unDrift: A versatile software for fast offline SPM image drift correction

• Tobias Dickbreder,
• Franziska Sabath,
• Lukas Höltkemeier,
• Ralf Bechstein and
• Angelika Kühnle

Beilstein J. Nanotechnol. 2023, 14, 1225–1237, doi:10.3762/bjnano.14.101

• import modules for a wide variety of scanning probe microscopes as well as tools for SPM data processing and analysis. This enables the user to chose between data processing in unDrift and Gwyddion. unDrift supports basic data processing methods such as leveling (mean plane, polynomial) and an automatic

Upscaling the urea method synthesis of CoAl layered double hydroxides

• Camilo Jaramillo-Hernández,
• Víctor Oestreicher,
• Martín Mizrahi and
• Gonzalo Abellán

Beilstein J. Nanotechnol. 2023, 14, 927–938, doi:10.3762/bjnano.14.76

• . For each sample, six spectra were taken with exposure times of 4 min each to later be averaged. XANES data treatment was performed by subtracting the pre-edge background followed by normalization by extrapolation of a quadratic polynomial fitted at the post-edge region of the spectrum using the ATHENA

On the use of Raman spectroscopy to characterize mass-produced graphene nanoplatelets

• Keith R. Paton,
• Konstantinos Despotelis,
• Naresh Kumar,
• Piers Turner and
• Andrew J. Pollard

Beilstein J. Nanotechnol. 2023, 14, 509–521, doi:10.3762/bjnano.14.42

• in the Wire 5.4 software (Renishaw plc., UK) based on an 11-point polynomial. Each spectrum was then normalised to give intensities between 0 and 1, and the spectra from each map were averaged. D band, G band, D’ band, and 2D band of all spectra, either individual or averaged, were fitted using

Straight roads into nowhere – obvious and not-so-obvious biological models for ferrophobic surfaces

• Wilfried Konrad,
• Christoph Neinhuis and
• Anita Roth-Nebelsick

Beilstein J. Nanotechnol. 2022, 13, 1345–1360, doi:10.3762/bjnano.13.111

• Equation 6 into the gas equation (: gas constant, n: number of gas particles, T: temperature) results in a cubic polynomial for the radius s of the contact line (see Figure 5): This polynomial has exactly one real and positive solution, provided pl > 0, T > 0, 0 ≤ ε ≤ π/2 and 0 ≤ θ ≤ π. This implies that

A super-oscillatory step-zoom metalens for visible light

• Yi Zhou,
• Chao Yan,
• Peng Tian,
• Zhu Li,
• Yu He,
• Bin Fan,
• Zhiyong Wang,
• Yao Deng and
• Dongliang Tang

Beilstein J. Nanotechnol. 2022, 13, 1220–1227, doi:10.3762/bjnano.13.101

• , we use the even aspherical phase profile rather than the parabolic phase profile for the phase modulation in these two metasurfaces, which can be denoted as: where r is the radial coordinate, R is the normalized radius of the metasurface, n represents the number of polynomial coefficients, and ai is

Micro-structures, nanomechanical properties and flight performance of three beetles with different folding ratios

• Jiyu Sun,
• Pengpeng Li,
• Yongwei Yan,
• Fa Song,
• Nuo Xu and
• Zhijun Zhang

Beilstein J. Nanotechnol. 2022, 13, 845–856, doi:10.3762/bjnano.13.75

• nanomechanical characteristics were tested using a nanoindenter (TriboIndenter, Hysitron Inc., USA). The reduced Young’s modulus, Er, is calculated as where β is a constant related to the shape of the head (for a Berkovich indenter, the value is 1.034). Ac is contact the area and a polynomial function of

Design and characterization of polymeric microneedles containing extracts of Brazilian green propolis

• Camila Felix Vecchi,
• Rafaela Said dos Santos,
• Jéssica Bassi da Silva and
• Marcos Luciano Bruschi

Beilstein J. Nanotechnol. 2022, 13, 503–516, doi:10.3762/bjnano.13.42

• show the interaction effects of the independent variables (P407 and EE or GE) on height and base measurements, strength, and printing area in the hard surface. To predict the optimal conditions, a polynomial equation was fitted correlating the relationship between the independent variables and the

• response: where Y is the response (the dependent variable) as function of X1 and X2, b0 is a constant term (the arithmetic mean response of nine batches), b1 and b2 are the estimated coefficients of linear terms, and b12 is the coefficient of the interaction effect. The polynomial terms X112 and X222

Theoretical understanding of electronic and mechanical properties of 1T′ transition metal dichalcogenide crystals

• Seyedeh Alieh Kazemi,
• Sadegh Imani Yengejeh,
• Vei Wang,
• William Wen and
• Yun Wang

Beilstein J. Nanotechnol. 2022, 13, 160–171, doi:10.3762/bjnano.13.11

• fitting a second-order polynomial to the change on the total energy versus applied strain. The data are obtained from post-processing the VASP calculated results using the VASPKIT code [45]. The average values of G and B of bulk TMDs are obtained using the Voigt–Reuss–Hill average method [16]: The values

A photonic crystal material for the online detection of nonpolar hydrocarbon vapors

• Evgenii S. Bolshakov,
• Aleksander V. Ivanov,
• Andrei A. Kozlov,
• Anton S. Aksenov,
• Elena V. Isanbaeva,
• Sergei E. Kushnir,
• Aleksei D. Yapryntsev,
• Aleksander E. Baranchikov and
• Yury A. Zolotov

Beilstein J. Nanotechnol. 2022, 13, 127–136, doi:10.3762/bjnano.13.9

• objects. An example is the detection of toluene in the presence of xylenes. We discovered that the response rate of the composite sensor is affected by the p-xylene/toluene ratio in the analyzed mixture. The relationship shown in Figure 6, correlates well (R2 = 0.995) with a 3rd-degree polynomial curve: t

The role of convolutional neural networks in scanning probe microscopy: a review

• Ido Azuri,
• Irit Rosenhek-Goldian,
• Neta Regev-Rudzki,
• Georg Fantner and
• Sidney R. Cohen

Beilstein J. Nanotechnol. 2021, 12, 878–901, doi:10.3762/bjnano.12.66

• linear decision boundary, that is, straight lines that can differentiate between samples from the different categories with respect to the given features (Figure 1). Higher-order polynomial degree decision boundaries are also used, but need to be set a priori and are limited only to the specific shape at

The nanomorphology of cell surfaces of adhered osteoblasts

• Christian Voelkner,
• Mirco Wendt,
• Regina Lange,
• Max Ulbrich,
• Martina Gruening,
• Susanne Staehlke,
• Barbara Nebe,
• Ingo Barke and
• Sylvia Speller

Beilstein J. Nanotechnol. 2021, 12, 242–256, doi:10.3762/bjnano.12.20

• different rows along the fast scan direction were aligned by adjusting the row offset such that the median value of the difference between two neighboring rows equaled zero. The images shown in Figure 2a and Figure 2e were further processed by subtracting 2D polynomial backgrounds using Igor Pro to

Understanding nanoparticle flow with a new in vitro experimental and computational approach using hydrogel channels

• Armel Boutchuen,
• Dell Zimmerman,
• Abdollah Arabshahi,
• John Melnyczuk and
• Soubantika Palchoudhury

Beilstein J. Nanotechnol. 2020, 11, 296–309, doi:10.3762/bjnano.11.22

• polynomial variation with respect to NP mass during the transport through soft hydrogel channels (Figure 7a). The average velocity of 0.09 mmol PVP/0.0017 mmol PEI-coated NPs of size 130 nm ranged from 0.47 to 0.58 cm·s−1 and was a third-order polynomial function of the NP mass with an R value of 0.87. NPs

• coated with 0.07 mmol PVP/0.005 mmol PEI of size 144 nm exhibited a flow velocity ranging between 0.51 and 0.61 cm·s−1 with a cubic polynomial fit with respect to mass concentration of NPs (R = 0.76). The flow velocity of 0.06 mmol PVP/0.007 mmol PEI-coated iron oxide NPs of size 69 nm varied between

• 0.55 and 0.64 cm·s−1 while the 140 nm sized NPs with 0.05 mmol PVP/0.008 mmol PEI coating showed a velocity range of 0.48–0.6 cm·s−1. General cubic polynomial trends in velocity with respect to NP mass concentration were also observed for these two iron oxide NPs, but with higher deviations compared to

Nonequilibrium Kondo effect in a graphene-coupled quantum dot in the presence of a magnetic field

• Levente Máthé and
• Ioan Grosu

Beilstein J. Nanotechnol. 2020, 11, 225–239, doi:10.3762/bjnano.11.17

• shape of the Kondo peak strongly depends on the bias voltage. Its amplitude reaches a maximum at eV = 0 and quickly drops when eV increases. The variation of the differential conductance near eV = 0 can be described by a second-degree polynomial function. The dependence of the differential conductance

• approximated by a second-degree polynomial function as has already been proposed in the U → ∞ case. The μR dependence of the zero-bias peak shows the same behavior as observed for U → ∞. Conclusion We studied the Kondo effect of a QD connected to pure monolayer graphene electrodes arranged in an armchair

Phase inversion-based nanoemulsions of medium chain triglyceride as potential drug delivery system for parenteral applications

• Eike Folker Busmann,
• Dailén García Martínez,
• Henrike Lucas and
• Karsten Mäder

Beilstein J. Nanotechnol. 2020, 11, 213–224, doi:10.3762/bjnano.11.16

• solutions of such surfactants increases nonlinearly with the solute concentration due to increasing polymer–solvent hydrogen bonding at low temperatures, which prevents the flow of solvent molecules in the solution and thus affects osmosis. This phenomenon is described by a modified polynomial van’t Hoff

• equation of 4th degree introduced by Huggins and Flory with the association or interacting constants b1, b2 and b3: The experimental data corresponded well to the modified polynomial van’t Hoff equation of 4th degree with a coefficient of determination of 99.865%. Thus, the equation was used for the

• thermal cycling. Solutions of the nonionic surfactant Kolliphor HS 15 showed a nonlinear increase of osmolality with increasing Kolliphor HS 15 concentration, which corresponds well to the modified polynomial van’t Hoff equation of 4th degree introduced by Huggins and Flory. This led to the hypertonicity

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

• -root and arctan functions are required. Typically the phase is calculated by using either a polynomial approximation [42] or the CORDIC algorithm [43]. Coherent demodulator The multifrequency coherent demodulator is a digital demodulation method based on mixing and precise integration over a fixed time

• the values of which are calculated based on the chosen filter order and bandwidth around the modeled frequency ωi. As the desired closed-loop polynomial has five coefficients, the coefficients of the pre-filter W(s) are of the form and are able to be obtained by solving Equation 21. The existing

A novel method to remove impulse noise from atomic force microscopy images based on Bayesian compressed sensing

• Yingxu Zhang,
• Yingzi Li,
• Zihang Song,
• Zhenyu Wang,
• Jianqiang Qian and
• Junen Yao

Beilstein J. Nanotechnol. 2019, 10, 2346–2356, doi:10.3762/bjnano.10.225

• problem where ε is the bound of the noise. The solution of Equation 3 is a non-deterministic polynomial problem (NP problem) [26]. When both the number of total elements of α and its non-zero elements are large, a solution of Equation 3 cannot be achieved in practice. Generally, the non-convex L0-norm can

In situ AFM visualization of Li–O₂ battery discharge products during redox cycling in an atmospherically controlled sample cell

• Kumar Virwani,
• Younes Ansari,
• Khanh Nguyen,
• Francisco José Alía Moreno-Ortiz,
• Jangwoo Kim,
• Maxwell J. Giammona,
• Ho-Cheol Kim and
• Young-Hye La

Beilstein J. Nanotechnol. 2019, 10, 930–940, doi:10.3762/bjnano.10.94

• . The graph reveals that during the initial stages, no discharge products appear in the images. At a discharge capacity of ≈4% the first deposits appear on the surface beyond which the measured volume of the precipitates can be fit to a second-order polynomial function of the cell discharge capacity. At

Bidirectional biomimetic flow sensing with antiparallel and curved artificial hair sensors

• Claudio Abels,
• Antonio Qualtieri,
• Toni Lober,
• Alessandro Mariotti,
• Lily D. Chambers,
• Massimo De Vittorio,
• William M. Megill and
• Francesco Rizzi

Beilstein J. Nanotechnol. 2019, 10, 32–46, doi:10.3762/bjnano.10.4

• for the bidirectional air flow measurements. As both flow sensor variants differed in offset voltage and output range, the signal amplitudes were normalized. The dots indicate measurement values and the lines represent polynomial curve fittings for visual guidance. For the antiparallel artificial hair

• second-order polynomial fit (R-square: 0.9919) was done for the forward air flow direction. It reached its saturation limit for backward air flow at −17.2 m s−1. The third-order polynomial fit for the antiparallel cantilevers (R-square: 0.9953) proposes an axially symmetrical sensitivity of 40 μV/(m s−1

Magnetic and luminescent coordination networks based on imidazolium salts and lanthanides for sensitive ratiometric thermometry

• Pierre Farger,
• Cédric Leuvrey,
• Mathieu Gallart,
• Pierre Gilliot,
• Guillaume Rogez,
• João Rocha,
• Duarte Ananias,
• Pierre Rabu and
• Emilie Delahaye

Beilstein J. Nanotechnol. 2018, 9, 2775–2787, doi:10.3762/bjnano.9.259

• calibration curves, resulting from the fit considering a linear function for Δ1, Δ(T) = Δ0 + mT (r2 = 0.998) and second-order polynomial functions, Δ(T) = Δ0 + a1T + a2T2, for Δ2 (r2 = 0.999) and Δ3 (r2 = 0.999). The bars depict the errors in the thermometric parameter resulting from the propagation of the

Pattern generation for direct-write three-dimensional nanoscale structures via focused electron beam induced deposition

• Lukas Keller and
• Michael Huth

Beilstein J. Nanotechnol. 2018, 9, 2581–2598, doi:10.3762/bjnano.9.240

• calibration experiment at a similar height z3D,i ≈ ζ would compensate for the reduced precursor coverage effect because ne = le/sF. Now we have For the set of values {(hi+1 − hi)/(z3D,i+1 − z3D,i)} vs the heights {z3D,i} obtained from the calibration experiment we perform a polynomial fit and obtain n ≤ 3

• will certainly be described quite well by a low-order polynomial. The values of the coefficients αn are stored in the settings file setf. This implies that setting the coefficients to α0 = 1 and αn = 0 for all n > 0 does deactivate the height-dependent deposition speed correction. At initialization the

• section 2.3.1). The calculated height corrections are shown as blue diamonds in the upper right plot. The corresponding fit to a polynomial function of order three is also shown in red. The coefficients from the fit have then been used in the settings file setf for deposit B. In consequence, the growth

Effective sensor properties and sensitivity considerations of a dynamic co-resonantly coupled cantilever sensor

• Julia Körner

Beilstein J. Nanotechnol. 2018, 9, 2546–2560, doi:10.3762/bjnano.9.237

• results in a sixth degree polynomial expression that can only be solved numerically. Consequently, for an estimate of the resonance frequencies, we consider the model from Figure 1c without the damping elements d1,2. The validity of this assumption is supported by comparison of simulation results for the

Preparation and morphology-dependent wettability of porous alumina membranes

• Dmitry L. Shimanovich,
• Alla I. Vorobjova,
• Daria I. Tishkevich,
• Alex V. Trukhanov,
• Maxim V. Zdorovets and
• Artem L. Kozlovskiy

Beilstein J. Nanotechnol. 2018, 9, 1423–1436, doi:10.3762/bjnano.9.135

• triangles) – 65 µm; 4 (purple circles) – 75 µm. The inset shows an SEM image of the outer surface. The black dotted line is a polynomial fit shown as a guide to the eye for all data sets. Contact angle measurements for the back side of the PAM as a function of pore diameter for various membrane thicknesses

• . The black dotted lines are polynomial fits shown as a guide to the eye for selected data sets. Physical characteristics (average values) of the experimental samples (before etching, as-produced amorphous membrane). Contact angle values for as-made PAMs obtained in 0.3 M oxalic acid (type I and type II

Formation and development of nanometer-sized cybotactic clusters in bent-core nematic liquid crystalline compounds

• Yuri P. Panarin,
• Sithara P. Sreenilayam,
• Jagdish K. Vij,
• Anne Lehmann and
• Carsten Tschierske

Beilstein J. Nanotechnol. 2018, 9, 1288–1296, doi:10.3762/bjnano.9.121

• director n. The order parameters S′ and S″ represent the degree of molecular orderings within clusters and the degree of ordering of clusters in the macroscopic sample, respectively. These are obtained from the following equations: Here P2 is the second order Legendre polynomial in angles θ and Θ in

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

• temperature with confidence intervals of the second-degree polynomial approximation. Radial distribution function for the Al and Pd nanoparticles containing 20000 atoms for the bulk crystal at a temperature of 300 K and after cooling, and at 1150 K for palladium before cooling, and at 750 K for aluminum

Electrostatic force spectroscopy revealing the degree of reduction of individual graphene oxide sheets

• Yue Shen,
• Ying Wang,
• Yuan Zhou,
• Chunxi Hai,
• Jun Hu and
• Yi Zhang

Beilstein J. Nanotechnol. 2018, 9, 1146–1155, doi:10.3762/bjnano.9.106

• images with tip biases of (b) 0 V, (c) 5 V and (d) −5 V of sample 0; EFM images of (e, f) sample 1, (g, h) sample 2, (i, j) sample 3, (k, l) sample 4, and (m, n) sample 5; (o) EFM spectra and the corresponding polynomial fits of samples 0–5 (the dashed vertical lines show the position of the biases at