Diamagnetic Force Research Articles

(Keynote) Releasing the Bubbles: Efficient Phase Separation in (Photo-)Electrochemical Devices in Microgravity Environment

One of the major challenges human space exploration faces is the absence of buoyancy forces in orbit. Consequently, phase separation is severely hindered which impacts a large variety of space technologies including propellant management devices, heat transfer and life support systems e.g., during the production of oxygen and the recycling of carbon dioxide. Of particular interest are hereby (photo-)electrochemical (PEC) devices as they can produce essential chemicals such as oxygen and hydrogen in two set-ups: either, by coupling the electrochemical cell to external photovoltaic cells as currently utilized on the International Space Station or by direct utilization of sunlight in a monolithic device, where integrated semiconductor-electrocatalyst systems carry out the processes of light absorption, charge separation and catalysis in analogy to natural photosynthesis in one system. The latter device is particularly interesting for space applications due to present mass and volume constraints. Here, we discuss two combined approaches to overcome phase separation challenges in (photo-)electrolyzer systems in reduced gravitational environments: using the hydrogen evolution reaction (HER) as a model reaction, we combine nanostructured, hydrophilic electrocatalyst surfaces for efficient gas bubble desorption with magnetically-induced buoyancy to direct the produced hydrogen gas bubbles on specific trajectories away from the (photo-)electrode surface. (Photo-)current-voltage (J-V) profiles obtained in microgravity environments generated for 9.2 s at the Bremen Drop Tower show that our systems can operate with our two-fold approach near terrestrial efficiencies. Simulations of gas bubble trajectories accompany our experimental observations, allowing us to attribute the achieved phase separation in the PEC cells to the increased electrode wettability as well as the systematic use of diamagnetic and Lorentz forces.

Bending a graphene cantilever by a diamagnetic force

The application of a magnetic field perpendicular to the surface of a graphene cantilever generates a bending force owing to the strong anisotropy of the magnetic susceptibility. We calculate the mechanically stable equilibrium shape of a graphene cantilever in the presence of a magnetic field by minimizing the magnetic and bending energies, which are calculated using the tight-binding model and the Tersoff–Brenner potential, respectively. Furthermore, the introduction of a continuous model enables the size-dependence of the displacement by bending to be considered.

Stable Levitation of Pyrolytic Graphite Above Circular Magnet Arrays

The rotation of circular and annular pyrolytic graphite (PG) disks levitating above circular magnet arrays can be used for a novel method of magnetic manipulation, whereas the condition of stable levitation has not been figured out yet. In this article, a method to analyze the diamagnetic forces sustained by levitated PG is proposed to investigate the mechanism of stable levitation. When using this method, the whole PG disk is divided into multiple regions according to the distribution of magnetic field in order to determine the resultant diamagnetic force. With the help of the method, the exclusive levitation height of PG disk was determined, and the relationship between the relative size of circular and annular disks to magnet and its ability of stable levitation was clarified. The proposed method is the first one able to investigate the position stability of levitated PG and provides insights into local forces without heavy workload of finete element method (FEM) calculation. The analysis results are verified by the simulation of distribution of potential energy and can be a new way of magnetic manipulation.

Dynamic and fluctuation properties of a graphene disk levitated by a diamagnetic force in air

A graphene disk can be levitated above a magnet by a repulsive force arising from their diamagnetic interaction if the product of the magnetic field and its gradient is sufficiently large. The diamagnetic force also causes the rotation of the graphene disk because of the strong anisotropy of the magnetic permeability of graphene; thus a motion of centroid and rotation are considered by solving simultaneous Langevin equations. Furthermore, the dependence of a fluctuations of the position and angle of the levitated graphene disk on the size and temperature is also explained.

Analysis and experiment of an airflow energy harvester based on diamagnetic levitation

This paper proposes an energy harvesting structure that can effectively generate electrical power. Diamagnetic levitation mechanism is utilized, with a floating magnet rotor levitated between two pyrolytic graphite plates just using a lifting magnet and airflow. The magnet rotor could be stably suspended under joint action of magnetic forces and diamagnetic forces, being driven to rotate by airflow. Three magnet rotors, with 1.5 mm, 3 mm and 4.5 mm thickness respectively, were adopted in the study so as to investigate the influence of structural parameters of the magnet rotor on the performance of the harvester. Simulation and experiment were carried out for the three magnet rotors. Among the tree magnet rotors, the 1.5 mm-thick one has the best output performance, with the lowest dynamic stability. Therefore, the energy harvester is to find tradeoff between output characteristics and dynamics. In this work, it was discovered that the peak output voltage of the energy harvester increased with the square of flowrate. As the flowrate increased to 3000 sccm, the 1.5 mm-thick rotor was rotating at a speed of 19729 rpm under standard temperature and pressure, with 1.255 V output voltage and 49 mW power. The diamagnetic levitation structure is expected to be applied to sensing, energy harvesting and air bearing under actuation of airflow due to its advantages of low friction, high rotation speed and large levitation space.

Numerical study on stability of diamagnetic levitation of a single-layer graphene sheet

Strong diamagnetic interactions enable carbon materials such as graphite plates and organisms to levitate stably in the atmosphere without active control. Although the repulsive force caused by diamagnetism becomes weak as the size of the object decreases, the necessary force against gravity also decreases. Thus, a nanocarbon material such as a single-layer graphene sheet may be levitated by the diamagnetic force. However, the stability worsens as the dimensions of the sheet decrease. The dominant factors affecting the stability of the diamagnetic levitation of nanomaterials are the Brownian motion and attractive surface forces such as the Casimir interactions. We calculate the potential energy of a square graphene sheet in two states, vertical and horizontal to a magnet, and considered the transition rate between these states based on Kramers’ theory for the escape problem. Furthermore, the stiction of a single-layer graphene sheet onto a substrate caused by the Casimir force, which discontinues the levitation, is examined.

Diamagnetically Enhanced Electrolysis and Phase Separation in Low Gravity

The management of fluids in space is complicated by the absence of relevant buoyancy forces. This raises significant technical issues for two-phase flow applications. Different approaches have been proposed and tested to induce phase separation in low gravity; however, further efforts are still required to develop efficient, reliable, and safe devices. The employment of diamagnetic buoyancy is proposed as a complement or substitution of current methods and as a way to induce the early detachment of gas bubbles from their nucleation surfaces. The governing magnetohydrodynamic equations describing two-phase flows in low gravity are presented with a focus on bubble dynamics. Numerical simulations are employed to demonstrate the reachability of current magnets under different configurations, compare diamagnetic and Lorentz forces on alkaline electrolytes, and suggest scaling up procedures. The results support the employment of new-generation centimeter-scale neodymium magnets for electrolysis, boiling, and phase separation technologies in space, which would benefit from reduced complexity, mass, and power requirements.

Searching spin-mass interaction using a diamagnetic levitated magnetic-resonance force sensor

Axion-like particles (ALPs) are predicted to mediate exotic interactions between spin and mass. We propose an ALP-searching experiment based on the levitated micromechanical oscillator, which is one of the most sensitive sensors for spin-mass forces at a short distance. The proposed experiment tests the spin-mass resonant interaction between the polarized electron spins and a diamagnetically levitated microsphere. By periodically flipping the electron spins, the contamination from nonresonant background forces can be eliminated. The levitated microoscillator can prospectively enhance the sensitivity by nearly $10^3$ times over current experiments for ALPs with mass in the range 4 meV to 0.4 eV.

Resolution of the paradox of the diamagnetic effect on the Kibble coil

Employing very simple electro-mechanical principles known from classical physics, the Kibble balance establishes a very precise and absolute link between quantum electrical standards and macroscopic mass or force measurements. The success of the Kibble balance, in both determining fundamental constants (h, N_A, e) and realizing a quasi-quantum mass in the 2019 newly revised International System of Units, relies on the perfection of Maxwell’s equations and the symmetry they describe between Lorentz’s force and Faraday’s induction, a principle and a symmetry stunningly demonstrated in the weighing and velocity modes of Kibble balances to within 1times 10^{-8}, with nothing but imperfect wires and magnets. However, recent advances in the understanding of the current effect in Kibble balances reveal a troubling paradox. A diamagnetic effect, a force that does not cancel between mass-on and mass-off measurement, is challenging balance maker’s assumptions of symmetry at levels that are almost two orders of magnitude larger than the reported uncertainties. The diamagnetic effect, if it exists, shows up in weighing mode without a readily apparent reciprocal effect in the velocity mode, begging questions about systematic errors at the very foundation of the new measurement system. The hypothetical force is caused by the coil current changing the magnetic field, producing an unaccounted force that is systematically modulated with the weighing current. Here we show that this diamagnetic force exists, but the additional force does not change the equivalence between weighing and velocity measurements. We reveal the unexpected way that symmetry is preserved and show that for typical materials and geometries the total relative effect on the measurement is approx 1times 10^{-9}.

Mechanical resonator to measure magnetic susceptibility of structurally intact bone

Magnetic susceptibility of structurally intact bone may play a role in low frequency (below 10 kHz), low field (below 10 mT amplitude) pulsed electromagnetic field (LF PEMF) treatment of fracture non-unions and an adjunct to cervical fusion surgery, approved by the U.S Food and Drug Administration (FDA). The aim of this study was to determine if a difference in PEMF treatment results in measurable differences in the bone magnetic susceptibility using a model of structurally intact rat vertebrae. We measured bone volume magnetic susceptibility by a custom built mechanical resonator comprising a diametrically-polarized NdFeB permanent dipole magnet cylinder (25.4 × 25.4 mm, height by diameter) rotated about its axis by a stepper motor at even intervals from 53 to 63 RPM, acting as a source of a local, oscillating magnetic field (mean field of 95 mT, gradient of 12 T/m) on an intact laboratory rat lumbar vertebrae (n = 21, from tissue repository from past studies on LF PEMF treatment in vivo) suspended 26.0 mm from magnet axis on a thin line of 80 mm nominal length forming a pendulum of nominal eigenfrequency of 100 Hz. The vertebra motion was captured by a video camera and the geometrical center of its 2D image motion was analyzed by ImagePro® and MATLAB® routines. The amplitude of bone oscillations (at twice the angular frequency of the rotating magnet) showed a characteristic pattern of resonance with the magnet rotational frequency. The amplitude maximum agreed with that calculated from a model of forced, damped harmonic oscillator and the diamagnetic tension force acting on bone. The calculated mean volume magnetic susceptibility (SI) of -was on the order of magnitude of literature value (|χ|≈10-5). The results point to the bone site-specific aspect of LF PEMF therapy and provide experimental and theoretical basis for a novel, rational method of designing next generation of effective LF PEMF therapies.

Highly Mobile Levitating Soft Actuator Driven by Multistimuli‐Responses

AbstractSoft actuators exhibit activeness and flexibility and are widely used as next‐generation intelligent devices. However, their locomotion depends on friction with contact surfaces that restrict their movement. To overcome this limitation, a noncontact‐type multiresponsive soft actuator that levitates in a magnetic field is proposed. This soft actuator can respond to humidity, heat, and diamagnetic repulsion force stimuli, resulting in high degrees of freedom and multiple motions. The soft actuator is fabricated by coating a highly hygroscopic membrane onto a diamagnetic graphite film, which enables the actuator to levitate in the magnetic field. Bending actuation is induced by the swelling mismatch between the two layers via the hygrothermal response. The translational force driven by local concentrated heating of the actuator leads to the realization of high‐speed linear and curvilinear motions. Frictionless rotational motion is also realized remotely with broad heating of an asymmetrically bent soft actuator, generating nonzero torque acting on the floating soft actuator. The proposed levitating soft actuators are applied to a fast and reliable capsule‐delivery gripper and a remotely controllable levitated motor. The soft actuator exhibits the potential to be applied in a wide range of applications, such as soft robotics and smart mechanical devices.

Lateral force calibration for atomic force microscope cantilevers using a suspended nanowire

Friction measurement via atomic force microscope (AFM) relies on accurate calibration for the torsional spring constant of the AFM cantilever and its lateral deflection sensitivity. Here we describe a method that employs a suspended nanowire (SNW) as a reference beam to quantify the torsional spring constant of AFM cantilevers. Based on the fact that a uniform SNW with cylindrical symmetry has an identical spring constant when bent in any direction perpendicular to its axis, the spring constant of the SNW in a normal direction is determined by an AFM cantilever with a known normal spring constant, and is subsequently used as a force transfer standard to calibrate the torsional spring constant of the AFM cantilever. The lateral deflection sensitivity can be accurately measured by pushing the AFM tip laterally on the groove edge. The calibration result is compared to the well-known diamagnetic lateral force calibrator method and shows an uncertainty of 15% or better. The presented method is applicable for the lateral force calibration of AFM cantilevers in a wide range of instruments including inverted configurations and in an ultrahigh vacuum.

Motional Dynamical Decoupling for Interferometry with Macroscopic Particles

We extend the concept of dynamical decoupling from spin to mechanical degrees of freedom of macroscopic objects, for application in interferometry. In this manner, the superposition of matter waves can be made resilient to many important sources of noise when these are driven along suitable paths in space. As a concrete implementation, we present the case of levitated (or free falling) nanodiamonds hosting a color center in a magnetic field gradient. We point out that these interferometers are inherently affected by diamagnetic forces, which restrict the separation of the superposed states to distances that scale with the inverse of the magnetic field gradient. Periodic forcing of the mechanical degree of freedom is shown to overcome this limitation, achieving a linear-in-time growth of the separation distance independent of the magnetic field gradient, while simultaneously protecting the coherence of the superposition from environmental perturbations.

How to increase the diamagnetic magnetic force of HOPG

How to increase the diamagnetic magnetic force of HOPG

Optical control and manipulation of diamagnetically levitated pyrolytic graphite

When levitating above an alternating-pole permanent magnet array, pyrolytic graphite can be displaced by asymmetric diamagnetic forces resulting from optically-induced, localized temperature changes and the thermal dependence of pyrolytic graphite’s magnetic susceptibility. In this paper, we present methods for addressable, automated position control of levitating pyrolytic graphite samples acting as milli-robots for small-scale assembly and manipulation applications using optical actuation and machine vision techniques. A simple control method is presented that harnesses interactions between complex magnetic fields and small-scale thermomagnetic and optical material properties. A user may dictate arbitrary desired milli-robot positions to a closed loop control system, which automatically detects and actuates milli-robots to the desired positions and works to maintain them there. Hardware requirements and considerations are discussed along with software calibration, image processing, and control methodologies. Results from experiments demonstrating automated position control of pyrolytic graphite milli-robots of various sizes levitating over various permanent magnet array configurations are presented. Sequential control of multiple milli-robots in close proximity without work surface segmentation is also demonstrated successfully. The observed effect of milli-robot size to magnet array grid spacing ratio on milli-robot in-plane motion is discussed, concluding that larger ratios result in smoother and faster motion control due to relative decreases in magnetic barrier forces on the pyrolytic graphite milli-robot and minimized separation between minimum free energy positions.

Dynamic characteristics and response research of low-frequency vibration harvester based on diamagnetic levitation

A low-frequency vibration energy harvester used to collect environmental vibration is proposed in this paper. The energy harvester mainly includes a diamagnetic stabilized levitation structure and elastic films as the stoppers. The floating magnet maintains a stable levitation in the vertical direction under the action of gravity, magnetic force and diamagnetic force. The elastic film is introduced to build a piecewise linear system which can increase the resonant frequency and extend the operating bandwidth for the energy harvester. The energy harvester prototype is designed, manufactured and tested. During the experiment, the working frequency range is extended from 2.1 Hz to 5.1 Hz under the excitation amplitude of 5 mm. The output voltage increases steadily from 59 mV to 159 mV within this frequency range. The experimental results under different harmonic excitation show that the harvester has the potential to work at a broadband and low-frequency range. The proposed harvester could power micro and intelligent equipment in a low-frequency vibration environment.

Optomechanical Actuation of Diamagnetically Levitated Pyrolytic Graphite

The magnetic susceptibility of pyrolytic graphite (PyG) is temperature dependent. Under an external magnetic field, a levitated PyG sample with a localized temperature change experiences unequal diamagnetic forces. In this paper, we present a study of the macroscale optomechanical displacement of a levitated PyG sample by using a laser source to locally increase the temperature. Dynamic finite-element method simulations show that a localized increase in the sample temperature, simulating a laser source, decreases the diamagnetic force in that local area, leading to the displacement of the PyG sample in the plane of the permanent magnet array. Experimental setups built using different laser sources and samples confirm the range of applicability of the actuation phenomenon to different conditions. An additional setup without moving parts reduced the likelihood by which airflow could have caused the displacement, as we suspect happened in the previous studies.

Pyrolytic carbon: applications of its diamagnetism in metrology

This paper presents some current or potential applications in metrology based on the diamagnetism of pyrolytic carbon (PyC). The magnetic repulsion force acting between a piece of PyC subjected to a magnetic flux can be used as magnetic spring either to control the position of the sensitive sensor element or to detect changes of a physical quantity to be measured. The first part of this paper provides examples briefly described of devices based on the diamagnetism of PyC for measuring mechanical quantities. There are two main configurations for magnetic levitation: one, used for measuring acceleration or inclination for instance, is based on the levitation of a PyC tile above a magnet or set of magnets; In the other, used to measure forces caused for example by contact or buoyancy, it is the permanent magnet that is levitated at a stable height above a fixed PyC tile. The second part describes current work at the Laboratoire Commun de Métrologie (LCM-LNE/CNAM) on the development of new laser power sensors using either diamagnetic force changes by photothermal excitation of electrons or diamagnetic torsion spring.

Comparison between Diamagnetic Magnetic Force by Graphite and PG Disks and Levitation Rotation of Non-controlled Magnetic Levitation Motor.

Comparison between Diamagnetic Magnetic Force by Graphite and PG Disks and Levitation Rotation of Non-controlled Magnetic Levitation Motor.

Space Magnetism and Superconductivity: Diamagnetic Expulsion, Meissner Effect, Magnetic Pressure and Quantum Trapping Lead to the Origin and Stability of the Saturn Rings

Existence of the magnetic field of Saturn and the temperature around 70 - 100 K nearby of it bring us to the idea of diamagnetism and superconductivity of the rings particles. The rings could emerge from the icy particles moving on chaotic orbits around Saturn within protoplanetary cloud. After appearance of the magnetic field of Saturn all chaotic orbits of icy particles start to shift to the magnetic equator plane, where there is a minimum of the particles magnetic energy, due to diamagnetic force of expulsion like Meissner phenomenon. Each particle comes to the stable position preventing its own horizontal and vertical shift. Particles are locked within three-dimensional magnetic well due to Abrikosov quantum vortex phenomenon for superconductor. This mechanism is valid and it works even particles have a small fraction of superconductor. Final picture is similar to the picture of iron particles forms the same shape around a magnet on laboratory table. Any other phenomena like gravity resonances, dusty plasma and others may bring some peculiarities to the final picture of the rings. It follows that magnetic field of Saturn and low temperature around of it are the main reason for the rings origin and the rings is product of the early time of the magnetic field of Saturn appearance. Additional matter to the rings also may come from the frozen water particles generated from the Saturn sputniks geysers due to magnetic coupling between planet and satellites. The data of Cassini mission to Saturn rings are conforming suggested theory of their origin and existence.