Magnetic Nanoparticles in Human Health and Medicine. Группа авторов

nanoparticles determine their stabilization in suspension. Therefore, it needs a stimulus to obtain an aggregation to create an imbalance and thus reduce repulsive terms of the interaction potential. As reported by Lin and coworkers (1989), the formation of the cluster is influenced by kinetic effects. Therefore, a high interaction potential (>10 kT) leads to a rapid aggregation of the nanoparticles in a disordered assembly due to kinetically trapped structure. Moreover, for moderately attractive potentials (2–3 kT), the formation of more ordered clusters is obtained due to the higher degree of reversibility in the interaction between the nanoparticles through the breakdown of the bonds activated thermally. In this context, the clustering process should take place near equilibrium to obtain a slow and controllable process.

      Furthermore, it is demonstrated that long‐range interactions concerning the assembling component sizes were preferred. However, many interaction forces, as van der Waals forces, act only on very low molecular distances. Therefore, to apply them on a larger molecular scale and to allow assembly, it needs to use small components, more precisely in the order of nanometers (2–30 nm).

Numerous factors influencing the strength of the colloidal interaction between nanoparticles are taken into account to obtain a monodisperse suspension of selectable dimensions of clusters with internal order. These factors could be considered as control parameters during the formation of clusters.

      For magnetic nanoparticles, van der Waals attraction and the dipole–dipole interaction of magnetic nanoparticles can lead to well‐ordered assembly structures.

      Therefore, in this section, we aim to describe the characteristics of various classes of interparticle interactions, as van der Waals, electrostatic, magnetic, and molecular at the nanoscale.

      In this regard, we focus on the nanoscale effects that emerge with respect to the smaller molecular systems or, the larger colloids. Furthermore, considerable attention has been posted on theoretical tools to describe interactions at different levels of approximation and finally on their limits.

      Each described interaction was accompanied by numerous experimental works to gain a better understanding, by allowing us to evaluate the effects of the assembling process for different interactions. Therefore, our purpose is to describe a general view of the different interparticle potentials to be implemented in the nanoparticle assembly.

      3.2.1 Molecular Interaction

      A variety of attractive short‐range forces, such as covalent bonds, dipolar interactions, hydrogen bond, and donor–acceptor interaction, are used to build both complex molecules and crystals (Desiraju 1995; Moulton and Zaworotko 2001). In this regard, hydrogen bonds allow the organization of nanorods in linear chains (Thomas et al. 2004; Guo and Dong 2011). Besides, there are reports in the literature on DNA as a linker for assembling particles selectively and reversibly (Alivisatos et al. 1996; Mirkin et al. 1996).

      Finally, other examples relate to dipole–dipole interactions between groups of photoisomerizable surfaces allowing rapid assembly and disassembly of ordered nanoparticles (Steiner 2002).

      In this context, these interactions give rise to interparticle potentials that allow the organization in highly ordered structures. These forces depend on the number of individual bonds (covalent or noncovalent) and the binding force characteristic of the molecular interaction. While the interactions can be quite weak, the forces between suitably functionalized surfaces can be quite strong due to the interaction of many molecular groups. These interactions show a variable length from nanometers to angstroms (molecular size λ) and depend on the specific interacting molecules. Therefore, the interactions will not take place based on the distance, but in contrast, they will be dependent on the λ factor as in an on–off mechanism.

      In this respect, the hydrogen bonds, as well as the polar interactions, are electrostatic (Abe et al. 1976; Steiner 2002) by allowing the nanoparticles (Johnson et al. 1997; Boal et al. 2000; Kimura et al. 2004) and nanorods (Thomas et al. 2004; Sun et al. 2008; Guo and Dong 2011) assembly.

      The hydrogen bonding is shown to induce the aggregation of metal nanoparticles functionalized with hydrogen bonding ligands where the degree of aggregation and order depends on the strength of the individual hydrogen bonds formed. Therefore, Nonappa and Ikkala (2018) in their work, provide an example, how the anisotropic colloidal interactions of H‐bonding nanoparticles can direct colloidal self‐assemblies of nanorods. Recently, Yue et al. (2015) described the formation of ZnO nanoparticle chains and demonstrated the importance of the nanoparticle–solvent interactions, notably, the hydrogen bond, in obtaining the stability of the chain structure by using different simulations. Therefore, the Molecular Dynamic (MD) confirmed the role of hydrogen bonding in stabilizing the chain‐like structure, and Dissipative Particle Dynamics (DPD) simulations revealed the importance of nanoparticle–solvent interactions in guiding anisotropic self‐assembly.

      3.2.2 Van der Waals Forces

      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