Understanding the Thermodynamics of the Binding of PAMAM Dendrimers to Graphene: A Combined Analytical and Simulation...

We investigate the thermodynamics of the binding of a poly(amidoamine) dendrimer to an uncharged graphene sheet as a function of the pH level using umbrella sampling simulations and a mean-field theory for generations three and four. We find that the dendrimer strongly binds to the graphene sheet ( $$ (100) kcal/mol) from our potential of mean force (PMF) calculations. In specific, we find that the dendrimer binds the most at neutral pH (∼7) and the least at low pH (∼4). We explain this nonmonotonic nature of the dendrimer's adsorption by studying the interactions contributing to the PMF, i.e., the dendrimer-graphene, dendrimer-water, and dendrimer-ion interactions. We also corroborate our PMF calculations with molecular mechanics generalized Born surface area analysis and free energies obtained from a mean-field theory of Flory-Huggins-Debye-Hückel type [ Muthukumar , M. , J. Chem. Phys. 2010 , 132 , 084901 ], including electrostatic interactions. We find that the van der Waals interactions between the dendrimer and the graphene alone cannot capture the accurate trends in the binding free energies (BEs) as a function of pH. The solvent and the counterions present in the system are also found to have a major influence on these trends. We demonstrate that the dendrimer-graphene and dendrimer-water interactions become favorable, whereas the dendrimer-ion interaction becomes unfavorable, as the dendrimer binds to graphene. These opposing effects lead to the observed nonmonotonicity in the BE trends. Our theoretical model also reproduces these trends in the subinteractions contributing to the PMF. To the best of our knowledge, this is a novel attempt where an equivalence between theory and simulations is made in the context of the dendrimer's adsorption.