der Waals forces influence the polydispersed nanoparticle assembling by improving their final arrangement through a size‐selective sorting effect (Ohara et al. 1995; Murthy et al. 1997; Lin et al. 2000). This effect was easily represented in two dimensions and resulted from the size‐dependent magnitude of the van der Waals interaction. The van der Waals forces can also influence the highly anisotropic nanoparticle assembly as nanorods (Jana 2004) and rectangular nanoparticles (Sau and Murphy 2005). In this regard, the nanorods interaction builds a side‐by‐side assembling rather than an end–end arrangement due to higher van der Waals forces. In this regard, recently, Rance et al. (2010) demonstrated how van der Waals interactions between nanoparticles significantly and crucially depend on the structural parameters of the component nanostructures. Moreover, the composition and structure of nanoparticle assemblies through van der Waals interactions was precisely controlled.
3.2.3 Magnetic Interaction
The assembly of the magnetic nanoparticles determines an alignment of the single magnetic moments in the direction of the surrounding magnetic field due to the influence of the nearby magnetic nanoparticles or to the applied external magnetic field, by allowing to have a specific directionality of interaction, inducing an increase (Bishop et al. 2009) (Figure 3.1).
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).
Figure 3.2 Electrostatic stabilization of the nanoparticles by (a) Derjaguin–Landau–Verwey–Overbeek (DLVO) colloidal‐stability theory‐based interaction potential profiles of nanoparticles combining van der Waals and electrostatic forces as a function of separation distance. (b) Interaction potential profiles for sterically stabilized nanoparticles as a function of separation distance.
Source: Stolarczyk et al. (2016). Reproduced with permission from John Wiley & Sons.
Therefore, the assembly of the nanoparticles is induced by the variation of the interaction force. When nanoparticles within a dispersion exhibit opposite sign charges, the assembly process begins with the alternating placement of the nanoparticles (Lalatonne et al. 2004) or the formation of core‐shell super‐structures (Sim et al. 2015). As previously reported, the surface charge determines aggregation or repulsion between the nanoparticles. Furthermore, the nanoparticles randomly and uncontrolled aggregate at the isoelectric point. Greater control of the assembling process is obtained for the pH‐sensitive ligands on the surface of the nanoparticles. The latter can be protonated or deprotonated, thus altering the surface charge density. In this case, the charge and the surface potential changes are observed during the interaction between nanoparticles (Butter et al.