Double layer effects in a model of proton discharge on charged electrodes

• Johannes Wiebe and
• Eckhard Spohr

Beilstein J. Nanotechnol. 2014, 5, 973–982, doi:10.3762/bjnano.5.111

• they are described in detail [16]. In the spirit of a maximally simplified model, ion–water and ion–platinum interactions were described by simple Lennard-Jones plus point charge models with ionic Lennard-Jones parameters taken from [35], which were combined with the Lennard-Jones parameters of the

• water model. Ion–platinum Lennard-Jones parameters were chosen as (ε, σ) = (0.218, 2.93) for Na+ and (1.345, 3.35) for Cl−, which, together with a harmonic tether potential for the Cl− ions guaranteed that the ions stayed adsorbed in the surface layer of the water molecules. Here, ε is in units of

Resonance of graphene nanoribbons doped with nitrogen and boron: a molecular dynamics study

• Ye Wei,
• Haifei Zhan,
• Kang Xia,
• Wendong Zhang,
• Shengbo Sang and
• Yuantong Gu

Beilstein J. Nanotechnol. 2014, 5, 717–725, doi:10.3762/bjnano.5.84

• -distance C–C interaction in the form of a typical Lennard-Jones (LJ) potential. The last term describes the dihedral-angle preferences in hydrocarbon configurations. For the other atomic interactions induced by the dopant atoms (i.e., C–B, C–N, and B–N), a typical Tersoff potential [26] was adopted. For

Tensile properties of a boron/nitrogen-doped carbon nanotube–graphene hybrid structure

• Kang Xia,
• Haifei Zhan,
• Ye Wei and
• Yuantong Gu

Beilstein J. Nanotechnol. 2014, 5, 329–336, doi:10.3762/bjnano.5.37

• energy and elastic properties of graphene and CNT well [24]. Basically, the REBO potential is given as Here, the first term represents the interaction between i and j atoms, which strongly depends on the coordination. The second term accounts for a longer-ranged interaction that is depicted by a Lennard

• -Jones (LJ) potential, while the last term represents an explicit 4-body potential that describes various preferences for dihedral angles in hydrocarbon configurations. A Tersoff potential [25] is adopted to describe the atomic interactions of C–B, C–N and B–N. The N–N bond is considered to be chemically

Manipulation of nanoparticles of different shapes inside a scanning electron microscope

• Boris Polyakov,
• Sergei Vlassov,
• Leonid M. Dorogin,
• Jelena Butikova,
• Mikk Antsov,
• Sven Oras,
• Rünno Lõhmus and
• Ilmar Kink

Beilstein J. Nanotechnol. 2014, 5, 133–140, doi:10.3762/bjnano.5.13

• Johnson–Kendall–Roberts (JKR) [23] or the Derjaguin–Müller–Toporov (DMT-M) model [24]. According to Tabor [25], the choice of the most suitable model is determined by the parameter where R is the radius of the sphere, γ is the work of adhesion, and z0 is the equilibrium spacing for the Lennard-Jones

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

• shows the tip in the attractive part of the van-der-Waals interaction. The force gradient in this field must not exceed the spring constant to avoid snap to contact. We take the attractive range of a Lennard-Jones type of potential The force gradient is proportional to the second derivative: To avoid

Large-scale atomistic and quantum-mechanical simulations of a Nafion membrane: Morphology, proton solvation and charge transport

• Pavel V. Komarov,
• Pavel G. Khalatur and
• Alexei R. Khokhlov

Beilstein J. Nanotechnol. 2013, 4, 567–587, doi:10.3762/bjnano.4.65

• interaction terms (a Lennard–Jones "9-6" potential for the van der Waals interactions and a Coulombic term for electrostatic interactions). We used the same force field both for the neutral and the charged species (hydronium cations and sulfonic acid anions SO3−). For the neutral species, Coulomb interactions

• acts against squeezing charged groups together below the Lennard–Jones contact distance, as expected. On the other hand, in the region of short interionic distances, including the region of the first minimum of W+–(r), the entropic contribution to the free energy is negative. As the distance increases

Plasticity of Cu nanoparticles: Dislocation-dendrite-induced strain hardening and a limit for displacive plasticity

• Antti Tolvanen and
• Karsten Albe

Beilstein J. Nanotechnol. 2013, 4, 173–179, doi:10.3762/bjnano.4.17

• kept close to 0 K by a Berendsen thermostat [17]. The nanoparticles were encapsulated inside a external repulsive spherical force field with a circular orifice interacting with the Cu atoms with a repulsive Lennard-Jones type potential. As the carbon atoms in a graphitic shell interact very weakly with

Calculation of the effect of tip geometry on noncontact atomic force microscopy using a qPlus sensor

• Julian Stirling and
• Gordon A. Shaw

Beilstein J. Nanotechnol. 2013, 4, 10–19, doi:10.3762/bjnano.4.2

• rather az, the z component of this amplitude. Effect on imaging and spectroscopy Simulated AFM data were produced by creating a Lennard-Jones potential for a simple 2-D square lattice, with a lattice constant of 3 Å, and a minimum potential of −3 eV at a distance of 0.5 Å (Figure 4a). For simplicity the

Probing three-dimensional surface force fields with atomic resolution: Measurement strategies, limitations, and artifact reduction

• Mehmet Z. Baykara,
• Omur E. Dagdeviren,
• Todd C. Schwendemann,
• Harry Mönig,
• Eric I. Altman and
• Udo D. Schwarz

Beilstein J. Nanotechnol. 2012, 3, 637–650, doi:10.3762/bjnano.3.73

• Lennard-Jones (L-J) and ionic). Even though these assumptions represent an oversimplification, as tip–sample contacts will relax upon tip approach and short-range interactions may differ substantially from those predicted by the potentials employed here, we still expect such simulations to provide

• valuable insights into the general trends that describe how tip asymmetry manifests in 3-D data sets. For the computations, the Lennard-Jones potential between two atoms VL-J was calculated by using Here r denotes the distance between the centers of the two atoms, ε the depth of the potential well, and σ

• ionized, a Coulomb potential VC was added to the Lennard-Jones interaction with ke reflecting the Coulomb constant, q1 and q2 the ionic charges, and r the distance between the ions. Total interaction potentials are obtained by summing up the individual potentials between each tip and substrate atom. The

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

• , germanium, etc). Recent improvements of this potential [103] do not modify the results presented below. In the case of graphite, the van der Waals interaction between two layers is described by a standard Lennard-Jones potential: with ε = 0.011 eV and σ = 3.2963 Å. Results and Discussion Graphite surface

• qualitative agreement with experiments [38][40][42][43] and calculated results [38][44]. Quantitative comparison may be tricky because parameters are different (working parameter set, reactive or inert tip, etc.). In [38], a tip–sample interaction model is based on a Lennard-Jones potential and gives similar

• results if one compares the scan line in Figure 2d. Of course, such a pairwise potential (Lennard-Jones or Buckingham potential) is not able to describe a reactive tip, and the contrast is explained in terms of the Pauli repulsion in the repulsive region. For the constant-frequency-shift mode at Δfset

Analysis of force-deconvolution methods in frequency-modulation atomic force microscopy

• Joachim Welker,
• Esther Illek and
• Franz J. Giessibl

Beilstein J. Nanotechnol. 2012, 3, 238–248, doi:10.3762/bjnano.3.27

• different approaches in solving it for the force. In this paper we compare the Sader–Jarvis deconvolution method and Giessibl’s matrix method. We use the analytical formulas of the Morse and Lennard-Jones model forces and the corresponding frequency shifts. The analytically calculated frequency shifts are

• 13.2.1 in [17]). Another potential commonly used to describe the interaction between two atoms is the Lennard-Jones potential. In contrast to the Morse potential, the Lennard-Jones potential is based on power functions and has only two parameters, that is, the equilibrium distance σ and the bond energy

• Ebond: The Lennard-Jones force law leads to the frequency shift [16]: with being the hypergeometric function (see section 15.3.1 in [17]). In this work we use both the Morse and the Lennard-Jones force laws as model systems to judge the quality of the force-deconvolution methods. Force-deconvolution

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

• and a quasi-one-dimensional corrugated surface. The following sections develop the calculation on the assumption that interactions are pairwise additive, beginning with a Lennard-Jones interaction between two atoms [24]. The formalism here closely follows that of [11], in which a detailed analytical

• theory was developed to model the adhesion of graphene to a sinusoidally corrugated substrate. This section is presented as follows: Development of the basic formalism for carrying out numerical integration of a Lennard-Jones potential, for a “point atom” interacting with a semi-infinite substrate. By

• compute frequency shifts for the spherical-tip/corrugated-surface system. We begin with the Lennard-Jones potential written as which represents the interaction between a pair of atoms separated by a distance r. Following the Hamaker procedure, we assume that the total interaction energy (atom–surface or

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

• Lennard-Jones and Derjaguin–Muller–Toporov forces. Keywords: AFM; atomic force microscopy; bimodal AFM; frequency shift; integral calculus applications; Introduction Since the invention of the atomic force microscope (AFM) [1], numerous AFM studies have been pursued in order to extract information from

• function and its integral (Figure 2b). Next, we demonstrate that the frequency shift in bimodal AFM is directly related to the half-derivative of the interaction force for two different tip–surface forces, namely Lennard-Jones forces and those described by the DMT model. We have compared the results

• obtained from Equation 6 with the results estimated from the half-derivative of the force (Equation 16) for a Lennard-Jones force and for the force appearing in the DMT model [49]. The force constant, resonant frequency and quality factor of the first and second flexural modes of the cantilever are

Direct monitoring of opto-mechanical switching of self-assembled monolayer films containing the azobenzene group

• Einat Tirosh,
• Enrico Benassi,
• Silvio Pipolo,
• Marcel Mayor,
• Michal Valášek,
• Veronica Frydman,
• Stefano Corni and
• Sidney R. Cohen

Beilstein J. Nanotechnol. 2011, 2, 834–844, doi:10.3762/bjnano.2.93

• characteristics. The indenter is an incompressible Lennard–Jones sphere. Whereas the QM model is focused on the single-molecule properties, the MD simulation allows for steric interactions between neighboring molecules. Comparison of experiment with computation As shown in Table 2, the results of the two

• indenter is a Lennard–Jones sphere with parameters set as: ε = 0.065 kJ/mol and σ = 1.425 nm. ε is chosen to give a negligible attraction with the SAM (it is one-tenth of the ε used in the GolP model [31] for Au atoms), and σ gives a van der Waals radius of 0.8 nm for the indenter, which is compatible with

Defects in oxide surfaces studied by atomic force and scanning tunneling microscopy

• Thomas König,
• Georg H. Simon,
• Lars Heinke,
• Leonid Lichtenstein and
• Markus Heyde

Beilstein J. Nanotechnol. 2011, 2, 1–14, doi:10.3762/bjnano.2.1

• considered as a capacitor, resulting in the following equation for the electrostatic energy Eel, which together with the non-electrostatic interaction such as a Lennard-Jones potential adds to the total energy, [18][19] Echarge is the energy due to electrostatic charging and EVS is the work done by the