Transport and Retention of Nanoscale C60 Aggregates in Water

Apr 11, 2008 - School of Civil and Environmental Engineering, Georgia Institute of ... Aqueous suspensions of nC60 aggregates (95 nm diameter, 1 to 3 ...
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Environ. Sci. Technol. 2008, 42, 3588–3594

Transport and Retention of Nanoscale C60 Aggregates in Water-Saturated Porous Media YONGGANG WANG,† YUSONG LI,‡ JOHN D. FORTNER,† JOSEPH B. HUGHES,† LINDA M. ABRIOLA,‡ AND K U R T D . P E N N E L L * ,†,§ School of Civil and Environmental Engineering, Georgia Institute of Technology, 311 Ferst Drive, Atlanta, Georgia 30332-0512, Department of Civil and Environmental Engineering, Tufts University, 200 College Avenue, Medford, Massachusetts 02155, and Department of Neurology, Emory University School of Medicine, 615 Michael Street, Atlanta, Georgia 30322

Received January 14, 2008. Revised manuscript received February 28, 2008. Accepted February 29, 2008.

Experimental and mathematical modeling studies were performed to investigate the transport and retention of nanoscale fullerene aggregates (nC60) in water-saturated porous media. Aqueous suspensions of nC60 aggregates (95 nm diameter, 1 to 3 mg/L) were introduced into columns packed with either glass beads or Ottawa sand at a Darcy velocity of 2.8 m/d. In the presence of 1.0 mM CaCl2, nC60 effluent breakthrough curves (BTCs) gradually increased to a maximum value and then declined sharply upon reintroduction of nC60-free solution. Retention of nC60 in glass bead columns ranged from 8 to 49% of the introduced mass, while up to 77% of the mass was retained in Ottawa sand columns. When nC60 suspensions were prepared in deionized water alone, effluent nC60 BTCs coincided with those of a nonreactive tracer (Br-), with minimal nC60 retention. Observed differences in nC60 transport and retention behavior in glass beads and Ottawa sand were consistent with independent batch retention data and theoretical calculations of electrostatic interactions between nC60 and the solid surfaces. Effluent concentration and retention profile data were accurately simulated using a numerical model that accounted for nC60 attachment kinetics and a limiting retention capacity.

Introduction Commercial production and use of fullerenes, including C60, is expected to increase dramatically over the next several decades (1, 2) and will inevitably lead to their release into the environment during manufacture, transport, application, and disposal. A number of studies have investigated the potential human health effects, aquatic toxicity, and antimicrobial properties of C60 fullerenes (3–6). Exposure of juvenile largemouth bass to an aqueous suspension of nanoscale fullerene aggregates (nC60) (0.5 mg/L) for 48 h resulted in lipid peroxidation and depletion of * Corresponding author phone: 404-894-9365; fax: 404-894-8266; e-mail: [email protected]. † Georgia Institute of Technology. ‡ Tufts University. § Emory University School of Medicine. 3588

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glutathione, a free radical scavenger (7). Similarly, Sayes et al. (8) reported that nC60 suspensions were cytotoxic toward three human cell lines at concentrations greater than 50 µg/L, which was attributed to lipid peroxidation resulting from the formation of reactive oxygen species. In contrast, far less attention has been directed toward understanding the mechanisms governing the behavior of C60 fullerenes in the environment, a critical component of risk assessment, life-cycle analysis and waste management. Although the inherent aqueous solubility of C60 in water is extremely low (18.0 MΩ/cm, Nanopure Model D4741, Barnstead International, Dubuque, IA) was added to the stirred C60saturated THF solution at a rate of 1 L/min. The combined suspension (500 mL) was transferred to a rotary evaporator (Rotovapor Model R210, Buchi, New Castle, DE) at 75° to remove THF, vacuum filtered through a 0.22 µm cellulose acetate membrane (Corning Inc., Corning, NY) into a clean, sterile 250 mL media bottle, and stored in the dark. The resulting aqueous suspension contained ca. 6.5 mg/L of nC60 aggregates with a mean diameter of 95 nm as determined by dynamic light scattering (Zetasizer Nano ZS, Malvern Instruments Ltd., Southborough, MA) (Figure S1, Supporting Information). nC60 suspensions were prepared in DI water containing 1.0 mM CaCl2 buffered to pH 7 with 0.065 mM NaHCO3 or DI water alone. The residual concentration of THF in a representative aqueous suspension was determined to be 0.12 mg/L using gas chromatography–mass spectrometry (GC-MS), with no detectable levels of γ-butyrolactone (GBL), which has been reported in THF-prepared nC60 suspensions (24). The concentration of nC60 in aqueous suspensions was determined using a Cary 3E UV–vis spectrophotometer (Varian Inc., Palo Alto, CA) at a wavelength of 344 ( 1 nm. The electrophoretic mobility of nC60 particles, measured using a ZetaPlus analyzer (Brookhaven Instruments Corp., Holtesville, NY), was converted to a ζ potential using the Henry equation. Details of the nC60 aggregate size, concentration, and ζ potential measurements are provided in the Supporting Information. Column Studies. A total of eight column experiments were conducted to measure the transport and retention of nC60 aggregates in water-saturated columns containing either glass beads or Ottawa sand. The column apparatus consisted of a Dynamax SD-200 pump (Varian Inc., Palo Alto, CA) equipped with a 25 mL pump head and pulse

TABLE 1. Experimental Conditions of nC60 Transport Studies Conducted in Water-Saturated Glass Columns Packed with Either 40–50 Mesh Glass Beads (GB) or Ottawa Sand (OS) column PVa (mL) GB-1 GB-2 GB-3 GB-4 OS-1 OS-2 OS-3 OS-4

28.0 28.0 28.0 28.0 26.5 27.2 27.2 25.8

θwb 0.38 0.38 0.38 0.38 0.36 0.37 0.37 0.35

C0c (mg/L) PWd (pv) ISe (mM) MBf (%) 2.44 1.34 1.34 3.06 2.33 2.25 1.34 2.31

3.0 3.0 3.0 3.0 3.0 4.56 3.0 3.45

3.065 3.065 3.065 0.0 3.065 3.065 3.065 0.0

95.8 100.5 94.6 100.6 98.4 97.6 102.2 100.2

a Aqueous phase pore volume. b Volumetric water content. Influent nC60 concentration. d Pulse width expressed in dimensionless pore volumes. e Ionic strength. f Mass balance of nC60. c

dampener, a Model 22 syringe pump (Harvard Apparatus, Inc., Holliston, MA), and a Retriever II fraction collector (Teledyne Isco Inc., Lincoln, NE) (Figure S3, Supporting Information). Borosolicate glass columns (15 cm length × 2.5 cm i.d.; Kontes, Vineland, NJ) were packed in 1 cm increments with the 40–50 mesh size fraction (d50 ) 0.36 mm) of either spherical glass beads (International Surface Preparation, Bellaire, TX) or F-42 Ottawa sand (U.S. Silica, Berkeley Springs, WV). Prior to use, the glass beads and Ottawa sand were thoroughly cleaned using a sequential acid wash, water rinse, and oven-drying procedure (see Supporting Information). The column end plates were fitted with two 40-mesh nylon screens and a 70 µm nylon filter (Spectrum Laboratories Inc., Rancho Dominguez, CA). To facilitate dissolution of entrapped gas, the packed columns were flushed with CO2 gas for at least 15 min prior to water imbibition. Deaired DI water containing 1.0 mM CaCl2 and 0.065 mM NaHCO3 was introduced into the column in an upflow mode at a Darcy velocity of 2.8 m/d. After complete saturation of the column with water (∼10 PV), a pulse (3 or 5 PV) of nC60 suspension (1.3 to 3.1 mg/L; 2.05 × 109 to 4.90 × 109 aggregates/mL) was introduced into the column with the syringe pump, which was followed by the injection of three pore volumes of C60-free solution at the same flow rate. This flow rate corresponds to a porewater velocity of 7.37 m/d, which yields a column residence time of approximately 0.5 h. The Reynolds number (Re) was equal to 0.011, which is several orders-of-magnitude below the limit of laminar flow in packed beds (Re < 1–10). Column effluent was collected continuously in 15 mL sterile plastic centrifuge tubes (Fisher Scientific, Fair Lawn, NJ) and analyzed for nC60 content by UV spectroscopy. At the conclusion of each transport experiment, the column was dissected into 1.5 cm increments, and retained nC60 aggregates were extracted by addition of 10 mL of DI water, agitated for 3 h (Labquake, Barnstead International, Dubuque, IA), followed by ultrasonication for 1 min. The concentration of nC60 particles in the supernatant was measured by UV spectroscopy, and the sample was then oven-dried at 105 ° for 8 h to obtain the dry weight of solid. Experimental conditions for the eight column studies are summarized in Table 1. Prior to nC60 injection a nonreactive tracer test was conducted to assess water flow and hydrodynamic dispersion in the columns. Three PV (ca. 85 mL) of 1.0 mM CaBr2 solution buffered to pH 7 with 0.065 mM NaHCO3 were introduced at a Darcy velocity of 2.8 m/d, followed by three PV of 1.0 mM CaCl2 and 0.065 mM NaHCO3 at the same flow rate. Effluent samples were collected continuously, and bromide concentrations were measured using an ion selective bromide electrode (Cole-Parmer Instrument Co., Vernon Hills, IL) connected to an Accumet Model VOL. 42, NO. 10, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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50 pH meter (Fisher Scientific, Fair Lawn, NJ). The resulting nonreactive tracer breakthrough curves (BTCs) were fit to the one-dimensional (1D) form of the advective-dispersive reactive (ADR) transport equation using the CXTFIT ver 2.0 (25) (see Supporting Information). Batch Retention. Batch reactor experiments were performed in 30 mL borosilicate glass vials (VWR International, Westchester, PA) to assess the attachment characteristics of nC60 particles following the method of Bradford et al. (26). Approximately 13 g of dry Ottawa sand or glass beads were combined with 13 mL of nC60 suspension at initial concentrations of ranging from 0.08 to 12.78 mg/L, prepared in DI water or 1.0 mM CaCl2 buffered to pH 7 with 0.065 mM NaHCO3. The contents of the batch reactors were mixed on an oscillating shaker for 3 h, and the concentration of nC60 in the supernatant was measured by UV spectroscopy. Mathematical Modeling. The transport and retention of nC60 aggregates was modeled using a modified version of the traditional 1D ADR transport equation: ∂2C ∂C ∂C Fb ∂S + ) D H 2 - vp ∂t θw ∂t ∂x ∂x

(2)

where, C is the concentration of nC60 in solution, S is the concentration of nC60 associated with the solid phase, t is time, x is the distance parallel to flow, Fb is the soil bulk density, and DH is the hydrodynamic dispersion coefficient. The kinetics of nC60 aggregate attachment was expressed as (27)follows: Fb ∂S Fb ) kattψC - kdetS θw ∂t θw

(3)

where katt is the rate of nC60 attachment, kdet is the rate of nC60 detachment, and ψ is related to the maximum nC60 retention capacity Smax by the following (28): ψ)

Smax - S Smax

(4)

When Smax is much larger than S, eq 4 reduces to unity and eq 3 will converge to the clean-bed filtration model (see Supporting Information). The rate of nC60 attachment katt can be expressed as follows (21): katt )

3(1 - θw)vp Rη0 2dc

(5)

where the collision efficiency factor (R) represents the fraction of nC60 that remain attached after collision and the single collector efficiency (η0) represents the frequency of nC60 collisions with the porous medium grain surfaces, which can be calculated using the following correlation (29): -0.715 0.052 η0 ) 2.4As1/3NR-0.081NPe Nvdw + 0.55AsNR1.675NA0.125 + 0.053 (6) 0.22NR-0.24NG1.11Nvdw

where As is the Happel correction factor, NR is the interception number, NPe is the Peclet number, Nvdw is the London-van der Waals attractive forces number, NA is the attraction number, and NG is the gravitational number. The three terms in eq 6 represent the contributions of diffusion, interception, and sedimentation processes, respectively, to particle collision. A modified version of the HYDRUS-1D model (23) was used to solve eqs 2-5.

Results and Discussion Transport and Deposition of nC60. Effluent BTCs for nC60 aggregate transport through water-saturated columns packed with either 40–50 mesh glass beads or Ottawa sand are shown in parts A and B, respectively, of Figure 1. Pulse 3590

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injections (3 or 5 PV) of the nC60 suspensions containing 1.0 mM CaCl2 as a background electrolyte yielded asymmetrical BTCs that gradually increased to a maximum value before declining sharply to relative concentrations (C/C0) approaching zero. For the glass bead columns, nC60 appeared in the column effluent after injecting ca. 1.1 PV of suspension, while in columns packed with Ottawa sand nC60 breakthrough occurred at ca. 1.8 PV. These data indicate that Ottawa sand had a greater capacity to retain nC60 aggregates relative to glass beads of the same size. During the initial breakthrough period, the area above the nC60 BTC (i.e., the region between the measured data points and a relative concentration (C/C0) of 1.0) corresponds to the mass of nC60 particles retained by the solid phase. Under ideal conditions (i.e., reversible, equilibrium) this retained mass would be eluted from the column upon the reintroduction of nC60-free water and would appear in the BTC as gradual decline in effluent concentration. However, the sharp reduction in relative concentration observed in the distal portion of the BTCs indicates that retained nC60 aggregates were not released from the solid phase and that the detachment coefficient (kdet) in eq 2 approaches zero under these experimental conditions. Such irreversible attachment is consistent with the findings of Chen and Elimelech (30) who reported that nC60 aggregates deposited on a silica-coated quartz surface in a 0.6 mM CaCl2 solution at pH 5.2 were not released until the rinse solution contained DI water adjusted to pH 12.3. For comparison purposes, representative BTCs obtained for 3 PV pulse injections of nonreactive tracer (Br-) are shown as dotted lines in Figure 1A,B. As anticipated, the fitted retardation factors (RF) for all of the tracer studies were equal to 1.0 ( 0.02, while the Peclet numbers (NPe) for the glass bead and Ottawa sand columns were approximately 230 and 180, respectively (see Supporting Information). The Peclet numbers correspond to hydrodynamic dispersivity values (R ) DH/νP) of 0.065 and 0.084 cm, respectively, which are consistent with the relatively small values of RD reported for laboratory-scale columns packed with uniform sand (31). Additionally, the symmetrical shape and absence of tailing in the nonreactive tracer BTCs indicate that physical nonequilibrium processes, such as rate-limited mass transfer into regions of immobile water and preferential flow paths, did not contribute to retention of nC60 aggregates or the observed asymmetry in the nC60 BTCs (Figure S4, Supporting Information). A nearly 2-fold increase (1.34 to 2.44 mg/L) in the concentration of nC60 injected into the glass bead columns (exp. GB-1) resulted in a steeper rise to a maximum relative concentration. At the lower concentration of 1.34 mg/L, the maximum or plateau concentration was not achieved after injecting 3 PV of nC60 suspension (exps. GB-2 and GB-3). However, the distal portion of the BTCs exhibited an identical shape irrespective of input concentration, suggesting that the capacity of the solid phase to retain nC60 had not been exceeded. For the Ottawa sand columns, increasing the input concentration did not yield a discernible change in the shape of the nC60 BTCs. At the higher input concentration of 2.44 mg/L, a 5 PV pulse of nC60 was required to reach a maximum relative effluent concentration of ca. 0.85 (exp. OS-2). The larger applied volume of nC60 (5 PV vs 3 PV) required to reach a maximum effluent concentration indicates that Ottawa sand possesses a greater capacity to retain nC60 aggregates relative to glass beads, which is consistent with the delayed nC60 breakthrough observed in the Ottawa sand columns. Electrostatic Interactions. Interaction energies between nC60 aggregates and the solid surface in 1.0 mM CaCl2 were calculated based on the Derjaguin-Landau-VerweyOverbeek (DLVO) theory (32). A Hamaker constant of 4.71

FIGURE 1. Measured and simulated nC60 breakthrough curves (A and B) and retention profiles (C and D) in water-saturated columns packed with either 40–50 mesh glass beads (open symbols) or Ottawa sand (solid symbols), respectively. Aqueous nC60 suspensions contained 1.0 mM CaCl2, buffered to pH 7 with 0.065 M NaHCO3, applied at a Darcy velocity of 2.8 m/d. × 10-21 J was estimated based on a C60-C60 Hamaker number of 7.5 × 10-20 (30), while ζ potentials of -55 mV (33), -30 mV (34), and -23.9 mV were used for glass beads, Ottawa sand, and nC60 aggregates, respectively. The resulting DLVO energy profiles indicate that a sizable repulsive energy barrier of ca. 42.3 kT and 29.5 kT existed between nC60 aggregates and glass beads and Ottawa sand, respectively (Figure S6, Supporting Information), consistent with the lower nC60 retention observed in the glass bead columns. The large primary electrostatic energy barrier should, in theory, prevent deposition of nC60 aggregates. A small secondary minimum attractive region was calculated for both Ottawa sand and glass beads, with depths of -0.04 kT and -0.03 kT at 43.3 and 48.1 nm from surface, respectively, which may have contributed to nC60 deposition. In addition, differences in surface roughness and mineral structure, which are not accounted for in DLVO theory, may have contributed to the greater nC60 retention observed in Ottawa sand columns. Two additional column experiments (GB-4 and OS-4) were performed with DI water alone (i.e., no background electrolyte or pH buffer) to further investigate the role of electrostatic interactions in nC60 aggregate retention. The resulting nC60 effluent BTCs obtained at a Darcy velocity of 2.8 m/d are shown in Figure 2. In contrast to the column experiments conducted at an ionic strength of 3.065 mM, nC60 effluent BTCs for both the glass bead and Ottawa sand columns coincided with nonreactive tracer (Br-), indicating that there was minimal retention of nC60

aggregates by the solid phases. Subsequent column extraction revealed that no measurable amounts of nC60 were retained by the glass beads, while less than 5% of the injected mass was recovered from the Ottawa sand column (Figure 2C,D). The observed enhancement in nC60 transport coincided with the larger absolute value of the ζ potential in DI water alone (-64.0 ( 2.0 mV) compared to that in 1.0 mM CaCl2 (-23.9 ( 3.1 mV). These data are consistent with the reported increase in nC60 aggregate mobility when the ionic strength was reduced from 100 mM NaCl to 1 mM (18), and they further support the importance of electrostatic interactions in nC60 retention. Retention of nC60. Immediately following each transport experiment, the columns were sectioned into ten 1.5 cm increments and nC60 aggregates were extracted from the solid phase by sonication in DI water. The resulting nC60 retention profiles for the glass bead and Ottawa sand columns are plotted in parts C and D, respectively, of Figure 1, where a distance of 0 cm corresponds to the column inlet. Overall mass balance recoveries were computed from the ratio of the nC60 mass injected and the sum of the mass recovered from the column effluent and solid phase extraction, and they ranged from 95 to 102%. For the glass bead columns, nC60 aggregate retention decreased with distance from the column inlet. In contrast, the retention of nC60 in the Ottawa sand columns was relatively uniform over the entire length of the column, and it was similar in magnitude regardless of the input concentration (Table 1). The relatively constant VOL. 42, NO. 10, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 2. Measured and simulated nC60 breakthrough curves (A and B) and retention profiles (C and D) in water-saturated columns packed with either 40–50 mesh glass beads (open symbols) or Ottawa sand (solid symbols), respectively. Aqueous nC60 suspensions were prepared in DI water and were applied at a Darcy velocity of 2.8 m/d. deposition profile in the Ottawa sand columns suggests that nC60 deposition approached a limiting capacity. To independently assess nC60 retention behavior, batch reactor experiments were conducted in which aqueous suspensions of nC60 were gently mixed with Ottawa sand and glass beads for a period of 3 h. In the presence of 1.0 mM CaCl2, Ottawa sand exhibited the greatest retention capacity, approaching 4 µg/g at an nC60 concentration of ca. 9.0 mg/L (Figure S7, Supporting Information). When DI water alone was used as the aqueous phase, retention of nC60 by Ottawa sand decreased substantially, yielding a solid phase concentration of 0.07 µg/g, consistent with the trends in observed in column experiment OS-4 (Figure 2D). As was anticipated from the column results, batch retention of nC60 by glass beads was considerably less than that measured for Ottawa sand. In the presence of 1.0 mM CaCl2, nC60 retention by glass beads approached a maximum value of ca. 0.9 µg/g. In DI water alone, nC60 retention by glass beads was negligible, consistent with the retention profile observed in column experiment GB-4 (Figure 2C). Mathematical Modeling. The mathematical model successfully captured the gradual increase and sharp decline of the nC60 BTCs observed with columns packed with either 40–50 mesh glass beads or Ottawa sand in the presence of 1.0 mM CaCl2 (Figure 1A,B). Soil bulk density (Fb) and volumetric water content (θw) were determined indepen3592

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dently from physical measurements of the column, while the hydrodynamic dispersion coefficient (DH) was obtained from the nonreactive tracer BTCs. On the basis of preliminary simulations, the particle detachment rate coefficient (kdet) was found to be negligible (ca. 1 × 10-4 1/h), consistent with the sharp reduction in effluent nC60 concentrations upon reintroduction of the nC60 free solution. These findings indicate that upon retention by the solid phase, nC60 particles are not subsequently released under constant flow and background electrolyte conditions. Thus, only two parameters, the particle attachment rate (katt) and retention capacity (Smax), were obtained by an optimization procedure that minimized the difference between the simulated and measured effluent concentration data (23). In the presence of 1.0 mM CaCl2, values of katt for the glass bead and Ottawa sand columns ranged from 3.6 to 4.4 1/h and from 7.3 to 9.2 1/h, respectively. The larger values of katt and Smax obtained for Ottawa sand relative to glass beads are consistent with the nearly 2-fold later breakthrough of nC60 particles observed in the column effluent (Figure 1A,B) and the greater retention capacity of Ottawa sand obtained in batch experiments. Collision efficiency factors (R) were calculated using eq 5 based on the measured values of katt, known column parameters (i.e., dc, vp, and θw), and the single collector efficiency (η0) calculated using eq 6. The resulting collision efficiency factors ranged from 0.066 to 0.079 for glass beads

TABLE 2. Simulation Parameters Used To Fit nC60 Breakthrough Curves in Water-Saturated Columns Packed with Either 40–50 Mesh Glass Beads (GB) or Ottawa Sand (OS) column

measured retention (%)

simulated retention (%)

measured Sma (µg/g)

simulated Smax (µg/g)

kattb (1/h)

rc

η0d

GB-1 GB-2 GB-3 GB-4 OS-1 OS-2 OS-3 OS-4

8.6 33.8 48.9 0.0 77.0 48.1 59.7 4.8

13.1 35.1 43.7 0.018 72.5 46.3 55.4 4.67

0.83 0.80 0.80 6.6 × 10-3 2.02 1.98 1.57 0.07

0.247 0.353 0.564 4.0 × 10-4 1.313 1.13 0.561 4.97 × 104

3.52 3.63 4.41 0.09 9.19 7.23 7.27 0.11

0.066 0.066 0.079 5.0 × 10-4 0.153 0.122 0.128 5.7 × 10-3

0.061 0.060 0.060 0.060 0.059 0.060 0.060 0.058

a Estimated retention capacity based on batch experiments. collector efficiency.

and from 0.122 to 0.153 for Ottawa sand (Table 2), which are in close agreement with the value of 0.05 reported in ref 19 for a continuous injection of THF-prepared nC60 aggregates (92 nm dia.) in columns packed with 40–50 mesh glass beads at an ionic strength of 5 mM (NaCl). Collision efficiency factors of less than 1 are considered to be unfavorable, indicating a net repulsive force between the nC60 aggregates and the solid surface. The 2-fold smaller collision efficiency factors obtained for glass beads compared to Ottawa sand are consistent with the nC60 transport and retention behavior observed in the column experiments. Calculated values of the single collector efficiency (η0) were ca. 0.06 for all column experiments (Table 2). The first term in eq 6 accounted for 99.9% of the calculated η0 value, suggesting that diffusion was the dominant mechanism governing the nC60 aggregate collisions with the porous media. The values of Smax obtained from model simulations ranged from 0.56 to 1.31 µg/g for Ottawa sand and from 0.25 to 0.56 µg/g for glass beads, and they are in general agreement with values estimated from the batch retention experiments (Table 2). Using the Smax value of 1.13 µg/g obtained in column experiment OS2, the fractional surface coverage (θs) is 1.9 × 10-3, based on the theoretical specific surface area of Ottawa sand (6.4 × 10-3 m2/g) and the nC60 aggregate diameter (100 nm). The fractional collector surface coverage can also be estimated from the effluent BTC (35) t

πr2arcqN0 θs )

∫ (1 - N/N )dt 0

0

3L(1 - θw)

(7)

where ra is the radius of the aggregate, rc is the radius of the collector or porous medium, q is the Darcy velocity, N0 is the influent particle concentration, and N is the effluent particle concentration. For column experiment OS2, the fractional surface coverage obtained from eq 7 is 2.4 × 10-3. Thus, Smax represents a maximum retention capacity, rather than monolayer coverage, which is very small due to the repulsive force between nC60 aggregates at low ionic strength. While the numerical model captured the relatively constant nC60 retention profiles obtained for Ottawa sand, simulated nC60 retention profiles for the glass bead columns failed to mimic the observed retention, which was greatest near the column inlet and approached zero at the column outlet (Figure 1C). Use of a classical clean-bed filtration model to simulate nC60 transport and retention in the glass bead columns yielded relatively poor fits to the effluent BTC data and provided only minimal improvements in predictions of nC60 retention near the column inlet (Figure S8, Supporting Information). Thus, the elevated retention of nC60 in the glass bead columns may have been due to

b

Attachment rate.

c

Collision efficiency factor.

d

Single

nC60 interactions with previously deposited aggregates near the column inlet, which were not considered in the models employed herein. In presence of water alone, nC60 aggregate transport and retention in glass beads and Ottawa sand was accurately captured by the numerical model (Figure 2). Simulated katt values were 0.09 and 0.11 1/h for glass beads and Ottawa sand, respectively, which yielded extremely small collision efficiency factors, consistent with a strong net repulsive force between the solid surface and nC60 aggregates under these conditions. Taken in concert, the experimental and mathematical modeling studies demonstrate the importance of electrostatic interactions in nC60 aggregate transport and deposition in water-saturated porous media as well as demonstrate the existence of a maximum or limiting nC60 retention capacity in an aquifer sand.

Supporting Information Available Detailed descriptions of additional experimental methods, nonreactive tracer tests, size of eluted aggregates, and cleanbed filtration modeling results are included as Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgments We thank Dr. Susan Burns and Dr. Nils Kroeger for use of their Brookhaven ZetaPlus and Malvern Zetasizer instruments, respectively, Dr. Jed Costanza for performing GC-MS analysis of THF and GBL, and Dr. Menachem (Meny) Elimelech for his helpful suggestions. This research has been supported by grant RD-832535 from the U.S. Environmental Protection Agency’s Science to Achieve Results (STAR) program. The work has not been subject to EPA review, and therefore, does not necessarily reflect the views of the Agency and no official endorsement should be inferred.

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