Attachment Efficiency of Nanoparticle Aggregation in Aqueous

Jan 18, 2012 - The new equation was employed to evaluate experimentally obtained attachment efficiencies to validate its applicability in describing t...
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Attachment Efficiency of Nanoparticle Aggregation in Aqueous Dispersions: Modeling and Experimental Validation Wen Zhang,† John Crittenden,†,‡ Kungang Li,† and Yongsheng Chen*,† †

School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States Brook Byers Institute for Sustainable Systems at Georgia Institute of Technology, 800 West Peachtree Street NW, Atlanta, Georgia 30332, United States

‡

S Supporting Information *

ABSTRACT: To describe the aggregation kinetics of nanoparticles (NPs) in aqueous dispersions, a new equation for predicting the attachment efficiency is presented. The rationale is that at nanoscale, random kinetic motion may supersede the role of interaction energy in governing the aggregation kinetics of NPs, and aggregation could occur exclusively among the fraction of NPs with the minimum kinetic energy that exceeds the interaction energy barrier (Eb). To justify this rationale, we examined the evolution of particle size distribution (PSD) and frequency distribution during aggregation, and further derived the new equation of attachment efficiency on the basis of the Maxwell−Boltzmann distribution and Derjaguin−Landau−Verwey−Overbeek (DLVO) theory. The new equation was evaluated through aggregation experiments with CeO2 NPs using time-resolved-dynamic light scattering (TR-DLS). Our results show that the prediction of the attachment efficiencies agreed remarkably well with experimental data and also correctly described the effects of ionic strength, natural organic matter (NOM), and temperature on attachment efficiency. Furthermore, the new equation was used to describe the attachment efficiencies of different types of engineered NPs selected from the literature and most of the fits showed good agreement with the inverse stability ratios (1/W) and experimentally derived results, although some minor discrepancies were present. Overall, the new equation provides an alternative theoretical approach in addition to 1/W for predicting attachment efficiency.

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INTRODUCTION Aggregation of nanoparticles (NPs) in aqueous dispersions involves the formation and growth of clusters and is controlled by both interfacial chemical reactions and particle transport mechanisms.1−4 The propensity of NPs to aggregate in aqueous environments determines not only their mobility, fate, and persistence, but also their toxicity.1−4 Many toxicological experiments have found it difficult to maintain real nanosized materials in the media,5−7 largely because NPs in aqueous phase are subject to slow or fast aggregation depending on solution chemistries.7,8 The observed toxic mechanisms are likely associated with the aggregation state and other dynamic physicochemical processes.9−12 Aggregation kinetics has been widely considered to be an influential factor for the mobility, © 2012 American Chemical Society

environmental fate, and biological effects of various NP systems.13−16 Aggregation kinetics of various engineered NP systems has been extensively studied using attachment efficiency (α),17−23 which is commonly determined by normalizing the hydrodynamic size growth rate in initial aggregation curves to the growth rate under the favorable (or fast) aggregation condition in which the ionic strength is equal to or greater than the critical coagulation concentration (CCC). According to the Special Issue: Transformations of Nanoparticles in the Environment Received: Revised: Accepted: Published: 7054

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Derjaguin−Landau−Verwey−Overbeek (DLVO) theory, α is equal to the inverse stability ratio (1/W), which is defined as1−3

efficiencies on surfaces.31,32 Thus, applying the Maxwell model in studying the attachment efficiency of NP aggregation kinetics would be interesting. In this study, we primarily used CeO2 NPs as a representative metal oxide NP to explore nanoscale aggregation kinetics. Important environmental effects such as ionic strength, natural organic matter (NOM), and temperature on attachment efficiency were all investigated theoretically and experimentally. Our previous study demonstrated that CeO2 dispersions have relatively uniform spherical shape and size distribution,22 which facilitates modeling research on aggregation kinetics. We derived the new equation for attachment efficiency (defined as the modified attachment efficiency or αm) by combining the Maxwell−Boltzmann distribution and DLVO theory. The new equation was employed to evaluate experimentally obtained attachment efficiencies to validate its applicability in describing the aggregation kinetics of CeO2 NPs. Finally, αm values were compared with the experimental attachment efficiency results and simulations using 1/W for a variety of different NPs (i.e., ZnO, α-Fe2O3, C60, Ag, and Si) selected from the literature to further support the general applicability of αm to different NP systems.

α = 1/W ⎡ ∞ vdw(h)/k T ) ⎤ exp(Uiwi B du⎥ · ≡⎢ λ(u) 2 ⎢⎣ 0 ⎥⎦ (2 + u)

∫

DLVO(h)/k T ) ⎤−1 ⎡ ∞ exp(Uiwi B ⎢ du⎥ λ(u) 2 ⎢⎣ 0 ⎥⎦ (2 + u)

∫

(1)

where h is the surface-to-surface separation distance between two particles (nm), u = h/r, r is the particle radius (nm), DLVO and Uiwi is the total interaction energy between two interacting particles, which is the sum of the van der Waals vdw attractive energy Uiwi and the electrical repulsive energy EL Uiwi . λ (h) corrects for hydrodynamic interactions between two particles and is expressed as follows:1−3 λ(u) = ((6(u)2) + (13(u)) + 2)/((6(u)2) + (4(u))). Despite the wide applications in many colloidal systems, the attachment efficiency calculation by eq 1 has some issues when applied to the nanoscale aggregation problems. For example, the calculated 1/W has been reported to be steeper than the experimental value.3,24 The discrepancy may arise from the assumption that van der Waals attraction is the sole driving force for particle aggregation, which could be true for colloidal particles. However, as we previously reported,14 the nanoscale transport of NPs is governed by both interaction energy and random Brownian diffusion according to interfacial force boundary layer (IFBL) theory. For small NPs, the role of interaction energy should be discounted appreciably owing to its relatively small particle size, whereas random kinetic energy plays a dominant role in the transport mechanism. In contrast, for colloidal particles, the interfacial interaction plays a major role because the random kinetic motion (i.e., diffusivity) is substantially lower than that of NPs according to the Stokes−Einstein equation. On the other hand, the good fit between 1/W and experimentally derived α is usually achieved by varying the Hamaker constant as a fitting parameter.1−4,17,24−26 However, the Hamaker constant (AH) reflects an intrinsic property of the material of the two interacting particles, which indicates the strength of long-range mutual attraction between two small volumes of the material. In this sense, the Hamaker constant should thus be a fixed value for the pairwise interactions of NPs, or at least should not vary significantly. In fact, the Hamaker constant (AH, 123) between particle 1 and particle 2 in solvent 3 can be calculated by the method of van Oss.14,27 NPs could be viewed as macromolecules owing to their small size relative to the dimensions of the electric double layer (EDL) surrounding their surface.28−30 Thus, aggregation may be explained by the Brønsted concept in the transition state theory, which indicates that intermolecular reactions occur only when the kinetic energy of the reacting molecules exceeds the reaction activation energy (Ea) and they undergo effective collisions. By analogy, the random movement of NPs must overcome the interaction energy barrier (Eb) and lead to effective oriented collisions for successful aggregation.28−30 The random kinetic energy distribution of dispersed particles can be described by the Maxwell−Boltzmann theory, and Eb can be estimated by the DLVO theory. The combination of these two theories leads to the Maxwell model or Maxwell approach, which has been used previously to estimate particle collision

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MATERIALS AND METHODS NPs. A water suspension of CeO2 NPs was purchased from Sigma Aldrich; the manufacturer’s reported diameter was 25− 50 nm. Unless indicated, an NP concentration of 20 mg-Ce/L was used in the aggregation kinetics experiments. The particle size distribution (PSD) and zeta potential were analyzed using dynamic light scattering (DLS) on a Zetasizer Nano ZS instrument (Malvern Instruments). The morphology and size of NPs were studied using a Philips EM420 transmission electron microscope (TEM) and Agilent 5500 Molecular Imaging atomic force microscope (AFM). Details of the characterizations were previously described,22 and are also mentioned briefly in section S1 of the Supporting Information (SI), where DLS, TEM, and AFM results are provided. Aggregation Kinetics. The aggregation experiments were performed using TR-DLS. The initial pH of the water solution was approximately 5.6 ± 0.1, and the ionic strength was varied by adding different amounts of 200-mM KCl stock solution. The hydrodynamic diameter of the NPs, as indicated by the Z-average value, was monitored immediately after the addition of NPs to the solution; a complete autocorrelation function was recorded every 5 s. The slope of hydrodynamic diameter versus time (dDH/dt), was determined by fitting a linear function to the experimental data recorded during a time interval when an approximately 30% increase in the original hydrodynamic diameter of CeO2 NPs occurred. The experimental determination of the aggregation attachment efficiency (α) is then calculated by normalizing the slopes obtained at different electrolyte concentrations by the slope obtained under “favorable” (fast) aggregation conditions.2 All experiments were repeated three times for each condition to confirm the observations, and the attachment efficiencies presented are the average results and the standard deviation is presented as the error bar. To study the effect of temperature on attachment efficiency, the temperature of the NP dispersion was varied by the Zetasizer Nano ZS instrument, which is equipped with a Thermal Cap that provides temperature stability when heating and cooling the sample over the range of 2 to 90 °C. To investigate the effect of NOM, Suwannee River Humic Acid (SRHA or HA) (standard II, 2S101H, 1−5 kDa, International 7055

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RESULTS AND DISCUSSION Analysis of the Time-Dependent Evolution of PSD. To support the rationale that random kinetic energy of primary NPs plays the dominant role in aggregation kinetics, we examined the time-dependent evolution of PSD, which is shown in Figure 1. CeO2 NPs in aqueous suspensions always

Humic Substances Society) solution was prepared and filtered through 0.4-μm membrane filters. The SRHA solution was stored in the dark at 4 °C. The SRHA solution was added along with KCl into the NP dispersion to final concentrations of 1 and 10 mg/L before TR-DLS measurements were conducted. Modified Attachment Efficiency. As indicated by the Maxwell approach, the primary and secondary energy minima could both be the deposition position for colloids.31−33 However, the secondary energy minimum is only critical for particles greater than approximately 0.5 μm, whereas NPs generally will not significantly deposit or aggregate in the secondary energy minimum but more likely in the primary energy minimum.33,34 Here we considered the role of Eb in aggregation kinetics and estimated the ratio of the number (ΔN) of particles with kinetic energy exceeding Eb to the total number (N) of particles with kinetic energy ranging from zero to infinity using the Maxwell−Boltzmann distribution: ⎛ m ⎞3/2 −mv 2 /2k T 2 B v dv ⎟ e ⎝ 2πkBT ⎠

∞

ΔNEb →∞ N0 →∞

=

∫vC 4π⎜

⎛ m ⎞3/2 −mv 2 /2k T 2 B v dv ⎟ e ⎝ 2πkBT ⎠

∞

Figure 1. Number-based PSD diagram. The legend indicates the Z-average diameters of the peaks measured at different aggregation times.

∫0 4π⎜ ∞

=

∫E e−EE1/2dE

exhibit a wide distribution of particle size and the formation and growth of aggregates are indicated by the shift of the peak intensity in the PSD, which corresponds to the intensityaveraged hydrodynamic size of NPs having the greatest population or number. As aggregation proceeded, the width of the PSD became larger and larger, which can also be observed from the TR-DLS data in Figure S2a. It is also worth noting that despite the broader size distribution, aggregation usually evolves to reach a quasi-steady state indicative of the depletion of the primary NPs. In the quasi-steady state, aggregates continued to grow at a slower rate than the initial linear growth stage, and the aggregation progress was likely governed by aggregate−aggregate interactions and collisions, leading to a more randomly fluctuating PSD. Moreover, gravity or differential sedimentation may also account for the random fluctuations in PSD and this is supported by the Peclet number calculation that measures the relative importance of Brownian motion and sedimentation is determined40

b

∞

∫0 e−EE1/2dE

(2)

where m is the molecular mass, kB is the Boltzmann constant (1.38 × 10−23 J/K), T is temperature (K), v is the velocity of random motion (m/s), Eb can be obtained from the DLVO theory equations that are shown in section S2 of the SI, and E is the random kinetic energy (kBT) of NPs. Equation 2 thus yields the ratio of NPs with a minimum velocity of v (or a minimum kinetic energy of Eb) over the total number of NPs. Note that the denominator is constant, and we can define the modified attachment efficiency (αm) as α m = δ·

Article

∞ −E 1/2 ΔN e E dE = δ· N Eb

∫

(3)

where δ physically accounts for the hydrodynamic damping effect (also called the drag effect) on the kinetic energy distribution of NPs as well as other potential discrepancies of the DLVO prediction. The Boltzmann velocity distribution applies ideally to dilute systems of noninteracting gas molecules.30 In aqueous phase, solvent molecules should dampen (or decrease) the kinetic motion of NPs, which is called velocity relaxation for Brownian particles.35 Both the collision efficiency and frequency should be lower than those in dilute systems (e.g., air).36,37 Moreover, the particle concentration and the medium viscosity may affect the kinetic energy distribution of NPs. To apply the Maxwell−Boltzmann distribution, the dispersed NPs are assumed to be Brownian particles (particles are moving continuously in Brownian motion with an average kinetic energy of 3 kBT/2) in dilute systems.38,39 Since environmentally relevant concentrations of most engineered NPs in the environment are probably within the range of a few ng/L to μg/L,41−43 the kinetic energy of NPs in aqueous phase should fit the Maxwell−Boltzmann distribution.

Pe =

2πΔρgr 4 3kBT

(4)

where Δρ is the density difference between dispersed NPs and dispersion medium and g is the acceleration due to gravity. When Pe ≪ 1 Brownian motion dominates and aggregation is perikinetic, whereas when Pe ≫ 1 aggregation is orthokinetic (differential sedimentation occurs). The density of bulk CeO2 is approximately 7650 kg/m3, and the difference between the bulk and nanosized or aggregated clusters of CeO2 is assumed to be negligible. Then, using eq 4, we can determine that when the diameter becomes greater than 660 nm, Pe starts to exceed 1 and gravity should be taken into account. Apparently, Figure S2a shows that at the hydrodyamic diameter of 600 nm or greater, the DLS data appeared more random and flutuating, indicative of the pronounced gravity effect. Conversely, in the initial aggregation regime, the small primary NPs form aggregates more readily due to their low interparticle energy barrier, high particle number density, and 7056

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hydrodynamic damping effect is considered, the ratio ΔN/N further decreases by approximately 7%, as shown in the inset of Figure 2b. Ionic strength influences attachment efficiency because of the dependence of Eb on ionic strength according to the DLVO theory (see Figure S3). A lower Eb at elevated ionic strength means a lower interparticle repulsion and results in a higher attachment efficiency according to eq 3. Clearly, the modified attachment efficiency usefully considers the roles of interaction energy and Brownian motion in describing the aggregation kinetics. Effect of NOM. NOMs, such as humic and fulvic acids, are ubiquitous in the environment, and under environmentally relevant conditions, the NP aggregation will be affected by NOMs.1,46,47 Indeed, at very low concentrations of HA (1 mg/L), no aggregation was found for CeO2 NPs even after addition of 100-mM KCl (results not shown). This observation indicates that HA adsorbed onto the surface of CeO2 NPs, and the steric repulsion increased and stabilized the NP dispersion.47 Moreover, van der Waals attraction could be altered owing to the changes in hydrophobicity that may lead to changes in the Hamaker constant (to be discussed below). Although incorporation of non-DLVO interactions (e.g., steric and acid−base forces) into the calculation of the interaction energy barrier is desirable, most parameters necessary for the calculation of the non-DLVO interaction energy, such as the adsorbed HA layer thickness, surface coverage fractions, and polar surface free energy for calculating the acid− base interaction, are either difficult to determine or not available in the literature.49 The effect of adsorbed HA on CeO2 NP properties and interparticle interactions is multifold (e.g., inducing acid−base, electrosteric, and bridging interactions besides the perturbation in van der Waals and electrostatic interactions).50,51 In this study, the classic DLVO theory was used to evaluate the interaction energy that only comprises van der Waals and electrostatic interactions, which are affected by the adsorbed NOM through altering the surface tension (or the Hamaker constant) and surface charge.11−52 The Hamaker constant (A121) for CeO2 NPs with HA adsorbed was computed using the van Oss method.27 Namely, A121 ≈ ((A11)1/2 − (A22)1/2)2, where A11 and A22 denote the Hamaker constants of HA-adsorbed surfaces (A22 ≈ 7.5 × 10−20 J) and water (A22 ≈ 3.7 × 10−20 J) in a vacuum.27,53 Thus, with HA adsorption, the Hamaker constant of CeO2 NPs (A121) was computed to be 6.6 × 10−21 J, while for pristine CeO2 NPs A121m ≈ 5.57 × 10−20 J,54 which is apparently higher than that of HA-adsorbed CeO2 NPs. Thus, with HA adsorption on CeO2 NPs a lower van der Waals attraction is expected, leading to an increasing energy barrier as supported by Figure 3a. The surface charge variation before and after addition of HA was indicated by the zeta potentials of CeO2 NPs, which are represented by electrophoretic mobility (EPM) and zeta potential in Figure S4. After HA was added to the NP dispersion, the EPM shifted from positive to negative, which implies the adsorption of HA on the surface of CeO2 NPs. This surface charge reversal owing to the adsorbed NOM has been observed experimentally in several other studies.47,55,56 The increased surface charge restabilized the CeO2 NP dispersion due to the elevated interaction energy barriers (Figure 3a). Because no aggregation was observed, as mentioned above, attachment efficiency cannot be determined experimentally. However, eq 3 allows us to estimate the attachment efficiency in the presence of HA, which is shown in Figure 3b (the result

more pronounced Brownian motion.22,44,45 The dominant role of primary NPs in the evolution of PSD and aggregation were also revealed by the particle size frequency in Figure S2b, which shows that the particle size frequency followed the power law distribution similar to the coagulation of colloids in natural waters.48 Moreover, it also indicated that small particles dominated the evolution of PSD and aggregation kinetics of CeO2 NPs, which supports the idea of assessing the kinetic energy of primary NPs with the Maxwell−Boltzmann distribution and the DLVO theory for calculating the attachment efficiency. Effect of Ionic Strength. Variable αm in eq 3 was first examined in the capability of reproducing the ionic strength effect on aggregation kinetics. Figure 2a shows the experimental

Figure 2. (a) Comparison of attachment efficiencies obtained from experiments and our model calculation for equal-sized CeO2 (100 nm diameter) as a function of ionic strength at pH 5.7 and 25 °C. (b) The ratio of the number (ΔN) over the total number (N) as a function of Eb, which is the minimum kinetic energy that ΔN particles have. The inset shows the same plot after consideration of the hydrodynamic damping effect (δ was 0.9352 for CeO2 NPs).

results with distinct unfavorable (slow) and favorable (fast) aggregation kinetics regimes, demarcated by the CCC of approximately 40 mM. The calculated αm was well fitted to the experimental data by varying the hydrodynamic damping factor (δ) as the fitting parameter. Other model parameters (e.g., the Hamaker constant) are provided in Table S1. The best fit (R2 ≈ 0.96) between the calculated and experimental data was achieved when the value of δ was 0.9352. Because δ is less than 1, our assumption on the physical meaning of δ holds well. As shown in Figure 2b, most NPs in the dispersion maintain low kinetic energies (≈ 0 kBT), which correspond to the highest ΔN/N ratio or attachment efficiency (≈ 1). The ratio for higher kinetic energy declines dramatically, and the highest possible kinetic energy is approximately 6−7 kBT. When the 7057

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Figure 4. (a) Temperature effect on attachment efficiency simulated using eq 3. Model parameters are shown in Table S2. (b) Experimental observations of the temperature effect on attachment efficiency of CeO2 NPs at different ionic strengths (15, 25, and 50 mM KCl). * Indicates a significant difference from the results of the other two temperatures (P < 0.01, Student’s t-test, n = 9).

Figure 3. (a) Effects of HA on the interaction energy barrier (Eb) between CeO2 NPs at 25 °C. (b) Calculated attachment efficiencies in the presence of HA at different concentrations. Solid lines are a guide to the eye.

in the absence of HA is shown in Figure 2a). Apparently, the attachment efficiencies of CeO2 NPs in the presence of HA were in the range of 10−40−10−20, and such a low order of magnitude certainly led to slow aggregation that can hardly be observed experimentally. Moreover, attachment efficiencies for HA of 10 mg/L were even lower than those for HA of 1 mg/L because of the lower negative surface charge and greater electrostatic repulsion, as discussed above. In the presence of a divalent electrolyte (e.g., Ca2+), the mechanisms of HA influence on NP aggregation kinetics are more complicated than in the presence of monovalent electrolytes. 1−26 Particularly, the presence of HA enhanced the CeO2 NP aggregation rate at high Ca2+ concentration, probably owing to bridging via Ca2+ complexation between aggregated CeO2 NPs.46,47 Clearly, analysis of the NOM effect on aggregation kinetics in divalent electrolyte solutions should incorporate non-DLVO forces in the calculation of Eb, which will be a future study. Effect of Solution Temperature. Figure 4a shows the potential temperature effect on attachment efficiency of CeO2 NPs that was simulated by eq 3. Interestingly, the temperature effect seems to be nonmonotonic as there is a “critical point” at an ionic strength of approximately 16 mM. For ionic strength greater than 16 mM, increasing the temperature from 5 to 45 °C led to an apparent decrease in the attachment efficiency. Conversely, for ionic strength less than 16 mM, increasing the temperature did not apparently change the attachment efficiency, which slightly increased with the increasing temperature as evidenced from the enlarged view of the dotted area in Figure 4a. However, temperature had no impact on attachment

efficiency when the ionic strength reaches unity at the CCC (approximately 35 mM for CeO2 NPs as determined in our previous work22), at which the simulated curves at different temperatures converged. Although temperature has been considered an important environmental factor for the stability and aggregation kinetics of NPs,52−57 the above observations and potential mechanisms have not been reported previously. To verify the above analysis, the experimentally derived attachment efficiencies from TR-DLS experiments are shown in Figure 4b and a group of the typical TR-DLS experiment results are shown in Figure S6, which consistently shows that the hydrodynamic diameters of CeO2 NPs grew faster when the temperature increased from 15 to 40 °C. However, at low ionic strength (15 mM), temperature clearly did not affect attachment efficiency with statistical significance. Conversely, at a higher ionic strength (25 mM), the attachment efficiency decreased significantly at 40 °C compared with 15 or 30 °C (P < 0.01, n = 9). Moreover, when the ionic strength was 50 mM, which is greater than the CCC, the experimentally derived attachment efficiencies under the three temperatures were not significantly different, which agreed with the simulation in Figure 4a. Temperature influences aggregation kinetics through affecting the random Brownian motion of particles and the collision frequency.48 Moreover, at elevated temperatures the interaction energy barrier (Eb) was found to decrease (Figure S5), which should increase the aggregation rate exponentially.48 Nevertheless, high temperatures also increase the potential disaggregation or the detachment, because the increased 7058

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Figure 5. Attachment efficiencies of six different types of NPs, including (a) CeO2, (b) hematite, (c) ZnO, (d) C60, (e) PVP-coated AgNPs, and (f) SiNPs, as a function of ionic strength. Black circles represent experimental results obtained from the literature. Red dashed lines are the simulated results for 1/W using eq 1. Green solid lines are the simulated results for αm using eq 3.

ZnO NPs and polyvinylpyrrolidone-coated silver NPs (PVPcoated AgNPs). For CeO2 and ZnO NPs, αm exhibited a better fit with experimental results than did 1/W, whereas 1/W fitted better for C60 NPs than αm did. For hematite NPs, both 1/W and αm slightly deviated from experimental data, although they were similar to each other. For Si NPs, both αm and 1/W were not in good agreement with the experimental data. The discrepancies between the simulated fits and experimental data could be due to the intrinsic limitations of classic DLVO theory and the lack of consideration of non-DLVO forces. For instance, PVP-coated AgNPs owing to the polymer capping agent had strong steric repulsion11,26 and thus led to significant discrepancies between the model and experimental data. The fitted values of δ are summarized in Table S3. Particularly, the δ for CeO2 NPs (0.9606) is close to our fitting result in the previous section (0.9352). The fitted values

Brownian motion of water molecules could increase the hydrodynamic shear on the particle surface and possibly destabilize the aggregated clusters of NPs.58 This may explain the decline in attachment efficiency with increasing temperature when the ionic strength was greater than 16 mM observed both theoretically and experimentally. Application of the Modified Attachment Efficiency in Various NP Systems. To further validate the applicability of eq 3 for describing the aggregation kinetics of NP dispersions, we compared the experimentally derived attachment efficiencies of various NP dispersions from the literature. Both 1/W and αm were plotted by means of curve fitting using eq 1 and eq 3, for which, as stated previously, the Hamaker constant and hydrodynamic damping factor were used as fitting parameters, respectively. Figure 5 shows that the model fits of 1/W and αm were generally in a good agreement with each other except for 7059

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of δ varied between 0.50 and 1.00, and there are many potential causes for the variations in δ. Apart from the possible fitting discrepancies, particle properties (e.g., particle size, shape, and surface hydrophobicity), solution characteristics (e.g., temperature and viscosity), and other experimental conditions could all contribute to the hydrodynamic damping through the interactions between water and particle surface. For example, the water molecules could adhere to the hydrophilic particles to form strong and relatively thick steric bumper layers and form an EDL by adsorbing counterions from the solution,59 which would affect the mobility of NPs differently depending on the thickness of the water layer or EDL. On the other hand, the hydrodynamic damping effect on the kinetic energy distribution of NPs in liquid results from the Stokesian drag force exerted on NPs.57,60 According to Stokes law, the drag force is linearly proportional to the projected area of the particle in the plane perpendicular to the flow direction (for a sphere, Ap = πr2),61 and large sized particles with large projected areas have greater drag forces and a greater extent of the velocity relaxation or damping. Moreover, the mean Brownian velocity (V̅ ) of particles in fluid is given by62 V̅ =

2kBT 2D = L̅ L̅ 6πr μ

ACKNOWLEDGMENTS This study was partially supported by the U.S. Environmental Protection Agency Science to Achieve Results Program Grant RD-83385601, Engineering Research Center (ERC)/ Semiconductor Research Corporation (SRC)/ESH grant (425.025), and the Brook Byers Institute for Sustainable Systems. Wentao Qin is thanked for his help with TEM operation.

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ASSOCIATED CONTENT

S Supporting Information *

Additional figures, text, and table. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

(1) Chen, K. L.; Mylon, S. E.; Elimelech, M. Aggregation kinetics of alginate-coated hematite nanoparticles in monovalent and divalent electrolytes. Environ. Sci. Technol. 2006, 40 (5), 1516−1523. (2) Saleh, N. B.; Pfefferle, L. D.; Elimelech, M. Aggregation kinetics of multiwalled carbon nanotubes in aquatic systems: Measurements and environmental implications. Environ. Sci. Technol. 2008, 42 (21), 7963−7969. (3) Chen, K. L.; Elimelech, M. Aggregation and deposition kinetics of fullerene (C-60) nanoparticles. Langmuir 2006, 22 (26), 10994− 11001. (4) Saleh, N. B.; Pfefferle, L. D.; Elimelech, M. Influence of biomacromolecules and humic acid on the aggregation kinetics of single-walled carbon nanotubes. Environ. Sci. Technol. 2010, 44 (7), 2412−2418. (5) Limbach, L. K.; Li, Y.; Grass, R. N.; Brunner, T. J.; Hintermann, M. A.; Muller, M.; Gunther, D.; Stark, W. J. Oxide nanoparticle uptake in human lung fibroblasts: Effects of particle size, agglomeration, and diffusion at low concentrations. Environ. Sci. Technol. 2005, 39 (23), 9370−9376. (6) Mutlu, G. M.; Budinger, G. R. S.; Green, A. A.; Urich, D.; Soberanes, S.; Chiarella, S. E.; Alheid, G. F.; McCrimmon, D. R.; Szleifer, I.; Hersam, M. C. Biocompatible nanoscale dispersion of single-walled carbon nanotubes minimizes in vivo pulmonary toxicity. Nano Lett. 2010, 10 (5), 1664−1670. (7) Auffan, M.; Rose, J.; Wiesner, M. R.; Bottero, J.-Y. Chemical stability of metallic nanoparticles: A parameter controlling their potential cellular toxicity in vitro. Environ. Pollut. 2009, 157 (4), 1127− 1133. (8) Pal, S.; Tak, Y. K.; Song, J. M. Does the antibacterial activity of silver nanoparticles depend on the shape of the nanoparticle? A study of the gram-negative bacterium Escherichia coli. Appl. Environ. Microbiol. 2007, 73 (6), 1712−1720. (9) Zhang, Y.; Chen, Y.; Westerhoff, P.; Hristovski, K.; Crittenden, J. C. Stability of commercial metal oxide nanoparticles in water. Water Res. 2008, 42 (8−9), 2204−2212. (10) Keller, A. A.; Wang, H.; Zhou, D.; Lenihan, H. S.; Cherr, G.; Cardinale, B. J.; Miller, R.; Ji, Z. Stability and aggregation of metal oxide nanoparticles in natural aqueous matrices. Environ. Sci. Technol. 2010, 44 (6), 1962−1967. (11) Petosa, A. R.; Jaisi, D. P.; Quevedo, I. R.; Elimelech, M.; Tufenkji, N. Aggregation and deposition of engineered nanomaterials in aquatic environments: Role of physicochemical interactions. Environ. Sci. Technol. 2010, 44 (17), 6532−6549. (12) Hotze, E. M.; Phenrat, T.; Lowry, G. V. Nanoparticle aggregation: Challenges to understanding transport and reactivity in the environment. J. Environ. Qual. 2010, 39 (6), 1909−1924. (13) Zhang, W.; Kalive, M.; Capco, D. G.; Chen, Y. Adsorption of hematite nanoparticles onto Caco-2 cells and the cellular impairments: Effect of particle size. Nanotechnology 2010, 21 (35), 355103. (14) Zhang, W.; Rittmann, B.; Chen, Y. Size effects on adsorption of hematite nanoparticles on E. coli cells. Environ. Sci. Technol. 2011, 45 (6), 2172−2178. (15) Liu, J. Y.; Hurt, R. H. Ion release kinetics and particle persistence in aqueous nano-silver colloids. Environ. Sci. Technol. 2010, 44 (6), 2169−2175. (16) Zhang, W.; Yao, Y.; Li, K.; Huang, Y.; Chen, Y. Influence of dissolved oxygen on aggregation kinetics of citrate-coated silver nanoparticles. Environ. Pollut. 2011, 159 (12), 3757−3762.

where D is the diffusion coefficient of particles in liquid, L̅ is the mean distance in one dimension that particle moves before striking another water molecule, and μ is the medium viscosity. Equation 5 implies that the hydrodynamic damping effect would increase as particle radius (r) or the medium viscosity increases. There is a pressing need for quantitative data on the aggregation kinetics of engineered NPs, which is pivotal to assessment of their environmental fate, transport, and toxicity. In this study, a new approach was presented for assessing the attachment efficiency of NP aggregation based on the Maxwell−Boltzmann distribution coupled with the DLVO theory, which is a first attempt to the best of our knowledge. A modified attachment efficiency (αm) equation was proposed and the equation successfully interpreted the effects of ionic strength, NOM, and temperature on aggregation kinetics. Furthermore, the definition of αm shows the balanced consideration of interfacial energy and Brownian motion in evaluating the aggregation kinetics of NP dispersions when compared with the inverse stability ratio (1/W). In light of its good agreement with experimental attachment efficiency data for CeO2 NPs and various other NP systems, αm could be an alternative theoretical approach in addition to 1/W and provide a deeper understanding of the aggregation mechanisms operating at nanoscale.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; phone: (+1) 404894-3089; fax: (+1) 404-894-2278. Notes

The authors declare no competing financial interest. 7060

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(17) Chen, K. L.; Elimelech, M. Relating colloidal stability of fullerene (C-60) nanoparticles to nanoparticle charge and electrokinetic properties. Environ. Sci. Technol. 2009, 43 (19), 7270−7276. (18) French, R. A.; Jacobson, A. R.; Kim, B.; Isley, S. L.; Penn, R. L.; Baveye, P. C. Influence of ionic strength, pH, and cation valence on aggregation kinetics of titanium dioxide nanoparticles. Environ. Sci. Technol. 2009, 43 (5), 1354−1359. (19) Gao, J.; Youn, S.; Hovsepyan, A.; Llaneza, V. L.; Wang, Y.; Bitton, G.; Bonzongo, J. C. J. Dispersion and toxicity of selected manufactured nanomaterials in natural river water samples: Effects of water chemical composition. Environ. Sci. Technol. 2009, 43 (9), 3322−3328. (20) Sharma, V. K. Aggregation and toxicity of titanium dioxide nanoparticles in aquatic environment-A Review. J. Environ. Sci. Health, Part A 2009, 44 (14), 1485−1495. (21) El Badawy, A. M.; Luxton, T. P.; Silva, R. G.; Scheckel, K. G.; Suidan, M. T.; Tolaymat, T. M. Impact of environmental conditions (pH, ionic strength, and electrolyte type) on the surface charge and aggregation of silver nanoparticles suspensions. Environ. Sci. Technol. 2010, 44 (4), 1260−1266. (22) Li, K.; Zhang, W.; Huang, Y.; Chen, Y. Aggregation kinetics of CeO2 nanoparticles in KCl and CaCl2 solutions: Measurements and modeling. J. Nanopart. Res. 2011, 10.1007/s11051-011-0548-z. (23) Yi, P.; Chen, K. L. Influence of surface oxidation on the aggregation and deposition kinetics of multiwalled carbon nanotubes in monovalent and divalent electrolytes. Langmuir 2011, 27 (7), 3588−3599. (24) Behrens, S. H.; Christl, D. I.; Emmerzael, R.; Schurtenberger, P.; Borkovec, M. Charging and aggregation properties of carboxyl latex particles: Experiments versus DLVO theory. Langmuir 2000, 16 (6), 2566−2575. (25) Buettner, K. M.; Rinciog, C. I.; E.Mylon, S. Aggregation kinetics of cerium oxide nanoparticles in monovalent and divalent electrolytes. Colloids Surf., A 2010, 366 (1−3), 74−79. (26) Huynh, K. A.; Chen, K. L. Aggregation kinetics of citrate and polyvinylpyrrolidone coated silver nanoparticles in monovalent and divalent electrolyte solutions. Environ. Sci. Technol. 2011, 45 (13), 5564−5571. (27) Oss, C. J. v. Interfacial Forces in Aquaeous Media, 2nd ed.; Taylor & Francis Group: Boca Raton, FL, 2006; pp 81−83. (28) Kallay, N.; Zalac, S. Stability of nanodispersions: A model for kinetics of aggregation of nanoparticles. J. Colloid Interface Sci. 2002, 253 (1), 70−76. (29) Ribeiro, C.; Lee, E. J. H.; Longo, E.; Leite, E. R. A kinetic model to describe nanocrystal growth by the oriented attachment mechanism. Chemphyschem 2005, 6 (4), 690−696. (30) Penn, R. L. Kinetics of oriented aggregation. J. Phys. Chem. B 2004, 108 (34), 12707−12712. (31) Shen, C.; Li, B.; Huang, Y.; Jin, Y. Kinetics of coupled primaryand secondary-minimum deposition of colloids under unfavorable chemical conditions. Environ. Sci. Technol. 2007, 41 (20), 6976−6982. (32) Hahn, M. W.; O’Melia, C. R. Deposition and reentrainment of Brownian particles in porous media under unfavorable chemical conditions: Some concepts and applications. Environ. Sci. Technol. 2003, 38 (1), 210−220. (33) Hahn, M. W.; Abadzic, D.; O’Melia, C. R. Aquasols: On the role of secondary minima. Environ. Sci. Technol. 2004, 38 (22), 5915−5924. (34) Tufenkji, N.; Elimelech, M. Breakdown of colloid filtration theory: Role of the secondary energy minimum and surface charge heterogeneities. Langmuir 2005, 21 (3), 841−852. (35) Rudyak, V. Y.; Krasnolutskii, S. L.; Ivanov, D. A. Molecular dynamics simulation of nanoparticle diffusion in dense fluids. Microfluid. Nanofluid. 2011, 11 (4), 501−506. (36) Laidler, K. J. Chemical Kinetics, 3rd ed.; Prentice Hall, 1997. (37) Houston, P. L. Chemical Kinetics and Reaction Dynamics, 2nd ed.; Dover Publications, 2006. (38) Pierres, A.; Benoliel, A.-M.; Zhu, C.; Bongrand, P. Diffusion of microspheres in shear flow near a wall: Use to measure binding rates between attached molecules. Biophys. J. 2001, 81 (1), 25−42.

(39) Kendall, K.; Dhir, A.; Du, S. F. A new measure of molecular attractions between nanoparticles near kT adhesion energy. Nanotechnology 2009, 20 (27) 275701−275704. (40) Kovalchuk, N. M.; Starov, V. M. Aggregation in colloidal suspensions: Effect of colloidal forces and hydrodynamic interactions. Adv. Colloid Interface Sci. 2011, DOI: 10.1016/j.cis.2011.05.009. (41) Klaine, S. J.; Alvarez, P. J. J.; Batley, G. E.; Fernandes, T. F.; Handy, R. D.; Lyon, D. Y.; Mahendra, S.; McLaughlin, M. J.; Lead, J. R. Nanomaterials in the environment: Behavior, fate, bioavailability, and effects. Environ. Toxicol. Chem. 2008, 27 (9), 1825−1851. (42) Gottschalk, F.; Sonderer, T.; Scholz, R. W.; Nowack, B. Modeled environmental concentrations of engineered nanomaterials (TiO2, ZnO, Ag, CNT, fullerenes) for different regions. Environ. Sci. Technol. 2009, 43 (24), 9216−9222. (43) Nowack, B.; Bucheli, T. D. Occurrence, behavior and effects of nanoparticles in the environment. Environ. Pollut. 2007, 150 (1), 5−22. (44) Zhang, W.; Yao, Y.; Sullivan, N.; Chen, Y. Modeling the primary size effects of citrate-coated silver nanoparticles on their ion release kinetics. Environ. Sci. Technol. 2011, 45 (10), 4422−4428. (45) Schwarzer, H. C.; Peukert, W. Prediction of aggregation kinetics based on surface properties of nanoparticles. Chem. Eng. Sci. 2005, 60 (1), 11−25. (46) Mylon, S. E.; Chen, K. L.; Elimelech, M. Influence of natural organic matter and ionic composition on the kinetics and structure of hematite colloid aggregation: Implications to iron depletion in estuaries. Langmuir 2004, 20 (21), 9000−9006. (47) Chen, K. L.; Elimelech, M. Influence of humic acid on the aggregation kinetics of fullerene (C-60) nanoparticles in monovalent and divalent electrolyte solutions. J. Colloid Interface Sci. 2007, 309 (1), 126−134. (48) Crittenden, J. Water Treatment: Principles and Design, 2nd ed.; Wiley, 2005. (49) Somasundaran, P.; Runkana, V.; Kapur, P. C. A population balance model for flocculation of colloidal suspensions by polymer bridging. Chem. Eng. Sci. 2006, 61 (1), 182−191. (50) Phenrat, T.; Song, J. E.; Cisneros, C. M.; Schoenfelder, D. P.; Tilton, R. D.; Lowry, G. V. Estimating attachment of nano- and submicrometer-particles coated with organic macromolecules in porous media: Development of an empirical model. Environ. Sci. Technol. 2010, 44 (12), 4531−4538. (51) Phenrat, T.; Saleh, N.; Sirk, K.; Kim, H. J.; Tilton, R. D.; Lowry, G. V. Stabilization of aqueous nanoscale zerovalent iron dispersions by anionic polyelectrolytes: adsorbed anionic polyelectrolyte layer properties and their effect on aggregation and sedimentation. J. Nanopart. Res. 2008, 10 (5), 795−814. (52) Grasso, D.; Subramaniam, K.; Butkus, M.; Strevett, K.; Bergendahl, J. A review of non-DLVO interactions in environmental colloidal systems. Rev. Environ. Sci. Biotechnol. 2002, 1 (1), 17−38. (53) Croucher, M. D.; Hair, M. L. Hamaker Constants and Principle of Corresponding States. J. Phys. Chem. 1977, 81 (17), 1631−1636. (54) Karimian, H.; Babaluo, A. A. Halos mechanism in stabilizing of colloidal suspensions: Nanoparticle weight fraction and pH effects. J. Eur. Ceram. Soc. 2007, 27 (1), 19−25. (55) O’Melia, C. R.; Au, K. K.; Penisson, A. C.; Yang, S. L. Natural organic matter at oxide/water interfaces: Complexation and conformation. Geochim. Cosmochim. Acta 1999, 63 (19−20), 2903− 2917. (56) Li, Q. L.; Elimelech, M. Organic fouling and chemical cleaning of nanofiltration membranes: Measurements and mechanisms. Environ. Sci. Technol. 2004, 38 (17), 4683−4693. (57) Nel, A. E.; Madler, L.; Velegol, D.; Xia, T.; Hoek, E. M. V.; Somasundaran, P.; Klaessig, F.; Castranova, V.; Thompson, M. Understanding biophysicochemical interactions at the nano-bio interface. Nat. Mater. 2009, 8 (7), 543−557. (58) Ryan, J. N.; Elimelech, M. Colloid mobilization and transport in groundwater. Colloids Surf., A 1996, 107, 1−56. (59) Bradford, S. A.; Torkzaban, S.; Walker, S. L. Coupling of physical and chemical mechanisms of colloid straining in saturated porous media. Water Res. 2007, 41 (13), 3012−3024. 7061

dx.doi.org/10.1021/es203623z | Environ. Sci. Technol. 2012, 46, 7054−7062

Environmental Science & Technology

Article

(60) Kim, H. Y.; Sofo, J. O.; Velegol, D.; Cole, M. W.; Lucas, A. A. van der Waals dispersion forces between dielectric nanoclusters. Langmuir 2007, 23 (4), 1735−1740. (61) Torkzaban, S.; Bradford, S. A.; Walker, S. L. Resolving the coupled effects of hydrodynamics and DLVO forces on colloid attachment in porous media. Langmuir 2007, 23 (19), 9652−9660. (62) Daugherty, R. L.; Franzini, J. B. Fluid Mechanics with Engineering Applications; McGraw-Hill: New York, 1965.

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