Concentration-Dependent Association Between Weakly Attractive Nanoparticles In Aqueous Solutions

Interactions between nanoparticles in solutions may impact many applications including delivery of nanomedicine, energy transfer between nanoparticles, and transport of nanomaterials. Recently, 100 nm diameter calcium phosphate enclosed liposomes (CaPELs) were used to probe nanoscale energy deposition in CaPELs in the form of X-ray induced energy transfer by 100 nm PEGylated gold nanoparticles (AuNPs) under X-ray irradiation. A jump was observed in the transfer efficiency as AuNP concentration rose above a threshold. The jump was proposed to be caused by each CaPEL associating with at least one AuNP at high enough AuNP concentrations. Brownian dynamics is used here to model the interaction between the weakly attractive nanomaterials of AuNPs and CaPELs. For a 6 kcal/mol binding energy between the two, the results indeed show that AuNPs and CaPELs form short-lived associations at room temperature in aqueous solutions, and the percentage of CaPELs in these associations jumps sharply to nearly 100% as AuNP concentration rises above a threshold. This agreement between the experimentally observed transfer efficiency trend and that obtained from Brownian dynamics simulation suggests a concentration-dependent, cooperative association between the weakly attractive AuNPs and CaPELs. The trend can also be duplicated using existing models such as Klotz or Hill equation with n greater than 3, implying a cooperative interaction of these nanomaterials similar to cooperative binding between ligands and proteins.