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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. 2003). Therefore, when the nanoparticles are very far apart, the charge is shielded; in contrast, the interactions occur when the nanoparticles get close. Fresnais and coworkers (2009) described the role of desalting kinetics on the nanoparticle clustering. About the assembly monitoring, different procedures were tested as direct mixing, dialysis, dilution, and quenching. Moreover, the kinetics of assembly of the electrostatic clusters were led by the rate dI_S/dt at which the salt was removed from the solution, where I_S denotes the ionic strength. Moreover, it was shown how the assembling process was driven by the desorption–adsorption transition of polymers on the nanoparticles surface. An ionic strength decrease caused the polymeric nanoparticles clustering. Furthermore, it was demonstrated that by regulating the desalination kinetics, the size of the clusters varied from 100 nm to over 1 μm. Meyer et al. (2006), in his work studied the influence of charges on the nanoparticles assembling process. It was demonstrated how the continuing accumulation of charges during the clustering process led to an increase in electrostatic repulsion. This phenomenon can be used to regulate the cluster growth process. On the base of the previously described work, Xia and coworkers (2012) showed the spontaneously assembling inorganic nanoparticle with nonuniform distributions in superparticles with core‐shell morphologies. The electrostatic repulsion and the van der Waals attraction led this self‐growth process.