What kind of interacion is there between a nanoparticle and its functionalizing coating?
In small nanoclusters/nanocrystals/quantum clusters (my goodness, they have so many names nowadays) in the size range around 13, 55 and 144 metal atoms,1 the ligands enter a real orbital interaction (dative bond2). They are ligated to the metal core (Puls et. al., 2014).

In DNA-ligated gold clusters, the phosphate groups are able to bond to the metal core and substitute the phosphine ligands it had before (Yunping et. al., 2003).

In larger nanoparticles,3 the tendency of the particles to agglomerate is much smaller. Some of them can be measured with TEM (Transmission Electron Microscopy) without full agglomeration. This is not given for the small 13 metal atom clusters. The big particles enter interactions with their surfactants for which the main contribution is given either by van der Waals forces, or by electrostatic interactions.



1 Those are some of the most common numbers in gold cluster chemistry, like $\text{Au}_{13}(\text{PR}_3)_{12}$ for example. 55 and 144 can be found in thiolated gold clusters.

2 It has covalent portions as well as ionic. It is, however, better understood if you think of coordination complexes. Only in this case, there is not only a single metal atom in the centre

3 i.e. 5 nm, 12 nm. I stated this because I am not aware of any case in which a 13-metal-atom cluster was analysed by TEM (Transmission Electron Microscopy). The conditions are simply too harsh, the ligand shell is ripped off and the little clusters experience a very strong tendency to agglomerate. You need specialised TEM equipment to acquire meaningful data. Nanoparticles of a few nanometers are less prone to show such a fast agglomeration.