Supporting Information. Heteroaggregation of titanium dioxide nanoparticles. with model natural colloids under environmentally. relevant conditions

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1 Supporting Information Heteroaggregation of titanium dioxide nanoparticles with model natural colloids under environmentally relevant conditions Antonia Praetorius,, Jérôme Labille,, Martin Scheringer, Antoine Thill,, Konrad Hungerbühler, and Jean-Yves Bottero, Institute for Chemical and Bioengineering, ETH Zurich, 893 Zurich, Switzerland, Aix-Marseille Université, CNRS, IRD, CEREGE UMR 733, Aix en Provence, France, International Consortium for the Environmental Implications of Nanotechnology, iceint, Aix en Provence, France, and Laboratoire Interdisciplinaire sur l Organisation Nanométrique et Supramoléculaire, UMR CEA-CNRS 399, CEA Saclay, Gif-sur-Yvette, France antonia.praetorius@chem.ethz.ch To whom correspondence should be addressed ETH Zurich CEREGE, Aix-Marseille Université iceint CEA Saclay S1

2 Section S1: Description of the Smolu-Model The aggregation data measured in this study is interpreted with the Smolu-Model, an aggregation model developed previously (1 ). The Smolu-Model is an aggregation model based on the numerical resolution of the Smoluchowski equations. A size gridding procedure is employed to divide the particles into classes of different sizes and control the number of differential equations to be solved. The model is parameterized to account for the properties of the particles and the solvent (including the shear rate of the system) and can be set up to account for different assumptions regarding the collision mode of the particles, namely for rectilinear, curvilinear or intermediate trajectories ( ). Table S1: Input parameters for simulations with Smolu-Model parameter symbol value (unit) minimum diameter for size gridding d min.1 (µm) maximum diameter for size gridding d max See Table S (µm) fractal dimension of aggregates d f See Table S density of primary particles ρ p (kg m 3 ) particle concentration conc p 1 (mg L 1 ) mean diameter of initial size distribution d avg See Table S (µm) standard deviation of initial size distribution σ See Table S maximum aggregate size D max See Table S density of solvent ρ w 1 (kg m 3 ) dynamic viscosity of solvent µ w.979 (kg m 1 s 1 ) temperature T See Table S (K) average shear rate G 1 (s 1 ) number of size classes NB CLASSE 5 start time of simulation t (s) end time of simulation t max 11 (s) time step of simulation dt 1 (s) collision mode decantation mode f coll mode v dec mode See Table S Stokes attachment efficiency alpha See Table S S

3 Table S: Smolu-Model input parameters for the different experiments solution salt conc. davg σ Df dmax Dmax T f mode coll SiO TiO global hetero conditions (mm) (µm) (µm) (µm) (K) ph 5, NaCl rectilinear <.1 < intermediate < intermediate intermediate intermediate intermediate ph 8, NaCl rectilinear <.1 - <.1 < rectilinear <.1 1 <.1 < rectilinear <.1 1 <.1 < rectilinear < rectilinear < intermediate intermediate intermediate mg/l SRHA rectilinear < mg/l SRHA rectilinear < mg/l SRHA rectilinear <.1 <.1 <.1 ph 8, CaCl rectilinear <.1 1 <.1 < rectilinear < rectilinear < intermediate < intermediate intermediate mg/l SRHA rectilinear < mg/l SRHA rectilinear < mg/l SRHA rectilinear <.1.. S3

4 Section S: Derivation of Equation 1 (determination of hetero ) The equation to derive hetero from the overall attachment efficiency of the heteroaggregates ( global ) and from the attachment efficiencies for aggregation for both the NPs ( NP ) and the NCs ( NC ) is based on the assumption that for each collision between two NP- NC primary heteroaggregates the attachment efficiency of that specific collision depends on the way the primary heteroaggregates face each other upon collision (Figure S1). If the heteroaggregates meet on the NP faces global is mainly determined by NP, if they meet on the NC faces global depends on NC facing one another global depends on hetero. and if they meet with one NP and one NC side NP NP interaction NC NC interaction NP NC interaction Figure S1: Overview of the different possibilities two NP NC heteroaggregates have to interact upon collision. The fraction of NC surface covered by NPs in the heteroaggregates, f NP, determines the probability with which each interaction type (NP-NP, NC-NC and NP-NC) is likely to occur, thereby weighting the effect of NP, NC and hetero on global (Equation S1). global = f NP NP }{{} NP NP interactions + (1 f NP ) NC }{{} NC NC interactions + (1 f NP ) f NP hetero }{{} NP NC interactions (S1) Since we determine NP and NC in the aggregation experiments, global in the heteroaggregation experiments and we can calculate f NP from the particle concentrations and size distributions of the NPs and NCs in the experiment, we can then calculate hetero as follows (Equation S corresponds to Equation 1 in the main text): hetero = global f NP NP (1 f NP) NC (1 f NP ) f NP (S) S4

5 f NP corresponds to the fraction of NC surface area effectively covered by NPs and is calculated as follows: f NP = Aproj NP,tot A NC,tot (S3) where A proj NP,tot is the total surface area that all NPs in the experimental system would cover when attached to the surface of all NCs and A NC,tot total surface area of all NCs in the system. A proj NP,tot diameter as the NP: essentially corresponds to the projected surface area of a disk of equal ( ) A proj NP,tot = π dnp N NP,tot (S4) where d NP is the average NP diameter and N NP,tot is the total number of NPs in the system. A NC,tot is calculated by multiplying the total number of NCs, N NC,tot, with the surface area of an NC of average diameter, d NC : A NC,tot = 4π ( dnc ) N NC,tot (S5) The total particle numbers N NP,tot and N NP,tot of NPs and NCs, respectively are calculated as follows: N NP/NC,tot = 3 4 π C mass ( dnp/nc NP/NC V exp ) 3 (S6) ρnp/nc where C mass NP/NC is the mass concentration of NPs or NCs, V exp is the total volume of the experimental system and ρ NP/NC is the density of the NPs or NCs. S5

6 EPM (1-8 m V -1 s -1 ) Section S3: Characteristics of TiO and SiO suspensions SiO -6 TiO ph Figure S: Electrophoretic mobility (EPM) of SiO and TiO particles as a function of ph (at 1mM NaCl concentration) S6

7 EPM (1-8 m V -1 s -1 ) SiO (NaCl, ph 8) TiO (NaCl, ph 8) SiO (CaCl, ph 8) TiO (CaCl, ph 8) salt concentration [mm] Figure S3: Electrophoretic mobility (EPM) of SiO and TiO particles as a function of NaCl/CaCl concentration at ph 8 A B Figure S4: Initial size distributions of TiO and SiO particles (A) and the suspended matter of the Rhône water sample (B). S7

8 D v,5 (µm) Section S4: Homoaggregation kinetics at ph 5 and ph 8 Before determining the heteroaggregation kinetics of the SiO -TiO system it was required to determine the aggregation attachment efficiency,, for both SiO and TiO at the different solution conditions to later calculate hetero from the laser diffraction data using Equation S mg/l SiO,.5M NaCl, ph 5 1 mg/l SiO,.6M NaCl, ph 5 1 mg/l SiO,.75M NaCl, ph 5 1 mg/l SiO,.5M NaCl, ph 5 1 mg/l SiO, 1M NaCl, ph 5 Smolu-Model, 1 mg/l SiO, =.3 Smolu-Model, 1 mg/l SiO, =.5 Smolu-Model, 1 mg/l SiO, =.1 Smolu-Model, 1 mg/l SiO, < time (s) Figure S5: Calibration of Smolu-Model at ph 5: aggregation of SiO at different NaCl concentrations At ph 5 the SiO particles are stable at a concentration of 5 mm NaCl and slowly start aggregating at 6 mm NaCl (Figure S5 ). The maximum aggregation rate is reached at an NaCl concentration of 5 mm, which is in accordance with the charge screening observed in the EPM measurements (Figure S3). The aggregation curves of SiO at ph 5 are used to adjust the Smolu-Model to the test system, varying the SiO concentration (5, 1 and mg/l) (Figure S6). Special care is taken to use well-defined and reproducible hydrological conditions for all experiments. A good fit is obtained between the D v,5 (median diameter of the volume distribution) curves of the aggregation and the Smolu-Model predictions (see Figure S5) and maximum SiO values of.3 are obtained for NaCl concentrations of 5 mm and higher (see Table S for all SiO values). At ph 8 the SiO requires S8

9 mg/l SiO,.5M NaCl, ph 5 1 mg/l SiO,.5M NaCl, ph 5 mg/l SiO,.5M NaCl, ph 5 Smolu-Model, 5 mg/l SiO, =.3 Smolu-Model, 1 mg/l SiO, =.3 Smolu-Model, mg/l SiO, =.3 D v,5 (µm) time (s) Figure S6: Calibration of Smolu-Model at ph 5: aggregation of SiO at different SiO concentrations a higher NaCl concentration to be destabilized (aggregation starts around 5 mm NaCl) which is expected from the more negative surface charge of the SiO at ph 8 compared to ph 5. At ph 8 aggregation experiments were also performed in the presence of CaCl as a divalent electrolyte and a destabilization of the SiO is observed at 1 mm CaCl and higher, which corresponds well to the more effective charge screening of the divalent Ca + counter ion compared to the monovalent Na + (Figure 3A, Figure S8A) (3, 4 ). The TiO NPs are stable at ph 5, 1 mm NaCl. At ph 8 the TiO NPs start aggregating at an NaCl concentration of 1 mm or.5 mm CaCl (Figure S7). It is important to note here that the aggregation kinetics of TiO NPs determined by DLS at a concentration of 1 mg/l because the instrument cannot reliably measure the NP s size distribution at lower concentrations. However, in the heteroaggregation experiments the TiO NP concentration is one order of magnitude lower, resulting in a much slower collision rate and hence slower aggregation kinetics than measured at 1 mg/l. The Smolu-Model was adjusted to represent the TiO particle properties and used to estimate the TiO values at ph 8 (Table S). S9

10 z-average (diameter, nm) z-average (diameter, nm) 14 A 14 B mm salt 1 mm NaCl 5 mm NaCl 1 mm NaCl mm salt.5 mm CaCl.5 mm CaCl 5 mm CaCl 4 6 time (s) time (s) 8 1 Figure S7: Stabiliy of TiO NPs at ph 8 under different NaCl and CaCl concentrations A B Figure S8: Heteroaggregation of SiO with TiO NPs under different solution conditions at ph 8. A: CaCl, B: CaCl + SRHA. SRHA = Suwannee River Humic Acid. Note: the monomers for 5 mm CaCl,.8 mg/l TiO, 1 mg/l SRHA (blue triangles) start below 1% due to a few large bubbles in the system; the model parameterisation was adjusted accordingly to correctly represent the aggregation kinetics S1

11 EPM (1-8 m V -1 s -1 ) EPM (1-8 m V -1 s -1 ) EPM (1-8 m V -1 s -1 ) EPM (1-8 m V -1 s -1 ) 1 1 SiO SiO no SRHA.1 mg/l SRHA 1 mg/l SRHA 1 mg/l SRHA no SRHA.1 mg/l SRHA 1 mg/l SRHA 1 mg/l SRHA NaCl concentration [mm] CaCl concentration [mm] TiO TiO no SRHA.1 mg/l SRHA 1 mg/l SRHA 1 mg/l SRHA no SRHA.1 mg/l SRHA 1 mg/l SRHA 1 mg/l SRHA 1 3 NaCl concentration [mm] CaCl concentration [mm] 8 1 Figure S9: Electrophoretic mobility as a function of NaCl/CaCl concentration at different SRHA concentrations S11

12 Section S5: Heteroaggregation in a natural water sample To evaluate the applicability of the new method to heteroaggregation between ENPs and suspended solids in complex real water samples we used a natural water sample from the Rhône River (Arles, France). The same experimental set-up was used as for the heteroaggregation experiments with SiO and the water chemistry of the natural sample was not manipulated. A water sample from the river Rhône (sampled on , in Arles, France) was used without further treatment or dilution. The Rhône water had a ph of 8.1 and a suspended matter content of 18.5 mg/l with an average size of µm (Figure S4B). The Rhône water was stored at 4 C in the dark, vigorously shaken before use to distribute suspended matter and all experiments were carried out within 1 days of the sampling date. 5 D v5 (µm) 15 1 Rhone water,. mg/l TiO Rhone water,.8 mg/l TiO Rhone water,.1 mg/l TiO time (s) Figure S1: Heteroaggregation of suspended particulate matter in a water sample from the Rhône River with different concentrations of TiO NPs. The addition of TiO NPs leads to a heteroaggregation of the suspended solids in the Rhône water and the TiO NPs; the observed overall heteroaggregation rate increases with increasing TiO concentration (.1,.8 and. mg/l) (Figure S1). The TiO concentration required for aggregating the suspended solids in the natural water sample was lower than in the experiments with SiO (heteroaggregation started only at a minimum TiO concen- S1

13 tration of.8 mg/l). This can be explained by the lower concentration of suspended solids (18.5 mg/l compared to 1 mg/l SiO ), which results in a higher surface coverage of suspended solids by TiO NPs and consequently a lower dose of TiO that is sufficient to induce aggregation of the suspended solids-tio heteroaggregates. The experiments show that TiO NPs do not only heteroaggregate with model particles but also with real suspended solids in natural waters at similar relative concentrations. Actual attachment efficiencies for heteroaggregation, hetero, were not determined for the natural water system because the suspended solids in the sample are constituted of several different types of natural colloids which cannot yet be represented in the current version of the Smolu-Model. However, the properties of the Rhône water closely match the conditions for favorable aggregation of our heteroaggregation experiments, therefore the measured hetero values in our SiO -TiO system can be used to approximate attachment efficiencies for heteroaggregation with real SPM under similar conditions. In the present case, the Rhône water has a ph of 8.1 and a CaCl concentration of 1.8 mm, which corresponds to a hetero value of 1.1 (measured at ph 8. and a CaCl concentration of 1 mm). Based on the rapid heteroaggregation kinetics observed in Figure S1, we therefore assume that a fast heteroaggregation would occur between TiO NPs and most SPM in the Rhône River, reducing their overall mobility in this surface water. S13

14 References (1) Thill, A.; Moustier, S.; Aziz, J.; Wiesner, M. R.; Bottero, J. Y. Flocs Restructuring during Aggregation: Experimental Evidence and Numerical Simulation. J. Colloid Interf. Sci. 1, 43, () Veerapaneni, S.; Wiesner, M. R. Hydrodynamics of Fractal Aggregates with Radially Varying Permeability. J. Colloid Interf. Sci. 1996, 177, (3) Hardy, W. B. A Preliminary Investigation of the Conditions which Determine the Stability of Irreversible Hydrosols. The Journal of Physical Chemistry 1899, 4, (4) Overbeek, J. T. G. The Rule of Schulze and Hardy. Pure and Applied Chemistry 198, 5, S14