Unveiling adsorption generality in polymeric macromolecules

Unveiling a general law for adsorption within macromolecules sets an important step forward in the design of nanomaterials with tunable and controllable properties. Reaching such a generalised control would have an important outcome in a plethora of possible fields, from biomedical applications up to materials science. In fact, the definition of classes regrouping adsorbing macromolecules with different geometrical or chemical properties would enormously simplify the design of controllable adsorbing materials, especially when geometrical or chemical constraints are set by the particular application. In this work we derive, through a combination of Scaling Theories and Molecular Dynamics Simulations, a general law for adsorption of spherical non-deformable colloidal nanoparticles within polymeric macromolecules of different geometries. Starting from the case of adsorption of a single colloid within macromolecular systems, we extend the results to the case in which finite adsorption takes place. We then derive simple predictions linking the adsorption potential to general properties of classes of macromolecules, and introduce a set of measurable quantities that can be exploited as an indirect measurement for loading.