# The Concept of Using 2D Self-Assembly of Magnetic Nanoparticles for Bioassays
## 3 Results
### Preparation of 2D Array of Magnetic-Nanoparticle Chains
Then, the process of diffusive sliding of the contact line of the droplet through the growing rings of nanoparticles begins, and the angle of the droplet decreases until the configuration of the contact line is no longer energetically convenient (the minimum Gibbs-free-energy condition is no longer satisfied) and the contact line jumps to a new position, where the angle of the droplet at the contact line increases again. The process of forming a ring of nanoparticles then repeats. The coated magnetic nanoparticles should not be too large because they must be able to flow to the edge of the droplet, due to the loss of droplet mass caused by the droplet evaporation. The placement of the colloid droplets can be automated and, for this purpose, for example, the extruder of a 3D printer can be used. However, the presence of too many droplets of magnetic liquid next to each other significantly alters the conditions of their drying (the drying time significantly increases), and over large areas the drying conditions become inhomogeneous. There are several parameters by which the density of rings present in the deposit of a dried magnetic-liquid droplet can be controlled under the same environmental conditions of temperature, pressure and humidity. These are: (1) the concentration of magnetic nanoparticles in the colloid, (2) the salt concentration in the solution and (3) the magnitude of a magnetic-field gradient, which can be applied under the sample or above the sample. Figure 2: Topography of the multi-ring structure of magnetic iron-oxide nanoparticles on LDPE thin film: (**a**) AFM image of an LDPE fragment coated with chains of magnetic nanoparticles using the methods in Figure 1, where white line 1 indicates the path along which the heights of the magnetic nanowires were measured. (**b**) AFM image of a fragment of a single nanowire. (**c**) TEM image of APTES-functionalized magnetic iron-oxide nanoparticles. (**d**) surface topography of LDPE along line 1 from panel (**a**). (**e**) EDX spectrum by TEM microscopy showing elemental composition for the area with magnetic nanoparticles (**c**) placed on a copper grid (method of measurement). In Figure 3, panels (a) and (b) show the effect of magnetic-nanoparticle concentration. The solution with a suspension of nanoparticles should be stable and sonicated long enough. On the other hand, panels (c) and (d) in Figure 3 show the effect of a concentration of NaCl salts on the resulting droplet deposit. Panels (e) and (f) in Figure 3 show the droplet deposit when, for the same concentration of magnetic nanoparticles, the droplets dry without the presence of a magnetic field and when a field gradient is applied. In the latter case, the magnetic field above the sample and below the sample can be further controlled. The effect of magnetic-field gradients on the formation of multiple-ring structures was discussed in [27]. Figure 3: Optical-microscopy images of the stains from a droplet of magnetic liquid dried on a stretched LDPE film for different parameters: (**a**) For the concentration 0.012 mg/mL of magnetic nanoparticles at zero concentration of NaCl salt. (**b**) The same as in (**a**) but for the nanoparticle concentration 0.045 mg/mL. (**c**) For the magnetic nanoparticle concentration 0.045 mg/mL at the concentration of NaCl salt equal to 0.2 mM. (**d**) The same as in (**c**) but for the salt concentration of 20 mM. (**e**,**f**) For  
different values of the external magnetic-field gradient for the same magnetic-nanoparticle concentration 0.045 mg/mL, respectively, in the absence of a magnetic field and when the droplet dries in the presence of a neodymium magnet (the residual magnetic-flux density \(B_{r}\approx 1\)T) placed at a distance of 2.5 mm below the LDPE film.