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

• biomolecules, it becomes necessary to control the maximum tip–sample interaction forces and stresses, such that undesirable irreversible changes do not occur in the sample. Second, the interpretation of the experiment requires the user to make assumptions and/or develop models that properly account for the

• speed, and then retracted at the same speed. Generally the desired information is the tip–sample interaction force curve, which for an elastic body is an analytical expression describing the force sensed by the AFM tip as a function of its vertical position above the sample. From this curve the user can

• analytical tip–sample interaction expressions in which the force is expressed as the sum of a Hertzian conservative interaction plus an indentation- and velocity-dependent dissipative interaction. Such 1-dimensional (1D) models have, for example, been used in the characterization of polymers [8][9

Kelvin probe force microscopy for local characterisation of active nanoelectronic devices

• Tino Wagner,
• Hannes Beyer,
• Patrick Reissner,
• Philipp Mensch,
• Heike Riel,
• Bernd Gotsmann and
• Andreas Stemmer

Beilstein J. Nanotechnol. 2015, 6, 2193–2206, doi:10.3762/bjnano.6.225

• weighting factors C' and C'' for AM and FM, respectively. To this end, we applied an analytic model of the electrostatic tip–sample interaction force [18] to the approximate geometry of a typically used cantilever (Olympus AC160), and we calculated C' and C'' as a function of tip–sample separation for

• . While the FM-KFM approach is clearly superior in terms of signal composition, several issues complicate its use in practice. First, it is often performed together with frequency modulated topography feedback that employs a PLL to determine Δf. The non-monotonous tip–sample interaction, by which Δf can

• perturbed by the tip–sample interaction force , where z(t) is the cantilever deflection, ω0 the eigenfrequency, k the spring constant, and Q the quality factor of the cantilever. For an oscillation with amplitude A and drive frequency ωd ≈ ω0, the interaction force can be approximated to where z0 is the

A simple method for the determination of qPlus sensor spring constants

• John Melcher,
• Julian Stirling and
• Gordon A. Shaw

Beilstein J. Nanotechnol. 2015, 6, 1733–1742, doi:10.3762/bjnano.6.177

• possible for qPlus sensors [10], and other sensors with cantilevered geometries [11], to reach quality factors in excess of 106 without inertial cancelling. Several methods have been developed to reconstruct the tip–sample interaction force from the frequency shift of an oscillating tip in ncAFM [12][13

• tip–sample interaction potential. The effect of the tip height and resulting parasitic tip rotation are carefully considered in terms of the error in the reconstructed tip–sample force. Modeling the qPlus sensor dynamics Figure 2 provides a model schematic of the qPlus sensor. The unconstrained tine

• introduce a model for the tip–sample interaction given by the Morse potential for a pair of silicon atoms: where is distance between the atoms, and V0 = 3.643 × 10−19 J, r0 = 235.7 pm, λ = 100 pm are taken from [36]. Using Equation 10 and Equation 11, Ω(x,z) is computed for a grid of points in the xz-plane

Nano-contact microscopy of supracrystals

• Adam Sweetman,
• Nicolas Goubet,
• Ioannis Lekkas,
• Marie Paule Pileni and
• Philip Moriarty

Beilstein J. Nanotechnol. 2015, 6, 1229–1236, doi:10.3762/bjnano.6.126

• of the tuning fork due to variations in the tip–sample interaction are tracked and, via the formula introduced by Sader and Jarvis [18], can be converted to force or potential energy measurements. The qPlus sensor facilitates, in principle, a straight-forward method of acquiring tunnelling current

• small amplitude (of order 0.1−0.3 nm, see below) normal to the surface. The use of constant height imaging (using a similar protocol to that described previously [30][33]) allows us to probe the tip–sample interaction on the repulsive branch of the frequency shift curve, which is typically not available

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

• function of the amplitude ratio, the amplitude values of the second mode and the kinetic energy ratios of the excited modes. We also study the phase contrast between different materials by including energy dissipation in the tip–sample interaction, by inverting the roles of the excited modes (indirect

• -over in the amount of power dissipated between Au and PS for those amplitude ratios (see below). In general, the introduction of dissipation processes in the tip–sample interaction reduces the material contrast observed in the phase shift of the 2nd mode (Figure 3d). This is in contrast with phase

• (20 versus 250 (no dissipation)). To clarify the dependence of the phase contrast with the power dissipated by the tip–sample interaction we plot the dissipated power as a function of A1/A01 for different materials. Figure 4a and 4b show, respectively, the total dissipated power for Au and PS. The

Capillary and van der Waals interactions on CaF₂ crystals from amplitude modulation AFM force reconstruction profiles under ambient conditions

• Annalisa Calò,
• Oriol Vidal Robles,
• Sergio Santos and
• Albert Verdaguer

Beilstein J. Nanotechnol. 2015, 6, 809–819, doi:10.3762/bjnano.6.84

• , and a third one in which the attractive force is almost constant, i.e., forms a plateau, up to 3–4 nm above the surface when the formation of a capillary neck dominates the tip–sample interaction. Keywords: amplitude modulation (AM) AFM; dynamic capillary interactions; dissipative nanoscale

• large tip–sample distances [12][13] and can exhibit unexpected distance dependencies [14]. Contact AFM measurements, in which the force is determined from the static deflection of the cantilever during approach [15], can readily record the tip–sample interaction force and have been used extensively to

• measurements, as for example amplitude modulation AM-AFM measurements, is that experimental observables, i.e., the phase lag of the cantilever relative to the driving force, can be directly related to the energy dissipated in the tip–sample interaction [31][32][33]. Identifying and separating individual

Influence of spurious resonances on the interaction force in dynamic AFM

• Luca Costa and
• Mario S. Rodrigues

Beilstein J. Nanotechnol. 2015, 6, 420–427, doi:10.3762/bjnano.6.42

• Luca Costa Mario S. Rodrigues ESRF, The European Synchrotron, 71 Rue des Martyrs, 38000 Grenoble, France CFMC/Dep. de Física, Universidade de Lisboa, Campo Grande 1749-016 Lisboa, Portugal 10.3762/bjnano.6.42 Abstract The quantification of the tip–sample interaction in amplitude modulation atomic

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

• mass of the cantilever tip, ω0 is the angular resonant frequency, Q the quality factor, k the spring constant of the fundamental resonance (first flexural mode) and Fts is the tip–sample interaction force. The above equation is applicable when the contributions from higher modes to the cantilever

• ) cosh (κn) = 0, where κn is the nth positive real root of the above equation and mc is the real mass of the cantilever. Additionally, the quality factor is defined as where Tip–sample interaction forces The simulator includes a variety of models and tip–surface force interactions. The interactions are

• of the cantilever. For bimodal AM we have considered a system of equations involving the first three flexural modes [39][45]. Each mode was described by a point-mass model. In this system the modes are coupled by the tip–sample interaction force. The equations of motion were integrated numerically

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

• amplification is kept constant with the PLL, the amount of drive signal needed to keep the amplitude constant is proportional to the power dissipated in the tip–sample interaction. The power dissipation (Pdiss) is calculated from the applied excitation signal (Vex·sin (2πf)) and the intrinsic power dissipation

• resonance. Panels b and e show the resonance frequency shift of the first higher resonant mode, and panels c and f show the drive amplitude needed to keep the first higher resonant mode at constant amplitude, related to the energy dissipation in the tip–sample interaction. a) Schematic of the drive

• microscopy, the ability to scan delicate samples in high resolution is required when investigating soft nanostructures. A related technique to the dissipation imaging described above, drive amplitude modulation (DAM) is an imaging mode that allows for the control of the dissipation in the AC-mode tip–sample

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

• Linear Maxwell sample has yielded sufficiently to allow the tip to oscillate at its free oscillation amplitude, without any tip–sample interaction). Since we are interested in the response of the Linear Maxwell sample with an intermittent contact probe, we have used a prescribed tip trajectory for the

• dissipative force term (FtsDISS) to the conservative force term(s) (FtsCON), such that the total tip–sample force can be expressed as Fts = FtsCON + FtsDISS. Usually the repulsive conservative portion of the tip–sample interaction force is defined through the Derjaguin–Muller–Toporov (DMT) model or a similar

• significant advantage of these models over the linear models discussed in previous sections is that they take into account the effect of a varying contact area on the stiffness and dissipative coefficient of the tip–sample interaction. As an initial attempt to blend the advantages of the linear spring–dashpot

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

• , constant-excitation FM-AFM and constant-amplitude FM-AFM [27]. Even more recently Herruzo et al. [9] succeeded for the first time in inverting the conservative tip–sample interaction force curve along with a depth-dependent, direction-independent tip–sample dissipation coefficient by using bimodal FM-AFM

• generally not possible to attribute with certainty the changes in the observables to the variation in surface material properties. Results This section comprises two main sub-sections. The first sub-section provides an analysis of the tip–sample interaction physics for ideal (prescribed) and numerically

• the tip–sample interaction for the standard linear solid model Sample response to prescribed sinusoidal trajectories As starting point, consider the interaction of an SLS surface with a cantilever tip that oscillates along a perfect sinusoidal trajectory. To simulate this, we prescribe that the tip

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

• Figure 3d provide the corresponding results for higher eigenmode amplitudes of 8 nm (the fundamental free amplitude was set to 100 nm in both cases). The oscillation amplitude of each eigenmode decreases with increasing tip–sample interaction (shorter distance between the cantilever and the sample) and

• simulations five eigenmodes of the AFM cantilever were modeled by using individual equations of motion for each, coupled through the tip–sample interaction forces as in previous studies [8][20]. Driven eigenmodes were excited through a sinusoidal tip force of constant amplitude, and frequency equal to 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

• , where zeq is the position of the cantilever above the sample), t = ωot is the dimensionless time, k is the cantilever force constant and Fts is the tip–sample interaction force. We have made the substitution A ≈ Ao = FoQ/k [14], where Fo is the amplitude of the excitation force, and we have combined the

• through the tip–sample interaction forces as in previous studies [9]. The first two eigenmodes were excited through respective sinusoidal tip forces of constant amplitude, with the drive frequencies matching the resonance frequencies. The equations of motion were integrated numerically and the amplitude

Energy dissipation in multifrequency atomic force microscopy

• Valentina Pukhova,
• Francesco Banfi and
• Gabriele Ferrini

Beilstein J. Nanotechnol. 2014, 5, 494–500, doi:10.3762/bjnano.5.57

• evolution is studied by wavelet analysis techniques that have general relevance for multi-mode atomic force microscopy, in a regime where few cantilever oscillation cycles characterize the tip–sample interaction. Keywords: band excitation; multifrequency atomic force microscopy (AFM); phase reference

• energy dissipation is a fundamental aspect of the tip–sample interaction, allowing to quantify compositional contrast variations at the nanoscale [2]. The applied forces and the energy delivered to the sample are relevant for the imaging and the manipulation of soft materials in a variety of environments

• duration reduce the acquisition time and allow for a multiparameter analysis. The latter will increase the physical information gained by the tip–sample interaction. Nonlinear interactions are extremely sensitive to small changes in the tip–sample interactions. Their exploitation will therefore improve the

Impact of thermal frequency drift on highest precision force microscopy using quartz-based force sensors at low temperatures

• Florian Pielmeier,
• Daniel Meuer,
• Daniel Schmid,
• Christoph Strunk and
• Franz J. Giessibl

Beilstein J. Nanotechnol. 2014, 5, 407–412, doi:10.3762/bjnano.5.48

• ]. In FM-AFM the frequency shift Δf = f – f0 of a mechanical oscillator with stiffness k upon tip–sample interaction is measured, while the oscillation amplitude A is kept constant. For quantitative force measurements the uncertainty in the force gradient is crucial [7]. Frequency shift and force

Uncertainties in forces extracted from non-contact atomic force microscopy measurements by fitting of long-range background forces

• Adam Sweetman and
• Andrew Stannard

Beilstein J. Nanotechnol. 2014, 5, 386–393, doi:10.3762/bjnano.5.45

• tip–sample interaction is usually modelled (for example using density functional theory (DFT) [1]) as the interaction between a small cluster of atoms (representing the tip) and a slab of surface atoms. In order to extract the short-range force from the frequency shift measurement, however, the

• monitoring the subsequent effect on the extracted short-range forces. The resultant short-range forces, extracted by both methods, for the tip–sample interaction over both the silicon adatoms and the C60 molecule are shown in Figure 2. Examining first the results on the C60 molecule, the ‘on-minus-off

Control theory for scanning probe microscopy revisited

• Julian Stirling

Beilstein J. Nanotechnol. 2014, 5, 337–345, doi:10.3762/bjnano.5.38

• replacing the operator , with an operator that describes the tip–sample interaction and signal amplification of the SPM to be modelled. The feedback response of an SPM, without the inclusion of mechanical resonances, calculated for four different topographies, and for a range of feedback gains. Topographies

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

• questions that require further attention within multifrequency AFM. Methods For the numerical simulations three eigenmodes of the AFM cantilever were modeled using individual equations of motion for each, coupled through the tip–sample interaction forces as in previous studies [9][38]. Driven eigenmodes

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

• ; Introduction It has long been recognized in the community that higher harmonics encode detailed information about the non-linearities of the tip–sample interaction in dynamic atomic force microscopy (AFM) [1][2][3][4][5]. Physically, non-linearities relate to the chemical and mechanical composition [6] of the

• damped environments [19][20], requires dealing with the recurrent challenge of detecting higher harmonics [1][3][21][22]. Higher harmonics are a result of the non-linear tip–sample interaction in the sense that the interaction effectively acts as the driving force of each harmonic component [7

• simple analytical formulae and ease the qualitative interpretation we consider the harmonics close to the modes only [6]. Then If the nth drive F0n is zero, then Equation 9 is the energy transferred to the nth harmonic of the cantilever through the tip–sample interaction. It should be noted that this is

Exploring the retention properties of CaF₂ nanoparticles as possible additives for dental care application with tapping-mode atomic force microscope in liquid

• Matthias Wasem,
• Joachim Köser,
• Sylvia Hess,
• Enrico Gnecco and
• Ernst Meyer

Beilstein J. Nanotechnol. 2014, 5, 36–43, doi:10.3762/bjnano.5.4

• factor of the cantilever and the phase angle. According to this equation the power lost by tip–sample interaction is proportional to the sine of the phase-lag. It is important to note that Equation 2 allows to calculate the total energy lost by tip–sample interactions but does not reveal how it is lost

Noise performance of frequency modulation Kelvin force microscopy

• Heinrich Diesinger,
• Dominique Deresmes and
• Thierry Mélin

Beilstein J. Nanotechnol. 2014, 5, 1–18, doi:10.3762/bjnano.5.1

• and F similar to Figure 1. The input is the resonance frequency variation Δf of the tip, which is subject to external influence (van-der-Waals or electrostatic tip–sample interaction), and which is to be tracked by a numerically controlled oscillator (NCO) that drives the piezo dither. To match the

Structural development and energy dissipation in simulated silicon apices

• Samuel Paul Jarvis,
• Lev Kantorovich and
• Philip Moriarty

Beilstein J. Nanotechnol. 2013, 4, 941–948, doi:10.3762/bjnano.4.106

• large variety of tip types are possible on the Si(100) surface, each demonstrating a different tip–sample interaction, and importantly, each exhibiting markedly different levels of measured dissipation [40]. Here we examine the effect that simple rotations of the simulated cluster can have on the tip

Peak forces and lateral resolution in amplitude modulation force microscopy in liquid

• Horacio V. Guzman and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2013, 4, 852–859, doi:10.3762/bjnano.4.96

• time dependent vertical displacement of the differential element of the beam placed at the x position, and Fts tip–sample interaction force. Equations 1 and 2 are numerically solved by using a fourth-order Runge–Kutta algorithm [40]. One should note that the use of Equations 1 and 2 in environments of

• low Q are valid for directly excited cantilevers, such as magnetic [41][42][43] or photothermal excitations [44][45]. The tip–sample interaction forces are modelled by using two different contact mechanics models, Hertz [29] and Tatara [30][31][32]. The widely used Hertz model gives the force as The

• –sample interaction force is a major issue in dynamic AFM because the force gives access to the materials properties of the sample; nonetheless the force is not a direct observable. Therefore, several methods have been proposed to reconstruct the force in dynamic AFM [12][13][14][15][16][17][18]. However

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

• + 3rd” because the 4th eigenmode was more novel experimentally. We first discuss the PE/PP contrast reversal in the higher eigenmodes. Broadly speaking, we could imagine two possible explanations for these results. First, it could be that the tip–sample interaction probed by the fourth eigenmode is

• significantly different to the interaction probed by the second eigenmode (e.g., due to viscoelasticity). Alternatively, it could be that there is a difference in the cantilever dynamics at the fourth eigenmode such that it responds to the exact same tip–sample interaction in a different way. Next we show

• [19]). Therefore, as a first approximation, consider the kinetic energy of a freely vibrating (no tip–sample interaction) cantilever eigenmode, which is (both kinetic and potential energy give the same result; derivation in Supporting Information File 1). For the conditions under which the data in

High-resolution nanomechanical analysis of suspended electrospun silk fibers with the torsional harmonic atomic force microscope

• Mark Cronin-Golomb and
• Ozgur Sahin

Beilstein J. Nanotechnol. 2013, 4, 243–248, doi:10.3762/bjnano.4.25

• -interaction forces twist the cantilever by a detectible amount. The high bandwidth of torsional motion allows accessing higher harmonics of the tip–sample-interaction forces to reconstruct tip–sample-force waveforms. This process involves calibration of the frequency response of the torsional mode by

• the surface topography and local mechanical response with high spatial resolution [20][31]. This mode uses a T-shaped cantilever with an offset tip. When used in dynamic AFM, the cantilever vibrates up and down, similar to conventional cantilevers. In addition to the vertical motion, tip–sample