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We optimized designs of permanent magnet systems to study the effect of magnetic nanoparticles on cell cultures in microslide channels. This produced two designs, one of which is based on a large cylindrical magnet that applies a uniform force density of 6 MN/m$^3$ on soft magnetic iron-oxide spherical nanoparticles at a field strength of over 300 mT. We achieved a force uniformity of better than 14% over the channel area leading to a concentration variation that was below our measurement resolution. The second design was aimed at maximizing the force by using a Halbach array. We indeed increased the force by more than one order of magnitude at force density values over 400 MN/m$^3$, but at the cost of uniformity. However, the latter system can be used to trap magnetic nanoparticles efficiently and to create concentration gradients. We demonstrated both designs by analyzing the effect of magnetic forces on the cell viability of human hepatoma HepG2 cells in the presence of bare Fe$_2$O$_3$ and cross-linked dextran iron-oxide cluster-type particles (MicroMod). Python scripts for magnetic force calculations and particle trajectory modeling as well as source files for 3D prints have been made available so these designs can be easily adapted and optimized for other geometries., Comment: 14 pages, 15 figures

We present a computational framework for two-scale asymptotic homogenization to determine the intrinsic magnetic permeability of composites. To this end, considering linear magnetostatics, both vector and scalar potential formulations are used. Our homogenization algorithm for solving the cell problem is based on the displacement method presented in Lukkassen et al. 1995, Composites Engineering, 5(5), 519-531. We propose the use of the meridional eccentricity of the permeability tensor ellipsoid as an anisotropy index quantifying the degree of directionality in the linear magnetic response. As application problems, 2D regular and random microstructures with overlapping and nonoverlapping monodisperse disks, all of which are periodic, are considered. We show that, for the vanishing corrector function, the derived effective magnetic permeability tensor gives the (lower) Reuss and (upper) Voigt bounds with the vector and scalar potential formulations, respectively. Our results with periodic boundary conditions show an excellent agreement with analytical solutions for regular composites, whereas, for random heterogeneous materials, their convergence with volume element size is fast. Predictions for material systems with monodisperse overlapping disks for a given inclusion volume fraction provide the highest magnetic permeability with the most increased inclusion interaction. In contrast, the disk arrangements in regular square lattices result in the lowest magnetic permeability and inadequate inclusion interaction. Such differences are beyond the reach of the isotropic effective medium theories, which use only the phase volume fraction and shape as mere statistical microstructural descriptors.

We present a spectrophotometer (optical density meter) combined with electromagnets dedicated to the analysis of suspensions of magnetotactic bacteria. The instrument can also be applied to suspensions of other magnetic cells and magnetic particles. We have ensured that our system, called MagOD, can be easily reproduced by providing the source of the 3D prints for the housing, electronic designs, circuit board layouts, and microcontroller software. We compare the performance of our system to existing adapted commercial spectrophotometers. In addition, we demonstrate its use by analyzing the absorbance of magnetotactic bacteria as a function of their orientation with respect to the light path and their speed of reorientation after the field has been rotated by 90 degrees. We continuously monitored the development of a culture of magnetotactic bacteria over a period of five days, and measured the development of their velocity distribution over a period of one hour. Even though this dedicated spectrophotometer is relatively simple to construct and cost-effective, a range of magnetic field-dependent parameters can be extracted from suspensions of magnetotactic bacteria. Therefore, this instrument will help the magnetotactic research community to understand and apply this intriguing micro-organism.

We optimised the magnetic field homogeneity of two canonical designs for mobile microfluidic NMR applications: two parallel magnets with an air gap and a modified Halbach array. Along with the influence of the sample length, general design guidelines will be presented. For a fair comparison the sensitive length of the sample has been chosen to be the same as the gap size between the magnets to ensure enough space for the transmitting and receiving unit, as well as basic electric shimming components. Keeping the compactness of the final device in mind, a box with an edge length 5 times the gap size has been defined, in which the complete magnet configuration should fit. With the chosen boundary conditions, the simple parallel cuboid configuration reaches the best homogeneity without active shimming (0.5$\mathrm{B_{s}}$, 41 ppm), while the Pseudo-Halbach configuration has the highest field strength (0.9$\mathrm{B_{s}}$, 994 ppm), assuming perfect magnets. However, permanent magnet configurations suffer from imperfections, such as magnetisation, fabrication and positioning errors, which results in worse magnetic field homogeneities than expected from simulations using a fixed optimised parameter set. We present a sensitivity analysis for a magnetic cube and the results of studies of the variations in the magnetisation and angle of magnetisation of magnets purchased from different suppliers, composed of different materials and coatings, and of different sizes. We performed a detailed Monte Carlo simulation on the effect of the measured distribution of magnetic properties on the mentioned configurations. The cuboid design shows a mean homogeneity of 430 ppm (std dev. 350 ppm), the Pseudo-Halbach has a mean homogeneity of 1086 ppm (std dev. 8 ppm)., Comment: 13 pages, 14 figures, 8 tables

We investigated whether we can detect enhanced magnetic nanoparticle uptake under application of a large magnetic force by tagging the particles with a fluorescent dye. Human liver cells were cultured in a micro-channel slide and exposed to two types of magnetic nanoparticles with a diameter of 100 nm at a concentration of 10000 particles/cell for 24 hours. Even though we achieved a magnetic force that exceeded the gravitational force by a factor of 25, we did not observe a statistically significant increase of immobilised particles per cell.

Interaction between dipolar forces, such as permanent magnets, generally leads to the formation of one-dimensional chains and rings. We investigated whether it was possible to let dipoles self-assemble into three-dimensional structures by encapsulating them in a shell with a specific shape. We found that the condition for self-assembly of a three-dimensional crystal is satisfied when the energies of dipoles in the parallel and antiparallel states are equal. Our experiments show that the most regular structures are formed using cylinders and cuboids and not by spheroids. This simple design rule will help the self-assembly community to realize three-dimensional crystals from objects in the micrometer range, which opens up the way toward previously unknown metamaterials., Comment: 4 pages

We investigate to what extent one can use a thermodynamic description of turbulent flow as a source of stochastic kinetic energy for three-dimensional self-assembly of magnetically interacting macroscopic particles. We confirm that the speed of the objects in the flow field generated in our system obeys the Maxwell--Boltzmann distribution, and their random walk can be defined by a diffusion coefficient following from the Einstein relation. However, we discovered that the analogy with Brownian dynamics breaks down when considering the directional components of the velocity. For the vectorial components, neither the equipartition theorem, nor the Einstein relation is obeyed. Moreover, the kinetic energy estimated from the random walk of individual objects is one order of magnitude higher than the value estimated from Boltzmann statistics on the interaction between two spheres with embedded magnets. These results show that introducing stochastic kinetic energy into a self-assembly process by means of turbulent flow can to a great extent be described by standard thermodynamic theory, but anisotropies and the specific nature of the interactions need to be taken into account.

We controlled and observed individual magnetotactic bacteria (Magnetospirillum gryphiswaldense) inside a 5 {\mu}m high microfluidic channel for over four hours. After a period of constant velocity, the duration of which varied between bacteria, all observed bacteria showed a gradual decrease in their velocity of about 25 nm/s$^2$. After coming to a full stop, different behaviour was observed, ranging from rotation around the centre of mass synchronous with the direction of the external magnetic field, to being completely immobile. Our results suggest that the influence of the high intensity illumination and the presence of the channel walls are important parameters to consider when performing observations of such long duration., Comment: 7 pages, 11 figures

We present an experimental study of the kinetics of orbitally-shaken macroscopic particles confined to a two-dimensional bounded domain. Discounting the forcing action of the external periodic actuation, the particles show translational velocities and diffusivity consistent with a confined random walk model. Such experimental system may therefore represent a suitable macroscopic analog to investigate aspects of molecular dynamics and self-assembly., Comment: Accepted to be published in Physical Review - E

Using the highly sensitive anomalous Hall effect (AHE) we have been able to measure the reversal of a single magnetic island, of diameter 220nm, in an array consisting of more than 80 of those islands. By repeatedly traversing the hysteresis loop, we measured the thermally actuated fluctuation of the switching field of the islands at the lower and higher ends of the switching field distribution. Based on a novel easy-to-use model, we determined the switching field in the absence of thermal activation, and the energy barrier in the absence of an external field from these fluctuations. By measuring the reversal of individual dots in the array as a function of temperature, we extrapolated the switching field and energy barrier down to 0K. The extrapolated values are not identical to those obtained from the fluctation of the switching field at room temperature, because the properties of the magnetic material are temperature dependent. As a result, extrapolating from temperature dependent measurements overestimates the energy barrier by more than a factor of two. To determine fundamental parameters of the energy barrier between magnetisation states, measuring the fluctuation of the reversal field at the temperature of application is therefore to be preferred. This is of primary importance to applications in data storagea and magnetic logic. For instance in fast switching, where the switching field in the absence of thermal activation plays a major role, or in long term data stability, which is determined by the energy barrier in the absence of an external field.

We present a thorough theoretical analysis of the magnetic torque on microfabricated elements with dimensions in the range of 100 to 500 {\mu}m and magneto-somes of magnetotactic bacteria of a few {\mu}m length. We derive simple equations for field dependent torque and magnetic shape anisotropy that can be readily used to replace the crude approximations commonly used. We illustrate and verify the theory on microfabricated elements and magnetotactic bacteria, by field depedent torque magnetometry and by observing their rotation in water under application of a rotating magnetic field. The maximum rotation frequency of the largest microfabricated elements agrees within error boundaries with theory. For smaller, and especially thinner, elements the measured frequencies are a factor of three to four too low. We suspect this is caused by incomplete saturation of the magnetisation in the elements, which is not incorporated in our model. The maximum rotation frequency of magnetotactic bacteria agrees with our model within error margins, which are however quite big due to the large spread in bacteria morphology. The model presented provides a solid basis for the analysis of experiments with magnetic objects in liquid, which is for instance the case in the field of medical microrobotics.

Current digital data storage systems are able to store huge amounts of data. Even though the data density of digital information storage has increased tremendously over the last few decades, the data longevity is limited to only a few decades. If we want to preserve anything about the human race which can outlast the human race itself, we require a data storage medium designed to last for 1 million to 1 billion years. In this paper a medium is investigated consisting of tungsten encapsulated by siliconnitride which, according to elevated temperature tests, will last for well over the suggested time., Comment: 19 pages, 11 figures

Techniques to reliably pick and place single nanoparticles into functional assemblies are required to incorporate exotic nanoparticles into standard electronic circuits. In this paper we explore the use of electric fields to drive and direct the assembly process, which has the advantage of being able to control the nano-assembly process at the single nanoparticle level. To achieve this, we design an electrostatic gating system, thus enabling a voltage controllable nanoparticle picking technique. Using the nonlinear Poisson-Boltzmann equation, we can successfully characterise the parameters required for single-particle placement, the key being single particle selectivity, in effect designing a system that can achieve this controllably. We then present the optimum design parameters required for successful single nanoparticle placements at ambient temperatures, an important requirement for nanomanufacturing processes., Comment: 15 pages, 6 figures

Recently, a silicon micromachining method to produce tetrahedral silicon particles was discovered. In this report we determine, using band structure calculations, the optical properties of diamond-lattice photonic crystals when assembled from such particles. We show that crystal structures built from silicon tetrahedra are expected to display small stop gaps. Wide photonic band gaps appear when truncated tetrahedral particles are used to build the photonic crystals. With truncated tetrahedral particles a band gap with a width of 23.6% can be achieved, which is more than twice as wide compared to band gaps in self-assembled diamond-lattices of hard-spheres. The width of the band gap is insensitive to small deviations from the optimal amount of truncation. This work paves the way to a novel class of silicon diamond-lattice band gap crystals that can be obtained through self-assembly. Such a self-assembly approach would allow for easy integration of these highly photonic crystals in existing silicon microfluidic and -electronic systems., Comment: Improvements to the text, changed equation 3, added reference 34