Strategies for determining heteroaggregation attachment efficiencies of engineered nanoparticles in aquatic environments

Heteroaggregation of engineered nanoparticles (ENPs) with suspended particulate matter (SPM) ubiquitous in natural waters often dominates the transport behaviour and overall fate of ENPs in aquatic environments. In order to provide meaningful exposure predictions and support risk assessment for ENPs, environmental fate and transport models require quantitative information about this process, typically in the form of the so-called attachment efficiency for heteroaggregation alpha(hetero). The inherent complexity of heteroaggregation-encompassing at least two different particle populations, various aggregation pathways and several possible attachment efficiencies (alpha values)-makes its theoretical and experimental determination challenging. In this frontier review we assess the current state of knowledge on heteroaggregation of ENPs with a focus on natural surface waters. A theoretical analysis presents relevant equations, outlines the possible aggregation pathways and highlights different types of alpha. In a second part, experimental approaches to study heteroaggregation and derive alpha values are reviewed and three possible strategies are identified: i) monitoring changes in size, ii) monitoring number or mass distribution and iii) studying indirect effects, such as sedimentation. It becomes apparent that the complexity of heteroaggregation creates various challenges and no single best method for its assessment has been developed yet. Nevertheless, many promising strategies have been identified and meaningful data can be derived from carefully designed experiments when accounting for the different concurrent aggregation pathways and clearly stating the type of alpha reported. For future method development a closer connection between experiments and models is encouraged.