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Aggregation of engineered nanoparticles (NPs) plays a crucial role in their environmental transport, fate,bioavailability and biological effects. This study investigated the temperature effect on the aggregation kinetics of CeO2 NPs in KCl and CaCl2 solutions using timeresolved dynamic light scattering. The results show that in KCl and CaCl2, the aggregation rate became faster as the temperature increased. The critical coagulation concentration (CCC) of CeO2 NPs went down from approximately 100 to 10 mM in KCl and from approximately 10 to 2 mM in CaCl2 solutions when the temperature increased from 4 to 37°C. The observations were analyzed in the framework of extended DerjaguinLandauVerweyOverbeek (EDLVO) theory in order to find out the mechanisms underlying the temperature effect. Moreover, a theoretical model developed on the basis of EDLVO theory and von Smoluchowski’s population balance equation was used to predict the aggregation kinetics of CeO2 NPs under different temperature. The model predictions agreed well with experimental data, suggesting that the model could be employed to predict the size change of NPs in solution. Overall, this work provides insights into NP aggregation using experimental and modeling approaches, and allows people to better understand and theoretically predict the environmental behavior and risk of NPs.
Keywords 
Nanoparticle; Aggregation; Temperature; EDLVO 
Introduction 
Recently, engineered nanoparticles (NPs) have received enormous attention owing to their potential commercial and industrial applications in many sectors, such as cosmetics, textiles, pharmaceutical, catalysts and electronics [1,2]. But meanwhile, the release of NPs into the environment will very likely happen along with their largescale manufacture and wide use, which will subsequently impose risks for ecosystems and human health [3]. It is thus important to evaluate the environmental and health risks of NPs before their mass production. Since the toxicological testing’s of NPs are expensive and timeconsuming, researchers are developing theoretical models to evaluate and predict the behavior and risks of NPs in environmental systems [46]. 
Previous studies have shown that the aggregation of NPs plays an important role in their environmental risks by influencing their transport, fate, bioavailability and biological effects [711]. Understanding the fundamental principles underlying the aggregation process of NPs and quantitatively describing this process are essential prerequisites for characterizing the environmental behavior of NPs and further quantifying the risk. The aggregation of NPs is fundamentally governed by the interfacial force between interacting particles, which includes several either attractive or repulsive forces. When the attractive force is greater than the repulsive force, NPs approach each other and aggregate; otherwise, NPs stay stable. The famous DerjaguinLandauVerweyOverbeek (DLVO) theory has been widely used to characterize the interfacial force between particles [12,13]. According to it, the vander Waals (vdW) force and electrostatic (EL) force compose the interfacial force. The DLVO theory achieved great success in explaining the stability of colloids in salt solutions. But for NP aggregation, many studies have found that a discrepancy exists between DLVO predictions and experimental observations [14]. This problem might be overcome by taking nonDLVO forces into account, such as the polar Lewis acid/base (AB) force [15] and steric force [16]. Here the AB force is the sum of the hydrophobic interaction force, hydrogenbonding force and hydration force [1517]. The precise theoretical analysis of NP interaction and quantitative description of NP aggregation can be obtained by incorporating those nonDLVO forces into the DLVO theory, which is known as the extended DLVO (EDLVO or XDLVO) theory [15]. 
On the basis of EDLVO theory, our previous studies have addressed the effects of ionic strength and natural organic matter on NP aggregation with modeling approaches [5,18]. It is well known that temperature also greatly influences the aggregation of NPs. Understanding the temperature effect is important for environmental and health risk assessments of NPs, as both natural water and human body fluids can be at temperatures that are remarkably different from the typically used room temperature. For example, river waters in some cold areas may be only 4°C, whereas the temperature of blood in the human body is as high as 37°C. NPs in these solutions would undergo different aggregation processes. The temperature effect, however, has not gained much attention in NP aggregation studies. In this study, we investigated the temperature effect on the aggregation of NPs in KCl and CaCl_{2} solutions using timeresolved dynamic light scattering (TRDLS). We selected CeO_{2} NP as a model NP owing to its extensive commercial applications [1921]. It has been listed as a priority nanomaterial for immediate testing by the Organization for Economic Cooperation and Development (OECD) [22]. We used the EDLVO theory to interpret the fundamentals of the temperature effect on NP aggregation. Furthermore, a kinetic model developed on the basis of EDLVO theory and von Smoluchowski’s population balance equation was used to predict the aggregation kinetics of CeO_{2} NPs, which were then compared with experimental observations. Our aim was to fundamentally understand the temperature effect on NP aggregation and theoretically predict the aggregation kinetics of NPs under different temperature, which were anticipated to benefit the predictive modeling research of environmental behavior and toxicity assessment of NPs. 
Materials and Methods 
Materials 
CeO_{2} NPs with a nominal diameter of 25 nm were purchased from SigmaAldrich. The atomic composition of the sample was verified using Xray diffraction (data not shown). The pH of the stock suspension was measured to be 4.5 by pH meter (Accumet model 15, Fisher Scientific Co., USA). KCl and CaCl_{2} stock solutions were prepared using ACS reagentgrade chemicals (Fisher Scientific Co., USA) and were filtered through 0.02 μm filters (VWR International, USA) before use. 
Characterization of CeO_{2} NPs 
The morphology and primary particle size of CeO2 NPs were determined using transmission electron microscopy (TEM). 5 μL of CeO_{2} NP suspensions were deposited on a copper grid (400 mesh size) coated with carbon film (Ted Pella, Redding, CA, USA). A Philips EM420 TEM was employed to acquire images. Particle size distribution (PSD) was obtained with DLS on a Zetasizer Nano ZS instrument (Malvern Instruments). Briefly, 1.5 mL of 10 mg/L CeO_{2} NP suspension was injected into a clean cuvette; the DLS instrument was then operated with a scattering angle of 173° from the incident laser beam, and the autocorrelation function automatically accumulated at least 10 runs for each sample. The electrophoretic motilities’ (EPMs) of 10 mg/L CeO_{2} NPs were measured for a range of K^{+} and Ca^{2+} concentrations under different temperatures using the Zetasizer Nano ZS instrument. At least four parallel measurements were made for each condition. The measurement began immediately after the desired conditions were achieved to minimize the interference of aggregation. 
Aggregation kinetics 
The aggregation kinetics experiments were carried out at pH 5.7, at which the CeO_{2} NPs are stable for at least 24 h. The pH values of the CeO_{2} NP, KCl and CaCl_{2} solutions were preadjusted to 5.7 to ensure that each measurement could start immediately after addition of K^{+} and Ca^{2+}. For the aggregation experiment, the sample holder of the Zeta sizer Nano ZS instrument was preheated or precooled to the desired temperature. A premeasured amount of KCl or CaCl_{2} was added to 1 mL of CeO_{2} NP suspension in a cuvette. The NP suspension was then shaken slightly and placed in the sample holder. 
Modeling the aggregation kinetics 
According to the EDLVO theory, the total interfacial force between two metal oxide NPs is comprised of the vdW force, EL force and AB force [15]. The total interfacial energy (VT) between NPs is computed by assuming that each force acts individually and is thus additive: V_{T}=V_{vdW}+V_{EL}+V_{AB} 
The vdW attractive energy (V_{vdW})between two identical spherical particles, which considers the retardation effect, can be computed using Equation (1) [23]: 
(1) 
where A_{H} is the Hamaker constant, which is 5.57×10^{20} J for CeO_{2} in water [24]. r is the particle radius. h is the separation distance between the interacting surfaces. λ_{c} is the “characteristic wavelength” of the interaction, which is often assumed to be 100 nm [25]. 
The EL repulsive energy (VEL) between two identical spheres of radii r in 11 electrolyte solutions (e.g., KCl) is given by Equation (2ac). In 21 electrolyte solutions (e.g., CaCl_{2}), Equation (2a) and (2b) are replaced by Equation (2d) and (2e), respectively [2628]: 
(2a) 
(2b) 
(2c) 
(2d) 
(2e) 
where n is the concentration of electrolytes; kB is the Boltzmann constant; T is absolute temperature; zi is the valency of the i^{th} ion; e is unit charge; ψSi is the surface potential of the interacting particles in an aqueous medium, which can be calculated from the EPMs of NPs (U_{E}) (Figure 1), the solution viscosity (μ) and permittivity (ε.ε_{0}) of water by the Smoluchowski Equation: ψ_{Si}=(U_{E} .μ)/(εε_{0}) [27]; ε_{0} is the vacuum permittivity; ε is the relative permittivity of water; κ^{1} is the Debye length; NA is Avogadro’s number; and I is the ionic strength (M), I=0.5·Σc_{i}z_{i}^{2}, where c_{i} is the molar concentration of the i^{th} ion. 
Finally, the AB energy (V_{AB}) between two identical spheres is expressed by Equation (3): 
(3) 
where λ is the correlation length or decay length of the molecules of the liquid medium, which is estimated to be 1 nm for pure water [29], and ΔG_{h0}^{AB} is the polar or AB free interaction energy between particles at the distance h_{0} [30], which is the minimum equilibrium distance due to Born repulsion, 0.157 nm [29]. 
Upon computing the total interaction energy (V_{T}), the aggregation kinetics of CeO_{2} NPs can be obtained by Equation (4), which was developed on the basis of the EDLVO theory and von Smoluchowski’s population balance equation [31]: 
(4) 
Where r_{t} is the particle radius at time t, a is the primary particle radius, n_{0} is the initial number concentration of primary particles, μ is the solution viscosity, and dF is the fractal dimension of aggregates. W is the stability ratio, which can be expressed by Equation (5) [32,33]: 
(5) 
where u is the normalized surfacetosurface separation distance (h) between two particles (u=h/a) and V_{A}(u) is the attractive energy. Here, vdW energy is the only contributing term to V_{A}(u) and thus V_{A}=V_{vdW}. λ(u) is the correction factor for the diffusion coefficient, which is related to the separation distance by Equation (6) [34]: 
(6) 
The number concentration of CeO_{2} NPs is determined from the mass concentration. The lattice parameter (al) of CeO_{2} unit cells is 5.4087 Å [35], and each unit cell contains four Ce atoms and eight O atoms. The number of Ce atoms (N) per CeO_{2} NP with radius r can be calculated by N=16π (r/al) 3/3. The mass of a single CeO_{2} NP is then obtained, and the number concentration of NPs can be computed. 
Results and Discussion 
Characterization of CeO_{2} NPs 
A TEM image of CeO_{2} NPs is presented in figure 1. The NPs have a relatively uniform size distribution. The inset in figure 1 shows the PSD diagram of CeO_{2} NPs, which was measured by DLS. Consistent with previous studies, the DLSmeasured NP size is larger than that determined by TEM [36,37]. This is probably owing to particle aggregation and the water layer surrounding the NP surface. The polydispersivity index (PDI) is quite small (∼0.1), indicating that CeO_{2} NPs are relatively monodispersed in solution. Figure 2 shows the zeta potentials of CeO_{2} NPs under different temperatures in KCl and CaCl_{2} solutions. The CeO_{2} NPs are positively charged under all tested conditions. The divalent ion (Ca^{2+}) is more effective than the monovalent ion (K^{+}) in screening the surface charge of NPs. As ionic strength increased, the zeta potential became smaller due to the compression of the electrical double layer surrounding the NP. The temperature effect is apparent; as the temperature increased, the zeta potential became less positive, which was consistent with previous studies [38,39]. The reason could be that increasing temperature favors proton desorption from the particle surface [38]. At higher temperature, the lower zeta potential of CeO_{2} NPs implies that the electrostatic repulsion force between particles is weaker, and this probably promotes the particle aggregation. 
Effect of temperature on the aggregation of CeO_{2} NPs in KCl and CaCl_{2} 
The representative aggregation kinetics profile of CeO_{2} NPs in KCl and CaCl_{2} solutions under different temperatures were presented in figure 2. As the temperature increased, the NP aggregation became faster. The attachment efficiency (α), or inverse stability ratio (1/W), was calculated by normalizing the initial slopes of aggregation kinetics curves with the slopes obtained in the diffusionlimited aggregation regime (Figure 3). The critical coagulation concentration (CCC) for CeO_{2} NPs in KCl was ca. 100, 40 and 10 mM at 4, 25 and 37°C, respectively. In CaCl_{2}, CCCs were ca. 10, 10 and 2 mM at 4, 25 and 37°C, respectively. The substantially lower CCCs for CeO_{2} NPs in Ca^{2+} solutions than those in K^{+} solutions is because divalent ions more effectively screen the surface charge of NPs and subsequently enhance the aggregation. Higher temperature leads to a smaller CCC and thus promotes NP aggregation. 
Higher temperature promotes NP aggregation for two reasons. First, the solution viscosity μ was smaller at higher temperature; according to Equation (4), the particle aggregation was thus enhanced. Second, the interaction energy between NPs also changes as the temperature increases. The total interfacial energy VT can be calculated using Equation (1)(3). Parameters involved in these equations could be either measured or computed. Surface potentials (ψ_{S}) of CeO_{2} NPs under different temperatures were calculated from the EPMs with the Smoluchowski equation [27]. The other major parameters are listed in table S1. 
The interaction energies for CeO_{2} NPs under different temperatures were computed and are presented in figure 2, which shows that the interaction energy between NPs is lower at a higher temperature in both KCl and CaCl_{2} solutions. The energy barrier reflects the aggregation tendency. The energy barrier diminished as the temperature increased. When the temperature increased from 4 to 37°C, the magnitude of the energy barrier decreased from 11 to 4 k_{B}T and from 7 to 1 k_{B}T in 0.01 M of KCl and 0.002 M CaCl_{2}, respectively. This suggests that NPs more easily overcome the energy barrier and aggregate at high temperatures. Moreover, according to Equation (1)(3), the EL force is the only force that is influenced by the change in temperature (Figure S4). Parameters in Equation (3), such as the surface potential of NPs, solution permittivity and Debye length, are affected by temperature. The temperature has no impact on vdW and AB forces. 
For a better understanding of the contribution of each energy term to the total interaction, the representative energy profiles are presented in figure 3 and figure S5 in the supporting information. Apparently, the AB repulsion energy contributes more relative to EL repulsion energy. This indicates that, compared with EDLVO theory, the conventional DLVO theory, which considers only EL and vdW energy, provides a less accurate description of the interfacial energy between CeO_{2} NPs. 
Modeling the aggregation kinetics of CeO_{2} NPs 
Equation (4) was used to model the aggregation kinetics of CeO_{2} NPs. The initial number concentration of CeO_{2} NPs is approximately 2.35×10^{15} particles/m^{3} in all aggregation experiments. The fractal dimension dF was reported to be ca. 1.8 [4043]. The total interaction energy VT was computed according to Equation (1)(3). The attractive energy, VA, equals the vdW energy (V_{vdW}). The AB free interaction energy between particles at the distance h_{0}, ΔG_{h0} AB, was consistent with our previous studies. Other parameters are listed in table S1. The modeling results were further compared with experimental observations, and representative comparisons are presented in figure 4 and figure S6 in the supporting information. At all temperatures, model predictions agreed well with experimental data. Some minor discrepancies between model predictions and experimental observations may be attributed to deviations in the surface potential of NPs and the size distribution of particles. 
Conclusion 
In conclusion, this work investigated the temperature effect on the aggregation of CeO_{2} NPs with both experimental and modeling approaches. As the temperature increased from 4°C to 37°C, the CCCs for CeO_{2} NPs decreased from ca. 100 to 10 mM in KCl and from ca. 10 to 2 mM in CaCl_{2}. The promotive effect of temperature on NP aggregation is ascribed to the smaller solution viscosity and lower interfacial energy barrier at higher temperature. For instance, the energy barrier height decreased from 11 to 4 kBT in 0.01 M KCl and from 7 to 1 kBT in 0.002 M CaCl_{2}, which resulted from the smaller repulsive EL energy at a higher temperature. The aggregation model based on the EDLVO theory gave fairly good predictions of NP aggregation under different temperatures. To the best of our knowledge, this is the first study to research the temperature effect on NP aggregation with modeling approaches, which is expected to benefit the theoretical predictions of the environmental behavior and biological effects of NPs and to further contribute to the environmental and health risk assessment of NPs. 
Acknowledgements 
This study was partially supported by the U.S. Environmental Protection Agency Science to Achieve Results Program Grant RD83385601 and Engineering Research Center (ERC)/Semiconductor Research Corporation (SRC)/ESH grant (425.025). 
Supporting Information 
Details about the EPMs of CeO_{2} NPs, representative aggregation kinetics profiles, attachment efficiencies, model parameters, interaction energy profiles, and other aggregation modeling profiles. This material is available free of charge via the Internet. 
References 

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