Subsurface Imaging of Soft Matter by AFM
Depth Modulation and Compositional Mapping by Trimodal AFM
- Subsurface Imaging of Soft Matter by AFM - Depth Modulation and Compositional Mapping by Trimodal AFM
- Fig. 1: Trimodal AFM setup.
- Fig. 2: (a) Amplitude vs. drive frequency for two different amplitudes. The solid lines represent the free amplitude response (away from the sample) and the dashed lines represent the engaged response. (b) and (c) show simulated indentation depth and peak force vs. cantilever position. The traces are labeled with the amplitude used for the first three eigenmodes (nm).
- Fig. 3: (a) Schematic of the experimental sample and scan lines. (b) Actual scan lines for two different third eigenmode amplitudes (0 nm and 27 nm). (c) Topography (top) and phase shift of the 2nd eigenmode (bottom). Each column represents two diferent experiments for two different third eigenmode amplitudes. Fundamental spring constant = 2.7 N/m, first eigenmode amplitude = 126 nm, second eigenmode amplitude = 1 nm (see also ref. ).
In recent years, a variety of dynamic force microscopy techniques have been developed to obtain surface compositional contrast and extract material properties simultaneously with topographical imaging. We describe here one such recent method, trimodal atomic force microscopy (trimodal AFM), which allows topographical imaging, compositional mapping and control of the tip-sample indentation during a single-pass 2-dimensional (2D) scan.
A clear trend in AFM is to expand its capabilities beyond topographical imaging and single-point force spectroscopy. Since the dynamic response of the AFM tip contains information on the tip-sample junction properties, it is in principle possible to rapidly acquire multidimensional data sets describing quantities such as the tip-sample stiffness vs. the 3D position of the tip, from which basic material properties can be inferred, such as elasticity or chemical composition. Recent developments in multifrequency AFM hold significant promise towards fully realizing this goal [1-8].
In the first multifrequency AFM method, introduced by Rodriguez and Garcia [2,3], the cantilever is simultaneously excited at its first two eigenfrequencies. The fundamental eigenmode is used to measure the topography through the amplitude modulation method (tapping-mode, AM-AFM), while the higher eigenmode is driven in open loop (i.e., without any feedback loops) to obtain additional information about the material properties. Depending on the cantilever and imaging parameters (primarily the response amplitude and dynamic spring constant), the sensitivity of the higher eigenmode can be significantly increased in comparison with the first eigenmode [2,3,8]. Building upon this bimodal method, we have introduced an additional excitation for a third eigenmode, in order to control the indentation depth during imaging . With this new trimodal method, the user can obtain information on the subsurface structure and properties at different depths, by varying the amplitude of the highest driven eigenmode, which can be beneficial for studying samples such as composite materials and biological structures.
Basic Principle of Trimodal Imaging
A scheme of trimodal AFM is shown in figure 1.
The cantilever is simultaneously excited at three different eigenfrequencies, and the tip response is analyzed by three separate lock-in amplifiers to determine each mode's amplitude and phase. The basic concept of this technique is that each eigenmode serves a different purpose: the fundamental eigenmode is used to measure the topography, the second eigenmode provides compositional contrast, and the third (or any higher) eigenmode is used to control tip-sample indentation.
The dynamic behavior and sensitivity of each cantilever eigenmode is determined primarily by its dynamic spring constant and its user-defined amplitude. The numerical simulation results in figure 2 give a clue on choosing suitable eigenmodes and oscillation amplitudes for trimodal AFM (see ref  for details).
Figure 2(a) shows amplitude vs. frequency curves for the cases of a "small" and a "large" free amplitude for an arbitrary eigenmode. The black solid lines show the response far away from the surface ("free") and the dashed red lines represent the "engaged" response (in the presence of the sample). As the figure indicates, smaller free amplitudes result in larger changes of the measured signals (e.g., response amplitude at the driving frequency) upon engaging the sample, indicating that the eigenmode becomes more sensitive as its free amplitude decreases. Figures 2(b) and (c) illustrate the tip-sample indentation and the corresponding peak forces as a function of cantilever position during a spectroscopy curve. The black and gray solid lines were calculated for fundamental eigenmode amplitudes of 100 and 110 nm, respectively (all other eigenmode amplitudes were set to zero). The blue line was calculated for a third eigenmode amplitude of 10 nm, while the fundamental eigenmode also oscillated with an amplitude of 100 nm.
The results show that both the indentation and peak force significantly increase when turning on the third eigenmode with a relatively small amplitude. The same increase in amplitude for the fundamental mode, however, only results in a small increase in indentation and peak force (compare black and gray curves). This is due to the higher dynamic spring constant of the third eigenmode (for an ideal cantilever the spring constant grows quadratically with the eigenmode frequency), which makes it less sensitive to the presence of the sample . Therefore, since large spring constants lead to low sensitivity and large indentation, one should choose the highest available eigenmode to control indentation. Small increases in this mode's oscillation amplitude will lead to relatively large increases in penetration.
Since high sensitivity is desired for compositional mapping, one should choose for this purpose the lowest of the available higher eigenmodes. The fundamental eigenmode is still reserved for topographical imaging. In the experiments of reference  compositional mapping was performed using the second eigenmode, as in the first bimodal AFM experiments [2,3], and indentation was controlled using the third eigenmode, although other eigenmode choices are also possible .
For our experimental validation we designed a model sample consisting of a hard silicon oxide substrate, covered by a soft polymer (PDMS) film (fig. 3(a)). Prior to spin coating of the polymer, glass nanoparticles (diameter ≈ 13 nm) were deposited onto the substrate, in order to introduce features that were buried under the polymer film (see ref  for details). The film was then scratched away on a portion of the sample to provide a height reference during the measurements. As is clear from the sample structure, the nanoparticles can only be observed with AFM if the film is sufficiently indented (the film thickness above the nanoparticles was ≈ 20 nm). See figure 3(a) for a schematic illustrating the maximum tip penetration along two scan lines corresponding to different indentation. Clearly, the nanoparticles are only visible during "scan2" since the indentation is small for "scan1." Figure 3(b) shows two experimental scan lines for our sample, for two different third eigenmode amplitudes (0 nm and 27 nm, blue and red solid lines, respectively). The measured film thickness decreases from ≈ 35 nm to ≈ 15 nm as the third eigenmode is turned on. The full images from which these scan lines were taken are shown in figure 3(c). In agreement with figure 3(b), the topography image also shows significantly decreased film thickness and the phase image reveals the nanoparticles for the high indentation setting. The opposite is true for the low indentation setting: the film thickness is greater and the nanoparticles are not visible. Residual polymer can also be observed on the reference (scratched) region.
We have described a trimodal AFM imaging scheme which can be used to obtain topographical and compositional sample information, while simultaneously controlling tip-sample indentation through changes in the free amplitude of a higher eigenmode. We demonstrated imaging of glass nanoparticles buried a few tens of nm below a PDMS film, without observing any noticeable damage of the sample. This added capability can offer significant advantages in the visualization of the subsurface of soft materials, especially those with heterogeneous structures.
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Prof. Santiago D. Solares (Corresponding author via e-mail request)
Babak Eslami, PhD
The George Washington University
Department of Mechanical and Aerospace Engineering
Washington, DC, USA
Dr. Daniel Ebeling
Institute of Applied Physics
Justus Liebig University