Accurate electromechanical characterization of soft molecular monolayers using piezo force microscopy

We report a new methodology for the electromechanical characterization of organic monolayers based on the implementation of dual AC resonance tracking piezo force microscopy (DART-PFM) combined with a sweep of an applied DC field under a fixed AC field. This experimental design allows calibration of the electrostatic component of the tip response and enables the use of low spring constant levers in the measurement. Moreover, the technique is shown to determine both positive and negative piezo response. The successful decoupling of the electrostatic component from the mechanical response will enable more quantitative electromechanical characterization of molecular and biomaterials and should generate new design principles for soft bio-compatible piezoactive materials. To highlight the applicability, our new methodology was used to successfully characterize the piezoelectric coefficient (d33) of a variety of piezoactive materials, including self-assembled monolayers made of small molecules (dodecane thiol, mercaptoundecanoic acid) or macromolecules (peptides, peptoids), as well as a variety of inorganic materials, including lead zirconate titanate [PZT], quartz, and periodically poled lithium niobate [PPLN]. Due to high differential capacitance, the soft organic monolayers demonstrated exceedingly large electromechanical response (as high as 250 pm V−1) but smaller d33 piezocoefficients. Finally, we find that the capacitive electrostatic response of the organic monolayers studied are significantly larger than conventional inorganic piezoelectric materials (e.g., PZT, PPLN, quartz), suggesting organic electromechanical materials applications can successfully draw from both piezo and electrostatic responses.

Since the discovery of piezoelectric activity in muscle tissue and other biological materials, the molecular origin of the electromechanical response has been a topic of interest. At the nanoscale, the electrical and mechanical properties of materials are oen linkedfor example giving rise to phenomena such as piezo-, exo-, and ferroelectricity. [1][2][3][4][5] These phenomena, in turn, enable a wide range of applications from sensing to optoelectronics. 3,4,[6][7][8][9][10][11][12][13][14][15] The piezoelectric effect (PE) comprises two effects: a direct effect, in which mechanical stress generates an electric charge. Inversely, the converse PE generates a mechanical response to an applied electric eld. Materials exhibiting piezoelectric response are generally non-centrosymmetric, polar, and poorly conductive. A range of materials exhibit piezoelectric properties including lead zirconate titanate (PZT), quartz, and various polymers such as polyvinylidene diuoride (PVDF). At the nanoscale the lack of centrosymmetry coupled with high polarities give rise to piezoelectric response, yielding a vast diversity of piezoelectric materials. For example, selfassembled monolayers, where the attachment of target molecules to surfaces inherently breaks symmetry and generates a polar system, have been shown recently to be inherently piezoelectric. 16 Accurate and reliable methods to measure piezoelectric outputs from a given material are vital to investigating these phenomena and realizing their potential range of applications. Atomic force microscopy (AFM) was initially developed to map the morphological variations in materials at the nanoscale. 6,17 Beyond simple topology and morphology, functional AFM methods have been developed to map properties including surface potential, charge transport, magnetic response, and piezoresponse. [17][18][19][20][21] The latter, piezo force microscopy (PFM), determines the mechanical response of materials to an applied electrical eld by measuring the converse piezoelectric effect. However, classical single frequency PFM suffers from low sensitivity and poor frequency tracking due to crosstalk in the phase feedback loop between material topology and electromechanical response. To increase sensitivity and avoid dielectric breakdown of materials, dual AC resonance tracking (DART) was developed by Kalinin to allow the use of small bias voltages while maintaining good frequency tracking despite varying topological features. 4,6,18,[20][21][22][23][24] Building on the principles of PFM, DART drastically improved the sensitivity of PFM measurements and helped move the eld towards more quantitative piezoelectric measurements. Beyond DART, the band excitation (BE) method was intended to overcome distortions associated with tip-sample interactions experienced in DART, in which the lever is excited at multiple frequencies around the fundamental frequency to alleviate shis in the fundamental, due to topography. 25 More recently, several groups have tried to reduce/eliminate these distortions by using high spring-constant (k l ) levers, with or without a xed external DC eld, or by creating new lever technologies, such as "inner paddled levers". 2,3,[26][27][28] These techniques reduce the electrostatic component of the measurement for specic cases; however, this may not be true for systems, such as organic polymers and biomaterials, in which the electrostatic component is quite large or where the Young's modulus of the material is small in comparison to the lever.
The above methods, particularly the use of high springconstant levers, perform best with materials in which the elastic modulus is signicantly higher than that of the lever. Unfortunately, when the modulus of the material under study is small in comparison to modulus of the lever, such as organic and biomaterials, the lever may deform the target surface, reducing or eliminating the sensitivity enhancements garnered by DART or band excitation techniques.
In this work, we describe a method for improved accuracy in measurements of the piezo-response (d 33 , the response of a material in the z-axis to a eld applied in the same axis) of so organic monolayers. The method entails the use of a so (low-k l ) lever, coupled with the quantication of the electrostatic component of tip response by completing a DC eld sweep in addition to the AC eld sweep already employed to measure the independent lever electrostatics. By compensating for the electrostatic component, the true d 33 of the material can be established.

Results and discussion
We recently measured the piezoresponse of xed polar molecular self-assembled monolayers, anchored by gold-thiol interactions to gold-coated glass substrates. 16 These well-formed monolayers represent model systems for the investigation and development of so, exible, xed polar organic piezoelectric materials. 29 In that work, piezoresponse was determined using DART-PFM by sweeping the applied AC electric eld and plotting the corresponding measured response against it. The slope of the linear regression should yield the effective d 33 (d eff ), in recognition of the lack of direct measurement of the true elds experienced by the material and minor yet contributing electromechanical effects, of the material under study, as illustrated in Fig. 1A. Unfortunately, the regression rarely passes through the origin due to electrostatic effects present when the tip is brought into contact with the surface; resulting in a sizeable inherent error in the measurement regardless of the care taken in the data acquisition.
The tip response can be determined as in eqn (1) 17,24 where cantilever response R is equal to the d eff (effective piezo coefficient) at the applied AC eld (V AC ) plus the contact stiffness (k c ) augmented by the differential capacitance in the z-axis, V AC, and the electrostatics at the surface composed of any applied or established DC eld (V DC ) and the contact potential voltage V CPD . 17,24 This equation relates the observed tip response to the piezoelectric response of the material combined with response due to tip-sample electrostatic interactions. Naturally, a conventional sweep of V AC to determine the piezo response (e.g., Fig. 1A), does not compensate for the electrostatic componentthe second term of eqn (1). Recent efforts have attempted to minimize this electrostatic response using high k l AFM levers to drive k c towards zero. This effectively reduces the electrostatic component but does not eliminate it. 27 Unfortunately, while using stiff, high k l , AFM levers lowers the electrostatic component with conventional ceramic-based piezoelectric materials, it is only effective in cases where (1) the electrostatic component is small compared to the effective piezoresponse from the material and (2) the elastic modulus of the surface is much greater than the tip.
In the case of so materials, such as organic and biomaterials, using stiff, high k l levers will likely cause signicant deformation of the target material. Since DART-PFM uses contact resonance for signal enhancement, the mismatch between the so surface and stiff AFM lever leads to small tune amplitudes even under large applied elds and thus poor signal to noise. An apt analogy to this situation would be measuring the response of grass with a hammercompressing the plant and limiting the observable response. Consequently, as proposed in the introduction, soer, low k l levers should minimize surface deformation in so organic and biomaterials; however, they bring additional complications in the form of signicant electrostatic contributions to the observed d eff . Unlike in traditional AC sweep methods here the electrostatic component is expected to be non-zero at zero applied eld highlighting the effects of electrostatics on the measurement system. To account for this electrostatic effect, we envisioned sweeping the DC eld to accurately determine the electrostatic component of the observed response, as well as the V DC point at which the electrostatic response is minimized (Fig. 1B). If successfully realized, we hypothesized this new technique would allow for increased quantitative accuracy in determining the d eff piezo response even in so materials.
To test the proposed DC eld sweeping DART-PFM technique, ve different levers were chosen with spring constants (k l ) varying from 0.02 to 2.8 N m À1 and used to determine the electromechanical response of four organic self-assembled Au-S monolayers (Scheme 1). These organic SAM systems were chosen due to their innate polar alignment; thus reducing or eliminating any electrostriction or exoelectric response of the lms in conjunction with being non ferroelectric. The SAMs tested included small molecule ligands (DDT, MUA) as well as bio-inspired peptide and peptoid oligomers (A and B) examined in our prior work. 16 The response of each target lm was measured at varying piezo stack voltages, generating varying effective k l values. Fig. 2 illustrates the resulting experiment, in which the recorded response for a given target material increases exponentially as the effective k l value of the lever used in the measurement decreases. The results conrm that for so materials like SAMs, using levers with spring constants comparable to the modulus of the material's leads to increased response. In some cases, experimental tip responses reach 250 pm V À1 , far exceeding previously reported electromechanical response in these so materials. Though the overall electromechanical response is high, as discussed below, these responses are inuenced more by electrostatics than the intrinsic piezo response of the materials (d 33 ). While the spring constant of the lever (k l ) is shown to inuence the response of the lms, it is merely contributing to changes in the contact stiffness (k c ). 17,20,24 As eqn (1) illustrates, while stiffer levers affect the response, it is the contact stiffness (k c ) that directly inuences the measurement. 24 While the distinction may seem subtle, k l is merely a single component of the contact. Thus, the spring constant of the contact derives from the lever, the mechanical response of the material in the x, y, and z-axis, inuence of surface electrostatics, and any tip-sample meniscus that may be present (e.g., in ambient conditions). Fortunately, these factors can be estimated by applying eqn (2) to the already measured k l values (as part of tip-sample tuning in DART-PFM). 17 Eqn (2) approximates the spring constant of contact (k c ) from the spring constant of the lever (k l ) by taking the ratio of the resonance frequency of the free lever (u 0 ) to the lever in contact with the sample (u 1 ) used in the DART experiment. 17 While the use of stiffer levers is correlated to an increased contact stiffness, using the calculated k c values to model tip response, yield better ts (Table 1), reecting the correct physics due to the higher spring constant of the contact stiffness dominating. The comparable ts of tip response to k l values, found in Table S1, † qualitatively maintain the same trenddecreased spring constant yields increased electromechanical tip response, albeit with lower quality of t (R 2 ).
However, as indicated in eqn (1), an ideal dependence would yield an exponent of k c À1 (example plot in ESI †), but the values determined by ts in Fig. 2 and Table 1 deviate signicantly. In all the organic monolayers, the tip response falls off faster than predicted (i.e., exponents closer to ca. À1.3) with increasing contact stiffness. We speculate that this derives from the stiffer levers distorting the monolayers instead of remaining at the interface. The only exception is for the peptoid B SAMs, in which the tip-response curve yields an exponent close to À1.0, suggesting that the peptoid lm is signicantly stiffer than the other lms, as conrmed by AMFM measurements discussed below, and consistent with expectations of a peptoid PPI helix. 27 While eqn (2) allows an approximate conversion of k l to k c values, assuming a uniform shi from the fundamental frequency of the lever to the measured frequency of the lever while interacting with surface, k c was also measured directly using amplitude modulated force microscopy (AMFM). 10,[30][31][32] Due to the trends observed in the original k l measurements, the k c was not directly measured by AMFM for all levers. Only the ASYELEC.01 R2 and the TR400PB (S) levers, 2.8 and 0.09 N m À1 respectively, were chosen as the relative extremes of contact stiffnesses observed in the initial study, (Table in ESI †). We note that the measured k c values deviate substantially from eqn (2) for stiffer levers, again suggesting that the stiffer levers are distorting the monolayers, effectively limiting the ability of the so materials to mechanically respond to the applied electric elds.
As mentioned above, while so levers give higher tip response, they also suffer from greater levels of electrostatic interference than stiffer levers. One way to account for this effect would be to apply a V DC to the tip that is equal to V CPD , thus eliminating the electrostatic term in eqn (1). Intuitively one simple solution would be to measure the V CPD by SKPFM, and then apply that V DC , as has been previously implemented. 27 The problem arises from the nature of the DART measurement where a V AC is applied on top of the V DC , altering the electrostatic environment around the contact, modulating the intrinsic V CPD of the sample. Instead, we swept the DC eld to nd the point of minimal tip response at which the contact potential equals the applied DC eld under a constant V AC (Fig. 1B).
The tip response (R) is the measured output of the DART experiment aer the simple harmonic oscillator (SHO) calculation corrects for the tip-sample resonance enhancement. This tip response can be separated, using eqn (1), into the intrinsic piezoresponse of the material and the electrostatic response. When V DC is equal to V CPD , the electrostatic component of the measurement will go to zero leaving only the mechanical response of the material under the applied eld. The organic SAM lms are intrinsically polar, permanent piezoelectric materials, since one end is attached via an Au-S bond. Consequently, one expects no ferroelectric hysteresis from sweeping V DC , only two intersecting lines of equal slope proportional to k c À1 dC/dz (Fig. 1B). The intersection point will represent the piezoelectric response d eff Â V AC . The results are highlighted in Fig. 3 and summarized in Table 2, in which three different AFM levers are used on two different organic SAMs. Fig. 3 establishes that the proposed new method works for xed polar molecular monolayer lms. The technique is demonstrated on two SAMs: one piezo active peptide 16 and a control of DDT, used to highlight the natural polarization of organic SAMs when adsorbed to a metallic surface. The high electrostatic component of the low k l levers is easily compensated through the new method. The results point to a piezoresponse range of À0.33 to 0.11 pm V À1 for DDT and À0.16 to 3.2 pm V À1 for peptide A. The measured d eff of peptide A using the 0.02 N m À1 lever is signicantly larger than the values determined with the stiffer levers.
Further, by highlighting three different spring constant levers ranging from 0.02 to 2.8 N m À1 the results from Fig. 2 can be reaffirmed. Here, lm response increases with decreasing k l  Paper due to electrostatic effects, reducing the maximal response at 2.0 V DC and 4.0 V AC from near 1000 pm to $3 pm. These results represent a greater than 300-fold decrease in measured response; moreover the inset charts in Fig. 3 demonstrate that at high k c , relative to the sample material, the instrument sensitivity bottoms out, effectively identifying the noise oor of the measurement technique. The inset charts emphasize the trend towards higher R 2 values where at high k c and k l , response is sporadic and hard to model in contrast to the low k l levers. The increase in sensitivity is further conrmed by the changes in the tune amplitude, at the described set points, from <2 V to >50 V. These, results reect the benets of the new method by demonstrating increased precision in the determination of the d eff for so monolayers through enhanced signal to noise ratios. Based on the evidence in Fig. 2 and 3, the use of so, lowspring-constant the TRS levers (0.09 N m À1 ) are less likely to perturb organic monolayers, and the DC-sweep DART-PFM technique enables separation of inherent piezoelectric response of a material from the electrostatic components to tip response. Consequently, TRS levers were used with DC-sweep DART-PFM across four organic SAMs and a quartz crystal microbalance (QCM). The latter serves as a non-ferroelectric control with known piezoresponse (d 33 ), while DDT and MUA SAMs were used as control organic monolayers with low expected piezoresponse, but varying hydrophobicity. If the contact stiffness depends on the effects of a meniscus at the tip sample interface under ambient conditions, modulating from a hydrophobic DDT monolayer to a hydrophilic MUA monolayer should reveal such effects on measured electromechanical response. Peptide A and peptoid B represent helical piezoactive materials with different backbone motifs that give rise to differences in helical propensity. 16 The DC-sweep DART-PFM response of these lms under a constant 3.0 V AC eld is illustrated in Fig. 4 and compiled in Table 3. The resulting eld plots yield d eff of the varying materials. QCM stands out with a d eff value consistent with literature (i.e. 1.68 pm V À1 vs. 2.3 pm V À1 ), 19 but the observed tip response (e.g., Fig. 4a) is much smaller, compared to the other monolayer samples. The low slope indicates that the magnitude of the d eff in quartz is not signicantly different from that of the monolayers, but its electrostatic component is minimal compared to the monolayer lms. This likely indicates that the ability of quartz to build a large differential capacitance in the z-axis is signicantly smaller in comparison to the SAMs. Further, these results reconrm previously reported conclusions that the helix forming peptide and peptoid have higher piezo electric coefficients than DDT and MUA. 16 More signicant than the magnitude of the tabulated piezo coefficients in Table 3 is the sign. Noticeably three out of four SAMs have a negative d eff , indicating that they compress under an applied eld. Only DDT produced a positive d eff , albeit close to zero. This negative piezo response differs from conventional piezo ceramics such as ZnO or PZT, but is similar to that observed in PVDF and a variety of piezoelectric materials. [33][34][35] Thus, the new method not only determines positive, but also negative piezoresponse, even at low applied voltages.
We note both the d eff and V CPD from the peptide A monolayer shis by applying different V AC between Fig. 3 and 4 (4.0 V AC and 3.0 V AC respectively). To test if the V CPD and d eff is subject to shiing under various experimental conditions a lm of peptoid B was tested against four different AC voltages sweeping through six DC voltages at each AC voltage. Extracting the surface potential under experimental conditions from Fig. 5A and comparing it to the applied AC eld a linear trend emerges. As the applied electric eld increases under the experimental conditions so does the V CPD . This indicates that a static V DC determined by sKPFM cannot be used directly to eliminate the   Fig. 5A represents the equivalent of eight experimental runs on one sample using the more traditional AC sweep method, thus conrming the repeatability of the new measurement system and the lack of dielectric brake down of the lms due to the applied elds.  Table 4).
The comparison between the molecular monolayers and quartz highlights a signicant shi of material response to an applied eld. The slopes of the plots in Fig. 3 represent the electrostatic component of the material response. When comparing the materials there is a signicant shi in the slope of the ts indicating a variation in the effect of electrostatics on the reported response. Quartz has a fundamentally shallower slope than any of the molecular lms. Likely the applied AC eld or the differential capacitance in the z-axis are the inuencing factors. The AC eld however is uniformly applied at 3.0 V across all samples and accounted for when the nal response is computed. In addition, a humidity-controlled chamber held at approximately 20% provides no likely outside source for eld augmentation, ensuring little to no variation in the meniscus formed at the tip-sample interface. Hence, the contribution from the differential capacitance in the z-axis is  Paper likely the source of the discrepancy in the overall measured response. This difference in capacitance is likely due to a difference between the relatively high dielectric constant of quartz (3 $ 4) compared to the lower dielectric constant of the SAMs (MUA 3 $ 2). 36,37 To test this hypothesis, several conventional hard-ceramic piezoelectric materials were tested, in addition to the nonferroelectric quartz material sampled above, including: ferroelectric PZT ($1 cm thick), PPLN ($1 mm thick), and a second non-ferroelectric material ZnO ($1 mm thick) (results in ESI †). In all three cases, the technique also worked for minimizing the electrostatic effect on tip response. Only ZnO gave responses indicating a large electrostatic effect from the measured response (see ESI †). The testing of PZT and PPLN mirrored the results of quartz, where the slopes of the ts are shallow, but present higher baseline piezo response. These results conrm that so-molecule based piezoelectric materials are fundamentally different from classical ceramic based materials and must be analyzed with new methods that allow for operation at higher signal to noise ratios while simultaneously removing the electrostatic component of the response. This has been demonstrated to be achievable by alternatively sweeping the V DC instead of the V AC and nding the point of inection where the V DC is equal to the V CPD and extracting the d eff from that point instead of the slope of the t.

Conclusions
This work has coupled multiple AFM techniques together to establish and validate a new method for quantitatively separating the electrostatic component from the purely piezoelectric response of low Young's modulus piezo-active materials using DART-PFM. We nd that organic monolayers, and other so electromechanical materials, require the use of low spring constant tips to better match the elastic modulus of the  materials. In turn, this increases the electrostatic component of the tip response, which can be minimized by sweeping the DC voltage until the minimum response is found. In principle, this point should reect the contact potential of the lm. We nd through scanning Kelvin probe microscopy that the potentials are close, but effects of applied elds during the DART-PFM experiment modulate the V DC potential that minimizes the electrostatic tip response. Elastic AMFM results established the necessity to match lever stiffness (k l ) with the modulus of the material under study. Simultaneously, AMFM results conrmed that the contact stiffness (k c ) is directly inuenced by the k l , yet k c is the optimal parameter for the accurate determination of the piezoelectric coefficient, unlike previous reports. 27 We nd incredibly large electromechanical tip responses, nearing 250 pm V À1 , which derive from large differential capacitance of the lms rather than the innate piezoresponse. This large electrostatic component from organic monolayers is in stark contrast to a range of inorganic materials studied, which may show greater intrinsic piezoresponse, but much lower electrostatic components. We speculate that while the organic monolayers have lower dielectric constants than piezo ceramics such as PZT, the differential capacitance is high due to their lower elastic modulus and thin layer thickness (e.g., $2 nm).
The new method of DC-sweep DART-PFM was used to determine the d eff piezoresponse and electrostatic components of four organic monolayers and four conventional inorganic piezo materials. The method nds peptide and peptoid SAMs with both positive and negative piezo response and, coefficients in agreement with previously reported values. 16 Control molecular SAMs composed of DDT and MUA show close to zero piezoresponse. While scans across multiple lms and different AC voltages do affect the measurement somewhat, the DC-sweep DART-PFM technique shows much improved reproducibility relative to previous efforts using varied AC voltages with DART-PFM.
We believe this new technique will improve accurate measurements of electromechanical response in organic and biomaterials. Moreover, the large electrostatic component of electromechanical response found in organic materials can likely be utilized for sensing or other applications.

Monolayer formation
Solvents and reagents were purchased from Sigma-Aldrich without further purication. Biogold substrates were purchased from Thermo Scientic and consist of a glass substrate with a titanium (10 nm) adhesion layer and gold (100 nm). The peptide and peptoid were synthesized and puried following procedures described previously. 16 Gold-thiol based self-assembled monolayers were prepared from 1.0 mM solutions of dodecane thiol (DDT) or mercaptoundecanoic acid (MUA) in ethanol, peptide in water, and peptoid in acetonitrile. The various solvents were used to ensure maximum solubility of target molecules and have no bearing on SAM formation. Substrates were prepared for SAM formation by multiple ethanol and water washings followed by a 15 minute sonication in the solvent used for deposition (ethanol for MUA/DDT, water for peptide and acetonitrile for peptoid). Aer the corresponding solvent wash, substrates were rinsed with solvent and dried with N 2 . SAMs were formed by placing clean/dry substrates into 1.0 mM thiol ligand solution for 24 hours in ambient conditions. Aer the deposition period, samples were removed from solution rinsed, dried with N 2 , covered and placed in a desiccator for a minimum of one hour before analysis. All samples were stored under vacuum conditions in a UV blocking container to prevent thiol oxidation. DART DART experiments were conducted at multiple tip-sample AC, and DC biases ranging from |0-4| V. Deection was set to À0.30 V with a tune z-voltage of $15 V and a scan z-voltage of $À7.0 V, to maximize signal and ensure stable contact between probe and sample during scanning, unless otherwise stated. Relative humidity was maintained below 30% with a dry N 2 purge inside the AFM enclosure. Each sample was examined in a 1.0 m Â 1.0 mm area with a rate of 0.75 Hz at a 90 scan angle to minimize topological artifacts. The topography, piezo-response amplitude and phase images were recorded and q-corrected to account for tip-sample resonance amplication using the builtin simple harmonic oscillator (SHO) function. 16,24 Histograms of the resulting q-corrected piezo-response amplitude were generated, and the mean value of the distribution was extracted and correlated with the appropriate applied DC and AC elds, as discussed below.

SKPFM
SKPFM measurements were conducted solely with the R2 levers to attain the contact potential difference (V CPD ) of each target material. Deection was set to $0.0 V via tuning, with a scan z-voltage of 100 V. Start and delta heights were set to 10 nm for all contact potential images (NAP scanning in Asylum soware) with a trigger voltage of 800 mV. A static 1.0 V DC eld was established for each measurement with no sample grounding due to the dielectric nature of the monolayers being examined. The implemented scan rate was 0.5 Hz at a 90 scan angle.

AMFM
AMFM measurements were conducted with R2 and TRS levers to represent the contact stiffness across the range of the cantilever k values represented. Mirroring conditions used in DART scans a deection of À0.30 V with tune/scan z voltages of $15.0 V and À7.00 V respectively were used. The manufacture provided tip radius for TRs ¼ 42 nm and 25 nm for R2 were used to model tip-sample interactions assuming spherical contact. Scan areas of 10.0 mm Â 1.0 mm.

Conflicts of interest
The authors declare no competing nancial interests.