Silver nanoparticles and silver nitrate in semi-natural waters – comparison of different non-linear models to calculate the average silver concentration after single and repeated application Silbernanopartikel und Silbernitrat in naturnahen Gewässern – Vergleich von unterschiedlichen nichtlinearen Modellen zur Berechnung der durch-schnittlichen Silberkonzentration bei einfacher und wiederholter Applikation

For the first part of the study, the applicability of different models for concentration calculation to the multiple application with silver nanoparticles and silver nitrate was tested. The investigations were performed within 32 aquatic microcosms (1 m³, tier 1), with 16 of the microcosms each exposed to silver nanoparticles and 16 to silver nitrate, each with four concentration steps in triplicates and four control microcosms each. In the second part of the study, the applicability of different nonlinear models/approximations in single application with silver nanoparticles in small laboratory batches (2 L water phase, static) was examined. This study seeks to answer the question of how reliable the calculations of the average total silver concentration in a water phase are after single and multiple application according to the 1st order model and the 2nd order model. To verify precision, the two models were compared with a third, nonlinear regression ("nlm" approximation). As expected, the 1st order model showed good mean coefficients of determination (R² = 0.975 to R² = 1.0) with single application of silver nanoparticles. With multiple applications of silver nanoparticles and silver nitrate, only unreliable calculations could be performed with the common 1st and 2nd order models compared to the "nlm" approximation. The calculated coefficient of determination for the experiments with silver nanoparticles and silver nitrate was R² ≤ 0.786 with the 1st order model, R² ≤ 0.604 with the 2nd order model and R² = 0.929 with the "nlm" approximation. The study shows that the contamination level of silver nanoparticles and silver nitrate can be more accurately determined with repeated application using the "nlm" approximation, but with simple application the common model (1st order) continues to yield precise results. These results help to better define and calculate the ecotoxicologically relevant concentrations.