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The interactions between the most straightforward molecular systems with no permanent charges or dipoles are always due to van der Waals forces, which originate from the electromagnetic fluctuations due to the continuous interactions that occur between opposite charges, within atoms and molecules (Bishop et al. 2009; Stolarczyk et al. 2016). These floating dipoles induce the polarization of nearby atoms or molecules, causing an induced dipole‐like interaction (Hamaker 1937). These fluctuations depend on the different parameters such as the fluctuation of the charge distributions, the rotating dipole, and the dipole‐induced interactions of the nearby molecules or atoms. Moreover, the interactions can be classified into dispersion‐type (London), orientation‐type (Keesom), or induction type (Debye) contributions (Lin et al. 1989). The dielectric properties are significant since the electromagnetic field of the permanent dipole influences the interaction. A relation of proportionality between the constant quantifying the interaction strength (Hamaker constant) and the static and frequency‐dependent material polarizability (dielectric function) was demonstrated. When the interacting objects increase their distance, a decrease in the force between inductive and induced dipoles is obtained, thus reducing the strength of the interaction, which is called delay. Hamaker (1937) demonstrated how the particle interaction depends on the van der Waals forces, thus elaborating an analytical expression. This expression shows an attractive interaction between similar materials and a repulsive interaction for different materials that act through a third medium (Casimir and Polder 1948). A different approach, element – surface integration approach was demonstrated by Bhattacharjee and Elimelech (1997), which allowed the calculation of the interaction energy between objects of arbitrary form. Furthermore, a further expression to describe the interaction energy of the spheres is the Derjaguin approximation. This expression was applied when the interaction is smaller than the particle size. Therefore, this approximation will hardly apply to interactions between nanoparticles.

Moreover, the van der Waals forces between colloidal particles were calculated using Dzyaloshinskii–Lifshitz–Pitaevskii (DLP) (Dzyaloshinskii et al. 1992; Lifshitz and Hamermesh 1992) by combining it with the Derjaguin approximation (Levins and Vanderlick 1992), to account for particle curvature with spherical or rod‐shaped particles. For intermediate separations, a standard approach is to use an additive Hamaker approach (1937).

Briefly, several methods to describe different types of nanoparticles were mentioned. In this regard, the DLP and Hamaker approaches gave consistent results for higher nanoparticle distances, compared to a certain disagree results for lower nanoparticle distances (10% of the diameter of the nanoparticles) (Bishop et al. 2009). However, the Hamaker approximation (1937) is applied due to the challenge to observe short distance nanoparticle interactions to obtain ordered assembly (Ninham 1999). Moreover, by controlling the van der Waals interactions through the use of appropriate stabilizing ligands or solvents, it is possible to drive the two‐ and three‐dimensional assembling processes of different nanostructures, nanoparticles (Harfenist et al. 1996), and nanorods (Sau and Murphy 2005).

By increasing the nanoparticle concentration, until reaching a solubility threshold, the nanoparticles nucleate and grow, to obtain an ordering assembly increase. It was interesting to observe how the van 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.