Theory and Methodology for Determining Nanoparticle Affinity for Heteroaggregation in Environmental Matrices Using Batch Measurements

In this study, we present a method for determining the relative affinity of nanoparticles (NPs) for an ensemble of other particles in a complex, heterogeneous suspension. We evaluated this method for NPs heteroaggregating with suspended solids present in activated sludge. A relationship was derived between the heterogeneous affinity coefficient, alpha , and measurements over time of the distribution coefficient, gamma , of NPs measured in supernatant versus those removed by heteroaggregation and subsequent settling. Application of this method, which uses a mathematical relationship to determine alpha from experimentally measured gamma values, to a series of metal and metal oxide NPs heteroaggregated with activated sludge indicated a relative affinity in the order of pristine CeO sub(2), TIO sub(2) NPs, and ZnO NPs > Ag(0) NPs surface-modified with polyvinylpyrrolidone (PVP) > citrate-functionalized CeO sub(2) NP > Ag(0) NPs surface-modified with gum arabic. This trend in relative affinity followed the observed trend in removal such that higher affinity corresponded to higher removals of NPs. Values of a were calculated from measured relative affinities using average diameter and concentration of the activated sludge particles. The value calculated for PVP-stabilized Ag(0) NPs was comparable to a value previously reported for the attachment of these same NPs to a biofilm. Calculations also yielded size dependence of a in the case of the two Ag(0) evaluated that may be linked to NP dissolution.