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 CeO2, TiO2 NPs, and ZnO NPs > Ag(0) NPs surface-modified with polyvinylpyrrolidone (PVP) > citrate-functionalized CeO2 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 alpha 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 alpha in the case of the two Ag(0) evaluated that may be linked to NP dissolution.