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

• + b)c + d to fit the long-range part of the curve (using the standard curve fitting toolbox in MATLAB), assuming the tip–surface configuration can be modelled as a simple geometric shape positioned above a plane. Here a is related to the Hamaker constant of the material and size of the tip, b

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

• a Hamaker constant of 2 × 10−19 J (no screening was considered for the simulations in air). Unless otherwise indicated, the trajectories shown indicate the true eigenmode or tip response, as opposed to the photodetector reading, which does not necessarily correspond to the true trajectory (as

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

• long range attractive forces are of interest here, the tip–sample force is simply [23] where R is the tip radius, H is the Hamaker constant and a0 is an intermolecular distance (a0 = 0.165 nm throughout and in all the data here, we consider d > a0 throughout). It is relevant to note that the Hamaker

• phase shifts Δ have been employed to map the composition through variations in the tip–sample Hamaker constant, H, in Equation 10. In this section, the presence of thermal noise is discussed with respect to the contrast in amplitude ΔAn and phase Δ in the presence and absence of external drive forces at

• variations above 1 pm. Practically, these results imply that while higher harmonic amplitudes depend on the value of the Hamaker constant, or sample composition, the amplitude values are typically in the order of 1 pm or fractions of a pm. This is also true for variations in higher harmonic amplitudes ΔAn

Ni nanocrystals on HOPG(0001): A scanning tunnelling microscope study

• Michael Marz,
• Keisuke Sagisaka and
• Daisuke Fujita

Beilstein J. Nanotechnol. 2013, 4, 406–417, doi:10.3762/bjnano.4.48

• interlayer is present, the Hamaker constant can be considered to be H = 4·10−19 J, and εr = 1 is valid. For simplicity, the electrical field is considered not to be influenced by the presence of the clusters and its value to be constant over the whole width of the cluster, leading to the convenient form E(z

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

• jumps and the second eigenmode contrast does not reverse. Calibrated cantilever parameters for the experiments. Simulation parameters. Hamaker constant and surface energy are tuned to match the experiment. All other values are measured or nominal values. Supporting Information The Supporting

Interpreting motion and force for narrow-band intermodulation atomic force microscopy

• Daniel Platz,
• Daniel Forchheimer,
• Erik A. Tholén and
• David B. Haviland

Beilstein J. Nanotechnol. 2013, 4, 45–56, doi:10.3762/bjnano.4.5

• additional exponential damping, which is defined as where H = 2.96 · 10−7 J is the Hamaker constant, R = 10 nm is the tip radius, γ = 2.2 · 10−7 Ns/m is the damping constant, zγ = 1.5 nm is the damping decay length and E* = 2.0 GPa is the effective stiffness. For the numerical integration of Equation 39 we

Repulsive bimodal atomic force microscopy on polymers

• Alexander M. Gigler,
• Christian Dietz,
• Maximilian Baumann,
• Nicolás F. Martinez,
• Ricardo García and
• Robert W. Stark

Beilstein J. Nanotechnol. 2012, 3, 456–463, doi:10.3762/bjnano.3.52

• can enhance material contrast with respect to conventional amplitude-modulation modes [7][8][14][15][16], with piconewton force sensitivity. Local variations of the Hamaker constant cause material contrast in the attractive imaging regime [8][15]. Repulsive bimodal force microscopy imaging has been

Models of the interaction of metal tips with insulating surfaces

• Thomas Trevethan,
• Matthew Watkins and
• Alexander L. Shluger

Beilstein J. Nanotechnol. 2012, 3, 329–335, doi:10.3762/bjnano.3.37

• Elastic constant: 148.7 N/m; natural frequency: 189000.0 Hz; setpoint amplitude: 5 nm; Q-factor: 10000.0. Macroscopic van der Waals: Hamaker constant: 0.999 eV; Tip radius: 18.0 nm (a) Side-on view of the structure of the Cr and W cluster tip models. (b) The structure of the periodic Cr tip model. (a

Graphite, graphene on SiC, and graphene nanoribbons: Calculated images with a numerical FM-AFM

• Fabien Castanié,
• Laurent Nony,
• Sébastien Gauthier and
• Xavier Bouju

Beilstein J. Nanotechnol. 2012, 3, 301–311, doi:10.3762/bjnano.3.34

• composed of a nanosphere to mimic the probe body supporting a cluster of atoms for the tip apex. The sphere has a radius R of 4 nm and its force of interaction with a surface is well described by if (r − R) « R [98]. Hk is the Hamaker constant (1 eV) and r the sphere–surface distance. The cluster has a

Modeling noncontact atomic force microscopy resolution on corrugated surfaces

• Kristen M. Burson,
• Mahito Yamamoto and
• William G. Cullen

Beilstein J. Nanotechnol. 2012, 3, 230–237, doi:10.3762/bjnano.3.26

• approximate solution [25]: in the limit z << R, where AH is the Hamaker constant for the tip–surface material system, given by AH = C1·π2·ρs·ρt. Equation 9 is sometimes used for fitting the vdW background in NC-AFM experiments [26][27]. However, for the tip radii modeled here, the limiting approximation is

Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculus

• Elena T. Herruzo and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2012, 3, 198–206, doi:10.3762/bjnano.3.22

• length scale of the interaction force. For the force which appears in the DMT model [51] where H is the Hamaker constant of the long-range van der Waals forces, d0 is the equilibrium distance, R is the tip radius and Eeff is the effective Young’s modulus, which is related to the Young’s moduli Et and Es

Distinguishing magnetic and electrostatic interactions by a Kelvin probe force microscopy–magnetic force microscopy combination

• Miriam Jaafar,
• Oscar Iglesias-Freire,
• Luis Serrano-Ramón,
• Manuel Ricardo Ibarra,
• Jose Maria de Teresa and
• Agustina Asenjo

Beilstein J. Nanotechnol. 2011, 2, 552–560, doi:10.3762/bjnano.2.59

• negligible at the distances used for MFM, the total force between the tip and the sample (Ft) is: The van der Waals [26] force between a spherical tip and a semi-infinite flat sample can be written as: where AH is the Hamaker constant that depends on the material, R is the tip radius and z is the tip–sample

Tip-sample interactions on graphite studied using the wavelet transform

• Giovanna Malegori and
• Gabriele Ferrini

Beilstein J. Nanotechnol. 2010, 1, 172–181, doi:10.3762/bjnano.1.21

• oscillations of a cantilever with an interacting tip. This analysis allows to retrieve the force gradients, the forces and the Hamaker constant in a measurement time of less than 40 ms. Keywords: AFM; force; graphite; thermal excitation; wavelet transforms; Introduction The non-contact atomic force

• retrieved. With this techniques force gradients and quality factors on graphite in air have been measured [9]. It was found that the attractive force gradient data are well reproduced by a nonretarded van der Waals function in the form HR/(3z3) (H is the Hamaker constant and R the tip radius of curvature

• radius of curvature given by the manufacturer (R = 10 nm). To promote this technique from proof of principle to a measurement of the Hamaker constant with a good lateral resolution, a thorough characterization of the tip radius of curvature is needed. Finally, we note that the whole force curve is

Review and outlook: from single nanoparticles to self-assembled monolayers and granular GMR sensors

• Alexander Weddemann,
• Inga Ennen,
• Anna Regtmeier,
• Camelia Albon,
• Annalena Wolff,
• Katrin Eckstädt,
• Nadine Mill,
• Michael K.-H. Peter,
• Jochen Mattay,
• Carolin Plattner,
• Norbert Sewald and
• Andreas Hütten

Beilstein J. Nanotechnol. 2010, 1, 75–93, doi:10.3762/bjnano.1.10

• resulting assemblies: An attractive potential is given by the van der Waals interaction which is caused by induced electric dipoles and acts along the connection line between them. For two interacting solid spheres Hamaker derived the expression for the interaction potential [50][51][52] with A the Hamaker

• constant, and R and δ the particle radius and the interparticle distance, respectively (compare Figure 9 (a)). Repulsive force contributions originate either from electric Coulomb forces or steric repulsion, depending on the nature of the particle stabilization. For instance, spherical particles which are