. Many mechanisms may govern the adsorption of the metal ions by the hybrid nanoparticles. Since the ion concentration and the cation charge are almost the same for all the four heavy metal ions in this study, the preferential binding of PEG bis(amine)-grated PMMA/SPIONs to larger metal ions should result from the physicochemical properties that vary with size, namely the ionic potential. This argument amounts to the acid-base theory. A larger ion radius leads to a lower surface charge density of the ion. This results in the variation of the ionic potential (I) with the radius (r) as in the equation below [36];
I=Z/r , where z is the ionic charge.
Another mechanism for the dependence of the binding efficiency to the ionic radius may result from the molecular structure of the PEG bis(amine) grafting layer. The ability of metal ions to bind to a particular organic ligand is known to be related to their size compatibility [33-41]. For PEG (bis)amine, the grafting process leaves the surface of the grafted PMMA/SPIONs with many NH2 end groups in the amorphous matrix of PEG chains. A larger ion should be able to bind better into this matrix, possibly with co-ordination of multiple NH2 groups. An extrapolation of the graph in Fig. 3 also suggests that this PEG (bis)amine matrix may not bind to ions with radius below 0.5 Å. A schematic model for the adsorption of metal ions by the PEG (bis)amine grafted PMMA/SPIONs is shown in Fig. 4. This model may also be applied to the mixed metal test, in which the adsorption capability of the grafted SPIONs becomes significantly lower for Pb(II) and Hg(II), since the PEG (bis)amine matrix should contain a limited number of NH2 binding sites. However, PEG chain would probably form coordination of hybrid nanopaticles bonds with metal ions and the water solubility of SPIONs would be affected because of the weaken ability to form hydrogen bonds with water [42].