixing ratio of 1 is shown in Figure 13A, with the height profile along the purple line in the image shown below the figure. The SLM in Figure 13A completely covered the exposed mica surface with sufficient incubation time (~25 min) and a sufficient lipid concentration (0.3 mg/mL), as evidenced by the lack of distinguishable features in the topography image. Likewise, the height profile across the image provides structural details regarding the roughness of the membrane surface, with the SLM smooth as expected.

Figure 13B presents a collection of approach sections of force curves captured on the SLM shown in Figure 13A. To achieve better statistics regarding the mechanical properties of the SLM, force curves were collected at equidistant points spaced at least 100 nm apart, covering almost the entire width of the SLM. The spacing between points (≥10x the indentation depth) was chosen to prevent indenting from occurring too close together. The force curves show a clear breakthrough event, as evidenced by the discontinuity or sudden jump between the ~0 and ~5 nm separation distances in the approach section of the force curves where the force drops precipitously from ~10 nN to ~5 nN. The average breakthrough force for the membrane shown in Figure 13A (Chol/POPC mixing ratio of 1) based on the approach curves in Figure 13B is calculated to be 9.25 ± 0.27 nN.

In contrast, Figure 13C shows an AFM topography image of the partial membrane or membrane patches formed by again incubating membranes at a Chol/POPC mixing ratio of 1, but at a much lower concentration of lipids (~15 µg/mL) and with a shorter incubation time (~5-6 min)⁴⁹. The height profile along the red line across the membrane patch in the center of the image is shown below the figure. The measurement across the partial bilayer provides the thickness of the SLM, shown by the black dashed lines in Figure 13C to be ~7 nm. However, this measured thickness also incorporates a 1-2 nm water layer between the membrane and the mica disk⁵⁰. It should be noted that the partial membrane is often only weakly attached to the mica surface, which can cause lipid particles to be removed from the edge of the partial membrane patches during scanning, but a slightly longer incubation time or lowering the imaging force can eliminate this difficulty.

Calibration of the AFM probe is crucial to accurately quantify SLM mechanical properties. In particular, although the tip spring constant remains consistent in air or fluid medium, the deflection sensitivity must be calibrated in the same medium where experiments are performed. It is critical to calibrate the deflection sensitivity immediately before each set of force curve acquisitions to ensure reproducible results, as the laser alignment and/or reflectivity of the backside coating can change over time, particularly in fluid. Very sharp probes are discouraged for capturing membrane force curves, as they easily puncture the SLM and might lead to measuring an erroneously low breakthrough force or no breakthrough at all. However, repeated use of the same tip without proper cleaning increases the chance of debris accumulating on the tip and thereby dulling the tip or affecting the tip-sample adhesive forces. A lack of breakthrough events evident in the approach force curves may also correspond to pushing only on mica rather than the actual membrane; thus, visual confirmation of membrane formation before capturing force curves is necessary.

Figure 7: Representative force-displacement (F-D) curves in air and fluid. Representative force curves obtained on (A) a loblolly pine in air with accompanying DMT model fit, and (B) a live MSC nucleus in PBS with an accompanying Hertz model fit. Insets in panels A and B show a zoom of the contact region of the corresponding approach curves (blue traces) with accompanying fit (green traces). In each panel, the initial tip-sample contact point (as determined by the fitting algorithm) is indicated by a green diamond, while the turn-around point (i.e., transition from approach to retract or withdraw) is indicated by a cyan circle. Please click here to view a larger version of this figure.

Figure 8: Comparison of silicon versus diamond probe tip wear. (A–D) Silicon probe tip. Series of models created by the blind tip reconstruction method following imaging of a tip characterization sample, demonstrating the evolution in radius of a stiff cantilever silicon tip probe (see Table of Materials) due to progressive tip wear experienced over the course of three sequential 85 µm x 85 µm (1024 x 1024 pixels) force curve-based images of a Bakken shale sample, conducted at a line scan rate of 0.1 Hz and force curve sampling rate of 2 kHz (i.e., ~20 million tip-sample interactions/image). (A) Tip as received (out of the box), prior to use. R = 11 nm. (B) Tip after one image (R = 43 nm). (C) Tip after two images (R = 94 nm). (D) Tip after three images (R = 129 nm). (E,F) Diamond probe tip. BTR models of the same diamond tip probe (see Table of Materials) obtained ~6 months apart. Between acquisition of the tip images used to generate the models shown in E and F, thousands of nanoindents were performed with the probe and hundreds of millions of tip-sample interactions during force curve-based imaging occurred. Nevertheless, due to the hardness of diamond, the estimated tip end radius of ~30 nm did not change within the uncertainty limits of the BTR technique between acquisition of the initial (E) and follow-up (F) images of the tip. The asperity observed in the earlier model (indicated by the black circle in panel E is most likely either an artifact of the BTR method or due to the presence of a nanoscale contaminant (e.g., dust particle) on the side of the tip. Please click here to view a larger version of this figure.

Figure 9: AFM topography and modulus maps of a loblolly pine sample. Representative AFM data acquired in air on a cross-sectioned loblolly pine sample embedded in resin to enable cantilever-based nanoindentation measurements on cell walls. (A) AFM topography image covering multiple cells acquired via a rapid force curve-based imaging mode, presented as a pseudo-3D depiction. (B) Elastic or Young's modulus map generated in real time by the AFM software by analyzing the force curve acquired at each pixel and fitting the data to the DMT model, showing that the cell walls are stiffer than the cell interiors. Note that the nominal, rather than measured, probe calibration parameters were used, so the modulus values should be treated as qualitative or only semiquantitative. (C) Overview of the ROI indicating the locations (eight lines consisting of 50 white crosshairs apiece spaced ≥100 nm apart) where 400 nanoindents (60 nm nominal ramp size, with a 1 µN trigger threshold corresponding to an average indentation depth of ~10 nm) were performed along selected cell walls following acquisition of the AFM image to enable the locating of indents with nanoscale precision. Scale bars = 20 µm (A,B). Abbreviations: AFM = atomic force microscopy; DMT = Derjaguin-Muller-Toporov. Please click here to view a larger version of this figure.

Figure 10: Co-localized AFM and SEM/EDS of a Bakken shale sample. (A) Secondary electron SEM image of a portion of a Bakken shale sample. (B) AFM topography image of the region indicated by the black box in A. Black oval indicates a region where the low aspect ratio of the probe leads to imaging of the probe sidewall rather than the steep, high aspect ratio surface topography feature. (C) EDS elemental composition map obtained for the SEM image shown in A. (D) AFM-derived elastic or Young's modulus map generated in the course of obtaining the AFM topography image in B, showing the mineral inclusion in the center of images A–D is significantly harder than the surrounding organic matrix. Scale bars = 50 µm. Abbreviations: AFM = atomic force microscopy; SEM = scanning electron microscopy; EDS = energy dispersive spectroscopy. Please click here to view a larger version of this figure.

Figure 11: Effect of probe tip radius and shape on the appearance of high aspect ratio features. Comparison of feature resolution obtained using either (A) an R≈ 30 nm low aspect ratio (tip half angle = 47°) diamond tip probe (see Table of Materials) or (B) an R≈ 10 nm high aspect ratio (tip half angle ≈ 19°) stiff silicon probe (nominal k = 200 N/m; see Table of Materials) to image the same location on a Bakken shale sample. (C–F) Zoomed-in images of the blue (C,D) and orange (E,F) boxed regions in A and B obtained with either the larger radius of curvature low aspect ratio diamond tip probe (C,E) or the sharper, higher aspect ratio stiff silicon tapping mode probe (D,F), highlighting the decreased feature resolution and introduction of tip sidewall artifacts in the AFM topography image obtained with the diamond tip probe due to its larger tip radius and half angle. The areas highlighted in C–F contain steep, deep well-like features that demonstrate the trade-offs in terms of lateral resolution, accurate tracking, and image fidelity between a more easily dulled, initially sharp silicon probe or a blunter, wear-resistant diamond tip probe. (G) Composite 3D image generated by combining AFM topography acquired with the sharp, higher aspect ratio stiff silicon probe with modulus data (overlaid colored skin) derived from rapid force curve imaging of the same area of the sample with the diamond tip probe. The features highlighted by the blue and white boxes in A and B are indicated in G as well. Please click here to view a larger version of this figure.

Figure 12: Cantilever-based nanoindentation on cells or nuclei. (A) A cell with radius R₁ located on a flat, rigid substrate is indented to a depth d by a spherical indenter with radius R₂. This figure was reproduced from Ding et al.⁴⁸. (B) Individual value plots of representative modulus measurements obtained from AFM cantilever-based nanoindentation experiments on mouse MSCs and isolated nuclei extracted from mouse MSCs. A total of 10 cells and 10 nuclei were measured five times each at an indentation depth of 500-600 nm (chosen to permit usage of the Hertz contact mechanics model). The resultant raw F-D curve data was processed using Atomic J²³ to calculate the elastic moduli. Due to the large innate variability of the cells, a 75^th percentile of the data is plotted. Cell and isolated nuclei exhibited no statistical difference in elastic modulus, with a measured average moduli of 0.75 ± 0.22 kPa and 0.73 ± 0.22 kPa, respectively. Similar data have been collected and analyzed to determine differences in nuclear stiffness due to mechanical stimulation, protein knockouts, and chemical treatments. Abbreviations: MSC = mesenchymal stem cell; AFM = atomic force microscopy; F-D = force-displacement. Please click here to view a larger version of this figure.

Figure 13: Morphology and nanomechanical properties of lipid bilayers. (A) AFM topography image showing the minimal height variation of a complete supported lipid membrane (SLM) composed of Chol/POPC at a mixing ratio of 1 that formed across the entire exposed mica surface with a long incubation time (~25 min) and high lipid concentration (0.3 mg/mL). The height profile along the purple line across the middle of the image is shown below the figure, providing structural details of the membrane surface. As expected, the SLM is extremely smooth. (B) Collection of approach sections of force curves captured on the SLM shown in A. Force curves were collected at equidistant points ≥100 nm apart covering almost the entire SLM. The force curves show a clear breakthrough event, as evidenced by the discontinuity or sudden jump in the approach section of the force curves. The average breakthrough force is 9.25 ± 0.27 nN. (C) Partial membrane or membrane patches formed by incubating membranes at a Chol/POPC mixing ratio of 1 with a shorter incubation time (~5-6 min) and lower lipid concentration (~15 µg/mL) relative to A⁴⁹. The height profile along the red line on the patch is shown below the image. The partial bilayer enables measurement of the thickness of the SLM, shown by the black dashed lines in the height profile. Note that the measured thickness also incorporates a 1-2 nm water layer between the membrane and the mica disk⁵⁰. This figure was adapted from Khadka et al.⁴⁹ with permission from Elsevier. Please click here to view a larger version of this figure.