Atomic Force Microscopy beyond Topography: Chemical Sensing of 2D Material Surfaces through Adhesion Measurements

Developing new functionalities of two-dimensional materials (2Dms) can be achieved by their chemical modification with a broad spectrum of molecules. This functionalization is commonly studied by using spectroscopies such as Raman, IR, or XPS, but the detection limit is a common problem. In addition, these methods lack detailed spatial resolution and cannot provide information about the homogeneity of the coating. Atomic force microscopy (AFM), on the other hand, allows the study of 2Dms on the nanoscale with excellent lateral resolution. AFM has been extensively used for topographic analysis; however, it is also a powerful tool for evaluating other properties far beyond topography such as mechanical ones. Therefore, herein, we show how AFM adhesion mapping of transition metal chalcogenide 2Dms (i.e., MnPS3 and MoS2) permits a close inspection of the surface chemical properties. Moreover, the analysis of adhesion as relative values allows a simple and robust strategy to distinguish between bare and functionalized layers and significantly improves the reproducibility between measurements. Remarkably, it is also confirmed by statistical analysis that adhesion values do not depend on the thickness of the layers, proving that they are related only to the most superficial part of the materials. In addition, we have implemented an unsupervised classification method using k-means clustering, an artificial intelligence-based algorithm, to automatically classify samples based on adhesion values. These results demonstrate the potential of simple adhesion AFM measurements to inspect the chemical nature of 2Dms and may have implications for the broad scientific community working in the field.

1. Cantilever movement during force-distance curves measurements, a brief explanation.
Regarding the Figure 1 in the main text, we can describe the movement of an AFM probe while measuring: When a free-standing AFM cantilever (I) gets its probe close enough to the surface, an attractive force with the substrate appears due to long range interactions (e.g.: van der Waals ones).This makes the cantilever to bend towards the substrate snaping into it (II).If the approaching step continues, the cantilever experiences repulsive forces and bends in the opposite direction while the tip indents the sample (III).In the detaching step (IV), the probe experiences significant attraction due to the superficial adhesion forces of the sample to the tip while bending more than in the previous approach step II.The value of the adhesion force is the depth of the well observed in the force-distance curve during this step (red trace in figure 1b in the main text).Finally, the probe is released from the tension so it can approach again (V).

AFM probe selection experiments.
In Table S1 it is possible to find all the main parameters for the probes used in this work.Note that these are the nominal values, the calibration made prior to the measurements allows to assess the specific resonance frequency and force constant for the specific probe used in each case.More information about the probes can be found free of charge on the next websites: https://www.brukerafmprobes.com/(For SCM-PIC, RTESPA-150, ScanAsyst Air and NPG-10A probes) Note that SCM-PIC has been replaced by SCM-PIC V2. https://www.budgetsensors.com/tapping-mode-afm-probe-tap300(For Tap 300-G).NPG-10 is a cantilever with four probes."A" probe has been used in all cases.
AFM images of MnPS3@H2O and MnPS3@PVP used for probe study and selection are displayed below.Two images of each sample were recorded with each probe for obtaining a mean value in each case.For the Adhesion-Thickness study, (ESI Section 4) the data on each 2D flake is considered individually.For simplicity, this close analysis has been performed only in the first image of each set.Regarding the metallic-coated probes (SCM-PIC and NPG-10A) the status of the probe was analysed after their utilisation.SEM imaging was done with EDX mapping, the results are depicted in Figures S11-S12.As can be seen, it is not possible to appreciate any degradation or peeling-off of the coating.
Moreover, the mapping signal of Au for NPG 10A, and Pt/Ir for SCM-PIC is homogenous all over the probe.

Reproducibility study of AFM probes.
A comparison between five different probes is discussed in the main text.A similar analysis was conducted with four ScanAsyst Air probes to evaluate the reproducibility of the method using different probes in different days and the results are depicted in Figure S13.In Table S2 is possible to compare the dispersibility of the data using either Adhesion or RA.The variation percentage of the data shown is analysed in Table S2, comparing the result obtained for Raw adhesion and RA.The analysis reveals how the use of RA instead of raw adhesion reduces the variation percentage of the data from ca. 50% to 15-20%.This is the expected effect, as RA considers in some way the status of the probe in each measurement.Table S2.Variation percentage (%RSD) for the mean Raw Adhesion and RA obtained between all the ScanAsyst Air probes used.

Adhesion-Thickness analysis.
As has been described in the main text.The possible effect of the sample height on the adhesion channel was studied.To do so, several areas of AFM pictures taken with each probe have been selected and analyzed as can be observed in Figures S1-S10c) pictures of each one.Mean thickness and adhesion data for each area on these pictures is shown in the next tables (Table S3-S8) Table S3.Mean height and adhesion for each area shown in Figure S1c  To evaluate the effect that the PFS can have on the measurements, we have compared the results yielded by SAA probes with the ones obtained with Tap300G probes.We have to consider the following: Tap 300G (Stiffness: 40 N/m) the PFS applied has been kept at 25 nN SAA (Stiffness: 0.4 N/m) the PFS applied has been kept at 1 nN The PFS is always fixed to the minimum value needed to get stable and reliable data, so avoiding unnecessary damage of the tip or the sample during the measurements.In Figure S22, the indentation and height data are plotted for the same areas studied in the adhesion-height analysis in the main text.As can be observed, by keeping constant PFS values, the degree of indentation and the thickness of the layers under study cannot be correlated, moreover, the range of indentation variations is very narrow in all cases but even lower for the SAA probe (less stiff).One step forward, we have performed additional adhesion measurements by using a SAA probe to scan 2 new samples, one with MnPS3@H2O (Figure S23) and another with MnPS3@PVP (Figure S24).In these new measurements, a continuous increase of the applied force to the tip (PFS) was performed.In both samples, indentation values measured on MnPS3@H2O and MnPS3@PVP flakes were almost invariable when low PFS were applied (PFS < 2), however, for larger PFS values, the indentation increased significantly (Figure S25a).From figures S23 and S24, several areas were highlighted (Figure S25, b and c) and the adhesion was analyzed individually for each area on each image and PFS.The results obtained were plotted on Figure S26 as raw adhesion and RA.Regarding the adhesion, there is a general trend for both kind of samples: higher PFS induce broader dispersion in adhesion values.However, while for MnPS3@H2O there is no relation between PFS, indentation, and raw adhesion or RA value, when MnPS3@PVP sample is inspected, the adhesion absolute values increase with the increase of the applied force to the tip (PFS) but are completely independent of the 2Dm thickness.More interestingly, when RA values instead of absolute adhesion values are used, they result almost independent of both, PFS (and indentation) and layers thicknesses (highlighting once more the relevance of the use of RA for consistency when comparing different experiments).The MnPS3@PVP dependencies can be attributed to the softer organic layer on the surface, which is more affected by a stronger contact, whereas MnPS3@H2O does not exhibit such dependencies.6. Statistical analysis of RA for MnPS3@H2O and MnPS3@PVP samples.
For performing a statistical study of the results obtained with SAA and RTESPA probes, 2-3 images have been analysed on each probe-sample couple ensuring that we have enough data for the further ANOVA and Shapiro analysis.g) topography channel, h) adhesion signal and i) areas selected for further analysis.
We have performed a typical ANOVA test (analysis of variance) to test if the groups of samples within each probe are different enough based on their RA values.ANOVA methods are a powerful tool usually employed to determine if there are significant differences between groups of data.It measures the differences between the means of the different groups.If the p-value is below a defined significance level (usually 0.05) means that there is enough evidence to reject the null hypothesis (the assumption that there are no differences between groups).By using Rstudio we compared with ANOVA (specifically through a t-test) the differences of the two types of samples (MnPS3@PVP and MnPS3@H2O) for each probe independently (ScanAsyst Air and RTESPA 150).Being confirmed that our data follows normality, we can apply the well-known t-test to determine if there are significant differences between the two groups of samples.We have obtained values of p-value of 2.007•10 -6 and 7.219•10 -6 while comparing RA values with sample type for each of the two experiments.This means that for each probe, the data obtained for MnPS3@PVP and MnPS3@H2O are statistically significant.K-means is one of the most popular clustering methods which aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean.It is one of the simplest unsupervised learning algorithms that solves the well-known clustering problem [1].This method could be summarized understanding the basic idea of the algorithm: relocate each point to its new nearest center (starting from an initial point not optimized), update the clustering centers by calculating the mean of the member points, and repeat the relocating-and-updating process until convergence criteria is satisfied [2].
The classification process was accomplished using Python through scikit-learn package.
Following the last idea, two categories were chosen that correspond to the two types of materials on the sample: Water and PVP.Convergence criteria were defined by default.As one could observe, both problem samples are well-defined, and their centroids are distant.To verify the performance of the classification, it was suggested the use of two evaluation metrics: Silhouette and Inertia analysis.As was commented briefly in the main text, the results obtained for MnPS3@H2O and MnPS3@PVP samples were compared to ME-MnPS3 flakes.These results have been assessed with two different types of probes, ScanAsyst and RTESPA-150.The comparison of the data is discussed in the main text, and here it is possible to find all the AFM images that yielded the data.
(Note that MnPS3@H2O and MnPS3@PVP samples were deeply studied in ESI section 6, hence,  Figure S36 RA values obtained on MoS2@H2O flakes and on MoS2@PVP with a SAA probe.

Figure S2 .
Figure S2.AFM images taken with Tap 300G probe on MnPS3@PVP samples.First sample: a)

Figure S6 .
Figure S6.AFM images taken with SCM-PIC probe on MnPS3@PVP samples.First sample: a)

Figure S10 .
Figure S10.AFM images taken with ScanAsyst Air probe on MnPS3@PVP samples.First

Figure S11 Figure S12
Figure S11SEM imaging and elemental analysis of a NPG-10A probe after using for AFM

Figure S22 .
Figure S22.Indentation vs height values registered on each area studied in the main text with the

Figure S23 .
Figure S23.AFM images of MnPS3@H2O obtained with PFS between 0.5nN and 10nN with a

Figure S24 .
Figure S24.AFM images of MnPS3@PVP obtained with PFS between 0.5nN and 10nN with a

Figure S25 .
Figure S25.a) Mean Indentation values vs PFS applied measured with a SAA probe on

Figure S28 .
Figure S28.AFM images taken with ScanAsyst Air probe on MnPS3@PVP samples.First

Figure S31 .
Figure S31.Boxplots of the obtained data in each of the experiments.The plot on the left Silhouette analysis helps to find the separation distance between the resulting clusters, its score has a range of[-1, 1].Thus, if the Silhouette score has a value near +1 that indicates the sample is far away from the neighboring clusters.A value of 0 indicates that the sample is on or very close to the decision boundary between two neighboring clusters and negative values indicate that those samples might have been assigned to the wrong cluster[3].On the other hand, Inertia tries to measure the compactness of each cluster by calculating the sum of squared distances of samples to their closest cluster center, weighted by the sample weights if provided.Lower inertia score indicates tighter and well-separated clusters.
those data have been already shown in FigureS27-S30).In the next figures, the images obtained for ME-MnPS3 samples with SAA and RTESPA-150 probes are presented.

Table S1 .
-List of probes used for this study and nominal parameters of each one.

Table S4 .
and S2c for the data obtained with Tap 300G probe.Mean height and adhesion for each area shown in FigureS3cand S4c for the data obtained with NPG-10A probe.

Table S5 .
Mean height and adhesion for each area shown in FigureS5cand S6c for the data obtained with SCM-PIC probe.

Table S6 .
Mean height and adhesion for each area shown in FigureS7cand S8c for the data obtained with RTESPA-150 probe.

Table S7 .
Mean height and adhesion for each area shown in FigureS9cand S10c for the data obtained with ScanAsyst Air probe.

Influence of the applied PeakForce Setpoint on the adhesion response of the probe.
First, we ran a Shapiro-Wilk normality test, which assesses whether a given sample follows a normal distribution.It specifically checks for normality.It retrieves a W metric, for which values close to 1 indicate that the data is close to a normal distribution, whereas values close to 0 suggest no normality.We have obtained values of W of 0.887 and 0.962 for data coming from ScanAsyst Air and RTESPA 150 experiments, respectively.

Table S8 :
Obtained inertia and Silhouette scores validating the accuracy of k-means method while classifying data from mixed samples.