Higher-dimensional Methods in AFM Including Machine Learning

Shortly following the invention of the first commercial atomic force microscope (AFM) in the late 1980’s, higher-dimensional methods began to be applied to complex material and biological systems. Collecting force-versus-distance curves in an X-Y array of locations, originally dubbed “force volume”, was the first of such “data cubes”. Given the extra “dimension” of information, one could extract maps of characteristic tip-sample adhesion (e.g., pull-off force) and model the contact mechanics to generate maps of Young’s modulus, for example [1]. The addition of other independent variables, such an applied electrical bias between tip and sample, along with dynamic methods wherein the tip is oscillated in Z at the microcantilever resonance frequency, enabled other kinds of data cubes pertinent to microelectronics, for example [2]. Further creative ideas expanded the number of independent variables and observables including multifrequency dynamic AFM (exciting and/or analyzing amplitude and phase at multiple oscillation frequencies) [2, 3] and infrared chemical microscopy (extending well below the diffraction limit of traditional IR methods) [4]. With modern data acquisition and computer systems, one is now equipped to collect and deeply analyze multidimensional data sets. Two examples in the author’s multiuser labs (serving industry and academia) [5] are Intermodulation AFM and AFM-IR. Intermodulation AFM is a resonant, multifrequency modality that vibrates the microcantilever (to which the tip is attached) at two tones near its fundamental flexural resonance to generate dozens of tones of response, thanks to frequency mixing due to nonlinear tip-sample interaction with distance (a well-known phenomenon in electrical engineering in the context of AC signal analysis in the presence of nonlinear circuit elements). This method both expands contrast mechanisms (of amplitude and phase at each of 40 mixing tones) and reconstructs the distance dependence of conservative and dissipative material response at each image pixel via a 40-term discrete Fourier transform of high-frequency tip motion (Z position and velocity), which executes one low-frequency beat per pixel location and thereby explores a range of distances [6]. We applied two machine-learning (ML) methods provided by the vendor: Linear Discriminant Analysis (LDA) and K-means clustering. The former determines linear combinations out of the 80 amplitude and phase images that generate high contrast/cleaner images. The latter finds clusters of similar distance-dependent curves of conservative and dissipative response and thereby generates stark contrast of material behavior (e.g., a three-color image in the case of three characteristic clusters, as shown in Fig. 1). We exemplify results on coatings of polymer and/or surfactant, surfactant and inorganic nanoparticles, and other mixed polymer-organic systems of interest to our industrial collaborators. Some of the most unique mappings are of solid-liquid mixed-phase coatings, wherein viscous response (along with the usual elastic response) is particularly elucidating. AFM-IR pulses IR laser light at the tip-sample interface, and in the case of soft matter mostly detects photothermal expansion locally via forces acting on the tip [4]. The IR pulse frequency is chosen to excite an eigenmode of the cantilever, whether the tip is pinned to the surface in contact mode or oscillating mostly free of the surface in dynamic modes. The amplification provided by eigenmodal resonances generates a useful signal even for small IR absorption (whereby small tip-sample interaction forces). We firstly exemplify results on coatings of polymer and drug (Fig 2), including variable depth perception (of isolated drug domains’ location and 3D shape) via mode selection and parameter settings. Both 2D imaging of concurrent datatypes (chemical, mechanical, frictional) and hyperspectral mapping are included in our analysis. Secondly, we applied AFM-IR to chemically identify phase segregated domains in a problematic sample wherein the embedding epoxy for microtomy had intermixed with the block polymer of interest (i.e., while epoxy resin was in the liquid phase). These results provided training data for LDA analysis within Intermodulation AFM, resulting in unique images that contrasted two kinds of nanoscale block polymer domains and differentiated both from the interpenetrating epoxy domains. (This latter result was not achievable with conventional phase imaging in AC/tapping AFM.) A) Frequency-domain amplitude of response of 40-tone signal for 2-toned excitation near 84 kHz, overlaid for three types of behavior located on the surface. B) Representative distance dependence derived from both the upside and downside of each beat (rendered as dark and light versions of each color), for both conservative (top) and dissipative (bottom) response at these locations. C) K-means clustered mapping of the three types of behavior: pure liquid surfactant (blue), protruding solid Si nanoparticles (maroon), and solid Si nanoparticles below liquid surfactant. A) Molecular structure of poly(butyl methacrylate) and dexamethasone drug. B) Representative AFM-IR spectrum collected at a spatial location exhibiting polymer and drug signal. C) Representative contact stiffness and IR absorbance images of isolated drug domains (bright) and continuous phase of polymer (dark/magenta). Coating thickness was ∼500 nm, and the IR Absorbance signal in this case (contact resonance mode, soft cantilever) derives from the full depth of the coating, thus a 2D projection of 3D content, akin to bright-field TEM.