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Figure 3.1 Interactions between magnetic nanoparticles. (a) Schematic illustration of the behavior of weakly interacting in magnetic particles; (b) interaction potential between superparamagnetic particles; (c) interactions between nanorods magnetized along their long axis and interacting end to‐end (left) or side‐by‐side (right).

      Source: Adapted with permission from Bishop et al. (2009). Copyright 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

      Thus, the applied magnetic field will cause the formation of aggregate phases from particles with smaller dipole moments than would be possible in the absence of the magnetic field (specifically, for about 2 kT). Moreover, the resulting phases are oriented concerning the field. Therefore, by using magnetic nanoparticles with characteristic dipole energy between 2 and 8 kT, it is even possible to induce an assembling/disassembling process by applying/removing the magnetic field as reported in Stolarczyk et al. (2016). These interactions allow the formation of chains (Tanase et al. 2001; Wu et al. 2009), wires (Tanase et al. 2005), or rings (Tripp et al. 2002, 2003) of one‐dimensional magnetic nanoparticles when the magnitude of the interaction exceeds about 8 kT as reported by Goyal et al. (2008). The super assembly can improve the order of the nanostructures due to the coherent alignment of the magnetic moments of all the nanoparticles (Pileni 2001; Singamaneni and Bliznyuk 2005). However, the magnetic interactions are not the only forces responsible for the assembling process. Indeed, they compete with other effects, such as those of van der Waals (and possibly other types) which become increasingly important as the size of the nanoparticles decreases. Lalatonne et al. (2004) studied the influence of two different interactions during the assembling process, van der Waals interactions and dipolar strength. They studied the transition of maghemite nanocrystal organization from chain‐like to random structures when nanoparticle solutions were evaporated under a magnetic field. It was observed that the dipole–dipole interactions between the maghemite particles do not have sufficient strength to cause the formation of chains.

      In contrast, when the distance between the nanocrystals is short, van der Waals forces determine assembling. An exciting example of self‐assembly by using magnetic forces was reported by Sim et al. (2015). Their work was about the encapsulation of Fe₃O₄ nanoparticles within the chaperonin GroEL protein. The chaperonin was decorated with metal ion‐binding molecules, triggering the polymerization in fibers a few microns long in the presence of Mg²⁺. These fibers subjected to an external magnetic field were assembled in thick bundles, dismantled when the magnetic field was removed. The properties of the nanoparticle assembling depend strongly on the particle size. Butter et al. (2003) studied the influence of nanoparticle size on the assembling process. An increase of their size, a sudden transition from separate particles to disordered, oriented linear aggregates and branched chains or networks is observed. When these aggregates are placed within a magnetic field, these chains align and form thick, elongated structures.

      3.2.4 Electrostatic Interaction

The surface electrostatic charge of the nanoparticle is a fundamental force to obtain interactions with the other nanoparticles. This charge may be due to several factors, such as a specific effect of ions absorption from the solution, a protonation/deprotonation effect of the surface groups, or the presence of charged ligands. Therefore, these interactions affect the situation of hydrophilic nanoparticles dispersed in polar solvents, such as water, unlike hydrophobic nanoparticles, dispersed in nonpolar solvents. The reason lies in the attraction of the counterions in solution by the charged nanoparticles, thus forming an electrical double layer (Bishop et al. 2009). In this regard, the Gouy–Chapman model approximates the electrostatic potential in the electric double layer through the combination of the Poisson equation with a Boltzmann ion distribution. Therefore, the obtained equation, called Poisson–Boltzmamm, allows the determination of the concentration profile of the ionic species outside a charged surface. The free energy of the interaction upon double‐layer overlap depends on and is associated with the potential electrochemical change of the dissolved ionic species. The energy interaction can be defined as electrostatic interaction or double‐layer electrical interaction due to the rigid coupling of ion concentration and electrical potential obtained through the Poisson–Boltzmann equation. The attractive or repulsive strength depends on the surface charge and the decay properties of the electric field. While the former depends on the surface charge density on the nanoparticle, the latter depends on the screening ability of the dissolved ions expressed by the inverse Debye length. By modifying both the surface charge and the Debye length of the double layer, an electrostatic interaction regulation was allowed (Stolarczyk et al. 2016) (Figure 3.2).