Polymeric microellipsoids with programmed magnetic anisotropy for controlled rotation using low (≈10 mT) magnetic fields

Polymeric microellipsoids with programmed magnetic anisotropy for controlled rotation using low (≈10 mT) magnetic fields
10 noviembre, 2019 Andrea Bonilla Brunner

Polymeric microellipsoids with programmed magnetic anisotropy for controlled rotation using low (≈10 mT) magnetic fields

Abstract

Polymeric magnetic spherical microparticles are employed as sensors/actuators in lab-on-a-chip applications, small-scale robotics and biomedical/biophysical assays. Achieving controlled stable motion of the microparticles in a fluid environment using low intensity magnetic fields is necessary to achieve much of their technological potential; this requires that the microparticle is magnetically anisotropic, which is difficult to achieve in spheres. Here we have developed a simple method to synthesise anisotropic ellipsoidal microparticles (average eccentricity 0.60 ± 0.14) by applying a magnetic field during synthesis, using a nanocomposite of polycaprolactone (PCL) with Fe3O4 nanowires. The “microellipsoids” are thoroughly characterised using optical microscopy, scanning electron microscopy (SEM), transmission electron microscopy (TEM) and energy dispersive X-ray spectroscopy (EDX). Their suitability for magnetically controlled motion is demonstrated by analysing their rotation in low magnetic fields (0.1, 1, 5, 10 and 20 mT) at varying rotational frequencies (1 Hz and 5 Hz). The microellipsoids are able to follow smoothly and continuously the magnetic field, while commercial spherical particles fail to continuously follow the magnetic field, and oscillate backwards and forwards resulting in much lower average angular speeds. Furthermore, only 23 % of commercial particles analysed rotated at 1 Hz and 26 % at 5 Hz, whereas 77 % of our ellipsoidal particles rotated at 1 Hz, and 74 % did at 5 Hz.

Graphical abstract

Keywords

Magnetic microparticlesPolymeric microparticlesMicromanipulationProgrammed magnetic anisotropyMicrofluidicsMicrorobots

1. Introduction

Magnetic polymer composites (MPCs) are widely used in microsystems and microrobotics as they simultaneously feature the processability and facile chemical functionalisation of polymers, and the possibility of using magnetic fields for actuation by exploiting the magnetic properties of the embedded nanostructures [[1][2][3]]. Magnetic fields are often preferred as external force generators due to their non-invasiveness, biological inertness, and better performance in comparison to other methods such as acoustic waves (including ultrasound) and electric fields [4].

MPC-based microstructures can be used to perform tasks in handling and assembling small objects and biological molecules, or sensing physical, biological or chemical molecules or functions [1,[5][6][7]]. In particular, MPCs shaped into spherical beads have been preferred as a favourite architecture for small-scale mechanical technologies due to the ease of fabrication, versatility and suitability for theoretical modelling. Spherical magnetic beads already play an important role in microfluidics; they can be made to link to target species and can be used for manipulation and/or detection in lab-on-a-chip systems [[8][9][10]] and protein and biomolecular purification and mixing. They are also used for generating and measuring forces at the micrometre scale in biophysical studies [[11][12][13]], in torque-generating assays [14], cellular mechanotransduction and microrheology, in magnetic twisting cytometry [15,16], in cellular, protein and nucleic acid manipulation in separation assays [17], in immunoassays [18], in magnetic flow cytometry [19], in magnetic separation in lab-on-a-chip microfluidic systems [20], in directed hyperthermia applications [11,21] and targeted drug delivery [22]. Most applications use commercial spherical MPC microparticles consisting of a polymeric matrix that confines magnetic spherical superparamagnetic Fe3O4 nanoparticles (NPs).

The particular case of anisotropic microparticles has attracted a significant attention over the past two decades [23]. Particle anisotropy can be conveyed by fabricating non-spherical shapes and/or non-uniform surface properties. In both cases, their physical properties differ from those of isotropic microparticles, making them potentially useful for assembly e.g. colloidal substitutes for liquid crystals and electrorheological fluids [24,25], designing photonic crystals with novel symmetries, controlling suspensions’ rheology [26] and suspensions’ optical properties [27], stabilising emulsions [28] and stabilising foams [29], engineering of biomaterials [30] and colloidal composites [31].

Beyond building structure, anisotropic particles are also useful for engineering dynamics at the microscale and actuation. In order to perform complex tasks and movements such as controlled rotation it is necessary to exert torque on the particle. One way of exerting magnetic torque on materials exhibiting magnetic moment is by controlling their shape anisotropy, which e.g. gives way to an easy-axis of magnetisation along the longest dimension in disks and rods. In a magnetic field, the most energetically favourable configuration is achieved when the easy axis of magnetisation aligns parallel to the direction of the applied field, producing rotation towards it [4,32].

One of the main drawbacks of using spherical microparticles confining NPs is that they have relatively low shape anisotropy (as we demonstrate later in the results section), and require high magnetic fields to align all of the magnetic moments of the NPs inside of them [21]. To obtain a more controlled magnetic response several strategies aimed at programming magnetic anisotropy in the structure have been developed [2,33]. Often these have involved top–down approaches such as inkjet printing [2] or photopatterning [33]. The applications of magnetic anisotropic particles include: (i) Fluid mixing in microfluidics and biosensing in small volumes of liquid: sample flow in small volumes and miniaturised channels is laminar [34]; and turbulent mixing between two liquids cannot be achieved. In lab-on-a-chip and microfluidic devices, it is crucial to attain a fast and adjustable mixing in applications in which several reactants or specimens are used. A magnetic microparticle that is able to rotate can be deployed in almost any environment to produce turbulence. This can find practical applications beyond mixing of reagents, for example, in extraction of specific micro/nano objects from a solution as they can be functionalised with specific molecules, proteins, bacteria or viruses. Turbulent flow can aid adsorption, prevents clustering of the target molecules/cells/microorganisms and from adhering to the container walls [35]. And (ii) biophysical assays: optical tweezers based on trapping polymer-based microbeads has revolutionised our understanding in motion in biological systems such as molecular motors, including the actions of ATP-synthases and bacterial flagellar motors. However, optical tweezers present drawbacks such as overheating of the samples. Magnetic tweezers are a promising alternative. However, they are currently used to manipulate commercial spherical microparticles, which prevents the advancement of the field, due to the intrinsic variability of their rotational behaviour [14,36].

Here we have synthesised magnetic nanocomposite microellipsoids based on a matrix of polycaprolactone (PCL) by a simple oil-in-water emulsion method. The polymer microellipsoids are formed in the emulsion in the presence of magnetite nanowires (Fe3O4), which are trapped in the particle matrix. During the synthesis, DC magnetic fields are used to align the nanowires and create magnetic (shape) anisotropy. The particles are thoroughly characterised using optical microscopy, scanning electron microscopy (SEM), transmission electron microscopy (TEM) and energy dispersive X-ray spectroscopy (EDX). Furthermore, the superior rotation properties at low magnetic field intensity in comparison to commercially available microparticles is demonstrated using rotating magnetic fields with field strengths of 0.1, 1, 5, 10 and 20 mT, at varying rotation frequencies (1 Hz and 5 Hz).

2. Materials and methods

2.1. Nanowire synthesis

Fe3O4 nanowires were prepared by hydrolysis of Fe3+ [37]. Briefly, a solution consisting of 420 mM FeCl3·4H2O, 210 mM FeSO4·7H2O and 1 M (NH2)2CO (all chemicals from Sigma Aldrich, UK) was prepared with deoxygenated Milli-Q water (Nitrogen flow for 30 min) and stirred for 10 min. The solution was then added to a Teflon flask and placed in an autoclave reactor. A 0.45T NdFeB magnet (First4magnets, UK) was positioned in the bottom of the autoclave to induce nanowire growth on the easy axis [38]. The reactor was placed in an oven at 130 °C for 6 h. After this time, the reactor was allowed to cool down at room temperature overnight. The resulting black magnetic dispersion was washed 3 times with deoxygenated water and freeze dried for 24 h.

2.2. Microellipsoid synthesis

Microellipsoids were synthesised by using the oil-in-water emulsion method, as illustrated in Fig. 1. The oil phase contained luperox (benzoyl peroxide, Sigma Aldrich) (2.5 % w/v), which acted as the initiator of PCL crosslinking, dissolved in dichloromethane at 0.5 mM. Synthesised Fe3O4 nanowires (described above) were dispersed in the PCL solution at a concentration of 0.5 % (w/v) which is at least 20 times smaller concentration than commercial particles (≈10–39 % of Fe3O4 content depending on the manufacturer). In order to achieve a homogeneous dispersion of nanowires in the oil phase, the solution was sonicated in a water bath for 5 min.

Fig. 1. Schematic representation of the oil-in-water emulsion synthesis of the microellipsoids. The oil phase contains benzoyl peroxide (2.5 % w/v) and 0.5 mM PCL dissolved in dichloromethane with 0.5 % Fe3O4 nanowires dispersed. The water phase consists of PVA 1.5 % w/v. The oil phase was emulsified into the water phase by stirring. Liquid agar (1 % w/v) was immediately added and settled at −20 °C during microellipsoid hardening in the presence of a static magnetic field of 0.25 T. Particles were left at room temperature overnight to allow PCL hardening while inducing orientation of the nanowires and creating the ellipsoidal shape.

The water phase consisted of soluble poly(vinyl alcohol) (PVA, Sigma Aldrich, UK) (1.5 % w/v) as a non-surfactant stabiliser. The oil phase was emulsified by adding it dropwise into the water phase while stirring at 3000 rpm (MS1 Minishaker IKA, UK), and emulsified for 10 min at this speed. Liquid agar (1 % w/v) was immediately added, mixed for 3 min and settled in the freezer at −20 °C for 10 min. Liquid agar was used to immobilise the microellipsoids, preventing them to collect back together into a bigger oil phase droplet, hence allowing them to harden individually. A static magnetic field of 0.25 T was applied during hardening to modify the orientation of the nanowires embedded within the polymeric structure. The gel was aged at room temperature overnight to allow particle hardening. Finally, microellipsoids were cleaned and sorted by size using density gradient centrifugation with a glucose column, at 3000 rpm for 7 min. The smallest microellipsoids (those corresponding to the first layer of the gradient) were used for this study. The microellipsoids were rinsed 3 times with ultrapure deionized (DI) water (Millipore MilliQ, UK) and kept at 4 °C. The dimensions distribution of the ellipsoid are given in the Fig. 2S in the Supplement.

2.3. Microellipsoid characterisation. TEM and SEM imaging

The microstructure and phase of the nanowires and the microellipsoids were analysed by TEM on a FEI Talos F200X instrument operated at 200 keV acceleration voltage. Both, TEM and scanning TEM (STEM) operation modes of the instrument were used for the study. STEM studies were performed in the high angle annular dark field (HAADF STEM) imaging mode and accompanied by elemental content analysis using energy dispersive spectroscopy EDX STEM. STEM and EDX STEM studies were carried out using a 0.8 nm probe size.

SEM images were acquired by a secondary electron detector in a Zeiss ULTRA 55 apparatus. The sample was dispersed on a Si wafer and dried.

2.4. Rotation experiments

The rotational motion of microellipsoids was characterised using a commercial magnetic actuation system (MFG-100-i, Magnebotix, Switzerland) mounted on an optical microscope (Olympus IX, Olympus). The magnetic actuation system consists of 4 pairs of solenoid coils which allow 3D manipulation of micrometer-size magnetic objects. Experiments were carried out in ultrapure DI water deionized water (Millipore MilliQ) applying various magnetic field amplitudes (0.1, 1, 5, 10 and 20 mT) for fields rotating at two different frequencies (1 and 5 Hz). Commercial superparamagnetic spherical polystyrene beads (nominal diameter: 2.0–2.9 μm, SPHERO™ Magnetic Particles: PM-20) were assessed as a control. Particle motion was recorded using a CCD camera (SCA 1400, Basler) at 30 frames per second (fps).

2.5. Image processing to analyse the rotation of the microellipsoids

A suite of image processing algorithms for single particle rotational tracking was custom-written in Matlab to quantitatively extract the orientation of all particles in each acquired video sequence. The program automatically detects all microellipsoids in each video frame via intensity thresholding. This operation results in a binary image with connected regions, i.e., masks, for each particle on top of a zero background. The ellipse that best fits the shape of each particle mask shape is then found to extract the particle centre-of-mass, major and minor axis lengths and orientation angle of the major axis with respect to the horizontal image axis. The eccentricity is calculated for each microellipsoid using the obtained major and minor axis lengths. Single-particle tracking is then achieved by linking particles found on subsequent frames. The linking decision is based on comparing the pair-wise distances between each particle on a given frame and all particles on the previous frame and choosing the assignment with the smallest pair-wise distance. After all tracking assignments are made, the result is a set of particle trajectories for each video analysed, so that the orientation angle of the particles as a function of time can be analysed.

The angular velocity of all the rotating colloids during uniform rotation (excluding oscillations) was calculated for particles that completed at least one 360° turn. Additionally, the effective frequency of rotation (number of full turns per second) of the colloids subjected to small field intensities (0.1 and 1 mT) was also quantified.

3. Results and discussion

3.1. Structural characterisation

Microellipsoids were synthesised as described in the materials and methods. The average microparticle yield is approximately 7 % for the particle size competent to this study (2−3 μm). This value is low due to the lack of particle size control of the emulsification process, resulting in a high particle size dispersion.

Fig. 2(a) shows two typical microellipsoids imaged by SEM displaying a clear ellipsoidal shape with different eccentricities (ε). ε represents how ellipsoidal a particle is (ε = 1 for infinite rods and ε = 0 for spheres), and is calculated using the formula:

for prolate ellipsoids with semiaxes a and b.

Fig. 2. a) SEM images of synthesised magnetic ellipsoidal particles with different eccentricities ε. b) TEM images of microellipsoids showing the nanowire structure embedded within the polymer matrix. c) Nanowire cluster formation due to the presence of a magnetic field during microparticle hardening. d) Histogram of ε values of the microellipsoids. e) TEM image of synthesised Fe3O4 nanowires and EDX analysis showing the structural composition of the nanowires (Supplementary data, Fig. S3).

PCL microparticles fabricated without nanowires and in the absence of a magnetic field using this method present a spherical shape (Fig. A.1, Supplementary material).

TEM was used to identify the arrangement of the Fe3O4 nanowires within the particle (Fig. 2(b)). The presence of a magnetic field during synthesis results in the formation of clusters (shown in Fig. 2(c)) which eventually determines the final ellipsoidal shape of the particle.

The images indicate that the magnetic field applied during the synthesis is not sufficient to align all the individual nanowires and overcome forces arising from the interaction between polymers and nanowires during crosslinking and colloid hardening. The formation of nanowire clusters could also be the result of attractive interactions between nanowires before the magnetic field was applied, or pre-clustering due to rotational forces during emulsification and particle formation from the oil phase. Despite this clustering, the magnetic field is sufficiently strong to orient clusters of wires so that the resulting particles exhibit an ellipsoidal shape. As a control, we performed the same synthesis protocol in the absence of a magnetic field (Supplementary Materials A, Fig. A2); in this case the most of the particles presented a spherical shape, highlighting the role of the magnetic field aligning the clusters during synthesis.

Future experiments regarding the fabrication of microparticles with nanoparticles embedded (instead of nanowires or nanoparticles attached to the surface) in the presence of an external magnetic field during hardening, could also, in principle, produce ellipsoidal shapes since nanoparticles could also align to the field producing stretching of the particle. In general, the elongated shape of a magnetic composite in the presence of a magnetic field is energetically more favourable. Previous work by Faraudo et al. [39] has shown that superparamagnetic microspheres can become aligned in certain conditions in fluid environments, where a key parameter is the magnetic coupling coefficient between the particles. However, due to their shape isotropy, a large magnetic gradient is needed for alignment even in water (10–30 T m−1). It is therefore reasonable to assume that producing alignment of nanoparticles in a polymeric matrix would require even larger magnetic fields that are not practical for a facile synthesis methods. Indeed, our results show that even with nanowires that are much larger and can align much easier than nanoparticles in a magnetic field, total alignment is not possible with the relatively low magnetic fields used in our work. However, the magnetic fields used in our paper succeed to produce ellipsoids by alignment of clusters of nanowires, which leads to the success of our initial purpose: to create anisotropic magnetic particles with a simple synthesis method.

In order to quantify ε for the microellipsoids, a and b were measured from optical microscopy images of the particles in solution as described above (Fig. B.1). The distribution of ε is shown in Fig. 2(d) for a total of 159 colloids analysed, confirming that the synthesis method clearly leads to ellipsoidal particles.

Finally, in Fig. 2(e) we show a TEM analysis of individual nanowires. EDX analysis of the nanowires embedded within the polymeric PCL lattice is also shown in Fig. 2(e), EDX allow us to identify that the nanowires consist of iron oxide, iron content is depicted in red and oxygen in green (see Fig. C.1 for details).

3.2. Angular velocity of the ellipsoidal colloids and comparison with commercial spherical colloids

In order to evaluate the performance of the microparticles, we monitored and analysed their movement subject to rotating magnetic fields, using the automatic method described in the materials section. Two examples of the application of the method are given in Fig. 3Fig. 3(a) displays a typical time sequence for the rotation of one of the microellipsoids in the presence of a 10 mT magnetic field rotating at a frequency of 1 Hz. Fig. 3(c) shows a sequence for a different particle and a 10 mT magnetic field rotating at 5 Hz. The initial orientation angle detected is between −90 degrees and +90 degrees, and smooth particle rotation with constant angular velocity is indicated by the clear periodicity and linearity of the angle versus time (blue traces in Fig. 3(b) and (d)).

Fig. 2. a) SEM images of synthesised magnetic ellipsoidal particles with different eccentricities ε. b) TEM images of microellipsoids showing the nanowire structure embedded within the polymer matrix. c) Nanowire cluster formation due to the presence of a magnetic field during microparticle hardening. d) Histogram of ε values of the microellipsoids. e) TEM image of synthesised Fe3O4 nanowires and EDX analysis showing the structural composition of the nanowires (Supplementary data, Fig. S3).

PCL microparticles fabricated without nanowires and in the absence of a magnetic field using this method present a spherical shape (Fig. A.1, Supplementary material).

TEM was used to identify the arrangement of the Fe3O4 nanowires within the particle (Fig. 2(b)). The presence of a magnetic field during synthesis results in the formation of clusters (shown in Fig. 2(c)) which eventually determines the final ellipsoidal shape of the particle.

The images indicate that the magnetic field applied during the synthesis is not sufficient to align all the individual nanowires and overcome forces arising from the interaction between polymers and nanowires during crosslinking and colloid hardening. The formation of nanowire clusters could also be the result of attractive interactions between nanowires before the magnetic field was applied, or pre-clustering due to rotational forces during emulsification and particle formation from the oil phase. Despite this clustering, the magnetic field is sufficiently strong to orient clusters of wires so that the resulting particles exhibit an ellipsoidal shape. As a control, we performed the same synthesis protocol in the absence of a magnetic field (Supplementary Materials A, Fig. A2); in this case the most of the particles presented a spherical shape, highlighting the role of the magnetic field aligning the clusters during synthesis.

Future experiments regarding the fabrication of microparticles with nanoparticles embedded (instead of nanowires or nanoparticles attached to the surface) in the presence of an external magnetic field during hardening, could also, in principle, produce ellipsoidal shapes since nanoparticles could also align to the field producing stretching of the particle. In general, the elongated shape of a magnetic composite in the presence of a magnetic field is energetically more favourable. Previous work by Faraudo et al. [39] has shown that superparamagnetic microspheres can become aligned in certain conditions in fluid environments, where a key parameter is the magnetic coupling coefficient between the particles. However, due to their shape isotropy, a large magnetic gradient is needed for alignment even in water (10–30 T m−1). It is therefore reasonable to assume that producing alignment of nanoparticles in a polymeric matrix would require even larger magnetic fields that are not practical for a facile synthesis methods. Indeed, our results show that even with nanowires that are much larger and can align much easier than nanoparticles in a magnetic field, total alignment is not possible with the relatively low magnetic fields used in our work. However, the magnetic fields used in our paper succeed to produce ellipsoids by alignment of clusters of nanowires, which leads to the success of our initial purpose: to create anisotropic magnetic particles with a simple synthesis method.

In order to quantify ε for the microellipsoids, a and b were measured from optical microscopy images of the particles in solution as described above (Fig. B.1). The distribution of ε is shown in Fig. 2(d) for a total of 159 colloids analysed, confirming that the synthesis method clearly leads to ellipsoidal particles.

Finally, in Fig. 2(e) we show a TEM analysis of individual nanowires. EDX analysis of the nanowires embedded within the polymeric PCL lattice is also shown in Fig. 2(e), EDX allow us to identify that the nanowires consist of iron oxide, iron content is depicted in red and oxygen in green (see Fig. C.1 for details).

3.2. Angular velocity of the ellipsoidal colloids and comparison with commercial spherical colloids

In order to evaluate the performance of the microparticles, we monitored and analysed their movement subject to rotating magnetic fields, using the automatic method described in the materials section. Two examples of the application of the method are given in Fig. 3Fig. 3(a) displays a typical time sequence for the rotation of one of the microellipsoids in the presence of a 10 mT magnetic field rotating at a frequency of 1 Hz. Fig. 3(c) shows a sequence for a different particle and a 10 mT magnetic field rotating at 5 Hz. The initial orientation angle detected is between −90 degrees and +90 degrees, and smooth particle rotation with constant angular velocity is indicated by the clear periodicity and linearity of the angle versus time (blue traces in Fig. 3(b) and (d)).

Fig. 4. Angular velocities of colloids calculated with the procedure shown in Fig. 3 (fitting linear segments of orientation angle vs time and averaging to obtain a mean particle rotation frequency) at different intensities of the rotating magnetic field at (a) 1 Hz and (b) 5 Hz field rotation frequencies. Ellipsoidal particles are shown in blue and commercial spherical particles are shown in red. Fractions at the top of the bars show the numbers of particles that completed at least one full 360° cycle divided by the total number of particles.

However, the previous analysis is not sufficient to evaluate the comparative performance of the particles, especially at low intensities of the magnetic field (0.1 mT, 1 mT). At low field strengths, the microellipsoids are able to smoothly follow the rotating magnetic field (see Video 1 in Supplementary information), whereas the commercial spherical microparticles do not follow the field rotation smoothly and display oscillations in orientation, backwards rotation and jumps in orientation (see Video 2 in Supplement). Fig. 5 shows a comparison of two representative examples of commercial microparticles and microellipsoids subject to a 1 mT, 1 Hz magnetic field (Videos 1, 2 corresponding to these images are available in Supplementary material).

Fig. 5. Comparison of spherical (commercial) microparticles and microellipsoids as they are actuated by a 1 mT magnetic field rotating at 1 Hz. (a) Representative examples of ellipsoidal (left) and spherical (right) colloid orientation angle vs. time graphs. At the bottom of each graph, the corresponding average rotation frequency (full rotation turns per second) is displayed for each case (see text). (b) Orientation angle of ellipsoidal (blue) and spherical (red) colloids vs. time corresponding to the same data depicted in (a). A sequence of images of the particle rotating at different times is included for the microellipsoid (top) and the spherical microparticle (bottom). Arrows depict the rotation direction of the, displaying oscillations and movement in the same (yellow arrows)/opposite (green arrows) direction to the applied magnetic field for the commercial spherical microparticles (corresponding Videos 1 and 2 are given in supplementary material). It is important to note that in the frames (t = 0.83, 1 s and 1.83 and 1.93 s), the microparticle turned to 0 degrees by rotating backwards. Some oscillation (back and forth change of the angle) is also observed.

Fig. 5(a) shows the reasonably smooth rotation of the microellipsoid, whereas Fig. 5(b) shows the angle versus time for the commercial spherical particle, which displays oscillations and back and forth rotations. Although the spherical microparticle returns to its minimum orientation angle (-90 degrees) as many times as the microellipsoid does, the microsphere does not actually perform the same number of total turns as the microellipsoid. This is because the microsphere in fact returns to the minimum angle by rotating backwards (green arrows) in some instances (see video 2 in the Supplement and Fig. 5(b)). Hence, the total number of turns per second is reduced to 0.48 Hz for the spherical microparticle, compared to 0.98 Hz for the microellipsoid (Fig. 5(a)).

Since, at low magnetic fields, smooth rotation is not achieved for the spherical microparticles (Fig. 5(b)), it is more useful, in order to compare their performance, to quantify the total number of full rotations per unit time observed from the videos. Fig. 6 shows violin plots of the number of full rotations per second for all the commercial microparticles and microellipsoids that completed at least one full turn, subject to a rotating field of (a) 0.1 mT and (b) 1 mT. These plots show the probability density of the data in order to visualise -in a more explicit way- the amount of particles rotating a number of times per second and their distribution in each of the cases. Each side of the middle lines in each plot is a kernel density estimation and the distribution of the data. The wider regions of the violin plot show a higher probability of the component of the population to take a given value. Violin plots in Fig. 6 were smoothed by a kernel density estimator evaluated at 40 points and were implemented using the Python.

Fig. 6. Violin plots of the average number of full rotations per second for commercial spherical microparticles (orange) and microellipsoids (blue) in the presence of (a) 0.1 mT and (b) 1 mT magnetic fields rotating at 1 Hz (left) and 5 Hz (right).

For the 0.1 mT, 1 Hz field, the microellipsoids rotated with a mean number of full rotations per second of (0.35 ± 0.19) Hz, while this value was (0.22 ± 0.01) Hz for the commercial microspheres. For the 0.1 mT, 5 Hz field, the microellipsoids’ average number of full rotations per second was (0.29 ± 0.15) Hz, while no commercial microparticle managed to perform a single full turn.

For the 1 mT, 1 Hz field, the average number of full rotations per second was (0.61 ± 0.27) Hz for the microellipsoids and (0.26 ± 0.13) Hz for the commercial particles. It is important to observe that the standard deviations for all field strengths and frequencies are larger for the microellipsoids than for the commercial particles. This is mainly due to a higher spread on rotation performance and a much larger number of assessed individual particles that complete at least one full turn for the microellipsoids compared to the commercial microparticles. This may be due to the different sizes of the microellipsoids and to variations in their magnetic (shape) anisotropy and/or inconsistent distribution of Fe3O4 nanowires within the particles due to the lack of nanoscale control of the fabrication process.

Taking all the recorded particles into account (microellipsoids and spherical microparticles), different behaviours were observed: from completely static particles -probably stuck to the bottom of the container- to particles rotating only a few degrees back and forth, particles completing only slightly less than a full 360 degree turn and particles moving backwards a few degrees and then forwards in an oscillating manner (only spherical microparticles). Behaviour deviating from smooth rotation in the direction of the field was mainly observed at the lowest intensities of the field and for the commercial spherical microparticles. This is a result of the particles not reaching the necessary energy to turn when trying to align to a rotating magnetic field. On the other hand, at higher intensities of the field, spherical particles agglomerate more.

These results demonstrate that the synthesised ellipsoidal colloids outperformed the spherical commercial microparticles at following the rotation of low magnetic fields. It is reasonable to hypothesise that the relatively strong magnetic torque experienced by ellipsoids in the external rotating magnetic fields (as compared to that exerted on the microspheres) is mainly due to global shape effects which create a deviation of the magnetisation vector inside ellipsoids with respect to the instantaneous direction of the applied field. This significant magnetic torque should allow a smooth rotation of ellipsoids. Local magnetic susceptibility anisotropy effects cannot be completely ruled out as they can arise from complex effects due to the arrangement of the nanowires and their interactions within the microelliosoids [40]. But the smooth rotation (even at low fields) points towards isotropic magnetic susceptibility within the ellipsoids, at least in the times and length scales probed here. The lower average effective rotation frequency measured for the commercial spherical microparticles and the appearance of oscillations and jumps in rotation are possibly due to their lower shape anisotropy (Fig. S.2 in the Supplementary material). It is also possible that stochastic heterogeneities of the iron oxide distribution in the microspheres can lead to fluctuations of the magnetic torque and thus to fluctuations of the rotation speed of the particles. Furthermore, the thickness of the nanoparticle layer covering the spherical polystyrene core in the commercial particles might not be totally homogeneous for all the particles, producing some of the variability of their performance. It is also likely that the higher content of magnetic material for the commercial particles (approximately 20 times higher than in the microellipsoids) makes them heavier and more likely to adhere to the surface of the underlying substrate. The higher mass should also affect their moment of inertia.

4. Conclusions

We report the synthesis of anisotropic, ellipsoidal microparticles following a novel, simple procedure based on the oil-in-water emulsion method. The microellipsoids are based on a lattice of biocompatible PCL with embedded Fe3O4 nanowires; the ellipsoidal shape is achieved by using a magnetic field during synthesis. In order to evaluate the comparative advantage that ellipsoidal particles offer with respect to existing commercial spherical particles for magnetic control, we compared the rotational dynamics for both types of particles in magnetic fields with varying intensities (0.1, 1, 5, 10 and 20 mT) and rotational frequencies (1 Hz and 5 Hz).

Both commercial and ellipsoidal particles are able to follow smoothly magnetic fields at the higher field strengths (10 and 20 mT). However, at low field strengths (0.1 and 1 mT), commercial spherical particles present a lower effective average rotation frequency than the ellipsoidal particles, due to the occurrence of oscillations and jumps in rotation. A large proportion of commercial microparticles do not complete a single 360° turn. In total, only 23 % of commercial particles analysed rotated for 1 Hz fields and 26 % for 5 Hz fields, whereas 77 % of our ellipsoidal particles rotated at 1 Hz, and 74 % did at 5 Hz. Furthermore, the number of individual commercial spherical microparticles able to rotate at higher field strengths (5, 10 and 20 mT) is very small (Fig. 4), owing to aggregation of the particles with increasing field strengths. On the other hand, our microellipsoids were capable of full rotation individually at higher field strengths avoiding aggregation.

Our results show the superior rotation performance of the ellipsoidal particles in rotating magnetic fields in comparison to spherical commercial particles as expected from their intrinsic shape anisotropy, even though their magnetic material content is at least 20 times smaller than that of the commercial particles. The ellipsoidal shape makes the fabricated microellipsoids amenable to simple computational tracking and to theoretical calculations and modelling, which are key considerations for designing and fine-tuning future applications. The method presented here can be easily substituted for other top-down approaches such as 3D printing (size restricted to printer resolution), electrospraying [41], continuous-flow microfluidics [42,43], soft lithography [44], etc. These methods could be fine-tuned by adapting them to other polymeric matrices and they present advantages over emulsification methods such as a better nanowire alignment, reduction of nanowire cluster formation -due to lack of rotational forces present during emulsification-, monodisperse size and ellipsoidal shape, control over the particle hardening process, uniform application of magnetic field, microparticle magnetic response optimisation, etc. However, these methods require infrastructure and expertise, which make them more unpractical for scaling-up as compared to the simple method presented in this paper.

Our simple fabrication and computational tracking method, along with a high (magnetic) shape anisotropy that allows for a better particle control using lower magnetic fields is better than existing methods based on commercial microparticles and makes our ellipsoids good candidates for many of the applications mentioned in the introduction section, such as biophysical studies, magnetic tweezers, microfluidics, nucleic acid and protein manipulation, microrheology, torque-generating assays, magnetically directed drug delivery, etc.

Declaration of Competing Interest

The authors listed above declare no competing financial interest.

Data availability

All the experimental data will be deposited and made available through the Oxford Research Archive portal (https://ora.ox.ac.uk/).

Acknowledgements

The author(s) would like to acknowledge networking support by the COST ActionCA16122. ABB gratefully acknowledges support from a Mexican government CONACYT scholarship and support by a STSM Grant from COST ActionCA16122.

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