Self-Assembly Magnetic Micro- and Nanospheres and the Effect of Applied Magnetic Fields

The impact of in-plane and perpendicular magnetic fields on the spatial arrangement of superparamagnetic nanospheres is explored. We utilize nanosphere self-organization methods like Spin Coating and Drop-Casting in the presence of magnetic fields. In this way, the additional parameter of the long range magnetic dipolar interactions is introduced to the competing nanosphere–surface and nanosphere–nanosphere interactions, which control order and agglomeration. We present a comparative analysis of the self-assembly characteristics with respect to the different methods and the effect of the applied field in different directions. Under zero field perfect hexagonal arrays can be obtained by spin coating. Parallel applied fields tend to create directional patterns, while perpendicular favor 3D-accumulation.


Introduction
Modern magnetic-material applications require homogeneous microstructures consisting of monodisperse magnetic entities. A facile route towards such microstructures is to exploit other materials as templates of model nanostructures via a "bottom-up", low-cost approach. Monodisperse nanosphere single-layers that tend to form 2D-hexagonal close packed patterns can be utilized either as templates for the deposition of "nanocaps" or as masks for the formation of triangular-like islands [1][2][3][4].
The underlying mechanisms of spontaneous nanosphere organization involve the formation of small aggregates of nanoparticles into larger structures, under the influence of capillary particle-particle, particle-substrate, and hydrodynamic forces [2][3][4][5][6][7]. Recently, Chandramohan et al. [8] developed a spin-coating method for the successful self-assembly of NPs with respect to hexagonal packing density and large area surface coverage. Crucial microscopic parameters are the centrifugal force, gravity, surface tension, and evaporation rate of the fluid and the substrate's hydrophilicity. These are controlled by the various solvent and nanosphere concentrations in the solution, the rotation speeds, and use of appropriate surfactants. They achieved high, defect-free, area coverage using variable rotation speed, under constant acceleration, allowing for optimal performance during the different stages of spin coating. A similar methodology had been proposed previously and studied both experimentally and theoretically [9].
A simpler approach for balancing between gravitational forces and suspension's evaporation rate, is based on drop casting [1,10,11]. By "cleaning" and tilting the substrate almost vertically, hexagonal packing with satisfactory area coverage can be achieved. The optimization is based on pinning the NPs to the substrate during fluid movement. Fluid evaporation can be delayed by drying in ambient conditions. Independently of the technique (spin coating, drop casting, and dip coating), fast evaporation rate of the

Materials and Methods
Aqueous solutions of polystyrene micro/nanospheres of diameters 0.27-1.31 µm, with incorporated iron oxide superparamagnetic nanospheres (MSNs) were obtained from MicroParticles GMBH. Iron oxide particles that are commonly employed for biomedical and similar applications include both magnetite (Fe 3 O 4 ) and maghemite (γ -Fe 2 O 3 ). The magnemite is derived from magnetite by adding vacancies (one-third of an atom out of the 2 atoms of the Fe +3 sites). These two phases are practically indistinguishable by most characterization techniques (with the exception of Mossbauer spectroscopy), especially in such small particle sizes, and in-between phases can exist. The exact crystal phase, is not crucial for their functionality, as it regards the aims of the present study. It is their superparamagnetic nature that permits them to be driven by external fields, while at zero field, they become essentially non-magnetic. Thus they will not agglomerate uncontrollably but only to the degree that the strength of the external field imposes.
The MSNs were deposited, as 1 × 1 cm 2 pieces of thermally oxidized Si wafers. These were covered by a 500 nm oxide layer, which is functionalized to improve wettability. The substrates were treated by a "piranha" solution (H 2 O 2 and H 2 SO 4 at a ratio of 1:1) to increase the surface's hydrophilicity. After that, the substrates were washed with ultrapure water and sonicated in an isopropyl alcohol bath for 10 min followed by drying with N 2 to remove the residual acid. This surface treatment was crucial in order to obtain a homogeneous solution deposition on the substrate's surface. The hydrophilicity was quantitatively evaluated by contact angle measurements. On the untreated SiO 2 surfaces, the solution had a contact angle of 46 • , suggesting a mild wettability. After the piranha treatment, the contact angle was lowered to 23 • . The contact angle could be further lowered down to 10 • by utilizing surfactants as Triton X-100 and sodium dodecyl sulfate (SDS). Triton X-100 was diluted with methanol at a ratio of 1:400 and then mixed with the MSNs solution. This straightforward procedure resulted in a high boiling point solution due to the presence of the Triton X-100. SDS, on the other hand, was utilized both before and after the MSNs solution was deposited on the surface with the drop casting method. The substrates were left in a 10% aqueous SDS suspension for 24 h. Typical contact angle measurements are presented in Figure 1. The droplet spreads on the surface in a more efficient way when using Triton X-100. Therefore, for the spin coating experiments, we suggest mixing of the initial aqueous solution with a surfactant; SDS is better suited for dip coating experiments similar to Rybczynski et al. [25] who employed a method of self-assembly based on a liquid-gas interface with SDS dipping.
Two different methods were utilized for the solution application to the substrate's surface and for the MSNs self-assembly: drop-casting and spin-coating.
Drop casting was performed using either the aqueous nanoparticle suspension as is or mixed with methanol and Triton X-100. Piranha treated substrates were placed on top of a base with variable inclination, ranging from 10° to 40°. To achieve magnetic organization, a small electromagnet was used to generate a magnetic field parallel to the substrate and perpendicular to the direction of the inclination. A schematic of the experimental setup geometry is depicted in Figure 2. In spin coating experiments, under perpendicular field, the surface-treated substrate was rotated on the platform of the spin coater, which was placed in the middle of a coil. For in-plane field application, the sample was rotated until the solution expands on the surface; then, it was removed from the spin coater and left to settle under the field on The droplet spreads on the surface in a more efficient way when using Triton X-100. Therefore, for the spin coating experiments, we suggest mixing of the initial aqueous solution with a surfactant; SDS is better suited for dip coating experiments similar to Rybczynski et al. [25] who employed a method of self-assembly based on a liquid-gas interface with SDS dipping.
Two different methods were utilized for the solution application to the substrate's surface and for the MSNs self-assembly: drop-casting and spin-coating.
Drop casting was performed using either the aqueous nanoparticle suspension as is or mixed with methanol and Triton X-100. Piranha treated substrates were placed on top of a base with variable inclination, ranging from 10 • to 40 • . To achieve magnetic organization, a small electromagnet was used to generate a magnetic field parallel to the substrate and perpendicular to the direction of the inclination. A schematic of the experimental setup geometry is depicted in Figure 2. The droplet spreads on the surface in a more efficient way when using Triton X-100. Therefore, for the spin coating experiments, we suggest mixing of the initial aqueous solution with a surfactant; SDS is better suited for dip coating experiments similar to Rybczynski et al. [25] who employed a method of self-assembly based on a liquid-gas interface with SDS dipping.
Two different methods were utilized for the solution application to the substrate's surface and for the MSNs self-assembly: drop-casting and spin-coating.
Drop casting was performed using either the aqueous nanoparticle suspension as is or mixed with methanol and Triton X-100. Piranha treated substrates were placed on top of a base with variable inclination, ranging from 10° to 40°. To achieve magnetic organization, a small electromagnet was used to generate a magnetic field parallel to the substrate and perpendicular to the direction of the inclination. A schematic of the experimental setup geometry is depicted in Figure 2. In spin coating experiments, under perpendicular field, the surface-treated substrate was rotated on the platform of the spin coater, which was placed in the middle of a coil. For in-plane field application, the sample was rotated until the solution expands on the surface; then, it was removed from the spin coater and left to settle under the field on In spin coating experiments, under perpendicular field, the surface-treated substrate was rotated on the platform of the spin coater, which was placed in the middle of a coil. For in-plane field application, the sample was rotated until the solution expands on the surface; then, it was removed from the spin coater and left to settle under the field on horizontal platform inside a coil. For the Triton X-100-treated samples, rotation speeds up to 8000 horizontal platform inside a coil. For the Triton X-100-treated samples, rotation speeds up to 8000 rpm with a standard acceleration rate of 200 rpm/s were used. The experimental setup is displayed in Figure 3. For the observation of the surface morphologies of the samples at different scales, we used a Zeiss Axio Imager A1m optical microscope fitted with a Canon 80DDSLR and a Scanning Electron Microscope (SEM, JEOL Ltd., Tokyo, Japan). The magnetic properties of the MSNs were studied using a vibrating sample magnetometer (VSM) of Lakeshore Cryotronics Inc. (Westerville, OH, USA). The morphology in small scale was studied with an atomic force microscopy (AFM) in tapping mode with a Bruker Multimode 3D Nanoscope (Ted Pella Inc., Redding, CA, USA) using a microfabricated silicon cantilever type TAP-300G, with a tip radius of <10 nm and a force constant of approximately 20-75 N m −1 .

Magnetic Measurements
In Figure 4, the magnetization curves obtained at room temperature with the help of a VSM are shown. There is no hysteresis, and the curves can be fitted to the Langevin function. This proves their superparamagnetic nature. Superparamagnetism is important for their functionality, in the sense that in a moderate field (e.g., 0.1 Tesla), they are already magnetized. On the other hand, at zero field they become essentially non-magnetic and would not tend agglomerate uncontrollably. The Langevin function fitting gives a magnetic moment (μ) ranging from μ = 16,600 μΒ for the larger polystyrene spheres to 51,100 μΒ for the smaller ones. This means that the larger polystyrene particles incorporate For the observation of the surface morphologies of the samples at different scales, we used a Zeiss Axio Imager A1m optical microscope fitted with a Canon 80DDSLR and a Scanning Electron Microscope (SEM, JEOL Ltd., Tokyo, Japan). The magnetic properties of the MSNs were studied using a vibrating sample magnetometer (VSM) of Lakeshore Cryotronics Inc. (Westerville, OH, USA). The morphology in small scale was studied with an atomic force microscopy (AFM) in tapping mode with a Bruker Multimode 3D Nanoscope (Ted Pella Inc., Redding, CA, USA) using a microfabricated silicon cantilever type TAP-300G, with a tip radius of <10 nm and a force constant of approximately 20-75 N m −1 .

Magnetic Measurements
In Figure 4, the magnetization curves obtained at room temperature with the help of a VSM are shown. There is no hysteresis, and the curves can be fitted to the Langevin function. This proves their superparamagnetic nature. Superparamagnetism is important for their functionality, in the sense that in a moderate field (e.g., 0.1 Tesla), they are already magnetized. On the other hand, at zero field they become essentially non-magnetic and would not tend agglomerate uncontrollably. The Langevin function fitting gives a magnetic moment (µ) ranging from µ = 16,600 µ B for the larger polystyrene spheres to 51,100 µ B for the smaller ones. This means that the larger polystyrene particles incorporate smaller iron oxide nanoparticles. Thus, the drop of saturation magnetization of the composite polystyrene/iron oxide spheres at smaller sizes must be assigned to reduced iron oxide content. The saturation magnetization of magnetite nanoparticles depends on the preparation conditions [26,27]. Some estimations can be done assuming a typical saturation magnetization value of 78 Am 2 /kg and the bulk density which gives M S = 405 kA/m. Then, the weight percent of the magnetic phase is estimated to 12.5%, 18.2%, and 23.8% for the 270 nm, 536 nm, and 1.31 µm spheres, respectively. For spherical magnetic nanoparticles, the diameter is given by, D = 3 6 π µ M S which yields 13.1, 11.7, and 9 nm respectively. Nanomaterials 2021, 11, x FOR PEER REVIEW 5 of 14 smaller iron oxide nanoparticles. Thus, the drop of saturation magnetization of the composite polystyrene/iron oxide spheres at smaller sizes must be assigned to reduced iron oxide content. The saturation magnetization of magnetite nanoparticles depends on the preparation conditions [26,27]. Some estimations can be done assuming a typical saturation magnetization value of 78 Am 2 /kg and the bulk density which gives MS = 405 kA/m. Then, the weight percent of the magnetic phase is estimated to 12.5%, 18.2%, and 23.8% for the 270 nm, 536 nm, and 1.31 μm spheres, respectively. For spherical magnetic nanoparticles, the diameter is given by, which yields 13.1, 11.7, and 9 nm respectively. Ms is the saturation magnetization, kBT is the thermal energy taken at T = 290 K, and μ is the total magnetic moment of each particle.

Self-Assembly under Zero Magnetic Field
To achieve small substrate sizes, the typical approach is drop casting of the aqueous nanoparticle suspension (without a surfactant addition) on the substrate's surface which is placed at an angle to the horizontal plane. The solvent drying rate and wetting behavior determines the kinetics of this process. The inclination of the substrate surface allows the optimization of the velocity of the droplet sliding motion and its asymmetric deformation in combination with the evaporation rate to achieve the largest possible monolayer covered area. Too high inclination will lead to accumulation of the material at the bottom edge of the material, while on the other hand, too low inclination results in thick multilayer MSNs stacks. Monolayer formation is based on the residual material along the trail of the sliding droplet, and it is limited within an intermediate area (≈3 mm) between the sparsely covered upper part and thick material accumulated at the lower part ( Figure 5). Then, structural coherence of the hexagonal arrays spans over 20-30 nanospheres and coexists with uncovered areas (Figure 6). Ms is the saturation magnetization, k B T is the thermal energy taken at T = 290 K, and µ is the total magnetic moment of each particle.

Self-Assembly under Zero Magnetic Field
To achieve small substrate sizes, the typical approach is drop casting of the aqueous nanoparticle suspension (without a surfactant addition) on the substrate's surface which is placed at an angle to the horizontal plane. The solvent drying rate and wetting behavior determines the kinetics of this process. The inclination of the substrate surface allows the optimization of the velocity of the droplet sliding motion and its asymmetric deformation in combination with the evaporation rate to achieve the largest possible monolayer covered area. Too high inclination will lead to accumulation of the material at the bottom edge of the material, while on the other hand, too low inclination results in thick multilayer MSNs stacks. Monolayer formation is based on the residual material along the trail of the sliding droplet, and it is limited within an intermediate area (≈3 mm) between the sparsely covered upper part and thick material accumulated at the lower part ( Figure 5). Then, structural coherence of the hexagonal arrays spans over 20-30 nanospheres and coexists with uncovered areas (Figure 6).

Self-Assembly in the Presence of Magnetic Field
The same drop-casting process was also performed under external magnetic field applied along two different directions: in-plane and perpendicular to the sample's surface. The applied field's strength was 0.11 Τ unless otherwise noted. Taking advantage of

Self-Assembly in the Presence of Magnetic Field
The same drop-casting process was also performed under external magnetic field applied along two different directions: in-plane and perpendicular to the sample's surface. The applied field's strength was 0.11 Τ unless otherwise noted. Taking advantage of

Self-Assembly in the Presence of Magnetic Field
The same drop-casting process was also performed under external magnetic field applied along two different directions: in-plane and perpendicular to the sample's surface. The applied field's strength was 0.11 T unless otherwise noted. Taking advantage of the superparamagnetic nature of the MSNs, different kinds of organization are achieved as follows.

•
In-Plane Field As opposite magnetic poles are created on the opposite ends of each sphere, along the field direction, the tendency of magnetic nanoparticles to form lines can be explained from these dipolar interactions or equivalently as a result of magnetic flux closure. This kind of structures are observed in sparsely covered areas (Figure 7). •

In-Plane Field
As opposite magnetic poles are created on the opposite ends of each sphere, along the field direction, the tendency of magnetic nanoparticles to form lines can be explained from these dipolar interactions or equivalently as a result of magnetic flux closure. This kind of structures are observed in sparsely covered areas (Figure 7). This is a common behavior of MSNs when they assemble in a solid-liquid interface [17]. At lower deposition angles, like φ = 10° (Figure 8), MSNs of 536 nm diameter form large (in μm) rectangular blocks organized along the applied magnetic field direction. Their structural coherence spans with lengths of 0.2-0.3 μm. The "cracks" between the blocks are attributed to the evaporation of the water solvent. This is a common behavior of MSNs when they assemble in a solid-liquid interface [17]. At lower deposition angles, like ϕ = 10 • (Figure 8), MSNs of 536 nm diameter form large (in µm) rectangular blocks organized along the applied magnetic field direction. Their structural coherence spans with lengths of 0.2-0.3 µm. The "cracks" between the blocks are attributed to the evaporation of the water solvent. •

Perpendicular Field
The application of a magnetic field perpendicular to the substrate's surface, results to the appearance of pyramidal 3D structures. The field was applied simultaneously with the solution drop casting on the surface. Different values of magnetic field, H1 = 0.06 T, H2 = 0.1 T, and H3 = 0.5 Τ were applied. This process results in increased concentration of the  The application of a magnetic field perpendicular to the substrate's surface, results to the appearance of pyramidal 3D structures. The field was applied simultaneously with the solution drop casting on the surface. Different values of magnetic field, H 1 = 0.06 T, H 2 = 0.1 T, and H 3 = 0.5 T were applied. This process results in increased concentration of the MSNs at the center of the sample. Here, also blocks of particles are formed as shown in Figure 9, for MSNs with 536 nm diameter but with irregular shapes when compared to those obtained by in-plane field. Since the field is out of plane, these flakes do not exhibit strong directionality within the substrate plane and tend to form radial patterns. Using stronger fields, nanosphere accumulation is enhanced at the center, and some of the blocks flake-off the substrate due to the strong attraction of the field. •

Perpendicular Field
The application of a magnetic field perpendicular to the substrate's surface, results to the appearance of pyramidal 3D structures. The field was applied simultaneously with the solution drop casting on the surface. Different values of magnetic field, H1 = 0.06 T, H2 = 0.1 T, and H3 = 0.5 Τ were applied. This process results in increased concentration of the MSNs at the center of the sample. Here, also blocks of particles are formed as shown in Figure 9, for MSNs with 536 nm diameter but with irregular shapes when compared to those obtained by in-plane field. Since the field is out of plane, these flakes do not exhibit strong directionality within the substrate plane and tend to form radial patterns. Using stronger fields, nanosphere accumulation is enhanced at the center, and some of the blocks flake-off the substrate due to the strong attraction of the field.

Spin Coating
According to the process described by Chandramohan et al. [8], we have prepared samples of different diameter. The rotation speed extended from 150 to 8000 rpm. The SC routine is summarized in Table 1. The effectiveness of the process was checked on non-magnetic PS nanospheres with 170 nm diameter and yielded high-quality hexagonal arrays, as presented in Figure 10.

Spin Coating
According to the process described by Chandramohan et al. [8], we have prepared samples of different diameter. The rotation speed extended from 150 to 8000 rpm. The SC routine is summarized in Table 1. The effectiveness of the process was checked on non magnetic PS nanospheres with 170 nm diameter and yielded high-quality hexagonal ar rays, as presented in Figure 10.  Prior to the all the experiments, the substrates were cleaned and dried according to the procedure described in Materials and Methods section. The self-organized spheres formed a dense 2D-hexagonal grid in all cases.

Spin Coating under Zero Field
For this process, the optimal ratio of MSNs solution ratio to the surfactant solution (Triton X-100 + methanol) was found to be 4:1. The structural coherence of the hexagona lattice is of the order of 10-30 spheres. Random voids among the MSNs configurations persist but in the form of point defects and not as extended areas as it was evident with the drop-casting technique ( Figure 11). By scaling down to 10 μm, one can more efficiently observe the formation of these small hexagonal areas. Similar behavior is presented in Colson et al. [9] regarding the formation of small or large monolayer HCP ordered areas In our case, we observed small hexagonal lattices with defects in between them, which We have applied this method using different MSNs solution and surfactant ratios. Prior to the all the experiments, the substrates were cleaned and dried according to the procedure described in Materials and Methods section. The self-organized spheres formed a dense 2D-hexagonal grid in all cases.

Spin Coating under Zero Field
For this process, the optimal ratio of MSNs solution ratio to the surfactant solution (Triton X-100 + methanol) was found to be 4:1. The structural coherence of the hexagonal lattice is of the order of 10-30 spheres. Random voids among the MSNs configurations persist but in the form of point defects and not as extended areas as it was evident with the drop-casting technique ( Figure 11). By scaling down to 10 µm, one can more efficiently observe the formation of these small hexagonal areas. Similar behavior is presented in Colson et al. [9] regarding the formation of small or large monolayer HCP ordered areas. In our case, we observed small hexagonal lattices with defects in between them, which restricts the structural coherence in the order of a small number of spheres. The defects are mainly dislocations, and they prevent a continuous large-scale formation of closepacked hexagonal lattice of MSNs. These small hexagonal lattices are attributed to the fast evaporation of the solvent [28].
Nanomaterials 2021, 11, x FOR PEER REVIEW 10 of 14 restricts the structural coherence in the order of a small number of spheres. The defects are mainly dislocations, and they prevent a continuous large-scale formation of closepacked hexagonal lattice of MSNs. These small hexagonal lattices are attributed to the fast evaporation of the solvent [28]. Figure 11. Self-assembly of spin coated 1.31 μm diameter MSNs to hexagonal monolayer arrays.

Spin Coating in Magnetic Field
•

In-Plane Field
By applying the field in-plane to the sample's surface, the MSNs are expected to align along the field's direction. Following the same routine as before, adjustments were needed to achieve the MSNs self-assembly. The first stages of the SC are required for the solution thinning. The SC processes are terminated at stage 3 (Table 1)

•
In-Plane Field By applying the field in-plane to the sample's surface, the MSNs are expected to align along the field's direction. Following the same routine as before, adjustments were needed to achieve the MSNs self-assembly. The first stages of the SC are required for the solution thinning. The SC processes are terminated at stage 3 (Table 1)  restricts the structural coherence in the order of a small number of spheres. The defects are mainly dislocations, and they prevent a continuous large-scale formation of closepacked hexagonal lattice of MSNs. These small hexagonal lattices are attributed to the fast evaporation of the solvent [28]. Figure 11. Self-assembly of spin coated 1.31 μm diameter MSNs to hexagonal monolayer arrays.

Spin Coating in Magnetic Field
•

In-Plane Field
By applying the field in-plane to the sample's surface, the MSNs are expected to align along the field's direction. Following the same routine as before, adjustments were needed to achieve the MSNs self-assembly. The first stages of the SC are required for the solution thinning. The SC processes are terminated at stage 3 (Table 1)

• Perpendicular Field
The in-situ process of the external field application perpendicular to the sample's surface is followed while the SC routine is active. The magnetic field value is H = 0.1 T, and it is applied before Stage 4 of the SC routines. The resulting configuration is displayed in Figure 13. The analysis reveals that the MSNs, under the application of magnetic field, formed areas of multilayers, which appear denser ( Figure 13). These, island-like, areas are separated by uncovered substrate areas. The dark brown areas, depicted in Figure 13, correspond to a greater number of piled-up layers, while the light brown areas correspond to monolayer. To note that a magnetized body placed in a uniform field will rotate to align its magnetic moment along field, but as the field then exerts two equal and opposite forces on its two "magnetic poles" there is no net force of translation. In an inhomogeneous field, on the other hand, it can be shown that a force proportional to the gradient of the field exists. Superparamagnetic particles, which do not possess a permanent magnetic moment but are magnetized by the existing field, experience a force proportional to the gradient of the square of the field. This mechanism can explain the tendency of the MSNs to accumulate as the already deposited magnetized spheres create a strong field gradient around them. Thus, the MSNs tend to concentrate on top of the existing islands forming multilayered structures while leaving uncovered substrate areas.
in Figure 13. The analysis reveals that the MSNs, under the application of formed areas of multilayers, which appear denser ( Figure 13). These, island separated by uncovered substrate areas. The dark brown areas, depicted in respond to a greater number of piled-up layers, while the light brown are to monolayer. To note that a magnetized body placed in a uniform field wil its magnetic moment along field, but as the field then exerts two equal and on its two "magnetic poles" there is no net force of translation. In an inhom on the other hand, it can be shown that a force proportional to the gradi exists. Superparamagnetic particles, which do not possess a permanent ma but are magnetized by the existing field, experience a force proportional of the square of the field. This mechanism can explain the tendency of the mulate as the already deposited magnetized spheres create a strong field g them. Thus, the MSNs tend to concentrate on top of the existing islands layered structures while leaving uncovered substrate areas.

Spin Coating Followed by SDS Post-Treatment
In this case, spin coating of the MSNs solution is followed by immers ered substrates in a 10 wt.% SDS-aqueous solution at a small angle follo from the SDS-aqueous surface. The samples are left to dry for 3 h in ambi This is a modification of the method by Rybczynski et al. using spin-coa drop casting [25]. A two-stage spin coating has been employed, after dropped on the surface. The SC routine proceeds as follows: (a) the samp 160 RPM/s for the solution to expand on the surface and (b) the rotation sp up to 800 RPM/s for 120 s, which was found as optimal. Large areas of he are obtained with structural coherence spanning of 10-20 MSNs (Figure 14

Spin Coating Followed by SDS Post-Treatment
In this case, spin coating of the MSNs solution is followed by immersion of the covered substrates in a 10 wt.% SDS-aqueous solution at a small angle followed by lift-off from the SDS-aqueous surface. The samples are left to dry for 3 h in ambient conditions. This is a modification of the method by Rybczynski et al. using spin-coating instead of drop casting [25]. A two-stage spin coating has been employed, after the solution is dropped on the surface. The SC routine proceeds as follows: (a) the sample is rotated at 160 RPM/s for the solution to expand on the surface and (b) the rotation speed is ramped up to 800 RPM/s for 120 s, which was found as optimal. Large areas of hexagonal arrays are obtained with structural coherence spanning of 10-20 MSNs (Figure 14).

Conclusions
We have studied the self-assembly of paramagnetic polystyrene nanospheres arrays obtained by spin coating and drop casting of their aqueous solutions. It is shown that using superparamagnetic nanospheres, it is possible to control their self-organization by magnetic fields and achieve more complex, or even 3D structures, beyond the typical hexagonal arrays. Self-organization in the mesoscopic scale, where the thermal energy cannot help the system finding its energy minima, is an interesting problem where subtle play of several competing kinetic processes defines the outcome. The use of superparamagnetic spheres adds the long range magnetic dipolar interactions to the competing nanoparticlesurface (substrate hydrophobicity-hydrophilicity) and the nearest neighbor nanoparticlenanoparticle interactions, which control order and agglomeration. An advantage of the superparamagnetic particles is that the strength of the interactions can be tuned by the applied field, and it is practically switched off when the external applied field is removed. The self-assembly of magnetically functional entities is much less studied compared to the vast existing literature of their non-magnetic counterparts. Magnetic forces favor agglomeration, which is usually not desirable in obtaining high-quality monolayers. However, it opens possibilities to obtain a richer variety of organized structures. The present work shows that, due to the long range of the magnetic forces, even weak fields can have a strong impact on self-organization patterns.

Conclusions
We have studied the self-assembly of paramagnetic polystyrene nanospheres arrays obtained by spin coating and drop casting of their aqueous solutions. It is shown that using superparamagnetic nanospheres, it is possible to control their self-organization by magnetic fields and achieve more complex, or even 3D structures, beyond the typical hexagonal arrays. Self-organization in the mesoscopic scale, where the thermal energy cannot help the system finding its energy minima, is an interesting problem where subtle play of several competing kinetic processes defines the outcome. The use of superparamagnetic spheres adds the long range magnetic dipolar interactions to the competing nanoparticle-surface (substrate hydrophobicity-hydrophilicity) and the nearest neighbor nanoparticle-nanoparticle interactions, which control order and agglomeration. An advantage of the superparamagnetic particles is that the strength of the interactions can be tuned by the applied field, and it is practically switched off when the external applied field is removed. The self-assembly of magnetically functional entities is much less studied compared to the vast existing literature of their non-magnetic counterparts. Magnetic forces favor agglomeration, which is usually not desirable in obtaining high-quality monolayers. However, it opens possibilities to obtain a richer variety of organized structures. The present work shows that, due to the long range of the magnetic forces, even weak fields can have a strong impact on self-organization patterns.