Introductory Dynamics: 2D Kinematics and Kinetics of Point Masses and Rigid Bodies

Motion is all around us, the universe is full of moving matter and this motion is surprisingly predictable. The field of science and engineering that studies time-dependent motion in the presence of forces is called Dynamics. In this book we will introduce the core concepts in dynamics and provide a comprehensive toolset to predict and analyse planar 2D motion of point masses and rigid bodies. The material includes kinematic analysis, Newton’s laws, Euler’s laws, the equations of motion, work, energy, impulse and momentum. Vector-based methods are discussed for systematically solving essentially any problem in 2D dynamics. The book provides a bachelor level introduction for any science and engineering student that can serve as a basis for more advanced courses in dynamics.TU Delft OPEN TextbookDynamics of Micro and Nano System

Optical absorption sensing with dual-spectrum silicon LEDs in SOI-CMOS technology

Silicon p-n junction diodes emit low-intensity, broad-spectrum light near 1120 nm in forward bias and between 400-900 nm in reverse bias (avalanche). For the first time, we experimentally achieve optical absorption sensing of pigment in solution with silicon micro LEDs designed in a standard silicon-on-insulator CMOS technology. By driving a single LED in both forward and avalanche modes of operation, we steer it's electroluminescent spectrum between visible and near-infrared (NIR). We then characterize the vertical optical transmission of both visible and NIR light from the LED through the same micro-droplet specimen to a vertically mounted discrete silicon photodiode. The effective absorption coefficient of carmine solution in glycerol at varying concentrations were extracted from the color ratio in optical coupling. By computing the LED-specific molar absorption coefficient of carmine, we estimate the concentration (∼0.040 mol L-1) and validate the same with a commercial spectrophotometer (∼0.030 mol L-1). With a maximum observed sensitivity of ∼1260 cm-1mol-1L, the sensor is a significant step forward towards low-cost CMOS-integrated optical sensors with silicon LED as the light source intended for biochemical analyses in food sector and plant/human health. Accepted Author ManuscriptDynamics of Micro and Nano System

Optical sensing of chlorophyll(in) with dual-spectrum Si LEDs in SOI-CMOS technology

Small and low-cost chlorophyll sensors are popular in agricultural sector and food-quality control.Combining such sensors with silicon CMOS electronics is challenged by the absence of silicon-integrated light-sources.We experimentally achieve optical absorption sensing of chlorophyll based pigments with silicon (Si) micro light-emitting diodes (LED) as light-source, fabricated in a standard SOI-CMOS technology.By driving a Si LED in both forward and avalanche modes of operation,we steer its electroluminescentspectrum between visible (400-900 nm) and near-infrared (1120 nm). For detection of chlorophyll in solution phase, the dualspectrum light from the LED propagates vertically through glycerol micro-droplets containing sodium copper chlorophyllin at varying relative concentrations. The transmitted light is detected via an off-chip Si photodiode. The visible to near-infrared color ratio (COR) of the photocurrent yields the effective absorption coefficient. We introduce the LED-specificmolar absorption coefficient as ametric to compute the absolute pigment concentration (0.019 ± 0.006 mol L-1) and validate the results by measurements with a hybrid spectrophotometer. With the same sensor, we also show noninvasive monitoring of chlorophyll in plant leaves. COR sensitivities $\sim 3.9 \times 10^{4}$ mol-1L and $\sim 5.3 \times 10^{4}$ mol-1L are obtained for two leaf species, where light from the LED propagates diffusely through the thickness of the leaf prior to detection by the photodiode. Our work demonstrates the feasibility of realizing fully CMOS-integrated optical sensors for biochemical analyses in food sector and plant/human health.Accepted Author ManuscriptDynamics of Micro and Nano System

Symmetry-Breaking-Induced Frequency Combs in Graphene Resonators

Nonlinearities are inherent to the dynamics of two-dimensional materials. Phenomena-like intermodal coupling already arise at amplitudes of only a few nanometers, and a range of unexplored effects still awaits to be harnessed. Here, we demonstrate a route for generating mechanical frequency combs in graphene resonators undergoing symmetry-breaking forces. We use electrostatic force to break the membrane's out-of-plane symmetry and tune its resonance frequency toward a one-to-two internal resonance, thus achieving strong coupling between two of its mechanical modes. When increasing the drive level, we observe splitting of the fundamental resonance peak, followed by the emergence of a frequency comb regime. We attribute the observed physics to a nonsymmetric restoring potential and show that the frequency comb regime is mediated by Neimark bifurcation of the periodic solution. These results demonstrate that mechanical frequency combs and chaotic dynamics in 2D material resonators can emerge near internal resonances due to symmetry-breaking.Dynamics of Micro and Nano SystemsQN/Steeneken La

Method to Determine the Closed-Loop Precision of Resonant Sensors from Open-Loop Measurements

Resonant sensors determine a sensed parameter by measuring the resonance frequency of a resonator. For fast continuous sensing, it is desirable to operate resonant sensors in a closed-loop configuration, where a feedback loop ensures that the resonator is always actuated near its resonance frequency, so that the precision is maximized even in the presence of drifts or fluctuations of the resonance frequency. However, in a closed-loop configuration, the precision is not only determined by the resonator itself, but also by the feedback loop, even if the feedback circuit is noiseless. Therefore, to characterize the intrinsic precision of resonant sensors, the open-loop configuration is often employed. To link these measurements to the actual closed-loop performance of the resonator, it is desirable to have a relation that determines the closed-loop precision of the resonator from open-loop characterisation data. In this work, we present a methodology to estimate the closed-loop resonant sensor precision by relying only on an open-loop characterization of the resonator. The procedure is beneficial for fast performance estimation and benchmarking of resonant sensors, because it does not require actual closed-loop sensor operation, thus being independent on the particular implementation of the feedback loop. We validate the methodology experimentally by determining the closed-loop precision of a mechanical resonator from an open-loop measurement and comparing this to an actual closed-loop measurement. Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Dynamics of Micro and Nano SystemsQN/Steeneken LabMicro and Nano Engineerin

Probing nanomotion of single bacteria with graphene drums

Motion is a key characteristic of every form of life1. Even at the microscale, it has been reported that colonies of bacteria can generate nanomotion on mechanical cantilevers2, but the origin of these nanoscale vibrations has remained unresolved3,4. Here, we present a new technique using drums made of ultrathin bilayer graphene, where the nanomotion of single bacteria can be measured in its aqueous growth environment. A single Escherichia coli cell is found to generate random oscillations with amplitudes of up to 60 nm, exerting forces of up to 6 nN to its environment. Using mutant strains that differ by single gene deletions that affect motility, we are able to pinpoint the bacterial flagella as the main source of nanomotion. By real-time tracing of changes in nanomotion on administering antibiotics, we demonstrate that graphene drums can perform antibiotic susceptibility testing with single-cell sensitivity. These findings deepen our understanding of processes underlying cellular dynamics, and pave the way towards high-throughput and parallelized rapid screening of the effectiveness of antibiotics in bacterial infections with graphene devices.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Dynamics of Micro and Nano SystemsQN/Steeneken LabBN/Cees Dekker La

Multimode Nonlinear Dynamics of Graphene Resonators

Mechanical nonlinearities dominate the motion of nanoresonators already at relatively small oscillation amplitudes. Although single and coupled two-degree-of-freedom models have been used to account for experimentally observed nonlinear effects, it is shown that these models quickly deviate from experimental findings when multiple modes influence the nonlinear response. Here, we present a nonlinear reduced-order modeling methodology based on finite-element method simulations for capturing the global nonlinear dynamics of nanomechanical resonators. Our physics-based approach obtains the quadratic and cubic nonlinearities of resonators over a wide frequency range that spans 70 MHz. To qualitatively validate our approach, we perform experiments on a graphene nanodrum driven optothermally and show that the model can replicate diverse ranges of nonlinear phenomena, including multistability, parametric resonance, and different internal resonances without considering any empirical nonlinear fitting parameters. By providing a direct link between microscopic geometry, material parameters, and nonlinear dynamic response, we clarify the physical significance of nonlinear parameters that are obtained from fitting the dynamics of nanomechanical systems, and provide a route for designing devices with desired nonlinear behavior.Dynamics of Micro and Nano SystemsMechanical EngineeringComputational Design and Mechanic

Graphene gas pumps

We report on the development of a pneumatically coupled graphene membrane system, comprising of two circular cavities connected by a narrow trench. Both cavities and the trench are covered by a thin few-layer graphene membrane to form a sealed dumbbell-shaped chamber. Local electrodes at the bottom of each cavity allow for actuation of each membrane separately, enabling electrical control and manipulation of the gas flow inside the channel. Using laser interferometry, we measure the displacement of each drum at atmospheric pressure as a function of the frequency of the electrostatic driving force and provide a proof-of-principle of using graphene membranes to pump attolitre quantities of gases at the nanoscale.Accepted Author ManuscriptQN/van der Zant LabQN/Steeneken LabDynamics of Micro and Nano System

Semi-permeability of graphene nanodrums in sucrose solution

Semi-permeable membranes are important elements in water purification and energy generation applications, for which the atomic thickness and strength of graphene can enhance efficiency and permeation rate while maintaining good selectivity. Here, we show that an osmotic pressure difference forms across a suspended graphene membrane as a response to a sucrose concentration difference, providing evidence for its semi-permeability. This osmotic pressure difference is detected via the deflection of the graphene membrane that is measured by atomic force microscopy. Using this technique, the time dependence of this deflection allows us to measure the water permeation rate of a single 3.4 µm diameter graphene membrane. Its value is close to the expected value of a single nanopore in graphene. The method thus allows one to experimentally study the semi-permeability of graphene membranes at the microscale when the leakage rate is minuscule. It can therefore find use in the development of graphene membranes for filtration, and can enable sensors that measure the concentration and composition of solutions.QN/Steeneken LabQN/AfdelingsbureauQN/van der Zant LabDynamics of Micro and Nano System

Diamagnetically levitating resonant weighing scale

Diamagnetic levitation offers stable confinement of an object from its environment at zero power, and thus is a promising technique for developing next generation unclamped resonant sensors. In this work, we realize a resonant weighing scale using a graphite plate that is diamagnetically levitating over a checkerboard arrangement of permanent magnets. We characterize the bending vibrations of the levitating object using laser Doppler vibrometry and use microgram glass beads to calibrate the responsivity of the sensor's resonance frequency to mass changes. The sensor is used for real-time measurement of the evaporation rate of nano-litre droplets with high-accuracy. By analyzing the resonator's frequency stability, we show that the millimeter graphite sensor can reach mass resolutions down to 4.0 ng, relevant to biological and chemical sensing concepts.Dynamics of Micro and Nano SystemsQN/Steeneken La