Tunable fractional Fourier transform implementation of electronic wave functions in atomically thin materials

• Daniela Dragoman

Beilstein J. Nanotechnol. 2018, 9, 1828–1833, doi:10.3762/bjnano.9.174

• coordinate x and the tangent θ to the ray/quantum trajectory at a y = const. plane and the same parameters (indexed by 0) at the y = 0 plane [15]: In Equation 5, valid when or , one has in optics and in the case of Schrödinger electrons. Whether the results above regarding Schrödinger electrons are not

• of the spinorial wave function satisfy the equation which is similar to Equation 2 if , , . As a result, the FrFT of order α is achieved after a propagation distance in graphene equal to and the trajectory of charge carriers in graphene is also periodic and described by Equation 5, with . Again, the

• implements a FrFT for negative UG potentials, while that in Figure 1b implements it for positive UG values. Figure 1a and Figure 1b depict also the trajectory of a ballistic electron. From Equation 4 and Equation 8 it follows that the last configuration implements a FrFT with a given α in a shorter distance

Atomistic modeling of tribological properties of Pd and Al nanoparticles on a graphene surface

• Alexei Khomenko,
• Miroslav Zakharov,
• Denis Boyko and
• Bo N. J. Persson

Beilstein J. Nanotechnol. 2018, 9, 1239–1246, doi:10.3762/bjnano.9.115

• one of a large number of available thermostats is used. Velocity rescaling by a constant factor, which corresponds to the desired temperature, is the simplest way to maintain the necessary temperature. Here we use the Berendsen thermostat [16][17] that does not give the trajectory of the true

Thermoelectric current in topological insulator nanowires with impurities

• Sigurdur I. Erlingsson,
• Jens H. Bardarson and
• Andrei Manolescu

Beilstein J. Nanotechnol. 2018, 9, 1156–1161, doi:10.3762/bjnano.9.107

• for quadratic dispersion (Schrödinger) where the Lorentz force always bends the electron trajectory towards the line of vanishing radial component of the magnetic field [27][28][29][30]. In fact, this is a classical effect known in the two-dimensional electron gas in inhomogeneous magnetic fields with

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

• 1 (Figure S1). The contact mechanics described by Equation 4 are strictly only valid for the approach portion of the indenter trajectory. A generalized approach has been derived by Ting, which is applicable for any arbitrary (a priori) known loading history [21]. In our simulations, where a priori

• 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

Dynamics and fragmentation mechanism of (C₅H₄CH₃)Pt(CH₃)₃ on SiO₂ surfaces

• Kaliappan Muthukumar,
• Harald O. Jeschke and
• Roser Valentí

Beilstein J. Nanotechnol. 2018, 9, 711–720, doi:10.3762/bjnano.9.66

• originally bonded to Pt, fragments and bonds to the adjacent vacant site, as observed in the 3 × 3 × 4 cell (see Figure 2d and Figure 3e). These DFT relaxed structures (as shown in Figure 3b–e) are considered as starting point for molecular dynamics simulations. The trajectory of the MD simulations for the

• four considered cases are shown in Figure 4. The analysis of the trajectory indicates that on the fully hydroxylated surfaces (Figure 4a) the molecule exhibits significant changes in orientation and a drift similar as we found for carbonyl precursors [11]. The Pt–Cp ring and Pt–methyl bonds fluctuate

• with a maximum of 5% and 1%, respectively. Apart from this, in the simulation window, we do not observe any further indications of the dissociation of the precursor molecules. The trajectory of MD simulations and arising configurations of (C5H4CH3)Pt(CH3)3 on the (25% and 50%) partially dehydroxylated

The nanofluidic confinement apparatus: studying confinement-dependent nanoparticle behavior and diffusion

• Stefan Fringes,
• Felix Holzner and
• Armin W. Knoll

Beilstein J. Nanotechnol. 2018, 9, 301–310, doi:10.3762/bjnano.9.30

• mean squared displacement (MSD) in one of the orthogonal directions x or y. For the x-direction and a time interval Δt, the MSD is given by where signifies the ensemble average, N is the number of observed positions per trajectory, Kα is a generalized diffusion coefficient and α is the anomalous

Material discrimination and mixture ratio estimation in nanocomposites via harmonic atomic force microscopy

• Weijie Zhang,
• Yuhang Chen,
• Xicheng Xia and
• Jiaru Chu

Beilstein J. Nanotechnol. 2017, 8, 2771–2780, doi:10.3762/bjnano.8.276

• are neglected. R is the tip radius and E* is the reduced modulus where v Poisson’s ratio. Combining Equation 2 and Equation 3 and utilizing numerical methods such as Runge–Kutta algorithms, the real-time oscillation trajectory of the tip can be achieved. The above contact model is based on the main

Material property analytical relations for the case of an AFM probe tapping a viscoelastic surface containing multiple characteristic times

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

Beilstein J. Nanotechnol. 2017, 8, 2230–2244, doi:10.3762/bjnano.8.223

• sinusoidal trajectory. From the rheological viewpoint, the characterization of viscoelastic materials has been classically performed by applying a well-defined input excitation (either stress or sample strain) to elicit a response, which is then measured. The measured output response and the well-defined

• classical rheology, we regard tapping-mode AFM as a non-standard excitation of a viscoelastic sample, and exploit the fact that the near sinusoidal nature of the tip deflection in this technique implies that the sample necessarily experiences a portion of that sinusoidal trajectory during the contact period

• tip trajectory for an AFM cantilever interacting with a viscoelastic surface in tapping-mode AFM (simulation details are provided in the figure caption). The instantaneous tip–sample distance, taking as reference the undeformed sample surface, is approximately given by: where Zeq refers to the average

Bi-layer sandwich film for antibacterial catheters

• Gerhard Franz,
• Florian Schamberger,
• Hamideh Heidari Zare,
• Sara Felicitas Bröskamp and
• Dieter Jocham

Beilstein J. Nanotechnol. 2017, 8, 1982–2001, doi:10.3762/bjnano.8.199

• layer, which had been coated by PPX-N (1650 and 2240 nm). According to the equivalent circuit in Figure 11, the intersection of the graph with the real axis close to the origin is related to the serial ohmic resistance RΩ of the NaOH solution. The semi-circle trajectory, which approaches the shape of a

Optical techniques for cervical neoplasia detection

• Tatiana Novikova

Beilstein J. Nanotechnol. 2017, 8, 1844–1862, doi:10.3762/bjnano.8.186

• –Chipman decomposition implies a sequential order of elementary polarimetric properties along the trajectory of the probing beam, whereas these polarimetric properties can be mixed within the volume of tissue. Nevertheless, these effective values of depolarization and retardance are found to be the

High-speed dynamic-mode atomic force microscopy imaging of polymers: an adaptive multiloop-mode approach

• Juan Ren and
• Qingze Zou

Beilstein J. Nanotechnol. 2017, 8, 1563–1570, doi:10.3762/bjnano.8.158

• +feedforward) applied to the z-piezo actuator (i.e., Uff+fb,k(jω) = Uff,k(jω) + Ufb,k(jω), see Figure 9), and the z-piezo displacement measured on the k-th scan line, respectively, and Hffd,k+1(·) denotes the desired trajectory that the z-piezo needs to track at the (k+1)-th scanline. Note that the ratio in

Functional dependence of resonant harmonics on nanomechanical parameters in dynamic mode atomic force microscopy

• Federico Gramazio,
• Matteo Lorenzoni,
• Francesc Pérez-Murano,
• Enrique Rull Trinidad,
• Urs Staufer and
• Jordi Fraxedas

Beilstein J. Nanotechnol. 2017, 8, 883–891, doi:10.3762/bjnano.8.90

• , represented by the force field Fts, between the cantilever tip and the surface [1]. Thus, the time dependent trajectory a(t) of the cantilever tip, which can be expressed in the harmonic limit by a(t) = A1cos(2πft), is transformed into a Fourier series with harmonic oscillations of amplitudes An and

Measuring adhesion on rough surfaces using atomic force microscopy with a liquid probe

• Juan V. Escobar,
• Cristina Garza and
• Rolando Castillo

Beilstein J. Nanotechnol. 2017, 8, 813–825, doi:10.3762/bjnano.8.84

• follows a different trajectory than during the approach (4–4′ in Figure 5b) giving rise to force–displacement curve hysteresis. The two discontinuities in the force values are called jump-to-contact in the approach curve and jump-off-contact in the withdrawal curve. It is important to mention that this

First examples of organosilica-based ionogels: synthesis and electrochemical behavior

• Andreas Taubert,
• Ruben Löbbicke,
• Barbara Kirchner and
• Fabrice Leroux

Beilstein J. Nanotechnol. 2017, 8, 736–751, doi:10.3762/bjnano.8.77

• thermostats (parameters as in [41]) for 5 ps. After this the simulation was done in an NVT ensemble to provide 2.5 ps production trajectory at 450 K which was analyzed with the software TRAVIS [43]. A forthcoming publication will provide more details and longer simulation times. Figure 1 shows the simulation

• increases the intramolecular bond to approximately 150 pm either a cation SO3 group or one of the tosylate anions is close. A very large O–H distance of a former intramolecular O–H group can correlate with both, a short O–H anion or cation distance. Moreover, inspection of the trajectory clearly shows that

Calculating free energies of organic molecules on insulating substrates

• Julian Gaberle,
• David Z. Gao and
• Alexander L. Shluger

Beilstein J. Nanotechnol. 2017, 8, 667–674, doi:10.3762/bjnano.8.71

• simulations. Despite this seemingly simple process, calculating free energies is far from trivial. In order to obtain converged results the ergodicity needs to be satisfied. The ergodic principle states that an infinite trajectory (in time) should sample all possible states of a system. However, in practice

• curves. Increasing the MD trajectory from 50 ns to 100 ns leads to a drop in the free energy of step adhesion from 0.5 eV to 0.35 eV. As MD simulation times are increased, the free energy continues to decrease as more and more of the higher-energy, low-probability configurational space is sampled. This

• free energy is plotted as a function of the molecule–step distance as obtained from a 100 ns MD trajectory. As one arm of the molecule attaches to the step edge, a large drop in entropy was observed. However, the free-energy profile seems to suggest a much more favourable interaction. In fact it

Dynamic of cold-atom tips in anharmonic potentials

• Tobias Menold,
• Peter Federsel,
• Carola Rogulj,
• Hendrik Hölscher,
• József Fortágh and
• Andreas Günther

Beilstein J. Nanotechnol. 2016, 7, 1543–1555, doi:10.3762/bjnano.7.148

• different times after the initial displacement of A = 200 μm. Figure 2b shows the corresponding density profiles. Depending on the initial energy, each particle follows its own phase-space trajectory and oscillates clockwise around the origin with its own fundamental frequency. Low energetic particles will

Experimental and simulation-based investigation of He, Ne and Ar irradiation of polymers for ion microscopy

• Lukasz Rzeznik,
• Yves Fleming,
• Tom Wirtz and
• Patrick Philipp

Beilstein J. Nanotechnol. 2016, 7, 1113–1128, doi:10.3762/bjnano.7.104

• between. The displacement of the noble gas atoms inside the polymer samples is described using the mean square displacement (MSD). Their trajectories have been recorded with a time step of dt = 0.2 ps, which makes 24000 trajectory points during the last 4.8 ns of the simulation. For each polymer sample

• positions from trajectory file, that is why the maximum displacement for He atom extends above the system size. The trajectories have been selected to reflect the average mobility of the rare gas species in HD-PMMA. Mean square displacement (MSD) of helium, neon and argon at 300 K in a) HD-PE, b) HD-PS, c

Signal enhancement in cantilever magnetometry based on a co-resonantly coupled sensor

• Julia Körner,
• Christopher F. Reiche,
• Thomas Gemming,
• Bernd Büchner,
• Gerald Gerlach and
• Thomas Mühl

Beilstein J. Nanotechnol. 2016, 7, 1033–1043, doi:10.3762/bjnano.7.96

• contribution for several reasons: its oscillation trajectory radius and sensor stiffness are mainly given by the cantilever. In contrast to that the sensor stiffness at the free end of the FeCNT can be described by the soft effective spring constant of the coupled system. Hence, only the monopole at the free

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

• . However, the instantaneous interaction stiffness experienced by the second eigenmode slowly changes along the trajectory of the first eigenmode. Because the second mode rides along the slower sinusoidal motion of the first mode, its time-averaged change in interaction stiffness Δk2 can be calculated by

• solves to Notably, this integral that determines Δk2 only depends on the trajectory of the first eigenmode because A2 is assumed small. c. Correction factor for power-law force model: β When integrating kint(δ) in Equation 6 and Equation 10 to obtain Δk1 and Δk2, respectively, for a power-law model as

Coupled molecular and cantilever dynamics model for frequency-modulated atomic force microscopy

• Michael Klocke and
• Dietrich E. Wolf

Beilstein J. Nanotechnol. 2016, 7, 708–720, doi:10.3762/bjnano.7.63

• surface [6]. In these simulations the tip motion is represented in a parametric way, e.g., by prescribing a sinusoidal trajectory normal or parallel to the surface. Recently situations attracted interest, where “the back-action of the tip–sample force on the cantilever can no longer be ignored” [22]. This

• their coupling can be studied. Moreover, the dynamic response of the tip due to its interaction with the substrate allows for the excitation of lateral degrees of freedom, which were suppressed, if the tip trajectory was fixed. They can give rise to a significant contribution to the dissipation signal

• A in Figure 2. The actual minimal distance is smaller than d due to the attractive forces between tip and substrate. The trajectory shows a hysteresis loop with significant displacements in all three dimensions. As the tip starts with zero temperature, the apex coordinates first do not fluctuate

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

Molecular machines operating on the nanoscale: from classical to quantum

• Igor Goychuk

Beilstein J. Nanotechnol. 2016, 7, 328–350, doi:10.3762/bjnano.7.31

• by f(x,t) or by boundary conditions. Hence, time-irreversibility within dissipative Langevin dynamics is a statistical effect due to averaging over many trajectories. Such an averaging cannot be undone, i.e., there is no way to restore a single trajectory from their ensemble average. Considering a

• as a force balance equation. The net heat exchange with the environment is [23], where denotes an ensemble average over many trajectory realizations. Furthermore, is the energy pumped into the motor turnovers, and is the useful work done against external torque. The fluctuations of the motor

• ψ = π/2, as shown in Figure 4a. Here, there are two cases that differ by V2 = 0, in one case, and V2≠ 0, in another one. Moreover, when dissipation is present within the corresponding Langevin dynamics, each and every trajectory remains time-reversal symmetric for ψ = 0. However, for strongly

Nanoscale rippling on polymer surfaces induced by AFM manipulation

• Mario D’Acunto,
• Franco Dinelli and
• Pasqualantonio Pingue

Beilstein J. Nanotechnol. 2015, 6, 2278–2289, doi:10.3762/bjnano.6.234

• be described as the parallel movement of a number of tips moving together along the same direction, like a blade. The final pattern could also depend on the number of scans. Tip trajectory: Gnecco et al. have also evidenced that ripple patterns could be obtained via circular or spiral trajectories of

Virtual reality visual feedback for hand-controlled scanning probe microscopy manipulation of single molecules

• Philipp Leinen,
• Matthew F. B. Green,
• Taner Esat,
• Christian Wagner,
• F. Stefan Tautz and
• Ruslan Temirov

Beilstein J. Nanotechnol. 2015, 6, 2148–2153, doi:10.3762/bjnano.6.220

• environment is not fully known. Here we present a further technical development that substantially improves the effectiveness of HCM. By adding Oculus Rift virtual reality goggles to our HCM set-up we provide the experimentalist with 3D visual feedback that displays the currently executed trajectory and the

• the analysis of manipulation trajectory data much simpler. It would also help to transfer knowledge between different users and/or experiments, thus facilitating systematic learning during which manipulation protocols are refined and corrected in multiple steps. Visualization of the manipulation

• trajectory data should therefore greatly increase the effectiveness of HCM and extend the range of its possible applications. Here we introduce a system that visualizes HCM data in real time by displaying the actual tip position as well as the history of its movements in 3D using Oculus Rift DK 2 (ORt

Possibilities and limitations of advanced transmission electron microscopy for carbon-based nanomaterials

• Xiaoxing Ke,
• Carla Bittencourt and
• Gustaaf Van Tendeloo

Beilstein J. Nanotechnol. 2015, 6, 1541–1557, doi:10.3762/bjnano.6.158

• discussed in the next subsection. The previous discussion of Cs correctors applies to the post-field of the objective lens, which corrects the electron trajectory of the exit electron wave after interaction with the specimen, and provides a more straightforward interpretation of the projected potential of