Deposition of Aggregated Nanoparticles — A Theoretical and

(22) Both theoretical and experimental studies found that, depending on the ... (31) A challenge in applying the SEI to calculate the interaction ener...
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Deposition of Aggregated Nanoparticles  A Theoretical and Experimental Study on the Effect of Aggregation State on the Affinity between Nanoparticles and a Collector Surface Shihong Lin†,‡ and Mark R. Wiesner*,†,‡ †

Department of Civil and Environmental Engineering, Duke University, P.O. Box 90287, Durham, North Carolina 27708, United States ‡ Center for the Environmental Implications of NanoTechnology (CEINT) S Supporting Information *

ABSTRACT: Theoretical and experimental approaches were employed to study the effect of aggregation on the affinity between nanoparticles (NPs) and a flat surface that is quantified by the attachment efficiency. Computer simulations were used to generate virtual aggregates formed via either diffusion limited cluster aggregation or reaction limited cluster aggregation. The colloidal interactions between the simulated aggregates and a flat surface were evaluated based on the surface element integration approach. It was found that the strength of colloidal interaction for the aggregated NPs was on the same order of magnitude as those for the primary particles and was significantly weaker than that for an equivalent sphere defined by the gyration radius of the aggregate. The results from the deposition experiments using quartz crystal microbalance suggested that the attachment efficiencies (unfavorable deposition) for aggregated NPs were higher at the initial stage but later became similar to that of the primary NPs when equilibrium deposition was reached. The high initial affinity was postulated to be attributable to secondary minimum deposition. These results suggest that it is the size of the primary particles, not that of the aggregates, that determines the strength of the colloidal interaction between the aggregate and an environmental surface.

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INTRODUCTION

nanoparticles and those surfaces as an interaction between a particle and a flat surface.15 Numerous studies have been conducted to understanding the hydrodynamics and transport of particle aggregates in aqueous environment.16−20 For example, aggregation might decrease the effective diffusivity of the nanoparticles by increasing the effective size within the diffusion dominant regime, which in turn decreases the single collector efficiency of nanoparticles in a porous medium.21 On the other hand, aggregation may also result in highly porous objects that have low drag coefficients compared with spherical objects of equal net density and radius of gyration,18 possibly offsetting the effects of increased size on diffusion coefficients and single collector efficiency. However, very limited, if there is any, effort has been devoted to understanding the theoretical aspect of colloidal interaction between a particle aggregate and a flat surface, even though many of the nanoparticles studied exist as aggregates. A better understanding of the colloidal interaction between a fractal aggregate and a surface is important as the deposition kinetics

The recent scientific interest in understanding the impact of nanoparticles on the environment has spurred extensive research to elucidate various aspects of environmental behavior of nanoparticles.1,2 Nanoparticles, if not protected with steric stabilizing agents, are sensitive to the change of solution chemistry and may aggregate in certain aqueous environments. The phenomenon of nanoparticle aggregation has been the subject of numerous studies3 due to its importance in determining environmental exposure,4 dissolution,5−8 reactivity,9−11 organic molecule adsorption,12 and toxicity.13,14 Equally important as aggregation for environmental impact of nanoparticles is deposition i.e. the attachment/adsorption of nanoparticles to environmental surfaces they encounter. Deposition of nanoparticles onto environmental surfaces not only determines their persistence in the aqueous system but also affects their interaction with targets at risk (e.g., microbes and plants). It is thus important to understand the kinetics of nanoparticle deposition and its influencing factors. For unaggregated particles, when the environmental surfaces of interest are considerably larger than the particles themselves (which is the case for nanoparticles), it is a reasonable approximation to model the colloidal interaction between the © 2012 American Chemical Society

Received: Revised: Accepted: Published: 13270

October 10, 2012 November 15, 2012 November 21, 2012 November 21, 2012 dx.doi.org/10.1021/es3041225 | Environ. Sci. Technol. 2012, 46, 13270−13277

Environmental Science & Technology

Article

For each simulated fractal aggregate, the energy for EDL interaction (VEDL), for vdW interaction (VvdW), and the total energy (VTotal) were evaluated for 62 different orientations each of which corresponds to a unique distribution of separation distance. The surface potentials of the particles and the flat surface were both assumed to be −25.7 mv (∼1 kBT/e, kB is the Boltzmann constant, T is the temperature, and e is the element charge). The Hamaker constant (Ah) for vdW interaction was arbitrated to be 10−20 J. A radius (a) of 10 nm was arbitrarily chosen for the primary particles. Three ionic strengths (IS) were used for evaluation, including 1 mM, 10 mM, and 100 mM, which corresponds to κa of 1.04, 3.3, and 10.4 (κ is the Debye constant). With the same surface chemistry and solution chemistry, the interactions between a flat surface and an equivalent sphere of the gyration radius of a corresponding fractal aggregate were also evaluated for comparison. Simulation of Fractal Aggregate Formation. To evaluate the interaction between a fractal aggregate and a surface, fractal aggregates were generated using the diffusionlimited-cluster-aggregation (DLCA) and the reaction-limitedcluster-aggregation (RLCA).35,36 In DLCA, a predetermined number (N) of particles were randomly distributed in a confined 3-dimensional lattice space. They were then allowed to walk randomly by one lattice per iteration. The simulation space assumed reflective boundaries. The collision of particle/ cluster with another particle/cluster was assumed to produce a new cluster that continued the random walks. The relative diffusivity of a cluster with a given size was modeled by assigning a probability of being chosen that was dependent on the number of primary particles in that cluster (i.e., smaller particles have higher chances to move in the simulation, representing a higher diffusivity). For the case of RLCA, the aggregate generating procedure was essentially the same except that the probability of successful attachment per collision (α) was assumed to be 0.01. The simulation terminates when all the particles or clusters aggregate to become a single cluster.

of aggregates is controlled by both the hydrodynamics of transport as well as the colloidal interaction. Relevant study is lacking probably due to the challenges in modeling interactions for colloidal aggregates the geometry of which are poorly defined because of the stochastic nature of aggregation. One of the most important features of colloidal aggregates is their fractal nature.22 Both theoretical and experimental studies found that, depending on the aggregation mode, colloidal aggregates can have very different structures as described by the fractal dimension (Df):23 diffusion limited cluster aggregation (DLCA) generates aggregates of a Df of about 1.8, and reaction limited aggregation (RLCA) produces aggregates of a Df of approximately 2.1.24 It is the purpose of this work to elucidate the effect of aggregation on the colloidal interaction between nanoparticles and a flat surface. Surface element integration (SEI) method25 was used to examine, theoretically, the potential energy of colloidal interaction (with a flat surface) for fractal aggregates generated in simulations of both DLCA and RLCA. Both the effects of fractal dimensions and aggregate size were investigated. Deposition experiments employing the quartzcrystal-microbalance (QCM) were also conducted to validate the theoretical predictions.

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THEORETICAL APPROACH Calculation of Potential Energy of Colloidal Interaction. In the following discussion, only electrical double layer (EDL) interaction and van der Waals (vdW) interaction are considered, i.e. we deal only with aggregates formed from particles that are (1) not modified by any polymeric coating to exert steric or electrosteric stabilization,26,27 or (2) particles that are very hydrophilic or very hydrophobic such that additional interaction forces (e.g., hydration force, hydrophobic interaction) have to been taken into account.28 For objects of surface irregularity, it is possible to calculate the interaction energy using the surface element integration (SEI) method.25 In fact, the SEI has been utilized to calculate the potential energy of colloidal interaction for spheroid,29 for particles of surface roughness30 and for collector surfaces of surface roughness.31 A challenge in applying the SEI to calculate the interaction energy for colloidal aggregates is the difficulty in describing the complexity of a fractal aggregate surface. However, based on the principle of the SEI method, it is mathematically equivalent to calculate the interaction energy between an aggregate and a flat surface by simply summing up the interaction energy between each primary particle and the flat surface (a more detailed discussion on the equivalence is given in the Supporting Information). To calculate the energy of EDL interaction between a primary particle and a flat surface, the exact analytical expression for EDL interaction between a sphere and a plate under constant potential (CP)32,33 was used. This expression extends the well-known Hogg-Healy-Fuerstenau (HHF) expression to the small κa (thick double layer) regime and yields the exact (to the extent that the linearization of Poisson− Boltzmann equation is proper) results as obtained by calculating the energy using stringent numerical methods.25,33 To calculate the energy of vdW interaction between a primary particle and a flat surface, the approximate expression for retarded vdW interaction proposed by Gregory was used.34 The details of these expressions for EDL and vdW interactions can be found in the Supporting Information.

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EXPERIMENTAL MATERIALS AND METHODS Synthesis of Gold Nanoparticles. The model nanoparticles we used in this study were gold nanoparticles (AuNPs) synthesized using a citrate reduction method.37 Briefly, 1 mL of 24.3 mM HAuCl4 solution was added to a boiling solution (106 mL) of 2.2 mM sodium citrate solution with rapid mixing. The resulting AuNPs were of a mean particle diameter of 8.5 nm with a coefficient of variation about 8%. Aggregation of Gold Nanoparticles. To obtain aggregates that can be used in deposition experiments, the AuNPs were destabilized by the addition of NaCl solution of various concentrations. Specifically, an aliquot of 0.1 mL of the synthesized AuNPs was added into a glass cuvette containing a 0.9 mL NaCl solution of known concentration (40, 50, and 60 mM) with rapid mixing by a vortex mixer (The same mixing ratio was also used for the deposition experiment.). Immediately after the mixing, time-resolved dynamic light scattering (DLS) was conducted on the mixture, with a scattering angle of 90 degrees using a goniometer (ALV/CGS 3, Germany), to monitor the evolution of intensity weighted hydrodynamic radius of the particles/aggregates. Aggregation of nanoparticles was promoted by the screening of the EDL interaction following addition of the indifferent electrolyte. It should be noted that we did not intend to identify the critical coagulation concentration (CCC) but to decide, based on trial aggregation experiments, on an electrolyte concentration such 13271

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Figure 1. Illustration of experimental design for the deposition experiments using QCM.

that (A) the aggregation occurred fast enough so that significant changes of aggregate size occurred during the aggregate formation stage of the experiment, and (B) the aggregation was slow enough so that an aggregate from RLCA would be produced and the aggregate size remained relatively stable during the deposition phase of the experiment (too fast aggregation may also lead to settling in the experiment). In other words, it was the goal of the controlled aggregation to attain, in the experimental time frame, aggregates of a relatively stable size that was large enough to be distinguished from that of the primary particles and yet small enough to produce aggregates (from RLCA) that were still subject to Brownian diffusion. A NaCl concentration of 60 mM was chosen for the electrolyte solution during deposition experiments, resulting in a final NaCl concentration of 54 mM after mixing with AuNPs. For diffusion-limited aggregation, the AuNPs were added to a solution containing 10 mM of pyridine which replaced the charged citrate on the nanoparticle surface and rapidly destabilized the AuNPs via charge neutralization.24 Deposition of AuNPs on a Silica Surface Monitored using QCM. To study the deposition kinetics of AuNPs, a quartz crystal microbalance (D300, Q-sense, Vastra Frolunda, Sweden) was used with a silica-coated surface (QX 303, Qsense). The details about the working mechanism of quartz crystal microbalance (QCM) and experimental procedures of using it for studying deposition kinetics have been published in previous articles.38−42 Two syringe pumps (NE-300, New Era Pump Systems Inc. Farmingdale, NY) were used to deliver the electrolyte solution and the AuNPs stock solution, respectively. For deposition of primary particles, the electrolyte solution and the AuNP suspension were mixed in the Y-connector (Biochem Fluidics, United Kingdom) before entering the QCM system. To obtain attachment efficiencies (α) that were comparable, favorable deposition experiments were conducted with some crystal chips coated with a cationic polyelectrolyte poly-L-lysine (Sigma-Aldrich, St. Louis, MO) following the procedure proposed by Chen and Elimelech.39 The PLL-coated surface was positively charged, and thus the deposition of negatively charged AuNPs onto a PLL-coated silica surface was considered favorable. The attachment efficiency at a given electrolyte concentration can then be calculated as

α=

dΔf(3) /dt (dΔf(3) /dt )fav

(1)

where dΔf(3)/dt is the shift rate of normalized resonance frequency at the third overtone, and (dΔf(3)/dt)fav is that under favorable deposition condition. To assess the effect of the aggregation state on attachment efficiencies, deposition experiments were conducted for four different scenarios: (1) deposition of AuNPs onto a silica surface immediately after the mixing of electrolyte solution and AuNPs; (2) deposition of AuNPs onto PLL-coated surface immediately after mixing; (3) deposition of aggregates of AuNPs onto silica surface 6000s (100 min) after mixing; and (4) deposition of aggregates of AuNPs onto PLL-coated surface 6000s after mixing. Scenarios 1 and 2 represent the unfavorable and favorable deposition of primary particles (or very small aggregates), respectively, whereas scenarios 3 and 4 represent the unfavorable and favorable deposition of relatively large aggregates, respectively. Schematic representations of the experimental setups for these scenarios are presented in Figure 1. It should be noted that a total flow rate of 1 mL/min was used (relatively high compared to flow rates used in other studies but still within the range of permissible flow rate for the instrument according to the user manual), resulting in a hydraulic retention time (HRT) of less than 1 min in the QCM device.

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RESULTS AND DISCUSSION Structure of Simulated Fractal Aggregates. Four types of fractal aggregates (FA) were generated including N = 100, 500, and 1000 via DLCA process and N = 1000 via RLCA process, with five samples simulated for each type. The simulated FA were characterized for their gyration radii Rg and fractal dimensions Df. The density−density correlation functions C(r) were calculated for each FA to estimate the Df based on the following relationship:22 C(r ) ∝ r d − Df

(2)

The initial slope of ln C(r) vs ln r should be equal to d − Df with d being the dimension of Euclidean space (three in this case). Figures 2A and 2B present two representative fractal aggregates composed of N = 1000 primary particles formed by DLCA and RLCA, respectively (more representative aggregates 13272

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structure than those formed via DLCA. Both being composed of 1000 primary particles of a radius a0, the Rg of the FA in Figure 2A was estimated to be 33.8 a0 while that of the FA in Figure 2B was estimated to be 24.3 a0. Analyzing the density− density correlation functions C(r) suggested a Df of 1.75 for FA formed via DLCA and a Df of 2.15 for FA formed via RLCA. Table S1 (Supporting Information) summarizes the structure characteristics of the simulated fractal aggregates. The FAs formed via DLCA yielded a Df of about 1.7 regardless of the number of primary particles the fractal aggregates contain, and that fractal aggregates from RLCA yielded a Df of about 2.1, which are consistent with the observations reported in the literature.24 Potential Energy of Colloidal Interaction. Figures 3A, 3B, and 3C present the total interaction energy curves calculated for the colloidal interaction between a DLCA1000 aggregate and a flat surface for IS = 1 mM, 10 mM, and 100 mM, respectively. The separation distance was defined as the shortest distance between the flat surface and nanoparticles that were closest to the surface. Significant variation can be observed for a given separation depending on the orientation of an aggregate. Based on either the orientation-averaged value (Vmean) or the minimum (Vmin), the energy barrier decreases slightly from IS = 1 mM to IS = 10 mM and is eliminated when IS was increased to 100 mM. This phenomenon is universal to almost all the FA tested regardless of their cluster size (number of primary particles) and structure, as can be seen from the Vmean and Vmin listed in Table 1. Such a monotonic decrease of energy barrier with increasing IS is consistent with the prediction of Derjaguin−Landau−Verwey−Overbeek (DLVO) theory43 applied to a single particle with Derjaguin Approximation (DA). The most important observation from these calculations is that, regardless of the solution chemistry, the barriers of potential energy for interaction between the FA and the flat surface (Figure 3 A, B, C) were of the same order of magnitude as that between the primary particle and the flat surface (dashed

Figure 2. (A) Fractal aggregate formed via DLCA with 1000 primary particles; (B) Fractal aggregate formed via RLCA with 1000 primary particles; (C) ln C(r)ln r curves for analyzing density−density correlation function of the two representative aggregates shown in (A) and (B).

of other types are available in the Supporting Information). The ln C(r) vs ln r curves of these two aggregates are analyzed and compared in Figure 2C. It is observed from visual inspection of the FA in Figures 2A and 2B that FA formed via RLCA have a more compact

Figure 3. (A)-(C) Total interaction energy between a flat surface and a fractal aggregate (DLA1000) with IS being 1 mM, 10 mM, and 100 mM, respectively. The data are presented using the standard Box-Whisker plot with the orange dots inside the boxes being the orientation-averaged interaction energy. (D) Interaction energy curves for an equivalent sphere defined by the gyration radius of a fractal aggregate DLA1000. 13273

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Table 1. Summary of Barrier of Interaction Energy Curve for Four Different Types of Fractal Aggregatesa Rg (nm) Vmean (kBT)

Vmin (kBT)

VES (kBT)

1 mM 10 mM 100 mM 1 mM 10 mM 100 mM 1 mM 10 mM 100 mM

DLA100

DLA500

DLA1000

RLA1000

primary

111.0 ± 8.3 3.8 ± 0.4 3.2 ± 0.3