Julian A. Sanelli

Spring constant calibration of atomic force microscope cantilevers of arbitrary shape

The spring constant of an atomic force microscope cantilever is often needed for quantitative measurements. The calibration method of Sader et al. [Rev. Sci. Instrum. 70, 3967 (1999)] for a rectangular cantilever requires measurement of the resonant frequency and quality factor in fluid (typically air), and knowledge of its plan view dimensions. This intrinsically uses the hydrodynamic function for a cantilever of rectangular plan view geometry. Here, we present hydrodynamic functions for a series of irregular and non-rectangular atomic force microscope cantilevers that are commonly used in practice. Cantilever geometries of arrow shape, small aspect ratio rectangular, quasi-rectangular, irregular rectangular, non-ideal trapezoidal cross sections, and V-shape are all studied. This enables the spring constants of all these cantilevers to be accurately and routinely determined through measurement of their resonant frequency and quality factor in fluid (such as air). An approximate formulation of the hydrodynamic function for microcantilevers of arbitrary geometry is also proposed. Implementation of the method and its performance in the presence of uncertainties and non-idealities is discussed, together with conversion factors for the static and dynamic spring constants of these cantilevers. These results are expected to be of particular value to the design and application of micro- and nanomechanical systems in general.

Electronic Spectra of Gas-Phase Polycyclic Aromatic Nitrogen Heterocycle Cations: Isoquinoline(+) and Quinoline(+)

Electronic spectra of the gas-phase isoquinoline(+)-Ar and quinoline(+)-Ar complexes are recorded using photodissociation spectroscopy by monitoring the Ar loss channel. The D(3)←D(0) and D(4)←D(0) band origins for isoquinoline(+)-Ar are observed at 15245 ± 15 cm(-1) and 21960 ± 15 cm(-1), respectively, whereas for quinoline(+)-Ar they appear at 16050 ± 15 cm(-1) and 21955 ± 15 cm(-1), respectively. Strong vibronic progressions for the D(3)←D(0) band systems of both isoquinoline(+)-Ar and quinoline(+)-Ar are modeled and assigned in terms of ring deformation and carbon-carbon stretch vibrational modes using time-dependent density functional theory calculations in conjunction with Franck-Condon simulations. The properties of the isoquinoline(+) and quinoline(+) molecules are compared with those of the isoelectronic naphthalene(+) molecule. The existence of strong progressions in the visible spectra of isoquinoline(+)-Ar and quinoline(+)-Ar suggests that the corresponding isoquinoline(+) and quinoline(+) molecular cations are unlikely to be responsible for diffuse interstellar bands.

Electronic absorptions of the benzylium cation

The electronic transitions of the benzylium cation (Bz(+)) are investigated over the 250-550 nm range by monitoring the photodissociation of mass-selected C(7)H(7)(+)-Ar(n) (n = 1, 2) complexes in a tandem mass spectrometer. The Bz(+)-Ar spectrum displays two distinct band systems, the S(1)←S(0) band system extending from 370 to 530 nm with an origin at 19,067 ± 15 cm(-1), and a much stronger S(3)←S(0) band system extending from 270 to 320 nm with an origin at 32,035 ± 15 cm(-1). Whereas the S(1)←S(0) absorption exhibits well resolved vibrational progressions, the S(3)←S(0) absorption is broad and relatively structureless. Vibronic structure of the S(1)←S(0) system, which is interpreted with the aid of time-dependent density functional theory and Franck-Condon simulations, reflects the activity of four totally symmetric ring deformation modes (ν(5), ν(6), ν(9), ν(13)). We find no evidence for the ultraviolet absorption of the tropylium cation, which according to the neon matrix spectrum should occur over the 260 - 275 nm range [A. Nagy, J. Fulara, I. Garkusha, and J. Maier, Angew. Chem., Int. Ed. 50, 3022 (2011)].

Effect of multiplicative noise on least-squares parameter estimation with applications to the atomic force microscope.

Measurement of the power spectral density of (stochastic) Brownian fluctuations of micro- and nano-devices is used frequently to gain insight into their mechanistic properties. Noise is always present in these measurements and can directly influence any parameter estimation obtained through a least-squares analysis. Importantly, measurements of the spectral density of stationary random signals, such as Brownian motion, inherently contain multiplicative noise. In this article, we theoretically analyze the impact of multiplicative noise on fit parameters extracted using a least-squares analysis. A general analysis is presented that is valid for any fit function with any number of fit parameters. This yields closed-form expressions for the expected value and variance in the fit parameters and provides a rigorous theoretical framework for a priori determination of the effect of measurement uncertainty. The theory is demonstrated and validated through Monte Carlo simulation of synthetic data and by comparison to power spectral density measurements of the Brownian fluctuations of an atomic force microscope cantilever - analytical formulas for the uncertainty in the fitted resonant frequency and quality factor are presented. The results of this study demonstrate that precise measurements of fit parameters in the presence of noise are inherently problematic - individual measurements of the power spectral density are capable of yielding fit parameters that are many standard deviations away from the mean, with finite probability. This is of direct relevance to a host of applications in measurement science, including those connected with the atomic force microscope.

Distortion in the thermal noise spectrum and quality factor of nanomechanical devices due to finite frequency resolution with applications to the atomic force microscope.

The thermal noise spectrum of nanomechanical devices is commonly used to characterize their mechanical properties and energy dissipation. This spectrum is measured from finite time series of Brownian motion of the device, which is windowed and Fourier transformed. Here, we present a theoretical and experimental investigation of the effect of such finite sampling on the measured device quality factor. We prove that if no spectral window is used, the thermal noise spectrum retains its original Lorentzian distribution but with a reduced quality factor, indicating an apparent enhancement in energy dissipation. A simple analytical formula is derived connecting the true and measured quality factors - this enables extraction of the true device quality factor from measured data. Common windows used to reduce spectral leakage are found to distort the (true) Lorentzian shape, potentially making fitting problematic. These findings are expected to be of particular importance for devices with high quality factors, where spectral resolution can be limited in practice. Comparison and validation using measurements on atomic force microscope cantilevers are presented.

Gas-phase electronic spectrum of the indole radical cation

The visible and near-UV electronic spectrum of the indole radical cation is measured in the gas phase by photodissociation of indole+–Ar and indole+–He complexes in a tandem mass spectrometer. A series of resolved vibronic transitions extending from 610 to 460 nm are assigned to the D2 ← D0 band system, while weak transitions between 390 and 360 nm are assigned to the D3 ← D0 system, and a stronger, broad, unresolved absorption between 350 and 300 nm is attributed to the D4 ← D0 system. Time-dependent density functional theory calculations are used to assign vibronic structure of the D2 ← D0 band system, and show that the main active vibrational modes correspond to in-plane ring deformations. The strongest D2 ← D0 vibronic transitions of indole+–He do not correspond with any catalogued diffuse interstellar bands, even considering band displacements of up to 50 cm−1possibly caused by the attached He atom.

Gas-phase electronic spectroscopy of the indene cation (C9H8(+)).

The electronic spectrum of the indene radical cation has been investigated through resonance-enhanced photodissociation of the weakly bound C9H8(+)-He and C9H8(+)-Arn (n = 1, 2) complexes in a tandem mass spectrometer. The D2 ← D0 band origin for indene(+)-He is observed at 17,379 ± 15 cm(-1), while the D2 ← D0 and D4 ← D0 band origins for indene(+)-Ar appear at 17,353 ± 15 cm(-1) and 28,254 ± 15 cm(-1), respectively. The vibronic structure of the D2 ← D0 band system is assigned by comparison with a simulated spectrum based on time-dependent density functional theory calculations, and is due mainly to progressions in ring deformation vibrational modes. Possible correspondences between the stronger visible transitions of the indene cation and diffuse interstellar bands observed towards the heavily reddened star HD 204827 are discussed.

Electronic spectrum of the propargyl cation (H2C3H(+)) tagged with Ne and N2.

The Ã(1)A1 ← X̃(1)A1 band system of the propargyl cation (H2C3H(+)) is measured over the 230-270 nm range by photodissociation of mass-selected H2C3H(+)-Ne and H2C3H(+)-N2 complexes in a tandem mass spectrometer. The band origin occurs at 37 618 cm(-1) for H2C3H(+)-Ne and 37 703 cm(-1) for H2C3H(+)-N2. Ground and excited state ab initio calculations for H2C3H(+) using the MCSCF and coupled-cluster (CC) response methods show that the ion has C2v symmetry in the ground X̃(1)A1 and excited Ã(1)A1 states and that the strong vibronic progression with a spacing of 630 cm(-1) is due to the C-C stretch vibrational mode, ν 5.

Electronic Spectroscopy of the 1,3-Cyclopentadiene Cation (C5H6+)

The gas-phase electronic spectrum of the 1,3-cyclopentadiene radical cation (C5H6(+)) has been investigated using resonance-enhanced photodissociation of mass-selected C5H6(+)-Ar complexes in a tandem mass spectrometer. The D1((2)B1) ← D0((2)A2) band system spans the 460-620 nm range, while the D2((2)B1) ← D0((2)A2) band system appears between 320 and 370 nm. The band origins for the two systems are estimated to occur at 16,560 ± 25 and 27,808 ± 25 cm(-1), respectively. The D1 ← D0 band system exhibits a distinctive series of broad peaks, which, with the aid of molecular vibrational frequencies and geometries calculated using time-dependent density functional theory, are assigned to progressions in totally symmetric ring deformation modes. The broadening arises from the Franck-Condon activity of low-frequency out-of-plane vibrational modes, unresolved rotational contours, and possibly homogeneous lifetime broadening caused by rapid internal conversion to the ground electronic state.

Electronic spectrum of 9-methylanthracenium radical cation

The predissociation spectrum of the cold, argon-tagged, 9-methylanthracenium radical cation is reported from 8000 cm(-1) to 44 500 cm(-1). The reported spectrum contains bands corresponding to at least eight electronic transitions ranging from the near infrared to the ultraviolet. These electronic transitions are assigned through comparison with ab initio energies and intensities. The infrared D1←D0 transitions exhibit significant vibronic activity, which is assigned through comparison with TD-B3LYP excited state frequencies and intensities, as well as modelled vibronic interactions. Dissociation of 9-methylanthracenium is also observed at high visible-photon energies, resulting in the loss of either CH2 or CH3. The relevance of these spectra, and the spectra of other polycyclic aromatic hydrocarbon radical cations, to the largely unassigned diffuse interstellar bands, is discussed.