Intermodal coupling spectroscopy of mechanical modes in microcantilevers

• Ioan Ignat,
• Bernhard Schuster,
• Jonas Hafner,
• MinHee Kwon,
• Daniel Platz and
• Ulrich Schmid

Beilstein J. Nanotechnol. 2023, 14, 123–132, doi:10.3762/bjnano.14.13

• excitation of the first mode of a cantilever with measurements being performed at its harmonics [37]. Another method involved clever designs such as T-shaped cantilevers [38] and inner-paddled cantilevers [39] aiming at reducing the noise impact on force reconstruction. Bimodal AFM is another addition to the

• multitonal responses, from which the force is reconstructed. In this paper, we are building towards a hybrid multifrequency approach different from the ones described above. The on-resonance measurement would follow frequency-modulated AFM or bimodal AFM while being assisted by a new off-resonance excitation

Reconstruction of a 2D layer of KBr on Ir(111) and electromechanical alteration by graphene

• Zhao Liu,
• Antoine Hinaut,
• Stefan Peeters,
• Sebastian Scherb,
• Ernst Meyer,
• Maria Clelia Righi and
• Thilo Glatzel

Beilstein J. Nanotechnol. 2021, 12, 432–439, doi:10.3762/bjnano.12.35

• a constant amplitude and controlled by the frequency shift. Bimodal AFM was used to combine the first flexural resonance (frequency of f1 ≈ 165 kHz, amplitude of A1 = 2–8 nm and a typical quality factor of Q1 = 30,000) or the second flexural resonance (frequency of f2 ≈ 1 MHz, amplitude of A2 = 200

Design of V-shaped cantilevers for enhanced multifrequency AFM measurements

• Mehrnoosh Damircheli and
• Babak Eslami

Beilstein J. Nanotechnol. 2020, 11, 1525–1541, doi:10.3762/bjnano.11.135

• no studies on the static and dynamic behavior of V-shaped cantilevers in multifrequency AFM due to their complex geometry. In this work, the static and dynamic properties of V-shaped cantilevers are studied while investigating their performance in multifrequency AFM (specifically bimodal AFM). By

• dimensions, the optimum V-shaped cantilever that can provide the maximum phase contrast in bimodal AFM between gold (Au) and polystyrene (PS) is found. Based on this study, it is found that as the length of the cantilever increases the 2nd eigenmode phase contrast decreases. However, the base width exhibits

• an optimum rectangular cantilever. Two sets of bimodal AFM experiments are carried out on Au-PS and PS-LDPE (polystyrene and low-density polyethylene) samples to verify the simulation results. Keywords: bimodal AFM; optimization; soft matter; surface characterization; V-shaped cantilevers

Stochastic excitation for high-resolution atomic force acoustic microscopy imaging: a system theory approach

• Edgar Cruz Valeriano,
• José Juan Gervacio Arciniega,
• Christian Iván Enriquez Flores,
• Susana Meraz Dávila,
• Joel Moreno Palmerin,
• Martín Adelaido Hernández Landaverde,
• Yuri Lizbeth Chipatecua Godoy,
• Aime Margarita Gutiérrez Peralta,
• Rafael Ramírez Bon and
• José Martín Yañez Limón

Beilstein J. Nanotechnol. 2020, 11, 703–716, doi:10.3762/bjnano.11.58

• acoustic microscopy (AFAM) [1], bimodal AFM [15], resonance tracking-atomic force acoustic microscopy (RT-AFAM) [7], band excitation [10], dual-frequency resonance-tracking atomic force microscopy [16], nanomechanical spectroscopy [2], G-mode [17] and triple frequency atomic force microscopy [18]. Even

Current measurements in the intermittent-contact mode of atomic force microscopy using the Fourier method: a feasibility analysis

• Berkin Uluutku and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2020, 11, 453–465, doi:10.3762/bjnano.11.37

• cantilever response near the fundamental frequency [20]. Similarly, bimodal AFM, which involves the excitation of the cantilever at two frequencies, also uses lock-in amplifiers or phase-locked loops to control or observe each frequency response [24][25]. More elaborate Fourier analysis techniques have also

A review of demodulation techniques for multifrequency atomic force microscopy

• David M. Harcombe,
• Michael G. Ruppert and
• Andrew J. Fleming

Beilstein J. Nanotechnol. 2020, 11, 76–91, doi:10.3762/bjnano.11.8

• . These demodulators were chosen as they are the most simple methods to implement in their respective configurations. This experiment further investigated open-loop and closed-loop demodulator performance at low and high tracking bandwidths. When compared to bimodal AFM, higher-harmonic AFM [15][60] has

Imaging of viscoelastic soft matter with small indentation using higher eigenmodes in single-eigenmode amplitude-modulation atomic force microscopy

• Miead Nikfarjam,
• Enrique A. López-Guerra,
• Santiago D. Solares and
• Babak Eslami

Beilstein J. Nanotechnol. 2018, 9, 1116–1122, doi:10.3762/bjnano.9.103

• versatility of the instrument, it has been proposed to use higher cantilever eigenmodes, either by themselves in single-eigenmode imaging [6][7][8][9] or within multifrequency techniques [10]. For example, in the original multifrequency AFM method, introduced by Garcia and coworkers and known as bimodal AFM

• higher eigenmodes. After briefly discussing the key theoretical concepts, we present numerical and experimental results involving the use of AM-AFM with the first eigenmode, AM-AFM with the second eigenmode, and bimodal AFM using the first two eigenmodes, and offer a simple guideline for the

• eigenmode, and bimodal AFM using the first two eigenmodes. In all cases, the product(s) kiAi of the active eigenmode(s) was/were kept constant. Figure 2a presents the peak force observed during the cantilever trajectory as a function of the setpoint ratio of the modulated amplitude. Figure 2b presents the

Lyapunov estimation for high-speed demodulation in multifrequency atomic force microscopy

• David M. Harcombe,
• Michael G. Ruppert,
• Michael R. P. Ragazzon and
• Andrew J. Fleming

Beilstein J. Nanotechnol. 2018, 9, 490–498, doi:10.3762/bjnano.9.47

• harmonic methods have demonstrated the ability to image relatively large biological objects, such as cells [14][15], while bimodal AFM has successfully imaged properties of protein complexes [16]. Intermodulation AFM is a novel extension to the bimodal method that focuses on the mixing products of a

High-stress study of bioinspired multifunctional PEDOT:PSS/nanoclay nanocomposites using AFM, SEM and numerical simulation

• Alfredo J. Diaz,
• Hanaul Noh,
• Tobias Meier and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2017, 8, 2069–2082, doi:10.3762/bjnano.8.207

• AFM, which is expected to modify the spacing of the embedded nanoclay particles, causing a change in the electrical conductivity and local mechanical properties. Bimodal AFM, together with numerical AFM simulation and SEM, is used to infer the internal distribution of the nanoclay. Finally, a one

• coatings, with the added multifunctionalities related to the nacre-like structure (i.e., gas barrier behavior, fire retardancy, etc.). Distribution of nanoclay in the film The distribution of nanoclay near the surface was investigated by bimodal AFM for the Laponite RD films. Bimodal AFM [61] is a dynamic

• and for particles with random orientation, among others. Since the calculation of the Young’s modulus with AFM methods is not reliable (as also discussed above) [51], the strain is measured instead and related to the peak imaging forces. The increased force obtained from bimodal AFM for increasing

Analysis and modification of defective surface aggregates on PCDTBT:PCBM solar cell blends using combined Kelvin probe, conductive and bimodal atomic force microscopy

• Hanaul Noh,
• Alfredo J. Diaz and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2017, 8, 579–589, doi:10.3762/bjnano.8.62

• modification of unidentified surface aggregates. The aggregates are characterized electrically by Kelvin probe force microscopy and conductive atomic force microscopy (C-AFM), whereby the correlation between local electrical potential and current confirms a defective charge transport. Bimodal AFM modification

• blend–electrode interface. In addition, we use bimodal AFM, a multifrequency AFM technique [18], to modify and remove the surface molecular layers. The series of AFM analyses and modification performed can be useful to better understand the nature of PSC surface defects. A detailed description of the

• considered for a proper fundamental understanding of the device physics and chemistry [32][33][34]. Nevertheless, the simulation provides useful qualitative insight for understanding C-AFM measurements on PSCs. Modification of surface aggregates by bimodal AFM Since the surface aggregates are defective with

Advanced atomic force microscopy techniques III

• Thilo Glatzel and
• Thomas Schimmel

Beilstein J. Nanotechnol. 2016, 7, 1052–1054, doi:10.3762/bjnano.7.98

• interaction in liquid media [28]. A software package, dForce, was also presented that allows for a better understanding of amplitude modulation and bimodal AFM experiments in air or liquid [29]. A method for the calibration of the torsional force by using human fibronectin and its monoclonal antibody was

Generalized Hertz model for bimodal nanomechanical mapping

• Aleksander Labuda,
• Marta Kocuń,
• Waiman Meinhold,
• Deron Walters and
• Roger Proksch

Beilstein J. Nanotechnol. 2016, 7, 970–982, doi:10.3762/bjnano.7.89

• of the cantilever dynamics in bimodal AFM experiments. Here, we present a simplified theory for bimodal AFM with a large fundamental resonance oscillation amplitude and small higher resonance amplitude. The theory is based on a binomial approximation of the weight function for extracting the

• derivation here begins in the context of a Hertzian contact with a paraboloidal tip and is then generalized to any tip shape described by a power-law profile. This theory is then experimentally applied to three variations of bimodal AFM involving different dynamic AFM modes of operation [42][43], namely

• amplitude modulation (AM) [1][18][19], phase modulation (PM) [43][44][45][46] and frequency modulation (FM) [23][36][47]. Finally, a method for extracting the tip size and tip shape from bimodal AFM approach curves is presented and demonstrated on a polystyrene sample. Figure 1 provides a diagram of the

Nanoscale effects in the characterization of viscoelastic materials with atomic force microscopy: coupling of a quasi-three-dimensional standard linear solid model with in-plane surface interactions

• Santiago D. Solares

Beilstein J. Nanotechnol. 2016, 7, 554–571, doi:10.3762/bjnano.7.49

• of imaging parameters that the user can vary generally increases with the sophistication of the method; for example, bimodal AFM requires more imaging parameters than single-mode amplitude-modulation AFM [34]. With regards to the complexity in the tip–sample interactions (described in the previous

High-bandwidth multimode self-sensing in bimodal atomic force microscopy

• Michael G. Ruppert and
• S. O. Reza Moheimani

Beilstein J. Nanotechnol. 2016, 7, 284–295, doi:10.3762/bjnano.7.26

• strain sensitivity on the fifth eigenmode leading to a remarkable signal-to-noise ratio. Experimental results using bimodal AFM imaging on a two component polymer sample validate that the self-sensing scheme can therefore be used to provide both the feedback signal, for topography imaging on the

• to strain sensitivity. The applicability of the multimodal self-sensing principle is verified by bimodal AFM experiments to obtain qualitative phase contrast on the higher eigenmode when imaging a soft polymer blend. Modeling Piezoelectric constitutive laws By sputtering a piezoelectric layer to the

• feedthrough is not compensated entirely which can be seen in the phase response. However, the de-embedded eigenmodes have enough dynamic range to be suitable for bimodal AM-AFM imaging as will be discussed in section Bimodal AFM application. Sensor sensitivity The optical lever method measures the bending

A simple and efficient quasi 3-dimensional viscoelastic model and software for simulation of tapping-mode atomic force microscopy

• Santiago D. Solares

Beilstein J. Nanotechnol. 2015, 6, 2233–2241, doi:10.3762/bjnano.6.229

• of force curve for bimodal AFM, showing a double impact. The blue arrows indicate in each case the position where the tip first reaches the sample, and the red arrows indicate the position where the tip leaves the sample. Van der Waals forces have been included in the attractive (noncontact) region

• interacting with a cavity on the surface with respect to a tip interacting with a flat surface; (d) typical Q3D force curves for bimodal AFM imaging using the first and third eigenmodes. Note that the level of indentation increases as A3 increases. Note also the resemblance to the force curve shown in Figure

• constant k = 4 N/m, eigenmode quality factors Q1 = 150, Q2 = 450, Q3 = 750; tip radius of curvature R = 20 nm, and SLS parameters (see Figure 1) k1 = k2 = 7.5 × 10−2 N/m/nm2, and c = 1.0 × 10−7 N s/m/nm2 (monomodal AFM) and 2.5 × 10−8 N s/m/nm2 (bimodal AFM). (a) Force curve for a 20 nm radius tip with a

Optimization of phase contrast in bimodal amplitude modulation AFM

• Mehrnoosh Damircheli,
• Amir F. Payam and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2015, 6, 1072–1081, doi:10.3762/bjnano.6.108

• Bimodal force microscopy has expanded the capabilities of atomic force microscopy (AFM) by providing high spatial resolution images, compositional contrast and quantitative mapping of material properties without compromising the data acquisition speed. In the first bimodal AFM configuration, an amplitude

• phase contrast improves by decreasing the energy of second mode relative to those of the first and third modes. Keywords: bimodal AFM; dynamic AFM; tapping mode; Introduction The atomic force microscope is a versatile and powerful tool for imaging, compositional mapping and modification of surfaces

• on the feedback schemes [16][17][18][19][20][21][22][23][24]. In the first bimodal AFM configuration (bimodal AM) [15][16], the feedback acts on the amplitude of the first mode by keeping it at a fixed value during imaging while the second mode operates in an open loop. The ability of bimodal AM to

Dynamic force microscopy simulator (dForce): A tool for planning and understanding tapping and bimodal AFM experiments

• Horacio V. Guzman,
• Pablo D. Garcia and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2015, 6, 369–379, doi:10.3762/bjnano.6.36

• experiments. The simulator presents the cantilever–tip dynamics for two dynamic AFM methods, tapping mode AFM and bimodal AFM. It can be applied for a wide variety of experimental situations in air or liquid. The code provides all the variables and parameters relevant in those modes, for example, the

• simulations. Finally, the accuracy of dForce has been tested against numerical simulations performed during the last 18 years. Keywords: bimodal AFM; dynamic AFM; nanomechanics; numerical simulations; tapping mode AFM; Introduction Numerical simulations have played a pivotal role to advance the

• the case of bimodal AFM, numerical simulations [39] preceded and paved the way to its experimental development [33][40]. The complexity of amplitude modulation AFM makes it difficult to develop reliable code accessible for both the large community of tapping mode AFM users and the emerging community

High-frequency multimodal atomic force microscopy

• Adrian P. Nievergelt,
• Jonathan D. Adams,
• Pascal D. Odermatt and
• Georg E. Fantner

Beilstein J. Nanotechnol. 2014, 5, 2459–2467, doi:10.3762/bjnano.5.255

• far remained the domain of a handful of highly-specialized instruments. In this report, we present high-resonance-frequency bimodal AFM imaging by using an AFM readout head designed for high-frequency drive and readout of small cantilevers. Our head is compatible with the Bruker MultiMode AFM, a

• /. d) Thermal noise peak of the second flexural mode of a FastScan A at 6.6 MHz. Bimodal AFM imaging of a PS/PMMA polymer blend with small, high-frequency cantilevers in both air (panels a–c) and water (panels d–f). Panels a and c show topography based on amplitude modulation of the fundamental

Probing viscoelastic surfaces with bimodal tapping-mode atomic force microscopy: Underlying physics and observables for a standard linear solid model

• Santiago D. Solares

Beilstein J. Nanotechnol. 2014, 5, 1649–1663, doi:10.3762/bjnano.5.176

• ]) is used and its complexities and non-idealities are simulated within bimodal AFM, which has become a popular multi-frequency method since its introduction ten years ago [11][12]. The SLS is a simple model that does not fully reproduce the behavior of true surfaces, but since it exhibits the correct

• ][35][36] methods. Within multi-frequency AFM, Lozano et al. analyzed the behavior of Vts and Pts for the original bimodal AFM method, which uses an open loop drive to excite the higher eigenmode [32][37]. Naitoh and coworkers reported bimodal experiments by using FM-AFM to drive both eigenmodes, in

• computed trajectories of the tip, both for single-mode and bimodal AFM. The second sub-section explores the effect of the SLS model parameters on the observables as well as the prospect for carrying out compositional mapping by using average quantities, such as the virial and dissipated power. Physics of

Multi-frequency tapping-mode atomic force microscopy beyond three eigenmodes in ambient air

• Santiago D. Solares,
• Sangmin An and
• Christian J. Long

Beilstein J. Nanotechnol. 2014, 5, 1637–1648, doi:10.3762/bjnano.5.175

• -eigenmode methods [19][20][21][22], which are of particular interest since their purpose is to carry out multiple characterization functions at the same time. Specifically, bimodal AFM methods were developed to perform simultaneous topographical imaging and compositional mapping [2][3], and trimodal methods

• interactions between them [20][21][22] (see also Figure 4c and Figure 4d below, which offer an experimental example in which not all eigenmodes oscillate in the same regime). As a result, the spectroscopy theory previously developed for bimodal AFM [25][26] is not necessarily applicable to multimodal AFM. The

Trade-offs in sensitivity and sampling depth in bimodal atomic force microscopy and comparison to the trimodal case

• Babak Eslami,
• Daniel Ebeling and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2014, 5, 1144–1151, doi:10.3762/bjnano.5.125

• experiments on Nafion® proton exchange membranes and numerical simulations illustrating the trade-offs between the optimization of compositional contrast and the modulation of tip indentation depth in bimodal atomic force microscopy (AFM). We focus on the original bimodal AFM method, which uses amplitude

• can also be accomplished when using bimodal AFM, although without the flexibility to independently optimize the sensitivity of the compositional mapping process. We discuss the trade-offs involved and provide an illustration of the dynamics complexities, including strong eigenmode coupling in some

• the sample surface is not affected by forces originating from physical contact. Instead, changes in the non-contact tip–sample interactions, which include van der Waals, electrostatic and magnetic forces, establish the basis for mapping sample topography and properties. In fact, the first bimodal AFM

Challenges and complexities of multifrequency atomic force microscopy in liquid environments

• Santiago D. Solares

Beilstein J. Nanotechnol. 2014, 5, 298–307, doi:10.3762/bjnano.5.33

• imaging conditions and to properly interpret the results, and no single recipe works in all cases. This paper explores through simulation the implications of the low-Q cantilever dynamics within the specific context of bimodal AFM imaging. The primary focus is on (i) the amplitude and phase “relaxation

• is generally smaller than the ratio of eigenfrequencies [21][26]. In the case of bimodal AFM, a similar phenonmenon takes place, where the driven higher eigenmode is perturbed every tip–sample impact and the perturbation relaxes in between successive taps. However, the situation is slightly different

• multiple tip–sample impacts for every cycle of the fundamental eigenmode (c). The simulation parameters are ν1 = 14.5 kHz, k1 = 0.03 N/m, Q1 = 2, Q2 = 6, Afree = 75 nm, Asetpoint = 55% and sample modulus of elasticity of 2 GPa (Hertzian contact). Bimodal AFM simulation illustrating the phase and amplitude

Unlocking higher harmonics in atomic force microscopy with gentle interactions

• Sergio Santos,
• Victor Barcons,
• Josep Font and
• Albert Verdaguer

Beilstein J. Nanotechnol. 2014, 5, 268–277, doi:10.3762/bjnano.5.29

• ° to 0°, is observed for n = 2 only. While these jumps of nearly 180° might be of interest they are ignored from now on. The reader can refer to recent works that discuss multiple regimes of operation in bimodal AFM [31][33]. It follows that variations in Hamaker are not detected by higher harmonic

Multiple regimes of operation in bimodal AFM: understanding the energy of cantilever eigenmodes

• Daniel Kiracofe,
• Arvind Raman and
• Dalia Yablon

Beilstein J. Nanotechnol. 2013, 4, 385–393, doi:10.3762/bjnano.4.45

• property contrast with high resolution. Bimodal AFM, where two eigenmodes are simultaneously excited, confers significant advantages over conventional single-frequency tapping mode AFM due to its ability to provide contrast between regions with different material properties under gentle imaging conditions

• . Bimodal AFM traditionally uses the first two eigenmodes of the AFM cantilever. In this work, the authors explore the use of higher eigenmodes in bimodal AFM (e.g., exciting the first and fourth eigenmodes). It is found that such operation leads to interesting contrast reversals compared to traditional

• bimodal AFM. A series of experiments and numerical simulations shows that the primary cause of the contrast reversals is not the choice of eigenmode itself (e.g., second versus fourth), but rather the relative kinetic energy between the higher eigenmode and the first eigenmode. This leads to the

Bimodal atomic force microscopy driving the higher eigenmode in frequency-modulation mode: Implementation, advantages, disadvantages and comparison to the open-loop case

• Daniel Ebeling and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2013, 4, 198–207, doi:10.3762/bjnano.4.20

• fundamental eigenmode is driven by using the amplitude-modulation technique (AM-AFM) while a higher eigenmode is driven by using either the constant-excitation or the constant-amplitude variant of the frequency-modulation (FM-AFM) technique. We also offer a comparison to the original bimodal AFM method, in

• 2004 Garcia and co-workers [2] reported on computational simulations of a bimodal AFM technique for the simultaneous imaging of topography and mapping of compositional contrast across the sample. Within their method the fundamental cantilever eigenmode was used to acquire the sample topography through

• -parallel relationship between phase and frequency can be easily observed in a trimodal experiment in which one higher eigenmode is driven in OL and another one is driven in FM [12][13], or in separate bimodal experiments conducted in AM-OL or AM-FM [7]. Figure 3 shows a comparison of bimodal AFM