Advances in nanomechanical property mapping by atomic force microscopy

Abstract

AFM-based mechanical property measurements are widely used in energy storage, polymer science, mechanobiology or nanomedicine. Mechanical properties are determined by expressing the experimental force in terms of a contact mechanics model. A nanomechanical map is generated by representing one or more mechanical parameters as a function of the tip's spatial coordinates. Force spectroscopy modes might be separated into two categories, adhesion and indentation. Here we describe the principles of AFM-based indentation modes to generate spatially resolved maps of the mechanical properties at the nanoscale. The review provides an update on the progress in nanomechanical mapping since 2019. The focus is on quantitative accuracy, spatial resolution, high-speed data acquisition, machine learning and viscoelastic property mapping. Two advanced applications which emerged from AFM-based indentation modes, nanomechanical tomography and volume imaging of solid-liquid interfaces, are also described.

Fig. 1. Nanomechanical mapping. (a) Classification of popular and emerging AFM-based indentation methods. A spatially-resolved map of mechanical properties is generated by performing measurements in each pixel of the sample surface. (b) Scheme of force volume (triangular z-displacement). (c) Scheme of force volume off-resonance (sinusoidal z-displacement). (d) Nanorheology. (e) Scheme of nanomechanical mapping by using a parametric method. A, ϕ and f are, respectively, the amplitude, phase shift and resonant frequency of the tip. (f) Milestones in the evolution of nanomechanical mapping (indentation modes). HS stands for high-speed. The time scale represent approximative dates.

Fig. 2. (a) Force–distance curve with approaching and retraction sections obtained on a live HeLa cell (top panel). Experimental data in black and a theoretical fitting in red. The arrows indicate the direction of the tip displacement. Bottom panel, schemes of the tip-sample distance for the positions marked in the FDC. (b) Force and z-displacement in a nanorheology experiment. The time lag between z-displacement and force is marked. Bottom panel. A schematic diagram of the experiment. The tip is oscillated with respect to the indentation I₀ defined by the set point force value.

Fig. 3. Schematic diagrams of the most common axisymmetric tip geometries in AFM nanomechanical mapping. From left to right, cylinder, conical tip, paraboloid and nanowire. The sample thickness h, tip geometry parameters, indentation I and projected radius of the contact area a are illustrated. The bottom stiffness effect is schematized for a paraboloid (white arrows).

Fig. 4. Bottom stiffness effect in nanoparticles. Apparent Young's modulus as a function of the NP diameter for three materials (10 kPa, 10 MPa and 1 GPa). The apparent Young's modulus was obtained by fitting a FDC with the Sneddon model for a paraboloid tip (R = 50 nm). The FDCs were generated by applying a maximum force of 0.1 nN for NPs of 10 kPa and 1 nN for the other NPs. The solid line represents the true modulus of the NP.

Fig. 5. Examples of nanomechanical mapping of surfaces and interfaces. (a) Elastic modulus map of a metal–organic-framework with angstrom-scale resolution (bimodal AFM). Reprinted with permission from ref. . Copyright 2017 American Chemical Society. (b) Stiffness map of a polyethylene film (bimodal AFM). The image shows a lamella with disordered end chains at the interface of the crystalline and amorphous phases (region I) and tightly packed polymer chains (region II). Adapted with permission from ref. . Copyright 2018 American Chemical Society. (c) Retardation time and loss tangent map of a PS-b-PMMA block co-polymer (bimodal AFM). Adapted with permission from ref. . Copyright 2019 Royal Society Chemistry. (d) High-spatial resolution map on a HeLa cell generated by combining topography and elastic modulus data (force volume). The map shows the fine structure of the actin filament network, the local variation of the modulus, and the size and shape of the nucleus. Reprinted with permission from ref. . Copyright 2025 Wiley-VCH GmbH. (e) Kymograph of the height and the elastic modulus of a growing collagen nanofibril. The images show the transition from the accretion of collagen precursors from the solution to the formation of a collagen nanofibril (five tropocollagen molecules) with the D-band structure. Imaging rate, 1.12 fps (256 × 256 pixels). Reprinted with permission from ref. . Copyright 2021 American Chemical Society.

Fig. 6. Topography images and mechanical property maps. (a) Topography and elastic modulus map (b) of the 20S proteasome. The bottom panels show the respective cross-sections along the marked lines of the images. The height and elastic modulus cross-sections are anti-correlated. The inset shows a scheme of the 20S proteasome (Protein Data Bank 5L4G). Proteasome images obtained by bimodal AFM. Reprinted with permission from ref. . Copyright 2018 Springer Nature. (c). Topography of the actin cytoskeleton; cell depth = 0–100 nm. (d). Viscous coefficient map, cell depth = 1000 nm. The viscous coefficient map shows components of the nucleus that are not resolved in the topographic image (c). Cell images obtained by force volume. Adapted with permission from ref. . Copyright 2019 American Chemical Society.

Fig. 7. Nanomechanical tomography. (a) Schematic of a tip–cell interface in force volume. (b) Force–distance curve acquired on a cell (NIH 3T3 fibroblast) immersed in buffer. (c) Nanotomography map of a cell. From top to bottom, topography of the cell surface (cell depth = 0 nm); topography of the actin cytoskeleton (cell depth = 0–100 nm); viscous coefficient map (cell depth = 1000 nm). Reprinted with permission from ref. . Copyright 2019 American Chemical Society. (d) Schematic of nanoendoscopy-AFM. The tip is repeatedly introduced inside the cell at different lateral positions. (e) Confocal microscopy image of a tip inside the cytosol pressing against the nucleus. The nanoneedle tip, cytoplasm, and nucleus were stained green, red, and blue, respectively. (f) Nanoendoscopy-AFM cell map of a HeLa cell. Panels d and f reprinted with permission from ref. Copyright 2021 AAAS. Panel e reprinted with permission from ref. .

Fig. 8. 3D-AFM. (a). Scheme of the xyz tip displacements in 3D-AFM imaging of solid–liquid interfaces. (b) 3D-AFM volume image of a collagen–water interface. Two hydration layers follow the contours of the collagen nanoribbon. The water covers the whole collagen nanoribbon surface. To facilitate interpretation, the image is divided in two regions, the collagen surface (brown) and the structure of the interfacial water (blue). Based on data from ref. . (c) TEM images of hydrophilic silicon-based tip. Arrows and dashed lines highlight the oxidation layer covering the silicon probe. Panel adapted with permission from ref. . Copyright 2023 American Chemical Society. (d) Force–distance curve measured on mica–water interface. (e) 2D force (x, z) map of a 200 mM KCl solution near a mica surface. Adapted with permission from ref. . Copyright 2019 Springer Nature. (f) 2D force (x, z) map of an ionic liquid on a graphite surface measured at two surface potentials. The light stripes show the layering of the ionic liquid molecules. Adapted with permission from ref. . Copyright 2020 American Chemical Society.

Ricardo Garcia

Jaime R. Tejedor