Exploring internal structures and properties of terpolymer fibers via real-space characterizations

• Michael R. Roenbeck and
• Kenneth E. Strawhecker

Beilstein J. Nanotechnol. 2023, 14, 1004–1017, doi:10.3762/bjnano.14.83

• we present internal structural characterizations of FIB-notched Technora® fibers using multifrequency AFM mapping. We observe a homogeneous microstructure throughout the fiber without any evidence of a fiber skin near the periphery. At the nanoscale, we observe a highly fibrillated structure well

• profiles, ET distributions, and other quantifications of AFM maps were characterized using the Gwyddion software package [27]. Additional details on multifrequency AFM mapping theory, analysis and applications have been provided in earlier literature reports [10][28][29]. Materials and methods overview. (a

• . Dashed line highlights a shear plane between the two notches. The fiber readily opens along this plane, exposing internal fiber surfaces for characterization. (c) Multifrequency AFM schematic. A cantilever is driven by a blue laser that simultaneously excites the cantilever at its first and second

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

• . Through such findings we aim to expand the field of multifrequency AFM with innumerable possibilities leading to improved signal-to-noise ratios, all accessible with no additional hardware. Keywords: atomic force microscopy; intermodal coupling; nonlinear mechanics; optomechanics; sideband cooling

• multifrequency AFM has improved both imaging contrast and the amount of extracted information from AFM experiments by exploiting the nonlinearity of the tip–surface interaction [32][33][34][35][36]. The methods applied excel in both their creativity and engineering prowess. A first example is on-resonance

• multifrequency AFM methods designed for controlling the sense mode to reach their ultimate goal of greater signal-to-noise ratios. These possibilities only multiply if the mechanical–mechanical interactions were only one aspect of a device. In a MEMS or NEMS device, such interactions would be useful to bridge

Quantitative dynamic force microscopy with inclined tip oscillation

• Philipp Rahe,
• Daniel Heile,
• Reinhard Olbrich and
• Michael Reichling

Beilstein J. Nanotechnol. 2022, 13, 610–619, doi:10.3762/bjnano.13.53

• has been applied. Additionally, a tilted cantilever has been found to lead to a modification of the tip–sample convolution [12], to enhance the sensitivity of the measurement to the probe side [13], and to influence results of multifrequency AFM and Kelvin probe force microscopy [14]. In the presence

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

• ; Introduction Since the invention of atomic force microscopy (AFM), different techniques have been introduced into the field to enhance and improve this nanotechnology equipment. In 2004, multifrequency AFM was introduced as a technique that can capture both topographical and material composition in a single

• , multifrequency AFM has gained the attention of different fields, such as, the measurement of nanoscale chemical and mechanical properties of human dentin [2], the mapping of viscoelastic materials [3], or the characterization of thin molecular films [4]. As different fields have implemented multifrequency AFM in

On the frequency dependence of viscoelastic material characterization with intermittent-contact dynamic atomic force microscopy: avoiding mischaracterization across large frequency ranges

• Enrique A. López-Guerra and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2020, 11, 1409–1418, doi:10.3762/bjnano.11.125

• ]) and band-excitation AFM [9][29], as well as dynamic methods based on multifrequency AFM [4][5] and multi-harmonic AFM [30][31] have also been implemented to measure an effective modulus of elasticity and an effective coefficient of dissipation (or analogous quantities) across the surface. All of these

• case), but would at least be able to begin probing the corresponding types of behavior, say with multifrequency AFM [5][38][44] using a higher (i.e., the 3rd or 4th) eigenmode of a traditional tapping-mode cantilever at a frequency of about 5–10 MHz (or higher with an instrument that has a higher

• , but all equations are coupled through the tip–sample force curve, as is customary in multifrequency AFM simulations [24][38][47][48] or in simulations of AFM imaging in liquid environments [49][50]. The higher eigenfrequencies have the customary rectangular-beam relationship to the fundamental

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

• previous multifrequency AFM experiments [47], falls in the same range as the 30th harmonic). Furthermore, improvements in the reconstruction may be possible due to the fact that the shape of the power spectrum envelope may be known, as is the case for Equation 13 and Equation 18, or could be approximated

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

• the cantilever according to the expression f−3dB = f0/2Q, where f0 is the fundamental resonance frequency. Assuming all other components in the z-axis feedback loop are also working at high speed [3], a low quality factor can demand a fast demodulator [12]. Multifrequency AFM (MF-AFM) is a major field

• conducted through higher-harmonic AFM imaging for both low and high tracking bandwidths. Multifrequency AFM Modulation and Demodulation Fundamentals Cantilever deflection signal model A single component of the cantilever deflection signal is modeled as a sine wave with carrier frequency fi, time-varying

• measurement noise. However, multifrequency AFM applications require an additional metric due to the large number of potentially closely spaced frequencies. For example, higher-harmonic imaging with single-frequency excitation results in small harmonic amplitudes that must be estimated in the presence of both

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

• short theoretical discussion of the key underlying concepts, along with numerical simulations and experiments to illustrate a simple recipe for imaging soft viscoelastic matter with reduced indentation. Keywords: higher eigenmodes; multifrequency AFM; soft matter; viscoelasticity; Introduction Since

• 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

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

• samples, allowing for biophysical processes to be studied [6][7][8]. Multifrequency AFM (MF-AFM) methods allow for the study of tip–sample interactions occurring at multiple frequencies [9]. This extends imaging information beyond the topography to a range of nanomechanical properties including sample

• setup The Lyapunov filter as a multifrequency AFM demodulator was validated through a series of imaging experiments where it is compared side-by-side to a lock-in amplifier. To ensure a fair comparison, the demodulators were tuned to the same tracking bandwidth in both experiments. This is required as

• significantly easier to implement, which is a priority when considering an extension to multiple frequencies. Block diagram of the multifrequency AFM control loop. Block diagram of a single-frequency Lyapunov filter. The pink shaded area highlights the calculation that can be done in parallel for multiple

A robust AFM-based method for locally measuring the elasticity of samples

• Alexandre Bubendorf,
• Stefan Walheim,
• Thomas Schimmel and
• Ernst Meyer

Beilstein J. Nanotechnol. 2018, 9, 1–10, doi:10.3762/bjnano.9.1

• dimensions of an ideal beam-shaped cantilever. However, most cantilevers used for measurements are not ideal. Thus, to achieve consistent results, the values of length and tip height have to be corrected. When measurements using the multifrequency AFM [15][16] method of Herruzo et al., which is based on the

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

• ), contact-resonance force microscopy (mechanical properties), and SEM combined with a variety of stress-strain AFM experiments and AFM numerical simulations (internal structure). We further study the nanoclay’s response to the application of pressure with multifrequency AFM and conductive AFM, whereby

• the AFM probe diameter. No pressure-induced changes in conductivity were observed in the clay-free polymer either. Keywords: biomimetics; conductive AFM; conductive nanocomposites; contact-resonance force microscopy; multifrequency AFM; transparent coatings; Introduction Bioinspired material designs

A review of demodulation techniques for amplitude-modulation atomic force microscopy

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

Beilstein J. Nanotechnol. 2017, 8, 1407–1426, doi:10.3762/bjnano.8.142

• commercial AFM systems. The performance metrics, tracking bandwidth and sensitivity to other frequency components, are especially important in high-speed [15][16][17][18] and multifrequency AFM [19] applications. As the tracking bandwidth directly affects the achievable scan rate, it should be maximized

• . However, this also increases the noise bandwidth. On the other hand, in multifrequency AFM applications, the sensitivity to other frequency components is of greatest concern. These applications may include multiple eigenmode contributions [20][21][22], higher harmonics [23][24][25], and multi-tone near

• methods can yield fast estimates with low latency, they may not be suitable for multifrequency AFM methods where non-integer multiples of the fundamental frequency are present in the deflection signal. The demand for a high tracking bandwidth while maintaining insensitivity to additional frequencies in

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

• force microscopy; multifrequency AFM; organic photovoltaics; polymer solar cells; surface defects; Introduction Polymer solar cells (PSCs) [1] have been widely studied due to the abundance of their constituents, their mechanical flexibility and light weight, as well as the possibility of low-cost roll

• 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

• aggregates, avoiding additional sample modification. Typically, multifrequency AFM uses the first eigenmode of the cantilever to control the tip–sample distance and acquire the topography, and higher eigenmodes to measure additional properties [37][38]. We have also previously shown that the peak forces can

Multimodal cantilevers with novel piezoelectric layer topology for sensitivity enhancement

• Steven Ian Moore,
• Michael G. Ruppert and
• Yuen Kuan Yong

Beilstein J. Nanotechnol. 2017, 8, 358–371, doi:10.3762/bjnano.8.38

• characteristics compared to the optical beam deflection method. The possibility of down scaling, parallelization of cantilever arrays and the absence of optical interference associated imaging artifacts have led to an increased research interest in these methods. However, for multifrequency AFM, the optimization

• multifrequency AFM and has the potential to provide higher resolution imaging on higher order modes. Keywords: atomic force microscopy; multifrequency AFM; multimodal AFM; piezoelectric cantilever, self-sensing; Introduction The invention of the atomic force microscope (AFM) [1] provided for the observation of

• with multiple frequencies has led to vast improvements in the nanomechanical characterization of the sample beyond it’s topography [16]. For these multifrequency AFM (MF-AFM) methods, higher order modes provide enhanced imaging properties such as higher modal stiffnesses and faster response times. It

Advanced atomic force microscopy techniques III

• Thilo Glatzel and
• Thomas Schimmel

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

• developed an advanced microscope capable of obtaining nanoscale topography as well as mechanical properties by multifrequency AFM at high speed. They combined recent progress in increased imaging speed and photothermal actuation in a unique and versatile AFM head using ultrasmall cantilevers [18]. Single

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

• AFM simulation. A multifrequency AFM simulation tool based on the above sample model is provided as supporting information. Keywords: atomic force microscopy; modeling; polymers; simulation; spectroscopy; standard linear solid; surface elasticity; surface energy; viscoelasticity; Introduction The

• dimensions. A third shortcoming of the approach presented is that it is based on linear viscoelasticity, which may not be applicable when large forces are rapidly applied to the surface, as in intermittent-contact multifrequency AFM methods [9][28]. In fact, the treatment of the in-plane surface forces is so

• properties, even an incorrect interpretation of the physics. One final case to consider is the interaction between different tip geometries and the 2D surface Young’s modulus within multifrequency AFM imaging [9]. As has been previously discussed [14][28][33], the interaction of the tip with the sample

Efficiency improvement in the cantilever photothermal excitation method using a photothermal conversion layer

• Natsumi Inada,
• Hitoshi Asakawa,
• Taiki Kobayashi and
• Takeshi Fukuma

Beilstein J. Nanotechnol. 2016, 7, 409–417, doi:10.3762/bjnano.7.36

• multifrequency AFM [10][11][12] have been developed based on dynamic-mode AFM. In dynamic-mode AFM, a stiff cantilever is mechanically oscillated at a frequency near its resonance frequency. The vibrational characteristics, such as frequency, amplitude and phase are monitored to detect interaction forces between

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

• forces during tip retract (this is also discussed in [10]). Figure 4d shows two force curves for the Q3D model in multifrequency AFM operation for different higher mode amplitudes, which exhibit the expected qualitative features (compare to the curve in Figure 1c). As expected, a larger amplitude in the

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

• multifrequency force microscopy methods [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. Bimodal force microscopy is a multifrequency AFM method that uses two eigenmode frequencies for excitation and detection (Figure 1) [9]. It has several configurations depending

• general those regimes appear when the modes are highly coupled. This happens when the energy of the first and second mode are comparable [35]. This context has also stimulated other multifrequency AFM variations such as trimodal AFM [39][40][41]. In trimodal AFM the first three flexural modes are excited

• these multifrequency AFM configurations. Conclusion We have studied the phase contrast in bimodal amplitude modulation AFM for the attractive and the repulsive interaction regimes as a function of the amplitude and amplitude ratio of the excited modes. We have found that the contrast increases by

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

• spatial resolution and contrast of different dynamic AFM methods has also been studied by simulations [28][30][31]. Finally, the emergence of multifrequency AFM [32] in particular bimodal [33][34], trimodal [35], intermodulation [36] or torsional harmonics [37] has been supported by simulations [38]. In

• of multifrequency AFM. The future applications and understanding of dynamic AFM operation will be enhanced if accurate simulators are easily accessible to the experimentalist. These factors promote the development of AFM simulation platforms such as VEDA [41][42]. Here we present a dynamic AFM

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

• modulation mode with oscillation amplitude below 1 nm. We believe that the combination of small cantilevers, clean photothermal actuation and high-frequency, low-noise deflection readout will be of great benefit for multifrequency AFM imaging faster and with less tip–sample dissipation. Experimental Optical

Modeling viscoelasticity through spring–dashpot models in intermittent-contact atomic force microscopy

• Enrique A. López-Guerra and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2014, 5, 2149–2163, doi:10.3762/bjnano.5.224

• –distance curves, dissipated energy and any inherent unphysical artifacts. We focus in this paper on single-eigenmode tip–sample impacts, but the models and results can also be useful in the context of multifrequency AFM, in which the tip trajectories are very complex and there is a wider range of sample

• deformation frequencies (descriptions of tip–sample model behaviors in the context of multifrequency AFM require detailed studies and are beyond the scope of this work). Keywords: atomic force microscopy; creep; dissipated energy; multifrequency; stress relaxation; tapping mode; viscoelasticity

• progress has been recently achieved with regards to fast and simultaneous topographical and spectroscopic characterization of viscoelastic materials through the use of multifrequency AFM [21]. This work represents an important milestone in rapid and quantitative multi-property characterization, although it

Dynamic calibration of higher eigenmode parameters of a cantilever in atomic force microscopy by using tip–surface interactions

• Stanislav S. Borysov,
• Daniel Forchheimer and
• David B. Haviland

Beilstein J. Nanotechnol. 2014, 5, 1899–1904, doi:10.3762/bjnano.5.200

• physical amplitude of a higher eigenmode. Keywords: atomic force microscopy; calibration; multimodal AFM; multifrequency AFM; Introduction Atomic force microscopy [1] (AFM) is one of the primary methods of surface analysis with resolution at the nanometer scale. In a conventional AFM an object is scanned

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

• imaging modes is now available, each with its own capabilities and applications. Among them, a family of techniques known as multifrequency AFM [2][3][4][5][6][7][8][9][10][11] has expanded considerably since the introduction of the first bimodal method by Rodriguez and Garcia in 2004 [12]. In

• multifrequency AFM the cantilever probe is driven simultaneously at more than one frequency, with the objective of creating additional channels of information in order to provide a more complete picture of the sample morphology and properties [2]. In the original method of Garcia and coworkers [12][13] the first

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

• operations and that the various issues compound with the added complexity of multifrequency AFM [9][29][30][31][32], such that more and more experience and knowledge is required from the user to carry out meaningful measurements. With multifrequency methods it can be more difficult to achieve suitable

• environments for which the eigenmode bandwidth is greater [21][26]. This phenomenon also occurs in multifrequency AFM with the added complexity that the tip–sample forces depend strongly on the parameters chosen to drive the higher eigenmodes, as well as on their nonlinear interaction with the fundamental

• differences between base- and tip-excited systems have also been previously discussed for single-mode operation [19][24][28], but as for the issues discussed in the two previous sections, they are worth revisiting here in the specific context of multifrequency AFM. These differences are not extremely relevant