Plasmonic nanotechnology for photothermal applications – an evaluation

• A. R. Indhu,
• L. Keerthana and
• Gnanaprakash Dharmalingam

Beilstein J. Nanotechnol. 2023, 14, 380–419, doi:10.3762/bjnano.14.33

• is the polarization density. P can be arrived at by solving the equation of motion for a single electron as Hence the expression relating the dielectric displacement (D) and the external electric field can be obtained as where is the natural frequency of oscillation of the electron cloud. Comparing

Recent progress in actuation technologies of micro/nanorobots

• Ke Xu and
• Bing Liu

Beilstein J. Nanotechnol. 2021, 12, 756–765, doi:10.3762/bjnano.12.59

• bubble whose natural frequency corresponds to the applied frequency vibrates and causes a microflow, while the other bubble remains motionless. Experiments show that the microrobot can be propelled to a desired position through electromagnetic actuation, and carry, release, and inject the drug. Based on

Vibration analysis and pull-in instability behavior in a multiwalled piezoelectric nanosensor with fluid flow conveyance

• Sayyid H. Hashemi Kachapi

Beilstein J. Nanotechnol. 2020, 11, 1072–1081, doi:10.3762/bjnano.11.92

• effects on the dimensionless natural frequency of fluid-conveying multiwalled piezoelectric nanosensors (FC-MWPENSs) based on cylindrical nanoshells is investigated using the Gurtin–Murdoch surface/interface theory. The nanosensor is embedded in a viscoelastic foundation and subjected to nonlinear van der

• constants, residual stress, piezoelectric constants and mass density, are considered for analysis of the dimensionless natural frequency with respect to the viscous fluid velocity and pull-in voltage of the FC-MWPENSs. Keywords: electrostatic excitation; piezoelectric nanosensor; pull-in voltage; stability

• dimensionless natural frequency with respect to viscous fluid velocity and pull-in voltage of fluid-conveying multiwalled piezoelectric nanosensors (FC-MWPENSs) subjected to direct electrostatic DC voltage with nonlinear excitation, nonlinear van der Waals force and viscoelastic foundation. As a guide to the

Current measurements in the intermittent-contact mode of atomic force microscopy using the Fourier method: a feasibility analysis

• Berkin Uluutku and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2020, 11, 453–465, doi:10.3762/bjnano.11.37

• effective mass of the cantilever, f0 its natural frequency, k its stiffness and Q its quality factor: Fexcitation is the sinusoidal driving force and the tip–sample interaction force, Finteraction, is based on the Hamaker equation [42]. The simulation parameters are provided in Table 1. In the power

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

• angular natural frequency (eigenfrequency) ω0 and the angular frequency of damped vibration (resonance frequency) ωd. The former remains unchanged in case of damping as it only depends on the properties spring constant k and effective mass meff of the system itself, i.e., = k/meff. The resonance

Electrospun one-dimensional nanostructures: a new horizon for gas sensing materials

• Muhammad Imran,
• Nunzio Motta and
• Mahnaz Shafiei

Beilstein J. Nanotechnol. 2018, 9, 2128–2170, doi:10.3762/bjnano.9.202

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

• fundamental eigenmode, where the former has a natural frequency that is approximately 6.27 times the fundamental eigenfrequency, the material will behave in a regime closer to the stiff-elastic behavior. That is, the material will exert larger opposing forces when it is impacted by the tip, which makes it

Mechanistic insights into plasmonic photocatalysts in utilizing visible light

• Kah Hon Leong,
• Azrina Abd Aziz,
• Lan Ching Sim,
• Pichiah Saravanan,
• Min Jang and
• Detlef Bahnemann

Beilstein J. Nanotechnol. 2018, 9, 628–648, doi:10.3762/bjnano.9.59

• oscillating electric field of the light. The photon frequency is designed to match with the natural frequency of the noble metal throughout the oscillation. This reduces the field on one side of the electron while increasing it on the other side of the noble metal. The development of this nonequilibrium

Multimodal cantilevers with novel piezoelectric layer topology for sensitivity enhancement

• Steven Ian Moore,
• Michael G. Ruppert and
• Yuen Kuan Yong

Beilstein J. Nanotechnol. 2017, 8, 358–371, doi:10.3762/bjnano.8.38

• voltage to displacement is modeled as a set of second order modes. The transfer function from voltage V to displacement d is [52] where for the i-th mode, ωi is the natural frequency, Qi is the quality factor and αi is the gain. While under motion, the strain on the piezoelectric transducer induces charge

Free vibration of functionally graded carbon-nanotube-reinforced composite plates with cutout

• Mostafa Mirzaei and
• Yaser Kiani

Beilstein J. Nanotechnol. 2016, 7, 511–523, doi:10.3762/bjnano.7.45

• matrix and, K is the stiffness matrix. Additionally, the mechanical displacement vector is denoted by X, which consists of the unknown displacements Uij, Vij, Wij, Xij and Yij. Since the free vibration response is under investigation, X = sin(ω t+φ) may be considered, where ω is the natural frequency

• case of plates without a cutout, an increase in the CNT volume fraction yields a higher natural frequency of the plate. The plates with an FG-X pattern of CNTs have higher frequencies in comparison to UD, FG-V and FG-O plates. Conclusion The natural frequencies of carbon-nanotube-reinforced, composite

• volume fraction results in higher frequencies of the plate with a cutout. Furthermore, FG-X plates have a higher natural frequency in comparison to the other three patterns of CNTs. It was also demonstrated that the variation of fundamental frequency of a perforated plate with respect to the hole size is

Charge and heat transport in soft nanosystems in the presence of time-dependent perturbations

• Alberto Nocera,
• Carmine Antonio Perroni,
• Vincenzo Marigliano Ramaglia and
• Vittorio Cataudella

Beilstein J. Nanotechnol. 2016, 7, 439–464, doi:10.3762/bjnano.7.39

• are anchored to two metallic leads under bias voltage. In this case, the quantum dot is embedded in the CNT itself. In [11][12] the motion of the CNT is actuated by a nearby antenna, which means that, when the external antenna frequency matches the natural frequency of the CNT beam, one can measure

High-bandwidth multimode self-sensing in bimodal atomic force microscopy

• Michael G. Ruppert and
• S. O. Reza Moheimani

Beilstein J. Nanotechnol. 2016, 7, 284–295, doi:10.3762/bjnano.7.26

• the quality factor Qi, natural frequency ωi and gain αi. Similarly, when a piezoelectric transducer is subjected to mechanical strain it becomes electrically polarized, producing a charge on the surface of the material, described by Equation 10. This direct piezoelectric effect can be modeled as a

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

• , the effective mass is m = k/ω2, FD is the driving force and Fts is the net tip–sample force. Typically, the drive frequency is set equal to the natural frequency ω0 since this leads to convenient simplifications. Furthermore, z is the position of the tip relative to its unperturbed equilibrium

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

• frequency different from the natural frequency is accounted for only through a rescaling of the effective mass and quality factor. Whereas, if a and are calibrated, the cantilever spring constant is not fixed to any value. The reasoning above assumes that the measurement corresponds to the position of the

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

• its natural frequency. The first three quality factors of the cantilever were set to Q1 = 220, Q2 = 450, and Q3 = 750 in all cases, and the rest of the parameters are indicated in the figure captions for each case. The equations of motion were integrated numerically and the amplitude and phase for the

• along one fundamental oscillation. The tip was oscillated along a numerically simulated trajectory (not prescribed) for tapping mode AFM. The parameters used for (c) are: cantilever position zc = 80 nm, natural frequency (f0) = 75 kHz, free amplitude (A01) = 100 nm, cantilever stiffness (km1) = 4 N/m

• the cantilever dynamics in (a) and (b) are: cantilever position zc = 80 nm, natural frequency (f0) = 50 kHz, free amplitude (A01) = 50 nm, cantilever stiffness (km1) = 10 N/m. The model parameters for (b) and (c) associated with the DMT contribution are: elastic sample modulus (Es) of 3 GPa, elastic

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

• viscoelastic surfaces. Methods The numerical simulations of the cantilever dynamics were carried out including three eigenmodes of the AFM cantilever as in previous studies [24][42]. Active eigenmodes, as indicated throughout the paper, were driven at their natural frequency. The surface was modeled in most

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 8), although there was little control on the selection of the regime. In general, higher free amplitudes, lower amplitude setpoints, and drive frequencies lower than the natural frequency favor the repulsive regime, but the result is also strongly determined by the cleanness and sharpness of the

• natural frequency. Chirp excitation functions [8][28] were used to construct the engaged amplitude vs frequency curves of Figure 5. The equations of motion were integrated numerically and the amplitude and phase of each eigenmode were calculated using the customary in-phase (Ii) and quadrature (Qi) terms

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

• becomes less sensitive (more difficult to perturb), which leads to larger phase values (closer to the neutral phase value of 90°, which is observed when no tip–sample forces are present and the eigenmode is driven at the natural frequency). However, since the relationship between the tip–sample forces and

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

• the resonance of graphene with different dopants, which may benefit their application as resonators. Keywords: dopant; graphene; molecular dynamics simulation; natural frequency; quality factor; resonance; Introduction Graphene has drawn intensive interest since its discovery in 2005 [1]. It has

• . The corresponding frequency spectrum of the GNR is derived from fast Fourier transformation. As shown in Figure 2b, the natural frequency of the external energy is about 228 GHz. As the energy is a square function of the velocity, i.e., the natural frequency of the GNR is half of the external energy

• 0.76%, 1.65% and 2.78%, a similar progression of the external energy is found. As shown in Figure 4b, the external energy of the GNR with 1.65% of dopants decreases quickly from 0.10 to 0.03 eV after 1200 ps of simulation time. A low Q of about 1610 is estimated with a corresponding natural frequency

Nanostructure sensitization of transition metal oxides for visible-light photocatalysis

• Hongjun Chen and
• Lianzhou Wang

Beilstein J. Nanotechnol. 2014, 5, 696–710, doi:10.3762/bjnano.5.82

• and facilitates the vectorial electron transfer. Plasmonic metal nanostructures as the photosensitizer Surface plasmon resonance (SPR) is the resonant photon-induced collective oscillation of valence electrons, which happens only if the frequency of photons matches the natural frequency of surface

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

• to lower frequencies (see Figure 10), while the frequency at which the phase is 90 degrees remains at the natural frequency. The natural frequency is the only frequency at which all the phase curves intersect for a given (ideal) cantilever driven in environments with different levels of damping (see

• peak is indicated by a thick red arrow on the graph (notice that this frequency is to the left of the natural frequency), and the corresponding phase can be found by following the vertical green line downwards until it intersects the phase response for this value of the quality factor. Now, if the

• were excited through a sinusoidal tip force or base displacement of constant amplitude and frequency equal to the natural frequency. Chirp excitation functions [35][39] were used to construct the amplitude vs frequency curves, where applicable. Most of the simulations for liquid environment used

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

• motion of the mth eigenmode where k(m), Q(m), ω(m), and z(m) are the spring constant, quality factor, natural frequency and position of the mth eigenmode. The term FD stands for the external driving force where the subscript without brackets, n, indicates the harmonic number. Note that here ωn = nω

Size-dependent characteristics of electrostatically actuated fluid-conveying carbon nanotubes based on modified couple stress theory

• Mir Masoud Seyyed Fakhrabadi,
• Abbas Rastgoo and
• Mohammad Taghi Ahmadian

Beilstein J. Nanotechnol. 2013, 4, 771–780, doi:10.3762/bjnano.4.88

• boundary conditions, the axial force is a compressive force because the clamped ends transform the axial force into a compression. According to the concepts of elasticity and vibration of continuous systems, the tensile force increases the natural frequency and buckling loads of the nanobeam, here the CNT

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

• -/nanoscale [1]. Although there are many different operating modes in AFM, one of the most popular is amplitude modulation (AM-AFM), commonly known as tapping mode, in which the cantilever is oscillated at its first natural frequency. AM-AFM provides two basic images of the surface, a height (topography

• theory. The natural frequency ω4, however, can be measured precisely, and the ratio ω4/ω3 is within 7% of the value predicted by beam theory, suggesting that the stiffness should not be too far from beam theory predictions either. Care was taken to tune the driving frequency exactly to the natural

• natural frequency, piezo resonances are generally only an issue in liquid [14]. However, on our instrument, piezo resonances can distort the higher eigenmode tuning curves significantly, especially for third and higher eigenmodes. Therefore, a thermally driven spectrum was obtained when the cantilever was

Bimodal atomic force microscopy driving the higher eigenmode in frequency-modulation mode: Implementation, advantages, disadvantages and comparison to the open-loop case

• Daniel Ebeling and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2013, 4, 198–207, doi:10.3762/bjnano.4.20

• tip–sample-distance feedback loop. These transient times scale as 2Q/ω0, with Q being the quality factor and ω0 the natural frequency [22]. Clearly, imaging becomes impractical when Q increases significantly (as in vacuum operations). In FM-AFM, this drawback is overcome by using the frequency shift

• degrees, corresponding to the natural frequency, where the cantilever is generally most sensitive to external forces and thus permits characterization with gentler impacts. Although the maximum amplitude (peak in the Lorentzian response) does not occur exactly at the natural frequency due to the influence

• of damping, which can be more significant when characterizing highly dissipative samples, the natural frequency is a well-defined condition, which allows the relatively easy implementation of amplitude control. That is, one can control the response amplitude by adjusting the drive amplitude, using a