Interpreting motion and force for narrow-band intermodulation atomic force microscopy

Intermodulation atomic force microscopy (ImAFM) is a mode of dynamic atomic force microscopy that probes the nonlinear tip-surface force by measurement of the mixing of multiple tones in a frequency comb. A high $Q$ cantilever resonance and a suitable drive comb will result in tip motion described by a narrow-band frequency comb. We show by a separation of time scales, that such motion is equivalent to rapid oscillations at the cantilever resonance with a slow amplitude and phase or frequency modulation. With this time domain perspective we analyze single oscillation cycles in ImAFM to extract the Fourier components of the tip-surface force that are in-phase with tip motion ($F_I$) and quadrature to the motion ($F_Q$). Traditionally, these force components have been considered as a function of the static probe height only. Here we show that $F_I$ and $F_Q$ actually depend on both static probe height and oscillation amplitude. We demonstrate on simulated data how to reconstruct the amplitude dependence of $F_I$ and $F_Q$ from a single ImAFM measurement. Furthermore, we introduce ImAFM approach measurements with which we reconstruct the full amplitude and probe height dependence of the force components $F_I$ and $F_Q$, providing deeper insight into the tip-surface interaction. We demonstrate the capabilities of ImAFM approach measurements on a polystyrene polymer surface.Comment: 12 pages, 7 figure

Josephson junction transmission lines as tunable artificial crystals

We investigate one-dimensional Josephson junction arrays with generalized unit cells as a circuit approach to engineer microwave band gaps. An array described by a lattice with a basis can be designed to have a gap in the electromagnetic spectrum, in full analogy to electronic band gaps in diatomic or many-atomic crystals. We derive the dependence of this gap on the array parameters in the linear regime, and suggest experimentally feasible designs to bring the gap below the single junction plasma frequency. The gap can be tuned in a wide frequency range by applying external flux, and it persists in the presence of small imperfections.Comment: 9 pages, 5 figure

The Role of Nonlinear Dynamics in Quantitative Atomic Force Microscopy

Various methods of force measurement with the Atomic Force Microscope (AFM) are compared for their ability to accurately determine the tip-surface force from analysis of the nonlinear cantilever motion. It is explained how intermodulation, or the frequency mixing of multiple drive tones by the nonlinear tip-surface force, can be used to concentrate the nonlinear motion in a narrow band of frequency near the cantilevers fundamental resonance, where accuracy and sensitivity of force measurement are greatest. Two different methods for reconstructing tip-surface forces from intermodulation spectra are explained. The reconstruction of both conservative and dissipative tip-surface interactions from intermodulation spectra are demonstrated on simulated data.Comment: 25 pages (preprint, double space) 7 figure

Phase imaging with intermodulation atomic force microscopy

Intermodulation atomic force microscopy (IMAFM) is a dynamic mode of atomic force microscopy (AFM) with two-tone excitation. The oscillating AFM cantilever in close proximity to a surface experiences the nonlinear tip-sample force which mixes the drive tones and generates new frequency components in the cantilever response known as intermodulation products (IMPs). We present a procedure for extracting the phase at each IMP and demonstrate phase images made by recording this phase while scanning. Amplitude and phase images at intermodulation frequencies exhibit enhanced topographic and material contrast.Comment: 6 pages, 6 page

Intermodulation in microresonators : for microwave amplification and nanoscale surface analysis

This work explores the effects of weak nonlinearity on harmonic oscillators.Two particular systems are studied experimentally: A superconductingresonator formed from a coplanar waveguide that oscillates at microwave frequencies,and the cantilever of an atomic force microscope (AFM) vibratingat ultrasonic frequencies. Both of these systems are described in the introduction,followed by a theory chapter giving a general theoretical framework for nonlinear oscillators. Basic properties of nonlinear oscillators, such asbifurcation and intermodulation, are explained using simple models. Experimental methods, including cryogenic and microwave measurement techniques,are described in some detail. The nonlinear superconducting resonator is studied for use as a parametric amplifier. A strong drive tone, called the pump, drives the oscillator nearthe point of bifurcation. A second, much weaker drive signal that is slightlydetuned from the pump, will cause energy to move from the pump to the signal, giving signal amplification. We have measured a signal gain greaterthan 22 dB in a bandwidth of 30 kHz, for a resonator pumped at 7.6 GHz.This type of amplifier is phase-sensitive, meaning that signals in phase withthe pump will be amplified, but signals in quadrature phase of the pump will be deamplified. Phase-sensitivity has important implications on the amplifier’snoise properties. With a parametric amplifier, a signal can be amplified without any additional noise being added by the amplifier, something that is fundamentally impossible for a standard amplifier. The vibrating AFM cantilever becomes a nonlinear oscillator when it is interacting with a surface. When driven with two frequencies, the amplitudeand phase of the cantilever’s response will develop mixing products, or intermodulation products, that are very sensitive to the exact form of the nonlinearity. Very small changes in the surface properties will be detectable when measuring the intermodulation products. Simultaneously measuring many intermodulation products, or acquiring an intermodulation spectrum,allows one to reconstruct the tip-surface interaction. Intermodulation AFM increases the sensitivity of the measurement or the contrast of the acquiredimages, and provides a means of rapidly measuring the nonlinear tip-surface interaction. The method promises to enhance the functionality of the AFM beyond simple topography measurement, towards quantitative analysis of the chemical or material properties of the surface.QC 20100812</p

Effects of levosimendan on renal blood flow and glomerular filtration in patients with acute kidney injury after cardiac surgery: a double blind, randomized placebo-controlled study

Abstract Background Acute kidney injury (AKI) is a common and serious complication after cardiac surgery, and current strategies aimed at treating AKI have proven ineffective. Levosimendan, an inodilatating agent, has been shown to increase renal blood flow and glomerular filtration rate in uncomplicated postoperative patients and in patients with the cardiorenal syndrome. We hypothesized that levosimendan through its specific effects on renal vasculature, a preferential vasodilating effect on preglomerular resistance vessels, could improve renal function in AKI-patients with who did not have clinical indication for inotropic support. Methods In this single-center, double-blind, randomized controlled study, adult patients with postoperative AKI within 2 days after cardiac surgery, who were hemodynamically stable with a central venous oxygen saturation (ScvO2) ≥ 60% without inotropic support were eligible for inclusion. After randomization, study drug infusions, levosimendan (n = 16) or placebo (n = 13) were given for 5 h. A bolus infusion of levosimendan (12 µg/kg), were given for 30 min followed by 0.1 µg/kg/min for 5 h. Renal blood flow and glomerular filtration rate were measured using infusion clearance of para-aminohippuric acid and a filtration marker, respectively. As a safety issue, norepinephrine was administered to maintain mean arterial pressure between 70–80 mmHg. Intra-group differences were tested by Mann–Whitney U-tests, and a linear mixed model was used to test time and group interaction. Results Twenty-nine patients completed the study. At inclusion, the mean serum creatinine was higher in the patients randomized to levosimendan (148 ± 29 vs 127 ± 22 µmol/L, p = 0.030), and the estimated GFR was lower (46 ± 12 vs 57 ± 11 ml/min/1.73 m2, p = 0.025). Levosimendan induced a significantly (p = 0.011) more pronounced increase in renal blood flow (15%) compared placebo (3%) and a more pronounced decrease in renal vascular resistance (− 18% vs. − 4%, respectively, p = 0.043). There was a trend for a minor increase in glomerular filtration rate with levosimendan (4.5%, p = 0.079), which did differ significantly from the placebo group (p = 0.440). The mean norepinephrine dose was increased by 82% in the levosimedan group and decreased by 29% in the placebo group (p = 0.012). Conclusions In hemodynamically stable patients with AKI after cardiac surgery, levosimendan increases renal blood flow through renal vasodilatation. Trial registration NCT02531724, prospectly registered on 08/20/2015. https://clinicaltrials.gov/ct2/show/NCT02531724?cond=AKI&cntry=SE&age=1&draw=2&rank=