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Development of Environmental Fate Models for Engineered NanoparticlesA Case Study of TiO2 Nanoparticles in the Rhine River Antonia Praetorius, Martin Scheringer,* and Konrad Hungerbühler Institute for Chemical and Bioengineering, ETH Zurich, Wolfgang-Pauli-Str. 10, 8093 Zurich, Switzerland S Supporting Information *

ABSTRACT: For a proactive risk assessment of engineered nanoparticles (ENPs) it is imperative to derive predicted environmental concentration (PEC) values for ENPs in different environmental compartments; PECs can then be compared to effect thresholds. From the basis of established multimedia environmental fate models for organic pollutants, we develop a new concept of environmental fate modeling for ENPs with process descriptions based on the specific properties of ENPs. Our new fate modeling framework is highly flexible and can be adjusted to different ENPs and various environmental settings. As a first case study, the fate and transport of TiO2 NPs in the Rhine River is investigated. Predicted TiO2 NP concentrations lie in the ng/L range in the water compartment and mg/kg in the sediment, which represents the main reservoir for the nanoparticles. We also find that a significant downstream transport of ENPs is possible. A fundamental process, the heteroaggregation between TiO2 NPs and suspended particulate matter (SPM), is analyzed in more detail. Our modeling results demonstrate the importance of both the SPM properties (concentration, size, density) as well as the affinity of TiO2 NPs and SPM, characterized by the attachment efficiency, αhet‑agg, on the transport potential of ENPs in a surface water system.

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INTRODUCTION The special physical and chemical properties of nanoscale particles and materials make these new materials attractive for a large range of industrial and commercial applications, which can be seen in their increased use and production during the last years.1 The special properties of engineered nanoparticles (ENPs) due to their small size and high surface-to-volume ratio represent an opportunity for technical development and novel or improved products and applications, but the potential risk associated with these new materials and their new properties is only poorly understood.2 With the continuously growing number of products containing ENPs, the environmental release of ENPs during production, use, and end-of-life becomes inevitable. Numerous experimental studies have been performed in the last years to understand the toxicity and effects of different ENPs to organisms as well as their behavior (e.g., aggregation and dissolution) in different environmental media.3−12 In a next step, the growing knowledge and understanding gained from these studies need to be integrated into a comprehensive assessment of the expected environmental behavior, transport, and, ultimately, risk of ENPs. Detection of ENPs in natural water systems is very challenging and suitable analytical methods are still under development.13−15 In this situation, it is important to start estimating possible environmental concentrations. Powerful tools suited for this purpose are © 2012 American Chemical Society

environmental fate models; these models can be used to predict exposure levels and transport behavior of ENPs and to support a proactive risk assessment of ENPs. Environmental fate models have been established and used to assess the fate and transport of organic chemicals for 30 years.16 A sound understanding of the relationship between the physicochemical properties of a chemical and its behavior in the environment, coupled with a detailed description of environmental processes, has enabled scientists to make accurate predictions of the fate of many different chemicals in various environmental systems. In the field of ENPs, on the other hand, predictive environmental fate modeling is still in its infancy. A few approaches and discussions on the possibilities and challenges in exposure modeling of ENPs have been presented recently. Mueller and Nowack17 derived PEC (predicted environmental concentration) values for Ag NPs, TiO2 NPs and CNTs (carbon nanotubes) in air, soil, and water in Switzerland using a substance flow analysis of ENPs in different products from the technosphere to air, water, and soil. These models were later refined by using a probabilistic material flow Received: Revised: Accepted: Published: 6705

December 16, 2011 March 30, 2012 April 13, 2012 April 13, 2012 dx.doi.org/10.1021/es204530n | Environ. Sci. Technol. 2012, 46, 6705−6713

Environmental Science & Technology

Article

Figure 1. Comparison of processes relevant to organic chemicals (left) and to nanoparticles (right). The ENPs are composed of a core (inner black dot) and a coating (pink layer).

for Ag NPs, but on the other hand, this model is not directly applicable to other ENPs such as TiO2 NPs. More emphasis on nanospecific processes was placed by Arvidsson et al.,22 who applied kinetic equations from colloid chemistry to include aggregation and sedimentation in a “limited exposure assessment” of TiO2 NPs. They point out the importance of the heteroaggregation of ENPs with natural colloid particles, but due to a lack of data and modeling limitations, this process was not included in their modeling concept. Quik et al.23 propose an adjustment of the European Union guidance for estimating concentrations of chemicals in water, which is based on dividing emission rates by rate constants of all removal processes acting on the substance. To make this approach suitable for ENPs, they propose to include dissolution and sedimentation as ENP-specific processes described by firstorder rate constants. However, only order-of-magnitude rate constants for these processes were extracted from the literature. This approach is a first step toward a risk assessment but does not yet give the possibility to follow the transport of an ENP in

analysis to account for the large uncertainties and variabilities of the model input parameters, both with respect to production volumes as well as the ENP behavior within and between the model compartments.18,19 Gottschalk et al.20 derived local PEC values for NPs of TiO2, ZnO, and Ag in Swiss rivers by coupling the material flow models to water flow information assessing both geographical and temporal variability. However, no ENP-specific physical or chemical transformation processes were modeled in this study but rather accounted for by running a “conservative” (no ENP transformation or sedimentation) and an “optimistic” scenario (fast ENP removal). Another exposure assessment specific to Ag NPs was conducted by Blaser et al.21 A mass flow analysis of silver from products containing Ag NPs was coupled with an environmental fate model to derive PEC values for silver in the Rhine River. In this special case of silver, it was assumed that all silver reaching the aquatic environment was present as the environmentally most stable species, silver sulfide (Ag2S), or sorbed to suspended sediments. On the one hand, this made it possible to bypass use of ENP-specific process descriptions 6706

dx.doi.org/10.1021/es204530n | Environ. Sci. Technol. 2012, 46, 6705−6713


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model, the transformation rate constant, ktransf, is a general term that can be replaced by the appropriate process, such as transformation of the ENP itself31 or an alteration of the coating.10,32 Aggregation, dissolution, and surface transformations will not lead to the ENPs' disappearing but rather to their being transformed into a new species, which can be represented in the environmental fate model in parallel to the parent ENP. The interaction of pollutants with naturally occurring suspended particulate matter (SPM) strongly affects the environmental transport of the chemical and needs to be described in fate models.33 For organic chemicals this interaction is described by the sorption coefficient, Kd, which is a partition coefficient calculated from the octanol-water partition coefficient, Kow.25 For ENPs, this approach is not valid, because it cannot be assumed that the ENPs are present in thermodynamic equilibrium between the aqueous and the SPM phase.34 ENPs do not form a true solution of a lowmolecular-weight substance in a solvent but form thermodynamically unstable suspensions of particles with high surface energy.28 Their interaction with SPM can be best described as a heteroaggregation process, where the ENPs collide with the SPM on the basis of their respective diffusion velocities and will stick to the SPM depending on the surface properties of both ENP and SPM. Correspondingly to the homoaggregation between the ENPs themselves, the heteroaggregation rate constant, khet‑agg, is calculated by multiplying the collision rate constant, kcoll, by the attachment efficiency for heteroaggregation, αhet‑agg. Finally, transport processes of pollutants in environmental media have to be characterized in order to predict mobility and transport pathways within and between environmental compartments.33 Both organic chemicals and ENPs are affected by transport processes such as advective transport with moving water (kflow) or processes coupled with the movement of SPM, such as sedimentation (kSPM sed ), sediment resuspension (kresusp), horizontal bed load transfer (ksed‑transfer), or burial in the deep sediment (kburial). In addition to this, the ENPs can deposit to the sediment compartment on their own by gravitational settling. The sedimentation rate constant, kNP sed, increases with increasing ENP density and size. On the other hand, truly dissolved organic chemicals diffuse between water and sediment (kdiff) and between water and air (kvol).25 In this study, the relevant processes influencing the environmental behavior of TiO2 NP in a river system were parametrized and combined to establish a model to estimate the steady-state distribution of TiO2 NPs along the Rhine River. River Model. The river model from Blaser et al.21 was adjusted to study the fate and transport of TiO2 NPs. The Rhine River is modeled over a length of 700 km between Basel (Switzerland) and Lobith (The Netherlands). The main river dimensions remain unchanged with respect to Blaser et al.21 and are summarized in Table S2 and Figure S1 (Supporting Information). The river is divided into 520 boxes and, to minimize numerical dispersion,35 the length of the boxes was made small close to the emission source (10 cm on the first 10 m) and was then increased to a length of 10 km on the last 600 km (see Table S2, Supporting Information). Each box is divided into a compartment of moving water (w1), stagnant water (w2), and sediment (sed) (Figure 2). All compartments are assumed to be well-mixed. The moving water compartment exchanges water with the stagnant water at a rate kexch12 (in s−1).21 At the same time, water in the stagnant

the environment and predict its behavior in different environmental settings. In this paper we present a new approach to environmental fate modeling of ENPs based on well-established multimedia box models for organic pollutants. By fully adjusting process descriptions to account for ENP-specific properties and behavior within the environment, it is possible to create a comprehensive framework for predicting the fate and transport of ENPs in aquatic environments. We demonstrate analogies and important differences in environmental fate modeling between ENPs and low-molecular-weight organic pollutants in a two-compartment freshwater-sediment system. This enables a better understanding of the processes most relevant to the distribution of ENPs in a river system and helps identify current data and knowledge gaps that need to be filled before more accurate predictions can be made. Our approach can be adjusted in the future to different ENPs and various environmental settings, including other compartments such as air or soil. As a proof-of-principle, a case study assessing the behavior of TiO2 NPs in the Rhine River is presented.

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METHODS Modeling Concept. In multimedia box models the environment of interest is divided into compartments of different types and dimensions, for example, air, water, soil, and sediment. Processes affecting a chemical’s behavior and transport in each compartment are parametrized and combined in a system of coupled mass-balance equations.24 Solving the model yields the chemical’s concentration in each compartment at steady state or as a function of time. The model results improve the understanding of a chemical’s fate and transport in a given environmental setting and can provide guidance in regulatory contexts.16 From the basis of established multimedia fate models for organic chemicals, an adjusted modeling concept was developed using nanospecific process descriptions. In this first model development a focus was set on the water compartment, but the model can be extended to accommodate other compartments, such as air and soil, with the appropriate process descriptions. An overview of the most important processes describing the behavior and transport of ENPs in aqueous environments is presented in Figure 1 alongside the corresponding process descriptions used in environmental fate modeling of organic chemicals. The transformation and degradation processes can strongly alter the environmental behavior and adverse effects of a chemical and determine its persistence. For organic chemicals the dominant loss process is characterized by their degradation rate constant, kdeg, which is generally calculated from the halflife, t1/2, of the chemical in the environmental medium of concern: kdeg = (ln 2)/t1/2.25 Most ENPs, on the other hand, will not degrade in the environment but undergo transformation processes altering their original properties. ENPs have a high tendency to aggregate due to their high surface energy.26−28 A homoaggregation rate constant, khomo‑agg, can be calculated by multiplying the ENPs’ collision rate, kcoll, by the attachment efficiency for homoaggregation, αhomo‑agg, which describes the surface interaction of the ENPs.27,29 Dissolution can occur for some ENPs and is best described by a dissolution rate constant, kdiss, specific to the ENP and the characteristics of the environmental medium.6 Surface transformations of the ENPs are likely to occur in natural environments and can alter the ENPs' properties and environmental behavior.30 In our 6707



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Figure 2. Processes acting on free TiO2 NPs (open arrows), on TiO2 bound to SPM (dashed arrows) and on both free and SPM-bound TiO2 (filled arrows) in the moving water (w1), stagnant water (w2), and sediment (sed) compartment of the Rhine River model.

effect is observed. The SPM characteristics, namely their type, concentration, and size distribution, are highly variable within a river system. For the purpose of demonstrating our new modeling approach, we chose to assume uniform conditions throughout the model within one model run but to vary the parameters in different runs, to understand their relative influence. The SPM in the model are represented as a lognormal particle size distribution with a mode of 5 μm (particle diameter) and spanning from 1.5 to 80 μm (Table S5, Supporting Information). In order to reflect different types and fractal geometries of SPM, the SPM density, ρSPM, was varied between 1.1 and 2.5 g cm−3 in different model runs. Their mass concentration was varied between 30 and 90 mg L−1 according to data obtained from the sediment database for the Rhine River from the German Federal Institute of Hydrology.36 This corresponds to SPM particle concentrations, CSPM particle, between 9.2 × 109 and 6.3 × 1010 particles m−3 (see Table S6, Supporting Information). Nanoparticle Characteristics. On their way from the industrial product or application through the wastewater stream to the river waters, NPs already undergo transformations. Therefore, it is reasonable to assume that the TiO2 NPs will not reach the river in a freely dispersed state but will already have aggregated to form larger particle assemblies. The initial size distribution of the aggregated TiO2 NPs was set to be lognormal with a mode at 300 nm (particle diameter) in accordance with the size of TiO2 NPs measured in a freshwater sample with characteristics close to the conditions in the Rhine River.5,9 In order to limit the computational effort, the nanoparticles in the distribution were assigned to five size classes. More details on the TiO2 NP properties and their size distribution are provided in the Supporting Information (Table S4 and Figure S2A). It is important to note that there is to date no accurate information available on the form and size of ENPs entering the environment. The TiO2 NP properties chosen in

water compartment is exchanged by the corresponding amount of moving water at a rate kexch21 (in s−1). The river flows at an average velocity, vriver,flow, of 1.3 m s−1,36 transporting the water in the moving water compartment from one box to the next with a transport rate constant of kriver,flow (in s−1) (Figure 2). The sediment is resuspended to the stagnant water compartment at an average velocity, vresusp, of 1.14 × 10−8 m s−1 37 and is buried in the deep sediment at a velocity, vburial, of 3.42 × 10−8 m s−1.37 Horizontal sediment transport at the surface of the sediment compartment takes place at an average velocity, vsed,transfer, of 3.0 kg s−1.36 Since the behavior of NPs in aqueous dispersions is greatly influenced by the physicochemical characteristics of the medium,3−5 the properties of the Rhine River were collected from a database of the “Deutsche Kommission zur Reinhaltung des Rheins” (German agency for contamination control of the Rhine).38 Average values for the year 2008 sampled from seven monitoring stations along the section of the river modeled in this paper were extracted from the database. The pH, water temperature, concentration of different ions, and dissolved organic carbon (DOC) concentration [to represent natural organic matter (NOM)] are listed in Table S1 (Supporting Information). The suspended particulate matter (SPM) present in all natural waters is expected to have a strong influence on the fate and transport behavior of ENPs.30 ENPs are likely to attach to SPM by heteroaggregation and will then be transported or deposited at the same rate as the SPM. One of the greatest challenges in designing environmental fate models for ENPs is the great complexity of SPM in terms of size, type, and concentration. Both the heteroaggregation and the SPM sedimentation rate depend on the density and size of the SPM. It is therefore possible to define scenarios where removal of ENPs from the water column to the sediment compartment is accelerated by SPM but also scenarios where the opposite 6708



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Figure 3. Effects of variations of αhet−agg (panels A−C) and ρSPM (panels D−F) on the TiO2 NP concentration in the moving water (in its free form or attached to SPM as a result of heteroaggregation) and in the sediment. The different TiO2 NP size classes behave very similar. Here the sum of all size classes is presented to illustrate the total TiO2 load in the river.

this study represent a possible scenario,5,9 but they can be adjusted in future studies once more information is available. The mass flow of TiO2 NPs entering the Rhine River in the first box of the model was assumed to be 0.14 t a−1 (0.39 kg day−1). This value was derived from mass flow model predictions of TiO2 NPs for Switzerland20 and scaled down according to the population of Basel. We assumed that the primary TiO2 NPs are uncoated and spherical. The incoming TiO2 NP mass flow was transformed to a particle flow for each of the five size classes. The fractal nature of the aggregates affects the hydrodynamics of the particles;39 here, the fractal nature of the aggregated TiO2 NPs is reflected by their specific density, which takes the fractal dimension into account (see eq S1, Supporting Information). The shape of the aggregated TiO2 NPs (and the SPM) is approximated by spherical particles. All model calculations are performed on the basis of particle numbers, both for the TiO2 NPs and the SPM. Processes. A literature review was performed to identify the most relevant processes that will affect the fate and transport of TiO2 NPs in aquatic environments. The processes relevant for

this modeling study in the Rhine River are depicted in Figure 2. The total amount of nanoparticles reaching natural waters is expected to be only in the ng/L range,20 which makes it reasonable to assume that the highly diluted TiO2 NPs do not collide frequently and homoaggregation is negligible compared to all other processes acting on the NPs, in particular with respect to heteroaggregation. In this study, the SPM particle concentration is at least 2 orders of magnitude higher than the TiO2 NP concentration in all cases (1010 SPM particles m−3 vs 108 TiO2 particles m−3), resulting in heteroaggregation being the dominant process. For this reason, the individual TiO2 size classes are not assumed to interact with each other and the model is run separately for each size class. Although it is one of the most relevant processes acting on NPs in freshwater systems, the heteroaggregation of NPs with naturally occurring SPM in the nano- and micrometer range has not yet been studied much and is still poorly understood. From a theoretical point of view, the heteroaggregation rate constant, khet‑agg, of NPs with SPM is best expressed by multiplying the collision frequency, kcoll, of the particles by the attachment 6709



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efficiency for heteroaggregation, αhet‑agg.29 We assume that the overall SPM concentration in the river does not change significantly as a result of heteroaggregation, so the process is expressed with a pseudo-first-order rate constant by multiplication by the SPM particle concentration, CSPM particle:

TiO2 i = 1, ..., nsizes ,

SPM j = 1, ..., nsizes

(1)

SPM 2 Where nTiO sizes and nsizes are the total number of TiO2 and SPM size classes, respectively. There are, to our knowledge, no measurements of αhet‑agg for the heteroaggregation of NPs and SPM available in the literature. αhet‑agg represents the probability that two colliding particles stick to each other and is always between 0 and 1. αhet‑agg depends on the surface properties of the colliding particles, which are influenced by the nature of the particles as well as the characteristics of the surrounding medium, such as pH, ion concentration, and the presence of NOM. By evaluating different values of αhet‑agg between 0.001 and 1 in different model runs, we cover the effect of a wide range of parameters on the surface properties of the TiO2 NPs and the SPM and are able to elucidate the influence and importance of this parameter on the overall fate and transport of TiO2 NPs in the Rhine River. The main transport mechanisms leading to collision of the particles are Brownian motion (perikinetic aggregation), fluid motion (orthokinetic aggregation), and differential settling:27

kcoll, ij =

2 2kBTwater (rTiO2, i + rSPM, j) 4 + G(rTiO2, i + rSPM, j)3 3μwater rTiO2, i·rSPM, j 3

TiO2 , i SPM, j + π (rTiO2, i + rSPM, j)2 ·| vset − vset |

for

TiO2 i = 1, ..., nsizes ,

SPM j = 1, ..., nsizes

(2)

where kB is the Boltzmann constant, Twater is the absolute temperature of the water, μwater is the dynamic viscosity of water, rTiO2,i and rSPM,j are the radii of the TiO2 NPs and SPM in size clases i and j, respectively, G is the shear rate of the water, 2,i and vTiO and vSPM,j are the settling velocities of TiO2 NPs and set set SPM, respectively. Since kcoll,ij depends on the particle size, it was calculated individually for all 25 combinations of a size class of TiO2 NPs (i) and SPM (j). Both the free TiO2 NPs as well as the TiO2 NPs attached to SPM settle from the water column to the sediment compartment. The settling velocity, vparticle (where “particle” can be set either TiO2 or SPM), is calculated for each TiO2 NP and SPM size class from Stokes’ law:27 particle = vset

2 ρparticle − ρwater 2 ·g ·rparticle μwater 9

RESULTS

Figure 3 shows the concentration of the TiO2 NPs as a function of the distance from the source for different conditions (always at steady-state). The concentration of free TiO2 NPs in the moving water compartment of the Rhine River exponentially decreases along the river from the point of emission (0 km) to the end of the section of the river studied (700 km) (Figure 3A,D). Simultaneously, the concentration of TiO2 NPs bound to SPM in the moving water rapidly increases to reach a maximum and then decreases exponentially toward the end of the river (Figure 3B,E). TiO2 NPs deposit with the SPM to the sediment, which leads to an increase of TiO2 NP concentration in the sediment (Figure 3C,F). In all simulations the concentration of TiO2 NPs in the sediment is several orders of magnitudes higher than in the moving water (both in the free form as well as bound to SPM), indicating the high potential of the sediment compartment to act as a reservoir for nanoparticles released to aqueous environments. The shape of the TiO2 NP concentration curves differ strongly depending on both the heteroaggregation attachment efficiency (αhet‑agg) and the characteristics of the SPM in the Rhine River, such as their density and concentration. An increase in α het‑agg leads to a linear increase in the heteroaggregation rate constant and thereby to a more efficient removal of free TiO2 NPs from the water column (Figure 3A). Simultaneously, at higher αhet‑agg values the concentration of TiO2 NPs attached to SPM in the water compartment increases and the concentration peak becomes narrower (Figure 3B). A similar trend is observed in the TiO2 NP concentration in the sediment compartment, where in all cases the peak TiO2 concentration is shifted away from the source due to the horizontal bed load transport of the sediment (Figure 3C). Increasing the SPM concentration, CSPM mass , also leads to a linear increase of the heteroaggregation rate constant and thereby to the same effects as an increase in αhet‑agg but with a less pronounced effect in the range of realistic concentrations for the Rhine River (30−90 mg L−1) (see Figure S3 in the Supporting Information). The importance of the SPM characteristics on the fate of the TiO2 NPs is illustrated by varying the density of the SPM, ρSPM (Figure 3D−F). At a fixed mass concentration of SPM, a lower ρSPM results in a higher SPM particle concentration and a lower settling velocity of the SPM. The heteroaggregation rate is decreased at lower ρSPM, because the contribution from differential settling is reduced and outweighs the increased collision frequency due to the higher SPM particle concentration. This effect is reflected by a slower removal of free TiO2 NPs from the water column (dark blue line in Figure 3D). At the same time, the reduced settling velocity at lower ρSPM values results in a slower removal of TiO2 NPs bound to SPM from the moving water compartment (Figure 3E) and a reduced accumulation of TiO2 NPs in the sediment compartment (Figure 3F). This means that when SPM with a small ρSPM is present in a given aqueous system, TiO2 NPs can potentially be transported with the SPM in the water column over long distances away from the emission source. The analysis of the contribution of the αhet‑agg, CSPM mass , and ρSPM parameters on the fate and behavior of TiO2 NPs in the Rhine River enables an assessment of extreme scenarios. In the case of large αhet‑agg, CSPM mass , and ρSPM values, the TiO2 NPs are very quickly removed from the water body, both in the free and SPM-bound form, and travel only about 50 km away from the

SPM, j k het ‐ agg, ij = αhet ‐ agg·kcoll, ij·Cparticle

for

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(3)

where ρparticle is the density of the TiO2 aggregates or the SPM, g is the gravitational acceleration on earth, and rparticle is the radius of the particle in the given TiO2 or SPM size class. The TiO2 NPs that attach to the SPM through heteroaggregation are assumed to settle at the same speed as the SPM. −1 SPM 2 The sedimentation rate constants, kTiO sed and ksed (in s ), are SPM 2 then obtained by dividing vTiO and v by the depth of the set set corresponding water compartment (hw1 and hw2). All model parameters and equations are described in detail in the Supporting Information. 6710



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Figure 4. Extreme scenario 1: high αhet‑agg, high ρSPM, and CSPM mass yield effective transfer into the sediment (green line). Extreme scenario 2: small αhet‑agg, small ρSPM, and CSPM mass yield slow TiO2 removal from the water column (red line).

both the ENPs and the SPM. Different possible surface coatings of the ENPs, for example, are thereby represented, as well as different types of SPM and a range of different water chemistries (pH, salt, and NOM concentrations), which also affect αhet‑agg. In addition, the challenge of parametrizing the complex nature of SPM in a freshwater system was approached by studying the influence of individual parameters of the SPM on the overall fate and transport behavior of the TiO2 NPs. The effects of varying the SPM density, ρSPM, demonstrate that the type of SPM present in a given aqueous system strongly influences the transport of the ENPs by affecting the heteroaggregation of ENPs with SPM and the sedimentation velocity of the heteroaggregate. The large range of possible SPM sizes in a turbulent river system was reflected by representing the SPM as a log-normal particle size distribution covering a range of 1.5−80 μm. The SPM concentration, CSPM mass , was varied within realistic ranges derived from monitoring data by the German Federal SPM Institute of Hydrology.36 The chosen Cmass ranges are representative of the global situation in the Rhine River but might not account for local SPM “hot-spots”, where a locally increased CSPM mass might lead to a faster removal of ENPs by heteroaggregation and sedimentation. Although water parameters (flow velocity, pH, salt and NOM concentration, ρSPM, and CSPM mass ) are variable along the course of the river, we chose to use uniform conditions throughout the model for a first conceptual demonstration. A more detailed parametrization does not lead to fundamental differences in the results but would yield less regular concentration curves. Once other parameters, in particular αhet‑agg, are better defined, it will be possible to derive more accurate local PEC values for TiO2 NPs along the Rhine River. In a future modeling study it will make sense to define the water parameters for each river segment as specifically as possible and also include TiO2 NP input from other wastewater treatment plants along the river. Such detailed modeling results can be used in risk assessment as well as for attempts at “safer by design” nanoparticles. An important advantage of our new environmental fate model for ENPs is the possibility to adjust it to study and predict the fate and transport behavior of ENPs in many different cases. Other ENPs can be modeled and more specific processes, such as dissolution or surface transformation, can be incorporated by using first-order rate constants of the relevant processes. The environmental and geographical parameters of the model can be modified to represent entirely different

source before being completely deposited in the sediment compartment (Figure 4, green line). In this scenario, the total flow of TiO2 NPs out of the last box of the model (700 km) is only 2.4 × 10−4 kg day−1; virtually all TiO2 NPs have been removed from the moving water. On the other hand, when all three parameters are very low, the TiO2 NPs stay in their free form in the water compartment for a longer time and are still present 700 km away from the source (Figure 4, red line). The total flow of TiO2 NPs out of the last box of the model is 0.36 kg day−1, which represents 92% of the input flow of 0.39 kg day−1 into the first box. The sediment compartment remains the major reservoir also in this case but presents a TiO2 concentration almost 2 orders of magnitude lower than in the previous case.

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DISCUSSION

Our environmental fate model for ENPs demonstrates that it is possible to adjust conventional multimedia fate models for organic pollutants to account for the specific properties of ENPs. Our results from a river model study indicate that, in certain cases, ENPs emitted to a freshwater system can be removed quickly from the water compartment by heteroaggregation and sedimentation and remain relatively close to their emission source. On the other hand, it is also possible for ENPs to be transported hundreds of kilometers away from their source, either in free form or attached to SPM. In order to minimize numerical dispersion,35 the model boxes in the first 100 km of the river were kept very small, meaning that the transport observed in our results is not a model artifact. This implies that the mobility of NPs in freshwater systems should not be underestimated, as fast removal by sedimentation cannot be expected in all cases. Our estimated TiO2 NP concentrations lie in the ng/L (108 particles m−3) range in the water compartment and in the mg/kg (1013 particles m−3) range in the sediment. The sediment concentrations exceed measured concentrations of persistent organic pollutants, such as polybrominated diphenyl ethers (PBDEs) and polychlorinated biphenyls (PCBs), which were detected in lake sediments in μg/kg ranges.40 Despite the important assumptions and simplifications made in this modeling study, our results are representative for a large range of realistic cases. The lack of experimental data on a central process, the heteroaggregation, was compensated for by varying the heteroaggregation attachment efficiency, αhet‑agg, within a realistic range (0.001−1). The variation in αhet‑agg accounts for numerous combinations of surface chemistries of 6711



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aqueous systems, such as lakes or estuaries. Furthermore, the model can be solved in a time-resolved manner to take into account variable emissions and environmental parameters and their effect on the fate and transport of ENPs.

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ASSOCIATED CONTENT

S Supporting Information *

Additional information on the dimensions of the river model and the Rhine water chemistry, a detailed description of the river model, a list of all parameters, and modeling results with varying SPM concentration. This material is available free of charge via the Internet at http://pubs-acs.org

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Gudrun Hillebrand from the Bundesanstalt für Gewässerkunde (German Federal Institute of Hydrology) for data on suspended sediments in the Rhine River. Funding by the Swiss National Science Foundation (NRP 64) is gratefully acknowledged.

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REFERENCES

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